Agilent Technologies 22A Specifications

Agilent
Spectrum Analysis Basics
Application Note 150
Table of Contents
Chapter 1 – Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4
Frequency domain versus time domain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4
What is a spectrum? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5
Why measure spectra? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .6
Types of measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .8
Types of signal analyzers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .8
Chapter 2 – Spectrum Analyzer Fundamentals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .10
RF attenuator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .12
Low-pass filter or preselector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .12
Tuning the analyzer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .12
IF gain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .16
Resolving signals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .16
Residual FM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .19
Phase noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .20
Sweep time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .22
Envelope detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .24
Displays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .25
Detector types . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .26
Sample detection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .27
Peak (positive) detection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .29
Negative peak detection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .29
Normal detection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .29
Average detection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .32
EMI detectors: average and quasi-peak detection . . . . . . . . . . . . . . . . . . . . . . . . . . . . .33
Averaging processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .33
Time gating . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .38
Chapter 3 – Digital IF Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .44
Digital filters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .44
The all-digital IF . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .45
Custom signal processing IC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .47
Additional video processing features . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .47
Frequency counting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .47
More advantages of the all-digital IF . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .48
Chapter 4 – Amplitude and Frequency Accuracy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .49
Relative uncertainty . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .52
Absolute amplitude accuracy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .52
Improving overall uncertainty . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .53
Specifications, typical performance, and nominal values . . . . . . . . . . . . . . . . . . . . . . .53
The digital IF section . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .54
Frequency accuracy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .56
2
Table of Contents
— continued
Chapter 5 – Sensitivity and Noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .58
Sensitivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .58
Noise figure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .61
Preamplifiers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .62
Noise as a signal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .65
Preamplifier for noise measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .68
Chapter 6 – Dynamic Range . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .69
Definition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .70
Dynamic range versus internal distortion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .70
Attenuator test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .74
Noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .74
Dynamic range versus measurement uncertainty . . . . . . . . . . . . . . . . . . . . . . . . . . . . .77
Gain compression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .80
Display range and measurement range . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .80
Adjacent channel power measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .82
Chapter 7 – Extending the Frequency Range . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .83
Internal harmonic mixing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .83
Preselection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .89
Amplitude calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .91
Phase noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .91
Improved dynamic range . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .92
Pluses and minuses of preselection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .95
External harmonic mixing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .96
Signal identification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .98
Chapter 8 – Modern Spectrum Analyzers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .102
Application-specific measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .102
Digital modulation analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .105
Saving and printing data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .106
Data transfer and remote instrument control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .107
Firmware updates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .108
Calibration, troubleshooting, diagnostics, and repair . . . . . . . . . . . . . . . . . . . . . . . . . .108
Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .109
Glossary of Terms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .110
3
Chapter 1
Introduction
This application note is intended to explain the fundamentals of swept-tuned,
superheterodyne spectrum analyzers and discuss the latest advances in
spectrum analyzer capabilities.
At the most basic level, the spectrum analyzer can be described as a
frequency-selective, peak-responding voltmeter calibrated to display the
rms value of a sine wave. It is important to understand that the spectrum
analyzer is not a power meter, even though it can be used to display power
directly. As long as we know some value of a sine wave (for example, peak
or average) and know the resistance across which we measure this value,
we can calibrate our voltmeter to indicate power. With the advent of digital
technology, modern spectrum analyzers have been given many more
capabilities. In this note, we shall describe the basic spectrum analyzer
as well as the many additional capabilities made possible using digital
technology and digital signal processing.
Frequency domain versus time domain
Before we get into the details of describing a spectrum analyzer, we might
first ask ourselves: “Just what is a spectrum and why would we want to
analyze it?” Our normal frame of reference is time. We note when certain
events occur. This includes electrical events. We can use an oscilloscope to
view the instantaneous value of a particular electrical event (or some other
event converted to volts through an appropriate transducer) as a function
of time. In other words, we use the oscilloscope to view the waveform of a
signal in the time domain.
Fourier1 theory tells us any time-domain electrical phenomenon is made
up of one or more sine waves of appropriate frequency, amplitude, and phase.
In other words, we can transform a time-domain signal into its frequencydomain equivalent. Measurements in the frequency domain tell us how
much energy is present at each particular frequency. With proper filtering,
a waveform such as in Figure 1-1 can be decomposed into separate sinusoidal
waves, or spectral components, which we can then evaluate independently.
Each sine wave is characterized by its amplitude and phase. If the signal
that we wish to analyze is periodic, as in our case here, Fourier says that the
constituent sine waves are separated in the frequency domain by 1/T, where
T is the period of the signal2.
1. Jean Baptiste Joseph Fourier, 1768-1830.
A French mathematician and physicist who
discovered that periodic functions can be expanded
into a series of sines and cosines.
2. If the time signal occurs only once, then T is infinite,
and the frequency representation is a continuum of
sine waves.
Figure 1-1. Complex time-domain signal
4
Some measurements require that we preserve complete information about the
signal - frequency, amplitude and phase. This type of signal analysis is called
vector signal analysis, which is discussed in Application Note 150-15, Vector
Signal Analysis Basics. Modern spectrum analyzers are capable of performing
a wide variety of vector signal measurements. However, another large group of
measurements can be made without knowing the phase relationships among
the sinusoidal components. This type of signal analysis is called spectrum
analysis. Because spectrum analysis is simpler to understand, yet extremely
useful, we will begin this application note by looking first at how spectrum
analyzers perform spectrum analysis measurements, starting in Chapter 2.
Theoretically, to make the transformation from the time domain to the frequency
domain, the signal must be evaluated over all time, that is, over ± infinity.
However, in practice, we always use a finite time period when making a
measurement. Fourier transformations can also be made from the frequency
to the time domain. This case also theoretically requires the evaluation of
all spectral components over frequencies to ± infinity. In reality, making
measurements in a finite bandwidth that captures most of the signal energy
produces acceptable results. When performing a Fourier transformation on
frequency domain data, the phase of the individual components is indeed
critical. For example, a square wave transformed to the frequency domain
and back again could turn into a sawtooth wave if phase were not preserved.
What is a spectrum?
So what is a spectrum in the context of this discussion? A spectrum is a
collection of sine waves that, when combined properly, produce the
time-domain signal under examination. Figure 1-1 shows the waveform of a
complex signal. Suppose that we were hoping to see a sine wave. Although
the waveform certainly shows us that the signal is not a pure sinusoid, it
does not give us a definitive indication of the reason why. Figure 1-2 shows
our complex signal in both the time and frequency domains. The frequencydomain display plots the amplitude versus the frequency of each sine wave
in the spectrum. As shown, the spectrum in this case comprises just two sine
waves. We now know why our original waveform was not a pure sine wave.
It contained a second sine wave, the second harmonic in this case. Does this
mean we have no need to perform time-domain measurements? Not at all.
The time domain is better for many measurements, and some can be made
only in the time domain. For example, pure time-domain measurements
include pulse rise and fall times, overshoot, and ringing.
Time domain
measurements
Frequency domain
measurements
Figure 1-2. Relationship between time and frequency domain
5
Why measure spectra?
The frequency domain also has its measurement strengths. We have
already seen in Figures 1-1 and 1-2 that the frequency domain is better
for determining the harmonic content of a signal. People involved in wireless
communications are extremely interested in out-of-band and spurious
emissions. For example, cellular radio systems must be checked for harmonics
of the carrier signal that might interfere with other systems operating at the
same frequencies as the harmonics. Engineers and technicians are also very
concerned about distortion of the message modulated onto a carrier.
Third-order intermodulation (two tones of a complex signal modulating each
other) can be particularly troublesome because the distortion components
can fall within the band of interest and so will not be filtered away.
Spectrum monitoring is another important frequency-domain measurement
activity. Government regulatory agencies allocate different frequencies for
various radio services, such as broadcast television and radio, mobile
phone systems, police and emergency communications, and a host of other
applications. It is critical that each of these services operates at the assigned
frequency and stays within the allocated channel bandwidth. Transmitters
and other intentional radiators can often be required to operate at closely
spaced adjacent frequencies. A key performance measure for the power
amplifiers and other components used in these systems is the amount of
signal energy that spills over into adjacent channels and causes interference.
Electromagnetic interference (EMI) is a term applied to unwanted emissions
from both intentional and unintentional radiators. Here, the concern is that
these unwanted emissions, either radiated or conducted (through the power
lines or other interconnecting wires), might impair the operation of other
systems. Almost anyone designing or manufacturing electrical or electronic
products must test for emission levels versus frequency according to
regulations set by various government agencies or industry-standard bodies.
Figures 1-3 through 1-6 illustrate some of these measurements.
6
Figure 1-3. Harmonic distortion test of a transmitter
Figure 1-4. GSM radio signal and spectral mask showing limits of
unwanted emissions
Figure 1- 5. Two-tone test on an RF power amplifier
Figure 1-6. Radiated emissions plotted against CISPR11 limits as
part of an EMI test
7
Types of measurements
Common spectrum analyzer measurements include frequency, power,
modulation, distortion, and noise. Understanding the spectral content of a
signal is important, especially in systems with limited bandwidth. Transmitted
power is another key measurement. Too little power may mean the signal
cannot reach its intended destination. Too much power may drain batteries
rapidly, create distortion, and cause excessively high operating temperatures.
Measuring the quality of the modulation is important for making sure a
system is working properly and that the information is being correctly
transmitted by the system. Tests such as modulation degree, sideband
amplitude, modulation quality, and occupied bandwidth are examples of
common analog modulation measurements. Digital modulation metrics
include error vector magnitude (EVM), IQ imbalance, phase error versus
time, and a variety of other measurements. For more information on these
measurements, see Application Note 150-15, Vector Signal Analysis Basics.
In communications, measuring distortion is critical for both the receiver
and transmitter. Excessive harmonic distortion at the output of a transmitter
can interfere with other communication bands. The pre-amplification stages
in a receiver must be free of intermodulation distortion to prevent signal
crosstalk. An example is the intermodulation of cable TV carriers as they
move down the trunk of the distribution system and distort other channels on
the same cable. Common distortion measurements include intermodulation,
harmonics, and spurious emissions.
Noise is often the signal you want to measure. Any active circuit or device
will generate excess noise. Tests such as noise figure and signal-to-noise ratio
(SNR) are important for characterizing the performance of a device and its
contribution to overall system performance.
Types of signal analyzers
While we shall concentrate on the swept-tuned, superheterodyne spectrum
analyzer in this note, there are several other signal analyzer architectures.
An important non-superheterodyne type is the Fourier analyzer, which
digitizes the time-domain signal and then uses digital signal processing (DSP)
techniques to perform a fast Fourier transform (FFT) and display the signal
in the frequency domain. One advantage of the FFT approach is its ability
to characterize single-shot phenomena. Another is that phase as well as
magnitude can be measured. However, Fourier analyzers do have some
limitations relative to the superheterodyne spectrum analyzer, particularly in
the areas of frequency range, sensitivity, and dynamic range. Fourier analyzers are typically used in baseband signal analysis applications up to 40 MHz.
Vector signal analyzers (VSAs) also digitize the time domain signal like
Fourier analyzers, but extend the capabilities to the RF frequency range
using downconverters in front of the digitizer. For example, the Agilent 89600
Series VSA offers various models available up to 6 GHz. They offer fast,
high-resolution spectrum measurements, demodulation, and advanced
time-domain analysis. They are especially useful for characterizing complex
signals such as burst, transient or modulated signals used in communications,
video, broadcast, sonar, and ultrasound imaging applications.
8
While we have defined spectrum analysis and vector signal analysis as
distinct types, digital technology and digital signal processing are blurring
that distinction. The critical factor is where the signal is digitized. Early
on, when digitizers were limited to a few tens of kilohertz, only the video
(baseband) signal of a spectrum analyzer was digitized. Since the video signal
carried no phase information, only magnitude data could be displayed.
But even this limited use of digital technology yielded significant advances:
flicker-free displays of slow sweeps, display markers, different types of
averaging, and data output to computers and printers.
Because the signals that people must analyze are becoming more complex, the
latest generations of spectrum analyzers include many of the vector signal
analysis capabilities previously found only in Fourier and vector signal
analyzers. Analyzers may digitize the signal near the instrument’s input,
after some amplification, or after one or more downconverter stages. In any
of these cases, relative phase as well as magnitude is preserved. In addition to
the benefits noted above, true vector measurements can be made. Capabilities
are then determined by the digital signal processing capability inherent in the
analyzer’s firmware or available as add-on software running either internally
(measurement personalities) or externally (vector signal analysis software)
on a computer connected to the analyzer. An example of this capability is
shown in Figure 1-7. Note that the symbol points of a QPSK (quadrature
phase shift keying) signal are displayed as clusters, rather than single points,
indicating errors in the modulation of the signal under test.
Figure 1-7. Modulation analysis of a QPSK signal measured with a
spectrum analyzer
We hope that this application note gives you the insight into your particular
spectrum analyzer and enables you to utilize this versatile instrument to
its maximum potential.
9
Chapter 2
Spectrum Analyzer
Fundamentals
This chapter will focus on the fundamental theory of how a spectrum analyzer
works. While today’s technology makes it possible to replace many analog
circuits with modern digital implementations, it is very useful to understand
classic spectrum analyzer architecture as a starting point in our discussion.
In later chapters, we will look at the capabilities and advantages that
digital circuitry brings to spectrum analysis. Chapter 3 will discuss digital
architectures used in modern spectrum analyzers.
RF input
attenuator
Mixer
IF gain
IF filter
Log
amp
Envelope
detector
Input
signal
Pre-selector, or
low-pass filter
Video
filter
Local
oscillator
Reference
oscillator
Sweep
generator
Display
Figure 2-1. Block diagram of a classic superheterodyne spectrum analyzer
Figure 2-1 is a simplified block diagram of a superheterodyne spectrum
analyzer. Heterodyne means to mix; that is, to translate frequency. And
super refers to super-audio frequencies, or frequencies above the audio
range. Referring to the block diagram in Figure 2-1, we see that an input
signal passes through an attenuator, then through a low-pass filter (later we
shall see why the filter is here) to a mixer, where it mixes with a signal from
the local oscillator (LO). Because the mixer is a non-linear device, its output
includes not only the two original signals, but also their harmonics and the
sums and differences of the original frequencies and their harmonics. If any
of the mixed signals falls within the passband of the intermediate-frequency
(IF) filter, it is further processed (amplified and perhaps compressed on a
logarithmic scale). It is essentially rectified by the envelope detector, digitized,
and displayed. A ramp generator creates the horizontal movement across the
display from left to right. The ramp also tunes the LO so that its frequency
change is in proportion to the ramp voltage.
If you are familiar with superheterodyne AM radios, the type that receive
ordinary AM broadcast signals, you will note a strong similarity between them
and the block diagram of Figure 2-1. The differences are that the output of a
spectrum analyzer is a display instead of a speaker, and the local oscillator is
tuned electronically rather than by a front-panel knob.
10
Since the output of a spectrum analyzer is an X-Y trace on a display, let’s see
what information we get from it. The display is mapped on a grid (graticule)
with ten major horizontal divisions and generally ten major vertical divisions.
The horizontal axis is linearly calibrated in frequency that increases from
left to right. Setting the frequency is a two-step process. First we adjust the
frequency at the centerline of the graticule with the center frequency control.
Then we adjust the frequency range (span) across the full ten divisions with
the Frequency Span control. These controls are independent, so if we change
the center frequency, we do not alter the frequency span. Alternatively, we
can set the start and stop frequencies instead of setting center frequency and
span. In either case, we can determine the absolute frequency of any signal
displayed and the relative frequency difference between any two signals.
The vertical axis is calibrated in amplitude. We have the choice of a linear
scale calibrated in volts or a logarithmic scale calibrated in dB. The log scale
is used far more often than the linear scale because it has a much wider
usable range. The log scale allows signals as far apart in amplitude as 70 to
100 dB (voltage ratios of 3200 to 100,000 and power ratios of 10,000,000 to
10,000,000,000) to be displayed simultaneously. On the other hand, the linear
scale is usable for signals differing by no more than 20 to 30 dB (voltage ratios
of 10 to 32). In either case, we give the top line of the graticule, the reference
level, an absolute value through calibration techniques1 and use the scaling
per division to assign values to other locations on the graticule. Therefore,
we can measure either the absolute value of a signal or the relative amplitude
difference between any two signals.
Scale calibration, both frequency and amplitude, is shown by annotation
written onto the display. Figure 2-2 shows the display of a typical analyzer.
Now, let’s turn our attention back to Figure 2-1.
Figure 2-2. Typical spectrum analyzer display with control settings
1. See Chapter 4, “Amplitude and Frequency
Accuracy.”
11
RF attenuator
The first part of our analyzer is the RF input attenuator. Its purpose is to
ensure the signal enters the mixer at the optimum level to prevent overload,
gain compression, and distortion. Because attenuation is a protective circuit
for the analyzer, it is usually set automatically, based on the reference level.
However, manual selection of attenuation is also available in steps of 10, 5, 2,
or even 1 dB. The diagram below is an example of an attenuator circuit with a
maximum attenuation of 70 dB in increments of 2 dB. The blocking capacitor
is used to prevent the analyzer from being damaged by a DC signal or a DC
offset of the signal. Unfortunately, it also attenuates low frequency signals
and increases the minimum useable start frequency of the analyzer to 100 Hz
for some analyzers, 9 kHz for others.
In some analyzers, an amplitude reference signal can be connected as shown
in Figure 2-3. It provides a precise frequency and amplitude signal, used by
the analyzer to periodically self-calibrate.
0 to 70 dB, 2 dB steps
RF input
Amplitude
reference
signal
Figure 2-3. RF input attenuator circuitry
Low-pass filter or preselector
The low-pass filter blocks high frequency signals from reaching the mixer.
This prevents out-of-band signals from mixing with the local oscillator and
creating unwanted responses at the IF. Microwave spectrum analyzers replace
the low-pass filter with a preselector, which is a tunable filter that rejects all
frequencies except those that we currently wish to view. In Chapter 7, we will
go into more detail about the operation and purpose of filtering the input.
Tuning the analyzer
We need to know how to tune our spectrum analyzer to the desired frequency
range. Tuning is a function of the center frequency of the IF filter, the
frequency range of the LO, and the range of frequencies allowed to reach
the mixer from the outside world (allowed to pass through the low-pass filter).
Of all the mixing products emerging from the mixer, the two with the greatest
amplitudes, and therefore the most desirable, are those created from the sum
of the LO and input signal and from the difference between the LO and input
signal. If we can arrange things so that the signal we wish to examine is either
above or below the LO frequency by the IF, then one of the desired mixing
products will fall within the pass-band of the IF filter and be detected to
create an amplitude response on the display.
12
We need to pick an LO frequency and an IF that will create an analyzer with
the desired tuning range. Let’s assume that we want a tuning range from
0 to 3 GHz. We then need to choose the IF frequency. Let’s try a 1 GHz IF.
Since this frequency is within our desired tuning range, we could have an
input signal at 1 GHz. Since the output of a mixer also includes the original
input signals, an input signal at 1 GHz would give us a constant output from
the mixer at the IF. The 1 GHz signal would thus pass through the system and
give us a constant amplitude response on the display regardless of the tuning
of the LO. The result would be a hole in the frequency range at which we
could not properly examine signals because the amplitude response would
be independent of the LO frequency. Therefore, a 1 GHz IF will not work.
So we shall choose, instead, an IF that is above the highest frequency to
which we wish to tune. In Agilent spectrum analyzers that can tune to 3 GHz,
the IF chosen is about 3.9 GHz. Remember that we want to tune from 0 Hz to
3 GHz. (Actually from some low frequency because we cannot view a 0 Hz
signal with this architecture.) If we start the LO at the IF (LO minus IF = 0 Hz)
and tune it upward from there to 3 GHz above the IF, then we can cover the
tuning range with the LO minus IF mixing product. Using this information,
we can generate a tuning equation:
fsig = fLO – fIF
where
fsig = signal frequency
fLO = local oscillator frequency, and
fIF = intermediate frequency (IF)
If we wanted to determine the LO frequency needed to tune the analyzer to
a low-, mid-, or high-frequency signal (say, 1 kHz, 1.5 GHz, or 3 GHz), we
would first restate the tuning equation in terms of fLO:
fLO = fsig + fIF
Then we would plug in the numbers for the signal and IF in the tuning
equation2:
fLO = 1 kHz + 3.9 GHz = 3.900001 GHz,
fLO = 1.5 GHz + 3.9 GHz = 5.4 GHz, or
fLO = 3 GHz; + 3.9 GHz = 6.9 GHz.
2. In the text, we shall round off some of the frequency
values for simplicity, although the exact values are
shown in the figures.
13
Figure 2-4 illustrates analyzer tuning. In this figure, fLO is not quite high
enough to cause the fLO – fsig mixing product to fall in the IF passband, so
there is no response on the display. If we adjust the ramp generator to tune
the LO higher, however, this mixing product will fall in the IF passband at
some point on the ramp (sweep), and we shall see a response on the display.
A
Freq range
of analyzer
fsig
IF
f
fLO – fsig
A
Freq range
of analyzer
fLO
f
fLO + fsig
Freq range of LO
fLO
f
Figure 2-4. The LO must be tuned to fIF + fsig to produce a response on the display
Since the ramp generator controls both the horizontal position of the trace on
the display and the LO frequency, we can now calibrate the horizontal axis of
the display in terms of the input signal frequency.
We are not quite through with the tuning yet. What happens if the frequency
of the input signal is 8.2 GHz? As the LO tunes through its 3.9 to 7.0 GHz
range, it reaches a frequency (4.3 GHz) at which it is the IF away from the
8.2 GHz input signal. At this frequency we have a mixing product that is
equal to the IF, creating a response on the display. In other words, the
tuning equation could just as easily have been:
fsig = fLO + fIF
This equation says that the architecture of Figure 2-1 could also result in a
tuning range from 7.8 to 10.9 GHz, but only if we allow signals in that range to
reach the mixer. The job of the input low-pass filter in Figure 2-1 is to prevent
these higher frequencies from getting to the mixer. We also want to keep
signals at the intermediate frequency itself from reaching the mixer, as
previously described, so the low-pass filter must do a good job of attenuating
signals at 3.9 GHz, as well as in the range from 7.8 to 10.9 GHz.
In summary, we can say that for a single-band RF spectrum analyzer, we
would choose an IF above the highest frequency of the tuning range. We would
make the LO tunable from the IF to the IF plus the upper limit of the tuning
range and include a low-pass filter in front of the mixer that cuts off below
the IF.
14
To separate closely spaced signals (see “Resolving signals” later in this
chapter), some spectrum analyzers have IF bandwidths as narrow as 1 kHz;
others, 10 Hz; still others, 1 Hz. Such narrow filters are difficult to achieve
at a center frequency of 3.9 GHz. So we must add additional mixing stages,
typically two to four stages, to down-convert from the first to the final IF.
Figure 2-5 shows a possible IF chain based on the architecture of a typical
spectrum analyzer. The full tuning equation for this analyzer is:
fsig = fLO1 – (fLO2 + fLO3 + ffinal IF)
However,
fLO2 + fLO3 + ffinal IF
= 3.6 GHz + 300 MHz + 21.4 MHz
= 3.9214 GHz, the first IF
3 GHz
3.9214 GHz
21.4 MHz
321.4 MHz
Envelope
detector
3.9 - 7.0 GHz
3.6 GHz
300 MHz
Sweep
generator
Display
Figure 2-5. Most spectrum analyzers use two to four mixing steps to reach the final IF
So simplifying the tuning equation by using just the first IF leads us to the
same answers. Although only passive filters are shown in the diagram, the
actual implementation includes amplification in the narrower IF stages.
The final IF section contains additional components, such as logarithmic
amplifiers or analog to digital converters, depending on the design of the
particular analyzer.
Most RF spectrum analyzers allow an LO frequency as low as, and even below,
the first IF. Because there is finite isolation between the LO and IF ports of
the mixer, the LO appears at the mixer output. When the LO equals the IF,
the LO signal itself is processed by the system and appears as a response
on the display, as if it were an input signal at 0 Hz. This response, called LO
feedthrough, can mask very low frequency signals, so not all analyzers allow
the display range to include 0 Hz.
15
•
IF gain
Referring back to Figure 2-1, we see the next component of the block diagram
is a variable gain amplifier. It is used to adjust the vertical position of signals
on the display without affecting the signal level at the input mixer. When the
IF gain is changed, the value of the reference level is changed accordingly to
retain the correct indicated value for the displayed signals. Generally, we do
not want the reference level to change when we change the input attenuator,
so the settings of the input attenuator and the IF gain are coupled together.
A change in input attenuation will automatically change the IF gain to offset
the effect of the change in input attenuation, thereby keeping the signal at a
constant position on the display.
Resolving signals
After the IF gain amplifier, we find the IF section which consists of the
analog and/or digital resolution bandwidth (RBW) filters.
Analog filters
Frequency resolution is the ability of a spectrum analyzer to separate two
input sinusoids into distinct responses. Fourier tells us that a sine wave
signal only has energy at one frequency, so we shouldn’t have any resolution
problems. Two signals, no matter how close in frequency, should appear as
two lines on the display. But a closer look at our superheterodyne receiver
shows why signal responses have a definite width on the display. The output
of a mixer includes the sum and difference products plus the two original
signals (input and LO). A bandpass filter determines the intermediate
frequency, and this filter selects the desired mixing product and rejects
all other signals. Because the input signal is fixed and the local oscillator
is swept, the products from the mixer are also swept. If a mixing product
happens to sweep past the IF, the characteristic shape of the bandpass filter
is traced on the display. See Figure 2-6. The narrowest filter in the chain
determines the overall displayed bandwidth, and in the architecture of
Figure 2-5, this filter is in the 21.4 MHz IF.
Figure 2-6. As a mixing product sweeps past the IF filter, the filter shape is traced on the display
So two signals must be far enough apart, or else the traces they make will fall
on top of each other and look like only one response. Fortunately, spectrum
analyzers have selectable resolution (IF) filters, so it is usually possible to
select one narrow enough to resolve closely spaced signals.
16
Agilent data sheets describe the ability to resolve signals by listing the 3 dB
bandwidths of the available IF filters. This number tells us how close together
equal-amplitude sinusoids can be and still be resolved. In this case, there
will be about a 3 dB dip between the two peaks traced out by these signals.
See Figure 2-7. The signals can be closer together before their traces merge
completely, but the 3 dB bandwidth is a good rule of thumb for resolution of
equal-amplitude signals3.
Figure 2-7. Two equal-amplitude sinusoids separated by the 3 dB BW
of the selected IF filter can be resolved
More often than not we are dealing with sinusoids that are not equal in
amplitude. The smaller sinusoid can actually be lost under the skirt of the
response traced out by the larger. This effect is illustrated in Figure 2-8. The
top trace looks like a single signal, but in fact represents two signals: one at
300 MHz (0 dBm) and another at 300.005 MHz (–30 dBm). The lower trace
shows the display after the 300 MHz signal is removed.
3. If you experiment with resolution on a spectrum
analyzer using the normal (rosenfell) detector mode
(See “Detector types” later in this chapter) use
enough video filtering to create a smooth trace.
Otherwise, there will be a smearing as the two
signals interact. While the smeared trace certainly
indicates the presence of more than one signal, it is
difficult to determine the amplitudes of the individual
signals. Spectrum analyzers with positive peak as
their default detector mode may not show the
smearing effect. You can observe the smearing by
selecting the sample detector mode.
