Numerical Short-Open-Load (SOL) Calibration Technique for Accurate Extraction of Electrically-Small Planar/Non-Planar Microstrip-Line Circuits

This article presents a numerical short-open-load (SOL) calibration technique for accurate extraction of electrically small planar/nonplanar microstrip-line (MSL) circuits and elements in the interface of 3-D full-wave algorithm or simulator. An additional matched-load condition is established at the reference plane and employed in the whole calibration process. In comparison with the traditional short-open calibration (SOC) method, the proposed SOL technique implemented in the interface of software does not inquire prior simulation of the internal current/voltage at the reference plane of two calibration standards but only needs to know the external port impedances of three calibration standards. After the description of entire extraction process, a few typical electrically small planar circuits, such as MSL open-end and step discontinuities, are first numerically deembedded, and their extracted circuit parameters are evidently confirmed with other published ones. Then, a nonplanar structure of a vertically placed shorting pin in the middle of MSL is studied with different sizes and positions to effectively extract the circuit parameters in the two presented equivalent models. Finally, a third-order Chebyshev filter is designed with pin-loaded MSL structures. Its frequency response is synthesized on the proposed SOL method to validate the correctness of the extracted circuit parameters and further demonstrate the usefulness of this method in synthesis design of electrically large microwave circuits. Good agreement among the filtering frequency responses from equivalent circuit model, full-wave simulation, and measurement has well revealed that the proposed SOL method is indeed accurate in numerical extraction of circuit elements and efficient in synthesis design of an entire circuit with prescribed specifications.