# Wave Impedance Determination for PCB SIWs Considering Metal Roughness Loss Effects

## TL;DR

This paper improves the modeling of waveguides by accounting for metal roughness effects, enhancing accuracy in predicting their electrical behavior.

## Contribution

A novel expression for complex wave impedance is introduced, incorporating conductor losses due to surface roughness.

## Key findings

- The proposed expression accurately models the complex impedance of substrate-integrated waveguides.
- Including conductor losses improves agreement between simulated and experimental insertion loss.
- The method enables accurate reconstruction of S-parameters for different waveguide widths.

## Abstract

This paper presents an expression to determine the complex wave impedance of a substrate-integrated waveguide for the dominant TE10 propagation mode, notably enhancing the accuracy in modeling the corresponding imaginary part. This was accomplished by systematically identifying the need to consider additional conductor losses caused by the interaction of the propagating fields with the conductor material. In fact, by using the proposed expression, the complex impedance can straightforwardly be determined by combining propagation constant data, and the resistance that represents the loss associated with longitudinal currents occurring at the top and bottom walls, which are influenced by the conductor surface roughness. This allows for completely describing the characteristics of the waveguide when assuming uniform propagation along its length. Furthermore, since the voltage–current, the power–current, and the power–voltage impedances can easily be obtained from the wave impedance, the proposal enables representing the matching characteristics of the waveguide for circuit design purposes. An agreement between simulated and experimental insertion loss is achieved for substrate-integrated waveguides of two different widths when reconstructing the corresponding S-parameters using the determined wave impedance.