Keysight Technologies Digital Communication Analyzer (DCA

Keysight Technologies
Digital Communication
Analyzer (DCA),
Measure Relative
Intensity Noise (RIN)
Application Note
Introduction
Laser intensity noise can be one of the limiting factors in the transmission of
analog or digital signals. It can reduce the signal-to-noise ratio and increase the
bit error rate, therefore degrading system performance. Laser intensity noise can
vary significantly depending on the properties of the laser, back reflections, and
optical or electrical filters after the optical/electrical (O/E) conversion. In order to
optimize communication links it is essential to accurately characterize the laser
intensity noise, compare it with the signal strength, and if necessary allow an
appropriate power budget.
Chapter 1 provides some background on laser intensity noise and how it affects
the noise of the received signal. It also explains common Relative Intensity Noise
(RIN) definitions.
Chapter 2 looks at the specifics of how the Keysight Technologies, Inc. 86100C
Infiniium DCA acquires data and characterizes RIN. It also describes the exact
sequence of steps and keystrokes for manual operation and lists useful hints and
caveats for typical measurement situations.
Chapters 3, 4 and 5 show alternative RIN measurements based on RF power
meters (IEEE 802.3ae method), electrical spectrum analyzers (Keysight 71400C
LSA method), and optical spectrum analyzers (Keysight 86142A OSA method).
Chapter 6 compares actual measurements using the different methods and
discusses potential challenges and limitations.
The appendix contains a collection of formulas, conversion tables and physical
constants that the reader might find useful when measuring RIN and other
parameters.
3 | Keysight | Digital Communication Analyzer (DCA), Measure Relative Intensity Noise (RIN) - Application Note
Table of Contents
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 02
Laser Intensity Fluctuations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 04
Oscilloscope Based Measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 07
Block diagram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 07
Measurement procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 08
Setups using square-wave patterns . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
RIN calculations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
RF Power Meter Based Measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
Block diagram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
Measurement procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
RIN calculations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
Electrical Spectrum Analyzer Based Measurements . . . . . . . . . . . . . . . . . . . . . . . . . . 17
Block diagram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
Alternative setups . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
Measurement procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
RIN calculations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
Optical Spectrum Analyzer Based Measurements. . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
Block diagram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
Measurement procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
RIN calculations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
RIN Measurement Comparisons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
Adjustable RIN source . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
DCA-J versus OSA comparison using the adjustable RIN source . . . . . . . . 22
DCA-J versus ESA comparison using an EML Source . . . . . . . . . . . . . . . . . 23
Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
Definitions and electrical-optical relationships . . . . . . . . . . . . . . . . . . . . . . . 25
Photodetector terminology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
Laser source terminology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
Modulation terminology. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
Noise terms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
Conversions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
Physical constants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
4 | Keysight | Digital Communication Analyzer (DCA), Measure Relative Intensity Noise (RIN) - Application Note
Laser Intensity
Fluctuations
In a receiver, laser intensity fluctuations can create noise that exceeds the thermal
noise of the load impedance and/or the shot noise of the photodetector. It therefore can become a limiting factor for the power budget of an optical link. If so, then
careful characterization of such fluctuations becomes essential to optimize system
performance.
Intensity fluctuations come primarily from the spectral properties of a laser. At very
low power levels a laser emits mostly spontaneous emission which, similar to the
light coming from an LED, covers a range of wavelengths. Above its lasing threshold,
a laser emits mostly stimulated emission and only a small amount of spontaneous
emission1. The stimulated emission is concentrated at or around one wavelength
and contains most of the power used for sending information along an optical fiber
(Figure 1). In a photodetector the stimulated emission interacts with any residual
spontaneous emission, effectively creating noise that can be observed electrically.
Most photodetectors create an output current that is proportional to the optical
power which in turn is proportional to the square of the electrical field. Because of
this nonlinear relationship between optical field strength and photodetector current,
photons with different optical frequencies create "beat signals" similar to the process happening in electrical nonlinear devices with multiple signals at their input (for
example, the mixer in a radio).
The stimulated emission (i.e., signal) in Figure 1 "beats" with the spontaneous emission right under it 2, and the spontaneous emission beats with itself. However, with
today's semiconductor lasers and in the absence of optical amplifiers the spontaneous-spontaneous beat noise is much smaller than the stimulated-spontaneous beat
noise and usually can be ignored.
Mkr 1(A)
1556.68 nm
-5.300 dBm
Center
1556.66 nm
-5.287 dBm
OSNR
47.213 dB/nm
10.00
REF: 0.00 dBm
dBm
-10.00
-30.00
10.00
dB/div
-50.00
-70.00
-90.00
RBW:
VBW:
1546.68
1 nm
194 Hz
nm
Sens: -80.00 dBm
ST:
1.25 3
1556.68
Avg:
Off
2.00 nm/div
In Vac
03:57PM
02 Jun 2004
1566.68
Figure 1. Distributed feedback (DFB) laser spectrum
The amount of beat noise generated in the photodetector depends on the receiver's
properties, particularly its bandwidth, and it matters only if it exceeds the noise in the
electronics. Therefore it makes more sense to characterize the effects of laser intensity fluctuations on the electrical signal after the optical/electrical (O/E) conversion.
1. The threshold is defined as the power above
which the stimulated emission exceeds the
spontaneous emission.
2. The frequency of the beat signal found in the
photocurrent is the difference between the
optical frequencies of the photons.
Relative Intensity Noise (RIN) describes the contributions of the laser intensity fluctuations to the electrical noise in the receiver relative to the signal power observed electrically. In general, RIN is normalized to a 1 Hz bandwidth so that it becomes easier to
compare laser intensity fluctuations when using receivers with different bandwidths.
5 | Keysight | Digital Communication Analyzer (DCA), Measure Relative Intensity Noise (RIN) - Application Note
Laser Intensity
Fluctuations
(continued)
The traditional definition of RIN (measured in 1/Hz or dB [1 Hz]) is the ratio
of the noise power N normalized to a 1 Hz bandwidth, and the average power PI
of the photocurrent – both observed electrically in the load impedance seen
by the photodetector. This definition of RIN requires either an unmodulated
laser, or an instrument that can accurately measure both N and PI within the
modulation pattern, such as the Keysight 86100C Infiniium DCA-J.
