# Equation used in simulation software

• deven
In summary, using software like Pspice, Psim, MATLAB simulink you can approximate non-linear equations and solve for node voltages.

#### deven

Can i know how this simulation softwares(like Pspice, Psim, MATLAB simulink) work ? Which methods they use to solve any circuit with non-linear elements ? How can we solve any circuit numerically ?

I don't know the specifics of how those software packages work but I do know that you can use http://en.wikipedia.org/wiki/State_space_%28controls%29" [Broken] to model just about any kind of circuit. Non-linear things can be approximated by some sufficiently complex linear differential equation and then plugged into the state space equation.

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Years ago, I took a course related to this. The textbook was written by E. J. Mastascusa, who seems to be alive and well with his own web site.
Anyway, as I recall, we went over solutions of linear problems - sources, R, L, C, transformers, and dependent sources. All of these could be built out of standardized "little" matrices.
From a description file, the parts are given values and associated nodes. The values are populated into the part's matrix, and the matrices are superimposed into one large matrix according to their nodes. Independent sources are attached in a vector - again, according to their nodes.

Invert the large matrix, multiply it by the source vector and viola', you have the node voltages. Of course, this is only good for linear systems. It's great for DC operating points and simple AC analysis (Just put in the complex numbers). There was some way to handle transients using Rung-Kutta, but I've forgotten how.

I'm pretty sure the guys at Berkly came up with an auto assembling matrix as well, but I don't know how they would handle the nonlinear equations. Some very simple systems, like a battery, resistor, and diode, cannot be solved in closed form, so I think they must use an iterative solution.

## 1. What is an equation used in simulation software?

An equation used in simulation software is a mathematical representation of a system or process that is used to predict future outcomes or behaviors. It is based on principles and laws of physics, chemistry, or other sciences, and is used to model complex systems or phenomena.

## 2. How are equations chosen for simulation software?

The equations used in simulation software are chosen based on the specific system or process being modeled. They are selected to accurately represent the behavior and interactions of the components of the system, and are often derived from fundamental laws and principles of science.

## 3. Can equations in simulation software be modified or customized?

Yes, equations in simulation software can be modified or customized to fit a specific scenario or to incorporate new data or variables. This allows for more accurate and precise simulations to be created for different applications.

## 4. What is the role of equations in simulation software?

The role of equations in simulation software is to provide a mathematical framework for predicting and understanding the behavior of a system. They allow for the simulation of complex scenarios and the analysis of various factors and variables that may affect the system.

## 5. Are equations the only factor in creating accurate simulations?

No, equations are not the only factor in creating accurate simulations. Other factors such as initial conditions, boundary conditions, and numerical methods also play a significant role in the accuracy and validity of simulations. It is important to carefully consider all aspects of a simulation in order to ensure its accuracy.