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P$ffiTI$
CIE{}RfrE
o
of
Generation
Low PhaseNoise
MicrowaveSignals
DieterScherer
September1981
o
Rt& Microwave
Measurement
Symposium
ancl
Exhibition
o ftE H"=EIITJ
1. Why are Low PhaseNoise Microwave
Signalsneeded?
Example Effectof LocalOscillator
1: PhaseNoiseon
ReceiverSelectivityin Multi Signal
Environment
ReceiverLO
Downconverted
Interfering Interfering
Signal Signal
Down-
Converted
Wanted
Signal
Wanted
Signal
Receiver lF Bandwidth
The receiver tries to see a weak wanted signal in the presence of a stmng interfering signal.
The downconversion processtransfers the noise sidebandsofthe receiver LO to both the wanted and
interfering IF signal. Sideband noise of the interfering IF signal falling into the IF bandwidth
submerges the wanted IF signal.
Example2=Etlect of CarrierPhaseNoisein a
o DopplerRadarSystem
@v --
Moving
/-r Object
9blect
(Stationaryfor \\\r^, |
Simplicity)
,rfP--. \1_.
fv
;\
'\-7-. _- \1
\r
V.fn
fD : 2'E; -
rltlr-.a-\
Glutter
Signal
fD : DoPPler shift
v : Speed of moving object
co : SPeedof light
fo : Carrier frequencY Stationary
Object
o
Signal
Transmitter
ClutterSignal
DopplerSignal
ClutterNoise SignalFrom
MovingObject
The receiver of the Doppler Radar System detects the weak frdquency shifted return signal from a
moving object as well-as a strong, unwanted return signal at fo from a large stationary object
(clutter signal).
The delay ofthe clutter return decorrelates the phase noise ofthe clutter signal from the trans-
mitter si-gxal. The resulting clutter noise at the IF port may exceed the weak Doppler signal'
2. BasicRepresentations Definition
and of O
PhaseNoise
In the Time Domain:
vt : Signalwith randomphasefluctuationA O (t)
v (t) - Vs cos [2 ntst + A 0 (t)]
OscilloscopeDisplay
V(t) : Vs Gos 2nlsl
o
at ao(t)
Frequency phaseare related
and by
1 d0(0
f(t):2n
-
Domain:
In the Frequency
Spectrum Ps
Analyzer n T P""u
Display /l\ | Ps
Pssb
fe
f6
o
.t2
o
c
o
o
(E
.c
o.s
Etl
do
lr tt
i c .-
Pssb(per1 Hz) .=
3(t^y - oo
Pg OE
ErE
=r-
6.9
.r- O
\e
"!. Hz-r'lF fm+
-E(fm) describes the RF power spectrum and is defined as the ratio of the single sideband power of
phase noise in alHzbandwidth (ft1 Hz away from the carrier frequency) to the total signal
power.
3. Key Relations {(!m), SA,O(fm),
of
Snf(fm)
For A@'ms<<1
Pssb
a$ml - l/z^d#ns- 1/z(fur, :
[ Ps
SpectralDensityof PhaseFluctuations
SnO(fm):AeQms:29(tm)
SpectralDensityof Frequency
Fluctuations
snt (rd : aril (fm): Pm (fd - zt1.,
sno v(tml
4. Three Basic Approaches
to obtain a "quiet" flow phase noise) microwave signal are considered in the following pages.
Oscillator
A. Build a Quiet Microwave
e.g., to build a 5 GHz oscillator,
use a bipolar transistor and a high Q
cavity resonator
B. Multiplya Low PhaseNoise HF or VHF Sourcb
100 MHz
GrystalOsc.
e.g., with a 100 MHz crystal oscillator
drive a step recovery diode multiplier
generating the 5 GHz signal.
Oscillatorto the Quiet
C. Phaselock Microwave
the
HF or VHFSource
100MHz
CrystalOsc.
e.g., combine the perforlnance
advantages of a 100 MHz crystal
oscillator and the 5 GHz
microwave oscillator by phase
locking the two sources via
a sampling phaselock loop.
