Spice Simulates Custom Random Distributions for Monte Carlo Analysis (.PDF Download)

Not all Spice versions perform Monte Carlo simulations. Even those that do may only have a small number of available distributions, much less custom ones. LTSpice, for example, has built-in random distributions limited to Uniform and Gaussian (defined by sigma, but no specified limit). Unfortunately, this excludes many real-world distributions such as Gaussian (with maximums of 2-sigma, 3-sigma, etc.), bimodal, triangular, and U-shaped for example. A review of web reference shows few solutions beyond the available functions.

However, using straightforward statistical theory, you can create a random process of any distribution listed above. Even histograms from manufacturers’ datasheets or your own lab measurements are easily simulated. What are the minimum requirements? A calculation tool having a uniform random-number generator and a lookup table function. We’ll apply the method here using Excel and Spice.

This statistical/simulation adventure was both fun and insightful. The nuts and bolts of creating a circuit simulation developed an intuitive understanding beyond the abstract statistical theories.