EE240B Discussion 9

Eric Chang

Berkeley Wireless Research CenterUC Berkeley

Announcement• Project phase 1 due tomorrow• Note: for inverter-based TIA, do not

neglect Cgd• Miller effect effectively adds it to the input

capacitance• The feedthrough zero can be safely

ignored since it’s at very high frequency (~gm/Cgd)

Comparator Choice

+ High speed; generally faster than StrongArmtype comparators

+ Design equations well understood and generally more accurate

- Power intensive- “analog” output- Large hysteresis

+ Digital output+ ~Zero hysteresis when

properly designed+ More power efficient- Slower than CML- Only general sizing

guidelines

CML Latch StrongArm-Type Latch

How to design comparator?• Comparator use positive feedback to

amplify small input signals• This means it is not LTI, and small signal

model eventually breaks• i.e. nothing you learn in this class applies

exactly• So what should we do?• Use small signal regime to guide

sizing/bias decisions• But ultimately validate circuit through

simulations

Common Comparator Issues• Hysteresis• Input-referred noise• Offset• Kickback• often just impact the previous block, not

the comparator itself

Hysteresis

• StrongArm latch waveforms• Input needs to be large enough to “flip” previous bit• Delay dependent on Vin

• Acceptable delay depends on the following digital flip-flop

Overdrive Recovery Test• Used to measure hysteresis

• Quantifies hysteresis with “minimum input amplitude”• Also get intrinsic offset (usually indicates layout quality).

1. Apply large negative input (~!""/$) for ~4 cycles• Cleans up initial conditions

2. Transition to a small positive input %&'. Sweep %&'until output flips• Can use combination of sweep + binary search

3. Repeat this procedure for high-to-low transition to find %&(

4. intrinsic offset = (%&' + %&()/$, Minimum input amplitude = (%&' − %&()/$

Comparator Noise?• As with all circuits,

comparator also has noise• CML noise analysis quite

straight-forward• StrongArm on the other

hand…• “transient noise” comes

to the rescue• Magically injects noise

during transient run• Specify randomization seed

to make simulation repeatable

• But how to calculate input-referred noise?

Noise (Standard Approach)1. Set input to constant

value !".2. Run long transient

with ~1000 cycles.3. Find percentage of 1’s

in output.4. Sweep !", plot

percentages, then fit CDF curve to get #(!%)

Assumes outputs of each cycle are independent (but is it?)

Noise (My Approach)• Instead of DC input,

alternate input between !"#$%& and !'&(' for even/odd cycles

• Only counts statistics on odd cycle outputs• Basically, use !"#$%& to

“initialize” the comparator

• To save time, use only a few data points (2-3) to fit the CDF• Other noise sources

usually dominates anyways

Comparator Offset (Standard)• Industry generally run Monte Carlo

simulation• Randomly vary each transistor

• Run transient simulation with slow input ramp• Also slower clock to reduce hysteresis

• Find input value at the output transition point• SLOOOOOOW…..• Offset only matters when you want reliable circuit• reliable circuit = more sigmas = more Monte Carlo

runs

Comparator Offset (Elad)• Manually compute n-sigma offsets of each

transistors• Insert offset voltage sources with worst case

polarity• Simulate to find effective input-referred

offset• Pessimistic, but fast• Also, pessimistic may be a good thing