EE141 Chapter 5 The Inverter April 10, 2003

Objective of This Chapter Use Inverter to know basic CMOS Circuits Operations Watch for performance Index such as Speed (Delay) Optimal Transistor Sizing Power Consumption

The CMOS Inverter: A First Glance out C L DD

CMOS Inverter N Well V DD PMOS 2l Contacts Out In Metal 1 Polysilicon NMOS GND

Two Inverters Vin Vout Vout Vin Share power and ground Abut cells Connect in Metal Vin Vout Vout Vin

CMOS Inverter First-Order DC Analysis DD in = out R n p VOL = 0 VOH = VDD VM = f(Rn, Rp) Rn, Rp: Channel Resistance in Saturation Mode

CMOS Inverter: Transient Response DD DD t pHL = f(R on .C L ) = 0.69 R C R p V out V out C L C L R n V = V = V in in DD (a) Low-to-high (b) High-to-low

Voltage Transfer Characteristic

PMOS Load Lines (Vdd = 2.5V) V in = V DD +V GS,p I D,n = - I D,p out DS,p V DS,p I Dp GSp =-2.5 =-1 V DS,p I Dn in =0 =1.5 V out I Dn in =0 =1.5 V in = V DD +V GSp I Dn = - I Dp V out = V DD +V DSp (Vdd = 2.5V)

CMOS Inverter Load Characteristics

CMOS Inverter VTC VM: Vin = Vout

Switching Threshold as a Function of Transistor Ratio NMOS and PMOS are in Saturation Modes For r = 1, and mobility NMOS = 2 PMOS, Wp = 2Wn

Switching Threshold as a Function of Transistor Ratio 1.8 1.7 1.6 1.5 1.4 V (V) 1.3 M 1.2 1.1 1 0.9 0.8 1 10 10 W /W p n

Simulated VTC

Impact of Process Variations 0.5 1 1.5 2 2.5 V in (V) out Good PMOS Bad NMOS Good NMOS Bad PMOS Nominal

Propagation Delay

CMOS Inverter Propagation Delay Approach 1

CMOS Inverter Propagation Delay Approach 2

CMOS Inverters V DD PMOS 1.2 m m =2l Out In Metal1 Polysilicon NMOS GND

Transient Response ? tp = 0.69 CL (Reqn+Reqp)/2 tpLH tpHL

Design for Performance Keep loading capacitances (CL) small Increase transistor sizes (add CMOS gain) Watch out for self-loading (for the previous stage)! Increase VDD (????)

Delay as a function of VDD

Device Sizing (for fixed load) Self-loading effect: Intrinsic capacitances dominate

NMOS/PMOS ratio tpLH tpHL tp b = Wp/Wn

Impact of Rise Time on Delay

Inverter Sizing

Inverter Chain In Out CL If CL is given: How many stages are needed to minimize the delay? How to size the inverters? May need some additional constraints.

Inverter Delay Minimum length devices, L=0.25mm Assume that for WP = 2WN =2W same pull-up and pull-down currents approx. equal resistances RN = RP approx. equal rise tpLH and fall tpHL delays Analyze as an RC network 2W W Delay (D): tpHL = (ln 2) RNCL tpLH = (ln 2) RPCL Load for the next stage:

Inverter with Load RW CL RW tp = k RWCL k is a constant, equal to 0.69 Delay RW CL RW Load (CL) tp = k RWCL k is a constant, equal to 0.69 Assumptions: no load -> zero delay Wunit = 1

Inverter with Load CP = 2Cunit 2W Cint CL W CN = Cunit Delay 2W Cint CL W Load CN = Cunit Delay = kRW(Cint + CL) = kRWCint + kRWCL = kRW Cint(1+ CL /Cint) = Delay (Internal) + Delay (Load)

Delay Formula Cint = gCgin with g  1 f = CL/Cgin - effective fanout R = Runit/W ; Cint =WCunit tp0 = 0.69RunitCunit

Apply to Inverter Chain Out CL 1 2 N tp = tp1 + tp2 + …+ tpN

Optimal Tapering for Given N Delay equation has (N-1) unknowns, Cgin,2 – Cgin,N Minimize the delay, find N - 1 partial derivatives Result: Cgin,j+1/Cgin,j = Cgin,j/Cgin,j-1 Size of each stage is the geometric mean of two neighbors Each stage has the same effective fanout (Cout/Cin) Each stage has the same delay

Optimum Delay and Number of Stages When each stage is sized by f and has same effective fanout f: Effective fanout of each stage: Minimum path delay

Example In Out CL= 8 C1 1 f f2 C1 CL/C1 has to be evenly distributed across N = 3 stages:

Optimum Number of Stages For a given load, CL and given input capacitance Cin Find optimal sizing f For g = 0, f = e, N = lnF

Optimum Effective Fanout f Optimum f for given process defined by g fopt = 3.6 for g=1

Impact of Self-Loading on tp No Self-Loading, g=0 With Self-Loading g=1

Normalized delay function of F

Buffer Design N f tp 1 64 65 2 8 18 3 4 15 4 2.8 15.3 1 64 1 8 64 1 4 16 64 1 64 22.6 2.8 8

Power Dissipation

Where Does Power Go in CMOS?

Dynamic Power Dissipation Vin Vout C L Vdd Energy/transition = C * V 2 L dd Power = Energy/transition * f = C * V 2 * f L dd Not a function of transistor sizes! Need to reduce C , V , and f to reduce power. L dd

Modification for Circuits with Reduced Swing

Node Transition Activity and Power

Transistor Sizing for Minimum Energy Goal: Minimize Energy of whole circuit Design parameters: f and VDD tp  tpref of circuit with f=1 and VDD =Vref

Transistor Sizing (2) Performance Constraint (g=1) Energy for single Transition

Transistor Sizing (3) VDD=f(f) E/Eref=f(f) F=1 2 5 10 20

Short Circuit Currents

How to keep Short-Circuit Currents Low? Short circuit current goes to zero if tfall >> trise, but can’t do this for cascade logic, so ...

Minimizing Short-Circuit Power Vdd =3.3 Vdd =2.5 Vdd =1.5

Leakage Sub-threshold current one of most compelling issues in low-energy circuit design!

Reverse-Biased Diode Leakage JS = 10-100 pA/mm2 at 25 deg C for 0.25mm CMOS JS doubles for every 9 deg C!

Subthreshold Leakage Component

Static Power Consumption Wasted energy … Should be avoided in almost all cases, but could help reducing energy in others (e.g. sense amps)

Principles for Power Reduction Prime choice: Reduce voltage! Recent years have seen an acceleration in supply voltage reduction Design at very low voltages still open question (0.6 … 0.9 V by 2010!) Reduce switching activity Reduce physical capacitance Device Sizing: for F=20 fopt(energy)=3.53, fopt(performance)=4.47