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5
PHASE
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Noise
Phase
ment Seminar
...,il' ' I
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.rl
Welcometo the Phase Noise Measurement Seminar.
Tbday,measuring and specifying phase noise has become
WELCOME THE
TO increasingly important as phase noise is often the
HEwLErr PAcKARD limiting factor in many RF and microwave systems.Both
ftit oscillators and deviceshave phase noise associatedwith
RF and ltlcrowave them that must be measured.
PhaseNolee lleasurementSemlnar
It,r
l\l
t\
so(f)l
\
I \---
2MH?
We want to encourageinteractive discussion
throughout today's seminar so that we can all share your
measurement problems and experiences.We hope to
benefit, too, with new applications awateness,
measurement conditions, and measurement technique. Tb
PHASE NOISE CHARACTERIZATION start, we'd like a list from you ofissues and concernsthat
OF SOURCES AND DEVICES you'd like to seeresolved in this seminar and in particular
the types ofsources or devicesthat you must characterize
and their frequency ranges.
TypicolSources: Crystol Oscillotors
YIG Oscillotors
SAWOscillotors
DROs
Synthesizers
Covity Oscillotors
Typicol Devices: Amplifiers
Multipliers
Dividers
WHATELSE?
/
These are the topics that we'll discusstoday. Where
SEMINARAGENDA practical, we shall demonstrate the measurement
conceptsusing both manual and automatic systems.We
L Bosis of Phose Noise shall also try to look more at the practical aspectsofthese
$ Wf'y is Phose Noise importont? measurements; many mathematical derivations are lefb
Whot is Phose Noise? to the expertise in the list ofreferences at the end ofyour
handout. Also note that in the back ofyour handout is a
Whot couses Phose Noise? glossary of symbols used in the seminar. (This glossary
Q u o n t i f y i n gP h o s e N o i s e will also be useful in your further reading of the
references,as some authors use different symbols for the
l l . M e o s u r e m e n tT e c h n i o u e s same parameter.)
on Sources
1. Direct Spectrum Method
2. Heterodyne/ Counter Method
3. Phose Detector Method
4. Freguency Discriminotor
Method
5. Summory of Source
M e o s u r e m e n tT e c h n i q u e s
l l l . M e o s u r e m e n to f T w o - P o r t
Phose Noise (Devices)
lV. Phose Noise Meosurement
on Pulsed Corriers
V. AM Noise Meosurement
WhV is Phase Noise Important?
There is obviously a difference in the short-term
stabilities of sources.But what is the
reason to quantify this difference?Primarily, as we shall
seefurther, short-term stability is often THE limiting
IMPORTANCE PHASENOISE
OF factor in an application. The three applications shown
VARIESWITH APPLICATION here all REQUIRE a certain level of performance in short-
term stability. Though the required level ofperformance
differs, short-term stability is crucial in each application.
Short-term stability is not a parameter that comesfor
free with good design in other areas. In fact, it is one of
the most expensive parameters to design for. Because
these three applications require different levels of
performance, it is very important to quantify and
measure the required short-term stability, and to then
choosethe right source for the application.
-
A high performance superheterodynereceiver serves as
a good example for illustration. Supposetwo signals are
LOCALOSCILTATOR PHASENOISE present at the input ofreceiver. These signals are to be
down-convertedto an IF where filters can separate the
AFFECTS RECEIVER SETECTIVITY desired signal for processing.Ifthe larger signal is
I N A M U LT I-S IGN AE N V IR ON M ENT
L desired, there should be no difficulty in recovering it. A
problem may arise, however, if the desired signal is the
smaller of the two. The phase noise of the LO is translated
directly to the mixer products. The translated noise in the
mixer may completely mask the smaller signal. Even
though the receiver's IF frlters may be sufficient to
remove the larger signal, the smaller signal is no longer
recoverable due to the LO phase noise. A noisy LO can
degrade a receiver's dynamic range as well as selectivity.
Wanted
Signal
Receiver lF Bandwidth
Doppler radars determine the velocity ofa target by
measuring the small shifts in frequency that the return
CARRIERPHASENOISE echoeshave undergone. Unfortunately, the return signal
includes much more than just the target echo.In the case
AFFECTSSENSITIVITY ofan airborne radar, the return echo also includes a large
OF A DOPPLERRADARSYSTE]UI "clutter" sigrral which is basically the unavoidable
frequency-shifted echofrom the ground. The ratio of main
beam clutter to target signal may be as high as 80 dB,
l'*t l e r L--ls-J
lmi I m \ which makes it difficult to separate the target signal from
#-
i6G-",i".".vo,
| the main beam clutter. The problem is greatly aggravated
Simpllclty)
when the received spectrum has frequency instabilities
._&{ I
causedby phase noise either on the transmitter oscillator
or the receiver LO. Such phase noise on the clutter signal
ro=r'* can partially or totally mask the target signal, depending
on its level and frequency separation from the carrier.