4.1 PhaseNoise of
FreeRunningOscillators
':1)-
l
F2kTB
'
,lnf
w,
pf 4,+/ Psavt
@': -+
Equivalent
PhaseFeedback Loop:
L(arm) : 1
-;Froad _
,_ _o
AOt(arm) --e- -+
Adt(rd AOz(rr)
t
Equivalent
Low pass for . fo
Resohator 2Qload AOZ(arm)
The elosed loop response of the phase feedback loop due to the perturbation A@l(r,m) is
rx.rrt6
,ru
Aol(a,m):
irffi^l!(gl
(w%
The phase perturbance, AO1(arm),or it's power spectral density, SAel, describes
+h1-, , and empirically the |
both the additive phase noise of the amplifir, ' P s
-E ,roisgeffect by fc
r 'r,/'.
av 1'
(Seealso 5.1 and 5.2)
u {g c:'^'---
n , . -/*rfr-/
-s6i :
I AO21(rm)rms: l, *q-
\''fm/ Lt
*.-l*,<
JV
purt t/;r
PhasePerturbation
saer
fc -+ f6
The resulting phase noise of the signal coupled out of the resonator is
' x sael
Ito*, :r#(#h)
st$mt:
ResultingPhaseNoise
fm- 3
Degradation due
g{tml to additivenoise
on Post amPlifier
tm-2
FZkT
Zfv
----
2
fc fe
-2o_ --> f6
Additive noise of the following amplifier establishes the phase'nolse trOO", FqkT
t-p r, 2
^./n \
f,Lf
4/I ). -
J Lrn /
Jn," ,Jo' &)'(,r#) o
4.2 Optimization PhaseNoise
of
in Oscillators
o MaximizeQtoaded
- Use resonator with maximal unloaded Q
- Maximize reactive energy stored in resonator
- Limit signal without degrading Q
o Minimizephaseperturbance
- Use device with low noise figure
- Maximize signal level
- Choose device with low flicker noise
- Minimize effect of flicker noise
o Coupleoutput signalfrom resonator
o Set low-noise floor
- Keep output signal sufficiently high
- Use low NF post amplifrer
eo
tr
b =oa Ps
3 aaE
.9 aaE b b 6g
o oe
g a9.e_ e e
Ea 6. o.
.=
E 8.E.g
E'E=
As
J
3 E;Eg s;EE E 3
*AE E:AE 3 6
"; " J E.E
L
o
G
F
.g .tr.:9= .o.9oE .9 .9
g,=Bg
U' = EL
c E=EH
o.e'EF
E.=tsP E
o.a.=: cL
E.
cL
p.bt
(E o o tr E (E
E 6- 6- ts E o |/Dce
o
F NN ol (\t ol
d
IF
oo
oo
o
o
oc)
or(J
o \\
; ;
z o
o
CD
tt
O) o)
| |
Sri I-
\l
o
a ct
E
oo
XX
o
X
o
\1
o
rz
s-r
cLr
CLi
ES
cL c
u?-
o lo !o tO I
t(,
I
tl'l,
or-l
l! F 6D A) (r) a) c,
E
a o
tt
(o
OO o o o
t
o
I
9o\
\
o
tt
o o
e. I 8t\
- vO
g od
g (E
-9
C
u?
d
o)
o
sf
= 3E\
NS
f
E
IL
o o
tr
o
NS
?r
N
I
=
NNNN
==-"
-"
a =
CT
E
==
9t o
@
oocDol
Rt+/\
lU lr
N
J
o. A
tr
O.+.
