# Propagation Time Delay Rising propagation delay time Propagation

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Propagation Time Delay Rising propagation delay time: Propagation delay =(Rising delay + Falling delay)/2 1

Single pole response of amplifier 2

Time delay due to dynamic response 3

Slew Rate of a Comparator If the rate of rise or fall of a comparator becomes large, the dynamics may be limited by the slew rate. Slew rate comes from the relationship, i = Cdv/dt where i is the current through a capacitor and v is the voltage across it. If the current becomes limited, then the voltage rate becomes limited. Therefore for a comparator that is slew rate limited we have, tp = ∆T =∆V/SR =(VOH- VOL)/2·SR where SR = slew rate of the comparator. 4

Find the propagation delay time of an open loop comparator that has a dominant pole at 103 radians/sec, a dc gain of 104, a slew rate of 1 V/µs, and a binary output voltage swing of 1 V. Assume the applied input voltage is 10 m. V. Solution The input resolution for this comparator is 1 V/104 or 0. 1 m. V. Therefore, the 10 m. V input is 100 times larger than vin(min) giving a k of 100. Therefore, we get tp =1/103 ln(2· 100/(2· 100 -1)) = 10 -3 ln(200/199) = 5. 01µs For slew rate considerations, we get tp =1/(2· 1 x 106) = 0. 5µs Therefore, the propagation delay time for this case is the larger or 5. 01µs. 5

Two-Stage Comparator An important category of comparators are those which use a high-gain stage to drive their outputs between VOH and VOL for very small input voltage changes. The two-stage op amp without compensation is an excellent implementation of a high-gain, open-loop comparator. 6

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Driving Large Capacitive Load Inverters clean up output Typically added at latch output. 9

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Input Noise on the Comparator Problem: Solution: Introduce Hysteresis 18

External Positive Feedback 19

Internal Positive Feedback 20

Chapter 10 Figure 14

Latched comparators • Pre-amplification followed by a track-and-latch. • Pre-amplification is used to obtain high resolution and to minimize “kickback” effects. • Kickback: charge transfer in or out of the input side when the track-and-latch goes from track mode to latch mode. • Pre-amplification has moderate gains, or small gains for higher speed • Output of pre-amp is small to drive digital. • It is amplified during track-and-latch modes by positive feedback which regenerates the analog signal into a full-scalar digital signal. 22

The inputs are initially applied to the outputs of the latch. Vo 1’ = initial input applied to vo 1 Vo 2’ = initial input applied to vo 2 Then positive feedback drives the higher of the two to digital 1 and the lower to digital 0 23

CMOS Latch 24

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There are several comparator circuit in the book, here is one from a paper by T. B. Cho and P. R. Gray, “A 10 b, 20 Msamples/s, 35 m. W pipeline A/D Converter, ” IEEE J. Solid-State Circuits, vol. 30, no. 3, pp. 166 -172, March 1995. 27

When phi_1 is low: 28

When phi_1 is high: 29