Signal Frcm
In a QuadraphasePhase Shift Keying system, the IQ
position of the information signal on the state diagram
dependson the amplitude and phase information after
tOCAt OSCILTATOR PHASE NOISE demodulation. Amplitude noise affects the distance from
AFFECTSTHE BIT ERRORRATE the origin while phase noise affects the angular
positioning. Close-in phase noise (or phasejitter in the
OF A OPSK SYSTEM time domain) on the system local oscillator affects the
system bit-error rate.
Sto te D i o g ro m
Phase noise is important in these applications, but
IS ALL NOISEIMPORTANT ALt OF where the noise is important (i.e., at what offset from the
TO carrier) differs. This graph shows some typical ranges of
THE PEOPLEALL OF THE TIME? offset frequencies where noise is important for different
applications. Becausethe range ofoffset frequencies
.o where phase noise is important changeswith the
o application, the type ofsource used also changes.
E
c)
'c
L
o
C)
o
o
.o
o
z
c)
a
o
_c
(L
(D
a
a
1 0 1 0 0 ' lk 1 0 k 1 0 0 k 1 M 1 0 M1 0 0 M
Offset from Corrier (Hz)
What is phase noise?What is a quantity with a
statistical randomness?
WHATIS PHASENOISE?
T\vovery different sourceswith many differences in
performance (and difference in cost!).One way they differ
is in their frequency stability. This difference in
frequency stability will definitely affect the type of
application that they will be used in. What is frequency
stability, and how can we describe the difference in
frequency stability ofthese two sources?
Gunn DiodeOscillator
Synthesized
Source
Frequency stability is generally defined by two
parameters: long-term and short-term stability. It is
LONG-TERTFREOUENCY
STABIUW commonly said that long-term frequency stability
describesthe variation in signal frequency that occurs
over long time periods, and short-term stability refers to
the variations that occur over time periods ofa few
secondsor less.
However, the dividing line between long-term and
time short-term stability is really a function ofapplication. For
(doys, months, yeors) example, in a communications system, all variations
o Slow chonge in overoge or which are slower than the narrowest carrier or data clock
tracking loop would be referred to as long-term, with the
nominol frequency dividing line being a fraction ofa second.On the other
hand, a timekeeping system would observeday-to-day
SHORT-TERTI FREOUEI{CY STABIUTY irregularities as short-term, with a dividing line
corresponding to the length of a mission, which might be
rt several days.
f6@ Long-term stability refers to slow changesin the
average frequency with time due to secular changes in the
resonator. It is usually expressedas a ratio, Af/ffor a
r (seconds)
given period of time - hours, days, or even months. Long-
term frequency stability is commonly called frequency
drift, and is usually linear or sometimes exponential.
o Instantaneous
frequencyvariations Short-term stability refers to changesin frequency
around nominal
the frequency which cannot be describedas offset (static error) or drift,
but are observedas random and/or periodic fluctuations
about a mean. They are usually describedin terms of
variations about the nominal frequency that occur over
time periods ofa few secondsor less.
This demonstration illustrates the difference in the
DEMONSTRATION frequency spectrum oftwo sourceswith different short-
term stability characteristics.
HP 8566 A,/8
StabilityComparison
Short-term stability is more familiar to most of us in
the frequency domain. Looking at a signal on an ideal
spectrum analyzer (one with infrnitely sharp filters and
SHORT-TERM
COMPARING no short-term instability of its own), all of the signal's
energ'ydriesnot occur at a single spectral line, but rather
FREOUENCYSTABILITIES someof the signal's energ"yoccurs at frequencies offset
from the nominal frequency.
lP ^",
16 dB/
Using a spectrum analyzer to observeour two example
sources,it's obvious that the sourcesdiffer in short-term
stability. How can we describe and quantify this
difference?What units can we use to comparewhat we
t can visually seehere? And once deciding upon units to
t/l h use, how can we measure these values?
VilI I
|l,I 1..,
[lt,ri il,
tr
I rl|l1ll ll'r I
llll lil rllltfl!
tl
CENTER IO.53I 462 g EHz SPAN 26. S kHz
RES Bf lgO Hz VBr IOO Hz SIP 6. SO a.c
In discussing short-term stability, there are two
"classes"offrequency variations - non-random (or
deterministic) and random. The frrst, deterministic (or
TYPESOF NOISE systematic, periodic, discrete, secular) are discrete signals
which appear as distinct componentson our ideal
m9.mE91 tft spectrum analyzer RF sideband spectrum. These signals,
commonly called spurious, can be related to known
phenomena in the signal source such as power line
frequency, vibration frequencies, or mixer products.
