Institut für Theoretische Elektrotechnik Dipl.-Ing. Jan Bremer Large Signal Modeling of Inversion-Mode MOS Varactors in VCOs MOS-AK Meeting 2009 2-3 April

Institut fürTheoretische

Elektrotechnik

Dipl.-Ing. Jan Bremer

Large Signal Modeling of Inversion-Mode MOS Varactors in VCOs

MOS-AK Meeting 2009 2-3 April 2009 at IHP in Frankfurt (Oder)

Jan Bremer Large Signal Capacitance Modeling 03.04.2009 page 2


Elektrotechnik

Overview

Motivation Large Signal Modeling of Varactors in VCOs Alternative Modeling Concept Simulation Results Conclusion



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Motivation

Tail-biased differential LCTank VCO

MOS varactor

Tuning range

CV-characteristic



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D=S=B MOS Varactor

R. L. Bunch and S. Raman, Large-Signal Analysis of MOS Varaktors in CMOS – Gm LC VCOs

Structure and CV-characteristic

Strongly nonlinear tuning characteristic

Advantages: Made from standard MOS-cell Falling and rising edge of the CV- characteristic can be used

Disadvantages:

Source-Drain-Bulk are short-circuited and connected to Vtune



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Accumulation Mode MOS Varactor


Structure and CV-characteristic

Not made from standard MOS-cell Nonlinear tuning characteristic

Advantages: Wider transition from Cmin to Cmax as inversion mode varactors Best Cmax / Cmin ratio

Lowest parasitic resistance

Disadvantages:

the p+ regions of drain and source are replaced with n+ regions



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Inversion Mode MOS VaractorStructure and CV-characteristic


Very sharp transition from Cmin to Cmax Susceptible to induced substrat noise

Advantages:

Made from standard MOS-cell Best linearity

Disadvantages:

Source-Drain are short-circuited and Bulk is connected to supply voltage (PMOS) or ground (NMOS)



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Overview




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Varactors incorporated into VCOs

Vtune=1 V

VDD=2,5 V

Vtank(t)

Vtank(t)



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Large Signal Varactor Modeling after R. L. Bunch

( )( ) ( )C

dv ti t C v t

dt

0

0

( ( ))

( ) /

C fAVG

f

rms i tC

rms dv t dt

0( ) sin( ) gatev t A t V

02 /

00 0 0

0

( sin( ) ) cos( ) cos( )AVG gateC C A t V t t dt

00

0

1 2( ( )) ( ) cos( )

2

T

C Cfrms i t i t t dt

T

Expression for C(v(t)) is needed

Averaging is subject for debate

Neglecting the higher harmonics

Amplitude of the output signal of the VCO is needed


Gate voltage

Ca

pa

cita

nce

A=0.1 V

A=1.0 V

A=0.5 V

Small-Signal



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Large Signal Varactor Modeling after A. Abidi I

Ceff

Fundamental

Harmonics 00

( ) ( ) cos( )C L mm

V t V t a m t

00 00

1( ) sin( )

Tm

L Lm

aI V t dt m t

L m L

2 0 0 00 0

( )( ) cos(2 ) sin( )C SS n m

n m

dV tI C t C n t m a m t

dt

0 0 20

1 1

2C C

L

0 2

1

2effC C C

2 00

( ) cos(2 )SS nn

C t C n t

( ) ( )C LI t I t

Kirchhoff and tank voltageas Fourier series:

Oscillating capacitance as Fourier series:

Complete inductor and capacitor current:

Comparing coefficients at every frequency gives:

E. Hegazi and A. A. Abidi, Varactor Characteristics, Oscillator Tuning Curves, and AM-FM Conversion



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Large Signal Varactor Modeling after A. Abidi II

Expression for C(v(t)) is needed

Includes only 1st and 2nd harmonic of the nonlinear varactor characteristic

Includes only the fundamental of the voltage, higher harmonics are neglected

Amplitude of the output signal of the VCO is needed

20

eff

idvC

A

Graphical ansatz to calculate Ceff :

Small signal capacitance approximated with a step function:

eff G tune THV V V V

22

min

22

max

1 for

1 for

eff

eff

V iV V

A C A

V iV V

A C A

2

max min 1min max( )sin 1

2eff eff eff

eff

V V VC C C CC

A A A

E. Hegazi and A. A. Abidi, Varactor Characteristics, Oscillator Tuning Curves, and AM-FM Conversion



Elektrotechnik

Overview




Elektrotechnik

t

t

t

t

t tt

t

1

(

1( )

1(

0

) (

0

))

d

LL

t tt

dV i VR Vdt

idi

Ldt

C V C VC V

Differential Equation System for a VCO

C(Vt)

