High-frequency behaviour of microstrip open-circuit terminations

The extensive use of open-circuit microstrip terminations as tuning stubs and, more recently, as antenna elements, demands design data on the frequency-dependent characteristics of the termination. A variational solution for the end admittance is formulated using discrete and continuous mode distributions to represent the radiation, evanescent and substrate surface-wave fields. Computed results for a variety of line widths on polyguide and alumina substrates are compared with available experimental and theoretical data. It is established that useful admittance curves can be readily calculated using a simple trial aperture field, and the functional form of the curves is independently predicted by a Hilbert-transform relationship. The frequency-dependent end admittance reveals the lower frequency range over which a given substrate is suitable for unshielded high-Q circuit applications and the higher-frequency region for microstrip antenna applications. The generation of substrate surface waves increases with frequency, and sets an upper frequency limit for microstrip antenna applications. Other practical issues of interest such as radiation patterns, intercircuit coupling and resonator losses are briefly considered and the usefulness of this approximate analysis, which represents the most complete treatment to date, is evident.