The secondtype ofphase instability is random in
nature, and is commonly called phase noise. The sources
ofrandom noisein an oscillator include thermal noise,
shot noise.and flicker noise.
ffirytt b Et
o Deterministic
(Discrete)
o C o n t i n u o u( R o n d o m )
s
Before proceeding to the definitions ofphase noise, let's
get a more intuitive feel. If one could design a perfect
IDEALSIGNAL oscillator, all signals could be describedlike this. In the
frequency domain, this represents a signal with all
energy at a single spectral line.
Yk) = AosinLntot
But in the real world, there's always a little something
wha,ro, extra on your signal. Unwanted amplitude and frequency
fluctuations are present on the signal. Note that the
frequency fluctuations are actually an added term to the
Ao ; norninol
onpllludo phase angle term ofthe equation ofa signal. Because
phase and frequency are related, you can speak
h = notttinof
lro4uonorl equivalently about unwanted frequency or phase
fluctuations.
REALWORLD
SIGNAL
r'tf"r
v $)= lr" + e(t)l vsinI Lnf^t +0(t)|
| l
l
whoro
t&) = onplitudo
lbrchustions
Q0)= phaso
lluotuftions
Concentrating frrst on the frequency fluctuations, let's
seewhat these fluctuations would look like on a signal. In
the time domain, phase is measured from a zero crossing,
IN THETIMEDOMAIN . .
. as illustrated by plotting the phase angle as the radius
PhaseJitter vector rotates at a constant angular rate determined by
the frequency. Random noise processes affect the signal
OscilloscopeDisplay throughout its period.
Let's look on just one particular time in which the sine
wave is perturbed for a short instant by noise. In this
perturbed area, the AV and Lt(or AO) correspondsto
another frequency. These perturbations repeat on each
cycle at a recognizable, somewhat constant repetition
rate. In fact, we will find that there is a signifrcant
amount of power in another signal whose period is the
V(l; =4ot,n [2rfo t + Ad(t)] period ofthe perturbation shown.
90" Thus, in a sideband spectrum (rms power vs.
frequency), we will observe a noticeable amount of power
v0) in the spectrum at the frequency corresponding to this
perturbation, with an amplitude related to the
180" 00 characteristics of the perturbations. Thus, frequency
variations, or phase noise since it is really instantaneous
phase fluctuations, occur for a given instant of time
within the cycle. How much time the signal spendsat any ^
270"
Angular Frequency f,'n".1ii""-J:x'J,::3i':::H:'.Hil*s,11
frequency domain.
Another way to think about phase noise is as a
continuous spectrum of infrnitely closephase modulation
sidebands,arising from a compositeoflow frequency
signals. A signal's stability can be describedas power
IN THE FREOUENCY DOMAIN... spectral density ofphase fluctuations or frequency
fluctuations (and later on we'll seethe power spectral
PowerSpectrelDenslty density of amplitude fluctuations).
N
E
g
o
q,
fo
Discussionsabout phase noise can be divided into two
topics: the total or "absolute" noise from an oscillator or
system that generates a signal and the added or "two-
port" noise that is added to a signal as it passesthrough a
device or system.
Absolute noise measurements on the output signal of a
ABSOLUTE (TOTAI} NOISE
system would include the noise that occurswhen the
signal is generated and the "two-port" noise addedby the
o Specified sources complete
on or system signal processingdevices.
system
"Tho-port" (or residual or additive) noise refers to the
noise of devices(amplifrers, dividers, delay lines). Tko-
port noise is the noise contributed by a device, regardless
ofthe noise ofthe reference oscillator used. One way to
look at "two-port" noise is how much noise would be added
by a device ifa perfect (noise-less)signal were input to it.
TWO-PORT The name "two-port" emphasizesthe contributed nature
ofthe noise ofdevices.
(RESIDUAIOR ADDITIVEI
NOISE
. Specified devices or subsystem
on
A "system" - such as a synthesizer - has both two-port
and absolute noise associatedwith it. The reference signal
of the synthesizer, comprising an oscillating element, has
absolute noise. The synthesizer circuitry - phase lock
'TWO-PORT V8. ABSOIUTE loops,multipliers, dividers, etc. - have some two-port
NOISE noise contribution. The integrated system, the
synthesizer, also has a value for absolute noise, or all
EXAMPLE: noise present at the output.
