# Monte Carlo Analysis and Simulation for Electronic Circuits

September 23, 2019

A good friend of mine recently quit his job to start a business in woodworking. While I appreciate his gusto and support him completely, I wish we could run an isolated analysis on the probability of failure in this business venture and many other risks in life. Predicting whether there is an officer around the corner as I pass someone, or the odds of me successfully completing my PhD would be quite welcome as opposed to leaving things up to blind fate and hard work.

However, I take no chances with varying parameters in electronics design. A typical PCB design consists of hundreds of components, and it’s foolish to assume that the values are strictly unchanging in every single PCB that is produced.

The fact is, electronics components like capacitors, resistors, inductors, and transistors are produced with a tolerance rate on their values. This means a 100 Ohm resistor may turn out to be 95 Ohm when measured. In some designs, accuracy is crucial, and the varying values can affect the functionality of the circuit.

To have a good idea on the probability of failure, PCB designers depend on the Monte Carlo analysis.

## What is Monte Carlo Analysis

Monte Carlo analysis is defined as a simulation process that generates probabilities of risk using a mathematical model. The method provides a range of possible results based on the varying parameters that are measured in the analysis. The method was developed by a scientist developing the atomic bomb during World War II.

Monte Carlo analysis is about generating predictive situational results based on distributing factors that may influence the outcome of the process. It takes into account the maximum and minimum threshold of each parameter and randomly iterates the simulation with different values.

Various types of probability distributions are used in Monte Carlo analysis. They represent how the possible outcome values are distributed and give a good picture of the risk when presented in a histogram chart. Commonly used probability distributions are the Gaussian and uniform models.

Depending on the parameters involved, completing a Monte Carlo analysis simulation may take hundreds or thousands of iterations. In contrast to single-point analysis, Monte Carlo gives you a better picture of what may go wrong in terms of probability.

## Monte Carlo Analysis And Circuit Yield

Let’s face it. When you’re manufacturing hundreds or thousands of PCB, you’ll be praying that you’ve spotted every mistake and have made amendments. It’s unimaginable to have a large number of the PCBs to be defective.

Monte Carlo analysis helps to predict the risk of defects in PCB manufacturing.

But the yield in PCB production must also take the tolerance of components into account. Sometimes, the fluctuation in parameters can result in a fraction of the production PCB to be rejected. Running the Monte Carlo analysis gives you a clearer picture of what to expect when the PCBs are produced.

Basically, Monte Carlo analysis is about running a series of analysis like transient, noise, and AC/DC sweep over a specific circuit by substituting the parameters with possible values from the specified tolerance.

## When Do You Need Monte Carlo Analysis in PCB Design?

Running a Monte Carlo analysis typically requires setting up the test parameters on the simulator. Is there a need to go through such a process on every PCB design you’re working on?

Well, it all depends on the nature of the design and the risk of failure in the production run. For example, a design involving simple LED arrays that functions on large tolerance may not need the Monte Carlo analysis to be done.

SMPS is one example where performing Monte Carlo analysis is helpful

However, if you’re working on designs like audio amplifiers, switching power supplies or high-frequency applications, you’ll want to know if the existing tolerance of components is sufficient to guarantee a minimal rejection rate.

Furthermore, with a tool that has a model library of over 34,000 models with parameter information available, setting up the parameters for a monte carlo analysis might end up being significantly easier than first imagined. For example, assigning varying tolerances should be a breeze for a strong SPICE tool. Settling for a necessary tool which makes you put in hours of mundane work seems like a painful precedence to set forth.

Generic Monte Carlo analysis is not going to give the total yield analysis accessible in PSpice’s advanced toolset. Whether it is through multiple goal analysis enabling you to analyze for a variety of necessities the design requires, or dynamic yield calculators allowing you to change minimum and maximum ranges dynamically, an advanced Monte Carlo analysis tool makes your yield optimization process both more effective and efficient, especially when it comes to split products, product differentiation, or meeting the needs of multiple groups of users.

It’s better to be safe than sorry by investing in a PCB design software with a Monte Carlo analysis tool. The OrCAD PSpice Simulator gives you the flexibility to set up the Monte Carlo simulation to accurately predict the yield estimation.