### Understanding the Decibel in Audio Measurements AN

```Keysight U8903A
Understanding the Decibel in
Audio Measurements
Application Note
Introduction
The decibel in audio measurement
In the radio frequency (RF) microwave test and measurement world, engineers often deal with the
power measurement unit of dBm instead of wattage, which is commonly known as watt (W). However,
engineers entering the audio measurement arena will need to understand one more
measurement unit known as dBu, which is decibel (dB) relative to 1 mW into 600 Ω. This application
note explains dBu and provides useful tips to assist you in accurately making and understanding audio
measurements.
03 | Keysight | U8903A Understanding the Decibel in Audio Measurements - Application Note
Rule of thumb
– For 50 Ω system
– dBV = dBm – 13 dB
– dBmV = dBm + 47 dB
– dBuV = dBm + 107 dB
– For 75 Ω system
– dBV = dBm – 11.25 dB
– dBmV = dBm + 48.75 dB
– dBuV = dBm + 108.75 dB
– For 600 Ω system
– dBV = dBm – 2.22 dB
– dBmV = dBm + 57.78 dB
– dBuV = dBm + 117.78 dB
Back to Basics
Understanding the decibel
(dB)
The decibel is a very commonly used
yet often misunderstood unit of
measurement. The “bel” in “decibel”
comes from the name of Alexander
Graham Bell. He was interested
in the way in which the human ear
responds to sound intensity. He used
a logarithmic scale to express this
sound intensity, in which range from
the softest sound to the loudest
(threshold of pain) sound, is one to a
billion (1012) or zero to 12 bels. The
decibel is one tenth of a “bel” and
is abbreviated as dB.
There are two primary benei ts to
using dB. The i rst is to express
very large or very small ratios in a
compact way; for example, +63 dB to
–153 dB is more concise than 2 x 106
to 0.5 x 10–15. Another advantage is
apparent when comparing quantities
used to multiply the gain or divide the
loss of several cascaded devices. dB
simplii es the mathematic process,
in that multiplication of numeric gain
is replaced by addition, and division
of numeric attenuation is replaced by
subtraction.
Deinition of decibel (dB)
dB is a logarithmic unit expressing
the ratio of two quantities. In power
measurement, the relative power is
deined as
and in voltage measurement, the
relative voltage is deined as
To describe dB as an absolute value,
a reference point must be known.
There are a number of different reference points, as dei ned below:
– dBm represents the power level
P1 with reference to 1 mW
– dBW represents the power level
P1 with reference to 1 W
– dBV represents the power level
V1 with reference to 1 Vrms
– dBmV represents the power level
V1 with reference to 1 mVrms
– dBuV represents the power level
V1 with reference to 1 uVrms
dBm is the most commonly used unit
in power measurement. For instance,
if an engineer is working in a known
industry standard environment, the
impedance of the test system is
usually 50 Ω in RF engineering, 75 Ω
in television engineering, and 600 Ω
in audio engineering. A conversion
formula will help engineers to convert
power measurement of dBm to any
unit of dBV, dBmV, or dBuV. Refer
to the rule of thumb shown on the
column on the left.
04 | Keysight | U8903A Understanding the Decibel in Audio Measurements - Application Note
Introduction to U8903A
The U8903A is a digital signal processing (DSP) based audio measurement system that combines both an
audio generator and analyzer. This
test set consists of two channels
each for the audio generator and
analyzer, and the output and input
conigurations are fully independent
of each other.
The U8903A audio generator has a
frequency range of 5 Hz to 80 kHz,
and the sine wave amplitude range
can cover from 0 Vrms to 8 Vrms
(11.3 Vp) for the unbalanced test
output coniguration and 0 Vrms to
16 Vrms (22.6 Vp) for the balanced
output coniguration. When using the
audio generator, you can generate
not only a basic sine waveform, but
also square, dual sine, variable phase,
noise, DC, multitone, and arbitrary
waveforms.
The U8903A audio analyzer has a
frequency measurement range of 10
Hz to 100 kHz with an amplitude
measurement range of <1 μVrms to
140 Vrms (200 Vp). In addition, the
U8903A is equipped with frequency
and time domain graph functions, as
well as sweep capability for frequency, amplitude, and phase. This allows
you to perform a wide range of audio
parameter measurements consisting
of voltage; frequency; total harmonics distortion, plus noise (THD + N);
signal-to-noise ratio (SNR); noise
level; SMPTE inter-modulation distortion; difference frequency distortion
(DFD); phase; and crosstalk.
The U8903A also supports the industrial standard of instrument connectivity such as GPIB, USB, and LAN.
