HP 11729C-2 User Manual
Product Note 11729C-2
Phase Noise Characterization of
Microwave Oscillators
Frequency Discriminator Method
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HEWLETT
PACKARD
Phase Noise Characterization of Microwave Oscillators
Frequency Discriminator Method
Table of Contents Page
Chapter 1: Introduction 3
Chapter 2: Phase Noise and its Effect on Microwave Systems 4
What is Phase Noise 4
Two-port and Absolute Noise 7
Why Phase Noise is Important 7
Digital Communications Systems 8
Analog Microwave Communications Systems 8
Doppler Radar System 8
Chapter 3: Phase Noise Measurements — Frequency
Discriminator Method 10
Common Measurement Techniques 10
Direct Measurement 10
Heterodyne/Counter Measurement 10
Carrier Removal/Demodulation 10
Measurement with a Phase Detector 11
Measurement with a Frequency Discriminator 12
The Delay Line/Mixer Frequency Discriminator Method 12
Basic Theory 12
The Discriminator Transfer Response 12
System Sensitivity 13
Optimum Sensitivity 14
Making A Measurement 15
System Setup 15
System Calibration 15
The Phase Noise Measurement 16
Chapter 4: HP 11729C Carrier Noise Test Set Theory of Operation
and Measurement Considerations 18
General Operation 18
Multiplier Chain 18
Demodulating and Bandpass Signal Processing 20
First Down Conversion 20
IF Processing and the Frequency Discriminator 20
Baseband Signal Processing 20
Phase Locked Loop/Quadrature Section 21
Chapter 5: Making Frequency (Phase) Noise Measurements
with the HP 11729C 22
System Setup 22
The Source 22
The 640 MHz Drive Signal 22
The Delay Line 23
System Operation 24
System Calibration 24
The Calibration Signal 24
System Response 25
The Discriminator Constant (Kd) 26
Measuring the Frequency (Phase) Noise 26
Measurement Corrections 27
Conversion to Other Units 27
Table of Contents (cont'd) Page
Chapter 6: Considerations in System Accuracy 29
Spectrum Analyzer 29
Relative Amplitude Accuracy 29
Resolution Bandwidth Accuracy 29
The IF Gain Accuracy 29
Spectrum Analyzer Frequency Response 29
System Parameters of the HP 11729C 30
Frequency Discriminator Flatness 30
Baseband Signal Processing Section Flatness 30
System Noise Floor 30
Measurement Procedure 31
Quadrature Maintenance 31
System Calibration 31
The Randomness of Noise 31
Overall Accuracy 31
Accuracy Without Error Correction 32
Accuracy With Error Correction 32
Appendix A: The Delay Line/Mixer Frequency
Discriminator Transfer Response 34
Appendix
Appendix C: System Sensitivity 38
Appendix D: Calibration and the Discriminator Constant Kd 40
Appendix E: The Importance of Quadrature 41
Appendix F: HP 11729C Programming Codes 42
Appendix G: References 43
B:
The Double-Balanced Mixer as a Phase Detector 36
As the performance of microwave radar and communication systems advances,
certain system parameters take on increased
importance.
One of these parameters that
must be measured is the spectral purity of microwave signal sources.
In the past, many techniques for measuring spectral purity have used complex,
dedicated instrumentation, often cumbersome in both size and operation and often
limited to narrow bands of operating frequency. The broadening focus on spectral
purity has created a need for measurement techniques that provide the high performance necessary for R&D requirements, and that can be automated for production
environments. Also, service applications require a versatile system with a broad
frequency and performance range.
The Hewlett-Packard 11729C Carrier Noise Test Set
is
a key element of a system that
provides convenient manual or automatic phase noise measurements. With appropriate companion instrumentation, phase noise measurements can be made on a
broad range of
This product
in Chapter
the phase noise of
sources,
note discusses
2.
Chapter 3 describes a frequency discriminator technique for measuring
from 10 MHz to 18 GHz.
phase noise and
sources.
The implementation of
its
effects on modern microwave systems
this
technique with the HP 11729C
is shown in Chapter 4. (See HP product note PN 11729B-1 for phase detector
method.) Chapter 5 outlines the measurement steps needed to make a phase noise
measurement, and the resultant measurement accuracy is derived in Chapter 6.