Figure 2-8. A low-level signal can be lost under skirt of the response
to a larger signal
17
Another specification is listed for the resolution filters: bandwidth selectivity
(or selectivity or shape factor). Bandwidth selectivity helps determine the
resolving power for unequal sinusoids. For Agilent analyzers, bandwidth
selectivity is generally specified as the ratio of the 60 dB bandwidth to the
3 dB bandwidth, as shown in Figure 2-9. The analog filters in Agilent analyzers
are a four-pole, synchronously-tuned design, with a nearly Gaussian shape4.
This type of filter exhibits a bandwidth selectivity of about 12.7:1.
3 dB
60 dB
Figure 2-9. Bandwidth selectivity, ratio of 60 dB to 3 dB bandwidths
For example, what resolution bandwidth must we choose to resolve signals
that differ by 4 kHz and 30 dB, assuming 12.7:1 bandwidth selectivity? Since
we are concerned with rejection of the larger signal when the analyzer is
tuned to the smaller signal, we need to consider not the full bandwidth, but
the frequency difference from the filter center frequency to the skirt. To
determine how far down the filter skirt is at a given offset, we use the
following equation:
H(∆f) = –10(N) log10 [(∆f/f0)2 + 1]
Where
H(∆f) is the filter skirt rejection in dB
N is the number of filter poles
∆f is the frequency offset from the center in Hz, and
RBW
f0 is given by
2 √ 21/N –1
For our example, N=4 and ∆f = 4000. Let’s begin by trying the 3 kHz RBW
filter. First, we compute f0:
3000
f0 =
= 3448.44
2 √ 21/4 –1
Now we can determine the filter rejection at a 4 kHz offset:
4. Some older spectrum analyzer models used five-pole
filters for the narrowest resolution bandwidths to
provide improved selectivity of about 10:1. Modern
designs achieve even better bandwidth selectivity
using digital IF filters.
18
H(4000) = –10(4) log10 [(4000/3448.44)2 + 1]
= –14.8 dB
This is not enough to allow us to see the smaller signal. Let’s determine H(∆f)
again using a 1 kHz filter:
1000
f0 =
= 1149.48
√
2 21/4 –1
This allows us to calculate the filter rejection:
H(4000) = –10(4) log10[(4000/1149.48)2 + 1]
= –44.7 dB
Thus, the 1 kHz resolution bandwidth filter does resolve the smaller signal.
This is illustrated in Figure 2-10.
Figure 2-10. The 3 kHz filter (top trace) does not resolve smaller signal;
reducing the resolution bandwidth to 1 kHz (bottom trace) does
Digital filters
Some spectrum analyzers use digital techniques to realize their resolution
bandwidth filters. Digital filters can provide important benefits, such
as dramatically improved bandwidth selectivity. The Agilent PSA Series
spectrum analyzers implement all resolution bandwidths digitally. Other
analyzers, such as the Agilent ESA-E Series, take a hybrid approach, using
analog filters for the wider bandwidths and digital filters for bandwidths of
300 Hz and below. Refer to Chapter 3 for more information on digital filters.
Residual FM
Filter bandwidth is not the only factor that affects the resolution of a
spectrum analyzer. The stability of the LOs in the analyzer, particularly the
first LO, also affects resolution. The first LO is typically a YIG-tuned oscillator
(tuning somewhere in the 3 to 7 GHz range). In early spectrum analyzer
designs, these oscillators had residual FM of 1 kHz or more. This instability
was transferred to any mixing products resulting from the LO and incoming
signals, and it was not possible to determine whether the input signal or the
LO was the source of this instability.
The minimum resolution bandwidth is determined, at least in part, by the
stability of the first LO. Analyzers where no steps are taken to improve upon
the inherent residual FM of the YIG oscillators typically have a minimum
bandwidth of 1 kHz. However, modern analyzers have dramatically improved
residual FM. For example, Agilent PSA Series analyzers have residual FM of
1 to 4 Hz and ESA Series analyzers have 2 to 8 Hz residual FM. This allows
bandwidths as low as 1 Hz. So any instability we see on a spectrum analyzer
today is due to the incoming signal.
19
Phase noise
Even though we may not be able to see the actual frequency jitter of a
spectrum analyzer LO system, there is still a manifestation of the LO
frequency or phase instability that can be observed. This is known as phase
noise (sometimes called sideband noise). No oscillator is perfectly stable.
All are frequency or phase modulated by random noise to some extent. As
previously noted, any instability in the LO is transferred to any mixing
products resulting from the LO and input signals. So the LO phase-noise
modulation sidebands appear around any spectral component on the display
that is far enough above the broadband noise floor of the system (Figure 2-11).
The amplitude difference between a displayed spectral component and the
phase noise is a function of the stability of the LO. The more stable the LO,
the farther down the phase noise. The amplitude difference is also a function
of the resolution bandwidth. If we reduce the resolution bandwidth by a
factor of ten, the level of the displayed phase noise decreases by 10 dB5.
Figure 2-11. Phase noise is displayed only when a signal is displayed far
enough above the system noise floor
The shape of the phase noise spectrum is a function of analyzer design, in
particular, the sophistication of the phase lock loops employed to stabilized
the LO. In some analyzers, the phase noise is a relatively flat pedestal out to
the bandwidth of the stabilizing loop. In others, the phase noise may fall away
as a function of frequency offset from the signal. Phase noise is specified in
terms of dBc (dB relative to a carrier) and normalized to a 1 Hz noise power
bandwidth. It is sometimes specified at specific frequency offsets. At other
times, a curve is given to show the phase noise characteristics over a range
of offsets.
Generally, we can see the inherent phase noise of a spectrum analyzer only
in the narrower resolution filters, when it obscures the lower skirts of these
filters. The use of the digital filters previously described does not change
this effect. For wider filters, the phase noise is hidden under the filter skirt,
just as in the case of two unequal sinusoids discussed earlier.
5. The effect is the same for the broadband noise floor
(or any broadband noise signal). See Chapter 5,
“Sensitivity and Noise.”
20
Some modern spectrum analyzers allow the user to select different LO
stabilization modes to optimize the phase noise for different measurement
conditions. For example, the PSA Series spectrum analyzers offer three
different modes:
• Optimize phase noise for frequency offsets < 50 kHz from the carrier
In this mode, the LO phase noise is optimized for the area close in to the
carrier at the expense of phase noise beyond 50 kHz offset.
• Optimize phase noise for frequency offsets > 50 kHz from the carrier
This mode optimizes phase noise for offsets above 50 kHz away from the
carrier, especially those from 70 kHz to 300 kHz. Closer offsets are
compromised and the throughput of measurements is reduced.
• Optimize LO for fast tuning
When this mode is selected, LO behavior compromises phase noise at
all offsets from the carrier below approximately 2 MHz. This minimizes
measurement time and allows the maximum measurement throughput
when changing the center frequency or span.
The PSA spectrum analyzer phase noise optimization can also be set to
auto mode, which automatically sets the instrument’s behavior to optimize
speed or dynamic range for various operating conditions. When the span is
≥ 10.5 MHz or the RBW is > 200 kHz, the PSA selects fast tuning mode. For
spans >141.4 kHz and RBWs > 9.1 kHz, the auto mode optimizes for offsets
> 50 kHz. For all other cases, the spectrum analyzer optimizes for offsets
< 50 kHz. These three modes are shown in Figure 2-12a.
The ESA spectrum analyzer uses a simpler optimization scheme than the
PSA, offering two user-selectable modes, optimize for best phase noise and
optimize LO for fast tuning, as well as an auto mode.
Figure 2-12a. Phase noise performance can be optimized for different
measurement conditions
Figure 2-12b. Shows more detail of the 50 kHz carrier offset region
21
In any case, phase noise becomes the ultimate limitation in an analyzer’s
ability to resolve signals of unequal amplitude. As shown in Figure 2-13,
we may have determined that we can resolve two signals based on the 3 dB
bandwidth and selectivity, only to find that the phase noise covers up the
smaller signal.
Sweep time
Analog resolution filters
If resolution were the only criterion on which we judged a spectrum analyzer,
we might design our analyzer with the narrowest possible resolution (IF)
filter and let it go at that. But resolution affects sweep time, and we care
very much about sweep time. Sweep time directly affects how long it takes
to complete a measurement.
Resolution comes into play because the IF filters are band-limited circuits
that require finite times to charge and discharge. If the mixing products are
swept through them too quickly, there will be a loss of displayed amplitude
as shown in Figure 2-14. (See “Envelope detector,” later in this chapter, for
another approach to IF response time.) If we think about how long a mixing
product stays in the passband of the IF filter, that time is directly proportional
to bandwidth and inversely proportional to the sweep in Hz per unit time, or:
Time in passband =
where
=
(RBW)(ST)
Span
RBW = resolution bandwidth and
ST = sweep time.
Figure 2-13. Phase noise can prevent resolution of unequal signals
22
RBW
Span/ST
Figure 2-14. Sweeping an analyzer too fast causes a drop in displayed
amplitude and a shift in indicated frequency
On the other hand, the rise time of a filter is inversely proportional to its
bandwidth, and if we include a constant of proportionality, k, then:
Rise time =
k
RBW
If we make the terms equal and solve for sweep time, we have:
k
(RBW)(ST)
=
or:
RBW
Span
ST =
k (Span)
RBW2
The value of k is in the 2 to 3 range for the synchronously-tuned,
near-Gaussian filters used in many Agilent analyzers.
The important message here is that a change in resolution has a dramatic
effect on sweep time. Most Agilent analyzers provide values in a 1, 3, 10
sequence or in ratios roughly equaling the square root of 10. So sweep time
is affected by a factor of about 10 with each step in resolution. Agilent PSA
Series spectrum analyzers offer bandwidth steps of just 10% for an even
better compromise among span, resolution, and sweep time.
Spectrum analyzers automatically couple sweep time to the span and
resolution bandwidth settings. Sweep time is adjusted to maintain a calibrated
display. If a sweep time longer than the maximum available is called for,
the analyzer indicates that the display is uncalibrated with a “Meas Uncal”
message in the upper-right part of the graticule. We are allowed to override
the automatic setting and set sweep time manually if the need arises.
Digital resolution filters
The digital resolution filters used in Agilent spectrum analyzers have an
effect on sweep time that is different from the effects we’ve just discussed for
analog filters. For swept analysis, the speed of digitally implemented filters
can show a 2 to 4 times improvement. FFT-based digital filters show an even
greater difference. This difference occurs because the signal being analyzed
is processed in frequency blocks, depending upon the particular analyzer.
For example, if the frequency block was 1 kHz, then when we select a 10 Hz
resolution bandwidth, the analyzer is in effect simultaneously processing the
data in each 1 kHz block through 100 contiguous 10 Hz filters. If the digital
processing were instantaneous, we would expect sweep time to be reduced
by a factor of 100. In practice, the reduction factor is less, but is still
significant. For more information on the advantages of digital processing,
refer to Chapter 3.
23
Envelope detector6
Spectrum analyzers typically convert the IF signal to video7 with an envelope
detector. In its simplest form, an envelope detector consists of a diode,
resistive load and low-pass filter, as shown in Figure 2-15. The output of the
IF chain in this example, an amplitude modulated sine wave, is applied to
the detector. The response of the detector follows the changes in the envelope
of the IF signal, but not the instantaneous value of the IF sine wave itself.
t
IF signal
Figure 2-15. Envelope detector
For most measurements, we choose a resolution bandwidth narrow enough
to resolve the individual spectral components of the input signal. If we fix
the frequency of the LO so that our analyzer is tuned to one of the spectral
components of the signal, the output of the IF is a steady sine wave with a
constant peak value. The output of the envelope detector will then be a
constant (dc) voltage, and there is no variation for the detector to follow.
However, there are times when we deliberately choose a resolution bandwidth
wide enough to include two or more spectral components. At other times,
we have no choice. The spectral components are closer in frequency than
our narrowest bandwidth. Assuming only two spectral components within
the passband, we have two sine waves interacting to create a beat note, and
the envelope of the IF signal varies, as shown in Figure 2-16, as the phase
between the two sine waves varies.
6. The envelope detector should not be confused with
the display detectors. See “Detector types” later
in this chapter. Additional information on envelope
detectors can be found in Agilent Application
Note 1303, Spectrum Analyzer Measurements and
Noise, literature number 5966-4008E.
7. A signal whose frequency range extends from zero
(dc) to some upper frequency determined by the
circuit elements. Historically, spectrum analyzers
with analog displays used this signal to drive the
vertical deflection plates of the CRT directly. Hence
it was known as the video signal.
24
Figure 2-16. Output of the envelope detector follows the peaks of the
IF signal
t
The width of the resolution (IF) filter determines the maximum rate at which
the envelope of the IF signal can change. This bandwidth determines how far
apart two input sinusoids can be so that after the mixing process they will
both be within the filter at the same time. Let’s assume a 21.4 MHz final IF
and a 100 kHz bandwidth. Two input signals separated by 100 kHz would
produce mixing products of 21.35 and 21.45 MHz and would meet the
criterion. See Figure 2-16. The detector must be able to follow the changes in
the envelope created by these two signals but not the 21.4 MHz IF signal itself.
The envelope detector is what makes the spectrum analyzer a voltmeter.
Let’s duplicate the situation above and have two equal-amplitude signals in
the passband of the IF at the same time. A power meter would indicate a
power level 3 dB above either signal, that is, the total power of the two.
Assume that the two signals are close enough so that, with the analyzer
tuned half way between them, there is negligible attenuation due to the
roll-off of the filter8. Then the analyzer display will vary between a value
that is twice the voltage of either (6 dB greater) and zero (minus infinity
on the log scale). We must remember that the two signals are sine waves
(vectors) at different frequencies, and so they continually change in phase
with respect to each other. At some time they add exactly in phase; at
another, exactly out of phase.
So the envelope detector follows the changing amplitude values of the peaks
of the signal from the IF chain but not the instantaneous values, resulting
in the loss of phase information. This gives the analyzer its voltmeter
characteristics.
Digitally implemented resolution bandwidths do not have an analog envelope
detector. Instead, the digital processing computes the root sum of the squares
of the I and Q data, which is mathematically equivalent to an envelope
detector. For more information on digital architecture, refer to Chapter 3.
Displays
Up until the mid-1970s, spectrum analyzers were purely analog. The
displayed trace presented a continuous indication of the signal envelope,
and no information was lost. However, analog displays had drawbacks. The
major problem was in handling the long sweep times required for narrow
resolution bandwidths. In the extreme case, the display became a spot
that moved slowly across the cathode ray tube (CRT), with no real trace
on the display. So a meaningful display was not possible with the longer
sweep times.
8. For this discussion, we assume that the filter is
perfectly rectangular.
Agilent Technologies (part of Hewlett-Packard at the time) pioneered a
variable-persistence storage CRT in which we could adjust the fade rate of
the display. When properly adjusted, the old trace would just fade out at
the point where the new trace was updating the display. This display was
continuous, had no flicker, and avoided confusing overwrites. It worked quite
well, but the intensity and the fade rate had to be readjusted for each new
measurement situation. When digital circuitry became affordable in the
mid-1970s, it was quickly put to use in spectrum analyzers. Once a trace had
been digitized and put into memory, it was permanently available for display.
It became an easy matter to update the display at a flicker-free rate without
blooming or fading. The data in memory was updated at the sweep rate, and
since the contents of memory were written to the display at a flicker-free
rate, we could follow the updating as the analyzer swept through its selected
frequency span just as we could with analog systems.
25
Detector types
With digital displays, we had to decide what value should be displayed for
each display data point. No matter how many data points we use across
the display, each point must represent what has occurred over some
frequency range and, although we usually do not think in terms of time
when dealing with a spectrum analyzer, over some time interval.
Figure 2-17. When digitizing an analog signal, what value
should be displayed at each point?
It is as if the data for each interval is thrown into a bucket and we apply
whatever math is necessary to extract the desired bit of information from our
input signal. This datum is put into memory and written to the display. This
provides great flexibility. Here we will discuss six different detector types.
In Figure 2-18, each bucket contains data from a span and time frame that is
determined by these equations:
Frequency:
Time:
bucket width = span/(trace points - 1)
bucket width = sweep time/(trace points - 1)
The sampling rates are different for various instruments, but greater accuracy
is obtained from decreasing the span and/or increasing the sweep time
since the number of samples per bucket will increase in either case. Even
in analyzers with digital IFs, sample rates and interpolation behaviors are
designed to be the equivalent of continuous-time processing.
Figure 2-18. Each of the 101 trace points (buckets) covers a
1 MHz frequency span and a 0.1 millisecond time span
26
The “bucket” concept is important, as it will help us differentiate the six
detector types:
Sample
Positive peak (also simply called peak)
Negative peak
Normal
Average
Quasi-peak
The first 3 detectors, sample, peak, and negative peak are easily understood
and visually represented in Figure 2-19. Normal, average, and quasi-peak
are more complex and will be discussed later.
One bucket
Positive peak
Sample
Negative peak
Figure 2-19. Trace point saved in memory is based on
detector type algorithm
Let’s return to the question of how to display an analog system as faithfully
as possible using digital techniques. Let’s imagine the situation illustrated in
Figure 2-17. We have a display that contains only noise and a single CW signal.
Sample detection
As a first method, let us simply select the data point as the instantaneous level
at the center of each bucket (see Figure 2-19). This is the sample detection
mode. To give the trace a continuous look, we design a system that draws
vectors between the points. Comparing Figure 2-17 with 2-20, it appears that
we get a fairly reasonable display. Of course, the more points there are in the
trace, the better the replication of the analog signal will be. The number of
available display points can vary for different analyzers. On ESA and PSA Series
spectrum analyzers, the number of display points for frequency domain traces
can be set from a minimum of 101 points to a maximum of 8192 points. As
shown in figure 2-21, more points do indeed get us closer to the analog signal.
Figure 2-20. Sample display mode using ten points to display the signal
of Figure 2-17
Figure 2-21. More points produce a display closer to an analog display
27
While the sample detection mode does a good job of indicating the randomness
of noise, it is not a good mode for analyzing sinusoidal signals. If we were
to look at a 100 MHz comb on an Agilent ESA E4407B, we might set it to
span from 0 to 26.5 GHz. Even with 1,001 display points, each display point
represents a span (bucket) of 26.5 MHz. This is far wider than the maximum
5 MHz resolution bandwidth.
As a result, the true amplitude of a comb tooth is shown only if its mixing
product happens to fall at the center of the IF when the sample is taken.
Figure 2-22a shows a 5 GHz span with a 1 MHz bandwidth using sample
detection. The comb teeth should be relatively equal in amplitude as shown
in Figure 2-22b (using peak detection). Therefore, sample detection does not
catch all the signals, nor does it necessarily reflect the true peak values of the
displayed signals. When resolution bandwidth is narrower than the sample
interval (i.e., the bucket width), the sample mode can give erroneous results.
Figure 2-22a. A 5 GHz span of a 100 MHz comb in the sample display mode
Figure 2-22b. The actual comb over a 500 MHz span using peak
(positive) detection
28
Peak (positive) detection
One way to insure that all sinusoids are reported at their true amplitudes is
to display the maximum value encountered in each bucket. This is the positive
peak detection mode, or peak. This is illustrated in Figure 2-22b. Peak is the
default mode offered on many spectrum analyzers because it ensures that
no sinusoid is missed, regardless of the ratio between resolution bandwidth
and bucket width. However, unlike sample mode, peak does not give a good
representation of random noise because it only displays the maximum value
in each bucket and ignores the true randomness of the noise. So spectrum
analyzers that use peak detection as their primary mode generally also offer
the sample mode as an alternative.
Negative peak detection
Negative peak detection displays the minimum value encountered in each
bucket. It is generally available in most spectrum analyzers, though it is not
used as often as other types of detection. Differentiating CW from impulsive
signals in EMC testing is one application where negative peak detection
is valuable. Later in this application note, we will see how negative peak
detection is also used in signal identification routines when using external
mixers for high frequency measurements.
Figure 2-23a. Normal mode
Figure 2-23b. Sample mode
Figure 2-23. Comparison of normal and sample display detection when measuring noise
Normal detection
9. rosenfell is not a person’s name but rather a
description of the algorithm that tests to see if the
signal rose and fell within the bucket represented
by a given data point. It is also sometimes written as
“rose’n’fell”.
10. Because of its usefulness in measuring noise, the
sample detector is usually used in “noise marker”
applications. Similarly, the measurement of channel
power and adjacent-channel power requires a
detector type that gives results unbiased by peak
detection. For analyzers without averaging detectors,
sample detection is the best choice.
To provide a better visual display of random noise than peak and yet avoid
the missed-signal problem of the sample mode, the normal detection mode
(informally known as rosenfell9) is offered on many spectrum analyzers.
Should the signal both rise and fall, as determined by the positive peak and
negative peak detectors, then the algorithm classifies the signal as noise.
In that case, an odd-numbered data point displays the maximum value
encountered during its bucket. And an even-numbered data point displays
the minimum value encountered during its bucket. See Figure 2-25. Normal
and sample modes are compared in Figures 2-23a and 2-23b.10
29
What happens when a sinusoidal signal is encountered? We know that as a
mixing product is swept past the IF filter, an analyzer traces out the shape of
the filter on the display. If the filter shape is spread over many display points,
then we encounter a situation in which the displayed signal only rises as the
mixing product approaches the center frequency of the filter and only falls as
the mixing product moves away from the filter center frequency. In either of
these cases, the pos-peak and neg-peak detectors sense an amplitude change
in only one direction, and, according to the normal detection algorithm, the
maximum value in each bucket is displayed. See Figure 2-24.
What happens when the resolution bandwidth is narrow, relative to a bucket?
The signal will both rise and fall during the bucket. If the bucket happens
to be an odd-numbered one, all is well. The maximum value encountered in
the bucket is simply plotted as the next data point. However, if the bucket is
even-numbered, then the minimum value in the bucket is plotted. Depending
on the ratio of resolution bandwidth to bucket width, the minimum value can
differ from the true peak value (the one we want displayed) by a little or a lot.
In the extreme, when the bucket is much wider than the resolution bandwidth,
the difference between the maximum and minimum values encountered in
the bucket is the full difference between the peak signal value and the noise.
This is true for the example in Figure 2-25. See bucket 6. The peak value of
the previous bucket is always compared to that of the current bucket. The
greater of the two values is displayed if the bucket number is odd as depicted
in bucket 7. The signal peak actually occurs in bucket 6 but is not displayed
until bucket 7.
Figure 2-24. Normal detection displays maximum values in buckets
where signal only rises or only falls
30
The normal detection algorithm:
If the signal rises and falls within a bucket:
Even numbered buckets display the minimum (negative peak)
value in the bucket. The maximum is remembered.
Odd numbered buckets display the maximum (positive peak)
value determined by comparing the current bucket peak with
the previous (remembered) bucket peak.
If the signal only rises or only falls within a bucket, the peak
is displayed. See Figure 2-25.
This process may cause a maximum value to be displayed one data point too
far to the right, but the offset is usually only a small percentage of the span.
Some spectrum analyzers, such as the Agilent PSA Series, compensate for
this potential effect by moving the LO start and stop frequencies.
Another type of error is where two peaks are displayed when only one
actually exists. Figure 2-26 shows what might happen in such a case. The
outline of the two peaks is displayed using peak detection with a wider RBW.
So peak detection is best for locating CW signals well out of the noise. Sample
is best for looking at noise, and normal is best for viewing signals and noise.
Buckets
1
2
3
4
5
6
7
8
9
Figure 2-25. Trace points selected by the normal detection algorithm
10
Figure 2-26. Normal detection shows two peaks when actually only one
peak exists
31
Average detection
Although modern digital modulation schemes have noise-like characteristics,
sample detection does not always provide us with the information we need.
For instance, when taking a channel power measurement on a W-CDMA
signal, integration of the rms values is required. This measurement involves
summing power across a range of analyzer frequency buckets. Sample
detection does not provide this.
While spectrum analyzers typically collect amplitude data many times in
each bucket, sample detection keeps only one of those values and throws
away the rest. On the other hand, an averaging detector uses all the data
values collected within the time (and frequency) interval of a bucket. Once
we have digitized the data, and knowing the circumstances under which
they were digitized, we can manipulate the data in a variety of ways to
achieve the desired results.
Some spectrum analyzers refer to the averaging detector as an rms detector
when it averages power (based on the root mean square of voltage). Agilent
PSA and ESA Series analyzers have an average detector that can average
the power, voltage, or log of the signal by including a separate control to
select the averaging type:
Power (rms) averaging averages rms levels, by taking the square root of the
sum of the squares of the voltage data measured during the bucket interval,
divided by the characteristic input impedance of the spectrum analyzer,
normally 50 ohms. Power averaging calculates the true average power, and
is best for measuring the power of complex signals.
Voltage averaging averages the linear voltage data of the envelope signal
measured during the bucket interval. It is often used in EMI testing for
measuring narrowband signals (this will be discussed further in the next
section). Voltage averaging is also useful for observing rise and fall behavior
of AM or pulse-modulated signals such as radar and TDMA transmitters.
Log-power (video) averaging averages the logarithmic amplitude values (dB)
of the envelope signal measured during the bucket interval. Log power
averaging is best for observing sinusoidal signals, especially those near
noise.11
Thus, using the average detector with the averaging type set to power provides
true average power based upon rms voltage, while the average detector with
the averaging type set to voltage acts as a general-purpose average detector.
The average detector with the averaging type set to log has no other equivalent.
11. See Chapter 5, “Sensitivity and Noise.”
12. Refer to Chapter 3 for more information on the FFT
analyzers. They perform math computations on
many buckets simultaneously, which improves the
measurement speed.
32
Average detection is an improvement over using sample detection for the
determination of power. Sample detection requires multiple sweeps to collect
enough data points to give us accurate average power information. Average
detection changes channel power measurements from being a summation
over a range of buckets into integration over the time interval representing
a range of frequencies in a swept analyzer. In a fast Fourier transfer (FFT)
analyzer12, the summation used for channel power measurements changes
from being a summation over display buckets to being a summation over
FFT bins. In both swept and FFT cases, the integration captures all the power
information available, rather than just that which is sampled by the sample
detector. As a result, the average detector has a lower variance result for the
same measurement time. In swept analysis, it also allows the convenience of
reducing variance simply by extending the sweep time.
EMI detectors: average and quasi-peak detection
An important application of average detection is for characterizing devices
for electromagnetic interference (EMI). In this case, voltage averaging, as
described in the previous section, is used for measurement of narrowband
signals that might be masked by the presence of broadband impulsive noise.
The average detection used in EMI instruments takes an envelope-detected
signal and passes it through a low-pass filter with a bandwidth much less than
the RBW. The filter integrates (averages) the higher frequency components
such as noise. To perform this type of detection in an older spectrum analyzer
that doesn’t have a built-in voltage averaging detector function, set the
analyzer in linear mode and select a video filter with a cut-off frequency
below the lowest PRF of the measured signal.
Quasi-peak detectors (QPD) are also used in EMI testing. QPD is a weighted
form of peak detection. The measured value of the QPD drops as the repetition
rate of the measured signal decreases. Thus, an impulsive signal with a given
peak amplitude and a 10 Hz pulse repetition rate will have a lower quasi-peak
value than a signal with the same peak amplitude but having a 1 kHz repetition
rate. This signal weighting is accomplished by circuitry with specific charge,
discharge, and display time constants defined by CISPR13.
QPD is a way of measuring and quantifying the “annoyance factor” of a signal.
