Abstract
Closed-form relations with equivalent circuits including mutual inductance effects for periodic array structures operating at terahertz (THz) ranges are developed and presented using the network synthesis method. The complete equivalent circuits taking into account of mutual inductances between unit cells and the periodic structures are given. The closed-form relations developed and given for unit cells and periodic arrays have been verified with 3-D electromagnetic (EM) simulator and Advanced Design System (ADS) circuit simulator. Several prototypes including <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$36\times35$ </tex-math></inline-formula> periodic array have been built and measured. It has been confirmed that the closed-form relations developed using the equivalent circuits for the periodic array structures including all the mutual inductance effects agree with the simulation and measurement results from microwave frequencies to THz ranges.
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