1/6Aadithya V. Karthik <aadithya@berkeley.edu> Feb 2014, BEARS lightning talk, Berkeley

ABCD: “Booleanizing” AnalogSystems for Verifying Chips

Aadithya V. Karthik,Sayak Ray, Pierluigi Nuzzo, Alan Mishchenko,

Robert Brayton, and Jaijeet Roychowdhury

EECS Dept., The University of California, Berkeley

Feb 2014, BEARS, Berkeley

2/6Aadithya V. Karthik <aadithya@berkeley.edu> Feb 2014, BEARS lightning talk, Berkeley

The Problem: Verifying a Chip

Specification

Chip designers

Chip

3/6Aadithya V. Karthik <aadithya@berkeley.edu> Feb 2014, BEARS lightning talk, Berkeley

Surrounded byDigital Logic

Example: SERDES

Analogparts

PLL

CDR I/O

The Problem: AMS Verification

Want to verify complete systemo e.g., eye opening height > 1V?

Proof or counter-example needed

>1V

4/6Aadithya V. Karthik <aadithya@berkeley.edu> Feb 2014, BEARS lightning talk, Berkeley

Our approach: “Booleanize” the analog parts

Best verification tools = all Boolean, no continuous

Digital componentsVerification tools accept

Analog components

Challenge: Analog models Digital models+Continuous Boolean

(don't mix)

SAR-ADC Boolean T/Happroximation Boolean

comparatorapproximation

Boolean DACapproximation

ALLBOOLEAN

Formal verification, high-speed simulation, test pattern generation, ...

ABCD: Booleanapproximation

… for the full combined system!

Fast

5/6Aadithya V. Karthik <aadithya@berkeley.edu> Feb 2014, BEARS lightning talk, Berkeley

ABCD in action

Analog Circuit Purely Boolean Model

ABCD

Bit Sequence

Example: Channel + Equalizer

6/6Aadithya V. Karthik <aadithya@berkeley.edu> Feb 2014, BEARS lightning talk, Berkeley

Circuits Successfully Booleanized

Charge pump

Equalizer

Delay line

Power grid

SAR-ADC

I/O signaling system