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External electric circuits attached to radio-frequency plasma discharges areessential for the power transfer into the discharge and are, therefore, a keyelement for plasma operation. Many plasma simulations, however, simplify oreven neglect the external network. This is because a solution of the circuit'sauxiliary differential equations following Kirchhoff's laws is required, whichcan become a tedious task especially for large circuits. This work proposes amethod, which allows to include electric circuits in any desiredradio-frequency plasma simulation. Conceptually, arbitrarily complex externalnetworks may be incorporated in the form of a simple netlist. The suggestedapproach is based on the harmonic balance concept, which splits the wholesystem into the nonlinear plasma and the linear circuit contribution. Amathematical formulation of the influence of the applied voltage on the currentfor each specific harmonic is required and proposed. It is demonstrated thatthis method is applicable for both simple global plasma models as well as morecomplex spatially resolved Particle-in-Cell simulations.

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