Figure 1. Keysight U8903A audio analyzer front and rear panel view
05 | Keysight | U8903A Understanding the Decibel in Audio Measurements - Application Note
Features of U8903A
Audio generator
– Frequency range: 5 Hz to 80 kHz
– Amplitude range:
– 0 Vrms to 8 Vrms (11.3 Vp) for
the unbalanced output
– 0 Vrms to 16 Vrms (22.6 Vp) for
the balanced output
– Waveforms:
– Sine
– Dual sine (SMPTE IMD, DFD)
– Square
– Variable phase
– Noise
– DC
– Multi-tones generation
– User-deined arbitrary waveforms
– Output connector:
– Balanced (XLR)
– Unbalanced (BNC)
– Output impedance:
– 50 Ω
– 600 Ω
Audio analyzer
– Frequency range: 10 Hz to 100 kHz
– Amplitude range: <1 μVrms to
140 Vrms (200 Vp)
– Input connector:
– Balanced (XLR)
– Unbalanced (BNC)
– Input coupling:
– DC
– AC
– Input ranging:
– Auto
– Manual
– Filters/bandwidth:
– Low pass (none/15 kHz/20
kHz/30 kHz/custom)
– High pass (none/22 Hz/100
Hz/400 Hz/custom)
– Weighting (A-weighting/CCIR
1k/CCIR 2k/C-Message/CCITT/
custom)
– Detectors:
– RMS
– Peak-to-peak
– Quasi Peak
– Measurement:
– AC level
– DC level
– Frequency
– Phase
– THD+N (ratio)
– THD+N (level)
– SNR
– Noise level
– SMPTE IMD
– DFD
– Cross talk
– Sweep capability:
– Voltage
– Frequency
– Phase
– Graph display views of the input
signals:
– Time domain
– Frequency domain
– Selectable measurement time
– Trigger mode:
– Free run
– External
– GPIB, LAN, and USB remote
interface
06 | Keysight | U8903A Understanding the Decibel in Audio Measurements - Application Note
dBu (dB relative to 1 mW into 600 Ω)
The Keysight U8903A audio analyzer is a complete audio measurement system that combines a
low-distortion signal source with a
signal analyzer. The signal source
has a selectable output impedance
of either 50 W or 600 W. For most
impedance uses only 50 Ω, but for
audio test applications the 600 Ω
source impedance is more commonly
used. In audio test applications, the
engineer has to consider another
decibel formula in the unit of voltage
measurement: dBu. dBu is deined
as dB relative to 1 mW into 600 Ω. It
is a logarithmic unit expressing the
relative voltage measurement with
reference to a voltage value of
0.7746 Vrms (voltage drops across
600 Ω that results in 1 mW of power).
Maximum output power
As mentioned earlier, 50 Ω is the
most commonly used source impedance. 50 Ω source impedance can
result in higher short-circuit current (for a constant voltage), and 10
times the frequency response over a
given length of cable than with 600 Ω
source impedance.
The U8903A has the maximum voltage source for unbalanced output
(Vs) of 8 V, and the following igures illustrate the maximum power
transfer the U8903A can deliver into
using the source impedance of 50 Ω
or 600 Ω.
From dBm deinition:
dBm = 10 log10 P1 ,
1mW
if a 600 Ω load results in 0 dBm
\ V = √600 × 0.001 = 0.7746Vrms
and,
dBV = 20 log10
V1
1Vrms
\ dBu = 20 log10
V1
0.7746Vrms
The “u” in dBu comes from the word
“unloaded”. It also implies that the
impedance is unspeciied and is likely
to be high. Thus, the 0.7746 Vrms is
an open circuit source.
1
Source and load impedance (50 Ω for both)
Vs
AC
Source
600 W
50 W
VL =
Output impedance
switch
VL
50 W
RL
50
×8V=4V
50 + 50
IL = 80 mA
P50W = 25.1 dBm
2
Source impedance of 50 Ω and load impedance of 600 Ω
Vs
AC
Source
600 W
50 W
Output impedance
switch
VL
600 W
VL =
RL
600 × 8 V = 7.385V
600 + 50
IL = 12.3 mA
P600W = 19.6 dBm
07 | Keysight | U8903A Understanding the Decibel in Audio Measurements - Application Note
Maximum output power (continued)
3
Source impedance of 600 Ω and load impedance of 600 Ω
Vs
AC
Source
4
600 W
50 W
600 × 8 V = 4 V
600 + 600
IL = 6.67 mA
VL =
Output impedance
switch
VL
600 W
RL
P600W = 14.3 dBm
Source impedance of 600 Ω and load impedance of 50 Ω
Vs
AC
Source
600 W
50 W
50 × 8 V = 0.615 V
50 + 600
IL = 12.3 mA
VL =
Output impedance
switch
VL
50 W
Understanding output
voltage
of DSP-based RF test equipments,
some RF engineers are able to perform audio measurements on RF instruments and then correlate the test
results with other audio instruments.
