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Tutorial on Modern Ultra Low Noise Microwave Transistor
Oscillator Design
Ulrich L. Rohde, Ph.D.*Chairman Synergy Microwave Corp.
*Prof. of RF Circuit and Microwave Circuit Design
Brandenburg University of Technology
Cottbus, Germany
Columbia UniversitySeptember 11, 2009
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A typical linear oscillator phase noise model (block diagram)Leeson Model
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A typical block diagram of feedback oscillator circuit
++−
+++
−
++−=
21
2122
21221
21
2122
212
212
21
)()1()()(
)1(1
)( CCCY
LYLY
CCCCCC
jLYCCC
YZ
Pp
P
P
P
pppacakageIN ωω
ωωωω
Colpitts oscillator with base-lead inductances and package capacitance. CC is neglected.The expression of input impedance is given as
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This Figure shows the R&S vector analyzer and the test fixture
Typical measurement setup for evaluation of large signal parameters (R&S vector analyzer and the test fixture for the transistor of choice )
Agilent now calls this X Parameters
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The bias, drive level, and frequency dependent S parameters are then obtained for practical use.
Measured large-signal S11 of the BFP520
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Measured large-signal S12 of the BFP520
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Measured large-signal S21 of the BFP520
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Measured large-signal S22 of the BFP520
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Typical transient simulation of a ceramic resonator-based high-Q oscillator (node of the voltagefor display is taken from the emitter)
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This Figure illustrates the start and steady-state oscillation conditions.
A typical start and steady-state oscillation conditions.Ra(A, f) is the starting negative Resistance, which gets lower as the amplitude increases.Therefore, feedback must be sufficient to maintain enough negative resistance to sustain oscillating.
Negative Resistance
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frequencylfundamentapeak
peak
VI
Y−
=1
121
)()(2)cos(
)()(21
0
11
1 0
111 xI
xIIIwtxIxIII dcpeakdcn
=⇒
+= ∑
∝
=
x = normalized drive level
xq
kTVpeak
=1
)(arg21 xGY msignalel =−
mdc
signalsmall gqkT
IY ==− /21
10
1
10
1arg21 )(
)(2)()(2
)(==
−
=
==
n
m
n
dcmsignalel xI
xIx
gxIxI
kTxqI
xGY
)()(2)(
][][
0
1
121
1arg21
xxIxI
gxG
YY
m
m
nsignalsmall
nsignalel ⇒==−
=−
)(arg2121 xGgYY mmsignalelsignalsmall >⇒> −−
Y21 Large Signal Calculation
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Plot shows the collector current as a function of time with respect to normalized base drive Voltage x.
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A typical phase noise plot of LC-based 1GHz oscillator as a function of x
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A typical block diagram where oscillator acts like a mixer.
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This equation is the linear Leeson equation, with the pushing effect omitted and the flicker term added byDieter Scherer (Hewlett Packard, about 1975); the final version with the pushing (supply voltage dependencyVCO effect added by Rohde 2004), is
+
+
+= 2
20
2
20 2
21
)2(1log10)(
msavm
c
Lmm f
kTRKP
FkTff
Qff
f
The resulting phase noise in linear terms can be calculated as
This pushing also applies to the VCO case.
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A typical phase noise plot for an ideal 1 GHz oscillator phase noise of about – 140 dBc/Hz at offset of 10 kHz offset, assuming unloaded Qof 1 million loaded Q of 500, noise factor 6 dB, flicker frequency 1kHz, oscillator voltage gain 1Hz/V, equivalent noise resistance of tuningdiode 1Ohm and average power at oscillator output 10 dBm. No diode contribution
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)()(1)())(()(' tedtti
CtitRR
dttdiL NNL =+−+ ∫
This is a nonhomogeneous differential equation, which can be simplified to [1, Ch-8, pp. 159-232]
[ ]+−+
++++− )())(()](cos[
)()](sin[)
)()(( 1
11
11 tItRRtt
dttdI
ttdt
tdtIL NLϕωϕω
ϕω
)()](cos[)(1)](sin[
)()()(11
121
12
11 tettdt
tdItt
dttdtItI
C N=
+
++
− ϕω
ωϕω
ϕωω
Further
where )(tR N is the average negative resistance under large signal condition.