SYNTHESIZER
.\ l
t
Absolute
10
The absolute noise ofthe reference and the synthesizer,
and the two-port noise of the synthesizer are compared
here. Though the units have not been explained yet, there
'TWO-PORT"vs. ABSOLUTE are still several important points about this graph. One,
NOISE typically two-port noise ofdevices is less than the
absolute noise on sources,in particular at higher carrier
frequencies. Second,even with a perfect reference, the
absolute noise ofthe system could never be below its two-
I
port noise level.
F_
5
o
6
z
$
d
What CausesPhase Noise?
In this section we will briefly look at the basics of noise
generation. What are thermal noise and noise figure and
THE BASICSOF NOISEGENERATION how are they related to phase noise?
Thermol Noise?
Noise Figure?
PhoseNoise?
11
Thermal noise is the mean available noise power per
THERMALNOISE HZ of bandwidth from a resistor at a temperature of TK.
As the temperature of the resistor increases,the kinetic
energ'yof its electrons increase and more power becomes
s?oolrum available. Thermal noise is broadband and virtuallv flat
Anol!{'z0r with frequency.
0ioploy
po,nl
w"o,
truautnqla'f
=
NP ttTB
K= Boltznrcn'g
congtatt
T = Ton?sroluro
K
B= Bondwidth
=
ForT 29oK
=-
dB!$ftO t1l dbn
=-zo+
Np Hz Hz
Noise Figure is simply the ratio of the signal-to-noise
ratio at the input ofa two-port device to the signal-to-noise
ratio at the output, in dB, at a source impedance
temperature of 290K. In other words, noise figure is a
NOISEFIGURE measure ofthe signal degradation as it passesthrough a
device. What do thermal noise and noise figure have to do
with phase noise?
t$/N)in (s/N)out
N
T
, =(6/N)in
'- I
@r-rlr,=,ron
($/NJg
F(dE) bo
=ro-, qs/N)oullrr,
I
,sot,
Whot lhormol ond
do no\bo nciuo,|iguro
houo,, with phoco,
lo do no\to?,
The noise power at the output of an amplifier can be
AMPLIFIER
OUTPUTNOISEAS A calculated if its gain and noise figure are known. The
noise at the output is given by Nour: FGkTB.
FUNCTION THERMAT
OF NOISE
The display shows the rms voltages of a signal and
AND NOISEFIGURE noise at the output of the amplifrer. lVe want to see how
this noise affects the phase noise of the amplifier.
=
Nout f cfib
lo-l^ lo+lm
6P;m1 A0 rm5r
Using phasor methods, we can calculate the effect of the
superimposednoise voltages on the carrier signal. We can
seefrom the phasor diagram that VN,-" producesa LA" ,
USINGPHASORRELATIONSHIPS term. For small AZ.-", LA, .: Vpr-,Ay'so".r..The total
LA, , can be found by adding the two individual phase
componentspowerwise. Squaring this result and dividing
by the bandwidth gives Ss(f), the spectral density ofphase
fluctuations, or phase noise. The phase noise is directly
proportional to the thermal noise at the input and the
noise frgure of the ampliflrer.
XJT
Ad;65
Forcmoll
L,.rms=# I rokrl
-l
-
,w
=Mrffi,/+
Afr6etotol
^ry=,f,
ss(r)= [*,J
13
In addition to a thermal noise floor of approximately
constant level with frequency, active devicesexhibit a
ACTUALPHASENOISE noise flicker characteristic which intercepts the thermal
noise floor at an empirically determined frequency f". For
offset frequencies below f-S6G) increaseswith f-r.
pl
ollcollronurrior,f
lo = crrrno,r
lruquunoy
o Phose noise "flicker" oppeors
(fc
o Rule of thumb: "flicker" noise is
*-120 dBc/Hz ol 1 Hz offset
In an oscillator, the white {oand flicker f-t phase
modulations causeeven greater slopesofnoise spectra.
Let's seehow that happens. First, add a resonator ofsome
NOISEPROCESSESIN quality factor Q to the output of an amplifier. Second,
connect the resonator output back to the amplifrer input
AN OSCILLATOR in the proper polarity for positive feedback.Third,
consider the {oand f-'ofthe amplifrer to be represented by
a phase modulator LZwith a perfect amplifrer. Next, any
oscillator will shift frequency in responseto a phase
change anywhere in its loop, Lf : LA$12q. Since fe and Q
fo+af are constants, then phase modulation is converted
directly to frequency modulation. This makes their
spectral slopes2 units more negative.
A f : A d2 0 e -
'
:
Slmple Feedback Model
So the oscillating loop itselfwill have noise slopesoff '
-3.
andf But the buffer amplifier found in most oscillators
adds its own f and f-'noise slopesto the output signal.
