Efficient Modelling of Passive Load Pins for Microstrip Structures within the Method of Moments

When modelling thin microstrip structures by the method of moments (MoM) using a stratified media Green´s function formulation, then run-time increases significantly when in addition to the horizontal current elements for the microstrip structure also vertical current elements for the feed pins towards ground must be taken into account. To avoid this, several approximate feed models by injecting a current by means of impressed surface charges have been proposed in the literature. We complement these models by proposing a technique allowing to model passive load impedances from a microstrip structure towards ground, taking also the additional inductance of the pin into account. Even though the formulation requires a modification of all MoM matrix elements, some terms can be decoupled, and the MoM matrix setup is almost as efficient as without loads.