INTRODUCTION University of California Berkeley College of Engineering Department of Electrical Engineering and Computer Science Robert. Brodersen EECS40 Analog Circuit Design ROBERT. BRODERSEN LECTURE
EECS 40 ANALOG INTEGRATED CIRCUITS INTRODUCTION I Robert. Brodersen, 779, 40 Cory Hall, rb@eecs.berkeley.edu This course will focus on the design of MOS analog integrated circuits with extensive use of Spice for the simulations. In addition, some applications of analog integrated circuits will be covered which will include RF amplification and discrete and continuous time filtering. Though the focus will be on MOS implementations, comparison with bipolar circuits will be given. Required Text Analysis and Design of Analog Integrated Circuits, 4th Edition, P.R. Gray, P. Hurst, S. Lewis and R.G. Meyer, John iley and Sons, 00 Supplemental Texts B. Razavi, Design of Analog CMOS Integrated Circuits, McGrawHill, 00. Thomas Lee, The Design of CMOS Radio Frequency Integrated Circuits, Cambridge University Press, 998 The SPICE Book, Andre Vladimirescu, John iley and Sons, 994 EECS 05: Microelectronic Devices and Circuits Prerequisites ROBERT. BRODERSEN LECTURE
IC Design Course Structure at Berkeley EE40 INTRODUCTION I EE05 EE40 Linear/Analog EE4 NonLinear EE4 Digital Linear Design Sensors, Transducers Interface Circuits Digital Processing Amplifiers, Filters, A/D & D/A s ROBERT. BRODERSEN LECTURE
University of California Berkeley College of Engineering Department of Electrical Engineering and Computer Science Robert. Brodersen EECS40 Analog Circuit Design Lectures on MOS DEVICE MODELS ROBERT. BRODERSEN LECTURE
Assumed Knowledge M a) KCL, KVL Kirchoff Laws b) Voltage, Current Dividers c) Thevenin, Norton Equivalents d) Port Equivalents e) Phasors, Frequency Response ROBERT. BRODERSEN LECTURE
V s i in R s + + ν in + a ν ν in Port Equivalent Circuit (Voltage in Voltage out) R in R out + ν out i out RL R in R out A ν ν in i in ν out i out ν out ν in R L i out 0 R L R S ν in 0 M i in i out V s + + ν in + a ν ν in R in R out + ν out + ν in R in + R out + a ν ν in ν out ν out a ν ν in a ν ν out a ν a ν ν R in in + R out R in ROBERT. BRODERSEN LECTURE
MOS Large Signal Equations M3 nchannel D I DS V DSAT G B V GS I DS Saturation S NMOS Linear Cutoff S G L D V DS n p n B ROBERT. BRODERSEN LECTURE
Cutoff : V GS < V T MOS Large Signal Equations (Cont.) M4 Linear : V GS > V T V DS < V DSAT V GS V T I DS k' Saturated : V GS V DS I DS > V T V DS L V V V GS T DS > V DSAT V GS V T k' ( V GS V T ) ( + λ V DS ) L ROBERT. BRODERSEN LECTURE
MOS Large Signal Equations (Cont.) M5 V T V To + γ [( φ f + V SB ) ( φ f ) ] V To Threshold Voltage @ V SB 0 φ f Fermi Potential 0.3 γ λ L Body Effect Factor Short Channel Effect idth of Device Length k' µ C ox ( V SB > 0) µ ν ε E V DS /L mobility Oxide Capacitance E ROBERT. BRODERSEN LECTURE
MOS Large Signal Equations (Cont.) M6 Body Effect : V To + γ V SB V T S G + + + + + + + + D n n γ q ε N A C ox V To 0 V BS ROBERT. BRODERSEN LECTURE
MOS Large Signal Equations (Cont.) M7 Short Channel Effect (λ): S G D X D X J Junction Depth L drawn L D Lateral Diffusion ~ 0.75 X J L L drawn L D L EFF L X D X D fv ( DS ) ROBERT. BRODERSEN LECTURE