N O IS E R OC E S S EIN
P S
AN OSCITLATOR
b e c o m e sf - z , f - 3
- AY ro
thruAf nd
20
Slmple Model wlth Bufler Ampllller
The resulting phase noise plot for an actual oscillator is
as shown. The frequency domain responseof a source
would include terms like Random Walk, Flicker and
White Phase Noise to describe the slope of spectral
density for given offsets.
NOISEPROCESSES
I N T H E F R E OU E N CD OMA IN
Y
-2
t R$dom walk Phas (whito FMI
15
SEMINARAGENDA
l. Bosis of Phose Noise
Why is Phose Noise importont?
Whot is Phose Noise?
Whot couses Phose Noise?
r) quqnl;lting Phose Noise
il. Meosurement Technioues
on Sources
1. Direct Soectrum Method
2. Heterodyne/Counter Method
3. Phose Detector Method
4. Frequency Discriminotor
Method
5. Summory of Source
M e o s u r e m e n tT e c h n i o u e s
ilt. Meosurement of Two-Port
Phose Noise (Devices)
lv. Phose Noise Meosurement
on Pulsed Corriers
AM Noise Meosurement
Quantifying Phase Noise
There are many different units used to quantify phase
noise. In this section we will examine the most common
ones,how they are derived and how they relate to one
another.
e
n4
{0)
500
OUANTIFYING
PHASENOISE
sy(f)
oots\
oyct
srt"
Due to random phase fluctuations, in the frequency
domain a signal is no longer a discrete spectral line but
spreadsout over frequencies both above and below the
nominal signal frequency in the form of modulation
sidebands.We need a way to quantify this frequency
PHASEFLUCTUATIONS instability, or phase noise.
IN THE FREOUENCY
DOIIAIN
!\
q,
3
o
o.
to fo
V(t)=Aosln[2rfs t +A@(l)]
Where 6(t) : rondom
phose fluctuotions
Due to the random nature ofthe instabilities, the phase
deviation is represented by a spectral density distribution
plot. The term spectral density describesthe energy
PHASENOISEIN TERMSOF distribution as a continuous function, expressedin units
POWERSPECTRAL DENSITY of energy within a given bandwidth. The phase
modulation ofthe carrier is actually equivalent to phase
modulation by a noise source.The short-term instabilities
are measured as low-level phase modulation of the
carrier. Four units used to quantify the spectral density
^[-.. are shown.
r\_
l
f0 SSgPhow
noisoloarr'r;r
36$) Spwtrol
donrity
of
phoso fluotudtlonc
$61(0Spoctrol
donsityof
I roqnnc,y
f luctuotionr
Sy(f) Jpoctrcl ol
&,nifty
'
lroctioncl
froquc,noy
fluciuotions
t7
A measure of phase instability often used is S6(f), the
sp(0 oR SPECTRAL
DENSITY
oF spectral density ofphase fluctuations on a per-Hertz
basis. If we demodulate the phase modulated signal using
PHASE FLUCTUATIONS a phase detector we obtain Vootas a function ofthe phase
fluctuations of the incoming signal. Measuring V",s on I
spectrum analyzer gives AV"-"(f) proportional b LA, ,(f).
s40
Sy*"(f)/K62 gives AZ2,-"(f) which is the spectral density
/'ra') an equivalent phase modulating sourcein rad2lHz. This
\;/ spectral density is particularly useful for analysis of
phase noise effects on systems which have phase sensitive
circuits such as digital FM communication links.
}lfstt corrioqt
lron ftzf
Demodulotephose modulotedsignol
with phose detector
=
AVoutKCl0in K6='tfrod
0nbpoolrum onolyzor
' X6
AVp6s(f) l$rrrtfl [vJ
svrrro
,.,,.-L0'76(i) Avrrme(fl - ,
- --, [roo'l
'
B K6tB K6' LHZJ
$vrr.(O = aehe' ryectrol
powo.r dtnsily tht'
ol
flustuationsoftho
voltoq{, out
ohaso'do,'lc,c'lor
Another common term for quantifying short term
S6s (0 OR SPECTRAL
DENSITY
oF frequency instability is Sa{l), the spectral density of
FREOUENCY FLUCTUATIONS frequency fluctuations on a per-Hertz basis. 56(0 can be
derived from S6(f) by transforming Af(t) from the time
domain to the frequency domain by_Laplacetransform.