Equation 1
N Electrical noise power (observed in the load impedance)
PI Photo current power (observed in the load impedance)
BN Noise bandwidth
IEEE 802.3ae defines RIN OMA (1/Hz or dB [1Hz]) as the ratio of the
electrically observed noise power N normalized to a 1 Hz bandwidth and the
electrical power PMOD of a square wave modulation dissipated in the load:
Equation 2
Navg PMOD BN Average electrical noise power (observed in the load impedance)
Modulation power (observed in the load impedance)
Noise bandwidth
If the average optical power remains the same and if the extinction ratio is
very high then both definitions yield approximately the same result. The
86100C Infiniium DCA-J can measure RIN OMA as well as RIN for the "1"
level. In the latter case, the DCA-J result is equivalent to the RIN of an
unmodulated laser with the optical power of the "1" level. For high extinction
ratios this level is almost 3 dB above the average optical power of the
modulated signal.
6 | Keysight | Digital Communication Analyzer (DCA), Measure Relative Intensity Noise (RIN) - Application Note
The electrical noise on the "1" level of a modulated signal is the same as the
noise observed on an unmodulated signal with the same power as the "1" level.
Due to its advanced triggering the 86100C can separate the power and noise
levels between the "1"s and "0"s. It therefore can measure RIN as well as RIN
OMA.
P1(opt)
P(opt)
OMA
(continued)
Figure 2 illustrates the conceptual differences between RIN and RIN OMA:
RIN measurements occur on unmodulated signals, and therefore relate the
electrical noise power N caused by the noise current in the load to the signal
power dissipated in the load. RIN OMA measurements occur on modulated
signal, and they relate the average electrical noise power to the electrical
power of the modulation.
P unmodulated
Laser Intensity
Fluctuations
P(avg
P0(opt)
0
0
Noise
Noise
Figure 2. Conceptual difference between RIN (left) and RIN OMA (right) (Top: optical signal,
bottom: noise current)
7 | Keysight | Digital Communication Analyzer (DCA), Measure Relative Intensity Noise (RIN) - Application Note
Oscilloscope Based
Measurements
The Keysight 86100C Infiniium DCA-J is a sampling oscilloscope with advanced
trigger and pattern lock capabilities. It allows amplitude measurements in the
traditional oscilloscope mode, such as optical modulation amplitude on square
wave patterns (Figure 3). In Jitter Mode it can lock onto patterns that are up
to 216 bits long and then separate random effects from interference. It can
therefore accurately measure RIN on a variety of patterns, including square
waves and industry-standard PRBS patterns.
Figure 3. OMA measurement on a square-wave signal
Block diagram
In order to measure RIN, the oscilloscope-based method needs a digitally
modulated signal. A pattern generator running at the nominal bit rate
modulates the device under test (DUT). In order to see the worst-case
intensity fluctuations due to reflections back to the DUT, use a polarization
controller, optical power splitter, and a reflector (these components are
optional if the target system has excellent return loss values).
86100C
Infiniium DCA-J
Polarization
controller
Single-mode coupler
DUT
Square wave or
0000011111 or
PRBS source
Adjustable
reflector
Figure 4. Keysight 86100C Infiniium DCA-J based setup1
1. Requires firmware revision 7.0 or higher and
Options 001, 200, 300
8 | Keysight | Digital Communication Analyzer (DCA), Measure Relative Intensity Noise (RIN) - Application Note
Oscilloscope Based
Measurements
(Continued)
In order to separate random noise from distortions such as overshoot, ringing,
or inter-symbol interference the pattern should be either a sequence of at
least five "0"s followed by the same amount of "1"s (effectively a square wave),
or a PRBS pattern such as 27–1 to 210 –1. Longer patterns (up to 216 –1) will
work as well. However, they usually increase the measurement time without
noticeably changing the RIN result.
The Keysight 86100C Infiniium DCA-J can detect subsequent "1"s and "0"s in
any pattern and therefore measure random fluctuations in the middle of such
a sequence (see Figure 5). Leading and trailing bits of the same value help to
separate inter-symbol interference and other pattern-dependent issues from
the sampling point.
Sampling Point
Bit
–3
–2
–1
0
1
2
3
Figure 5. Sample point to measure random amplitude variations
We'll take advantage of this feature so that we accurately measure only the
random noise on the "1" and "0" levels (as well as the "1" and "0" powers)
before calculating RIN or RIN OMA.
Measurement procedure
1. The pattern length should not be an integer
multiple of the dividend, e.g. do not use 27
(128) if your trigger is a divided clock such as
1/2, 1/4, etc. of your bit rate. Otherwise you
may get incomplete eyes or inaccurate results.
–– If simulating reflections is important then substitute the DUT in Figure 4 with an
Keysight 8161xA Return Loss Meter and adjust the reflection to the worst case
allowed in the intended transmission system.
–– Connect the DUT (laser/transceiver) and turn the modulation on. Use a PRBS
pattern such as 2N–1 (N = 7 to 16), or a square wave consisting of at least five "0"s
followed by the same number of "1"s.
–– Verify that the DCA-J receives a good signal: press DEFAULT SETUP, then
OSCILLOSCOPE MODE and finally AUTOSCALE. The instrument will warn you if the
optical signal is too small or if it cannot find a useful trigger signal.
–– If your clock exceeds 3.2 GHz then check the GENERAL TRIGGER SETUP: click on
the TRIG button at the lower-right of the screen and select the "DIVIDED (3 to
13 GHz)" trigger mode (Figure 6).
Figure 6. Trigger setup for trigger signals > 3.2 GHz1
9 | Keysight | Digital Communication Analyzer (DCA), Measure Relative Intensity Noise (RIN) - Application Note
Oscilloscope Based
Measurements
–– In order to have a well-defined low-pass frequency response click on
the appropriate vertical channel button at the bottom of the screen
and activate the desired filter:
(Continued)
Figure 7. Reference receiver filter setting
–– Now you should see an eye diagram like the one in Figure 8 on the
left. If not, chances are the oscilloscope isn't correctly triggered.
To verify, select FREE RUN in the menu in Figure 6 and press AUTO
SCALE. If there was a signal but no trigger then the screen shows a
band of random samples. Without any signal there would be just a
flat line.
Figure 8. PRBS eye diagram in oscilloscope mode (left: triggered, right: free run)
10 | Keysight | Digital Communication Analyzer (DCA), Measure Relative Intensity Noise (RIN) - Application Note
Oscilloscope Based
Measurements
(Continued)
–– Activate JITTER MODE. Click on the arrow pointing up to lift the shade
with all the graphs. Pick the AMPLITUDE measurement group on the
left and select AMPLITUDE RESULTS (Figure 9):
Figure 9. RIN "1' level result in jitter mode
–– Click on "SETUP & INFO" in the right lower corner of the screen and
go to "CONFIGURE ...", "AMPLITUDE MEASUREMENTS". Decide
whether you want RIN measured just for the "1" level or for the optical
modulation amplitude (OMA1), and select "dB" or "dB/Hz"2 as the unit
for RIN.