Imagine listening to a radio station suffering from interference. If you hear
an occasional “pop” caused by noise once every few seconds, you can still
listen to the program without too much trouble. However, if that same
amplitude pop occurs 60 times per second, it becomes extremely annoying,
making the radio program intolerable to listen to.
Averaging processes
There are several processes in a spectrum analyzer that smooth the variations
in the envelope-detected amplitude. The first method, average detection, was
discussed previously. Two other methods, video filtering and trace
averaging, are discussed next.14
13. CISPR, the International Special Committee on
Radio Interference, was established in 1934 by a
group of international organizations to address
radio interference. CISPR is a non-governmental
group composed of National Committees of the
International Electrotechnical Commission (IEC),
as well as numerous international organizations.
CISPR’s recommended standards generally form
the basis for statutory EMC requirements adopted
by governmental regulatory agencies around the
world.
14. A fourth method, called a noise marker, is
discussed in Chapter 5, “Sensitivity and Noise”.
A more detailed discussion can be found in
Application Note 1303, Spectrum Analyzer
Measurements and Noise, literature number
5966-4008E.
33
Video filtering
Discerning signals close to the noise is not just a problem when performing
EMC tests. Spectrum analyzers display signals plus their own internal noise,
as shown in Figure 2-27. To reduce the effect of noise on the displayed signal
amplitude, we often smooth or average the display, as shown in Figure 2-28.
Spectrum analyzers include a variable video filter for this purpose. The
video filter is a low-pass filter that comes after the envelope detector and
determines the bandwidth of the video signal that will later be digitized to
yield amplitude data. The cutoff frequency of the video filter can be reduced
to the point where it becomes smaller than the bandwidth of the selected
resolution bandwidth (IF) filter. When this occurs, the video system can no
longer follow the more rapid variations of the envelope of the signal(s)
passing through the IF chain. The result is an averaging or smoothing of
the displayed signal.
Figure 2-27. Spectrum analyzers display signal plus noise
Figure 2-28. Display of figure 2-27 after full smoothing
34
The effect is most noticeable in measuring noise, particularly when a wide
resolution bandwidth is used. As we reduce the video bandwidth, the peakto-peak variations of the noise are reduced. As Figure 2-29 shows, the degree
of reduction (degree of averaging or smoothing) is a function of the ratio of
the video to resolution bandwidths. At ratios of 0.01 or less, the smoothing
is very good. At higher ratios, the smoothing is not so good. The video filter
does not affect any part of the trace that is already smooth (for example,
a sinusoid displayed well out of the noise).
Figure 2-29. Smoothing effect of VBW-to-RBW ratios of 3:1, 1:10, and 1:100
35
If we set the analyzer to positive peak detection mode, we notice two things:
First, if VBW > RBW, then changing the resolution bandwidth does not make
much difference in the peak-to-peak fluctuations of the noise. Second, if
VBW < RBW, then changing the video bandwidth seems to affect the noise
level. The fluctuations do not change much because the analyzer is displaying
only the peak values of the noise. However, the noise level appears to change
with video bandwidth because the averaging (smoothing) changes, thereby
changing the peak values of the smoothed noise envelope. See Figure 2-30a.
When we select average detection, we see the average noise level remains
constant. See Figure 2-30b.
Because the video filter has its own response time, the sweep time increases
approximately inversely with video bandwidth when the VBW is less than
the resolution bandwidth. The sweep time can therefore be described by
this equation:
ST ≈
k(Span)
(RBW)(VBW)
The analyzer sets the sweep time automatically to account for video
bandwidth as well as span and resolution bandwidth.
Figure 2-30a. Positive peak detection mode; reducing video bandwidth
lowers peak noise but not average noise
Figure 2-30b. Average detection mode; noise level remains constant,
regardless of VBW-to-RBW ratios (3:1, 1:10, and 1:100)
Trace Averaging
Digital displays offer another choice for smoothing the display: trace
averaging. This is a completely different process than that performed using
the average detector. In this case, averaging is accomplished over two or
more sweeps on a point-by-point basis. At each display point, the new
value is averaged in with the previously averaged data:
Aavg =
where
36
(n n– 1) A
prior avg
( )
1
+ n An
Aavg = new average value
Aprior avg = average from prior sweep
An= measured value on current sweep
n = number of current sweep
Thus, the display gradually converges to an average over a number of sweeps.
As with video filtering, we can select the degree of averaging or smoothing.
We do this by setting the number of sweeps over which the averaging occurs.
Figure 2-31 shows trace averaging for different numbers of sweeps. While
trace averaging has no effect on sweep time, the time to reach a given degree
of averaging is about the same as with video filtering because of the number
of sweeps required.
In many cases, it does not matter which form of display smoothing we pick.
If the signal is noise or a low-level sinusoid very close to the noise, we get the
same results with either video filtering or trace averaging. However, there is a
distinct difference between the two. Video filtering performs averaging in real
time. That is, we see the full effect of the averaging or smoothing at each point
on the display as the sweep progresses. Each point is averaged only once,
for a time of about 1/VBW on each sweep. Trace averaging, on the other
hand, requires multiple sweeps to achieve the full degree of averaging, and
the averaging at each point takes place over the full time period needed to
complete the multiple sweeps.
As a result, we can get significantly different results from the two averaging
methods on certain signals. For example, a signal with a spectrum that
changes with time can yield a different average on each sweep when we
use video filtering. However, if we choose trace averaging over many sweeps,
we will get a value much closer to the true average. See Figures 2-32a and b.
Figure 2-31. Trace averaging for 1, 5, 20, and 100 sweeps, top to bottom
(trace position offset for each set of sweeps)
37
Figure 2-32b. Trace averaging
Figure 2-32a. Video filtering
Figure 2-32. Video filtering and trace averaging yield different results on FM broadcast signal
Time gating
Time-gated spectrum analysis allows you to obtain spectral information
about signals occupying the same part of the frequency spectrum that are
separated in the time domain. Using an external trigger signal to coordinate
the separation of these signals, you can perform the following operations:
• Measure any one of several signals separated in time; for example, you
can separate the spectra of two radios time-sharing a single frequency
• Measure the spectrum of a signal in one time slot of a TDMA system
• Exclude the spectrum of interfering signals, such as periodic pulse edge
transients that exist for only a limited time
Why time gating is needed
Traditional frequency-domain spectrum analysis provides only limited
information for certain signals. Examples of these difficult-to-analyze signals
include the following signal types:
• Pulsed RF
• Time multiplexed
• Time domain multiple access (TDMA)
• Interleaved or intermittent
• Burst modulated
38
In some cases, time-gating capability enables you to perform measurements
that would otherwise be very difficult, if not impossible. For example,
consider Figure 2-33a, which shows a simplified digital mobile-radio
signal in which two radios, #1 and #2, are time-sharing a single frequency
channel. Each radio transmits a single 1 ms burst, and then shuts off while
the other radio transmits for 1 ms. The challenge is to measure the unique
frequency spectrum of each transmitter.
Unfortunately, a traditional spectrum analyzer cannot do that. It simply
shows the combined spectrum, as seen in Figure 2-33b. Using the time-gate
capability and an external trigger signal, you can see the spectrum of just
radio #1 (or radio #2 if you wished) and identify it as the source of the
spurious signal shown, as in Figure 2-33c.
Figure 2-33a. Simplified digital mobile-radio signal in time
domain
Figure 2-33c. Time-gated spectrum of signal #1 identifies
it as the source of spurious emission
Figure 2-33b. Frequency spectrum of combined signals. Which
radio produces the spurious emissions?
Figure 2-33d. Time-gated spectrum of signal #2 shows it is
free of spurious emissions
39
Time gating can be achieved using three different methods that will be
discussed below. However, there are certain basic concepts of time gating
that apply to any implementation. In particular, you must have, or be able to
set, the following four items:
• An externally supplied gate trigger signal
• The gate control, or trigger mode (edge, or level)
• The gate delay setting, which determines how long after the trigger
signal the gate actually becomes active and the signal is observed
• The gate length setting, which determines how long the gate is on and
the signal is observed
Controlling these parameters will allow us to look at the spectrum of the
signal during a desired portion of the time. If you are fortunate enough to
have a gating signal that is only true during the period of interest, then you
can use level gating as shown in Figure 2-34. However, in many cases the
gating signal will not perfectly coincide with the time we want to measure
the spectrum. Therefore, a more flexible approach is to use edge triggering
in conjunction with a specified gate delay and gate length to precisely define
the time period in which to measure the signal.
RF signal
Gate signal
Figure 2-34. Level triggering: the spectrum analyzer only measures the frequency spectrum
when gate trigger signal is above a certain level
Consider the GSM signal with eight time slots in Figure 2-35. Each burst is
0.577 ms and the full frame is 4.615 ms. We may be interested in the spectrum
of the signal during a specific time slot. For the purposes of this example,
let’s assume that we are using only two of the eight available time slots, as
shown in Figure 2-36. When we look at this signal in the frequency domain in
Figure 2-37, we observe an unwanted spurious signal present in the spectrum.
In order to troubleshoot the problem and find the source of this interfering
signal, we need to determine the time slot in which it is occurring. If we wish
to look at time slot 2, we set up the gate to trigger on the rising edge of burst
0, then specify a gate delay of 1.3 ms and a gate length of 0.3 ms, as shown
in Figure 2-38. The gate delay assures that we only measure the spectrum
of time slot 2 while the burst is fully on. Note that the gate delay value is
carefully selected to avoid the rising edge of the burst, since we want to allow
time for the RBW filtered signal to settle out before we make a measurement.
Similarly, the gate length is chosen to avoid the falling edges of the burst.
Figure 2-39 shows the spectrum of time slot 2, which reveals that the spurious
signal is NOT caused by this burst.
40
Timeslots
0
1
2
3
4
5
6
7
Timeslots
Figure 2-35. A TDMA format signal (in this case, GSM) with eight time slots
Figure 2-37. The signal in the frequency domain
Figure 2-36. A zero span (time domain) view of the two time slots
Figure 2-38. Time gating is used to look at the spectrum of time slot 2
Figure 2-39. Spectrum of the pulse in time slot 2
41
There are three common methods used to perform time gating:
• Gated FFT
• Gated video
• Gated sweep
Gated FFT
Some spectrum analyzers, such as the Agilent PSA Series, have built-in FFT
capabilities. In this mode, the data is acquired for an FFT starting at a chosen
delay following a trigger. The IF signal is digitized and captured for a time
period of 1.83 divided by resolution bandwidth. An FFT is computed based
on this data acquisition and the results are displayed as the spectrum. Thus,
the spectrum is that which existed at a particular time of known duration.
This is the fastest gating technique whenever the span is not wider than the
FFT maximum width, which for PSA is 10 MHz.
To get the maximum possible frequency resolution, choose the narrowest
available RBW whose capture time fits within the time period of interest.
That may not always be needed, however, and you could choose a wider RBW
with a corresponding narrower gate length. The minimum usable RBW in
gated FFT applications is always lower than the minimum usable RBW in
other gating techniques, because the IF must fully settle during the burst in
other techniques, which takes longer than 1.83 divided by RBW.
Gated video
Gated video is the analysis technique used in a number of spectrum
analyzers, including the Agilent 8560, 8590 and ESA Series. In this case,
the video voltage is switched off, or to “negative infinity decibels” during the
time the gate is supposed to be in its “blocked” mode. The detector is set to
peak detection. The sweep time must be set so that the gates occur at least
once per display point, or bucket, so that the peak detector is able to see
real data during that time interval. Otherwise, there will be trace points
with no data, resulting in an incomplete spectrum. Therefore, the minimum
sweep time is N display buckets times burst cycle time. For example, in GSM
measurements, the full frame lasts 4.615 ms. For an ESA spectrum analyzer
set to its default value of 401 display points, the minimum sweep time for
GSM gated video measurements would be 401 times 4.615 ms or 1.85 s. Some
TDMA formats have cycle times as large as 90 ms, resulting in long sweep
times using the gated video technique.
RF
step
attenuator
Mixer
IF resolution
bandwidth IF log
filter
amplifier
Envelope
detector
(IF to video)
RF
input
-$ dB
Video
bandwidth
filter
Peak/sample
detector
Reset
Gate control
Display logic
Local
oscillator
Scan generator
Display
Figure 2-40. Block diagram of a spectrum analyzer with gated video
42
Analog-digital
converter
Gated sweep
Gated sweep, sometimes referred to as gated LO, is the final technique.
In gated sweep mode, we control the voltage ramp produced by the scan
generator to sweep the LO. This is shown in figure 2-41. When the gate is
active, the LO ramps up in frequency like any spectrum analyzer. When the
gate is blocked, the voltage out of the scan generator is frozen, and the LO
stops rising in frequency. This technique can be much faster than gated video
because multiple buckets can be measured during each burst. As an example,
let’s use the same GSM signal described in the gated video discussion earlier
in this chapter. Using a PSA Series spectrum analyzer, a standard, non-gated,
spectrum sweep over a 1 MHz span takes 14.6 ms, as shown in Figure 2-42.
With a gate length of 0.3 ms, the spectrum analyzer sweep must be built up
in 49 gate intervals (14.6 divided by 0.3), or. If the full frame of the GSM
signal is 4.615 ms, then the total measurement time is 49 intervals times
4.615 ms = 226 ms. This represents a significant improvement in speed
compared to the gated video technique which required 1.85 s for 401 data
points. Gated sweep is available on the PSA Series spectrum analyzers.
RF
step
attenuator
Mixer
Envelope
detector
(IF to video)
IF resolution
bandwidth IF log
filter
amplifier
Video
bandwidth
filter
Peak/sample
detector
Analog-digital
converter
RF
input
Display logic
Local
oscillator
Scan generator
Gate
control
Display
Figure 2-41. In gated sweep mode, the LO sweeps only during gate interval
Figure 2-42. Spectrum of the GSM signal
43
Chapter 3
Digital IF Overview
Since the 1980’s, one of the most profound areas of change in spectrum
analysis has been the application of digital technology to replace portions
of the instrument that had previously been implemented as analog circuits.
With the availability of high-performance analog-to-digital converters, the
latest spectrum analyzers digitize incoming signals much earlier in the signal
path compared to spectrum analyzer designs of just a few years ago. The
change has been most dramatic in the IF section of the spectrum analyzer.
Digital IFs1 have had a great impact on spectrum analyzer performance, with
significant improvements in speed, accuracy, and the ability to measure
complex signals through the use of advanced DSP techniques.
Digital filters
A partial implementation of digital IF circuitry is implemented in the Agilent
ESA-E Series spectrum analyzers. While the 1 kHz and wider RBWs are
implemented with traditional analog LC and crystal filters, the narrowest
bandwidths (1 Hz to 300 Hz) are realized using digital techniques. As shown
in Figure 3-1, the linear analog signal is mixed down to an 8.5 kHz IF and
passed through a bandpass filter only 1 kHz wide. This IF signal is amplified,
then sampled at an 11.3 kHz rate and digitized.
21.4 MHz
Log
Video
ADC
µC
Linear
Sample and hold
at 11.3 kHz
3rd LO
8.5 kHz CF
1 kHz BW
Figure 3-1. Digital implementation of 1, 3, 10, 30, 100, and 300 Hz resolution filters in ESA-E Series
Once in digital form, the signal is put through a fast Fourier transform
algorithm. To transform the appropriate signal, the analyzer must be fixedtuned (not sweeping). That is, the transform must be done on a time-domain
signal. Thus the ESA-E Series analyzers step in 900 Hz increments, instead
of sweeping continuously, when we select one of the digital resolution
bandwidths. This stepped tuning can be seen on the display, which is
updated in 900 Hz increments as the digital processing is completed.
As we shall see in a moment, other spectrum analyzers, such as the PSA Series,
use an all-digital IF, implementing all resolution bandwidth filters digitally.
1. Strictly speaking, once a signal has been digitized,
it is no longer at an intermediate frequency, or IF.
At that point, the signal is represented by digital
data values. However, we use the term “digital IF”
to describe the digital processing that replaces the
analog IF processing found in traditional spectrum
analyzers.
44
A key benefit of the digital processing done in these analyzers is a bandwidth
selectivity of about 4:1. This selectivity is available on the narrowest filters,
the ones we would be choosing to separate the most closely spaced signals.
In Chapter 2, we did a filter skirt selectivity calculation for two signals
spaced 4 kHz apart, using a 3 kHz analog filter. Let’s repeat that calculation
using digital filters. A good model of the selectivity of digital filters is a
near-Gaussian model:
∆f α
H(∆f) = –3.01 dB x
RBW/2
[
where
]
H(∆f) is the filter skirt rejection in dB
∆f is the frequency offset from the center in Hz, and
α is a parameter that controls selectivity. α = 2 for an ideal
Gaussian filter. The swept RBW filters used in Agilent
spectrum analyzers are based on a near-Gaussian model with an α
value equal to 2.12, resulting in a selectivity ratio of 4.1:1.
Entering the values from our example into the equation, we get:
4000
[ 3000/2
]
H(4 kHz) = –3.01 dB x
2.12
= –24.1 dB
At an offset of 4 kHz, the 3 kHz digital filter is down –24.1 dB compared
to the analog filter which was only down –14.8 dB. Because of its superior
selectivity, the digital filter can resolve more closely spaced signals.
The all-digital IF
The Agilent PSA Series spectrum analyzers have, for the first time, combined
several digital techniques to achieve the all-digital IF. The all-digital IF brings
a wealth of advantages to the user. The combination of FFT analysis for
narrow spans and swept analysis for wider spans optimizes sweeps for the
fastest possible measurements. Architecturally, the ADC is moved closer
to the input port, a move made possible by improvements to the A-to-D
converters and other digital hardware. Let’s begin by taking a look at the
block diagram of the all-digital IF in the PSA spectrum analyzer, as shown
in Figure 3-2.
Custom IC
Anti-alias
filter
I, Q
ADC
Prefilter
Ranging
rules
Counter
I
-1
Q
r,
log (r)
log
log
log
Hilbert
transform
VBW
pwr
v
log
pwr
v
log
Display
det
log
log
log
Autoranging ADC system
RISC processor
FFT
Display
Processing
log/lin
dB/div
Display
Figure 3-2. Block diagram of the all-digital IF in the Agilent PSA Series
45
In this case, all 160 resolution bandwidths are digitally implemented.
However, there is some analog circuitry prior to the ADC, starting with
several stages of down conversion, followed by a pair of single-pole prefilters
(one an LC filter, the other crystal-based). A prefilter helps prevent succeeding
stages from contributing third-order distortion in the same way a prefilter
would in an analog IF. In addition, it enables dynamic range extension via
autoranging. The output of the single-pole prefilter is routed to the autorange
detector and the anti-alias filter.
As with any FFT-based IF architecture, the anti-alias filter is required to
prevent aliasing (the folding of out-of-band signals into the ADC sampled
data). This filter has many poles, and thus has substantial group delay.
Even a very fast rising RF burst, downconverted to the IF frequency, will
experience a delay of more than three cycles of the ADC clock (30 MHz)
through the anti-alias filter. The delay allows time for an impending large
signal to be recognized before it overloads the ADC. The logic circuitry
controlling the autorange detector will decrease the gain in front of the ADC
before a large signal reaches it, thus preventing clipping. If the signal envelope
remains small for a long time, the autoranging circuit increases the gain,
reducing the effective noise at the input. The digital gain after the ADC is
also changed to compensate for the analog gain in front of it. The result is a
“floating point” ADC with very wide dynamic range when autoranging is
enabled in swept mode.
Amplitude
(log)
ADC
clipping threshold
Prefilter gain
Typical
analog IF
response
Digital IF RBW response
Noise floor after autoranging
Typical LO phase noise
Frequency or time
Figure 3-3. Autoranging keeps ADC noise close to carrier and lower than LO noise
or RBW filter response
Figure 3-3 illustrates the sweeping behavior of the PSA analyzer. The
single-pole prefilter allows the gain to be turned up high when the analyzer
is tuned far from the carrier. As the carrier gets closer, the gain falls and the
ADC quantization noise rises. The noise level will depend on the signal level
frequency separation from the carrier, so it looks like a step-shaped phase
noise. However, phase noise is different from this autoranging noise. Phase
noise cannot be avoided in a spectrum analyzer. However, reducing the
prefilter width can reduce autoranging noise at most frequency offsets from
the carrier. Since the prefilter width is approximately 2.5 times the RBW,
reducing the RBW reduces the autoranging noise.
46
Custom signal processing IC
Turning back to the block diagram of the digital IF (Figure 3-2), after the
ADC gain has been set with analog gain and corrected with digital gain, a
custom IC begins processing the samples. First, it splits the 30 MHz IF samples
into I and Q pairs at half the rate (15 Mpairs/s). The I and Q pairs are given
a high-frequency boost with a single-stage digital filter that has gain and
phase approximately opposite to that of the single pole analog prefilter. Next,
I and Q signals are low-pass filtered with a linear-phase filter with nearly
ideal Gaussian response. Gaussian filters have always been used for swept
spectrum analysis, because of their optimum compromise between frequency
domain performance (shape factor) and time-domain performance (response
to rapid sweeps). With the signal bandwidth now reduced, the I and Q pairs may
be decimated and sent to the processor for FFT processing or demodulation.
Although FFTs can be performed to cover a segment of frequency span up to
the 10 MHz bandwidth of the anti-alias filter, even a narrower FFT span, such
as 1 kHz, with a narrow RBW, such as 1 Hz, would require FFTs with 20 million
data points. Using decimation for narrower spans, the number of data points
needed to compute the FFT is greatly reduced, speeding up computations.
For swept analysis, the filtered I and Q pairs are converted to magnitude
and phase pairs. For traditional swept analysis, the magnitude signal is
video-bandwidth (VBW) filtered and samples are taken through the display
detector circuit. The log/linear display selection and dB/division scaling
occur in the processor, so that a trace may be displayed on any scale
without remeasuring.
Additional video processing features
The VBW filter normally smoothes the log of the magnitude of the signal,
but it has many additional features. It can convert the log magnitude to a
voltage envelope before filtering, and convert it back for consistent behavior
before display detection.
Filtering the magnitude on a linear voltage scale is desirable for observing
pulsed-RF envelope shapes in zero span. The log-magnitude signal can also
be converted to a power (magnitude squared) signal before filtering, and
then converted back. Filtering the power allows the analyzer to give the
same average response to signals with noise-like characteristics, such as
digital communications signals, as to CW signals with the same rms voltage.
An increasingly common measurement need is total power in a channel or
across a frequency range. In such a measurement, the display points might
represent the average power during the time the LO sweeps through that
point. The VBW filter can be reconfigured into an accumulator to perform
averaging on either a log, voltage or power scale.
Frequency counting
Swept spectrum analyzers usually have a frequency counter. This counter
counts the zero crossings in the IF signal and offsets that count by the known
frequency offsets from LOs in the rest of the conversion chain. If the count
is allowed to run for a second, a resolution of 1 Hz is achievable.
Because of its digitally synthesized LOs and all-digital RBWs, the native
frequency accuracy of the PSA Series analyzer is very good (0.1% of span).
In addition, the PSA analyzer includes a frequency counter that observes
not just zero crossings, but also the change in phase. Thus, it can resolve
frequency to the tens of millihertz level in 0.1 second. With this design, the
ability to resolve frequency changes is not limited by the spectrum analyzer,
but rather is determined by the noisiness of the signal being counted.
47
More advantages of the all-digital IF
We have already discussed a number of features in the PSA Series: power/
voltage/log video filtering, high-resolution frequency counting, log/linear
switching of stored traces, excellent shape factors, an average-across-the
display-point detector mode, 160 RBWs, and of course, FFT or swept
processing. In spectrum analysis, the filtering action of RBW filters causes
errors in frequency and amplitude measurements that are a function of the
sweep rate. For a fixed level of these errors, the all-digital IF’s linear phase
RBW filters allow faster sweep rates than do analog filters. The digital
implementation also allows well-known compensations to frequency and
amplitude readout, permitting sweep rates typically twice as fast as older
analyzers, and excellent performance at even four times the sweep speed.
The digitally implemented logarithmic amplification is very accurate.
Typical errors of the entire analyzer are much smaller than the measurement
uncertainty with which the manufacturer proves the log fidelity. The log
fidelity is specified at ±0.07 dB for any level up to –20 dBm at the input mixer
of the analyzer. The range of the log amp does not limit the log fidelity at low
levels, as it would be in an analog IF; the range is only limited by noise around
–155 dBm at the input mixer. Because of single-tone compression in upstream
circuits at higher powers, the fidelity specification degrades to ±0.13 dB for
signal levels up to –10 dBm at the input mixer. By comparison, analog log
amps are usually specified with tolerances in the ±1 dB region.
Other IF-related accuracies are improved as well. The IF prefilter is analog
and must be aligned like an analog filter, so it is subject to alignment errors.
But it is much better than most analog filters. With only one stage to
manufacture, that stage can be made much more stable than the 4- and
5-stage filters of analog IF-based spectrum analyzers. As a result, the gain
variations between RBW filters is held to a specification of ±0.03 dB, ten
times better than all-analog designs.
The accuracy of the IF bandwidth is determined by settability limitations in
the digital part of the filtering and calibration uncertainties in the analog
prefilter. Again, the prefilter is highly stable and contributes only 20 percent
of the error that would exist with an RBW made of five such stages. As a
result, most RBWs are within 2 percent of their stated bandwidth, compared
to 10 to 20 percent specifications in analog-IF analyzers.
The most important purpose of bandwidth accuracy is minimizing the
inaccuracy of channel power and similar measurements. The noise bandwidth
of the RBW filters is known to much better specifications than the 2 percent
setting tolerance, and noise markers and channel-power measurements are
corrected to a tolerance of ±0.5 percent. Therefore, bandwidth uncertainties
contribute only ±0.022 dB to the amplitude error of noise density and
channel-power measurements.
Finally, with no analog reference-level-dependent gain stages, there is no
“IF gain” error at all. The sum of all these improvements means that the
all-digital IF makes a quantum improvement in spectrum analyzer accuracy.
It also allows you to change analyzer settings without significantly impacting
measurement uncertainty. We will cover this topic in more detail in the
next chapter.
48
Chapter 4
Amplitude and
Frequency Accuracy
Now that we can view our signal on the display screen, let’s look at amplitude
accuracy, or perhaps better, amplitude uncertainty. Most spectrum analyzers
are specified in terms of both absolute and relative accuracy. However,
relative performance affects both, so let’s look at those factors affecting
relative measurement uncertainty first.
Before we discuss these uncertainties, let’s look again at the block diagram
of an analog swept-tuned spectrum analyzer, shown in Figure 4-1, and see
which components contribute to the uncertainties. Later in this chapter, we
will see how a digital IF and various correction and calibration techniques
can substantially reduce measurement uncertainty.
RF input
attenuator
Mixer
IF gain
IF filter
Log
amp
Envelope
detector
Input
signal
Video
filter
Pre-selector, or
low-pass filter
Local
oscillator
Reference
oscillator
Sweep
generator
Display
Figure 4-1. Spectrum analyzer block diagram
Components which contribute to uncertainty are:
•
•
•
•
•
•
•
1. For more information, see the Agilent PSA
Performance Spectrum Analyzer Series Amplitude
Accuracy Product Note, literature number
5980-3080EN.
Input connector (mismatch)
RF Input attenuator
Mixer and input filter (flatness)
IF gain/attenuation (reference level )
RBW filters
Display scale fidelity
Calibrator (not shown)
An important factor in measurement uncertainty that is often overlooked
is impedance mismatch. Analyzers do not have perfect input impedances,
and signal sources do not have ideal output impedances. When a mismatch
exists, the incident and reflected signal vectors may add constructively or
destructively. Thus the signal received by the analyzer can be larger or
smaller than the original signal. In most cases, uncertainty due to mismatch
is relatively small. However, it should be noted that as spectrum analyzer
amplitude accuracy has improved dramatically in recent years, mismatch
uncertainty now constitutes a more significant part of the total measurement
uncertainty. In any case, improving the match of either the source or
analyzer reduces uncertainty1.