= o ul \)
oo c 3* A
cc
x
UJ
oo
EE
oo
o
E
o
S
E
S
E
o:
P l.:\Si
-=
=
o
UJ
5 =
F
L
o 00 o a a B. ts
al o
c
o
PE
ct t\
G trtr
ooSP
sf o
o jj
E E 1'*o a
; e :s g
E oo o EE=
+.
oo
.H
o I
ia L
oo o
fl I !t
NN
TE
oo
E
o
N
-6 Es
f3
ao a
3
A tg ts
4.4 Examples Low PhaseNoise
of
Oscillators
o
o -60
tt
U
.C
H
p ElipolarTransistor
=
tt c)sc.with Tunable
C
o -80 c;oaxialResonatol T Osc. with-
o 'unable
N
t6GHz
- [Coaxial
I \Resonator at 6 GHz
.E -
100
.9
o
E
L
.9
L
L
G
-120 \
\
o
o
o
.!2 \
o - \
z 140
o
o
(u 00 MHz
.tr
o. \ Crystal
\- Osc.
t, - 1 6 0
c
o
.ct
-.1
o -- -a_Da ra--
p lHz CrystalO
a \
-g - 1 {
ot 80r
C
a 1 0 Hz 100 1 kHz 100 kHz MHz
Offset from Carrier
With the exception of the two tunable microwave oscillators, these examples of fixed oscillators give
an indication of state of the art performance regarding low phase noise.
The two tunable oscillators at 6 GHz are shown to demonstrate the performance dilference between
GaAs FET's and bipolar transistors observed in otherwise comparable circuits.
4.5 High O ResonatorEmPloyed
as
Postresonator
Equivalent
Circuit:
adt(r,,m) Ad2(arm)
1
Lt(arm):.
{ra-
t-
-;m-OL
,o
';@ {dg
AdZ( :
;Zgr_ q, " .'
I T-
i2rm Qn
@o
Phasenoise with high Q post resonator
(and low Q resonatorin oscillatorfeedback)
\
92ktml \
Phasenoise \
with high Q lr '
resonator applied
in oscillator
feedback
fo fo
2Qn 2Ql
The application of a high Q postresonator lowers phase noise of an oscillator signal outside the
bandwidth ofthe resonator. The above graph also suggeststhat lower phase noise can be obtained
by applying the high Q resonator in the oscillator feedback.
13
4.6 Stabilization Oscillator
of with
Frequency Discriminator
Oscillator
I
Frequency
I DelayLine Discriminator
Loop ! (for qrr .{l
Equivalent
frequencyfeedbackloop:
OscillatorNoise
Af osc Afeul (fm)
Oscillator
Frequency
Loop Amplifier Discriminator
VnD
-A(fm) Discriminator
Noise
Reduction of oscillator noise (Afor. or AOosc):
- ra;
ffout - A0out
- 1
4; t+ KoKDA(f. )
Frequency fluction caused by discriminator noise (Vnp)
AIbut (fm) : VnD t*
" 1 *t
KqKpA
Phase noise caused by discriminator noise (obtained by integrating Aforrl (fp)):
(fm) = Vr.rp*=f
A@out ,,
fpI(p 1 * 1-
K6KpA'
The limitations of this system lie in the discriminatornoise, gain, and bandwidth. The frequency discriminator
typically consistsof a delay line or microwave resonator and a mixer operating as a phase detector.
Multiplication a Stable
of
HF or VHF Source
Xtal Oscillator Multiplier
f1 12: nxll
rfr AtZ: nxAfl
a0t L62: nxAdl
"31 .t2: n2 9t
I
-160dBc
I
10 MHz 100MHz
Theoretical degradation of phase noise (with ideal multiplier)
82_ 20 lgn
"91
5.1 PhaseNoiseCausedby AdditiveNoise
in Amplifiers
F1kTB F2kTB
Psavl Psav
* *
Jl _ 10
Example:
Psavl _ +16 dBm Psav2 - 0 dBm
F1:5dB F2-5dB
Equivalent
Circuit Equivalentphasenoise
generator
SAOI : SAOI + SAO2: nz IIIL * EAkT
-
Psavl - Psavz
Example:
SAOI _ -174dBm + 5dB - 16dBm + 2OdB: -165d8
SAOz _ -174 dBm + 5dB - 0dBm - -169d8 T
r
SAOI_ -163.5d8 !t
$
I
gT - 7z SAOI - -166.5 dBc
Obviously, high signal levels and low noise figure amplifiers on both ends of the multiplier
minimize the effect of additive noise.