–– By default noise and amplitude levels are averaged across all "1"s and
"0"s. In order to measure them only in areas where overshoot, ringing,
and inter-symbol interference is unlikely, define at least two leading
and trailing consecutive identical digits (CIDs, see Figure 10). Then
the 86100C samples data in the center bit of the pattern that meet
the CID criteria.
Figure 10. Amplitude measurement configuration
1. The Amplitude Results tab displays OMA as
"Signal Amp" for electrical and “Modul’n Amp”
for optical signals.
2. Unless you activate a reference receiver filter
(see Figure 7) "db/Hz" may be not available.
11 | Keysight | Digital Communication Analyzer (DCA), Measure Relative Intensity Noise (RIN) - Application Note
Oscilloscope Based
Measurements
–– (Optional) While observing the RIN result adjust the polarization
controller to find the worst case:
(Continued)
Figure 11. RIN OMA result (normalized to 1 Hz)
The Amplitude tab in Figure 11 shows the modulation amplitude (=OMA
for optical channels) and the random noise (RN) as optical power levels.
Equation 1, however, uses electrical power levels. Because a photocurrent
is proportional to the optical power1, the corresponding electrical power
in the load is linear to the square of the optical power. Instead of Equation
2 we must use the formula:
Equation 3
in order to manually calculate RIN OMA from the RN(rms) and modulation
Amplitude results shown in Figure 11. For reference receivers using a 4th
order Bessel-Thomson low-pass with a 3-dB bandwidth oft 3/4 of the bit rate
the noise bandwidth BN is about 0.8 * bit rate (see also Table 3).
1. After subtracting any dark current
12 | Keysight | Digital Communication Analyzer (DCA), Measure Relative Intensity Noise (RIN) - Application Note
Setups using square-wave
patterns
Although the 86100C Infiniium DCA-J can make accurate RIN measurements on
PRBS patterns, you can also use square wave patterns like 0000011111. Such
patterns can be easily created using a pattern generator like the Keysight N4903A
High-Performance Serial BERT: define a custom pattern, set the pattern length to
twice the number of consecutive identical digits, set half of the bits to zero and the
other half to one, and run it at the nominal bit rate of the transceiver under test.
Alternatively, you can use a pulse generator as a square-wave source configured to
deliver a pulse with 50% duty cycle. Set its frequency to nominal clock rate/(2*N),
N being the number of consecutive zeroes followed by the same amount of ones
(N = 5 in Figure 12). When this frequency also triggers the DCA-J then you need to
configure the trigger as a sub-rate (Trigger Divide Ratio is 1:2*N and the pattern
length as 2*N) (Figure 13). Instead of a simple 01 pattern (i.e., the square wave at
a lower frequency) the DCA-J then "sees" and therefore characterizes the desired
pattern and bit rate.
Desired
Pattern
...
0
0
0
0
0
1
1
1
1
1
...
Pulse
Generator
10/fbit rate
1/fbit rate
Assumed
Clock Rate
Figure 12. Square wave from pulse generator simulating 0000011111 pattern
Figure 13. Pattern lock setup for square-wave modulation (pulse generator: 1.03125 GHz
square wave simulating a 0000011111 pattern at 10.3125 Gb/s)
Square-wave patterns in conjunction with a sub-rate trigger allow you to
measure RIN or RIN OMA as prescribed in some standards. However, they
rarely create good eye diagrams. Because of the 86100C Infiniium DCA-J's capability to identify consecutive identical bits (see Figure 10) and make measurements in their center it is usually faster and easier to analyze a transmitter's eye
diagram, jitter and amplitude performance (such as OMA and RIN) using the same
PRBS pattern.
13 | Keysight | Digital Communication Analyzer (DCA), Measure Relative Intensity Noise (RIN) - Application Note
RIN calculations
The Keysight 86100C Infiniium DCA-J can calculate RIN by using the definition of RIN (see Equation 1) or the definition of RIN OMA (see Equation 2):
–– The RIN measurement takes only data from the "1" level in order to
calculate N, PI and RIN. Therefore the result represents the case of an
unmodulated laser whose optical power equals the "1" level.
–– The RIN OMA measurement takes data from both the "1" level and the
"0" level in order to calculate, N, PMOD and RIN OMA. Therefore the
result is within the measurement uncertainty to the RINxOMA measurement method recommended in IEEE 802.3ae (see section 3).
–– The noise bandwidth BN is 1.05 times the bandwidth of the reference
receiver (fourth order Bessel-Tomson low-pass behavior with
f 3–dB = 3/4 of the bit rate).
–– A wide-bandwidth sampling oscilloscope like the 86100C Infiniium
DCA-J measures only the total noise N integrated over all frequencies passing the lowpass filter. If a laser has relaxation oscillations or
frequencydependent noise power densities then they are filtered: if
they are high enough in frequency then the low-pass filter will remove
them completely, otherwise the instrument will see the accumulated
effect (spectral densities integrated from DC to BN), and will average
them out when dividing N/BN.
–– A higher number of consecutive identical digits may occur less frequently in a PRBS pattern but further decreases the likelihood that
deterministic amplitude variations such as inter-symbol interference
affects the accuracy of the RIN measurement.
–– The dynamic range of the RIN depends on the DUT's signal power Psig,
the details of the O/E conversion and the electronic noise internal to
the specific module in use (see Table 1).
The noise model of the 86100C Infiniium DCA-J (see Figure 14) allows us
to calculate the dynamic range of the RIN measurement. Table 1 shows
typical values when using popular modules.
Reference
Plane
G
NF
PD
RL
Amplifier
with noise
BN
Low-pass
filter
Electronic
noise
High-speed
sampler
Processing
& display
Figure 14. Noise model for a wide-bandwidth oscilloscope based RIN measurement (e.g.,
DCA-J) (G = 0 dB and NF = 0 dB in modules without a pre-amplifier)
The 86100C Infiniium DCA-J does not subtract its own noise from N. It is
therefore possible to further increase the dynamic range by ~5 to 10 dB: both
in local operation as well as under remote control you can measure all power
and noise values, then subtract the instrument's actual noise in the absence
of no input signal, and finally calculate RIN or RIN OMA using the formulas
above.
14 | Keysight | Digital Communication Analyzer (DCA), Measure Relative Intensity Noise (RIN) - Application Note
RIN calculations
Table 1. Typical dynamic ranges for selected RIN measurement scenarioes1
(continued)
Bit Rate
[Gb/s]
Noise
BW
[GHz]
Min.