49
The general expression used to calculate the maximum mismatch error
in dB is:
Error (dB) = –20 log[1 ± |(ρanalyzer)(ρsource)|]
where ρ is the reflection coefficient
Spectrum analyzer data sheets typically specify the input voltage standing
wave ratio (VSWR). Knowing the VSWR, we can calculate ρ with the following
equation:
ρ=
(VSWR–1)
(VSWR+1)
As an example, consider a spectrum analyzer with an input VSWR of 1.2 and
a device under test (DUT) with a VSWR of 1.4 at its output port. The resulting
mismatch error would be ±0.13 dB.
Since the analyzer’s worst-case match occurs when its input attenuator is
set to 0 dB, we should avoid the 0 dB setting if we can. Alternatively, we can
attach a well-matched pad (attenuator) to the analyzer input and greatly
reduce mismatch as a factor. Adding attenuation is a technique that works
well to reduce measurement uncertainty when the signal we wish to measure
is well above the noise. However, in cases where the signal-to-noise ratio is
small (typically ≤7 dB), adding attenuation will increase measurement error
because the noise power adds to the signal power, resulting in an erroneously
high reading.
Let’s turn our attention to the input attenuator. Some relative measurements
are made with different attenuator settings. In these cases, we must consider
the input attenuation switching uncertainty. Because an RF input
attenuator must operate over the entire frequency range of the analyzer,
its step accuracy varies with frequency. The attenuator also contributes
to the overall frequency response. At 1 GHz, we expect the attenuator
performance to be quite good; at 26 GHz, not as good.
The next component in the signal path is the input filter. Spectrum analyzers
use a fixed low-pass filter in the low band and a tunable band pass filter
called a preselector (we will discuss the preselector in more detail in
Chapter 7) in the higher frequency bands. The low-pass filter has a better
frequency response than the preselector and adds a small amount of
uncertainty to the frequency response error. A preselector, usually a
YIG-tuned filter, has a larger frequency response variation, ranging from
1.5 dB to 3 dB at millimeter-wave frequencies.
50
Following the input filter are the mixer and the local oscillator, both of
which add to the frequency response uncertainty. Figure 4-2 illustrates what
the frequency response might look like in one frequency band. Frequency
response is usually specified as ± x dB relative to the midpoint between the
extremes. The frequency response of a spectrum analyzer represents the
overall system performance resulting from the flatness characteristics and
interactions of individual components in the signal path up to and including
the first mixer. Microwave spectrum analyzers use more than one frequency
band to go above 3 GHz. This is done by using a higher harmonic of the local
oscillator, which will be discussed in detail in Chapter 7. When making
relative measurements between signals in different frequency bands, you
must add the frequency response of each band to determine the overall
frequency response uncertainty. In addition, some spectrum analyzers
have a band switching uncertainty which must be added to the overall
measurement uncertainty.
Frequency response
Signals in the same harmonic band
+0.5 dB
0
- 0.5 dB
BAND 1
Specification: ±0.5 dB
Figure 4-2. Relative frequency response in a single band
After the input signal is converted to an IF, it passes through the IF gain
amplifier and IF attenuator which are adjusted to compensate for changes in
the RF attenuator setting and mixer conversion loss. Input signal amplitudes
are thus referenced to the top line of the graticule on the display, known as the
reference level. The IF amplifier and attenuator only work at one frequency
and, therefore, do not contribute to frequency response. However, there is
always some amplitude uncertainty introduced by how accurately they can be
set to a desired value. This uncertainty is known as reference level accuracy.
Another parameter that we might change during the course of a measurement
is resolution bandwidth. Different filters have different insertion losses.
Generally, we see the greatest difference when switching between LC filters
(typically used for the wider resolution bandwidths) and crystal filters
(used for narrow bandwidths). This results in resolution bandwidth
switching uncertainty.
The most common way to display signals on a spectrum analyzer is to use a
logarithmic amplitude scale, such as 10 dB per div or 1 dB per div. Therefore,
the IF signal usually passes through a log amplifier. The gain characteristic
of the log amplifier approximates a logarithmic curve. So any deviation from
a perfect logarithmic response adds to the amplitude uncertainty. Similarly,
when the spectrum analyzer is in linear mode, the linear amplifiers do not
have a perfect linear response. This type of uncertainty is called display
scale fidelity.
51
Relative uncertainty
When we make relative measurements on an incoming signal, we use either some
part of the same signal or a different signal as a reference. For example, when we
make second harmonic distortion measurements, we use the fundamental of the
signal as our reference. Absolute values do not come into play; we are interested
only in how the second harmonic differs in amplitude from the fundamental.
In a worst-case relative measurement scenario, the fundamental of the
signal may occur at a point where the frequency response is highest, while
the harmonic we wish to measure occurs at the point where the frequency
response is the lowest. The opposite scenario is equally likely. Therefore,
if our relative frequency response specification is ±0.5 dB as shown in
Figure 4-2, then the total uncertainty would be twice that value, or ±1.0 dB.
Perhaps the two signals under test might be in different frequency bands of the
spectrum analyzer. In that case, a rigorous analysis of the overall uncertainty
must include the sum of the flatness uncertainties of the two frequency bands.
Other uncertainties might be irrelevant in a relative measurement, like
the RBW switching uncertainty or reference level accuracy, which apply
to both signals at the same time.
Absolute amplitude accuracy
Nearly all spectrum analyzers have a built-in calibration source which
provides a known reference signal of specified amplitude and frequency.
We then rely on the relative accuracy of the analyzer to translate the absolute
calibration of the reference to other frequencies and amplitudes. Spectrum
analyzers often have an absolute frequency response specification, where
the zero point on the flatness curve is referenced to this calibration signal.
Many Agilent spectrum analyzers use a 50 MHz reference signal. At this
frequency, the specified absolute amplitude accuracy is extremely good:
±0.34 dB for the ESA-E Series and ±0.24 dB for the PSA Series analyzers.
It is best to consider all known uncertainties and then determine which
ones can be ignored when doing a certain type of measurement. The range
of values shown in Table 4-1 represents the specifications of a variety of
different spectrum analyzers.
Some of the specifications, such as frequency response, are frequency-range
dependent. A 3 GHz RF analyzer might have a frequency response of ±0.38 dB,
while a microwave spectrum analyzer tuning in the 26 GHz range could have
a frequency response of ±2.5 dB or higher. On the other hand, other sources
of uncertainty, such as changing resolution bandwidths, apply equally to
all frequencies.
Table 4-1. Representative values of amplitude uncertainty for common spectrum analyzers
Amplitude uncertainties (±dB)
Relative
RF attenuator switching uncertainty
Frequency response
Reference level accuracy (IF attenuator/gain change)
Resolution bandwidth switching uncertainty
Display scale fidelity
Absolute
Calibrator accuracy
52
0.18 to 0.7
0.38 to 2.5
0.0 to 0.7
0.03 to 1.0
0.07 to 1.15
0.24 to 0.34
Improving overall uncertainty
When we look at total measurement uncertainty for the first time, we may
well be concerned as we add up the uncertainty figures. The worst case view
assumes that each source of uncertainty for your spectrum analyzer is at the
maximum specified value, and that all are biased in the same direction at the
same time. Since the sources of uncertainty can be considered independent
variables, it is likely that some errors will be positive while others will be
negative. Therefore, a common practice is to calculate the root sum of
squares (RSS) error.
Regardless of whether we calculate the worst-case or RSS error, there are
some things that we can do to improve the situation. First of all, we should
know the specifications for our particular spectrum analyzer. These
specifications may be good enough over the range in which we are making
our measurement. If not, Table 4-1 suggests some opportunities to improve
accuracy.
Before taking any data, we can step through a measurement to see if any
controls can be left unchanged. We might find that the measurement can be
made without changing the RF attenuator setting, resolution bandwidth, or
reference level. If so, all uncertainties associated with changing these controls
drop out. We may be able to trade off reference level accuracy against display
fidelity, using whichever is more accurate and eliminating the other as an
uncertainty factor. We can even get around frequency response if we are
willing to go to the trouble of characterizing our particular analyzer2. This
can be accomplished by using a power meter and comparing the reading of
the spectrum analyzer at the desired frequencies with the reading of the
power meter.
The same applies to the calibrator. If we have a more accurate calibrator, or
one closer to the frequency of interest, we may wish to use that in lieu of the
built-in calibrator. Finally, many analyzers available today have self-calibration
routines. These routines generate error coefficients (for example, amplitude
changes versus resolution bandwidth), that the analyzer later uses to correct
measured data. As a result, these self-calibration routines allow us to make
good amplitude measurements with a spectrum analyzer and give us more
freedom to change controls during the course of a measurement.
Specifications, typical performance, and nominal values
When evaluating spectrum analyzer accuracy, it is very important to have a
clear understanding of the many different values found on an analyzer data
sheet. Agilent Technologies defines three classes of instrument performance
data:
Specifications describe the performance of parameters covered by the product warranty over a temperature range of 0 to 55 °C (unless otherwise noted).
Each instrument is tested to verify that it meets the specification, and takes
into account the measurement uncertainty of the equipment used to test the
instrument. 100% of the units tested will meet the specification.
2. Should we do so, then mismatch may become a
more significant error.
Some test equipment manufacturers use a “2 sigma” or 95% confidence
value for certain instrument specifications. When evaluating data sheet
specifications for instruments from different manufacturers, it is important
to make sure you are comparing like numbers in order to make an accurate
comparison.
53
Typical performance describes additional product performance information
that is not covered by the product warranty. It is performance beyond
specification that 80% of the units exhibit with a 95% confidence level over
the temperature range 20 to 30 °C. Typical performance does not include
measurement uncertainty. During manufacture, all instruments are tested
for typical performance parameters.
Nominal values indicate expected performance, or describe product
performance that is useful in the application of the product, but is not
covered by the product warranty. Nominal parameters generally are not
tested during the manufacturing process.
The digital IF section
As described in the previous chapter, a digital IF architecture eliminates
or minimizes many of the uncertainties experienced in analog spectrum
analyzers. These include:
Reference level accuracy (IF gain uncertainty)
Spectrum analyzers with an all digital IF, such as the Agilent PSA Series,
do not have IF gain that changes with reference level. Therefore, there is no
IF gain uncertainty.
Display scale fidelity
A digital IF architecture does not include a log amplifier. Instead, the log
function is performed mathematically, and traditional log fidelity uncertainty
does not exist. However, other factors, such as RF compression (especially for
input signals above –20 dBm), ADC range gain alignment accuracy, and ADC
linearity (or quantization error) contribute to display scale uncertainty. The
quantization error can be improved by the addition of noise which smoothes
the average of the ADC transfer function. This added noise is called dither.
While the dither improves linearity, it does slightly degrade the displayed
average noise level. In the PSA Series, it is generally recommended that
dither be used when the measured signal has a signal-to-noise ratio of greater
than or equal to 10 dB. When the signal-to-noise ratio is under 10 dB, the
degradations to accuracy of any single measurement (in other words, without
averaging) that come from a higher noise floor are worse than the linearity
problems solved by adding dither, so dither is best turned off.
RBW switching uncertainty
The digital IF in the PSA Series includes an analog prefilter set to 2.5 times
the desired resolution bandwidth. This prefilter has some uncertainty in
bandwidth, gain, and center frequency as a function of the RBW setting. The
rest of the RBW filtering is done digitally in an ASIC in the digital IF section.
Though the digital filters are not perfect, they are very repeatable, and some
compensation is applied to minimize the error. This results in a tremendous
overall improvement to the RBW switching uncertainty compared to analog
implementations.
54
Examples
Let’s look at some amplitude uncertainty examples for various measurements.
Suppose we wish to measure a 1 GHz RF signal with an amplitude of –20
dBm. If we use an Agilent E4402B ESA-E Series spectrum analyzer with Atten
= 10 dB, RBW = 1 kHz, VBW = 1 kHz, Span = 20 kHz, Ref level = –20 dBm, log
scale, and coupled sweep time, and an ambient temperature of 20 to 30 °C, the
specifications tell us that the absolute uncertainty equals ±0.54 dB plus the
absolute frequency response. An E4440A PSA Series spectrum analyzer
measuring the same signal using the same settings would have a specified
uncertainty of ±0.24 dB plus the absolute frequency response. These values
are summarized in Table 4-2.
Table 4-2. Amplitude uncertainties when measuring a 1 GHz signal
Source of uncertainty
Absolute amplitude accuracy
Frequency response
Absolute uncertainty of
1 GHz, –20 dBm signal
E4402B
E4440A
±0.54 dB
±0.24 dB
±0.46 dB
±0.38 dB
Total worst case uncertainty
Total RSS uncertainty
Typical uncertainty
±1.00 dB
±0.69 dB
±0.25 dB
±0.62 dB
±0.44 dB
±0.17 dB
At higher frequencies, the uncertainties get larger. In this example, we wish
to measure a 10 GHz signal with an amplitude of –10 dBm. In addition, we
also want to measure its second harmonic at 20 GHz. Assume the following
measurement conditions: 0 to 55 °C, RBW = 300 kHz, Atten = 10 dB, Ref
level = –10 dBm. In Table 4-3, we compare the absolute and relative amplitude
uncertainty of two different Agilent spectrum analyzers, an 8563EC (analog
IF) and an E4440A PSA (digital IF).
Table 4-3. Absolute and relative amplitude accuracy comparison (8563EC and E4440A PSA)
Source of uncertainty
Calibrator
Absolute amplitude acc.
Attenuator
Frequency response
Band switching uncertainty
IF gain
RBW switching
Display scale fidelity
Total worst case uncertainty
Total RSS uncertainty
Typical uncertainty
Measurement of a 10 GHz signal at -10dBm
Absolute uncertainty of
Relative uncertainty of second
fundamental at 10 GHz
harmonic at 20 GHz
8563EC
E4440A
8563EC
E4440A
±0.3 dB
N/A
N/A
N/A
N/A
±0.24 dB
N/A
N/A
N/A
N/A
N/A
N/A
±2.9 dB
±2.0 dB
±(2.2 + 2.5) dB ±(2.0 + 2.0) dB
N/A
N/A
±1.0 dB
N/A
N/A
N/A
N/A
N/A
N/A
N/A
N/A
N/A
N/A
N/A
±0.85 dB
±0.13 dB
±3.20 dB
±2.24 dB
±6.55 dB
±4.13 dB
±2.91 dB
±2.01 dB
±3.17 dB
±2.62 dB
±2.30 dB
±1.06 dB
±4.85 dB
±2.26 dB
55
Frequency accuracy
So far, we have focused almost exclusively on amplitude measurements.
What about frequency measurements? Again, we can classify two broad
categories, absolute and relative frequency measurements. Absolute
measurements are used to measure the frequencies of specific signals.
For example, we might want to measure a radio broadcast signal to verify
that it is operating at its assigned frequency. Absolute measurements are also
used to analyze undesired signals, such as when doing a spur search. Relative
measurements, on the other hand, are useful to know how far apart spectral
components are, or what the modulation frequency is.
Up until the late 1970s, absolute frequency uncertainty was measured in
megahertz because the first LO was a high-frequency oscillator operating
above the RF range of the analyzer, and there was no attempt to tie the LO to
a more accurate reference oscillator. Today’s LOs are synthesized to provide
better accuracy. Absolute frequency uncertainty is often described under
the frequency readout accuracy specification and refers to center frequency,
start, stop, and marker frequencies.
With the introduction of the Agilent 8568A in 1977, counter-like frequency
accuracy became available in a general-purpose spectrum analyzer and
ovenized oscillators were used to reduce drift. Over the years, crystal
reference oscillators with various forms of indirect synthesis have been
added to analyzers in all cost ranges. The broadest definition of indirect
synthesis is that the frequency of the oscillator in question is in some way
determined by a reference oscillator. This includes techniques such as phase
lock, frequency discrimination, and counter lock.
What we really care about is the effect these changes have had on frequency
accuracy (and drift). A typical readout accuracy might be stated as follows:
±[(freq readout x freq ref error) + A% of span + B% of RBW + C Hz]
Note that we cannot determine an exact frequency error unless we know
something about the frequency reference. In most cases we are given an
annual aging rate, such as ±1 x 10-7 per year, though sometimes aging is
given over a shorter period (for example, ±5 x 10-10 per day). In addition,
we need to know when the oscillator was last adjusted and how close it was
set to its nominal frequency (usually 10 MHz). Other factors that we often
overlook when we think about frequency accuracy include how long the
reference oscillator has been operating. Many oscillators take 24 to 72 hours
to reach their specified drift rate. To minimize this effect, some spectrum
analyzers continue to provide power to the reference oscillator as long as the
instrument is plugged into the AC power line. In this case, the instrument is
not really turned “off,” but more properly is on “standby.” We also need to
consider the temperature stability, as it can be worse than the drift rate.
In short, there are a number of factors to consider before we can determine
frequency uncertainty.
56
In a factory setting, there is often an in-house frequency standard available
that is traceable to a national standard. Most analyzers with internal
reference oscillators allow you to use an external reference. The frequency
reference error in the foregoing expression then becomes the error of the
in-house standard.
When making relative measurements, span accuracy comes into play.
For Agilent analyzers, span accuracy generally means the uncertainty in
the indicated separation of any two spectral components on the display.
For example, suppose span accuracy is 0.5% of span and we have two signals
separated by two divisions in a 1 MHz span (100 kHz per division). The
uncertainty of the signal separation would be 5 kHz. The uncertainty would
be the same if we used delta markers and the delta reading would be 200 kHz.
So we would measure 200 kHz ±5 kHz.
When making measurements in the field, we typically want to turn our
analyzer on, complete our task, and move on as quickly as possible. It is
helpful to know how the reference in our analyzer behaves under short warm
up conditions. For example, the Agilent ESA-E Series of portable spectrum
analyzers will meet published specifications after a five-minute warm up time.
Most analyzers include markers that can be put on a signal to give us
absolute frequency, as well as amplitude. However, the indicated frequency
of the marker is a function of the frequency calibration of the display, the
location of the marker on the display, and the number of display points
selected. Also, to get the best frequency accuracy we must be careful to
place the marker exactly at the peak of the response to a spectral component.
If we place the marker at some other point on the response, we will get a
different frequency reading. For the best accuracy, we may narrow the span
and resolution bandwidth to minimize their effects and to make it easier to
place the marker at the peak of the response.
Many analyzers have marker modes that include internal counter schemes
to eliminate the effects of span and resolution bandwidth on frequency
accuracy. The counter does not count the input signal directly, but instead
counts the IF signal and perhaps one or more of the LOs, and the processor
computes the frequency of the input signal. A minimum signal-to-noise ratio
is required to eliminate noise as a factor in the count. Counting the signal
in the IF also eliminates the need to place the marker at the exact peak of
the signal response on the display. If you are using this marker counter
function, placement anywhere sufficiently out of the noise will do. Marker
count accuracy might be stated as:
±[(marker freq x freq ref error) + counter resolution]
We must still deal with the frequency reference error as previously discussed.
Counter resolution refers to the least significant digit in the counter readout,
a factor here just as with any simple digital counter. Some analyzers allow
the counter mode to be used with delta markers. In that case, the effects of
counter resolution and the fixed frequency would be doubled.
57
Chapter 5
Sensitivity and Noise
Sensitivity
One of the primary uses of a spectrum analyzer is to search out and measure
low-level signals. The limitation in these measurements is the noise generated
within the spectrum analyzer itself. This noise, generated by the random
electron motion in various circuit elements, is amplified by multiple gain
stages in the analyzer and appears on the display as a noise signal. On a
spectrum analyzer, this noise is commonly referred to as the Displayed
Average Noise Level, or DANL1. While there are techniques to measure
signals slightly below the DANL, this noise power ultimately limits our ability
to make measurements of low-level signals.
Let’s assume that a 50 ohm termination is attached to the spectrum analyzer
input to prevent any unwanted signals from entering the analyzer. This passive
termination generates a small amount of noise energy equal to kTB, where:
k = Boltzmann’s constant (1.38 x 10–23 joule/°K)
T = temperature, in degrees Kelvin
B = bandwidth in which the noise is measured, in Hertz
Since the total noise power is a function of measurement bandwidth, the value is
typically normalized to a 1 Hz bandwidth. Therefore, at room temperature, the
noise power density is –174 dBm/Hz. When this noise reaches the first
gain stage in the analyzer, the amplifier boosts the noise, plus adds some of
its own. As the noise signal passes on through the system, it is typically high
enough in amplitude that the noise generated in subsequent gain stages adds
only a small amount to the total noise power. Note that the input attenuator
and one or more mixers may be between the input connector of a spectrum
analyzer and the first stage of gain, and all of these components generate
noise. However, the noise that they generate is at or near the absolute
minimum of –174 dBm/Hz, so they do not significantly affect the noise level
input to, and amplified by, the first gain stage.
While the input attenuator, mixer, and other circuit elements between the
input connector and first gain stage have little effect on the actual system
noise, they do have a marked effect on the ability of an analyzer to display
low-level signals because they attenuate the input signal. That is, they reduce
the signal-to-noise ratio and so degrade sensitivity.
We can determine the DANL simply by noting the noise level indicated on
the display when the spectrum analyzer input is terminated with a 50 ohm
load. This level is the spectrum analyzer’s own noise floor. Signals below this
level are masked by the noise and cannot be seen. However, the DANL is not
the actual noise level at the input, but rather the effective noise level. An
analyzer display is calibrated to reflect the level of a signal at the analyzer
input, so the displayed noise floor represents a fictitious, or effective noise
floor at the input.
1. Displayed average noise level is sometimes
confused with the term “Sensitivity”. While related,
these terms have different meanings. Sensitivity is
a measure of the minimum signal level that yields a
defined signal-to-noise ratio (SNR) or bit error rate
(BER). It is a common metric of radio receiver
performance. Spectrum analyzer specifications are
always given in terms of the DANL.
58
The actual noise level at the input is a function of the input signal. Indeed,
noise is sometimes the signal of interest. Like any discrete signal, a noise
signal is much easier to measure when it is well above the effective (displayed)
noise floor. The effective input noise floor includes the losses caused by the
input attenuator, mixer conversion loss, and other circuit elements prior to
the first gain stage. We cannot do anything about the conversion loss of the
mixers, but we can change the RF input attenuator. This enables us to control
the input signal power to the first mixer and thus change the displayed
signal-to-noise floor ratio. Clearly, we get the lowest DANL by selecting
minimum (zero) RF attenuation.
Because the input attenuator has no effect on the actual noise generated in
the system, some early spectrum analyzers simply left the displayed noise
at the same position on the display regardless of the input attenuator
setting. That is, the IF gain remained constant. This being the case, the input
attenuator affected the location of a true input signal on the display. As input
attenuation was increased, further attenuating the input signal, the location
of the signal on the display went down while the noise remained stationary.
Beginning in the late 1970s, spectrum analyzer designers took a different
approach. In newer analyzers, an internal microprocessor changes the IF
gain to offset changes in the input attenuator. Thus, signals present at the
analyzer’s input remain stationary on the display as we change the input
attenuator, while the displayed noise moves up and down. In this case, the
reference level remains unchanged. This is shown in Figure 5-1. As the
attenuation increases from 5 to 15 to 25 dB, the displayed noise rises
while the –30 dBm signal remains constant. In either case, we get the best
signal-to-noise ratio by selecting minimum input attenuation.
Figure 5-1. Reference level remains constant when changing input attenuation
Resolution bandwidth also affects signal-to-noise ratio, or sensitivity. The
noise generated in the analyzer is random and has a constant amplitude over
a wide frequency range. Since the resolution, or IF, bandwidth filters come
after the first gain stage, the total noise power that passes through the filters
is determined by the width of the filters. This noise signal is detected and
ultimately reaches the display. The random nature of the noise signal causes
the displayed level to vary as:
10 log (BW2/BW1)
where
BW1 = starting resolution bandwidth
BW2 = ending resolution bandwidth
59
So if we change the resolution bandwidth by a factor of 10, the displayed
noise level changes by 10 dB, as shown in Figure 5-2. For continuous wave
(CW) signals, we get best signal-to-noise ratio, or best sensitivity, using the
minimum resolution bandwidth available in our spectrum analyzer2.
Figure 5-2. Displayed noise level changes as 10 log(BW2/BW1)
A spectrum analyzer displays signal plus noise, and a low signal-to-noise ratio
makes the signal difficult to distinguish. We noted previously that the video
filter can be used to reduce the amplitude fluctuations of noisy signals while
at the same time having no effect on constant signals. Figure 5-3 shows how
the video filter can improve our ability to discern low-level signals. It should
be noted that the video filter does not affect the average noise level and so
does not, by this definition, affect the sensitivity of an analyzer.
2. Broadband, pulsed signals can exhibit the opposite
behavior, where the SNR increases as the bandwidth
gets larger.
3. For the effect of noise on accuracy, see “Dynamic
range versus measurement uncertainty” in
Chapter 6.
In summary, we get best sensitivity for narrowband signals by selecting the
minimum resolution bandwidth and minimum input attenuation. These settings
give us best signal-to-noise ratio. We can also select minimum video bandwidth
to help us see a signal at or close to the noise level3. Of course, selecting
narrow resolution and video bandwidths does lengthen the sweep time.
Figure 5-3. Video filtering makes low-level signals more discernable
60
Noise figure
Many receiver manufacturers specify the performance of their receivers in
terms of noise figure, rather than sensitivity. As we shall see, the two can
be equated. A spectrum analyzer is a receiver, and we shall examine noise
figure on the basis of a sinusoidal input.
Noise figure can be defined as the degradation of signal-to-noise ratio as a
signal passes through a device, a spectrum analyzer in our case. We can
express noise figure as:
F=
where
Si/Ni
So/No
F= noise figure as power ratio (also known as noise factor)
Si = input signal power
Ni = true input noise power
So = output signal power
No = output noise power
If we examine this expression, we can simplify it for our spectrum analyzer.
First of all, the output signal is the input signal times the gain of the analyzer.
Second, the gain of our analyzer is unity because the signal level at the
output (indicated on the display) is the same as the level at the input
(input connector). So our expression, after substitution, cancellation,
and rearrangement, becomes:
F = No/Ni
This expression tells us that all we need to do to determine the noise figure
is compare the noise level as read on the display to the true (not the effective)
noise level at the input connector. Noise figure is usually expressed in terms
of dB, or:
NF = 10 log(F) = 10 log(No) – 10 log(Ni).
We use the true noise level at the input, rather than the effective noise level,
because our input signal-to-noise ratio was based on the true noise. As we
saw earlier, when the input is terminated in 50 ohms, the kTB noise level at
room temperature in a 1 Hz bandwidth is –174 dBm.
We know that the displayed level of noise on the analyzer changes with
bandwidth. So all we need to do to determine the noise figure of our
spectrum analyzer is to measure the noise power in some bandwidth,
calculate the noise power that we would have measured in a 1 Hz bandwidth
using 10 log(BW2/BW1), and compare that to –174 dBm.
For example, if we measured –110 dBm in a 10 kHz resolution bandwidth,
we would get:
NF = [measured noise in dBm] – 10 log(RBW/1) – kTBB=1 Hz
–110 dBm –10 log(10,000/1) – (–174 dBm)
–110 – 40 + 174
24 dB
4. This may not always be precisely true for a given
analyzer because of the way resolution bandwidth
filter sections and gain are distributed in the IF chain.
