EKV Modelling of MOS Varactors and LC Tank Oscillator Design Wolfgang Mathis TET Leibniz Universität Hannover Jan-K. Bremer NXP Hamburg MOS-AK Workshop 01 6. 7. April 01, Dresden
Content: Motivation: VCO VCO Design Process LC Tank VCO Model MOS Varactor Models Varactors incorporated into VCOs Conclusions
Motivation: VCO (voltage controlled oscillator) Demodulator in Processors frequency division and multiplication Input signal Frequency multiplier Divided output signal
Motivation: VCO MOS varactor CV-characteristic differential pair baised LC Tank VCO linear tuning range
VCO Design Process VCO design toolbox: f center =.4 GHz Tuning Range 15% V supply =.5 V VCO design process is not a simple task nonlinear behavior state space Variation of one circuit parameter specifications - Variation of the frequency or amplitude of the output signal - Generation of stable oscillations simulation Systematical design flow (incl. nonlinear behavior) better initial values Estimation of the resulting tuning range Finding the starting point of a stable oscillation Calculation of the output amplitude Stability analysis Optimization Systematical design flow Nonlinear modeling Our toolbox Experience Literature Measurements Hand calculations initial values
Circuit Simulation Transient analysis: ( il uc coordinates) dx Bx ( ) Fxut (, ( )) dt = + initial values DC operational points Small signal analysis: (time domain) dx% F F Bx ( op) = ( xop, U0) x% + ( xop, U0) u% dt x u Small signal analysis: (frequency domain) F F sb( xop) X% = ( xop, U0) X% + ( xop, U0) U% x u ( xop : Operational Point) Limit Cycles
LC Tank VCO Model C t (v t,v tune ) C t (v t,v tune ) differential pair baised LC Tank VCO i d (v t ) describing equations
Nonlinear Circuit Model for a LC Tank VCO v t C(v t,v tune ) v t Circuit Analysis
Nonlinear Circuit Model for a LC Tank VCO Tank resistance: R t 1 1 1 1 = + + + Rvp, Rip, Risubp,, R0 1 Current of the differential pair: v i ( v ) I 1 d v t t t = bias νn ν n A.Bunomo, Determining the Oscillation of differential VCOs, 003 dv 1 1 t d t dt RtCt( vt, Vtune) Ct( vt, Vtune) vt = Ct ( vt, Vtune) + dil 1 i L 0 0 dt L t i ( v ) Equivalent circuit of the inductor: C t (v t,v tune )?
D=S=B MOS Varactor Structure and CV-characteristic R. L. Bunch and S. Raman, Large- Signal Analysis of MOS Varaktors in CMOS G m LC VCOs Source-Drain-Bulk are short-circuited and connected to V tune Advantages: Made from standard MOS-cell Falling and rising edge of the CVcharacteristic can be used Disadvantages: Strongly nonlinear tuning characteristic
Accumulation Mode MOS Varactor Structure and CV-characteristic R. L. Bunch and S. Raman, Large- Signal Analysis of MOS Varaktors in CMOS G m LC VCOs, IEEE J. SC-38, 003 the p + regions of drain and source are replaced with n + regions Advantages: Wider transition from C min to C max as inversion mode varactors Best C max / C min ratio Lowest parasitic resistance Disadvantages: Not made from standard MOS-cell Nonlinear tuning characteristic
Inversion Mode MOS Varactor Structure and CV characteristic PMOS Source-Drain are short-circuited and Bulk is connected to supply voltage (PMOS) or ground (NMOS) Advantages: Consist of standard MOS transistor Monotone slope Good C min /C max ratio Disadvantages: R. L. Bunch and S. Raman, Large-Signal Analysis of MOS Varaktors in CMOS G m LC VCOs Very sharp transition from C min to C max Susceptible to induced substrat noise Nonlinear characteristic à difficult modelling
Intrinsic MOS Capacitances EKV (quasi-static) Intrinsic capacitances: C Q where Q = C V q x x y = ± x OX t x Vy x, y = g, d, s, b (Normalized) intrinsic node charges: EKV model valid in the whole inversion region q q d D q qs s 3 3 4 3xrev + 6xrevxfor + 4xrevxfor + x for 1 = n q 15 ( x ) for x + rev 3 3 4 3xfor + 6xfor xrev + 4xfor xrev + x rev 1 = n q 15 ( x ) for x + rev ( ) 1 6 1 nq QqB b = γ VP + φ+ 10 qi V t n s Q d q ( Q + ) i x for for n with: = ln 1+ q 1 = + 4 = 1+ g i e for v v p s V total charge: p γ + φ + 10 6 ( φ : = φ ) fermi ( Q + Q + Q Q ) Q = + s i x d rev rev = ln 1+ 1 = + 4 b OX p d M. Bucher, C. Lallement, C. Enz, F. Théodoloz, and F. Krummenacher, The EPFL-EKV MOSFET model for circuit simulation, Technical Report, Kluwer, 1999 i e rev v v
Simplified capacitance model EKV Neglecting the slight bias dependence of the slope factor C C gs gd = = C C ox ox 1 1 3 ( x + for xrev) 1 1 3 ( x + for xrev) x + rev x + rev x for x + for x + for xrev C n n 1 C n 1 C 1 q q gb 1 c gs c gs gd q gb = Cox n q Cox C C gd ox Normalized capacitance* C gb C gs / C gd NMOS transistor width = 100 µm V tune = 1V C bs / C bd C = ( n 1) C, C = ( n 1) C bs q gs bd q gd Gate voltage * Normalization to Cox
total varactor capacitance (N-MOS) Extrinsic (parasitic) MOS capacitances: with: F. Pregaldiny, C. Lallement, and D. Mathiot. A simple efficient model of parasitic capacitances of deep-submicron LDD MOSFETs. Solid- State Electronics, 00.