dtttItRIT
tRt
TtNN )][cos)()(2)(
0
2
0
ϕω +
= ∫
−
Non-Linear Oscillator Equation
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[ ]
[ ] [ ] 20
2max
2
2
26621
44
11
211
3
0]1[
)(1log10)(
yy
kyyY
yYYkk
kq
p
+
+
+×=+
+
+
ω
Where
2
1
CCy = 2
2222
020 CVL
kTRkccωω
=224
02
22
1cc
m
AFbf
mc
VL
gIK
gqIk
ωωω
+=
2402 )( += βωk
222
3
Ckkk =
£
And The SSB Phase Noise Is:
First ever complete and correct large signal phase noise calculation (Rohde 2004)
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A typical 1 GHz oscillator circuit
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A CAD Simulated (Ansoft Designer) phase noise plot for 1 GHz oscillator circuit
A CAD Simulated (MATLAB) phase noise plot for 1 GHz oscillator circuit
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The quality factor of the coupled resonator network previously shown is given by
01
220
022
0
00 2)1()1(2
)1()1(2
2)]([
0Q
Qcoupled ≈
++
→+
+⇒
∂∂
=<<
=
β
ωω ββ
ββ
ωφω
ω
Resonator#1[Zr]
Resonator#2[Zr]
Coupling-Network
[Zc]
RP RPL C L C
CC
[Zr] [Zr]
[Zc]
V0
Iin
Resonator#1 Resonator#2 Activ
e Dev
ice: B
ipolar
/FETs
CCc=β
LRCRQ P
P ωω ==0
Capacitive coupled 2 resonators
Multiple Magnetically Coupled Resonators
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+ -Vcc(8V)
O/P
1000 pF100 nH
1000 pF
2.2 pF
2.2 pF
100 nH
560 pF
BC 857
BC 857
Q1
Q2
Q3
100 nH
6.8 nH
Resonator#1 Resonator#2
CC CC1
Resonator
RPR LPR CPR
33 pF
Ω10000
Ω7500
Ω2.8
Ω82
Ω4700
pFCnHL
R
PR
PR
PR
7.4512000
==
Ω=
NEC 688300.4 pF0.47 pF
∗1C
2C
CR
O
CR
O
BufferAmp
CR
O
Equivalent Representation of CRO
68 nH
Ω10000
Circuit with Resonators
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Measured phase noise plots for the single resonator (1-resonator) and the identical coupled resonator (2-resonator
CAD simulated phase noise plot for the single resonator (1-resonator) and the identical coupled resonator (2-resonators)
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Layout of the MCLR VCO (500MHz-2500MHz) (Patented)
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0.0
25
50
75
100
125
Q
Frequency (GHz)0.5 1.5 2.5 3.5 4.5 5.5
Uncoupled Resonator
Coupled Resonator
MCPTR (Multi Coupled Planar Transmission Line Resonators)
150
175
Optimum Operating Modeand Optimum Class of Operation
Measured Q of resonators (uncoupled, coupled and MCLR)
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optmmm
c
m fkTRK
PFkT
ff
mmQff
dmd
+
+
−+ 2
20
02
0
20 2
21
)]1(2[1log10
0,
5.0ωω
φ
φφ
unloadedopt
Qddm
opt
=
⇒→
=
Cc
C1
C2
ibn
vbn
rb icn
BaseCollector
Emitter
B''
C
re1 = re||(1/Y21)
inr
F (Noise Factor)
Cv
re1Rn(t)
Rn(t): Negative Resistance
Cry
stal
+
+
+++
++=
++
+
21)(
21
)(1 2
22
221
121
121
221 e
Tcb
eb
c rff
CCYCCC
rr
rCCC
CCYF
β
Noise Optimization
Coupling Factor = 0.5
Noise Factor of Oscillator
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Layout of 1GHz Colpitts oscillator (Ceramic resonator oscillator)
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Simulated phase noise plot of for CRO
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Measured phase noise plot of the CRO
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Parallel Configuration (3-terminal Device) Bipolar/FETs
Dynamically Tuned Junction Capacitance (Cbc , Cbe ,Cce)
DynamicallyTracking Conduction
Angle
Tuning-DiodeNetwork
Dynamically Tuned Tracking-Filter &Buffer Amplifier
RF Output
Stubs(S1.S2....S8)
DynamicallyTracking Noise
Filter
Noise ImpedanceTransfer Network
B C
E
Noise FeedbackDC-Bias Network
DynamicallyGain Stabilization
Network
Feedback Network
Hybrid Resonance Mode Coupling Resonator
Block diagram of a user-defined MCLR VCO
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Layout of dual-band RCO (Patent pending)
Phase noise plot of the dual-band VCO
Thank You
Are there any questions?