3
L Phase Noise and its Effect on Microwave Systems
WHAT IS PHASE NOISE? Frequency stability can be defined as the degree to which an oscillating source
produces the same frequency throughout a specified period of
microwave source exhibits some amount of frequency
be broken down into two components—long-term and short-term stability.
Long-term stability describes the frequency variations that occur over long time
periods, expressed in parts per million per hour, day, month, or year. Short-term
frequency stability contains all elements causing frequency changes about the nominal frequency of less than a few seconds duration. This product note deals with
short-term frequency stability.
Mathematically, an ideal sinewave can be described by
V(t) = VoSin (27rfot)
where V0 = nominal amplitude,
27rf0t = linearly growing phase component,
and f0 = nominal frequency.
But an actual signal is better modeled by
instability.
time.
Every RF and
This
stability
can
be
V(t) = [v0+e(t)] sin [27rf0t + A<ftt)]
where e(t) = amplitude fluctuations,
and A</>(t) = randomly fluctuating phase term or phase noise.
This randomly fluctuating phase term
analyzer (one which had no sideband noise of
two types of fluctuating phase terms. The first, deterministic, are discrete signals
appearing as distinct components in the spectral density plot. These signals, commonly called
as power line frequency, vibration frequencies, or mixer products.
The second type of phase instability is random in nature, and is commonly called
phase noise. The sources of random sideband noise in an oscillator include thermal
noise, shot noise, and flicker noise.
Many terms exist to quantify the characteristic randomness of phase noise. Essentially, all methods measure the frequency or phase deviations of the source under test
in either the frequency or time
other, all of the terms that characterize phase noise are also related.
One fundamental description of phase instability or phase noise
of phase fluctuations on a per-Hertz basis. The term spectral density describes the
energy distribution
unit bandwidth. Thus
spurious,
as a
can be related to known phenomena in the signal source such
continuous function, expressed in units of phase variance per
S^fj,,)
(Figure 2.1b) may be considered as
domain.
A<£(t)
could be observed on an ideal spectrum
its
own) as in Figure 2.1a. There are
Since frequency and phase are related to each
is the
spectral density
A4>L(fm) rad
BW used to measure Ac/^ Hz
where BW (bandwidth) is negligible with respect to any changes in S^ versus the
fourier frequency or offset frequency fm.
4
2
Figure
2.1.
CW Signal sidebands viewed in
the frequency domain.
A.
2.1.a.
RF sideband spectrum. 2.1.b. Phase noise sidebands.
Another useful measure of the noise energy
S^(fm)
by
a simple
tion sidebands are such that the total phase deviations are much much less than 1
radian (A$pk«l radian).
J^(fm)
is
an indirect measure of
observed on a spectrum analyzer. Figure 2.2 shows that the
Standards defines
to the total signal power (at an offset fm Hertz away from the carrier). The phase
modulation sideband is based on a per Hertz of bandwidth spectral density and f
equals the Fourier frequency or offset frequency.
■S?(U
J?f (fm) is usually presented logarithmically as a spectral density of
tion sidebands in the plot of the phafrequency domain, expressed
carrier per Hz (dBc/Hz), as shown in Figure 2.3
approximation which
noise
J^(fm)
as
the ratio of the power in one phase modulation sideband
power density (in one phase modulation sideband)
total signal power P
= single sideband (SSB) phase noise to carrier ratio per Hz.
is
J?(fm), which
has
generally negligible error if the modula-
energy easily related to the RF power spectrum
is
then directly related to
U.S.
National Bureau of
r
ssb
the phase
in dB
modula-
relative to the
m
s
Figure 2.2. Deriving i?(fm) from a spectrum analyzer display.
Figure 2.3. ¥ (im) described logarithmically as a function of offset frequency.
Caution must be exercised when :/'(fm) is calculated from the spectral density of the
phase fluctuations
angle
criterion.
