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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)(

QQ

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

QQ

QQ

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

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