Noise figure is independent of bandwidth4. Had we selected a different
resolution bandwidth, our results would have been exactly the same.
For example, had we chosen a 1 kHz resolution bandwidth, the measured
noise would have been –120 dBm and 10 log(RBW/1) would have been 30.
Combining all terms would have given –120 – 30 + 174 = 24 dB, the same
noise figure as above.
61
The 24 dB noise figure in our example tells us that a sinusoidal signal must
be 24 dB above kTB to be equal to the displayed average noise level on this
particular analyzer. Thus we can use noise figure to determine the DANL for
a given bandwidth or to compare DANLs of different analyzers on the same
bandwidth.5
Preamplifiers
One reason for introducing noise figure is that it helps us determine how much
benefit we can derive from the use of a preamplifier. A 24 dB noise figure,
while good for a spectrum analyzer, is not so good for a dedicated receiver.
However, by placing an appropriate preamplifier in front of the spectrum
analyzer, we can obtain a system (preamplifier/spectrum analyzer) noise
figure that is lower than that of the spectrum analyzer alone. To the extent
that we lower the noise figure, we also improve the system sensitivity.
When we introduced noise figure in the previous discussion, we did so on
the basis of a sinusoidal input signal. We can examine the benefits of a
preamplifier on the same basis. However, a preamplifier also amplifies noise,
and this output noise can be higher than the effective input noise of the
analyzer. As we shall see in the “Noise as a signal” section later in this chapter,
a spectrum analyzer using log power averaging displays a random noise
signal 2.5 dB below its actual value. As we explore preamplifiers, we shall
account for this 2.5 dB factor where appropriate.
Rather than develop a lot of formulas to see what benefit we get from a
preamplifier, let us look at two extreme cases and see when each might apply.
First, if the noise power out of the preamplifier (in a bandwidth equal to
that of the spectrum analyzer) is at least 15 dB higher than the DANL of the
spectrum analyzer, then the noise figure of the system is approximately that
of the preamplifier less 2.5 dB. How can we tell if this is the case? Simply
connect the preamplifier to the analyzer and note what happens to the noise
on the display. If it goes up 15 dB or more, we have fulfilled this requirement.
On the other hand, if the noise power out of the preamplifier (again, in the
same bandwidth as that of the spectrum analyzer) is 10 dB or more lower
than the displayed average noise level on the analyzer, then the noise figure
of the system is that of the spectrum analyzer less the gain of the preamplifier.
Again we can test by inspection. Connect the preamplifier to the analyzer;
if the displayed noise does not change, we have fulfilled the requirement.
But testing by experiment means that we have the equipment at hand.
We do not need to worry about numbers. We simply connect the preamplifier
to the analyzer, note the average displayed noise level, and subtract the gain
of the preamplifier. Then we have the sensitivity of the system.
What we really want is to know ahead of time what a preamplifier will do
for us. We can state the two cases above as follows:
If
NFpre + Gpre
Then NFsys
≥
=
NFsa + 15 dB,
NFpre – 2.5 dB
≤
=
NFsa – 10 dB,
NFsa – Gpre
And
5. The noise figure computed in this manner cannot be
directly compared to that of a receiver because the
“measured noise” term in the equation understates
the actual noise by 2.5 dB. See the section titled
“Noise as a signal” later in this chapter.
62
If
NFpre + Gpre
Then NFsys
Using these expressions, we’ll see how a preamplifier affects our sensitivity.
Assume that our spectrum analyzer has a noise figure of 24 dB and the
preamplifier has a gain of 36 dB and a noise figure of 8 dB. All we need to
do is to compare the gain plus noise figure of the preamplifier to the noise
figure of the spectrum analyzer. The gain plus noise figure of the preamplifier
is 44 dB, more than 15 dB higher than the noise figure of the spectrum
analyzer, so the noise figure of the preamplifier/spectrum-analyzer
combination is that of the preamplifier less 2.5 dB, or 5.5 dB. In a 10 kHz
resolution bandwidth, our preamplifier/analyzer system has a sensitivity of:
kTBB=1 + 10 log(RBW/1) + NFsys
= –174 + 40 + 5.5
= –128.5 dBm
This is an improvement of 18.5 dB over the –110 dBm noise floor without the
preamplifier.
There might, however, be a drawback to using this preamplifier, depending
upon our ultimate measurement objective. If we want the best sensitivity but
no loss of measurement range, then this preamplifier is not the right choice.
Figure 5-4 illustrates this point. A spectrum analyzer with a 24 dB noise
figure will have an average displayed noise level of –110 dBm in a 10 kHz
resolution bandwidth. If the 1 dB compression point6 for that analyzer is
0 dBm, the measurement range is 110 dB. When we connect the preamplifier,
we must reduce the maximum input to the system by the gain of the
preamplifier to –36 dBm. However, when we connect the preamplifier,
the displayed average noise level will rise by about 17.5 dB because the
noise power out of the preamplifier is that much higher than the analyzer’s
own noise floor, even after accounting for the 2.5 dB factor. It is from this
higher noise level that we now subtract the gain of the preamplifier. With
the preamplifier in place, our measurement range is 92.5 dB, 17.5 dB less
than without the preamplifier. The loss in measurement range equals the
change in the displayed noise when the preamplifier is connected.
Spectrum analyzer
0 dBm
Spectrum analyzer and preamplifier
1 dB compression
Gpre
System 1 dB compression
110 dB
spectrum
analyzer
range
–110 dBm
92.5 dB
system
range
DANL
DANL
System sensitivity
–36 dBm
–92.5 dBm
Gpre
–128.5 dBm
Figure 5-4. If displayed noise goes up when a preamplifier is connected, measurement range is
diminished by the amount the noise changes
6. See the section titled “Mixer compression” in
Chapter 6.
63
Finding a preamplifier that will give us better sensitivity without costing
us measurement range dictates that we must meet the second of the above
criteria; that is, the sum of its gain and noise figure must be at least 10 dB
less than the noise figure of the spectrum analyzer. In this case the displayed
noise floor will not change noticeably when we connect the preamplifier,
so although we shift the whole measurement range down by the gain of the
preamplifier, we end up with the same overall range that we started with.
To choose the correct preamplifier, we must look at our measurement needs.
If we want absolutely the best sensitivity and are not concerned about
measurement range, we would choose a high-gain, low-noise-figure
preamplifier so that our system would take on the noise figure of the
preamplifier, less 2.5 dB. If we want better sensitivity but cannot afford to
give up any measurement range, we must choose a lower-gain preamplifier.
Interestingly enough, we can use the input attenuator of the spectrum analyzer
to effectively degrade the noise figure (or reduce the gain of the preamplifier,
if you prefer). For example, if we need slightly better sensitivity but cannot
afford to give up any measurement range, we can use the above preamplifier
with 30 dB of RF input attenuation on the spectrum analyzer. This attenuation
increases the noise figure of the analyzer from 24 to 54 dB. Now the gain plus
noise figure of the preamplifier (36 + 8) is 10 dB less than the noise figure of
the analyzer, and we have met the conditions of the second criterion above.
The noise figure of the system is now:
NFsys
= NFSA – GPRE
= 54 dB – 36 dB
= 18 dB
This represents a 6 dB improvement over the noise figure of the analyzer
alone with 0 dB of input attenuation. So we have improved sensitivity by 6 dB
and given up virtually no measurement range.
Of course, there are preamplifiers that fall in between the extremes.
Figure 5-5 enables us to determine system noise figure from a knowledge
of the noise figures of the spectrum analyzer and preamplifier and the
gain of the amplifier. We enter the graph of Figure 5-5 by determining
NFPRE + GPRE – NFSA. If the value is less than zero, we find the corresponding
point on the dashed curve and read system noise figure as the left ordinate
in terms of dB above NFSA – GPRE. If NFPRE + GPRE – NFSA is a positive value,
we find the corresponding point on the solid curve and read system noise
figure as the right ordinate in terms of dB above NFPRE.
System Noise
Figure (dB)
NFSA – Gpre + 3 dB
NFpre + 3 dB
NFSA – Gpre + 2 dB
NFpre + 2 dB
NFSA – Gpre + 1 dB
NFpre + 1 dB
NFpre
NFSA – Gpre
NFpre – 1 dB
NFpre – 2 dB
–10
–5
0
+5
+10
NFpre + Gpre – NFSA (dB)
Figure 5-5. System noise figure for sinusoidal signals
64
NFpre – 2.5 dB
Let’s first test the two previous extreme cases.
As NFPRE + GPRE – NFSA becomes less than –10 dB, we find that system noise
figure asymptotically approaches NFSA – GPRE. As the value becomes greater
than +15 dB, system noise figure asymptotically approaches NFPRE less 2.5
dB. Next, let’s try two numerical examples. Above, we determined that the
noise figure of our analyzer is 24 dB. What would the system noise figure be
if we add an Agilent 8447D, a preamplifier with a noise figure of about 8 dB
and a gain of 26 dB? First, NFPRE + GPRE – NFSA is +10 dB. From the graph
of Figure 5-5 we find a system noise figure of about NFPRE – 1.8 dB, or about
8 – 1.8 = 6.2 dB. The graph accounts for the 2.5 dB factor. On the other
hand, if the gain of the preamplifier is just 10 dB, then NFPRE + GPRE – NFSA
is –6 dB. This time the graph indicates a system noise figure of
NFSA – GPRE + 0.6 dB, or 24 – 10 + 0.6 = 14.6 dB7. (We did not introduce
the 2.5 dB factor previously when we determined the noise figure of the
analyzer alone because we read the measured noise directly from the display.
The displayed noise included the 2.5 dB factor.)
Many modern spectrum analyzers have optional built-in preamplifiers
available. Compared to external preamplifiers, built-in preamplifiers simplify
measurement setups and eliminate the need for additional cabling. Measuring
signal amplitude is much more convenient with a built-in preamplifier,
because the preamplifier/spectrum analyzer combination is calibrated as a
system, and amplitude values displayed on screen are already corrected for
proper readout. With an external preamplifier, you must correct the spectrum
analyzer reading with a reference level offset equal to the preamp gain. Most
modern spectrum analyzers allow you to enter the gain value of the external
preamplifier from the front panel. The analyzer then applies this gain offset
to the displayed reference level value, so that you can directly view corrected
measurements on the display.
Noise as a signal
So far, we have focused on the noise generated within the measurement
system (analyzer or analyzer/preamplifier). We described how the measurement
system’s displayed average noise level limits the overall sensitivity. However,
random noise is sometimes the signal that we want to measure. Because of
the nature of noise, the superheterodyne spectrum analyzer indicates a value
that is lower than the actual value of the noise. Let’s see why this is so and
how we can correct for it.
By random noise, we mean a signal whose instantaneous amplitude has
a Gaussian distribution versus time, as shown in Figure 5-6. For example,
thermal or Johnson noise has this characteristic. Such a signal has no discrete
spectral components, so we cannot select some particular component and
measure it to get an indication of signal strength. In fact, we must define
what we mean by signal strength. If we sample the signal at an arbitrary
instant, we could theoretically get any amplitude value. We need some
measure that expresses the noise level averaged over time. Power, which
is of course proportionate to rms voltage, satisfies that requirement.
7. For more details on noise figure, see Agilent
Application Note 57-1, Fundamentals of RF and
Microwave Noise Figure Measurements, literature
number 5952-8255E.
65
We have already seen that both video filtering and video averaging reduce
the peak-to-peak fluctuations of a signal and can give us a steady value.
We must equate this value to either power or rms voltage. The rms value
of a Gaussian distribution equals its standard deviation, σ.
Figure 5-6. Random noise has a Gaussian amplitude distribution
Let’s start with our analyzer in the linear display mode. The Gaussian noise
at the input is band limited as it passes through the IF chain, and its envelope
takes on a Rayleigh distribution (Figure 5-7). The noise that we see on
our analyzer display, the output of the envelope detector, is the Rayleigh
distributed envelope of the input noise signal. To get a steady value, the
mean value, we use video filtering or averaging. The mean value of a Rayleigh
distribution is 1.253 σ.
But our analyzer is a peak-responding voltmeter calibrated to indicate the
rms value of a sine wave. To convert from peak to rms, our analyzer scales
its readout by 0.707 (–3 dB). The mean value of the Rayleigh-distributed
noise is scaled by the same factor, giving us a reading that is 0.886 σ (l.05 dB
below σ). To equate the mean value displayed by the analyzer to the rms
voltage of the input noise signal, then, we must account for the error in the
displayed value. Note, however, that the error is not an ambiguity; it is a
constant error that we can correct for by adding 1.05 dB to the displayed
value.
In most spectrum analyzers, the display scale (log or linear in voltage)
controls the scale on which the noise distribution is averaged with either
the VBW filter or with trace averaging. Normally, we use our analyzer in the
log display mode, and this mode adds to the error in our noise measurement.
The gain of a log amplifier is a function of signal amplitude, so the higher
noise values are not amplified as much as the lower values. As a result, the
output of the envelope detector is a skewed Rayleigh distribution, and the
mean value that we get from video filtering or averaging is another 1.45 dB
lower. In the log mode, then, the mean or average noise is displayed 2.5 dB
too low. Again, this error is not an ambiguity, and we can correct for it8.
8. In the ESA and PSA Series, the averaging can be
set to video, voltage, or power (rms), independent
of display scale. When using power averaging, no
correction is needed, since the average rms level is
determined by the square of the magnitude of the
signal, not by the log or envelope of the voltage.
66
This is the 2.5 dB factor that we accounted for in the previous preamplifier
discussion, whenever the noise power out of the preamplifier was
approximately equal to or greater than the analyzer’s own noise.
Figure 5-7. The envelope of band-limited Gaussian noise has a Rayleigh distribution
Another factor that affects noise measurements is the bandwidth in which
the measurement is made. We have seen how changing resolution bandwidth
affects the displayed level of the analyzer’s internally generated noise.
Bandwidth affects external noise signals in the same way. To compare
measurements made on different analyzers, we must know the bandwidths
used in each case.
Not only does the 3 dB (or 6 dB) bandwidth of the analyzer affect the
measured noise level, the shape of the resolution filter also plays a role.
To make comparisons possible, we define a standard noise-power bandwidth:
the width of a rectangular filter that passes the same noise power as our
analyzer’s filter. For the near-Gaussian filters in Agilent analyzers, the
equivalent noise-power bandwidth is about 1.05 to 1.13 times the 3 dB
bandwidth, depending on bandwidth selectivity. For example, a 10 kHz
resolution bandwidth filter has a noise-power bandwidth in the range of
10.5 to 11.3 kHz.
If we use 10 log(BW2/BW1) to adjust the displayed noise level to what we
would have measured in a noise-power bandwidth of the same numeric value
as our 3 dB bandwidth, we find that the adjustment varies from:
10 log(10,000/10,500) = –0.21 dB
to
10 log(10,000/11,300) = –0.53 dB
In other words, if we subtract something between 0.21 and 0.53 dB from the
indicated noise level, we shall have the noise level in a noise-power bandwidth
that is convenient for computations. For the following examples below, we
will use 0.5 dB as a reasonable compromise for the bandwidth correction9.
9. ESA Series analyzers calibrate each RBW during
the IF alignment routine to determine the noise
power bandwidth. The PSA Series analyzers
specify noise power bandwidth accuracy to within
1% (±0.044 dB).
67
Let’s consider the various correction factors to calculate the total correction
for each averaging mode:
Linear (voltage) averaging:
Rayleigh distribution (linear mode):
3 dB/noise power bandwidths:
Total correction:
1.05 dB
–.50 dB
0.55 dB
Log averaging:
Logged Rayleigh distribution:
3 dB/noise power bandwidths:
Total correction:
2.50 dB
–.50 dB
2.00 dB
Power (rms voltage) averaging:
Power distribution:
3 dB/noise power bandwidths:
Total correction:
0.00 dB
–.50 dB
–.50 dB
Many of today’s microprocessor-controlled analyzers allow us to activate a
noise marker. When we do so, the microprocessor switches the analyzer into
the power (rms) averaging mode, computes the mean value of a number of
display points about the marker10, normalizes and corrects the value to a
1 Hz noise-power bandwidth, and displays the normalized value.
The analyzer does the hard part. It is easy to convert the noise-marker value
to other bandwidths. For example, if we want to know the total noise in a
4 MHz communication channel, we add 10 log(4,000,000/1), or 66 dB to the
noise-marker value11.
Preamplifier for noise measurements
Since noise signals are typically low-level signals, we often need a preamplifier
to have sufficient sensitivity to measure them. However, we must recalculate
sensitivity of our analyzer first. We previously defined sensitivity as the
level of a sinusoidal signal that is equal to the displayed average noise floor.
Since the analyzer is calibrated to show the proper amplitude of a sinusoid,
no correction for the signal was needed. But noise is displayed 2.5 dB too low,
so an input noise signal must be 2.5 dB above the analyzer’s displayed noise
floor to be at the same level by the time it reaches the display. The input and
internal noise signals add to raise the displayed noise by 3 dB, a factor of
two in power. So we can define the noise figure of our analyzer for a noise
signal as:
NFSA(N) = (noise floor)dBm/RBW – 10 log(RBW/1) – kTBB=1 + 2.5 dB
If we use the same noise floor that we used previously, –110 dBm in a
10 kHz resolution bandwidth, we get:
NFSA(N) = –110 dBm – 10 log(10,000/1) – (–174 dBm) + 2.5 dB = 26.5 dB
10. For example, the ESA and PSA Series compute the
mean over half a division, regardless of the number
of display points.
11. Most modern spectrum analyzers make this
calculation even easier with the Channel Power
function. The user enters the integration bandwidth
of the channel and centers the signal on the
analyzer display. The Channel Power function then
calculates the total signal power in the channel.
68
As was the case for a sinusoidal signal, NFSA(N) is independent of resolution
bandwidth and tells us how far above kTB a noise signal must be to be equal
to the noise floor of our analyzer.
When we add a preamplifier to our analyzer, the system noise figure and
sensitivity improve. However, we have accounted for the 2.5 dB factor in our
definition of NFSA(N), so the graph of system noise figure becomes that of
Figure 5-8. We determine system noise figure for noise the same way that we
did previously for a sinusoidal signal.
System Noise
Figure (dB)
NFSA – Gpre + 3 dB
NFpre + 3 dB
NFSA – Gpre + 2 dB
NFpre + 2 dB
NFSA – Gpre + 1 dB
NFpre + 1 dB
NFSA – Gpre
NFpre
–10
–5
0
+5
+10
NFpre + Gpre – NFSA (dB)
Figure 5-8. System noise figure for noise signals
69
Chapter 6
Dynamic Range
Definition
Dynamic range is generally thought of as the ability of an analyzer to measure
harmonically related signals and the interaction of two or more signals; for
example, to measure second- or third-harmonic distortion or third-order
intermodulation. In dealing with such measurements, remember that the
input mixer of a spectrum analyzer is a non-linear device, so it always
generates distortion of its own. The mixer is non-linear for a reason. It must
be nonlinear to translate an input signal to the desired IF. But the unwanted
distortion products generated in the mixer fall at the same frequencies as
the distortion products we wish to measure on the input signal.
So we might define dynamic range in this way: it is the ratio, expressed in dB,
of the largest to the smallest signals simultaneously present at the input of
the spectrum analyzer that allows measurement of the smaller signal to a
given degree of uncertainty.
Notice that accuracy of the measurement is part of the definition. We shall
see how both internally generated noise and distortion affect accuracy in the
following examples.
Dynamic range versus internal distortion
To determine dynamic range versus distortion, we must first determine just
how our input mixer behaves. Most analyzers, particularly those utilizing
harmonic mixing to extend their tuning range1, use diode mixers. (Other
types of mixers would behave similarly.) The current through an ideal diode
can be expressed as:
i = Is(eqv/kT–1)
where
IS = the diode’s saturation current
q = electron charge (1.60 x 10–19 C)
v = instantaneous voltage
k = Boltzmann’s constant (1.38 x 10–23 joule/°K)
T= temperature in degrees Kelvin
We can expand this expression into a power series:
i = Is(k1v + k2v2 + k3v3 +...)
where
k1 = q/kT
k2 = k12/2!
k3 = k13/3!, etc.
Let’s now apply two signals to the mixer. One will be the input signal that
we wish to analyze; the other, the local oscillator signal necessary to create
the IF:
v = VLO sin(ωLOt) + V1 sin(ω1t)
If we go through the mathematics, we arrive at the desired mixing product
that, with the correct LO frequency, equals the IF:
k2VLOV1 cos[(ωLO – ω1)t]
1. See Chapter 7, “Extending the Frequency Range.”
70
A k2VLOV1 cos[(ωLO + ω1)t] term is also generated, but in our discussion
of the tuning equation, we found that we want the LO to be above the IF, so
(ωLO + ω1) is also always above the IF.
With a constant LO level, the mixer output is linearly related to the input
signal level. For all practical purposes, this is true as long as the input signal
is more than 15 to 20 dB below the level of the LO. There are also terms
involving harmonics of the input signal:
(3k3/4)VLOV12 sin(ωLO – 2 ω1)t,
(k4 /8)VLOV13 sin(ωLO – 3ω1)t, etc.
These terms tell us that dynamic range due to internal distortion is a
function of the input signal level at the input mixer. Let’s see how this works,
using as our definition of dynamic range, the difference in dB between the
fundamental tone and the internally generated distortion.
The argument of the sine in the first term includes 2ω1, so it represents
the second harmonic of the input signal. The level of this second harmonic
is a function of the square of the voltage of the fundamental, V12. This fact
tells us that for every dB that we drop the level of the fundamental at the
input mixer, the internally generated second harmonic drops by 2 dB.
See Figure 6-1. The second term includes 3ω1, the third harmonic, and the
cube of the input-signal voltage, V13. So a 1 dB change in the fundamental
at the input mixer changes the internally generated third harmonic by 3 dB.
Distortion is often described by its order. The order can be determined by
noting the coefficient associated with the signal frequency or the exponent
associated with the signal amplitude. Thus second-harmonic distortion is
second order and third harmonic distortion is third order. The order also
indicates the change in internally generated distortion relative to the change
in the fundamental tone that created it.
Now let us add a second input signal:
v = VLO sin(ωLO t) + V1 sin(ω1t) + V2 sin(ω2t)
This time when we go through the math to find internally generated distortion,
in addition to harmonic distortion, we get:
(k4/8)VLOV12V2 cos[ωLO – (2 ω1 – ω2)]t,
(k4/8)VLOV1V22 cos[ωLO – (2 ω2 – ω1)]t, etc.
D dB
D dB
2D dB
D dB
3D dB
3D dB
3D dB
w
2w
3w
2w1 – w2 w1
w2
2w2 – w1
Figure 6-1. Changing the level of fundamental tones at the mixer
71
These represent intermodulation distortion, the interaction of the two
input signals with each other. The lower distortion product, 2ω1 – ω2, falls
below ω1 by a frequency equal to the difference between the two fundamental
tones, ω2 – ω1. The higher distortion product, 2ω2 – ω1, falls above ω2 by the
same frequency. See Figure 6-1.
Once again, dynamic range is a function of the level at the input mixer. The
internally generated distortion changes as the product of V12 and V2 in the
first case, of V1 and V22 in the second. If V1 and V2 have the same amplitude,
the usual case when testing for distortion, we can treat their products as
cubed terms (V13 or V23). Thus, for every dB that we simultaneously change
the level of the two input signals, there is a 3 dB change in the distortion
components, as shown in Figure 6-1.
This is the same degree of change that we see for third harmonic distortion
in Figure 6-1. And in fact, this too, is third-order distortion. In this case,
we can determine the degree of distortion by summing the coefficients
of ω1 and ω2 (e.g., 2ω1 – 1ω2 yields 2 + 1 = 3) or the exponents of V1 and V2.
All this says that dynamic range depends upon the signal level at the
mixer. How do we know what level we need at the mixer for a particular
measurement? Most analyzer data sheets include graphs to tell us how
dynamic range varies. However, if no graph is provided, we can draw
our own2.
We do need a starting point, and this we must get from the data sheet. We
shall look at second-order distortion first. Let’s assume the data sheet says
that second-harmonic distortion is 75 dB down for a signal –40 dBm at the
mixer. Because distortion is a relative measurement, and, at least for the
moment, we are calling our dynamic range the difference in dB between
fundamental tone or tones and the internally generated distortion, we have
our starting point. Internally generated second-order distortion is 75 dB
down, so we can measure distortion down 75 dB. We plot that point on a
graph whose axes are labeled distortion (dBc) versus level at the mixer
(level at the input connector minus the input-attenuator setting). See
Figure 6-2. What happens if the level at the mixer drops to –50 dBm? As
noted in Figure 6-1, for every dB change in the level of the fundamental at
the mixer there is a 2 dB change in the internally generated second harmonic.
But for measurement purposes, we are only interested in the relative change,
that is, in what happened to our measurement range. In this case, for every
dB that the fundamental changes at the mixer, our measurement range also
changes by 1 dB. In our second-harmonic example, then, when the level at
the mixer changes from –40 to –50 dBm, the internal distortion, and thus our
measurement range, changes from –75 to –85 dBc. In fact, these points fall
on a line with a slope of 1 that describes the dynamic range for any input
level at the mixer.
2. For more information on how to construct a
dynamic range chart, see the Agilent PSA
Performance Spectrum Analyzer Series Product
Note, Optimizing Dynamic Range for Distortion
Measurements, literature number 5980-3079EN.
72
We can construct a similar line for third-order distortion. For example,
a data sheet might say third-order distortion is –85 dBc for a level of –30 dBm
at this mixer. Again, this is our starting point, and we would plot the point
shown in Figure 6-2. If we now drop the level at the mixer to –40 dBm, what
happens? Referring again to Figure 6-1, we see that both third-harmonic
distortion and third-order intermodulation distortion fall by 3 dB for every
dB that the fundamental tone or tones fall. Again it is the difference that
is important. If the level at the mixer changes from –30 to –40 dBm, the
difference between fundamental tone or tones and internally generated
distortion changes by 20 dB. So the internal distortion is –105 dBc. These
two points fall on a line having a slope of 2, giving us the third-order
performance for any level at the mixer.
TOI
0
SHI
–10
rd
do
2n
3rd
–30
er
ord
er
–20
–40
–50
(dBc)
No
ise
–60
(1
0k
Hz
BW
)
–70
Maximum 2nd order
dynamic range
–80
–90
–100
–60
Maximum 3rd order
dynamic range
Optimum
mixer levels
–50
–40
–30
–20
Mixer level (dBm)
–10
0
+10
Figure 6-2. Dynamic range versus distortion and noise
73
Sometimes third-order performance is given as TOI (third-order intercept).
This is the mixer level at which the internally generated third-order distortion
would be equal to the fundamental(s), or 0 dBc. This situation cannot be
realized in practice because the mixer would be well into saturation.
However, from a mathematical standpoint, TOI is a perfectly good data
point because we know the slope of the line. So even with TOI as a starting
point, we can still determine the degree of internally generated distortion
at a given mixer level.
We can calculate TOI from data sheet information. Because third-order
dynamic range changes 2 dB for every dB change in the level of the
fundamental tone(s) at the mixer, we get TOI by subtracting half of the
specified dynamic range in dBc from the level of the fundamental(s):
TOI = Afund – d/2
where
Afund = level of the fundamental in dBm
d = difference in dBc between fundamental and distortion
Using the values from the previous discussion:
TOI = –30 dBm – (–85 dBc)/2 = +12.5 dBm
Attenuator test
Understanding the distortion graph is important, but we can use a simple
test to determine whether displayed distortion components are true input
signals or internally generated signals. Change the input attenuator. If
the displayed value of the distortion components remains the same, the
components are part of the input signal. If the displayed value changes, the
distortion components are generated internally or are the sum of external
and internally generated signals. We continue changing the attenuator until
the displayed distortion does not change and then complete the measurement.