S,^(fm)
Figure
5
because
2.4.
the
calculation of
the measured phase noise of a free running
.'J
(fm)
is
dependent on
VCO
the
small
described
Figure 2.4. Region of validity of
in units of jSf
(fm),
illustrates the erroneous results that can occur if
the
instantaneous
phase modulation exceeds a small angle. Approaching the carrier, =^(fm) obviously
increases in error
as
it indicates a relative level of+45 dBc/Hz at a 1 Hz
offset (45 dB
more noise power at a 1 Hz offset in a 1 Hz bandwidth than in the total power of the
signal); which is of course invalid.
Figure 2.4 shows a 10 dB/decade line drawn over the plot, indicating a peak phase
deviation of 0.2 radians integrated over any one decade of offset frequency. At
approximately 0.2 radians the power in the higher order sidebands of the phase
modulation is still insignificant compared to the power in the first order sideband
which insures that the calculation of -5?(fm) remains valid. Above the line the plot of
Jz?(fm) becomes increasingly invalid, and
S^(fm)
must be used to represent the phase
noise of the signal.
^[!m)dBc^Hi
l„,
01 (set
from Carrier (Hi)
Another common term for quantifying short term frequency instability (phase noise)
is SAf(fm), the spectral density of frequency fluctuations. Again the term spectral
density describes the energy distribution as a continuous function, expressed in units
of frequency variance per unit bandwidth. Thus,
AfUU
SAKU
BW used to measure AL
SAf(fm)
can be considered as
Hz
Hz
2
where BW is negligible with respect to any changes in S^, versus fm.
Because frequency
J£(fm),
and
SAf(fm)
is
the time rate of
change
can be related as shown.
of
phase,
the
three
common terms S0(fm),
SAf(fm) (for region of validity)
S^(lm) — f 2
As shown in Chapter
tional to SAf(fm)- However, since phase noise
3,
a frequency discriminator outputs a voltage directly propor-
is
typically specified
as
<£(fm)
or S0(fm),
the graphical relationship to these other units is shown in Figure 2.5.
Sv(fm)
is the power spectral density of the voltage fluctuations out of the detection
system. For small BW,
Sv(fm)
may be considered as
6
Figure 2.5. The phase noise
sized
10
GHz source plotted
of a
in
synthe-
terms
of
phase fluctuations, frequency fluctuations,
andi?(fm).
Sii ((„,) dBHi/Hi -10
S.,
(W dBr/Hz
r Hi ill HI
IOOHI
I hHj 10 tHj 10(! kHi 1 MHi
'm Oltsel from Carrier
(Hz)
lOMHl
AVUU
Sv(fm)
=
Because
of
the large magnitude variations
convenient to talk about phase noise in logarithmic terms.
SAKW
expressed logarithmically is
S^(fm)
expressed logarithmically is
i?(fm) expressed logarithmically is i?(fm) [dBc/Hz] = 10 log
The relations between
S^(fm)
[dBr/Hz] = SAKU
and
&(fj [dBc/Hz]
BW used to measure AV
S^f,,,)
S^f,,,),
S^(fm), and^f(fm) become
[dBHz/Hz] - 20 log
= S^U
[dBHz/Hz] - 20 log
n
of
the phase noise on an oscillator,
S^Q
[dBHz/Hz] = 20 log
[dBr/Hz] = 20 log . .,—per Hz
l(Hz)
l(Hz)
2
V
H7
-3dB
Af(Hz)
. ,„ .
1 (Hz)
A<Krad)
it is
per Hz
-per Hz
TWO PORT AND
ABSOLUTE NOISE
where dBHz/Hz
one radian
is dB
per Hz
relative to one Hz per
bandwidth,
and
dBc/Hz
Hz
bandwidth, dBr/Hz
is dB
relative
to a
is dB
relative to
carrier
per Hz
bandwidth.
There are two different types of
phase noise and absolute phase noise. Two-port phase noise refers
phase
noise commonly specified. They are two-port
to
the noise of
devices. Amplifiers, mixers, and multipliers have two-port phase noise. Two-port
noise results from the noise contributed by a device, regardless of the noise of the
driving source. Absolute phase noise refers
to
the total phase noise present
at
the
output of a source or system. It is a function of both the device two-port phase noise
and the oscillator noise.
