Monte Carlo Analysis

[IntuitiveAnalog]

Hi everyone,

I want to do monte carlo analysis of a circuit by varying its device width . I am writing the syntax as given below :

.param W1=gauss(2.072u,0.2,1)

and the using sweep monte=30 in ac analysis. Everything is fine upto this point but when I rewrite the syntax as below

.param W1=gauss(2.072u,0.0667,3)
then the results are quite different .
My question is what parameters we are passing in the gauss function in parenthesis . If I am not wrong the first value is the mean value , second one is percentage deviation and third one is sigma . If this is the case then why two results have so much difference? I am particularly confused about sigma .

Thanks in advance

 

[erikl]

... what parameters we are passing in the gauss function in parenthesis . If I am not wrong the first value is the mean value , second one is percentage deviation and third one is sigma .

Don't know your MC/gauss syntax. Which SPICE variant do you use?

In SPECTRE this would be

parameters W1=2.072
vary W1 dist=gauss std=3

... for sigma specification, resp.

parameters W1=2.072
vary W1 dist=gauss N=0.0667 percent=yes

for percentage specification.

cf. pp. 731-732 of the Spectre® Circuit Simulator Reference, Product Version 5.0 September 2003

 

[IntuitiveAnalog]

Thanks erikl
I am using Synopsys HSPICE.
So in HSPICE can we give both percentage variation and sigma together?

 

[IntuitiveAnalog]

One more question erikl...are both of the syntax given below equivalent
.param W1=gauss(2.072u,0.2,1) and .param W1=gauss(2.072u,0.1,2) ?
I mean to say whether 20% variation at 1 sigma and 10% variation at 2 sigma are same or not?

 

[erikl]

So in HSPICE can we give both percentage variation and sigma together?

Yes.

... are both of the syntax given below equivalent
.param W1=gauss(2.072u,0.2,1) and .param W1=gauss(2.072u,0.1,2) ?
I mean to say whether 20% variation at 1 sigma and 10% variation at 2 sigma are same or not?

No: sigma specifies rel_variation at the sigma level.
For example, if sigma=3, then the standard deviation is rel_variation divided by 3.
(s. HSPICE® User Guide: Simulation and Analysis
Version B-2008.09, September 2008, Appendix A: Statistical Analysis p. 880).

So with the first expression you have a standard deviation of 20%,
with the second one you get a standard deviation of 10%/2 = 5% .