1

, , , , 0

1 1 1 12t

v p i p i sub p

RR R R R

Tank resistance:2

tanktanktank 2

( ) 1d biasnn

V Vi V I

A.Bunomo, „Determining the Oscillation of differential VCOs“, 2003

Current of the differential pair:

Equivalent circuit of the inductor:

( )?t tC V



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Intrinsic Capacitance Model based on EKV

1

1

1 1

( , ) ( )

1 1

( , ) ( )

( , ) ( , )11

( , ) ( , )

gs oxgss f r gsw f

gd oxgss r f gsw r

gbs f r gbw f rgb ox

gbs f r gbw f r

C Cc i i c i

C Cc i i c i

c i i c i inC C

n c i i c i i

( 1) , ( 1)bs gs bd gdC n C C n C

2

2( , ) 1

3

( ) ( )

rgss f r

f r

gsw f f f

ic i i

i i

c i i G i

2

22( , ) 1

3

( , ) ( ) ( )

f r

gbs f r

f r

gbw f r f f r r

i ic i i

i i

c i i i G i i G i

C. Enz, F. Krummenacher and E. Vittoz, ”An Analytical MOS Transistor Model Valid in All Regions of Operation and Dedicated to Low-Voltage and Low-Current Applications”, Analog Integrated Circuits and Signal Processing, Kluwer, 1995

1

11

2

f

f f

G i

i i

Interpolation function:With:

Interpolated intrinsic capacitances:

Gate Voltage

No

rmal

ized

Ca

pa

cita

nce

s

Cgb

Cgs / Cgd

Cbs / Cbd

NMOS transistorWidth = 100 µmVtune = 0V



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Voltage dependant Varactor Capacitance

,Varactor Gate tune gs gd gb bs bdC V V C C C C C 0 0

NMOS

PMOS

,Varactor Gate tune gs gd gb bs bdC V V C C C C C 0 0

Gate Voltage

Gate Voltage

Ca

pa

cita

nce

Ca

pa

cita

nce



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Simulation Results with IHP SGB25 Technology

NMOS transistorWidth = 100 µmVtune = 0V

Cap

acita

nce

Gate Voltage



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Effective Large Signal Capacitance

Vtank(t)

Assuming complete symmetry between the two MOS-varactors:

( ) ( )( ) ( )

2 2t t

x y

v t v tv t v t

Complete varactor capacitance is a series connection of two MOSFETs:

1 2

,

1 2

, ,2 2

,, ,

2 2

t ttune tune

v eff t tunet t

tune tune

v vC V C V

C v Vv v

C V C V



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Overview




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Cap

acita

nce

Gate Voltage

VDD=2.5 V

NMOS transistorWidth = 250 µmVtune = 0.9V

Vtank(t)

Tank AmplitudeC

apac

itanc

e



Elektrotechnik


Cap

acita

nce

Gate Voltage

VDD=2.5 V

NMOS transistorWidth = 250 µmVtune = 1.5V

Vtank(t)

Tank AmplitudeC

apac

itanc

e



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Tank Amplitude

Cap

acita

nce

Cap

acita

nce

Tank Amplitude

Vtune= 0.2 V

Vtune= 0.4 VVtune= 0.6 V

Vtune= 0.8 V

Vtune= 1.0 V

Vtune= 2.0 V

Vtune= 1.8 V

Vtune= 1.6 V

Vtune= 1.4 V

NMOS transistorWidth = 250 µm



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Dimensioning Varactors in the VCO Design Process

Design of a 2.4 GHz LC Tank VCO with 20 percent tuning range

t

t

t

t

t tt

t

1

(

1( )

1(

0

) (

0

))

d

LL

t tt

dV i VR Vdt

idi

Ldt

C V C VC V

Time [ns]

Tan

k am

plitu

de [V

]



Elektrotechnik

Overview




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Conclusion

An implementation of an analytical small signal capacitance model for inversion mode MOS varactors based on the EKV model was presented

Simulation results for the small signal capacitance are in good accordance to simulation results that were obtained by using Spectre simulator

If the varactors are incorporated into a VCO a large signal analysis of the varactor capacitance is needed

Two well-established large signal varactor capacitance modeling concepts have been presented and analyzed

An alternative capacitance model in dependency of the output signal of the VCO including higher harmonics was presented

Using this nonlinear modeling approach it is possible to set up a complete nonlinear VCO model that is only dependant of circuit and process parameters

Goal: Parameter optimization in advance of the actual design flow



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The End

Thank you for your attention!

Documents

Institut für Theoretische Elektrotechnik Dipl.-Ing. Jan Bremer Large Signal Modeling of Inversion-Mode MOS Varactors in VCOs MOS-AK Meeting 2009 2-3 April