Power
[dBm]
Max.
Average
Power
[dBm]
NEP
[dBm]
86105B
1.250
10.3125
(unfiltered)
0.98
8.04
≈22
–12
–12
N/A
3
3
3
86105C
1.250
10.3125
(unfiltered)
0.98
8.04
≈22
–21
–17
N/A
86106B
10.3125
(unfiltered)
8.04
≈44
86116A
(unfiltered)
86116B
86116C
Module
Dynamic Range
RIN dB [1Hz]
Pmin
Pmax
–5 dBm
–20
–20
–19
–106
–115
–119
–136
–145
–149
–120
–129
–133
–3
–3
–3
–29
–26
–24
–116
–120
–121
–142
–146
–147
–138
–142
–143
–7
N/A
3
3
–16
–16
–118
–125
–138
–145
–122
–129
≈70
N/A
10
–10
–134
–148
–118
(unfiltered)
≈90
N/A
10
–10
–136
–150
–120
43
(unfiltered)
33
≈90
–3
N/A
10
10
–10
–10
–119
–136
–143
–150
–115
–120
For modules not listed use the following approximation:
Equation 4
Nopt(dark) Noise Equivalent Power (NEP) of the instrument/module in the absence of any input signal (i.e., measured electrcal RMS noise
expressed as external optical power)
Popt(max) Maximum average optical power for which you can still get an accurate
eye diagram
BN Noise bandwidth for the chosen instrument setting
Popt(max) and Nopt(dark) can be found in the Technical Specifications. In addition the actual
Nopt(dark) of any module can be easily determined: disconnect any fiber going to the module, choose FREE RUN for trigger, select the desired bandwidth or bit rate for the channel
of interest, and measure its AC rms value (Figure 15).
1. Typical values based on Technical Specifications dated 7/2006. Data subject to change
without notice.
Figure 15. Intrinsic noise measurement: Nopt(dark) = 3.7μW
15 | Keysight | Digital Communication Analyzer (DCA), Measure Relative Intensity Noise (RIN) - Application Note
RF Power Meter Base
Measurements
IEEE 802.3ae specifies a RIN OMA setup based on an RF power meter, an
AC coupler (fmin < 1 MHz) and a low-pass filter (f–3 dB ≈ bit rate). Optionally
a low-noise amplifier can help overcoming high noise figures of the RF
power meter.
Block diagram
The DUT is modulated with a 0000011111 pattern at the nominal bit rate
which equals a square wave running at fsw = bit rate / 10. In order to see
the worst-case intensity fluctuations, a polarization controller, optical
power splitter and a reflector reflect optical power back into the DUT.
O/E
Polarization
controller Single- converter
mode
coupler
Amplifier
(optional)
DUT
Low-pass RF power meter
filter
(f < MHz to> BN)
BN
AC coupling
(fmin < MHz)
Square wave or
0000011111
pattern gen.
Adjustable
reflector
Figure 16. IEEE 802.3ae based setup for RIN OMA
Measurement procedure
–– Adjust the optical reflector to simulate the worst-case return loss situation
expected in the communication system (you may have to calibrate the
reflection using an optical return loss meter).
–– Zero/calibrate the power meter while the laser and its modulation are turned
off.
–– Activate the laser without any modulation and adjust the polarization controller
until you get the maximum reading on the RF power meter. This is Navg
Equation 2.
–– Turn modulation on and note the modulation power PMOD on the RF power
meter.
–– Calculate RIN OMA using Equation 2 (see Table 3 to calculate BN of the lowpass
filter).
16 | Keysight | Digital Communication Analyzer (DCA), Measure Relative Intensity Noise (RIN) - Application Note
RIN calculations
The RF Power Meter based method directly implements the definition
of RIN OMA. In order to compare its results with other methods several
aspects need to be kept in mind:
–– If the laser is directly modulated then the intensity noise seen by
the power meter (with modulation turned off) approximately equals
the average intensity noise (N1 + N0)/2 under modulation as long as
the average power of the modulated signal equals the power of the
unmodulated signal.
–– If the laser is externally modulated and the average power remains
constant with or without modulation then the intensity noise seen by
the power meter (with modulation turned off) can be up to 3 dB less
than the average intensity noise (N1 + N0)/2 under modulation.
–– The IEEE 802.3ae recommends a low-pass filter with a corner frequency ≈ bit rate. This frequency is higher than that of a reference receiver
(which has a corner frequency ≈ 3/4 of the bit rate). Because the RIN
OMA equation normalizes the measurement to a 1 Hz bandwidth, the
result should be the same as with the 86100C unless there are major
intensity fluctuations in the frequency range between about 75% and
100% of the bit rate, or below the cutoff frequency of the AC coupling
in the IEEE 802.3ae setup (the 86100C modules are DC coupled).
Reference
Plane
G
BN
NF
PD
RL
Amplifier
with noise
Low-pass
filter
Processing
& display
Figure 17. Noise model for a RF power meter based RIN OMA measurement
Assuming that the extinction ratio of the modulated light is high (> 10 dB), the lowpass filter has f–3 dB = 10.3125 GHz (BN ≈ 11 GHz), G = 20 dB, NF = 8 dB and
rPD = 0.8 A/W then the dynamic range of this setup is approximately –151 dB[1 Hz]
for OMA = 0 dBm, and –131 dB[1Hz] for OMA = –10 dBm.
17 | Keysight | Digital Communication Analyzer (DCA), Measure Relative Intensity Noise (RIN) - Application Note
Electrical Spectrum
Analyzer Based
Measurements
The Keysight 71400C/714001C Lightwave Signal Analyzer (LSA) was the first instrument on the market to measure RIN. Although discontinued, some customers still use it
today, and many refer to it when discussing RIN measurements. At its core is an electrical spectrum analyzer with a calibrated optical front end. The LSA measures RF power
as a function of frequency, effectively doing the same as the RF Power Meter based
setup except that the modulation and the noise are spectrally resolved, and that the O/E
converter also captures the DC photocurrent, effectively allowing the measurement of
the average optical power.
Block diagram
The LSA measures RIN of a laser that is not modulated. The calibrated signal path and
the DC current meter in the O/E allow measuring RIN as defined in Equation 1.
Polarization
controller
DUT
Single-mode
coupler
71400C/71401C
Lightwave Signal Analyzer
Adjustable
reflector
Figure 18. Lightwave signal
analyzer setup
Figure 19. RIN spectrum
of a Fabry-Perot laser
(fluctuations in the modal
distribution contribute to
additional intensity noise)
Alternative setups
The alternative setup in Figure 20 tries to emulate the LSA hardware with discreet
building blocks: external, DC coupled O/E, voltage meter (with a 50 Ohm DC-coupled
load at its input), and a spectrum analyzer with low intrinsic noise1. However, all
calculations have to be made manually.