sL+6) This gives LK1 : : f LA(f),-" or Afn ;^" : P LAz (f),^,
$)
"
which is the spectral density offrequency fluctuations in
lr,7 Hz'lHz. Note So1fl: fzSoff) [Hz"lHz]. Caution must be
l") taken when using S6(f) and Ss(O to compare the phase
noise ofsources at different frequencies,
lron oo"ir,nf pt]
offsot
5s1Ounfu, de,riuod s66)
lron
| daf,(t)
Af(t] =
'
?.n dt
Troncl
ormoA the,
into troquonoy ....,
donoin
=4unhr)
,rtff)
/' ll
=
Afim6(fl t'ti'rms6)hzl
sor,(f)=
N'rmsff)
q
= lHz'l
5a1(l) tt sq$) t - l
lJlz I
Sy(f),the spectral density offractional frequency
fluctuations allows direct comparison between sourcesof
s y (0 oR SPECTRALDENSTTY different carrier frequencies. S"(f) is also related to Ss(f)
OF FRACTIONAL ancl Sa{fl. Using the same Laplace transform approach on
Af(tyf" we seethat the spectral density offractional
FREOUENCY FLUCTUATIONS frequency fluctuations is equal to the spectral density of
frequency fluctuation divided by fo2.
sv0
frl
LH'J
}ffseft corrio,r,
lron I pzf
'yff) isroldlt'dto
560 | dAo(t)
Af(t) zr dl
\ , 1 j=
T= h
lronslorwd lho
inlo lrogvo,ncy .,...
domoln
v0=* toct
.tt0
rli^r$)=#Adi'sr)
--io,-l--* sotil rl
s.,6,Ltd'rns(t),!'
I
"yur lqJ
(D
"C is an inclirect measure of noise energy easily
related to the RF power spectrum observedon a spectrum
analyzer. J (0 is defrned as a the ratio ofthe power in one
phase modulation sideband on a per-Hertz basis, to the
total signal power. J (f) is usually presented
SINGTE SIDEBAND PHASENOISE logarithmically as a plot of phase modulation sidebands
in the frequency domain, expressedin dB relative to the
POWER
/ O OR SIDEBAND carrier per Hertz of bandwidth [dBc/Hz]. We will seethat
WITHRESPECT CARRIER
TO LEVEL J (f) can be derived from S6(f) using phase modulation
theory.
t I
{(f) l-\
----.
[,r,ll
l"ll \
ollottlroncorrior, fF,z)
I
J (0 - Power DcngiU (Onc Phos6 Modulotlon Sldcbond)
Corricr Powcr H
2(l) con b. dcrlvcd from s/ (l) uslng Phoac Modulotlon Thcory
19
Phase modulation at a rate off* producescarrier
sidebandsspacedsymmetrically about the carrier at
PHASEMODULATTON tm ...
AT intervals which are multiples of the modulation rate. The
amplitude of the carrier and sidebandsare determined by
the modulation index(p) which is equal to LAp"^x.
fo-fn fo fo+fm
Producessidebondsof fm
intervolsfrom corrier.
Amplitudeof corrier ond sidebonds
ore determined by L/ peok,
the modulotionndex (P).
i
Bessel functions relate the carrier amplitude to the
sideband amplitude. Here we seeBessel coe{Iicients for
BESSELFUNCTIONS the first 10 sidebandsas a function of the modulation
RELATECARRIERAMPLITUDE index, LAo"4.. We can relate 56(0 to l(D by making an
important assumption. "C(f) refers to the power density
TO SIDEBANDAMPUTUDE one phase modulation sideband. We can seefrom the
graph that the sideband power will be restricted to the
Jn(F)
frrst sideband only for modulation indices <<1 radian.
t.0
For the same restriction, the relative amplitude of the
carrier will always be one, and the slope of the Bessel
:2 n=g function will be 72.
Ope.aling Region
Thus for LA o.^u< < l.we have V""6(fl/V" : YzLA .
p"uu(fl
Then P""s(f)/P, : %LAi.^u(f). Converting the peak phase
deviation to an rms val-ueand normalizing to alHz
bandwidth we have Ln(I) : lzSq(f).
FOR L/pear << I RADTAN
u1':ro', = = t,
t, ti,py6)(cinusoidotAg)
Vspk 1'
W="*a = l aororortf)
vr' ?t +'r'
Pssbo
=tll7 Mr^r(+)1'
?6 +t I
Ps59(f) r
- -zaOlr"rtfl
lroa;l
% B-- rrz- T lnr.,
P3e50
| = d l i l = L s 6 l,a
t+)
T I B=tHz LH'
Caution must be exercisedwhen -C(flis calculated from
the spectral density ofthe phase fluctuations becauseof
(0
the small angle criterion. This plot of "C resulting from
REGION VALIDITY
OF OF the phase noise of a free running VCO illustrates the
,(f) erroneous results that can occur ifthe instantaneous
t(f) : +_
" phase modulation exceedsa small angle. Approaching the
carrier, "C(0is obviously increasingly in error as it
reachesa relative level of + 45 dBclHz at a t Hz offset (45
E X T F t 1O F F . 8 6 { O E X 7 R E F . 3 2 8 K H Z P K B E V F
dB more noise power at atHz offset in a 1 Hz bandwidth
that the total power in the signal.)