16
5.2 PhaseNoiseGa-used Multiplicativ"
by +)
Noisein Amplifiers
FKtB
Empiricalcharactenzation phasenoisecausedby
of
fr noise:
Sno:ffi(l+lqrr)
sao
+fm
The corner frequency, fc, is very device depqndent. It can range from 1 kHz (ow frequency bipolar
transistor) to 100 MHz (GaAs FET). The ftype of increase in phase noise close to the carrier is
caused by low frequency device noise modtrlating the phase of the passing RF signal by
modulating the transconductance and the input and output impedances of the amplifier.
17
5.3 Reduction + Related
I of
PhaseNoisein'Amplifiers
r-
I
I OptimumSource Low frequencyfeedback
I lmpedance
I (for low frequencies
+ and RF)
1
The effect offnoise can be reduced by
o negative feedback at low frequencies (bias stabilization)
o negative feedback for the RF signal
r designing the RF amplifier for low noise figure also at low frequencies (optimum source
impedance)
o choosing a device with low rroir"
f
o choosing a device with good linearity
18
5.4 Some PhaseNoise Measurements
on PowerAmplifiers
- 140
.9 2-510MHzPowerAm1
Amplifier
o
E
t
(t*ttl,-?loo
27 dBm
L
o 500 MHz
L
G - 150
o
9E
-o
Eg 500 MHz Video Amplifier
9=
-o - 160
+20 dBm @r500 MHz
6l!
OI
G-
o.tr
tgt ' -
(E -170
.ct 10 MHzAmplifier 10-1000 MHz
o
p +20 dBm @ 10 MHz Power Amplifier
a (zHL 2-81@ s00 MHz
.at +28dBm
ctt - 180
c
a 1 kliz 1 0 kHz 1 0 0kHz
Offset from Carrier
The above examples do not represent performance limits. Only the 10 MHz amplifier is a design
where consideration was given to low phase noise performan@ by the choice of the active device
(2N5943) and by RF and low frequency feedback.
Multiplication
5.5 Methods Frequency
of
Basic Methods t<
of Harmonic Nonlinear .g laactnzl
Generation Device Example ca tkHzOffs-et
Nonlinear
Reactance:
Varactor Varactor
Multiplier
Comb Step Recovery 500MHzx 11 - 160
Generation Diode (11thHarmonic
throughSnap (Snap diode) selected)
Action
Nonlinear
Conductance:
Diode Schottky 1 0 M H zx 2 < -169
Multiplier Barrier Schottkydiode
Diode Doubler
Transistor Bipolar 1MHzx35 -172
Multiplier Transistor Transistor
' FET (currentmode
*1,
"l
Dual gate FET
(Si and GaAs)
switch)
*Referred input signal.
to
Frequency multipliers can be grouped according to the two basic principles of operation: harmonic
generation by nonlinear reactance (capacitance) and harmonic generation by nonlinear conduc-
tance.
Multipliers with nonlinear capacitance typically resemble more efficient, simpler circuits. But they
g"tre".te significantly more phase noise than multipliers based on nonlinear conductance, like a
S.ttottt y barrier diode doubler. Higher AM to PM conversion efficiency as well as charge
fluctuations due to fluctuations of minority carrier lifetimes are speculated to causethis difference.