Sometimes engineers encounter
problems with their RF signal analyzer when measuring two different
sources of supply that are identical in
stimulus setup: for example, output
frequency (FL) and output voltage
(VL). The RF signal analyzer receives
very divergent measurement results
that show both inputs are unequal in
amplitude or bandwidth. Scenarios 1
and 2 illustrate these situations.
RL
P50W = 8.8 dBm
Scenario 1
One signal generator that combines audio signal and RF carrier with
50 Ω output source impedance (see Figure 1).
One signal generator
combining baseband and RF
with 50 Ω source impedance
Figure 1. Signal analyzer results for scenario 1
RF signal analyzer
impedance
08 | Keysight | U8903A Understanding the Decibel in Audio Measurements - Application Note
Understanding output voltage (continued)
Scenario 2
Two standalone audio generator and one RF modulator (see Figure 2).
Audio generator with 600 Ω
output source impedance by
default
RF modulator
with 50 Ω source
impedance
RF signal analyzer
impedance
Figure 2. Signal analyzer results for scenario 2
Due to the default setting of the audio generator, its source impedance has to be set to 600 Ω. Therefore, the output
voltage VL for scenario 2 is no longer equal to scenario 1.
The correct output voltage (VL) for both scenarios is shown below.
Scenario 1
One signal generator that combines audio signal and RF carrier with 50 Ω output source impedance.
Vs
600 W
AC
Source
50 W
Audio source
VL
50 W
RL
RF signal generator
VL = 1 VS
2
Figure 3. Voltage delivered to RF signal generator
09 | Keysight | U8903A Understanding the Decibel in Audio Measurements - Application Note
Scenario 2
Two standalone audio generator and
one RF modulator.
Vs’
600 W
AC
Source
50 W
Audio generator
VL’
50 W
RL
RF modulator
VL’ = 1 VS’
13
In order to match these two scenarios
and to get an equal voltage output,
VL’ must be equal to VL. Therefore,
the source voltage output in scenario
2 must be set to
Figure 4. Voltage delivered to RF modulator
VS’ = 13 VS
2
Case study
If an engineer sets the voltage output
of an audio generator that comes with
a ixed source impedance of 50 Ω, VS
= 2 V (8.24 dBu), then its voltage will
drop across at 50 Ω load impedance,
VL = 1 V (see Figure 3).
If the engineer sets up another output
of an audio generator with source
impedance of 600 Ω, then in order to
get the output performance similar
to the previous 50 Ω system, the
engineer needs to set a higher output
voltage of VS’ = 13 V (24.5 dBu).
Therefore, it will also deliver VL’ = 1
V to the same 50 Ω load impedance
(see Figure 4).
dBu (in 50 Ω) to dBu (in 600 Ω)
conversion is a technique for verifying and conirming that the source
impedance of the audio analyzer is
the reason for the divergent measurement results in the RF signal analyzer.
As a rule of thumb, dBu (in 600 Ω) =
dBu (in 50 Ω) + 16.26 dB.
The U8903A comes with a switchable
source impedance of 50 Ω or 600 Ω.
Once the engineer has veriied and
conirmed the root cause, he or she
just needs to modify the setting of the
output source impedance in order to
get the appropriate
output voltage.
10 | Keysight | U8903A Understanding the Decibel in Audio Measurements - Application Note
Summary
This application note is not intended as a textbook, but rather
to refresh engineers’ knowledge
of the decibel and to provide an
introduction to new users of the
U8903A in audio measurement.
It is important that every engineer reviews these concepts,
understand, familiarize these
measurements from time-totime. This basic review will help
many engineers carry out their
more effectively and eficiently
in various test applications such
as those in manufacturing environment, R&D design, and QA
inspection.
Related Keysight Literatures
Publication title
Pub number
U8903A Audio Analyzer Data Sheet
5990-3831EN
U8903A Audio Analyzer User’s Guide
U8903-90002
U8903A Audio Analyzer Quick Start Guide
U8903-90006
U8903A Audio Analyzer Programmer’s Reference
U8903-90027
Migrating Code from the 8903B to U8903A, Application Note
5990-4135EN
8903B Audio Analyzer 20 Hz to 100 kHz Product Overview
5980-2701
8903B Audio Analyzer: 8903E Distortion Analyzer Technical
Speciications
5968-1390E
8903B Audio Analyzer: 8903E Distortion Analyzer Product Brochure
5953-8429
8903B Audio Analyzer Operation and Calibration Manual
08903-90079
8903B Audio Analyzer Service Manual Volume 1 & 2
08903-90062
11 | Keysight | U8903A Understanding the Decibel in Audio Measurements - Application Note
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