A more sophisticated input file for Monte Carlo simulation is distributed with the file /examples/Monte_Carlo/MC_ring.sp (or git repository). Due to its length it is not reproduced here, but some comments on its enhancements over example 1 (22.5.1) are presented in the following.

A 25-stage ring oscillator is the circuit used with a transient simulation. It comprises of CMOS inverters, modeled with BSIM3. Several model parameters (vth, u0, tox, L, and W) shall be varied statistically between each simulation run. The frequency of oscillation will be measured by a fft and stored. Finally a histogram of all measured frequencies will be plotted.

The function calls to sunif(0) and sgauss(0) return uniformly or Gaussian distributed random numbers. A function unif, defined by the line

define unif(nom, var) (nom + (nom*var) * sunif(0))

will return a value with mean nom and deviation var relative to nom.

The line

set n1vth0=@n1[vth0]

will store the threshold voltage vth0, given by the model parameter set, into a variable n1vth0, ready to be used by unif, aunif, gauss, or agauss function calls.

In the simulation loop the altermod command changes the model parameters before a call to tran. After the transient simulation the resulting vector is linearized, a fft is calculated, and the maximum of the fft signal is measured by the meas command and stored in a vector maxffts. Finally the contents of the vector maxffts is plotted in a histogram.

For more details, please have a look at the strongly commented input file MC_ring.sp.