Penn ESE370 Fall DeHon 1 ESE370: Circuit-Level Modeling, Design, and Optimization for Digital Systems Day 8: September 21, 2012 Delay and RC Response
Delay is RC Charging Penn ESE370 Fall DeHon 2
Delay is RC Charging Strategy Understand switch state 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
Wire Resistances Penn ESE370 Fall DeHon 24
First Order Model Switch –Resistive driver As dig in, understand: –More sophisticated view –How can we engineer –Tradeoffs Penn ESE370 Fall DeHon 25
Equivalent Resistance What resistances might transistors contribute? –How many cases? –Assume Ron same all tr, Resistance of each? Penn ESE370 Fall DeHon 26
Equivalent Resistance What resistances might transistors contribute? 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
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
Measuring/Characterizing Drive with a gate –Not an ideal source Measure loaded gate –Typical loading – FO4 Penn ESE370 Fall DeHon 34
HW2 Recommendation Penn ESE370 Fall DeHon 35
Rise/Fall Rise and Fall time may differ –Why? –What is ratio? Penn ESE370 Fall DeHon 36 InputRout 00Ron/2 01Ron 10Ron 112Ron
Admin HW3 posted Penn ESE370 Fall DeHon 37
Delay is RC Charging Penn ESE370 Fall DeHon 38