Equivalent Circuit Approximation to the Connector-Line Transition at High Frequencies using Two Microstrip Lines and Data Fitting
DOI:
https://doi.org/10.13052/2021.aces.J.361205Keywords:
Microstrip line, electrical transitions, equivalent circuit, data fitting, least-squares method, overdetermined system, ABCD parameters, SMA connector, textile electronics.Abstract
This article presents a method of obtaining an equivalent lumped element circuit to model the electrical connector-line transitions in the ultra-high frequency (UHF) band. First, the scattering matrices of two microstrip transmission lines that are otherwise identical but have the physical lengths of dd and 2d2d are measured. Next, the theoretical model of the lines cascaded with the connector-line transitions modeled as lumped element circuits is established. The selection of the line lengths to be dd and 2d2d results in an over determined system of equations that links the circuit component values to the two-port network parameters of the cascaded system. Finally, the least-squares data fitting procedure yields the best-fit component values. The results show that in our tested scenario, 3-component reactive circuit models well the transitions. Compared with the previous methods, the proposed approach does not require knowledge of the dielectric properties of the substrate of the measured transmission lines. This property integrates the method with our previous work on estimating a microstrip line substrate’s relative permittivity and loss tangent. The obtained transition circuit model is also validated through the testing of two quarter-wave transformers. The lines and transformers are implemented on a textile substrate to highlight the method’s applicability to wearable textile-based electronics.
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