Polarization
O/E
controller Single- converter
mode
coupler
DUT
1. Or an external low-noise pre-amplifier like in
the IEEE 802.3ae setup in order to maximize
sensitivity.
Performance
spectrum analyzer
Adjustable
reflector
Digital
multimeter
Figure 20. Electrical
spectrum analyzer setup
18 | Keysight | Digital Communication Analyzer (DCA), Measure Relative Intensity Noise (RIN) - Application Note
Measurement procedure
This section focuses on how to characterize RIN using the alternative
setup. To a large degree it emulates the method used in the 71400C/71401C
Lightwave Signal Analyzer (LSA).
–– Measure the offset voltage of the O/E converter in the absence of any input
signal. Terminate the voltage meter with 50 Ohm so that the O/E sees the
same impedance as when connected to the spectrum analyzer.
–– Turn the laser on and measure its power (replace the O/E in Figure 20 with an
optical power meter). Do not use any modulation.
–– Connect the O/E, measure the output voltage and subtract any offset. Calculate the electrical signal power PI dissipated by the load (= V2 /50 Ω).
–– Connect the O/E to a Spectrum Analyzer with a low noise floor and measure
N versus frequency (start frequency < 1 MHz, stop frequency > bit rate of
communication system). Use the polarization controller to find the worst-case
scenario, and/or to observe the effect of back reflections.
–– The noise measured with the signal applied should exceed the noise floor by at
least 5 dB – otherwise use trace subtraction in order to see RIN levels around
or only slightly above the instrument's noise floor.
–– Either pick a "typical" noise power density (N/BN) on the screen, or calculate
the average noise power density by integrating the trace on the spectrum analyzer over frequency and then dividing it by the frequency span.
–– Calculate RIN as (N/BN)/PI, Figure 29 shows a measurement example imported
into a spreadsheet in order to subtract the instrument's intrinsic noise and to
calculate the integral over the traces.
RIN calculations
The 71400C/71401C Lightwave Signal Analyzer (LSA) automatically makes RIN
measurements. Based on Equation 1 the marker reads the RIN normalized to 1 Hz
at any frequency over the span of the sweep. Because it can put a shutter in front
of the photo detector the LSA can measure its own noise floor and the average
photo current (see noise model in Figure 21). This architecture allows the instr
ment to automatically subtract any dark current and its own noise floor from N, effectively maximizing its dynamic range to better than –160 dB[1 Hz]
DC
Reference
Plane
BN
G
NF
PD
RL
Amplifier
with noise
Local
oscillator
Bandpass
filter
Processing
& display
Figure 21. Noise model for a spectrum analyzer based RIN measurement (e.g., 71400C)
19 | Keysight | Digital Communication Analyzer (DCA), Measure Relative Intensity Noise (RIN) - Application Note
Optical Spectrum
Analyzer Based
Measurements
In many cases RIN can be estimated based on optical spectrum analyzer
measurements. Many modern distributed feedback (DFB) or electroabsorption
modulated lasers (EML) have a large enough OSNR and a narrow enough spontaneous emission range so that RIN is almost exclusively dominated by the stimulated spontaneous beat noise: The Keysight 8614XX Optical Spectrum Analyzer
(OSA) provides yet
Equation 5
Block diagram
αsig-se
is a factor that depends on how the stimulated (signal) and the spontaneous emissions are polarized. αsig-se is 1 for completely unpolarized
spontaneous emission and 4 if both the spontaneous and the stimulated
emission are polarized 100% and in the same orientation.
OSNRWVL
Optical Signal-To-Noise Ratio in the wavelength domain
λ
c
Center wavelength of the signal
Speed of light
The Keysight 8614XX Optical Spectrum Analyzer (OSA) provides yet another way to
characterize the intensity noise of a laser or transmitter. It resolves the spectrum in
the wavelength domain, effectively showing the stimulated emission as a peak rising many tens of decibels above the spontaneous emission.
Polarization
controller
Single-mode
coupler
DUT
Optical
spectrum analyzer
Adjustable
reflector
Figure 22. Optical spectrum analyzer setup
20 | Keysight | Digital Communication Analyzer (DCA), Measure Relative Intensity Noise (RIN) - Application Note
Measurement procedure
–– Connect the laser to the OSA and setup the wavelength range and amplitude
scale so that you get a measurement similar to the one shown in Figure 1.
"PEAK FIND"/"PEAK TO CENTER", 0.5 to 2 nm Resolution Bandwidth (RBW),
20 to 100 nm span, and sensitivity better than –70 dBm usually provide good
results.
–– Determine the signal power using marker 1.
–– Measure the spontaneous emission density by measuring the optical signal-tonoise ratio (OSNR) normalized to 1 nm (check the noise marker options). The
OSNR markers interpolate the spontaneous emission under the signal.
–– Adjust the polarization controller to find the worst-case OSNR.
–– Calculate using Equation 6.
Equation 6
RIN calculations
The OSA provides valuable insights into the root cause of intensity noise by characterizing the spontaneous emission over wavelength:
–– It is an indirect measurement because RIN and RIN OMA are defined in the
electrical domain.
–– The polarization factor αsig-se can be hard to determine accurately: if you know
that the spontaneous emission is not or only slightly polarized then use
αsig-se ≈ 1, if it is highly polarized, then use αsig-se ≈ 4.
–– The high sensitivity and averaging features of the OSA nevertheless allow you
to measure large OSNR numbers and therefore determine RIN values that exceed the thermal and other noise limitations of the electrical methods.
21 | Keysight | Digital Communication Analyzer (DCA), Measure Relative Intensity Noise (RIN) - Application Note
RIN Measurement
Comparisons
A detailed analysis of the measurement accuracy is extremely complex and depends
on many, sometimes unspecified performance aspects of the actual mainframe and
module being used. Instead of a major mathematical analysis this chapter compares
specific measurement result from different devices under test and different measurement methods.
If the time-domain method used in the 86100C Infiniium DCA-J provides the same
RIN results as an optical-domain method and as a frequency-domain method then
users can rely on the DCA-J while enjoying its ease-of use. It turns out the DCA-J
results are indeed very comparable to other methods as long as the average noise
from the DUT exceeds the intrinsic noise of the instrument.
