# Solving Electromagnetic Problems With Electromagnetic Finite Element Analysis

### Key Takeaways

• The non-homogeneity of a solution area makes the finite element method an ideal one for electromagnetic problem solving.

• Electromagnetic field analysis is a state-of-the-art simulation technique that can help with field analysis in a problem domain under consideration.

• Electromagnetic finite element analysis of dynamic and time-varying problems determines the field distribution by considering the field transients as well as the mechanical transients. Electromagnetic field

Imagine you are designing a motor for an internal application. At some point, you will want to analyze the armature reaction, which is capable of distorting the current, voltage, and flux in a machine. So, how should you conduct this analysis?

For this particular case, you should use electromagnetic finite element analysis to obtain flux distribution. Let’s learn more about what electromagnetic finite element analysis is and how it can be used to solve electromagnetic problems.

## Electromagnetic Finite Element Analysis

Electrical engineering deals with electric fields, magnetic fields, and electromagnetic fields. The working principle of many electromechanical devices is based on the electromagnetic theory. In fact, it’s becoming a basic requirement to analyze electric fields, magnetic fields, or electromagnetic fields when trying to solve electromagnetic problems in electrical engineering.

When mathematically expressed, most electromagnetic problems form partial differential equations or integral equations. Usually, the finite element method or finite difference method is used to solve partial differential equations and the method of moments is used to solve integral equations. The finite element method accounts for the non-homogeneity of a solution area, which makes it ideal for electromagnetic problem solving.

## The Steps of Electromagnetic Finite Element Analysis

Electromagnetic finite element analysis is a versatile method capable of solving problems involving electric fields, magnetic fields, and their interactions. The electromagnetic finite element analysis method involves four steps to achieve a solution for an electromagnetic problem:

1. Discretization of the solution region into finite elements.
2. Deriving the governing equations for an individual element.
3. Assembling all the finite elements in the solution region.
4. Solving the set of equations obtained.

With these steps, static, dynamic, or quasi-static electromagnetic problems can be solved.

## Solving Problems With Electromagnetic Finite Element Analysis

### Static Problems

When working on a static problem, the electric and magnetic fields are completely decoupled. In these types of problems, the electric or magnetic field can be analyzed using electromagnetic finite element analysis.

### Dynamic Problems

In dynamic and time-varying problems, coupling between the electric and magnetic fields exists. Electromagnetic finite element analysis of dynamic and time-varying problems determines the field distribution by considering the field transients as well as the mechanical transients. For example, when designing a rotary machine, the rotating motion, vibrations, damping, and load forces are included as functions of the position, speed, or time in the electromagnetic finite element analysis.

### Quasi-Static Problems

In quasi-static problems, coupling between the electric and magnetic fields may be through eddy currents, which are induced by a magnetic field in the machine or equipment of interest. Usually, the frequency of quasi-static electromagnetic problems falls within a few Hertz to tens of kiloHertz. Electromagnetic finite element analysis can be used to solve quasi-static problems existing in electrical transformers, motors, generators, solenoids, magnets, and electromagnets.

When you want to build and validate an electromechanical prototype of your own, electromagnetic finite element analysis is the best analysis tool to help you in the process. By using electromagnetic finite element analysis, you can understand the field quantities inside a prototype and can ensure that real prototyping is a success without many manufacturing iterations. Cadence offers 3D FEM EM simulation and an analysis simulator that can reduce the cost involved in product development by eliminating prototype manufacturing iterations.