institut für theoretische elektrotechnik dipl.-ing. jan bremer large signal modeling of...
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![Page 1: 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](https://reader035.vdocuments.us/reader035/viewer/2022062713/56649cdb5503460f949a5b0b/html5/thumbnails/1.jpg)
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)
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Jan Bremer Large Signal Capacitance Modeling 03.04.2009 page 2
Institut fürTheoretische
Elektrotechnik
Overview
Motivation Large Signal Modeling of Varactors in VCOs Alternative Modeling Concept Simulation Results Conclusion
![Page 3: 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](https://reader035.vdocuments.us/reader035/viewer/2022062713/56649cdb5503460f949a5b0b/html5/thumbnails/3.jpg)
Jan Bremer Large Signal Capacitance Modeling 03.04.2009 page 3
Institut fürTheoretische
Elektrotechnik
Motivation
Tail-biased differential LCTank VCO
MOS varactor
Tuning range
CV-characteristic
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Jan Bremer Large Signal Capacitance Modeling 03.04.2009 page 4
Institut fürTheoretische
Elektrotechnik
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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Jan Bremer Large Signal Capacitance Modeling 03.04.2009 page 5
Institut fürTheoretische
Elektrotechnik
Accumulation Mode MOS Varactor
R. L. Bunch and S. Raman, Large-Signal Analysis of MOS Varaktors in CMOS – Gm LC VCOs
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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Jan Bremer Large Signal Capacitance Modeling 03.04.2009 page 6
Institut fürTheoretische
Elektrotechnik
Inversion Mode MOS VaractorStructure and CV-characteristic
R. L. Bunch and S. Raman, Large-Signal Analysis of MOS Varaktors in CMOS – Gm LC VCOs
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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Jan Bremer Large Signal Capacitance Modeling 03.04.2009 page 7
Institut fürTheoretische
Elektrotechnik
Overview
Motivation Large Signal Modeling of Varactors in VCOs Alternative Modeling Concept Simulation Results Conclusion
![Page 8: 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](https://reader035.vdocuments.us/reader035/viewer/2022062713/56649cdb5503460f949a5b0b/html5/thumbnails/8.jpg)
Jan Bremer Large Signal Capacitance Modeling 03.04.2009 page 8
Institut fürTheoretische
Elektrotechnik
Varactors incorporated into VCOs
Vtune=1 V
VDD=2,5 V
Vtank(t)
Vtank(t)
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Jan Bremer Large Signal Capacitance Modeling 03.04.2009 page 9
Institut fürTheoretische
Elektrotechnik
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
R. L. Bunch and S. Raman, Large-Signal Analysis of MOS Varaktors in CMOS – Gm LC VCOs
Gate voltage
Ca
pa
cita
nce
A=0.1 V
A=1.0 V
A=0.5 V
Small-Signal
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Jan Bremer Large Signal Capacitance Modeling 03.04.2009 page 10
Institut fürTheoretische
Elektrotechnik
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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Jan Bremer Large Signal Capacitance Modeling 03.04.2009 page 11
Institut fürTheoretische
Elektrotechnik
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
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Jan Bremer Large Signal Capacitance Modeling 03.04.2009 page 12
Institut fürTheoretische
Elektrotechnik
Overview
Motivation Large Signal Modeling of Varactors in VCOs Alternative Modeling Concept Simulation Results Conclusion
![Page 13: 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](https://reader035.vdocuments.us/reader035/viewer/2022062713/56649cdb5503460f949a5b0b/html5/thumbnails/13.jpg)
Jan Bremer Large Signal Capacitance Modeling 03.04.2009 page 13
Institut fürTheoretische
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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Jan Bremer Large Signal Capacitance Modeling 03.04.2009 page 14
Institut fürTheoretische
Elektrotechnik
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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Jan Bremer Large Signal Capacitance Modeling 03.04.2009 page 15
Institut fürTheoretische
Elektrotechnik
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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Jan Bremer Large Signal Capacitance Modeling 03.04.2009 page 16
Institut fürTheoretische
Elektrotechnik
Simulation Results with IHP SGB25 Technology
NMOS transistorWidth = 100 µmVtune = 0V
Cap
acita
nce
Gate Voltage
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Jan Bremer Large Signal Capacitance Modeling 03.04.2009 page 17
Institut fürTheoretische
Elektrotechnik
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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Jan Bremer Large Signal Capacitance Modeling 03.04.2009 page 18
Institut fürTheoretische
Elektrotechnik
Overview
Motivation Large Signal Modeling of Varactors in VCOs Alternative Modeling Concept Simulation Results Conclusion
![Page 19: 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](https://reader035.vdocuments.us/reader035/viewer/2022062713/56649cdb5503460f949a5b0b/html5/thumbnails/19.jpg)
Jan Bremer Large Signal Capacitance Modeling 03.04.2009 page 19
Institut fürTheoretische
Elektrotechnik
Effective Large Signal Capacitance
Cap
acita
nce
Gate Voltage
VDD=2.5 V
NMOS transistorWidth = 250 µmVtune = 0.9V
Vtank(t)
Tank AmplitudeC
apac
itanc
e
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Jan Bremer Large Signal Capacitance Modeling 03.04.2009 page 20
Institut fürTheoretische
Elektrotechnik
Effective Large Signal Capacitance
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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Jan Bremer Large Signal Capacitance Modeling 03.04.2009 page 21
Institut fürTheoretische
Elektrotechnik
Effective Large Signal Capacitance
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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Jan Bremer Large Signal Capacitance Modeling 03.04.2009 page 22
Institut fürTheoretische
Elektrotechnik
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
]
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Jan Bremer Large Signal Capacitance Modeling 03.04.2009 page 23
Institut fürTheoretische
Elektrotechnik
Overview
Motivation Large Signal Modeling of Varactors in VCOs Alternative Modeling Concept Simulation Results Conclusion
![Page 24: 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](https://reader035.vdocuments.us/reader035/viewer/2022062713/56649cdb5503460f949a5b0b/html5/thumbnails/24.jpg)
Jan Bremer Large Signal Capacitance Modeling 03.04.2009 page 24
Institut fürTheoretische
Elektrotechnik
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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Jan Bremer Large Signal Capacitance Modeling 03.04.2009 page 25
Institut fürTheoretische
Elektrotechnik
The End
Thank you for your attention!