Simulation results NMOS varactor: EKV vs. Spectre RF (BSIM 3.3) 0.35 µm CMOS technology C35 from AMS (austria micro systems)
Simulation results NMOS varactor: EKV vs. Spectre RF (BSIM 3.3) 0.35 µm CMOS technology C35 from AMS (austria micro systems) But: even the simplified capacitance model is too complex for an analytical design method
Hyperbolic Tangent Approximation A. Grebennikov and F. Lin, An efficient CAD-oriented large-signal MOSFET model, IEEE Transactions on Microwave Theory and Techniques, 000 S v is defined as the slope of C v,total at the inflection point V G =V G,ip Parameters S v, C v,min, C v,max and V G,ip have to be identified from experimental data or circuit simulation The EKV based varactor capacitance model allows determination of analytical expressions for the parameters in dependency on individual design parameters Using a least square approximation algorithm we derived semi-analytical expressions for S v, C v,min, C v,max and V G,ip
Simulation results C v,min (V tune ), comparison of the EKV based analytical solution with the least square approximation Comparison of the EKV based analytical expression with the hyperbolic tangent approximation
Varactors incorporated into VCOs V tune =1 V V DD =3.3 V V tank (t) V tank (t)
Instantaneous varactor capacitance single-ended back-to-back varactor configuration Assuming complete symmetry between the two MOS-varactors: vt() t vt() t vx() t vy() t = Voff + Voff Complete varactor capacitance is a series connection of two MOSFETs: C ( v, V ) vinst, t tune = vt vt C1, Vtune C, Vtune vt vt C1, Vtune + C, Vtune Instantaneous capacitance of two NMOS varactors in back-to-back configuration
Average large signal capacitance The tuning sensitivity of a VCO is defined as: Simulation based design of Siprak/Roithmeier * Oscillation frequency (first order approximation): Averaged large signal capacitance: VCO amplitude v t is unknown a-priori trail and error * D. Siprak, A. Roithmeier, Varactor modeling methodology for simulation of the VCO tuning sensitivity, ICMTS, 004
Analysis of VCO tuning sensitivity Our modeling concepts allows: an analytical expression of the averaged large signal varactor capacitance C v,avg, analytical expression for the tuning sensitivity function in dependency on the tuning voltage Parameter: V t, max
Systematic nonlinear VCO design flow dv 1 1 i ( V ) t d t dt RtCt( vt, Vtune) Ct( vt, Vtune) Vt = Ct ( vt, Vtune) + dil 1 i L 0 0 dt L t Approximation of frequency and amplitude Calculation of starting point Stability analysis Bifurcation analysis Bremer, J.-K.; Zorn, C.; Przytarski, J.; Mathis, W.;, "A nonlinear systematic design flow for LC tank VCOs based on large signal capacitance modeling," ISCAS 009 Bremer, J.-K.; Reit, M.; Mathis, W., "Nonlinearity and Dynamics of RF Oscillators: Analysis and Design Implications", ISCAS 010 Averaging method Harmonic Balance Uses the stability analysis Analytical expressions Higher averaging orders Bremer, J.-K.; Zorn, C.; Przytarski, J.; Mathis, W. An efficient VCO Design Flow using the Method of Harmonic Balance ISTET 009 Initial values from BA Including higher harmonics Numerical solution
Conclusion Systematical design flow An implementation of an analytical small signal capacitance model for inversion mode MOS varactors based on the EKV model was presented A large signal capacitance model for the included varactors 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 dependent of circuit and process parameters Outlook: Phase noise coupling