Noise
There is another constraint on dynamic range, and that is the noise floor of
our spectrum analyzer. Going back to our definition of dynamic range as the
ratio of the largest to the smallest signal that we can measure, the average
noise of our spectrum analyzer puts the limit on the smaller signal. So
dynamic range versus noise becomes signal-to-noise ratio in which the
signal is the fundamental whose distortion we wish to measure.
We can easily plot noise on our dynamic range chart. For example, suppose
that the data sheet for our spectrum analyzer specifies a displayed average
noise level of –110 dBm in a 10 kHz resolution bandwidth. If our signal
fundamental has a level of –40 dBm at the mixer, it is 70 dB above the
average noise, so we have a 70 dB signal-to-noise ratio. For every dB that
we reduce the signal level at the mixer, we lose 1 dB of signal-to-noise ratio.
Our noise curve is a straight line having a slope of –1, as shown in Figure 6-2.
If we ignore measurement accuracy considerations for a moment, the best
dynamic range will occur at the intersection of the appropriate distortion
curve and the noise curve. Figure 6-2 tells us that our maximum dynamic
range for second-order distortion is 72.5 dB; for third-order distortion,
81.7 dB. In practice, the intersection of the noise and distortion graphs is
not a sharply defined point, because noise adds to the CW-like distortion
products, reducing dynamic range by 2 dB when using the log power scale
with log scale averaging.
74
Figure 6-2 shows the dynamic range for one resolution bandwidth. We
certainly can improve dynamic range by narrowing the resolution bandwidth,
but there is not a one-to-one correspondence between the lowered noise
floor and the improvement in dynamic range. For second-order distortion,
the improvement is one half the change in the noise floor; for third-order
distortion, two-thirds the change in the noise floor. See Figure 6-3.
TOI
0
SHI
–10
rd
do
2n
3rd
–30
er
ord
er
–20
–40
(dBc)
–50
No
ise
(1
0k
Hz
BW
N
–60 oi
)
se
(1
kH
zB
W
)
–70
2nd order
dynamic range improvement
–80
3rd order
dynamic range improvement
–90
–60
–50
–40
–30
–20
Mixer level (dBm)
–10
0
+10
Figure 6-3. Reducing resolution bandwidth improves dynamic range
75
The final factor in dynamic range is the phase noise on our spectrum analyzer
LO, and this affects only third-order distortion measurements. For example,
suppose we are making a two-tone, third-order distortion measurement on
an amplifier, and our test tones are separated by 10 kHz. The third-order
distortion components will also be separated from the test tones by 10 kHz.
For this measurement we might find ourselves using a 1 kHz resolution
bandwidth. Referring to Figure 6-3 and allowing for a 10 dB decrease in
the noise curve, we would find a maximum dynamic range of about 88 dB.
Suppose however, that our phase noise at a 10 kHz offset is only –80 dBc.
Then 80 dB becomes the ultimate limit of dynamic range for this measurement,
as shown in Figure 6-4.
–10
–20
–30
–40
–50
(dBc)
–60
–70
Phase noise
(10 kHz offset)
–80
Dynamic range
reduction due
to phase noise
–90
–100
–110
–60
–50
–40
–30
–20
Mixer level (dBm)
–10
0
+10
Figure 6-4. Phase noise can limit third-order intermodulation tests
In summary, the dynamic range of a spectrum analyzer is limited by three
factors: the distortion performance of the input mixer, the broadband noise
floor (sensitivity) of the system, and the phase noise of the local oscillator.
76
Dynamic range versus measurement uncertainty
In our previous discussion of amplitude accuracy, we included only those
items listed in Table 4-1, plus mismatch. We did not cover the possibility
of an internally generated distortion product (a sinusoid) being at the
same frequency as an external signal that we wished to measure. However,
internally generated distortion components fall at exactly the same
frequencies as the distortion components we wish to measure on external
signals. The problem is that we have no way of knowing the phase
relationship between the external and internal signals. So we can only
determine a potential range of uncertainty:
Uncertainty (in dB) = 20 log(l ± 10d/20)
where d = difference in dB between the larger and smaller sinusoid
(a negative number)
See Figure 6-5. For example, if we set up conditions such that the internally
generated distortion is equal in amplitude to the distortion on the incoming
signal, the error in the measurement could range from +6 dB (the two signals
exactly in phase) to -infinity (the two signals exactly out of phase and so
canceling). Such uncertainty is unacceptable in most cases. If we put a limit
of ±1 dB on the measurement uncertainty, Figure 6-5 shows us that the
internally generated distortion product must be about 18 dB below the
distortion product that we wish to measure. To draw dynamic range curves
for second- and third-order measurements with no more than 1 dB of
measurement error, we must then offset the curves of Figure 6-2 by 18 dB
as shown in Figure 6-6.
6
5
4
3
2
1
0
–30
–25
–20
–15
–10
–5
Maximum
error (dB)
–1
–2
–3
–4
–5
–6
–7
–8
Delta (dBc)
Figure 6-5. Uncertainty versus difference in amplitude between two sinusoids at the
same frequency
77
Next, let’s look at uncertainty due to low signal-to-noise ratio. The distortion
components we wish to measure are, we hope, low-level signals, and often
they are at or very close to the noise level of our spectrum analyzer. In such
cases, we often use the video filter to make these low-level signals more
discernable. Figure 6-7 shows the error in displayed signal level as a function
of displayed signal-to-noise for a typical spectrum analyzer. Note that the
error is only in one direction, so we could correct for it. However, we usually
do not. So for our dynamic range measurement, let’s accept a 0.3 dB error
due to noise and offset the noise curve in our dynamic range chart by 5 dB
as shown in Figure 6-6. Where the distortion and noise curves intersect, the
maximum error possible would be less than 1.3 dB.
0
–10
–20
ord
e
r
de
or
d
2n
r
–30
3r d
–40
ise
No
(dBc)
–50
5 dB
–60
–70
–80
18 dB
18 dB
–90
–100
–60
–50
–40
–30
–20
Mixer level (dBm)
Figure 6-6. Dynamic range for 1.3 dB maximum error
78
–10
0
+10
Let’s see what happened to our dynamic range as a result of our concern
with measurement error. As Figure 6-6 shows, second-order-distortion
dynamic range changes from 72.5 to 61 dB, a change of 11.5 dB. This is one
half the total offsets for the two curves (18 dB for distortion; 5 dB for noise).
Third-order distortion changes from 81.7 dB to about 72.7 dB for a change
of about 9 dB. In this case, the change is one third of the 18 dB offset for the
distortion curve plus two thirds of the 5 dB offset for the noise curve.
7
Error in displayed signal level (dB)
6
5
4
3
2
1
0
0
1
2
3
4
5
6
7
8
Displayed S/N (dB)
Figure 6-7. Error in displayed signal amplitude due to noise
79
Gain compression
In our discussion of dynamic range, we did not concern ourselves with how
accurately the larger tone is displayed, even on a relative basis. As we raise
the level of a sinusoidal input signal, eventually the level at the input mixer
becomes so high that the desired output mixing product no longer changes
linearly with respect to the input signal. The mixer is in saturation, and the
displayed signal amplitude is too low. Saturation is gradual rather than
sudden. To help us stay away from the saturation condition, the 1-dB
compression point is normally specified. Typically, this gain compression
occurs at a mixer level in the range of –5 to +5 dBm. Thus we can determine
what input attenuator setting to use for accurate measurement of high-level
signals3. Spectrum analyzers with a digital IF will display an “IF Overload”
message when the ADC is over-ranged.
Actually, there are three different methods of evaluating compression. A
traditional method, called CW compression, measures the change in gain of
a device (amplifier or mixer or system) as the input signal power is swept
upward. This method is the one just described. Note that the CW compression
point is considerably higher than the levels for the fundamentals indicated
previously for even moderate dynamic range. So we were correct in not
concerning ourselves with the possibility of compression of the larger
signal(s).
A second method, called two-tone compression, measures the change in
system gain for a small signal while the power of a larger signal is swept
upward. Two-tone compression applies to the measurement of multiple
CW signals, such as sidebands and independent signals. The threshold of
compression of this method is usually a few dB lower than that of the CW
method. This is the method used by Agilent Technologies to specify spectrum
analyzer gain compression.
A final method, called pulse compression, measures the change in system
gain to a narrow (broadband) RF pulse while the power of the pulse is swept
upward. When measuring pulses, we often use a resolution bandwidth much
narrower than the bandwidth of the pulse, so our analyzer displays the signal
level well below the peak pulse power. As a result, we could be unaware of
the fact that the total signal power is above the mixer compression threshold.
A high threshold improves signal-to-noise ratio for high-power, ultra-narrow
or widely chirped pulses. The threshold is about 12 dB higher than for
two-tone compression in the Agilent 8560EC Series spectrum analyzers.
Nevertheless, because different compression mechanisms affect CW, two-tone,
and pulse compression differently, any of the compression thresholds can
be lower than any other.
Display range and measurement range
3. Many analyzers internally control the combined
settings of the input attenuator and IF gain so that
a CW signal as high as the compression level at
the input mixer creates a deflection above the top
line of the graticule. Thus we cannot make incorrect
measurements on CW signals inadvertently.
80
There are two additional ranges that are often confused with dynamic range:
display range and measurement range. Display range, often called display
dynamic range, refers to the calibrated amplitude range of the spectrum
analyzer display. For example, a display with ten divisions would seem
to have a 100 dB display range when we select 10 dB per division. This is
certainly true for modern analyzers with digital IF circuitry, such as the
Agilent PSA Series. It is also true for the Agilent ESA-E Series when using
the narrow (10 to 300 Hz) digital resolution bandwidths. However, spectrum
analyzers with analog IF sections typically are only calibrated for the first
85 or 90 dB below the reference level. In this case, the bottom line of the
graticule represents signal amplitudes of zero, so the bottom portion of
the display covers the range from –85 or –90 dB to infinity, relative to the
reference level.
The range of the log amplifier can be another limitation for spectrum
analyzers with analog IF circuitry. For example, ESA-L Series spectrum
analyzers use an 85 dB log amplifier. Thus, only measurements that are within
85 dB below the reference level are calibrated.
The question is, can the full display range be used? From the previous
discussion of dynamic range, we know that the answer is generally yes. In fact,
dynamic range often exceeds display range or log amplifier range. To bring
the smaller signals into the calibrated area of the display, we must increase
IF gain. But in so doing, we may move the larger signals off the top of the
display, above the reference level. Some Agilent analyzers, such as the
PSA Series, allow measurements of signals above the reference level without
affecting the accuracy with which the smaller signals are displayed. This is
shown in Figure 6-8. So we can indeed take advantage of the full dynamic
range of an analyzer even when the dynamic range exceeds the display range.
In Figure 6-8, even though the reference level has changed from –8 dBm
to –53 dBm, driving the signal far above the top of the screen, the marker
readout remains unchanged.
Figure 6-8. Display range and measurement range on the PSA Series
Measurement range is the ratio of the largest to the smallest signal that
can be measured under any circumstances. The maximum safe input level,
typically +30 dBm (1 watt) for most analyzers, determines the upper limit.
These analyzers have input attenuators settable to 60 or 70 dB, so we can
reduce +30 dBm signals to levels well below the compression point of the
input mixer and measure them accurately. The displayed average noise
level sets the other end of the range. Depending on the minimum resolution
bandwidth of the particular analyzer and whether or not a preamplifier is
being used, DANL typically ranges from –115 to –170 dBm. Measurement
range, then, can vary from 145 to 200 dB. Of course, we cannot view a
–170 dBm signal while a +30 dBm signal is also present at the input.
81
Adjacent channel power measurements
TOI, SOI, 1 dB gain compression, and DANL are all classic measures of
spectrum analyzer performance. However, with the tremendous growth of
digital communication systems, other measures of dynamic range have
become increasingly important. For example, adjacent channel power (ACP)
measurements are often done in CDMA-based communication systems to
determine how much signal energy leaks or “spills over” into adjacent or
alternate channels located above and below a carrier. An example ACP
measurement is shown in Figure 6-9.
Figure 6-9. Adjacent channel power measurement using PSA Series
Note the relative amplitude difference between the carrier power and the
adjacent and alternate channels. Up to six channels on either side of the
carrier can be measured at a time.
Typically, we are most interested in the relative difference between the
signal power in the main channel and the signal power in the adjacent or
alternate channel. Depending on the particular communication standard,
these measurements are often described as “adjacent channel power ratio”
(ACPR) or “adjacent channel leakage ratio” (ACLR) tests. Because digitally
modulated signals, as well as the distortion they generate, are very noise-like
in nature, the industry standards typically define a channel bandwidth
over which the signal power is integrated.
In order to accurately measure ACP performance of a device under test
(DUT), such as a power amplifier, the spectrum analyzer must have better
ACP performance than the device being tested. Therefore, spectrum analyzer
ACPR dynamic range has become a key performance measure for digital
communication systems.
82
Chapter 7
Extending the
Frequency Range
As more wireless services continue to be introduced and deployed, the
available spectrum becomes more and more crowded. Therefore, there has
been an ongoing trend toward developing new products and services at higher
frequencies. In addition, new microwave technologies continue to evolve,
driving the need for more measurement capability in the microwave bands.
Spectrum analyzer designers have responded by developing instruments
capable of directly tuning up to 50 GHz using a coaxial input. Even higher
frequencies can be measured using external mixing techniques. This chapter
describes the techniques used to enable tuning the spectrum analyzer to
such high frequencies.
Internal harmonic mixing
In Chapter 2, we described a single-range spectrum analyzer that tunes
to 3 GHz. Now we wish to tune higher in frequency. The most practical way
to achieve such an extended range is to use harmonic mixing.
But let us take one step at a time. In developing our tuning equation in
Chapter 2, we found that we needed the low-pass filter of Figure 2-1 to
prevent higher-frequency signals from reaching the mixer. The result was
a uniquely responding, single band analyzer that tuned to 3 GHz. Now we
wish to observe and measure higher-frequency signals, so we must remove
the low-pass filter.
Other factors that we explored in developing the tuning equation were the
choice of LO and intermediate frequencies. We decided that the IF should
not be within the band of interest because it created a hole in our tuning
range in which we could not make measurements. So we chose 3.9 GHz,
moving the IF above the highest tuning frequency of interest (3 GHz). Since
our new tuning range will be above 3 GHz, it seems logical to move the new IF to
a frequency below 3 GHz. A typical first IF for these higher frequency ranges
in Agilent spectrum analyzers is 321.4 MHz. We shall use this frequency in
our examples. In summary, for the low band, up to 3 GHz, our first IF is
3.9 GHz. For the upper frequency bands, we switch to a first IF of 321.4 MHz.
Note that in Figure 7-1 the second IF is already 321.4 MHz, so all we need to
do when we wish to tune to the higher ranges is bypass the first IF.
Low band
3 GHz
path
Atten
3.9214 GHz
321.4 MHz
21.4 MHz
Analog or
Digital IF
Input
signal
High
band path
3 - 7 GHz
To
external
mixer
3.6 GHz
300 MHz
321.4 MHz
Preselector
Sweep generator
Display
Figure 7-1. Switching arrangement for low band and high bands
83
In Chapter 2, we used a mathematical approach to conclude that we needed
a low-pass filter. As we shall see, things become more complex in the situation
here, so we shall use a graphical approach as an easier method to see what is
happening. The low band is the simpler case, so we shall start with that. In
all of our graphs, we shall plot the LO frequency along the horizontal axis
and signal frequency along the vertical axis, as shown in Figure 7-2. We know
we get a mixing product equal to the IF (and therefore a response on the
display) whenever the input signal differs from the LO by the IF. Therefore,
we can determine the frequency to which the analyzer is tuned simply by
adding the IF to, or subtracting it from, the LO frequency. To determine our
tuning range, then, we start by plotting the LO frequency against the signal
frequency axis as shown by the dashed line in Figure 7-2. Subtracting the
IF from the dashed line gives us a tuning range of 0 to 3 GHz, the range that
we developed in Chapter 2. Note that this line in Figure 7-2 is labeled “1–”
to indicate fundamental mixing and the use of the minus sign in the tuning
equation. We can use the graph to determine what LO frequency is required
to receive a particular signal or to what signal the analyzer is tuned for a
given LO frequency. To display a 1 GHz signal, the LO must be tuned to
4.9 GHz. For an LO frequency of 6 GHz, the spectrum analyzer is tuned
to receive a signal frequency of 2.1 GHz. In our text, we shall round off
the first IF to one decimal place; the true IF, 3.9214 GHz, is shown on the
block diagram.
1+
Signal frequency (GHz)
10
LO
+IF
5
1–
–IF
0
4
5
LO frequency (GHz)
6
7
Figure 7-2. Tuning curves for fundamental mixing in the
low band, high IF case
Now let’s add the other fundamental-mixing band by adding the IF to the
LO line in Figure 7-2. This gives us the solid upper line, labeled 1+, that
indicates a tuning range from 7.8 to 10.9 GHz. Note that for a given LO
frequency, the two frequencies to which the analyzer is tuned are separated
by twice the IF. Assuming we have a low-pass filter at the input while
measuring signals in the low band, we shall not be bothered by signals in
the 1+ frequency range.
84
Next let’s see to what extent harmonic mixing complicates the situation.
Harmonic mixing comes about because the LO provides a high-level drive
signal to the mixer for efficient mixing, and since the mixer is a non-linear
device, it generates harmonics of the LO signal. Incoming signals can mix
against LO harmonics, just as well as the fundamental, and any mixing
product that equals the IF produces a response on the display. In other words,
our tuning (mixing) equation now becomes:
fsig = nfLO ± fIF
where
n = LO harmonic
(Other parameters remain the same as previously discussed)
Let’s add second-harmonic mixing to our graph in Figure 7-3 and see to what
extent this complicates our measurement procedure. As before, we shall first
plot the LO frequency against the signal frequency axis. Multiplying the
LO frequency by two yields the upper dashed line of Figure 7-3. As we did
for fundamental mixing, we simply subtract the IF (3.9 GHz) from and add
it to the LO second-harmonic curve to produce the 2– and 2+ tuning ranges.
Since neither of these overlap the desired 1– tuning range, we can again argue
that they do not really complicate the measurement process. In other words,
signals in the 1– tuning range produce unique, unambiguous responses on
our analyzer display. The same low-pass filter used in the fundamental mixing
case works equally well for eliminating responses created in the harmonic
mixing case.
2+
Signal frequency (GHz)
15
2xLO
1+
10
2–
LO
5
1–
0
4
5
6
LO frequency (GHz)
7
Figure 7-3. Signals in the “1 minus” frequency range produce
single, unambiguous responses in the low band, high IF case
85
The situation is considerably different for the high band, low IF case.
As before, we shall start by plotting the LO fundamental against the signalfrequency axis and then add and subtract the IF, producing the results shown
in Figure 7-4. Note that the 1– and 1+ tuning ranges are much closer together,
and in fact overlap, because the IF is a much lower frequency, 321.4 MHz
in this case. Does the close spacing of the tuning ranges complicate the
measurement process? Yes and no. First of all, our system can be calibrated
for only one tuning range at a time. In this case, we would choose the 1–
tuning to give us a low-end frequency of about 2.7 GHz, so that we have
some overlap with the 3 GHz upper end of our low band tuning range. So
what are we likely to see on the display? If we enter the graph at an LO
frequency of 5 GHz, we find that there are two possible signal frequencies
that would give us responses at the same point on the display: 4.7 and 5.3 GHz
(rounding the numbers again). On the other hand, if we enter the signal
frequency axis at 5.3 GHz, we find that in addition to the 1+ response at an
LO frequency of 5 GHz, we could also get a 1– response. This would occur if
we allowed the LO to sweep as high as 5.6 GHz, twice the IF above 5 GHz.
Also, if we entered the signal frequency graph at 4.7 GHz, we would find a
1+ response at an LO frequency of about 4.4 GHz (twice the IF below 5 GHz)
in addition to the 1– response at an LO frequency of 5 GHz. Thus, for every
desired response on the 1– tuning line, there will be a second response
located twice the IF frequency below it. These pairs of responses are
known as multiple responses.
With this type of mixing arrangement, it is possible for signals at different
frequencies to produce responses at the same point on the display, that is,
at the same LO frequency. As we can see from Figure 7-4, input signals at
4.7 and 5.3 GHz both produce a response at the IF frequency when the LO
frequency is set to 5 GHz. These signals are known as image frequencies,
and are also separated by twice the IF frequency.
Clearly, we need some mechanism to differentiate between responses
generated on the 1– tuning curve for which our analyzer is calibrated, and
those produced on the 1+ tuning curve. However, before we look at signal
identification solutions, let’s add harmonic-mixing curves to 26.5 GHz and
see if there are any additional factors that we must consider in the signal
identification process. Figure 7-5 shows tuning curves up to the fourth
harmonic of the LO.
Signal frequency (GHz)
10
Image frequencies
1+
LO
1–
5.3
4.7
0
3
4 4.4
5
LO frequency (GHz)
5.6
6
Figure 7-4. Tuning curves for fundamental mixing in the high
band, low IF case
86
In examining Figure 7-5, we find some additional complications. The
spectrum analyzer is set up to operate in several tuning bands. Depending
on the frequency to which the analyzer is tuned, the analyzer display is
frequency calibrated for a specific LO harmonic. For example, in the 6.2
to 13.2 GHz input frequency range, the spectrum analyzer is calibrated for
the 2– tuning curve. Suppose we have an 11 GHz signal present at the input.
As the LO sweeps, the signal will produce IF responses with the 3+, 3–, 2+
and 2– tuning curves. The desired response of the 2– tuning curve occurs
when the LO frequency satisfies the tuning equation:
11 GHz = 2 fLO – 0.3
fLO = 5.65 GHz
Similarly, we can calculate that the response from the 2+ tuning curve
occurs when fLO = 5.35 GHz, resulting in a displayed signal that appears
to be at 10.4 GHz.
The displayed signals created by the responses to the 3+ and 3– tuning curves
are known as in-band multiple responses. Because they occur when the LO is
tuned to 3.57 GHz and 3.77 GHz, they will produce false responses on the
display that appear to be genuine signals at 6.84 GHz and 7.24 GHz.
30
4+
4–
25
Signal frequency (GHz)
Band 4
3+
20
3–
Band 3
15
2+
In-band
multiple
responses
11
Apparent location of an
10.4
input signal resulting from
10
+
the response to the 2
tuning curve
Apparent locations of
in-band multiples of an
11 GHz input signal
2–
Band 2
1+
7.24
6.84
1–
5
Band 1
Band 0
(lowband)
0
3
3.57 3.77
4
5.35
5.65
5
LO frequency (GHz)
6
7
Figure 7-5. Tuning curves up to 4th harmonic of LO showing in-band multiple responses
to an 11 GHz input signal.
87
Other situations can create out-of-band multiple responses. For example,
suppose we are looking at a 5 GHz signal in band 1 that has a significant third
harmonic at 15 GHz (band 3). In addition to the expected multiple pair caused
by the 5 GHz signal on the 1+ and 1– tuning curves, we also get responses
generated by the 15 GHz signal on the 4+, 4–, 3+,and 3– tuning curves. Since
these responses occur when the LO is tuned to 3.675, 3.825, 4.9, and 5.1 GHz
respectively, the display will show signals that appear to be located at 3.375,
3.525, 4.6, and 4.8 GHz. This is shown in Figure 7-6.
30
4+
4–
25
Band 4
3+
Signal frequency (GHz)
20
3–
Out-of-band
multiple responses
Band 3
15
2+
2–
10
Band 2
1+
1–
5
Band 1
Band 0
(lowband)
0
3
3.675 3.825
4
4.7 4.9 5.1 5.3
5
LO frequency (GHz)
6
7
Figure 7-6. Out-of-band multiple responses in band 1 as a result of a signal in band 3
Multiple responses generally always come in pairs1, with a “plus” mixing
product and a “minus” mixing product. When we use the correct harmonic
mixing number for a given tuning band, the responses will be separated
by 2 times fIF. Because the slope of each pair of tuning curves increases
linearly with the harmonic number N, the multiple pairs caused by any
other harmonic mixing number appear to be separated by:
2fIF (Nc/NA)
1. Often referred to as an “image pair.” This is
inaccurate terminology, since images are actually
two or more real signals present at the spectrum
analyzer input that produce an IF response at the
same LO frequency.
88
where
Nc = the correct harmonic number for the desired tuning band
NA = the actual harmonic number generating the multiple pair
Can we conclude from this discussion that a harmonic mixing spectrum
analyzer is not practical? Not necessarily. In cases where the signal frequency
is known, we can tune to the signal directly, knowing that the analyzer will
select the appropriate mixing mode for which it is calibrated. In controlled
environments with only one or two signals, it is usually easy to distinguish
the real signal from the image and multiple responses. However, there are
many cases in which we have no idea how many signals are involved or
what their frequencies might be. For example, we could be searching for
unknown spurious signals, conducting site surveillance tests as part of a
frequency-monitoring program, or performing EMI tests to measure
unwanted device emissions. In all these cases, we could be looking for
totally unknown signals in a potentially crowded spectral environment.
Having to perform some form of identification routine on each and every
response would make measurement time intolerably long.
Fortunately, there is a way to essentially eliminate image and multiple
responses through a process of prefiltering the signal. This technique is
called preselection.
Preselection
What form must our preselection take? Referring back to Figure 7-4, assume
that we have two signals at 4.7 and 5.3 GHz present at the input of our
analyzer. If we were particularly interested in one, we could use a band-pass
filter to allow that signal into the analyzer and reject the other. However,
the fixed filter does not eliminate multiple responses; so if the spectrum is
crowded, there is still potential for confusion. More important, perhaps, is
the restriction that a fixed filter puts on the flexibility of the analyzer. If we
are doing broadband testing, we certainly do not want to be continually
forced to change band-pass filters.
The solution is a tunable filter configured in such a way that it automatically
tracks the frequency of the appropriate mixing mode. Figure 7-7 shows the
effect of such a preselector. Here we take advantage of the fact that our
superheterodyne spectrum analyzer is not a real-time analyzer; that is, it
tunes to only one frequency at a time. The dashed lines in Figure 7-7 represent
the bandwidth of the tracking preselector. Signals beyond the dashed lines
are rejected. Let’s continue with our previous example of 4.7 and 5.3 GHz
signals present at the analyzer input. If we set a center frequency of 5 GHz
and a span of 2 GHz, let’s see what happens as the analyzer tunes across this
range. As the LO sweeps past 4.4 GHz (the frequency at which it could mix
with the 4.7 GHz input signal on its 1+ mixing mode), the preselector is tuned
to 4.1 GHz and therefore rejects the 4.7 GHz signal. Since the input signal
does not reach the mixer, no mixing occurs, and no response appears on the
display. As the LO sweeps past 5 GHz, the preselector allows the 4.7 GHz
signal to reach the mixer, and we see the appropriate response on the display.
The 5.3 GHz image signal is rejected, so it creates no mixing product to
interact with the mixing product from the 4.7 GHz signal and cause a false
display. Finally, as the LO sweeps past 5.6 GHz, the preselector allows the
5.3 GHz signal to reach the mixer, and we see it properly displayed. Note in
Figure 7-7 that nowhere do the various mixing modes intersect. So as long
as the preselector bandwidth is narrow enough (it typically varies from
about 35 MHz at low frequencies to 80 MHz at high frequencies) it will
greatly attenuate all image and multiple responses.