Adjustable RIN source
In order to compare RIN measurements made with different instruments or methods
it is desirable to have a source whose properties can be adjusted as desired. Figure
23 shows a potential setup: a distributed feedback laser provides an externally modulated signal while an Erbium-doped fiber amplifier (EDFA) adds lots of spontaneous
emission. The first optical attenuator conditions the signal so that the output of the
EDFA has the desired optical signal-to-noise ratio (OSNR). The second attenuator
decreases the EDFA output power to prevent overloading sensitive instruments like
the 86100C Infiniium DCA-J. Finally an optical filter reduces the spectral width of
the spontaneous emission to about ±1 nm around the signal.
210—1 PRBS
10.3125 Gb/s
DFB Laser
with LiNb03
modulator
Erbium-doped
fiber amplifier
Optical
attenuator
Optical
attenuator
Optical
filter
Figure 23. Adjustable RIN source
Because the Keysight 86146B Optical Spectrum Analyzer (OSA) can act as a
highquality optical filter with selectable bandwidth and tunable center wavelength,
it is convenient to replace the optical filter in Figure 23 with such an instrument. The
OSA measurement allows you to conveniently adjust the OSNR (a smaller EDFA input
signal increases the EDFA's spontaneous emission) and then the signal power to the
desired levels. Finally the OSA can be stopped at the laser's wavelength. Its optical
output then includes the signal1 plus the spontaneous emission but only over a wavelength range determined by the OSA's resolution bandwidth (RBW).
Mkr 1(A)
1556.67 nm
0.021 dBm
Center
1556.65 nm
-0.033 dBm
OSNR
19.986 dB/nm
2.50
REF: 0.00 dBm
dBm
-2.50
-7.50
2.50
dB/div
-12.50
-17.50
1. The 86146B has about 5 dB loss when operated as a tunable filter. It is recommended to
verify the optical signal with a power meter
and adjust the second attenuator before connecting the OSA's output with the DCA-J.
-22.50
RBW:
VBW:
1546.67
2 nm
2.1 kHz
nm
Sens: -70.00 dBm
ST:
114 ms
1556.67
Avg:
Figure 24. Spectrum of adjustable RIN source
Off
12:14PM
03 Jun 2004
2.00 nm/div
1566.67
In Vac
22 | Keysight | Digital Communication Analyzer (DCA), Measure Relative Intensity Noise (RIN) - Application Note
DCA-J versus OSA
comparison using the
adjustable RIN source
If the average power, OSNR, and the spontaneous emission bandwidth are known then
it is possible to calculate RIN and RIN OMA. Table 2 shows the noise and RIN results
calculated from OSA measurements (Figure 24), and compares them with measurements
made by the 86100C Infiniium DCA-J with an 86105B module (Figure 25, Figure 26).
The random noise differences as well as the RIN result differences are well within the
measurement uncertainties of the OSA and the DCA-J, proving that the accuracy of the
DCA-J is excellent as long as the random noise exceeds its intrinsic electronic noise1.
Figure 25. Signal power levels
Figure 26. RIN "1" level (left) and RIN OMA (right)
Table 2. DCA-J versus calculated results based on OSA measurements
(All noise levels include the noise from the insturment’s electronics)
1. To measure the intrinsic noise of any DCA-J
module, go to oscilloscope mode and measure
the Vrms (AC). Optical channels will display
the noise equivalent power (NEP) in Watts or
dBm.
2. Because the DCA-J / 86105B used here has
about 12 μW NEP, the results for the "0" level
are dominated by the instrument's intrinsic
noise and not by the input signal.
OSA Measurement
DCA –J Measurement
Paverage: 0.02 dBm
0.021 dBm
0.140 dBm
Wavelength
1556.67 nm
N/A
OSNR
20.0 dB/nm
N/A
Optical Bandwidth
Calculation
(RBW = 2 nm)
N/A
2.1 nm
Noise (“1” Level)
N/A
49.3 μW
50.6 μW
Noise Bandwidth
N/A
7.9 GHz
7.84 GHz
Noise (“0” Level)2
N/A
14.2 μW
15.3 μW
RIN (“1” level)
N/A
–131 dB/Hz
–130.3 dB/Hz
RIN OMA
N/A
–131 dB/Hz
–133.4 dB/Hz
23 | Keysight | Digital Communication Analyzer (DCA), Measure Relative Intensity Noise (RIN) - Application Note
DCA-J versus ESA
comparison using
an EML source
Many short- or medium reach applications use EML transmitters. EML stands for
externally modulated laser which consists of a distributed feedback (DFB) laser
integrated with an electro-absorptive modulator (EAM). The particular device used
to compare the DCA-J with RIN measurements based on the electrical spectrum
analyzer (ESA) method had a significant spontaneous emission spectrum. The EAM
modulated the signal (i.e., stimulated emission) and only part of the spontaneous
emission (Figure 27). Therefore the difference between the random noise on the "0"
level" and the "0" level should depend less on the modulation's extinction ratio, and
RIN OMA might suffer a little bit. An optical filter could improve that by suppressing
most of the spontaneous emission and passing only the spectrum around the signal,
however, it would increase cost and reduce the optical power budget of the
transmission channel.
Mkr 1(A)
1543.7 nm
-6.332 dBm
1.32
REF: -8.68 dBm
dBm
-18.68
-38.68
10.00
dB/div
-58.68
-78.68
-98.68
RBW:
VBW:
1500.0
2 nm
2.1 kHz
nm
Sens: -65.06 dBm
ST:
566 ms
1575.0
Avg:
Off
08:54AM
02 Sep 2005
1650.0
15.0 nm/div
In Vac
Figure 27. EML spectra ("1" level, average power and "0" level)
The random noise (RN) for the "0" level in Figure 28 is only 2.7 times smaller than the
one for the "1" level but clearly above the 1.7 μW noise equivalent power (NEP) of the
DCA-J / 86105C electronics. RIN OMA exceeds the –128 dB[1 Hz] specifications for
the intended communication system, and therefore it is not necessary to filter the
optical spectrum.
Figure 28. RIN OMA Result for an Externally Modulated Laser (EML)
24 | Keysight | Digital Communication Analyzer (DCA), Measure Relative Intensity Noise (RIN) - Application Note
DCA-J versus ESA
comparison using
an EML source
(continued)
Figure 29 shows the electrical spectrum after the device-under-test (DUT)
was connected to a 10 GHz O/E converter. The top trace shows the power
spectrum when modulation was on, the other two show the relative intensity
noise for the "1" and "0" levels. The integral over the top trace provides the
modulation amplitude while the integral over the bottom traces represents the
total random noise.
