Penn ESE370 Fall DeHon 1 ESE370: Circuit-Level Modeling, Design, and Optimization for Digital Systems Day 8: September 15, 2014 Delay and RC Response

Delay is RC Charging Penn ESE370 Fall DeHon 2

Delay is RC Charging Strategy Understand switch state (zeroth order) Break into stages For each stage –Understand R drive –Understand C load Penn ESE370 Fall DeHon 3

Today RC Charging RC Step Response What is the C? What is the R? Measuring Delay Penn ESE370 Fall DeHon 4

90% Rise Time? Penn ESE370 Fall DeHon 5

What does response look like? Penn ESE370 Fall DeHon 6 about 2ps for 90% rise

Vmeasure? Current across Resistor? Current into Capacitor? Penn ESE370 Fall DeHon 7 Governing Equations? (KCL)

Equations Penn ESE370 Fall DeHon 8

Solve Vmeasure Penn ESE370 Fall DeHon 9 What’s Vmeasure?

What does look like? Penn ESE370 Fall DeHon 10

Shape of Curve x e -x 1-e -x Penn ESE370 Fall DeHon 11 Fillin on board

Shape of Curve x e -x 1-e -x /e = /e 2 = Penn ESE370 Fall DeHon 12

Risetime: 10—90% Penn ESE370 Fall DeHon 13 T rise ~= 2.2ps

What is C? Penn ESE370 Fall DeHon 14

Capacitance Wire MOSFET gate Logical Gate Fanout -- Total gate load Penn ESE370 Fall DeHon 15

First Order Model Switch –Loads input capacitively As dig in, understand: –Origin of capacitance –How can we engineer –Tradeoffs Penn ESE370 Fall DeHon 16

Logic Gate Input Capacitance Capacitance on –A input? –B input? Penn ESE370 Fall DeHon 17

Fanout Number of things to which a gate output connects Penn ESE370 Fall DeHon 18

Fanout in Circuit Output routed to many gate inputs Penn ESE370 Fall DeHon 19

Fanout in Circuit Maximum fanout? Second? Min? Penn ESE370 Fall DeHon 20

Lumped Capacitive Load Penn ESE370 Fall DeHon 21

What is R? Penn ESE370 Fall DeHon 22

Resistance Wire resistance –Supply to transistor source –Transistor output gate it is driving Transistor equivalent resistance Penn ESE370 Fall DeHon 23

First Order Model Switch –Resistive driver As dig in, understand: –More sophisticated view –How can we engineer –Tradeoffs Penn ESE370 Fall DeHon 24

Equivalent Resistance What resistances might transistors contribute? –How many cases? –Assume Ron same all tr, Resistance of each? Penn ESE370 Fall DeHon 25

Equivalent Resistance What resistances might transistors contribute? Penn ESE370 Fall DeHon 26 InputRout 00Ron/2 01Ron 10Ron 112Ron

Rise/Fall Rise and Fall time may differ –Why? –What is ratio? Penn ESE370 Fall DeHon 27 InputRout 00Ron/2 01Ron 10Ron 112Ron

Lumped Resistive Source Penn ESE370 Fall DeHon 28 R trnet = parallel and series combination of R tr

Measuring Delay Penn ESE370 Fall DeHon 29

Measuring Gate Delay Next stage starts to switch before first finishes Measure 50%--50% Penn ESE370 Fall DeHon 30 67ps 80ps t del = 13ps

Characterizing Gate/Technology Delay measure will be –Function of load on gate –Function of input rise time Which, in turn, may be a function of input loading Penn ESE370 Fall DeHon 31

Delay vs. Risetime Penn ESE370 Fall DeHon 32 10ps delay 20ps delay 1ps rise100ps rise (if didn’t know input rise, wouldn’t know what a 13ps delay meant)

Characterizing Gate/Technology Delay measure will be –Function of load on gate –Function of input rise time Which, in turn, may be a function of input loading Want to understand typical –At least comparable Penn ESE370 Fall DeHon 33

Standard Measurement for Characterization Drive with a gate –Not an ideal source –Input rise time typically would see in circuit Measure loaded gate –Typical loading – FO4 Penn ESE370 Fall DeHon 34

HW3 Recommendation Penn ESE370 Fall DeHon 35

Measurement for Characterization Drive with a gate –Not an ideal source (how change if drive ideal?) –Input rise time typically would see in circuit Measure loaded gate –Typical loading – FO4 Penn ESE370 Fall DeHon 36

Measurement for Characterization Drive with a gate –Not an ideal source –Input rise time typically would see in circuit Measure loaded gate –Typical loading – FO4 (how change unloaded?) Penn ESE370 Fall DeHon 37

Delay is RC Charging Penn ESE370 Fall DeHon 38

Admin “Normal Week” –3 Lecture Week (all here) Office Hours –Monday – Ron 7pm –Tuesday – Andre 4:15pm –Wednesday – Ron 7pm ngspice –Good to get running on laptop Penn ESE370 Fall DeHon 39