# A generic method for equipping arbitrary rf discharge simulation frameworks with external lumped element circuits

## TL;DR

This paper introduces a versatile method to integrate external lumped element circuits into any RF plasma simulation framework using harmonic balance, simplifying the modeling of complex external networks.

## Contribution

The proposed approach allows arbitrary external circuits to be incorporated into plasma simulations via a simple netlist and harmonic balance, streamlining complex circuit inclusion.

## Key findings

- Applicable to simple and complex plasma models
- Enables inclusion of arbitrary external circuits
- Reduces complexity of circuit integration

## Abstract

External electric circuits attached to radio-frequency plasma discharges are essential for the power transfer into the discharge and are, therefore, a key element for plasma operation. Many plasma simulations, however, simplify or even neglect the external network. This is because a solution of the circuit's auxiliary differential equations following Kirchhoff's laws is required, which can become a tedious task especially for large circuits. This work proposes a method, which allows to include electric circuits in any desired radio-frequency plasma simulation. Conceptually, arbitrarily complex external networks may be incorporated in the form of a simple netlist. The suggested approach is based on the harmonic balance concept, which splits the whole system into the nonlinear plasma and the linear circuit contribution. A mathematical formulation of the influence of the applied voltage on the current for each specific harmonic is required and proposed. It is demonstrated that this method is applicable for both simple global plasma models as well as more complex spatially resolved Particle-in-Cell simulations.