The calculations return RIN = 133.8 dB[1Hz] for the "1" level and RIN
OMA =136.5 dB [1Hz]. Small optical reflections in the measurement setup cause
the laser's linewidth to broaden (the lower traces rise by three magnitudes
at low frequencies). Nevertheless the ESA method of measuring RIN agrees
well with the DCA-J.
Figure 29. Electrical spectrum analyzer (ESA) results
25 | Keysight | Digital Communication Analyzer (DCA), Measure Relative Intensity Noise (RIN) - Application Note
Appendix
Definitions and
electricaloptical relationships
Photodetector terminology
The output current from a photodetector is linear to the optical power input.
Because electrical power is proportional to the square of the current, doubling
the optical power causes twice as much current and quadruples the electrical
power. It is therefore essential to clearly identify whether a value applies to
the optical or the electrical domain.
Optical power Popt(t) [W] is the momentary total power arriving at the
photodetector, and is a function of time in modulated systems. Avoid
confusing it with the average optical power Pavg (T=time period until the
modulation pattern repeats itself):
Equation 7
Responsivity rPD [A/W] describes the conversion ratio of a photodetector (PD):
Equation 8
Load resistance RL [Ω] is the real part of the impedance seen by the
photo detector (Figure 30). It usually represents the input impedance of a
measurement path or instrument.
ip
ishot
Reference
Plane
ith
BN
RL
V
Figure 30. Basic noise model
Laser source terminology
Stimulated emission is the main Signal power Psig (t) [W] emitted by a
laser1. Stimulated emission is often highly polarized. Grating-based Optical
Spectrum Analyzers measure the average stimulated emission (peak in
Figure 1) as well as the spontaneous emission (see below).
Spontaneous Emission is a random emission of photons. It occurs over
a wider wavelength range and can be described as a power density in the
wavelength domain pse [W/m] or frequency domain ρse [W/Hz].
Equation 9
1. "LASER" is an acronym for "Light Amplification
by Stimulated Emission of Radiation.
26 | Keysight | Digital Communication Analyzer (DCA), Measure Relative Intensity Noise (RIN) - Application Note
Laser source terminology
(continued)
The total spontaneous emission power Pse [W] often can be approximated as ρse*
Bopt(f) (frequency domain) or ρse * Bopt(λ) (wavelength domain). This approximation
works well when narrow optical filters are used (e.g., in wavelength-division multiplexing systems). The exact definition is1:
Equation 10
Laser threshold is the point where the stimulated emission starts to exceed
the spontaneous emission. Below that the optical power is not strong enough
to cause a lot of stimulated emission. Above the threshold the stimulated
emission becomes very effective and dominates the emitted light.
Optical-signal-to-noise-density ratio OSNR (measured in 1/Hz or dB[1Hz]) is the
ratio between the optical power and the spectral density of unintended fluctuations.
Equation 11
Optical bandwidth Bopt [Hz] or [m] specifies the 3-dB (1/2 power) bandwidth of a
broadband source (like spontaneous emission) or a filter (like a demultiplexer in WDM
systems). If the optical bandwidth is much smaller than the center wavelength (or frequency) then use this approximation to convert values from wavelength domain to the
frequency domain and vice versa:
Equation 12
Optical filters tend to roll off faster than the electrical low-pass filters shown in Table 3.
Therefore their noise bandwidth is about the same as their 3-dB bandwidth. For broadband and unfiltered sources (such as spontaneous emission) Bopt is often 10% to 20%
larger than their 3-dB bandwidth2.
Modulation terminology
Optical modulation amplitude OMA (W) is the difference between the average "1" level
and the average "0" level of bits that are not distorted by interference. It usually is measured in the center of the eye in the middle of a 00000 and a 11111 sequence:
Equation 13
1. A popular method is to interpolate the spontaneous emission under the signal in order to
calculate the integral.
2. Figure 1: Spontaneous emission 3-dB bandwidth ( 55 nm, power density pse =
–5.3 – 47.213 dBm = 5.9 nW/nm. Trace integration (interpolated signal) leads to Pse=
306 nW, therefore Bopt = 306/5.9 nm = 52 nm.
Extinction ratio ER [dB or no unit] is the ratio of the average "1" level to the average "0"
level of an optically modulated signal. It usually is measured in the center of the eye:
Equation 14
27 | Keysight | Digital Communication Analyzer (DCA), Measure Relative Intensity Noise (RIN) - Application Note
Noise terms
Relative intensity noise RIN (measured in 1/Hz or dB[1Hz]) is the ratio of the electrically observed noise power normalized to a 1 Hz bandwidth and the power of the
photocurrent I:
Equation 15
Equation 16
This definition of RIN requires either an unmodulated laser (Popt = Pavg), or an instrument that can measure both N and PI at the same point in the modulation pattern. The
Keysight 86100C Infiniium DCA-J1 is a time-domain instrument (oscilloscope) that takes
many samples of logical "1"s (or "0"s) in the center of the eye diagram (see Figure 5),
determines N1, N0, PI1, PI0, and calculates RIN as an average spectral density.
The Keysight 71400C/71401C Lightwave Signal Analyzer 2 (LSA) is a frequency domain
instrument (spectrum analyzer) that measures spectral densities and normalizes the
power observed within its resolution bandwidth to 1 Hz. You need to integrate the noise
density trace in order to calculate N.
RIN OMA (measured in 1/Hz or dB[1Hz]) is the ratio of the electrically observed noise
power normalized to a 1 Hz bandwidth and the electrical modulation power of a square
wave:
Equation 17
N1, N0, P1 and P 0 are the electrical noise and signal powers for the "1" and "0" levels.
Total noise NT [W] is the combination of all noise sources observed at the reference
plane (see Figure 30).
Equation 18
The 86100C Infiniium DCA-J can switch a low-pass filter between the photodetector
and the sampling circuit. Therefore the noise bandwidth varies for the noise sources in
parentheses in Equation 19 while the sampler and its following electronics add a filterindependent noise term (Nsampler ≈ 1 to 5 nW):
Equation 19
The 71400C/71401C LSA has a pre-amplifier with a noise figure between 6 and 8 dB. We
can model this amplifier and the rest of the instrument as "noise-free" if we instead apply
a noise factor (F ≈ 4 to 7) to the thermal noise Nth of RL :
1. With Options 001, 200, 300 and firmware
revision 7.0.
2. Discountinued product.
Equation 20
28 | Keysight | Digital Communication Analyzer (DCA), Measure Relative Intensity Noise (RIN) - Application Note
Noise terms
(continued)
Thermal noise power Nth [W] is the Johnson-Nyquist noise observed in the
load RL over the effective noise bandwidth BN. In today's electronic systems
the thermal noise density versus frequency is practically constant ("white"
noise). The thermal noise poses a signal-independent lower limit for any
measurement1 (k = Boltzmann constant, T = absolute temperature).