20
5.6 Example:500 MHzStep Recovery
Diode PulseGenerator
+2O
+10
Pour o +24 dBm Drive
[dBm1
-10
4681012 18 GHz
Comb frequency
-130
"g I
Phase Noise of 5.5 GHz Combline
[dBc/]lzl +24 dBm Drive
I
\ I
- 140 I
- 150
\Il
100 Hz 1 kHz 10 kHz 100kHz
Offset from carrier
Phase noise measured on the above step recovery diode pulse generator (HP 33004A) proved to be
quite sensitive to the drive level. Optimurr results were obtained at +24 dBm. More phase noise is
generated with increased drive levels, especially as the pulse peak starts to drive the diode into
breakdown, and with decreaseddrive levels where the comb line signal becomeslow enough to be
degraded by additive noise.
Although the impedance matching network at the input of the multiplier circuit is optimum at 500
MHz, frequency deviations of -+L}Vocan be tolerated with only slightly reduced conversion perfor-
manoe.
21
5.7 Example: MHzSchottkyBarrierDiodeDoubler
10
HP 5082-2810 .o1p.F
+13 dBm
HP 5082-2810
Schottky Barrier Diode
@ 2O MHz
I < -163 dBc
o 1 kHzotfset
The low flicker noise and the virtual absenceof minority carrier storage maker the Schottky barrier
diode a good choice as a nonlinear component for low phase noise frequency multiplication.
22
5.8 Exampleof a Low Phase Noise
Multiplication
Scheme Microwave
for
Signal Generation
r -1
8662ASynthesized
Signal Generator
Reference
Section 40 MHzXtal
| | r-r l-r Le_t r_t I i
'nxz
i
!.or.to.rTp
Hz Steps
i -.1
rl-lll;
I
a 10-20 MHz
j ";'-"^'^'l':'-
, .1 Hz Steps |
| --
b ____J
Step Recovery
-
Diode +7 dBm
640 MHz -Amp (33004A) lsolator e.g. 5.12GHz e.g. 5.6 GHz
+3 dBm
0 dBm -6 dBm
r\
fh( ffi0zryythesized Signal Generator is used here to generate a very stable and quiet microwave
sigMhe reference section of this low phase noise RF synthesizer doubles the 10 MHz Xtal signal
six times. Monolithic crystal filters are employed at 40 and 160 MHz to reduce sideband noise. The
auxiliary output signal at M0 MHz drives a step recovery diode multiplier generating 640 MHz
comb lines useful up to 18 GHz.
To obtain a continuous synthesized microwave signal (500 to 1000 MHz bandwidth), one comb line
is singled out by a bandpass filter and mixed with the standard .01 to 1280 MHz output of the
8662A.
23
PhaseNoiseof a Synthesized
MicrowaveSignalUsingthe 8602A
Synthesized
SignalGenerator
()
o -60
t,
LI
t
.F
tt
'=
t -80 \
c
o
@
N
t \ComO Line Signal
\ \tt.12GHz
._c - 1 0 0
o
$ 640
E I \uxiliary
L
o -120 \Output _
L
o PotentialPhase
o NoiseContribution
o \
\ of 8662A
o --- --\
,2 - 140 \ \-
o \
z z Xtal Oscillaor
t \ \
o
o
(E
,E
o.
t - 160 -..- --
tr
G --
ll
a--_a
--
o
tt
a
o -180
ctt
g 10 Hz 100 Hz 1 kHz 10 kHz 100 kHz 1 MHz
a Offset from Carrier
6. Principal
Comparison Between
Frequency Multiplication HF-Source
of
and Fundamental Microwave Oscillator
I
t\
t
_t ]to" HFAmp
8'u-
itou,,* Amp
:
ftrr,Vy n x f;.gp
PhaseNoiseof
HF-Source,
multiplied PhaseNoiseof
tpw Microwave
Oscillator
@
Close-inphase 1
noise :(+q-\',o",, / rrrw \2 saepw
fm2\ Zenr I ifr\t6r- /
Noisefloor n2 '
lsae HF
Amp ,lsoer* o'o
g'HF - ( Qp* saexr
Close-inphasenoise ratio gt w- \-OHF /\2 Sae,rw
sag
?'HF- n) 'SAelrw AMP
Noisefloor ratio HF
si-w- "-
emp
With identical Q at flar and frw and neglecting device differences, the multiplied HF source and
the microwave oscillator would have comparable close-in noise. However, resonators with much
higherQareavailableatHF (e.g.,2 x 106for10MHzXtal)andmorelikelytheactivedeviceofthe
HF oscillator causes less phase perturbation due to lower flicker noise. Tie multiplied HF source
therefore will have lower close-in phase noise than the fundamental microwave Lscillator.