The procedures described in this note are for making absolute phase noise measurements on microwave
important
synthesized
in
sources
measurements of
sources.
In
general,
the absolute phase noise of a source
the final system application. However, two-port noise
might
also
be
devices,
measured prior
the HP 3047 A Phase Noise Measurement System
to
system integration. For two-port
of
is
most
devices
is a
good
or
solution. HP application note AN 57-1 provides a comprehensive review of funda-
mentals
of
noise characteristics of iwo-ptin networks.
7
WHY PHASE NOISE
IS IMPORTANT
Phase noise on signal sources
signal levels span a wide dynamic range. The frequency offset of concern and the
tolerable level of noise at this offset vary greatly for different microwave systems.
Sideband phase
system sensitivity.
noise
is
a concern in frequency conversion applications where
can convert
into the
information passband and limit
the
overall
Figure
2.6.
Effect of LO noise
conversion application.
in
frequency
This general
input to the frequency conversion system, where they are to be mixed with a local
oscillator signal fLO (Figure 2.6a) down to an intermediate frequency (IF) for
processing. The phase noise of
mixer products (Figure 2.6b). Note that though the system's IF filtering may be
sufficient to resolve the larger signal's mixing product (fpfLo). the smaller signal's
mixing product (f2-fLo) is
noise.
its selectivity. Three specific examples of frequency conversion applications where
phase noise is important follow.
2.6.a. Inputs to mixer.
case is
illustrated in Figure
the
no
longer recoverable due to the translated local oscillator
The noise on the local oscillator thus degrades the system's sensitivity
2.6.
Suppose two desired signals f ] and f2 are
local oscillator will be directly translated onto the
as
well as
Digital Communications System
Analog Microwave
Communications System
2.6.b. IF output.
In digital communications, phase noise very close to the carrier (less than 1 kHz) is
important. Close-in phase noise (or phase jitter in the time domain) on the system
local oscillator (LO) affects the system bit-error rate.
In many analog communications systems, modulation information exists at least
several hundred kHz away from the carrier. Initially, the signal-to-noise ratio is
sufficiently high. However, in each repeater station, the incoming signal
usually with a down &
on the carrier. If the signal passes through several repeater stations, the level of this
broadband noise induced by the
Too high a level of broadband noise on each system local oscillator will affect the
signal-to-noise (or system sensitivity) at the receiving end of a multiple repeater
system.
up
conversion method, increasing the
L.O.
can increase and start to mask the information.
level
is
amplified,
of broadband noise
Doppler Radar System
Figure
2.7.
Effect of carrier phase noise
Doppler radar system.
Doppler radars determine the velocity of a target by measuring the small shifts in
frequency that the return echoes have undergone. In actual systems, however, the
return signal is much more than just the target echo. The return includes a large
'clutter' signal from the large, stationary earth (Figure 2.7). If this clutter return is
decorrelated by the delay time difference, the phase noise from
partially or even totally mask the target signal. Thus, phase noise on the local
oscillator can set the minimum signal level that must be returned by a target in order
to be detectable.
in i
the local
oscillator can
9
3 Phase Noise Measurements—Frequency Discriminator Method
COMMON MEASUREMENT
TECHNIQUES
Direct Spectrum Measurement
Heterodyne/Counter Measurement
There
are several
of advantages and disadvantages. This brief summary of
methods also adds a few comments about their applicability.
The most straightforward method of
into a spectrum analyzer, directly measuring the power spectral density of the
oscillator. However, this method may be significantly limited by the spectrum
analyzer's dynamic range, resolution, and its own LO phase noise.
Though this direct measurement is not useful for measurements close-in to a drifting
carrier, it provides a convenient method for qualitative, quick evaluation on sources
with relatively high noise. The following conditions make the measurement valid:
A. the spectrum analyzer
the noise of the Device Under Test (DUT);
B.
since the
the DUT must be significantly below its own phase
suffice.)
