# Electromagnetic Simulation Using the Partial Element Equivalent Circuit Method

### Key Takeaways

• The PEEC method is a type of electromagnetic simulation that relies on the integral formulation of Maxwell’s equation.

• The basic formulation in the PEEC method is the electric field integral equation (EFIE) full-wave solution to Maxwell’s equation.

• Advantages of the PEEC method include:

1.  Only materials in the system are discretized, which reduces the number of cells.
2.  Solution variables are also the circuit variables.

Have you noticed the CE symbol on electronic products? This symbol indicates the product meets safety, health, environmental, and electromagnetic compatibility (EMC) standards. The CE symbol indicates a product meets EMC standards

Meeting EMC standards is essential, as they regulate electromagnetic effects between the product and other neighboring equipment. Electromagnetic effects can affect the performance of electronic systems, and if those effects cross the electromagnetic compatibility (EMC) limits,  it can result in a product’s withdrawal from the market.

In electronic product research and development, conducting electromagnetic simulations during the design stage is essential to predicting the electromagnetic effects on electronic products. Simulating real-world scenarios helps to confirm the proper functioning of a product and checks compliance with EMC regulations.

There are various electromagnetic simulation methods including the Finite Difference Time Domain Method (FDTD), Finite Element Method (FEM), Method of Moments (MoM), and Partial Element Equivalent Circuit (PEEC) method. The FEM and FDTD methods are based on the partial differential equation form of Maxwell’s equation, whereas the MoM and PEEC methods rely on the integral formulation of Maxwell’s equation. Each of these methods is suitable for different applications: FEM and FDTD work well for scattering problems, the MoM method is preferable for planar structures, and the PEEC method is ideal for electrical packaging analysis and PCB analysis.

In this article, we will examine the fundamentals of the PEEC method.

## The Partial Element Equivalent Circuit Method

If you want a circuit-based solution for electromagnetic problems, utilize the partial element equivalent circuit (PEEC) method. The PEEC method offers a full-wave electromagnetic electrical modeling technique entirely based on equivalent circuits. With the same equivalent circuit, it is possible to conduct both circuit and EM simulation. The PEEC method formulates solutions for electromagnetic problems as a circuit model, instead of solving field equations consisting of field variables such as potential, current, voltage, or charge.

The PEEC method was developed by Dr. Albert E. Ruehli, and resembles the MoM method based on the integral formulation of Maxwell’s equations. The basic formulation in the PEEC method is the electric field integral equation (EFIE) full-wave solution to Maxwell’s equation.

The general form of EFIE is transformed into PEEC formulation and the equivalent circuit is derived from this formulation. The PEEC method provides an equivalent circuit from the EFIE in terms of partial elements, which are resistance, coefficients of potential, and partial inductances. This approach makes it easy to study the circuit using circuit solvers in the time and frequency domain.

With the PEEC method, all developments in the time domain can be extended to the frequency domain without any restriction, and vice versa. Techniques such as macro models, simplified PEEC models, and special circuit formulations are adapted to achieve PEEC model solutions.

### Applications

The PEEC method is suitable for free-space simulations and time, as well as frequency domain analysis. This method is popular in research and industrial development due to its full-wave and full-spectrum possibilities.  The combined EM and circuit simulations of large systems are the main application areas for the PEEC method.

## Advantages of the PEEC method

PEEC model-based solutions provide significant electronic improvements such as the inclusion of dielectrics, incident fields, and scattering formulations. Its equivalent circuit revolves around heterogeneous, mixed circuit, and electromagnetic field problems, which make it easily analyzed using circuit theory or circuit solvers like SPICE. As PEEC is based on integral formulation, advantages to using the method (as opposed to differential formulation based electromagnetic simulation) include:

• Discretization of the structure - In differential formulation-based methods such as FEM and FDTD, the entire system is discretized. In the PEEC method, only the materials are discretized. This difference is reflected as a higher number of cells in differential formulation based techniques and fewer cells in integral formulation methods. In the PEEC method, there is cell flexibility (mixed orthogonal and non-orthogonal) in volume and surface cell discretization, which offers excellent modeling possibilities.

• Solution variables - FEM and FDTD present solutions in field variables such as electric field intensity or magnetic field intensity. The post-processing of the variables is required to convert them to currents and voltages in the system. However, in integral formulation based methods, the solution is directly expressed in circuit variables such as currents and voltages. This makes the PEEC method suitable for electronic interconnect packaging, electromagnetic interference (EMI), and PCB analysis.

When you want to simulate a PCB for EM problems and circuit functioning, then consider the PEEC method. With a PEEC equivalent circuit, you can conduct combined circuit and electromagnetic simulation. Since PEEC is based on the integral formulation of Maxwell's equation, it requires less discretization and solution variables are the same as the circuit variables. If you are planning to conduct time and frequency domain analysis for your product design, then develop the PEEC model for restriction-free switching between time and frequency domain.

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