Time-Domain Segmentation based Massively Parallel Simulation

Bichen WuDept. Micro/nano electronicsTsinghua Univ., Beijing, ChinaEmail:cunfuwbc@gmail.comMobile: +86 152 1056 0855

Background• On the one hand, transient circuit simulation is time

consuming• Sigma-Delta ADC: 71h• SAR ADC: 41h• FLASH ADC: 38h• PLL: 148h

• On the other hand, we got strong parallel computing resource• Many core, distributed computing

• How can we increase the circuit simulation efficiency with parallel computing?

Circuit simulation Transient circuit simulation is to solve the

initial condition problem of the following differential equation

Backward Euler was used to convert the above to sequence of discrete equations

Previous parallel circuit simulation Domain decompositionA New Partitioning Method for Parallel Simulation of VLSI Circuits on Transistor Level （ 1996 ）

Parallel numerical integral methodWavePipe: Parallel Transient Simulation of Analog and Digital Circuits on Multi-Core Shared-Memory Machines(DAC 2008)

Multi-algorithm parallelHierarchical Multi-algorithm Parallel Circuit Simulation (TCAD 2011)

Time domain segmentation based parallel simulation

Method descriptiont0 tend

t0

t1

t2

Time domain segmentation based parallel simulation

In general, solution of equation is dependent on initial condition

Uncertainty brought by time domain segmentation may leads to erroneous result

Short memory assumption

Short memory ： the state of the circuit at a certain time point is correlated only to the a limited history of the the input as well as the internal state of the circuit.

Circuits such as ADC ， possess short memory property

A

D

Analog input

Digital output

Calculating SNDR through transient simulation for ADC

A

DAnalog input

Digital output

Fourier Transfor

m Power spectrum density

Two examples5bits FLASH ADC Fsam=3.75GHz, Ttotal=2us, Tov=6ns

Time for serial simulation ： 38hNumber of segmentation ： 1 ， 2 ， 4 ， 8 ， 100

6bits SAR ADC Fsam=2GHz, Ttotal=8us, Tov=13.3ns

Time for serial simulation ： 41hNumber of segmentation ： 1 ， 2 ， 4 ， 8 ， 100

Transient simulation for ADCPower spectrum density of FLASH ADC(left) and SAR ADC （ right ） output, with serial and parallel simulation

FLASH SAR

Transient simulation for ADC

Result

Transient simulation for Sigma-Delta ADC

Sigma-Delta modulatorBecause of integrator, it’s not short memory

Transient simulation for Sigma-Delta ADC

Direct segmentation with the modulator output of modulator brings erroneous result

Time domain deviation between serial and parallel result

Frequency domain deviation between serial and parallel result

Transient simulation for Sigma-Delta ADC

Uncertainty brought by time domain segmentation

Transient simulation for Sigma-Delta ADC

Digital filter realized in

matlab

Solution:

Transient simulation for Sigma-Delta ADC

Result showed efficiency enhancement with high accuracy

Transient simulation for PLL

Phase lock loop(PLL) is not short memory circuit Self-driven system Integral property

f[ ] h(t)+-

Transient simulation for PLL

Phase lock loop(PLL)The expression of the phase growth in the equation above is as follow.

Let

So we get:

Transient simulation for PLL

Phase lock loop(PLL)

Transient noise analysis

PSD of 1/f noise generated in serial and parallel

Parallel:

Serial

The bandwidth gets wider

Transient noise analysis

1/f noise in TDSM

serial parallel

Summary We proposed TDSM for transient circuit simulation

Testified on FLASH ， SAR ， Sigma-Delta ADC

Maximum 78X acceleration with 100 cores parallelization

Efficient for phase noise simulation for PLL, testified by behavior model.

Proposed 1/f noise generator that support TDSM,

testified on a single transistor

Now submitted to DAC 2013