This time domain method down-converts the signal under test to an intermediate
frequency. The down-converting signal must be of greater stability than the signal to
be measured. Then a high resolution frequency counter repeatedly counts the IF
signal frequency, with the time period between each measurement held
allows several calculations of the fractional frequency difference, y, over the time
period
used.
in the time domain corresponds to
methods of making phase
SSB
phase noise at the offset of interest must
spectrum analyzer
From
these values
will
for
noise
measurements, each with
some
of
the
phase
noise measurement inputs the test signal
measure total noise power, the amphtude noise
noise.
(Typically 10 dB will
y,
the Allan variance, oy(r) can
Sy(fm)
in the frequency domain.
its
own set
most common
be
lower than
constant.
be
computer. ay(r)
of
This
Figure
3.1.
Heterodyne frequency measure-
ment.
Carrier Removal/Demodulation
This method gives particularly useful results for short-term frequency instabilities
occurring over periods of time greater than 10 ms (less than 100 Hz offset from the
carrier in the frequency domain), where the phase noise is increasing rapidly. Using
the heterodyne/counter method is ideal for close-in measurements on frequency
standards. However, it
carrier greater than 10 kHz (Figure 3.1), or for measuring noise which is flat or
decreasing slowly vs. offset frequency fm (as a function having a frequency domain
slope of l/fm or less).
DUT
is
not well suited for measurements of noise at offsets from the
©■
Mosi of the techniques for phase noise measurements fall into this class. Increased
sensitivity results
ing the noise on the resultant baseband signal. Most common of this class are
1) measurements with a phase detector and 2) measurements with a frequency
discriminator. Figure 3.2 compares
heterodyne/counter measurement.
by
nulling
the
carrier, or demodulating the carrier and then measur-
some
typical sensitivities of these methods and
the
It.)
Figure 3.2. Comparison of typical system
sensitivities at 10 GHz.
10 100 Ik 10k 100k
tm Otlsalfrom Carrier (Hi)
Measurement with a Phase Detector
Figure 3.3. Basic phase detector method.
The basic phase detector or two-source method (Figure 3.3) uses a double-balanced
mixer
to
convert phase fluctuations
the same frequency (f0) are input into the
with a low-pass filter
(LPF)
out of phase (phase quadrature) the difference frequency will
output voltage of
0V.
Riding on this dc signal are ac voltage fluctuations that are
leaving
into
baseband
mixer.
the
difference frequency. If
voltage
The sum
fluctuations. Two
frequency
(2^)
the two signals
be 0 Hz
with an average
signals
is
filtered
at
off
are 90°
linearly proportional to the phase noise of both sources.
S,;,ffm}
Saieband
Analyzer
As mentioned above, for the mixer to act as a phase detector, the two signals need to
be 90°
out of
phase.
Usually
this
quadrature condition
is
maintained by
phase
locking
the two signals. Phase locking requires that at least one of the sources be
electronically tunable and requires some type of circuitry
to drive
the tunable source.
The quadrature condition is indicated by zero volts dc at the output of the phase
detector and can be monitored with an oscilloscope or a dc volt meter.
Figure 3.2 indicates that the phase detector method
yields
the best overall sensitivity.
However, because the two signals must be phase locked, the phase detector method
works optimally with fairly stable sources. The reference source must have lower
phase noise than the DUT, and measurements made inside the loop bandwidth
(bandwidth used to phase lock the two sources) require correction, increasing the
complexity of the phase detector method. See HP product note PN 11729B-1 for a
complete discussion of the phase detector method.
11
Measurement with a Frequency
Discriminator
THE DELAY LINE/MIXER
FREQUENCY DISCRIMINATOR
METHOD
Basic Theory
Unlike the phase detector method, the frequency discriminator method does not
require a second reference source phase locked to the source under test (Figure 3.4).
This makes the frequency discriminator method extremely useful for measuring
sources that are difficult to phase lock, including sources that are microphonic or
drifting
quickly.
It
can
also be
used to measure
sources
with
high-level,
low-rate phase
noise, or high close-in spurious sidebands, conditions which can pose serious problems
for the phase detector
method.
Frequency discriminators can
be
implemented in
several common ways including cavity resonators, RF bridges, and a delay line/
mixer. A wide band delay line/mixer frequency discriminator is easy to implement
using the HP 11729C Carrier Noise Test Set and common coaxial cable. This
wide-band approach will be discussed in detail in this and subsequent chapters.