The noise floor of each source is established by additive noise in the amplifier following the
oscillator and can be assumed comparable. Since the noise floor of the HF source is addilionally
multiplied by n, the fundamental microwave source yields a lower noise floor.
25
to
6.1 MicrowaveOscillatorPhase-Locked
HF and VHF Source
()
o
t
s
p
i -80
t,
g
G
o
N
I
.s- 1 0 0
o
o
G -_10 MHzXtalOsc
-referred
to 5 GHz
.9 -120
(g
o \ 100 MHz Xtal Osc
o
o 1 referredto 5 GHz
.t2 - 1 4 0
o 5 GHz Bipolar
z
o Transistor
o Osc with
o
-c
o. Cavity
t, - 160 Resonator
c
G
Il
o
tt
a
-g
Et
tr 1 0H z 100Hz 1 kHz 10 kHz 100kHz 1 MHz
a
Offsetfrom Garrier
10 MHz Xtal Osc 100MHzXtal Osc 5 GHz Cavity Osc
100MHz
schottky Diode Loop Step Recovery
Multiplier Filter DiodeMultiplier
(400 Hz Bandwidth) (50 kHz Bandwidth)
The above system is a paper design of a low phase noise S-band source. It combines the optimum
segments of phase noise sidebands of 3 sources, a 10 MHz crystal oscillator, a 100 MHz (7th
overtone) crystal oscillator, and a 5 GHz bipolar transistor oscillator with a cavity resonator.
The multipliers linking the oscillators are chosen such that their phase noise contribution is
negligible. This requires a Schottky barrier diode multiplier in the first link and an efficient step
recovery diode multiplier in the second link.
26
with 2
7.1 PhaseNoiseMeasurement
Sourcesand PhaseDetector
Source
Under
Test
lsolation
Reference Amplifiers
Source
AVrms
Attenuator
Wave Analyzer
SpectrumAnalyzer
: kd - Phasedetector constant
A@rms AVrms - VB peakfor sinusoidalbeat signal
4
for double-balanced mixer in linear operation
(AVrms)2 Hz)
(1
A$ml - V2S^d(fm):1/c
vB2rms
A double-balanced mixer is used here as a phase detector. It requires both signals to be in phase
quadrature steady statewise. Most sources would drift out of quadrature during the period of
measunement and therefone have to be phaselocked in a narrow band phaselock loop. The amplifiers
should prevent injection locking.
A noise floor as low as -172 dBc at 1 kHz offset has been measured with this setup using a high
level mixer and a low noise post amplifi'er.
27
AutomaticPhaseNoiseTest Systemfor
MicrowaveSources
Step Recovery
Diode
Power Multiplier
- - -l
i o' M;;";;;s-"'pr*-
640 MHz Amp (33004A)
+ 3 . 0d B m Microwave
Source
Under Test
+29 dBm
.01 to 320 MHz Hz step or DC FM)
HP 8662A
L__ _ Synth. Sig. Gen. (1280MHz)
10 MHz
Reference
D C F M I n p u tI
10 MHz
Double-Balanced Mixer
(Used as Phase Detector)
HP 9825Aor
85A Controller
HP 3582A{.02 Hz to 25.5 kHz}
HP 3585A (10 Hz to 40 MHz)
The HP 8662A provides both a very quiet 640 MHz auxiliary reference output to down convert the
microwave source under test and a .01to 1280 MHz RF signal for phase comparison with the IF of
the microwave down converter. The microwave filter and mixer can be replaced by a broadband
microwave sampler. The 8662A performs automatic calibration by a programmed frequency and
level offset. Quadrature setting on the mixer-phase detector is controlled by probing the beat signal
with a pnogrammablevoltmeter and stopping the phase advanceof the 8662A when the beat signal
voltage is sulliciently close to 0. This assumesthat the 8662A and the source under test are driven
by the same reference oscillator. With no common reference, the 86624 can be phaselocked in a
narrow bandwidth to the microwave source (e.g., free-running oscillator) via its DC FM port.