MOS Large Signal Equations (Cont.) M8 I k' ( A ) D I k' ( B ) D ( B) I D V DS λ ( V GS V T ) L EFF Modeled as ( V GS V T ) ( + λ V DS ) L I DS ( A) I D V DS k' ( V GS V T ) dv DS L EFF dl EFF ( A) I D V DS dx D λ I D I D L EFF dv DS ROBERT. BRODERSEN LECTURE 3
MOS Large Signal Equations (Cont.) λ L EFF dx D L dv DS dx D dv DS eak function of V DS ε ( V X DS V DSAT ) D q N A Fixed ε Dielectric constant of silicon N A Substrate doping dx D dv DS ε q N A V DS V DSAT ROBERT. BRODERSEN LECTURE 3
MOS Large Signal Equations (Cont.) M9 G I DS Ideal λi DS Longer Channel (Increasing L) S L D V DS /L is the parameter of interest C G L C OX ROBERT. BRODERSEN LECTURE 3
MOS Small Signal Model (Low Frequency) M0 M I DS G + g m ν gs D V GS r o g mbs ν bs S + V SB B I DS di DS ν gs + dv GS dv BS di DS di ν bs + DS dv DS ν ds g m g mbs /r o ROBERT. BRODERSEN LECTURE 3
MOS Small Signal Model (Cont.) M In Saturation : g m di DS k' ( V dv GS V T ) ( + λ V DS ) GS L g m + k' ( V GS V T ) L hat is V DSAT? G S V GS V T + V DSAT I DS g m V DSAT k' V DSAT k' I DS L L k' ( V GS V T ) L k' V DSAT so, L I DS k' L k' V DSAT L and from above, ROBERT. BRODERSEN LECTURE 3
MOS Small Signal Model (Cont.) M3 g mbs calculation : di DS g mbs g mb dv BS k' ( V GS V T ) ( + λ V DS ) L dv T dv BS dv T dv BS γ χ ( φ f + V SB ) 0.5 g mbs k' ( V GS V T ) ( + λ V DS ) χ L g m g mbs χ g m χ γ ( φ f + V SB ) 0.5 ROBERT. BRODERSEN LECTURE 3
MOS Small Signal Model (Cont.) M4 C ox 0.3 G g mbs χ g m 0. S n C js n D 5V 0V V BS γ 0.5 φ f 0.3 k 90e6 λ 0.0 V To 0.7 Qchannel duetovgs C ox ν gs Qchannel duetovbs C js ν bs χ C js C ox ROBERT. BRODERSEN LECTURE 3
MOS Small Signal Model (Cont.) M5 r o calculation : di DS g r mds o dv DS d d V DS k' ( V GS V T ) ( + λ V DS ) L k' r o ( V GS V T ) λ L λ I r DS o r 0 λ I DS ROBERT. BRODERSEN LECTURE 3
MOS Small Signal Model (Cont.) Comparison with Spice Level : M6 VTO V To 0.5.0V PHI φ f 0.6 GAMMA γ 0.05 0.5 LAMBDA λ 0.0 0. KP k' µ C ox nmos 50 00µ A V pmos nmos 3 ROBERT. BRODERSEN LECTURE 3
LECTURES ON SPICE Summary: g m k' I DS L g mbs χ g γ χ ( φ f + V SB ) 0.5 r 0 λ I DS g m I DS I V DS DSAT k' L m V GS V T MOS Small Signal Model (Cont.) V DSAT k' V DSAT L I DS V DSAT V DSAT V GS V T I V GS V DS T + k' L I DS k' ( V GS V T ) L V T V To + γ [( φ f + V SB ) ( φ f ) ] ROBERT. BRODERSEN LECTURE 4
LECTURES ON SPICE University of California Berkeley College of Engineering Department of Electrical Engineering and Computer Science Robert. Brodersen EECS40 Analog Circuit Design Lectures on SPICE ROBERT. BRODERSEN LECTURE 4
Spice Transistor Model : LECTURES ON SPICE SP M 3 4 nch Lµ 0µ AD( ) AS( ) PD( ) PS( ) NRD( ) parasitic resistors G area of drain S L D 3 4 ROBERT. BRODERSEN LECTURE 4
SPICE LECTURES ON SPICE SP Initial Operationg Point DC currents and Voltages Linearize Around OP Point Solve Eqn. New Operating Point No DC Converge? Yes Increment Time Analysis Types : DC op point.op DC sweeps AC & Transient No End of Time Interval Yes STOP ROBERT. BRODERSEN LECTURE 4