On this graph the 10 dB/decadeline is drawn on the plot
for a peak phase deviation of0.2 radians integrated over
any one decadeof offset frequency. At approximately 0.2
radians the power in the higher order sidebandsofthe
phase modulation is still insignifrcant comparedto the
power in the first order sideband which ensures the
calculation of J(0 is still valid. Above the line the plot of
J (0 is increasingly invalid and Ss(0 must be used to
represent the phase noise ofthe signal.
rg t@ lK IBK l00x ri lff
L(f) (dBclHzl vs {tHzl aAiH:
2L
Frequency stability is also defrned in the time domain
with a sample variance known as the Allan variance.
Oy(?) OR STANDARDDEVtATtoN o"(t) is the standard deviation offractional frequency
fluctuations Af/fo. A short r will produce short-term
OF FRACTIONAL information, while for a long r, the short term
FREOUENCY FTUCTUATTONS instabilities will tend to average out and you will be left
(TIMEDOMAIN} with longer-term information.
r $uondc)
oy'(r)= Alon -
vorionr.o (!r*r-Tr)'
-t*!
y L= outrog|Touer
- f
lnloruol lonq
i
=
11 #of sonplos, = pariod ooch
7 ol sanplo,
. stotistiool
nooauru,
There are equations available to translate between the
CONVERSION
BETWEENTIME AND time and frequency domains. The translations apply to
noise processes having particular slopes,and tend to
FREOUENCYDOMAIN reverse the independent variable axis. An example ofone
such equation for a slope of I (f) of f-'is given here.
&$) or s6G)
olloot pl
lron corr\or,t
l\ r lsocondl
For
orcnplo,lor ol{tl) asl-L.
slogo
ffi
vdcrr/ | tt
O y ( i )= ' T T-'"
'to
. fi acowi t ronolst o
so obl
. rnuorlingoros
22
Residual FM is a familiar measure of frequency
RELATINGRESIDUAL TO
FM instability that is related to Ss(D. Residual FM is the
total rms frequency deviation with a specifiedbandwidth.
,e(0 s/(0
oR Commonly used bandwidths are 50Hz to 3kHz, 300H2 to
3kHz, and 2|Hzto 15kHz. Only the short-term frequency
6a1ff) instability occuring at rates within the bandwidth is
T ."1 indicated. No information regarding the relative
lHz'l weighting ofinstability rates is conveyed.The presenceof
L-r.J large spurious signals at frequencies near the frequency
ofthe signal under test can greatly exaggerate the
measured level ofresidual FM since the spurious signals
are detected as FM sidebands.
olfsa,t oorrior,f
lrorn l*z)
ros7n = $lal rme
frl,qul/nc,y
douiotion
with'in
bsndwidth
spr,c,ifiod
= =
Sa1(fl AlLrncfl +t s6$)
BD
= rb
ru,'Fn[' ,@
=
Io'
23
II. Measurement Tbchniques on Sources
SETII{AR AGENDA
l. Bosis of Phose Noise
Why is Phose Noise importont?
Whot is Phose Noise?
Whot couses Phose Noise?
Quontifying Phose Noise
c) tt. Meosurement
Techniques
on Sources
1. Direct Spectrum Method
2. Heterodyne/Counter Method
3. Phose Detector Method
4. Frequency Discriminotor
Method
5. Summory of Source
Meosurement Techniques
lll. Meosurement of Two-Port
Phose Noise (Devices)
lV. Phose Noise Meosurement
on Pulsed Corriers
V. AM Noise Meosuremenr
Here are four representative sourcesthat will be used
PHASENOISEOF TYPICAL
SOUFCES throughout the seminar in judging and comparing the
FORMEASUREMENTTECHNIOUE COMPARISON capabilites of the four measurement methods.
10 MHz OROAT SMESZEB REE.EUNNING
ru lGHz 4110ft VmATOGk
F
24
1. Direct Spectrrrm Method
The simplest, easiest, and perhaps oldest method for
phase noise analysis ofsources is the direct spectrum
technique. Here, the Device Under Tbst (DUT) is input
into a spectrum analyzer tuned to the carrier frequency,
directly measuring the power spectral density of the
oscillator in terms of J (fl.
