  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.