28
SystemNoiseFloor of AutomaticTest
Set at 10 GHz
e
6 -60
c
y
p
=
E
F -80
o
N
E
l. afezn DG
in Fir
c
-100
;
T
o
c
L
o @ 10GHz
F -tzo
- 1 20-
o
o
+.
o
.12
-140
z - 1 40-
o
o
(E
G
o.
- -160 .
(!
60
.ct
o
a
o
E -180-
-1 80
n1( 1 0
gt
1 RI{z 10 kHz 100 klts 1 MHz
Offset from Carrier
GLOSSARY SYMBOLS
OF
B Bandwidth
FKTB Availablenoise power in bandwidthB
fo Carrierfrequency
fc Cornerfrequencyof flicker noise
f.6 Fourierfrequency (sideband-,offset', modulation,
baseband-frequency)
(0 lnstantaneousrequency
f
a(r) Instantaneous frequencyfluctuation
8$ml Ratioof singlesideband phasenoiseto totalsignal
powerin a 1 Hzbandwidth Hertzfrom the carrier.
f6
Ps Signalpower
Pssb Powerof single sideband
Ps av Availablesignal power
Qtoad Qualityfactor of loadedresonator
sat(fm) Spectraldensityof frequencyfluctuations
sae(rm) Spectraldensityof phaseperturbation
sao(rm) Spectraldensityof phasenoise
t Time
v(t) Instantaneous voltage
Vs Peakvoltageof sinusoidalsignal
ae(t) Instantaneous fluctuationof phaseperturbance
a0(t) Instantaneous phasefluctuation
(t) Angular frequency
30
REFERENCES
1) Baugh, Richard,
A. "Low Noise FrequencyMultiplication",
Proc. 26th Annual
of Symp.
Control,pp. 48-54, June1972.
on Frequency
2) Halford, wainwright,
D., T.A.,"FlickerNoise Phase RF Amplifiers
A.E.,Barnes, of in
and Frequency
Multipliers:
characterization, & cure", Proc. 22ndAnnual
cause of
Symp.on Frequency pp.
Control. 340-341, 1968.
3) Howe,D.A.,"Frequency
DomainStabilityMeasurements:TutorialIntroduction",
A
NBSTechnicalNote679,March1976.
4) Leeson, D.B.,"A simpleModel Feedback
of oscillator
Noise
spectrum",
Proc.IEEE,
Vol. 54, pp. 329-330, February
1966.
5)Scherer,
Dieter,"DesignPrinciples TestMethods Low Phase
and for NoiseRF and
MicrowaveSources",Hewlett-Packard and Microwave
RF Measurement Symposium,
October1978. (Alsoedited version Microwaves,
in -
"Today'sLesson Learnabout
Low-NoiseDesign",part 1, pp.116- 122, Apnl 1979,part 2, pp.72-77 May 1g7g).
,
6) Scherer, Chan,8.,
D., Crilly,W., lves, Mathiesen, "Low Noise Signal
F., D., RF Genera-
Journal,pp.12-22,February
Hewlett-Packard
tor Design", 1981.
7) shoaf,J.H,, Halford,D., Risley,
A.s., "Frequencystabilityspecification
and
Measurement: Frequency Microwave
High and signals",NBs Technical Note632,
January 1973.
31
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