PHASENOISEMEASUREMENT
OF SOURCES
1 . D i r e c t S p e c t r u mA n o l y s i s
SpeclrumAnalYzer
O-
Device
Under
Test (DUT)
HP makes a number of high-quality spectrum analyzers
that might be appropriate for direct spectrum analysis of
sources.Analyzers covering from sub-Hertz to 22 GHz are
DIRECT SPECTRUM available, to cover the frequency range of any DUT.
M E A S U R E ME N TH OIC E S
C
20 Hzlo 40 MHz
e-* l-", 3.ssnl synrhes
ized
1 Hz to 40 MHz
O...-.---.-------.--*l-'tro.^l Synrhesized
10 MHz to 40 GHz
O-ll-Hp8s6ill
100Hz to 1.5GHz
G-t-npr56&A/B I synrhesized
10 MHz lo22GHz
o-_tl*,6,Al
100 Hz to 22 GHz
l{p
O---.--.----.------*f8s66dl synrhesized
25
Of all the analyzers listed, the best choicesfor direct
DIRECT
SPECTRU]S spectrum analysis are those listed here. These are all
analog spectrum analyzers with synthesizedLO's, and
MEASURE]UIENT
CHOICES narrow resolution bandwidths.
As we will seelater, spectrum analyzers with
o 20 Hz to 40 MHz synthesized local oscillators offer the optimum
o 3 Hz RBW min. i@) performance for direct spectrum analysis ofphase noise.
o -137 dBm to +30 dBm
o SynthesizedL0
o 100 Hz to 1.5 GHz
@ffi1 o 1 0 H z R B Wm i n .@ )
o -134 dBm to +30 dBm
lt===il"".IFE:il
rrc o SynthesizedLO
Mffi
f ,,==r
EA
ilFF:ll
o 100 Hz to 22 GHz
o 10 Hz RBWmin.(@)
o -134 dBm to +30 dBm
IE o SynthesizedLO
This demonstration illustrates the measurement of the
single sidebandphasenoise, f (f), ofa source.
DEI'ONSTRATION
A typical spectrum analyzer display would look like
I N T E R P R E T IN G E R E S U L TS
TH this. What is "C(0 at a 10 kHz offset for this test source?
P ,/f\
t (r) = -j*I! fd3c/srl Here, the power in the carrier P" is read as + 7 dBm.
rs
The marker reads -67 dBm, 10 kHz away from the
1 . M e o s u r e o r r i e r l e v e lP ,
c carrier. P""6minus P" is equal to -74 dBc. But is this
equal to J (0?
2. M e o s u r e i d e b o n dl e v e l P " u 6 f )
s (
3. Apply Corrections
46564 ot 64AMHZ- 01.ec! Spcctrum Mcthod
ATTEN 20 dB
, _ REF
Ln 1O.A den
ra dB/
{l yl,,il
tlltu,,
lr!t
W I t, a!
CENTER 646.648 MHz SPAN IOA kHz
RES Bl I kHz VAY 196 Hz SIP 3. OO scc
In the direct spectrum technique, there are two
correction factors that must be used on our value for P""6
DIRECT SPECTRUMANATYSIS (f).
minus P" in order to yield "C First, J (0 is specifredin a
Corrcctlon Factoru one hertz bandwidth, and our measurement bandwidth on
the previous slide was not one hertz. Tlpically, in the
direct spectrum technique, it's impossible (and very
1. Noise bondwidthnormolizotion impractical in terms of time) to make measurements in a
2. Effect of spectrum onolyzer one hertz bandwidth. We also must be careful that our
measurement circuitry doesnot effect the quantity we are
circuitry trying to measure, and that it measures it accurately.
27
Normalizing to aLHz noise bandwidth from a given
measurement bandwidth is a simple mattet, involving a
CORRECTINGFOR... simple power relationship. Looking back two slides, what
is our measurement bandwidth?
1 . N o i s eb o n d w i d t h o r m o l i z o t i o n
n
Foctors : 10 log -Pio-
BtHt
wnere
B,,.', meosurement
is
bondwidth
B 19, is one hertz noise
bondwidth
But J({) requires us to normalize to an equivalent I Hz
noise bandwidth. A spectrum analyzer's 3 dB resolution
bandwidth is not its equivalent noise bandwidth. (Noise is
BUT-RESOLUTION DWIDTH
BAN defrned as any signal which has its energy present over a
frequency band significantly wider than the spectrum
+ NOISEBANDWIDTH analyzer resolution BW; ie, any signal where individual
Analog Spectrum Analyzer spectral componentsare not resolved.) The noise
bandwidth is defined as the bandwidth ofan ideal
rectangular filter having the sam◦ Jabse Service Manual Search 2024 ◦ Jabse Pravopis ◦ onTap.bg ◦ Other service manual resources online : Fixya ◦ eServiceinfo