89
Signal frequency (GHz)
1+
6
5.3
1–
4.7
4
3
Preselector
bandwidth
2
3
4
4.4
5
LO frequency (GHz)
5.6
6
Figure 7-7. Preselection; dashed lines represent bandwidth
of tracking preselector
The word eliminate may be a little strong. Preselectors do not have infinite
rejection. Something in the 70 to 80 dB range is more likely. So if we are
looking for very low-level signals in the presence of very high-level signals,
we might see low-level images or multiples of the high-level signals. What
about the low band? Most tracking preselectors use YIG technology, and
YIG filters do not operate well at low frequencies. Fortunately, there is a
simple solution. Figure 7-3 shows that no other mixing mode overlaps the
1– mixing mode in the low frequency, high IF case. So a simple low-pass filter
attenuates both image and multiple responses. Figure 7-8 shows the input
architecture of a typical microwave spectrum analyzer.
Low band
3 GHz
path
Atten
3.9214 GHz
321.4 MHz
21.4 MHz
Analog or
Digital IF
Input
signal
High
band path
3 - 7 GHz
To
external
mixer
3.6 GHz
300 MHz
321.4 MHz
Preselector
Sweep generator
Figure 7-8. Front-end architecture of a typical preselected spectrum analyzer
90
Display
Amplitude calibration
So far, we have looked at how a harmonic mixing spectrum analyzer responds
to various input frequencies. What about amplitude?
The conversion loss of a mixer is a function of harmonic number, and the
loss goes up as the harmonic number goes up. This means that signals of
equal amplitude would appear at different levels on the display if they
involved different mixing modes. To preserve amplitude calibration, then,
something must be done. In Agilent spectrum analyzers, the IF gain is
changed. The increased conversion loss at higher LO harmonics causes a
loss of sensitivity just as if we had increased the input attenuator. And since
the IF gain change occurs after the conversion loss, the gain change is
reflected by a corresponding change in the displayed noise level. So we
can determine analyzer sensitivity on the harmonic-mixing ranges by noting
the average displayed noise level just as we did on fundamental mixing.
In older spectrum analyzers, the increase in displayed average noise level
with each harmonic band was very noticeable. More recent models of Agilent
spectrum analyzers use a double-balanced, image-enhanced harmonic mixer
to minimize the increased conversion loss when using higher harmonics.
Thus, the “stair step” effect on DANL has been replaced by a gentle sloping
increase with higher frequencies. This can be seen in Figure 7-9.
Figure 7-9. Rise in noise floor indicates changes in sensitivity with
changes in LO harmonic used
Phase noise
In Chapter 2, we noted that instability of an analyzer LO appears as phase
noise around signals that are displayed far enough above the noise floor.
We also noted that this phase noise can impose a limit on our ability to
measure closely spaced signals that differ in amplitude. The level of the phase
noise indicates the angular, or frequency, deviation of the LO. What happens
to phase noise when a harmonic of the LO is used in the mixing process?
Relative to fundamental mixing, phase noise (in decibels) increases by:
where
20 log(N),
N = harmonic of the LO
91
For example, suppose that the LO fundamental has a peak-to-peak deviation
of 10 Hz. The second harmonic then has a 20 Hz peak-to-peak deviation; the
third harmonic, 30 Hz; and so on. Since the phase noise indicates the signal
(noise in this case) producing the modulation, the level of the phase noise
must be higher to produce greater deviation. When the degree of modulation
is very small, as in the situation here, the amplitude of the modulation side
bands is directly proportional to the deviation of the carrier (LO). If the
deviation doubles, the level of the side bands must also double in voltage;
that is, increase by 6 dB or 20 log(2). As a result, the ability of our analyzer
to measure closely spaced signals that are unequal in amplitude decreases
as higher harmonics of the LO are used for mixing. Figure 7-10 shows the
difference in phase noise between fundamental mixing of a 5 GHz signal and
fourth-harmonic mixing of a 20 GHz signal.
Figure 7-10. Phase noise levels for fundamental and 4th harmonic mixing
Improved dynamic range
A preselector improves dynamic range if the signals in question have
sufficient frequency separation. The discussion of dynamic range in Chapter 6
assumed that both the large and small signals were always present at the
mixer and that their amplitudes did not change during the course of the
measurement. But as we have seen, if signals are far enough apart, a
preselector allows one to reach the mixer while rejecting the others. For
example, if we were to test a microwave oscillator for harmonics, a
preselector would reject the fundamental when we tuned the analyzer
to one of the harmonics.
Let’s look at the dynamic range of a second-harmonic test of a 3 GHz
oscillator. Using the example from Chapter 6, suppose that a –40 dBm signal
at the mixer produces a second harmonic product of –75 dBc. We also know,
from our discussion, that for every dB the level of the fundamental changes
at the mixer, measurement range also changes by 1 dB. The second-harmonic
distortion curve is shown in Figure 7-11. For this example, we shall assume
plenty of power from the oscillator and set the input attenuator so that when
we measure the oscillator fundamental, the level at the mixer is –10 dBm,
below the 1 dB compression point.
92
From the graph, we see that a –10 dBm signal at the mixer produces a
second-harmonic distortion component of –45 dBc. Now we tune the analyzer
to the 6 GHz second harmonic. If the preselector has 70 dB rejection, the
fundamental at the mixer has dropped to –80 dBm. Figure 7-11 indicates
that for a signal of –80 dBm at the mixer, the internally generated distortion
is –115 dBc, meaning 115 dB below the new fundamental level of –80 dBm.
This puts the absolute level of the harmonic at –195 dBm. So the difference
between the fundamental we tuned to and the internally generated second
harmonic we tuned to is 185 dB! Clearly, for harmonic distortion, dynamic
range is limited on the low-level (harmonic) end only by the noise floor
(sensitivity) of the analyzer.
–45
–50
Internal distortion (dBc)
–60
–70
–80
–90
–100
–110
–115
–120
–90
–80
–70
–60
–50
–40
–30
–20
–10
0
Mixed level (dBm)
Figure 7-11. Second-order distortion graph
What about the upper, high-level end? When measuring the oscillator
fundamental, we must limit power at the mixer to get an accurate reading
of the level. We can use either internal or external attenuation to limit
the level of the fundamental at the mixer to something less than the 1 dB
compression point. However, since the preselector highly attenuates the
fundamental when we are tuned to the second harmonic, we can remove
some attenuation if we need better sensitivity to measure the harmonic.
A fundamental level of +20 dBm at the preselector should not affect our
ability to measure the harmonic.
Any improvement in dynamic range for third-order intermodulation
measurements depends upon separation of the test tones versus preselector
bandwidth. As we noted, typical preselector bandwidth is about 35 MHz at
the low end and 80 MHz at the high end. As a conservative figure, we might
use 18 dB per octave of bandwidth roll off of a typical YIG preselector filter
beyond the 3 dB point. So to determine the improvement in dynamic range,
we must determine to what extent each of the fundamental tones is
attenuated and how that affects internally generated distortion. From
the expressions in Chapter 6 for third-order intermodulation, we have:
(k4/8)VLOV12V2 cos[ωLO – (2ω1 – ω2)]t
and
(k4/8)VLOV1V22 cos[ωLO – (2ω2 – ω1)]t
93
Looking at these expressions, we see that the amplitude of the lower
distortion component (2ω1 – ω2) varies as the square of V1 and linearly
with V2. On the other side, the amplitude of the upper distortion component
(2ω2 – ω1) varies linearly with V1 and as the square of V2. However,
depending on the signal frequencies and separation, the preselector may
not attenuate the two fundamental tones equally.
Consider the situation shown in Figure 7-12 in which we are tuned to the
lower distortion component and the two fundamental tones are separated
by half the preselector bandwidth. In this case, the lower-frequency test tone
lies at the edge of the preselector pass band and is attenuated 3 dB. The
upper test tone lies above the lower distortion component by an amount
equal to the full preselector bandwidth. It is attenuated approximately
21 dB. Since we are tuned to the lower distortion component, internally
generated distortion at this frequency drops by a factor of two relative to the
attenuation of V1 (2 times 3 dB = 6 dB) and equally as fast as the attenuation
of V2 (21 dB). The improvement in dynamic range is the sum of 6 dB + 21 dB,
or 27 dB. As in the case of second harmonic distortion, the noise floor of
the analyzer must be considered, too. For very closely spaced test tones,
the preselector provides no improvement, and we determine dynamic range
as if the preselector was not there.
3 dB
21 dB
27 dB
Figure 7-12. Improved third-order intermodulation distortion; test tone
separation is significant, relative to preselector bandwidth
The discussion of dynamic range in Chapter 6 applies to the low-pass-filtered
low band. The only exceptions occur when a particular harmonic of a low
band signal falls within the preselected range. For example, if we measure
the second harmonic of a 2.5 GHz fundamental, we get the benefit of the
preselector when we tune to the 5 GHz harmonic.
94
Pluses and minuses of preselection
We have seen the pluses of preselection: simpler analyzer operation,
uncluttered displays, improved dynamic range, and wide spans. But there
are some minuses, relative to an unpreselected analyzer, as well.
First of all, the preselector has insertion loss, typically 6 to 8 dB. This loss
comes prior to the first stage of gain, so system sensitivity is degraded by the
full loss. In addition, when a preselector is connected directly to a mixer, the
interaction of the mismatch of the preselector with that of the input mixer
can cause a degradation of frequency response. Proper calibration techniques
must be used to compensate for this ripple. Another approach to minimize
this interaction would be to insert a matching pad (fixed attenuator) or
isolator between the preselector and mixer. In this case, sensitivity would
be degraded by the full value of the pad or isolator.
Some spectrum analyzer architectures eliminate the need for the matching
pad or isolator. As the electrical length between the preselector and mixer
increases, the rate of change of phase of the reflected and re-reflected signals
becomes more rapid for a given change in input frequency. The result is a
more exaggerated ripple effect on flatness. Architectures such as those used
in the ESA Series and PSA Series include the mixer diodes as an integral
part of the preselector/mixer assembly. In such an assembly, there is minimal
electrical length between the preselector and mixer. This architecture thus
removes the ripple effect on frequency response and improves sensitivity by
eliminating the matching pad or isolator.
Even aside from its interaction with the mixer, a preselector causes some
degradation of frequency response. The preselector filter pass band is
never perfectly flat, but rather exhibits a certain amount of ripple. In most
configurations, the tuning ramp for the preselector and local oscillator come
from the same source, but there is no feedback mechanism to ensure that
the preselector exactly tracks the tuning of the analyzer. Another source
of post-tuning drift is the self-heating caused by current flowing in the
preselector circuitry. The center of the preselector passband will depend
on its temperature and temperature gradients. These will depend on the
history of the preselector tuning. As a result, the best flatness is obtained
by centering the preselector at each signal. The centering function is typically
built into the spectrum analyzer firmware and selected either by a front panel
key in manual measurement applications, or programmatically in automated
test systems. When activated, the centering function adjusts the preselector
tuning DAC to center the preselector pass band on the signal. The frequency
response specification for most microwave analyzers only applies after
centering the preselector, and it is generally a best practice to perform this
function (to mitigate the effects of post-tuning drift) before making amplitude
measurements of microwave signals.
95
External harmonic mixing
We have discussed tuning to higher frequencies within the spectrum analyzer.
For internal harmonic mixing, the ESA and PSA spectrum analyzers use the
second harmonic (N=2–) to tune to 13.2 GHz, and the fourth harmonic (N=4–)
to tune to 26.5 GHz. However, what if you want to test outside the upper
frequency range of the spectrum analyzer? Some spectrum analyzers provide
the ability to bypass the internal first mixer and preselector and use an
external mixer to enable the spectrum analyzer to make high frequency
measurements2. For external mixing we can use higher harmonics of the
1st LO. Typically, a spectrum analyzer that supports external mixing has two
additional connectors on the front panel. An LO OUT port routes the internal
first LO signal to the external mixer, which uses the higher harmonics to mix
with the high frequency signals. The external mixer’s IF output connects to
the analyzer’s IF IN port. As long as the external mixer uses the same
IF frequency as the spectrum analyzer, the signal can be processed and
displayed internally, just like any signal that came from the internal first
mixer. Figure 7-13 illustrates the block diagram of an external mixer used
in conjunction with a spectrum analyzer.
External harmonic mixer
Input
signal
3 GHz
Atten
3.9214 GHz
321.4 MHz
21.4 MHz
Analog or
digital IF
Input
signal
3 - 7 GHz
3.6 GHz
Preselector
321.4 MHz
Sweep
generator
Figure 7-13. Spectrum analyzer and external mixer block diagram
2. For more information on external mixing, see
Agilent Application Note 1485, External Waveguide
Mixing and Millimeter Wave Measurements with
Agilent PSA Spectrum Analyzers, literature number
5988-9414EN.
96
300 MHz
Display
Table 7-1 shows the harmonic mixing modes used by the ESA and PSA at
various millimeter wave bands. You choose the mixer depending on the
frequency range you need. Typically, these are standard waveguide bands.
There are two kinds of external harmonic mixers; those with preselection
and those without. Agilent offers unpreselected mixers in six frequency bands:
18 to 26.5 GHz, 26.5 to 40 GHz, 33 to 50 GHz, 40 to 60 GHz, 50 to 75 GHz,
and 75 to 110 GHz. Agilent also offers four preselected mixers up to 75 GHz.
Above 110 GHz, mixers are available from other commercial manufacturers
for operation up to 325 GHz.
Some external mixers from other manufacturers require a bias current to set
the mixer diodes to the proper operating point. The ESA and PSA spectrum
analyzers can provide up to ±10 mA of DC current through the IF OUT port
to provide this bias and keep the measurement setup as simple as possible.
Table 7-1. Harmonic mixing modes used by ESA-E and PSA Series with external mixers
Band
K (18.0 to 26.5 GHz)
A (26.5 to 40.0 GHz)
Q (33.0 to 50.0 GHz)
U (40.0 to 60.0 GHz)
V (50.0 to 75.0 GHz)
E (60.0 to 90.0 GHz)
W (75.0 to 110.0 GHz)
F (90.0 to 140.0 GHz)
D (110.0 to 170.0 GHz)
G (140.0 to 220.0 GHz)
Y (170.0 to 260.0 GHz)
J (220.0 to 325.0 GHz)
Harmonic mixing mode (Na)
Preselected
Unpreselected
n/a
6–
+
8
8–
+
10
10–
10+
10–
14+
14–
n/a
16–
n/a
18–
n/a
20–
n/a
24–
n/a
32–
n/a
38–
n/a
46–
Whether performing harmonic mixing with an internal or an external mixer,
the issues are similar. The LO and its harmonics mix not only with the RF
input signal, but any other signal that may be present at the input as well.
This produces mixing products that can be processed through the IF just
like any other valid signals. There are two ways to deal with these unwanted
signals. A preselector designed into the external mixer will offer you the same
type of tunable filter, as in the spectrum analyzer, for the frequency band of
interest. Figure 7-14 shows a spectrum analyzer and an external mixer with
internal preselection. The benefits and drawbacks of a preselected external
mixer are very similar to those for the preselector inside the spectrum
analyzer. The most significant drawback of preselected mixers is the
increased insertion loss due to the filter, resulting in lower sensitivity for
the measurement. Preselected mixers are also significantly more expensive
than unpreselected mixers. For these reasons, another way to deal with
these unwanted signals has been designed into the spectrum analyzer. This
function is called “signal identification.”
97
External harmonic mixer
Input
signal
3 GHz
Atten
321.4 MHz
3.9214 GHz
21.4 MHz
Analog or
digital IF
Input
signal
3 - 7 GHz
3.6 GHz
Preselector
300 MHz
321.4 MHz
Sweep
generator
Display
Figure 7-14. Block diagram of spectrum analyzer and external mixer with built-in preselector
Signal identification
Even when using an unpreselected mixer in a controlled situation, there
are times when we must contend with unknown signals. In such cases, it is
quite possible that the particular response we have tuned onto the display
has been generated on an LO harmonic or mixing mode other than the one
for which the display is calibrated. So our analyzer must have some way
to tell us whether or not the display is calibrated for the signal response in
question. For the purposes of this example, assume that we are using an
Agilent 11970V 50 to 75 GHz unpreselected mixer, which uses the 14– mixing
mode. A portion of this millimeter band can be seen in Figure 7-15.
The Agilent E4407B ESA-E spectrum analyzer offers two different
identification methods: Image shift and Image suppress. We shall first
consider the image shift method. Looking at Figure 7-16, let’s assume that
we have tuned the analyzer to a frequency of 58.5 GHz. The 14th harmonic
of the LO produces a pair of responses, where the 14– mixing product appears
on screen at the correct frequency of 58.5 GHz, while the 14+ mixing product
produces a response with an indicated frequency of 57.8572 GHz, which is
2 times fIF below the real response. Since the ESA has an IF frequency of
321.4 MHz, the pair of responses is separated by 642.8 MHz.
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Figure 7-15. Which ones are the real signals?
75
16+ 16– 14+ 14–
70
12+
18+ 18–
10+
65
Apparent
location of
image pair
12–
10–
60
Input frequency (GHz)
58.5
57.8572
55
8+
50
8–
45
40
6+
35
6–
30
25
3
4
5
LO frequency (GHz)
6
7
Figure 7-16. Harmonic tuning lines for the E4407B ESA-E spectrum analyzer
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Let’s assume that we have some idea of the characteristics of our signal,
but we do not know its exact frequency. How do we determine which is the
real signal? The image-shift process retunes the LO fundamental frequency
by an amount equal to 2fIF/N. This causes the Nth harmonic to shift by 2fIF.
If we are tuned to a real signal, its corresponding pair will now appear at the
same position on screen that the real signal occupied in the first sweep. If we
are tuned to another multiple pair created by some other incorrect harmonic,
the signal will appear to shift in frequency on the display. The ESA spectrum
analyzer shifts the LO on alternate sweeps, creating the two displays shown
in Figures 7-17a and 7-17b. In Figure 7-17a, the real signal (the 14– mixing
product) is tuned to the center of the screen. Figure 7-17b shows how the
image shift function moves the corresponding pair (the 14+ mixing product)
to the center of the screen.
Figure 7-17a. 14 – centered
Figure 7-17b. 14+ centered
Figure 7-17. Alternate sweeps taken with the image shift function
Let’s examine the second method of signal identification, called image
suppression. In this mode, two sweeps are taken using the MIN HOLD
function, which saves the smaller value of each display point, or bucket,
from the two sweeps. The first sweep is done using normal LO tuning values.
The second sweep offsets the LO fundamental frequency by 2fIF/N. As we
saw in the first signal ID method, the image product generated by the correct
harmonic will land at the same point on the display as the real signal did
on the first sweep. Therefore, the trace retains a high amplitude value. Any
false response that shifts in frequency will have its trace data replaced by
a lower value. Thus, all image and incorrect multiple responses will appear
as noise. This is shown in Figure 7-18.
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Figure 7-18. The image suppress function displays only real signals
Note that both signal identification methods are used for identifying correct
frequencies only. You should not attempt to make amplitude measurements
while the signal identification function is turned on. Note that in both
Figures 7-17 and 7-18, an on-screen message alerts the user to this fact.
Once we have identified the real signal of interest, we turn off the signal
ID function and zoom in on it by reducing the span. We can then measure
the signal’s amplitude and frequency. See Figure 7-19.
To make an accurate amplitude measurement, it is very important that you
first enter the calibration data for your external mixer. This data is normally
supplied by the mixer manufacturer, and is typically a table of mixer conversion
loss, in dB, at a number of frequency points across the band. This data is
entered into the ESA’s amplitude correction table. This table is accessed by
pressing the [AMPLITUDE] key, then pressing the {More}, {Corrections},
{Other} and {Edit} softkeys. After entering the conversion loss values, apply
the corrections with the {Correction On} softkey. The spectrum analyzer
reference level is now calibrated for signals at the input to the external mixer.
If you have other loss or gain elements between the signal source and the
mixer, such as antennas, cables, or preamplifiers, the frequency responses of
these elements should be entered into the amplitude correction table as well.
Figure 7-19. Measurement of positively identified signal
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Chapter 8
Modern Spectrum Analyzers
In previous chapters of this application note, we have looked at the
fundamental architecture of spectrum analyzers and basic considerations
for making frequency-domain measurements. On a practical level, modern
spectrum analyzers must also handle many other tasks to help you accomplish
your measurement requirements. These tasks include:
• Providing application-specific measurements, such as adjacent channel
power (ACP), noise figure, and phase noise
• Providing digital modulation analysis measurements defined by industry
or regulatory standards, such as GSM, cdma2000, 802.11, or Bluetooth
• Performing vector signal analysis
• Saving data
• Printing data
• Transferring data, via an I/O bus, to a computer
• Offering remote control and operation over GPIB, LAN, or the Internet
• Allowing you to update instrument firmware to add new features and
capabilities, as well as to repair defects
• Making provisions for self-calibration, troubleshooting, diagnostics,
and repair
• Recognizing and operating with optional hardware and/or firmware to
add new capabilities
Application-specific measurements
In addition to measuring general signal characteristics like frequency and
amplitude, you often need to make specific measurements of certain signal
parameters. Examples include channel power measurements and adjacent
channel power (ACP) measurements, which were previously described in
Chapter 6. Many spectrum analyzers now have these built-in functions
available. You simply specify the channel bandwidth and spacing, then press
a button to activate the automatic measurement.
The complementary cumulative distribution function (CCDF), showing
power statistics, is another measurement capability increasingly found in
modern spectrum analyzers. This is shown in Figure 8-1. CCDF measurements
provide statistical information showing the percent of time the instantaneous
power of the signal exceeds the average power by a certain number of dB.
This information is important in power amplifier design, for example,
where it is important to handle instantaneous signal peaks with minimum
distortion while minimizing cost, weight, and power consumption of
the device.
102
Other examples of built-in measurement functions include occupied
bandwidth, TOI and harmonic distortion, and spurious emissions
measurements. The instrument settings, such as center frequency, span,
and resolution bandwidth, for these measurements depend on the specific
radio standard to which the device is being tested. Most modern spectrum
analyzers have these instrument settings stored in memory so that you
can select the desired radio standard (GSM/EDGE, cdma2000, W-CDMA,
802.11a/b/g, and so on) to properly make the measurements.
Figure 8-1. CCDF measurement
103
RF designers are often concerned with the noise figure of their devices,
as this directly affects the sensitivity of receivers and other systems. Some
spectrum analyzers, such as the PSA Series and ESA-E Series models, have
optional noise figure measurement capabilities available. This option provides
control for the noise source needed to drive the input of the device under
test (DUT), as well as firmware to automate the measurement process and
display the results. Figure 8-2 shows a typical measurement result, showing
DUT noise figure (upper trace) and gain (lower trace) as a function of
frequency. For more information on noise figure measurements using a
spectrum analyzer, see Agilent Application Note 1439, Measuring Noise
Figure with a Spectrum Analyzer, literature number 5988-8571EN.
Figure 8-2. Noise figure measurement
Similarly, phase noise is a common measure of oscillator performance.
In digitally modulated communication systems, phase noise can negatively
impact bit error rates. Phase noise can also degrade the ability of Doppler
radar systems to capture the return pulses from targets. Many Agilent
spectrum analyzers, including the ESA, PSA, and 8560 Series offer optional
phase noise measurement capabilities. These options provide firmware
to control the measurement and display the phase noise as a function of
frequency offset from the carrier, as shown in Figure 8-3.
Figure 8-3. Phase Noise measurement
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Digital modulation analysis
The common wireless communication systems used throughout the world
today all have prescribed measurement techniques defined by standardsdevelopment organizations and governmental regulatory bodies. Optional
measurement personalities are commonly available on spectrum analyzers
to perform the key tests defined for a particular communication format.
For example, if we need to test a transmitter to the Bluetooth wireless
communication standard, we must measure parameters such as:
•
•
•
•
•
•
•
•
•
Average/peak output power
Modulation characteristics
Initial carrier frequency tolerance
Carrier frequency drift
Monitor band/channel
Modulation overview
Output spectrum
20 dB bandwidth
Adjacent channel power
These measurements are available on the Agilent ESA-E Series spectrum
analyzer with appropriate options. For more information on Bluetooth
measurements, please refer to Agilent Application Note 1333, Performing
Bluetooth RF Measurements Today, literature number 5968-7746E. Other
communication standards-based measurement personalities available on
the ESA-E Series include cdmaOne and GSM/GPRS/EDGE.
Measurement capabilities for a wide variety of wireless communications
standards are also available for the PSA Series spectrum analyzers.
Optional measurement personalities include:
•
•
•
•
•
•
•
•
•
GSM/EDGE
W-CDMA
HSDPA
cdma2000
1xEV-DO
1xEV-DV
cdmaOne
NADC and PDC
TD-SCDMA
Figure 8-4 illustrates an error vector magnitude (EVM) measurement
performed on a GSM/EDGE signal. This test helps diagnose modulation
or amplification distortions that lead to bit errors in the receiver.
Figure 8-4. EVM measurement results and constellation display
105
Not all digital communication systems are based on well-defined industry
standards. Engineers working on non-standard proprietary systems or the
early stages of proposed industry-standard formats need more flexibility
to analyze vector-modulated signals under varying conditions. This can be
accomplished in two ways. First, modulation analysis personalities are
available on a number of spectrum analyzers. Alternatively, more extensive
analysis can be done with software running on an external computer. For
example, the Agilent 89600 Series vector signal analysis software can be
used with either the ESA or PSA Series spectrum analyzers to provide
flexible vector signal analysis. In this case, the spectrum analyzer acts as
an RF downconverter and digitizer. The software communicates with the
spectrum analyzer over a GPIB or LAN connection and transfers IQ data to
the computer, where it performs the vector signal analysis. Measurement
settings, such as modulation type, symbol rate, filtering, triggering, and record
length, can be varied as necessary for the particular signal being analyzed.
Saving and printing data
After making a measurement, we normally want to keep a record of the
test data. We might simply want to make a quick printout of the instrument
display. Depending on the particular analyzer and printer model, we might
use the parallel, RS-232, or GPIB ports to connect the two units.
Very often, we may want to save measurement data as a file, either in the
spectrum analyzer’s internal memory or on a mass-storage device such as a
floppy disk. In this case, there are several different kinds of data we may
wish to save. This could include:
• An image of the display - Preferably in a popular file format, such as
bitmap, .GIF, or Windows metafile.
• Trace data - Saved as X-Y data pairs representing frequency and amplitude
points on the screen. The number of data pairs can vary. Modern spectrum
analyzers such as the ESA and PSA Series allow you to select the desired
display resolution by setting a minimum of 2 up to a maximum of 8192
display points on the screen. This data format is well suited for transfer
to a spreadsheet program on a computer.
• Instrument state - To keep a record of the spectrum analyzer settings,
such as center frequency, span, reference level, and so on, used in the
measurement. This is useful when documenting test setups used for
making measurements. Consistent test setups are essential for maintaining
repeatable measurements over time.
Most Agilent spectrum analyzers come with a copy of Agilent’s IntuiLink
software. This software lets you transfer instrument settings and trace data
directly to a Microsoft® Excel spreadsheet or Word document.
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Data transfer and remote instrument control
In 1977, Agilent Technologies (part of Hewlett-Packard at that time)
introduced the world’s first GPIB-controllable spectrum analyzer, the 8568A.