LECTURES ON SPICE 4 V A SP3 + V B R 4 I + R R R 3 I 4 3 G i /R i Node : ( G + G 4 ) V G V G 4 V 4 + I 0 Node : G V + ( G + G + G 3 ) V G 3 V 3 0 Node 3 : G 3 V + G 3 V 3 I 4 0 Node 4 : G 4 V G 4 V 4 + I 4 0 V V B V 3 V 4 V A ROBERT. BRODERSEN LECTURE 4
LECTURES ON SPICE SP4 G +G 4 G 0 G 4 0 V 0 G G +G +G 3 G 3 0 0 0 V 0 0 G 3 G 3 0 0 V 3 0 G 4 0 0 G 4 0 V 4 0 0 0 0 0 0 I V B 0 0 0 0 I 4 V A Current src G F V C B R I E Votlage src Total # of EQNS Nn + n v + n l n # of circuit nodes n v # of independent voltage srcs n l # of inductors ROBERT. BRODERSEN LECTURE 4
Matrix Solution LECTURES ON SPICE SP5 A x b we need Solve by Gaussian Elimination (0) denotes iteration step e e e 3 a a a 3 a a a 3 a 3 a 3 a 33 x x x 3 b b b 3 Eliminate a,a 3 ( ) e e ( ) e e 0 ( ) a e a ( ) e 3 e 3 0 ( ) a 3 e a xxx 0 xx 0 xx ROBERT. BRODERSEN LECTURE 4
LECTURES ON SPICE SP6 Then eliminate a 3 () ( ) e ( ) e ( ) e 3 ( ) e ( ) e e 3 ( ) ( ) a 3 ( ) e ( ) a xxx 0 xx 00x Upper triangular matrix can be solved ( ) a ( ) a ( ) 0 a ( ) a 3 ( ) a 3 x x b ( ) b ( ) 0 0 a 33 x 3 ( ) b 3 ( ) b x 3 3 ( ) a 33 b ( ) ( x a ( ) 3 x 3 ) ( ) a b ( 0 ) x a ( 0 ) ( 3 x 3 a x ) a Solution ROBERT. BRODERSEN LECTURE 4
Accuracy LECTURES ON SPICE SP7 A Can t divide by 0 or small numbers, so pivoting is used to reorder eqn s (Basically renumbering nodes). Puts maximum values on diagonal. R Ω R 0kΩ.000 V V 0 G 0k + G If the computer only has 4 digits of precision then we get, Actually, V V 000V, 0000V, V V 0 V V V + V 0 V, V ROBERT. BRODERSEN LECTURE 4
To control accuracy LECTURES ON SPICE SP8.options PIVTOL <values> (0 8 ) This sets the allowable range of conductance values. *ERROR* : Maximum entry...at STEP... is less than PIVTOL Probably means you have an incorrect element or floating node ROBERT. BRODERSEN LECTURE 4
Solution of the DC equations with nonlinear models LECTURES ON SPICE SP9 I D I S e I G G V V D V TH + I A I G Need to find this point I A G I G V D I D I D,G I D ROBERT. BRODERSEN LECTURE 4
NewtonRaphson Iteration : LECTURES ON SPICE SP0 Make guess of next operation point in iteration Start at initial guess and linearize diode eqn. + I A G G D0 V D (0) I D0 ROBERT. BRODERSEN LECTURE 4
LECTURES ON SPICE SP Current value I D0 Solution finds this point Slope of G D0 I D V D Solve for V D, becomes V D () Linearize at this point Find new point ROBERT. BRODERSEN LECTURE 4
LECTURES ON SPICE Convergence SP Keep iterating until all voltages and currents are within a a tolerance value. () i V n ε Vn node voltage n at iteration i REL( V) max V ( i + ) () i ( n, V n ) + ABS( V) The convergence check is : ( i + ) V n () i V n ε Vn REL( V) 0 4 (Default 0 3 ROBERT. BRODERSEN LECTURE 4 ) ABS( V) 0 6 (Default 50µV ) ABS(V) should be at least two orders of magnitude below required accuracy. These values would give part in 0 4 accuracy down to 00µV resolution
SP3 Current convergence is broken into two types; MOS and NOT MOS MOS 6 ABSMOS ABSOLUTE( 0 ) RELMOS RELATIVE( 0.5) NOTMOS 9 ABSI ABSOLUTE( 0 ) RELI RELATIVE( 0.0) ITL # of steps in iteration (00) hen you get *ERROR* no convergence in DC analysis and the last node voltages Then it hasn t converged in 00 times something is probably wrong with your netlist ROBERT. BRODERSEN LECTURE