Equation 21
Noise bandwidth BN [Hz] describes the effective bandwidth of a low pass filtering
white noise: an ideal low pass has a rectangular shape with no attenuation or gain
between DC and BN, and infinite attenuation for all frequencies greater than BN. If
the amplitude transfer function a(f) is known then BN can be calculated as:
Equation 22
Table 3. Ratio of BN to corner bandwidth
Low Pass Filter Type
BN / f –3 dB
1st order (e.g., RC low-pass)
1.56
2nd order Critical Damping
1.21
2nd order Bessel-Thompson
1.15
2nd order Butterworth
1.11
4th order Critical Damping
1.13
4th order Bessel-Thompson (DCA frequency response with filter ON)
1.046
4th order Butterworth
1.026
Gaussian
1.000
Shot noise reflects the statistical fluctuation of a current flowing though
a transition due to the quantitative nature of electrons. It creates a
Shot noise power Nshot [W] in the load resistance RL (e = elementary charge):
Equation 23
The shot noise current poses a signal-dependent lower limit for any measurement.
1. In the absence of any averaging or other
noise-reduction processing.
29 | Keysight | Digital Communication Analyzer (DCA), Measure Relative Intensity Noise (RIN) - Application Note
Noise terms
(continued)
Spontaneous-spontaneous beat noise Nse-se [W] is generated in the
photodetector because the spontaneous emission "mixes" with itself due
to the nonlinear behavior of a photodetector1:
Equation 24
Equation 25
αse-se varies between 1 and 4 depending on how much spontaneous emission
is polarized. Most semiconductor lasers will emit spontaneous emission that is
somewhat polarized.
Signal-spontaneous beat noise Nsig-se [W] is generated in the photodetector
because the signal "mixes" with the spontaneous emission due to the nonlinear
behavior of a photodetector:
Equation 26
Equation 27
αse-se varies between 0 and 4 depending on the polarization degree and state
of the spontaneous emission. It equals 4 for spontaneous emission that is polarized
exactly as the signal 2, 1 for perfectly unpolarized spontaneous emission, and 0 in the
unlikely case that the spontaneous emission is completely polarized but in a state
orthogonal to that of the signal.
Noise equivalent power [W] models a receiver's noise generation by combining all of
its internal noise into an equivalent optical power that needs to be applied to the input
of an ideal (noise-free) receiver in order to generate the same total output noise NT:
Equation 28
Noise factor (F) describes the noise contributions of an amplifier or sampler
independent of the actual gain: F is the ratio between the actual output noise
power and the amplified input noise power (NF = Noise Figure [dB]).
1. The photocurrent is proportional to the optical
power which in turn is proportional to the
square of the sum of the field vectors of the
electromagnetic wave.
2. At the photodetector. While traveling through
regular optical fibers, light often changes its
state of polarization (but rarely its degree).
Equation 29
30 | Keysight | Digital Communication Analyzer (DCA), Measure Relative Intensity Noise (RIN) - Application Note
Conversions
Optical power ratios
Table 4. Relationship between ER, "1" Level, "0" Level, OMA and average power
(above: log scale, below: linear terms)
ER
3.00
3.50
4.00
5.00
6.00
7.00
8.00
9.00
10.00
11.00
12.00 14.00 17.00
20.00
00
dB
P1/Pavg
1.25
1.41
1.55
1.82
2.04
2.22
2.37
2.50
2.60
2.68
2.74
2.92
2.97
0.00
dB
P0/Pavg
–1.75
–2.09
–2.45 –3.18
–3.96
–4.78
–5.63 –6.50
–7.40
–8.32
–9.26 –11.2
–14.1
–17.0
??
dB
OMA/Pavg
–1.77
–1.16
–0.65 0.17
0.78
1.25
1.62
1.91
2.14
2.32
2.46
2.66
2.84
2.92
3.01
dB
ER
1.995
2.239
2.512
3.162
3.981
5.01
6.31
7.94
10.0
12.6
15.8
25
50
100
00
P1/Pavg
1.332
1.382
1.431 1.519
1.598
1.667
1.726
1.776
1.818
1.853
1.881 1.923
1.961
1.980
1.000
P0/Pavg
0.668
0.618
0.569 0.481 0.402
0.333
0.274
0.224
0.182
0.147
0.119
0.077
0.039
0.020
0.000
OMA/Pavg
0.665
0.765
0.861 1.039
1.335
1.453 1.553
1.636
1.706
1.763
1.847
1.922
1.960
2.000
1.197
2.84
AC signal power versus optical modulation amplitude
Photocurrent
Optical signal
P1 * rPD
P1
Pavg
OMA
P6
OMA * rPD
P1 * rPD
t
t
Modulation power
Current (after AC coupling)
+ 1/2 * OMA * rPD
1/
4
t
* OMA2 * r2PD * RL
OMA * rPD * RL
- 1/2 * OMA * rPD
t
Figure 31. OMA to AC power conversion (square wave and sine wave example)
AC power (rms) for a square-wave modulation (square-wave period << receiver bandwidth1):
Equation 30
AC power (rms)2 for a sine-wave modulation (fmod << receiver bandwidth):
Equation 31
1. IEEE 802.3ae recommends using a simple pattern of 5 "0"s followed by 5 "1"s running at the
nominal bit rate.
2. In the absence of any DC a sine wave has half
the average electrical power than a square
wave with the same peak-to-peak amplitude.
31 | Keysight | Digital Communication Analyzer (DCA), Measure Relative Intensity Noise (RIN) - Application Note
Conversions
(continued)
Threshold when shot noise starts to exceed Thermal Noise (amplifier with
Noise Figure NF1):
Equation 32
For T = 300K, F = 2.5 (8 dB), RL = 50 Ω , and rPD = 0.8 A/W, Equation 32 yields
P Th = .8 mW (– dBm).
RIN Dynamic range when limited by thermal noise:
Equation 33
Physical constants
1. Noise factor F = 10NF/10.
Name
Symbol
Value
Absolute temperature
(T0)
0 K (–237.15 °C)
Boltzmann constant
(k)
1.380651 * 10–23 J/K (= 8.617343 * 10–05 eV/K)
Elementary charge
(e)
1.602177 * 10–19 C
Plank's constant
(h)
4.135667 * 10–15 eVs (= 6.626069 * 10–34 Js)
Speed of light
(c)
2.997925 * 10 08 m/s
32 | Keysight | Digital Communication Analyzer (DCA), Measure Relative Intensity Noise (RIN) - Application Note
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