The GPIB interface (also known as HP-IB or IEEE-488) made it possible to
control all major functions of the analyzer and transfer trace data to an
external computer. This innovation paved the way for a wide variety of
automated spectrum analyzer measurements that were faster and more
repeatable than manual measurements. By transferring the raw data to a
computer, it could be saved on disk, analyzed, corrected, and operated on
in a variety of ways.
Today, automated test and measurement equipment has become the norm,
and nearly all modern spectrum analyzers come with a variety of standard
interfaces. The most common one remains GPIB, but in recent years,
Ethernet LAN connectivity has become increasingly popular, as it can
provide high data transfer rates over long distances and integrates easily
into networked environments such as a factory floor. Other standard
interfaces used widely in the computer industry are likely to become
available on spectrum analyzers in the future to simplify connectivity
between instrument and computer.
A variety of commercial software products are available to control spectrum
analyzers remotely over an I/O bus. You can also write your own software
to control spectrum analyzers in a number of different ways. One method is
to directly send programming commands to the instrument. Older spectrum
analyzers typically used proprietary command sets, but newer instruments,
such as Agilent’s ESA and PSA spectrum analyzers, use industry-standard
SCPI (standard commands for programmable instrumentation) commands.
A more common method is to use standard software drivers, such as
VXIplug&play drivers, which enable higher-level functional commands to the
instrument without the need for detailed knowledge of the SCPI commands.
Most recently, a new generation of language-independent instrument drivers,
known as “interchangeable virtual instrument,” or IVI-COM drivers, has
become available for the ESA and PSA families. The IVI-COM drivers are
based on the Microsoft Component Object Model standard and work in a
variety of PC application development environments, such as the Agilent
T&M Programmers Toolkit and Microsoft’s Visual Studio .NET.
Some applications require that you control the spectrum analyzer and
collect measurement data from a very long distance. For example, you may
want to monitor satellite signals from a central control room, collecting
data from remote tracking stations located hundreds or even thousands
of kilometers away from the central site. The ESA and PSA Series spectrum
analyzers have software options available to control these units, capture
screen images, and transfer trace data over the Internet using a standard
Web browser.
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Firmware updates
Modern spectrum analyzers have much more software inside them than
do instruments from just a few years ago. As new features are added to the
software and defects repaired, it becomes highly desirable to update the
spectrum analyzer’s firmware to take advantage of the improved performance.
The latest revisions of spectrum analyzer firmware can be found on the
Agilent Technologies website. This firmware can be downloaded to a file
on a local computer. A common method to transfer new firmware into the
spectrum analyzer is to copy the firmware onto several floppy disks that are
then inserted into the spectrum analyzer’s floppy disk drive. Some models,
such as the PSA Series, allow you to transfer the new firmware directly into
the spectrum analyzer using the Ethernet LAN port.
It is a good practice to periodically check your spectrum analyzer model’s
Web page to see if updated firmware is available.
Calibration, troubleshooting, diagnostics, and repair
Spectrum analyzers must be periodically calibrated to insure that the
instrument performance meets all published specifications. Typically, this
is done once a year. However, in between these annual calibrations, the
spectrum analyzer must be aligned periodically to compensate for thermal
drift and aging effects. Modern spectrum analyzers such as the ESA and
PSA Series have built-in alignment routines that operate when the instrument
is first turned on, and during retrace at predetermined intervals, or if the
internal temperature of the instrument changes. These alignment routines
continuously adjust the instrument to maintain specified performance.
In the past, spectrum analyzers normally had to be turned on in a stable
temperature environment for at least thirty minutes in order for the
instrument to meet its published specifications. The auto-alignment
capability makes it possible for the ESA and PSA spectrum analyzers to
meet published specifications within five minutes.
Modern spectrum analyzers usually have a service menu available. In
this area, you can perform useful diagnostic functions, such as a test of
the front panel keys. You can also display more details of the alignment
process, as well as a list of all optional hardware and measurement
personalities installed in the instrument. When a spectrum analyzer is
upgraded with a new measurement personality, Agilent provides a unique
license key tied to the serial number of the instrument. This license key
is entered through the front panel keypad to activate the measurement
capabilities of the personality.
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Summary
The objective of this application note is to provide a broad survey of basic
spectrum analyzer concepts. However, you may wish to learn more about
many other topics related to spectrum analysis. An excellent place to start
is to visit the Agilent Technologies Web site at www.Agilent.com and search
for “spectrum analyzer.”
Agilent Technologies Signal Analysis Division would like to dedicate this
application note to Blake Peterson, who recently retired after more than 46 years
of outstanding service in engineering applications and technical education for
Agilent customers and employees. One of Blake’s many accomplishments includes
being the author of the previous editions of Application Note 150. To our friend
and mentor, we wish you all the best for a happy and fulfilling retirement!
109
Glossary of Terms
Absolute amplitude accuracy: The uncertainty of an amplitude
measurement in absolute terms, either volts or power. Includes relative
uncertainties (see Relative amplitude accuracy) plus calibrator uncertainty.
For improved accuracy, some spectrum analyzers have frequency response
specified relative to the calibrator as well as relative to the mid-point
between peak-to-peak extremes.
ACPR: Adjacent channel power ratio is a measure of how much signal
energy from one communication channel spills over, or leaks into an adjacent
channel. This is an important metric in digital communication components
and systems, as too much leakage will cause interference on adjacent
channels. It is sometimes also described as ACLR, or adjacent channel
leakage ratio.
Amplitude accuracy: The uncertainty of an amplitude measurement. It can
be expressed either as an absolute term or relative to another reference point.
Amplitude reference signal: A signal of precise frequency and amplitude
that the analyzer uses for self-calibration.
Analog display: The technique in which analog signal information (from the
envelope detector) is written directly to the display, typically implemented
on a cathode ray tube (CRT). Analog displays were once the standard method
of displaying information on a spectrum analyzer. However, modern spectrum
analyzers no longer use this technique, but instead, use digital displays.
Average detection: A method of detection that sums power across a
frequency interval. It is often used for measuring complex, digitally
modulated signals and other types of signals with noise-like characteristics.
Modern Agilent spectrum analyzers typically offer three types of average
detection: power (rms) averaging, which measures the true average power
over a bucket interval; voltage averaging, which measures the average
voltage data over a bucket interval; and log-power (video) averaging, which
measures the logarithmic amplitude in dB of the envelope of the signal
during the bucket interval.
Average noise level: See Displayed average noise level.
Bandwidth selectivity: A measure of an analyzer’s ability to resolve
signals unequal in amplitude. Also called shape factor, bandwidth selectivity
is the ratio of the 60 dB bandwidth to the 3 dB bandwidth for a given
resolution (IF) filter. For some analyzers, the 6 dB bandwidth is used in
lieu of the 3 dB bandwidth. In either case, bandwidth selectivity tells us
how steep the filter skirts are.
Blocking capacitor: A filter that keeps unwanted low frequency signals
(including DC) from damaging circuitry. A blocking capacitor limits the
lowest frequency that can be measured accurately.
CDMA: Code division multiple access is a method of digital communication
in which multiple communication streams are orthogonally coded, enabling
them to share a common frequency channel. It is a popular technique
used in a number of widely used mobile communication systems.
Constellation diagram: A display type commonly used when analyzing
digitally modulated signals in which the detected symbol points are plotted
on an IQ graph.
110
Delta marker: A mode in which a fixed, reference marker has been
established and a second, active marker is available that we can place
anywhere on the displayed trace. A read out indicates the relative frequency
separation and amplitude difference between the reference marker and
the active marker.
Digital display: A technique in which digitized trace information, stored
in memory, is displayed on the screen. The displayed trace is a series of
points designed to present a continuous looking trace. While the default
number of display points varies between different models, most modern
spectrum analyzers allow the user to choose the desired resolution by
controlling the number of points displayed. The display is refreshed (rewritten
from data in memory) at a flicker-free rate; the data in memory is updated
at the sweep rate. Nearly all modern spectrum analyzers have digital flat
panel LCD displays, rather than CRT-based analog displays that were used
in earlier analyzers.
Display detector mode: The manner in which the signal information is
processed prior to being displayed on screen. See Neg peak, Pos peak,
Normal and Sample.
Digital IF: An architecture found in modern spectrum analyzers in which
the signal is digitized soon after it has been downconverted from an RF
frequency to an intermediate frequency (IF). At that point, all further signal
processing is done using digital signal processing (DSP) techniques.
Display dynamic range: The maximum dynamic range for which both the
larger and smaller signal may be viewed simultaneously on the spectrum
analyzer display. For analyzers with a maximum logarithmic display of
10 dB/div, the actual dynamic range (see Dynamic range) may be greater
than the display dynamic range.
Display scale fidelity: The uncertainty in measuring relative differences in
amplitude on a spectrum analyzer. The logarithmic and linear IF amplifiers
found in analyzers with analog IF sections never have perfect logarithmic
or linear responses, and thus introduce uncertainty. Modern analyzers with
digital IF sections have significantly better display scale fidelity.
Display range: The calibrated range of the display for the particular display
mode and scale factor. See Linear and Log display and Scale factor.
Displayed average noise level: The noise level as seen on the analyzer’s
display after setting the video bandwidth narrow enough to reduce the
peak-to-peak noise fluctuations such that the displayed noise is essentially
seen as a straight line. Usually refers to the analyzer’s own internally
generated noise as a measure of sensitivity and is typically specified in
dBm under conditions of minimum resolution bandwidth and minimum
input attenuation.
Drift: The very slow (relative to sweep time) change of signal position on
the display as a result of a change in LO frequency versus sweep voltage.
The primary sources of drift are the temperature stability and aging rate
of the frequency reference in the spectrum analyzer.
111
Dynamic range: The ratio, in dB, between the largest and smallest
signals simultaneously present at the spectrum analyzer input that can
be measured to a given degree of accuracy. Dynamic range generally refers
to measurement of distortion or intermodulation products.
Envelope detector: A circuit element whose output follows the envelope,
but not the instantaneous variation, of its input signal. In a superheterodyne
spectrum analyzer, the input to the envelope detector comes from the final
IF, and the output is a video signal. When we put our analyzer in zero span,
the envelope detector demodulates the input signal, and we can observe
the modulating signal as a function of time on the display.
Error vector magnitude (EVM): A quality metric in digital communication
systems. EVM is the magnitude of the vector difference at a given instant
in time between the ideal reference signal and the measured signal.
External mixer: An independent mixer, usually with a waveguide input
port, used to extend the frequency range of those spectrum analyzers
designed to utilize external mixers. The analyzer provides the LO signal
and, if needed, mixer bias. Mixing products are returned to the analyzer’s
IF input.
FFT (fast Fourier transform): A mathematical operation performed on
a time-domain signal to yield the individual spectral components that
constitute the signal. See Spectrum.
Flatness: See Frequency response.
Frequency accuracy: The uncertainty with which the frequency of a signal
or spectral component is indicated, either in an absolute sense or relative
to some other signal or spectral component. Absolute and relative frequency
accuracies are specified independently.
Frequency range: The minimum to maximum frequencies over which a
spectrum analyzer can tune. While the maximum frequency is generally
thought of in terms of an analyzer’s coaxial input, the range of many
microwave analyzers can be extended through use of external waveguide
mixers.
Frequency resolution: The ability of a spectrum analyzer to separate closely
spaced spectral components and display them individually. Resolution of
equal amplitude components is determined by resolution bandwidth. The
ability to resolve unequal amplitude signals is a function of both resolution
bandwidth and bandwidth selectivity.
Frequency response: Variation in the displayed amplitude of a signal as a
function of frequency (flatness). Typically specified in terms of ± dB relative
to the value midway between the extremes. Also may be specified relative
to the calibrator signal.
Frequency span: The frequency range represented by the horizontal axis
of the display. Generally, frequency span is given as the total span across
the full display. Some earlier analyzers indicate frequency span (scan width)
on a per-division basis.
112
Frequency stability: A general phrase that covers both short- and long-term
LO instability. The sweep ramp that tunes the LO also determines where a
signal should appear on the display. Any long term variation in LO frequency
(drift) with respect to the sweep ramp causes a signal to slowly shift its
horizontal position on the display. Shorter term LO instability can appear
as random FM or phase noise on an otherwise stable signal.
Full span: For most modern spectrum analyzers, full span means a frequency
span that covers the entire tuning range of the analyzer. These analyzers
include single band RF analyzers and microwave analyzers such as the ESA
and PSA Series that use a solid-state switch to switch between the low and
preselected ranges.
NOTE: On some earlier spectrum analyzers, full span referred to a sub-range.
For example, with the Agilent 8566B, a microwave spectrum analyzer that
used a mechanical switch to switch between the low and preselected ranges,
full span referred to either the low, non-preselected range or the high,
preselected range.
Gain compression: That signal level at the input mixer of a spectrum
analyzer at which the displayed amplitude of the signal is a specified number
of dB too low due just to mixer saturation. The signal level is generally
specified for 1 dB compression, and is usually between +3 and –10 dBm,
depending on the model of spectrum analyzer.
GSM: The global system for mobile communication is a widely used digital
standard for mobile communication. It is a TDMA-based system in which
multiple communication streams are interleaved in time, enabling them
to share a common frequency channel.
Harmonic distortion: Unwanted frequency components added to a signal
as the result of the nonlinear behavior of the device (e.g. mixer, amplifier)
through which the signal passes. These unwanted components are
harmonically related to the original signal.
Harmonic mixing: The utilization of the LO harmonics generated in a
mixer to extend the tuning range of a spectrum analyzer beyond the range
achievable using just the LO fundamental.
IF gain/IF attenuation: Adjusts the vertical position of signals on the
display without affecting the signal level at the input mixer. When changed,
the value of the reference level is changed accordingly.
IF feedthrough: A raising of the baseline trace on the display due to an
input signal at the intermediate frequency passing through the input mixer.
Generally, this is a potential problem only on non-preselected spectrum
analyzers. The entire trace is raised because the signal is always at the
IF, i.e. mixing with the LO is not required.
Image frequencies: Two or more real signals present at the spectrum
analyzer input that produce an IF response at the same LO frequency.
Because the mixing products all occur at the same LO and IF frequencies,
it is impossible to distinguish between them.
113
Image response: A displayed signal that is actually twice the IF away from
the frequency indicated by the spectrum analyzer. For each harmonic of the
LO, there is an image pair, one below and one above the LO frequency by the
IF. Images usually appear only on non-preselected spectrum analyzers.
Incidental FM: Unwanted frequency modulation on the output of a device
(signal source, amplifier) caused by (incidental to) some other form of
modulation, e.g. amplitude modulation.
Input attenuator: A step attenuator between the input connector and first
mixer of a spectrum analyzer. Also called the RF attenuator. The input
attenuator is used to adjust level of the signal incident upon the first mixer.
The attenuator is used to prevent gain compression due to high-level and/or
broadband signals and to set dynamic range by controlling the degree of
internally generated distortion. In some analyzers, the vertical position of
displayed signals is changed when the input attenuator setting is changed,
so the reference level is also changed accordingly. In modern Agilent
analyzers, the IF gain is changed to compensate for input attenuator
changes, so signals remain stationary on the display, and the reference
level is not changed.
Input impedance: The terminating impedance that the analyzer presents to
the signal source. The nominal impedance for RF and microwave analyzers
is usually 50 ohms. For some systems, e.g. cable TV, 75 ohms is standard.
The degree of mismatch between the nominal and actual input impedance
is given in terms of VSWR (voltage standing wave ratio).
Intermodulation distortion: Unwanted frequency components resulting
from the interaction of two or more spectral components passing through
a device with non-linear behavior (e.g. mixer, amplifier). The unwanted
components are related to the fundamental components by sums and
differences of the fundamentals and various harmonics, e.g. f1 ± f2, 2f1 ± f2,
2f2 ± f1, 3f1 ± 2f2, and so forth.
Linear display: The display mode in which vertical deflection on the display
is directly proportional to the voltage of the input signal. The bottom line
of the graticule represents 0 V, and the top line, the reference level, some
non-zero value that depends upon the particular spectrum analyzer. On
most modern analyzers, we select the reference level, and the scale factor
becomes the reference level value divided by the number of graticule
divisions. Although the display is linear, modern analyzers allow reference
level and marker values to be indicated in dBm, dBmV, dBuV, and in
some cases, watts as well as volts.
LO emission or feedout: The emergence of the LO signal from the
input of a spectrum analyzer. The level can be greater than 0 dBm on
non-preselected spectrum analyzers but is usually less than –70 dBm on
preselected analyzers.
114
LO feedthrough: The response on the display when a spectrum analyzer
is tuned to 0 Hz, i.e. when the LO is tuned to the IF. The LO feedthrough
can be used as a 0-Hz marker, and there is no frequency error.
Log display: The display mode in which vertical deflection on the display
is a logarithmic function of the voltage of the input signal. We set the
display calibration by selecting the value of the top line of the graticule,
the reference level, and scale factor in dB/div. On Agilent analyzers, the
bottom line of the graticule represents zero volts for scale factors of 10 dB/div
or more, so the bottom division is not calibrated in these cases. Modern
analyzers allow reference level and marker values to be indicated in dBm,
dBmV, dBuV, volts, and in some cases, watts. Earlier analyzers usually
offered only one choice of units, and dBm was the usual choice.
Marker: A visible indicator that we can place anywhere along the displayed
signal trace. A read out indicates the absolute value of both the frequency
and amplitude of the trace at the marked point. The amplitude value is given
in the currently selected units. Also see Delta marker and Noise marker.
Measurement range: The ratio, expressed in dB, of the maximum signal
level that can be measured (usually the maximum safe input level) to the
lowest achievable average noise level. This ratio is almost always much
greater than can be realized in a single measurement. See Dynamic range.
Mixing mode: A description of the particular circumstance that creates a
given response on a spectrum analyzer. The mixing mode, e.g. 1+, indicates
the harmonic of the LO used in the mixing process and whether the input
signal is above (+) or below (–) that harmonic.
Multiple responses: Two or more responses on a spectrum analyzer display
from a single input signal. Multiple responses occur only when mixing
modes overlap and the LO is swept over a wide enough range to allow
the input signal to mix on more that one mixing mode. Normally not
encountered in analyzers with preselectors.
Negative peak: The display detection mode in which each displayed point
indicates the minimum value of the video signal for that part of the
frequency span and/or time interval represented by the point.
Noise figure: The ratio, usually expressed in dB, of the signal-to-noise
ratio at the input of a device (mixer, amplifier) to the signal-to-noise ratio
at the output of the device.
Noise marker: A marker whose value indicates the noise level in a 1 Hz
noise power bandwidth. When the noise marker is selected, the sample
display detection mode is activated, the values of a number of consecutive
trace points (the number depends upon the analyzer) about the marker
are averaged, and this average value is normalized to an equivalent value
in a 1 Hz noise power bandwidth. The normalization process accounts
for detection and bandwidth plus the effect of the log amplifier when we
select the log display mode.
115
Noise sidebands: Modulation sidebands that indicate the short-term
instability of the LO (primarily the first LO) system of a spectrum analyzer.
The modulating signal is noise, in the LO circuit itself and/or in the LO
stabilizing circuit, and the sidebands comprise a noise spectrum. The mixing
process transfers any LO instability to the mixing products, so the noise
sidebands appear on any spectral component displayed on the analyzer
far enough above the broadband noise floor. Because the sidebands are
noise, their level relative to a spectral component is a function of resolution
bandwidth. Noise sidebands are typically specified in terms of dBc/Hz
(amplitude in a 1 Hz bandwidth relative to the carrier) at a given offset from
the carrier, the carrier being a spectral component viewed on the display.
Phase noise: See Noise sidebands.
Positive peak: The display detection mode in which each displayed point
indicates the maximum value of the video signal for that part of the
frequency span and/or time interval represented by the point.
Preamplifier: An external, low noise-figure amplifier that improves system
(preamplifier/spectrum analyzer) sensitivity over that of the analyzer itself.
Preselector: A tunable bandpass filter that precedes the input mixer of
a spectrum analyzer and tracks the appropriate mixing mode. Preselectors
are typically used only above 2 GHz. They essentially eliminate multiple and
image responses and, for certain signal conditions, improve dynamic range.
Quasi-peak detector (QPD): A type of detector whose output is a function
of both signal amplitude as well as pulse repetition rate. The QPD gives
higher weighting to signals with higher pulse repetition rates. In the limit,
a QPD will exhibit the same amplitude as a peak detector when measuring
a signal with a constant amplitude (CW) signal.
Raster display: A TV-like display in which the image is formed by scanning
the electron beam rapidly across and slowly down the display face and
gating the beam on as appropriate. The scanning rates are fast enough to
produce a flicker-free display. Also see Vector display and Sweep time.
Reference level: The calibrated vertical position on the display used as
a reference for amplitude measurements. The reference level position is
normally the top line of the graticule.
Relative amplitude accuracy: The uncertainty of an amplitude
measurement in which the amplitude of one signal is compared to the
amplitude of another regardless of the absolute amplitude of either.
Distortion measurements are relative measurements. Contributors to
uncertainty include frequency response and display fidelity and changes
of input attenuation, IF gain, scale factor, and resolution bandwidth.
Residual FM: The inherent short-term frequency instability of an oscillator
in the absence of any other modulation. In the case of a spectrum analyzer,
we usually expand the definition to include the case in which the LO is
swept. Residual FM is usually specified in peak-to-peak values because
they are most easily measured on the display, if visible at all.
116
Residual responses: Discrete responses seen on a spectrum analyzer display
with no input signal present.
Resolution: See Frequency resolution.
Resolution bandwidth: The width of the resolution bandwidth (IF) filter
of a spectrum analyzer at some level below the minimum insertion loss
point (maximum deflection point on the display). For Agilent analyzers,
the 3 dB bandwidth is specified; for some others, it is the 6 dB bandwidth.
Rosenfell: The display detection mode in which the value displayed at each
point is based upon whether or not the video signal both rose and fell during
the frequency and/or time interval represented by the point. If the video
signal only rose or only fell, the maximum value is displayed. If the video
signal did both rise and fall, then the maximum value during the interval is
displayed by odd-numbered points, the minimum value, by even-numbered
points. To prevent the loss of a signal that occurs only in an even-numbered
interval, the maximum value during this interval is preserved, and in the
next (odd-numbered) interval, the displayed value is the greater of either
the value carried over or the maximum that occurs in the current interval.
Sample: The display detection mode in which the value displayed at each
point is the instantaneous value of the video signal at the end of the
frequency span and/or time interval represented by the point.
Scale factor: The per-division calibration of the vertical axis of the display.
Sensitivity: The level of the smallest sinusoid that can be observed on a
spectrum analyzer, usually under optimized conditions of minimum
resolution bandwidth, 0 dB RF input attenuation, and minimum video
bandwidth. Agilent defines sensitivity as the displayed average noise level.
A sinusoid at that level will appear to be about 2 dB above the noise.
Shape factor: See Bandwidth selectivity.
Signal identification: A routine, either manual or automatic, that indicates
whether or not a particular response on the spectrum analyzer’s display
is from the mixing mode for which the display is calibrated. If automatic,
the routine may change the analyzer’s tuning to show the signal on the
correct mixing mode, or it may tell us the signal’s frequency and give us
the option of ignoring the signal or having the analyzer tune itself properly
for the signal. Generally not needed on preselected analyzers.
Span accuracy: The uncertainty of the indicated frequency separation of
any two signals on the display.
Spectral purity: See Noise sidebands.
Spectral component: One of the sine waves comprising a spectrum.
117
Spectrum: An array of sine waves of differing frequencies and amplitudes
and properly related with respect to phase that, taken as a whole, constitute
a particular time-domain signal.
Spectrum analyzer: A device that effectively performs a Fourier transform
and displays the individual spectral components (sine waves) that constitute
a time-domain signal. Phase may or may not be preserved, depending upon
the analyzer type and design.
Spurious responses: The improper responses that appear on a spectrum
analyzer display as a result of the input signal. Internally generated
distortion products are spurious responses, as are image and multiple
responses.
Sweep time: The time to tune the LO across the selected span. Sweep
time does not include the dead time between the completion of one sweep
and the start of the next. In zero span, the spectrum analyzer’s LO is fixed,
so the horizontal axis of the display is calibrated in time only. In non-zero
spans, the horizontal axis is calibrated in both frequency and time, and
sweep time is usually a function of frequency span, resolution bandwidth,
and video bandwidth.
Time gating: A method of controlling the frequency sweep of the spectrum
analyzer based on the characteristics of the signal being measured. It is
often useful when analyzing pulsed or burst modulated signals; time
multiplexed signals, as well as intermittent signals.
TDMA: Time division multiple access is a digital communication method
in which multiple communication streams are interleaved in time, enabling
them to share a common frequency channel.
Units: Dimensions of the measured quantities. Units usually refer to
amplitude quantities because they can be changed. In modern spectrum
analyzers, available units are dBm (dB relative to 1 milliwatt dissipated
in the nominal input impedance of the analyzer), dBmV (dB relative to
1 millivolt), dBuV (dB relative to 1 microvolt), volts, and in some analyzers,
watts. In Agilent analyzers, we can specify any units in both log and
linear displays.
Vector diagram: A display type commonly used when analyzing digitally
modulated signals. It is similar to a constellation display, except that in
addition to the detected symbol points, the instantaneous power levels
during state transitions are also plotted on an IQ graph.
Vector display: A display type used in earlier spectrum analyzer designs,
in which the electron beam was directed so that the image (trace, graticule,
annotation) was written directly on the CRT face, not created from a series
of dots as in the raster displays commonly used today.
118
Video: In a spectrum analyzer, a term describing the output of the envelope
detector. The frequency range extends from 0 Hz to a frequency typically
well beyond the widest resolution bandwidth available in the analyzer.
However, the ultimate bandwidth of the video chain is determined by the
setting of the video filter.
Video amplifier: A post-detection, DC-coupled amplifier that drives the
vertical deflection plates of the CRT. See Video bandwidth and Video filter.
Video average: A digital averaging of a spectrum analyzer’s trace
information. The averaging is done at each point of the display independently
and is completed over the number of sweeps selected by the user. The
averaging algorithm applies a weighting factor (1/n, where n is the number
of the current sweep) to the amplitude value of a given point on the current
sweep, applies another weighting factor [(n – 1)/n] to the previously
stored average, and combines the two for a current average. After the
designated number of sweeps are completed, the weighting factors remain
constant, and the display becomes a running average.
Video bandwidth: The cutoff frequency (3 dB point) of an adjustable low
pass filter in the video circuit. When the video bandwidth is equal to or less
than the resolution bandwidth, the video circuit cannot fully respond to
the more rapid fluctuations of the output of the envelope detector. The
result is a smoothing of the trace, i.e. a reduction in the peak-to-peak
excursion of broadband signals such as noise and pulsed RF when viewed
in the broadband mode. The degree of averaging or smoothing is a function
of the ratio of the video bandwidth to the resolution bandwidth.
Video filter: A post-detection, low-pass filter that determines the
bandwidth of the video amplifier. Used to average or smooth a trace.
See Video bandwidth.
Zero span: That case in which a spectrum analyzer’s LO remains fixed
at a given frequency so the analyzer becomes a fixed-tuned receiver. The
bandwidth of the receiver is that of the resolution (IF) bandwidth. Signal
amplitude variations are displayed as a function of time. To avoid any loss
of signal information, the resolution bandwidth must be as wide as the
signal bandwidth. To avoid any smoothing, the video bandwidth must be
set wider than the resolution bandwidth.
119
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Printed in U.S.A., April 27, 2004
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