The delay line/mixer implementation of a frequency discriminator (Figure 3.4)
converts the short-term frequency fluctuations of a source into voltage fluctuations
that can be measured
by a
baseband spectrum analyzer. The conversion
is
a two part
process, first converting the frequency fluctuations into phase fluctuations, and then
converting the phase fluctuations to voltage fluctuations.
The frequency fluctuation to phase fluctuation transformation (Af—-A<£) takes place
in the delay line. The nominal frequency arrives at the double-balanced mixer at a
particular phase. As the frequency changes slightly, the phase shift incurred in the
fixed delay time will change proportionally. The delay line converts the frequency
change at the line input to a phase change at the line output when compared to the
undelayed signal arriving at the mixer in the second path.
Figure 3.4. Basic delay line/mixer frequency discriminator method.
The Discriminator
Transfer Response
The double-balanced mixer, acting as a phase detector, transforms the instantaneous
phase fluctuations into voltage fluctuations (A#->AV). With the two input signals
90°
out of phase
(phase
quadrature),
the voltage out
is
proportional to the input phase
fluctuations. The voltage fluctuations can then be measured by a baseband spectrum
analyzer and converted to phase noise units.
DUT
KV,V*)
N—**SpHlltr
tuieclor
Phase
Shllter
Appendix A develops the complete transformation from frequency fluctuations
(phase
noise)
to voltage fluctuations by the delay line/mixer frequency discriminator.
The important equation is the final magnitude of the transfer response.
AV(fm) = K^27rrdAf(fm)
sin(7rfmrd)
Where AV(fm) represents the voltage fluctuations out of the discriminator and Af(fm)
represents the frequency fluctuations of the device under test
(DUT).
K^,
is
the phase
12
detector constant (phase to voltage translation)
as
developed in Appendix
B.
rd is
the
amount of delay provided by the delay line and fm is the frequency offset from the
carrier that the phase noise measurement is made.
Ti
System Sensitivity
Figure 3.5. Nulls in sensitivity of delay line
discriminator.
A frequency discriminator's system sensitivity
is
determined by the transfer response.
As shown below, it is desirable to make both the phase detector constant K0 and the
amount of delay rd large so that the voltage fluctuations AV out of a frequency
discriminator will be measurable for even small frequency fluctuations Af.
sin(7rfmrd)
AV(fJ = K
27TT
0
d
(TrfmTd)
Af(fm)
NOTE: The system sensitivity is independent of carrier frequency f0.
The magnitude of the sinusoidal output term of the frequency discriminator is
proportional to sin(7rfmrd)/(7rfmrd). This implies that the output response will have
peaks and nulls, with the first null occurring at fm = l/rd. Increasing the rate of a
modulation signal applied to the system will cause nulls to appear at frequency
multiples of l/rd (Figure 3.5).
Delay rd lOOni
0
to
FM Input \
DUT
20 MH* /C\AJ
Magnitude
ol Trans lor
Response
Measurement Limit WMhoiil
Correction
Quad
"V
Q<-
ftirj-d lm " 10 MHz lm 20 MHi
t„.
OIIHI
Irom Carrier (Hi)
To
avoid having
made at offset frequencies (fm) much
to
compensate for
the sin
less
(x)/x
response,
than l/rd. It
measurements
is
possible to measure at offset
are
typically
frequencies out to and beyond the null by scaling the measured results using the
transfer
equation.
The transfer function shows that increasing rd increases the sensitivity of
However, increasing rd also decreases the
without compensating for the sin(x)/x
However, the sensitivity of the system
offset frequencies (fm) that can
response.
For example a 200
gets very
poor near
the
be
ns
delay
the
nulls.
system.
measured
line
will
have better sensitivity close to the carrier than a 50 ns line, but will not be usable
beyond 2.5 MHz offsets without compensating for the sin(x)/x response; the 50 ns
line is usable to offsets of 10 MHz.
Increasing the delay, rd, also increases the attenuation of the
direct effect on the sensitivity provided by the delay
line,
line.
While this has no
it
does
reduce the signal into
the phase detector and can result in decreased K^ and decreased system sensitivity.
13
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