Time-Domain Green's Functions for Microstrip Structures Using Cagniard–de Hoop Method

Abstract

Time-domain Green's functions are required for transient analyzes of many structures using the time-domain integral equation method. In this paper, we express the generalized reflection coefficient of the microstrip structure in terms of a geometric optics series so that by applying the Cagniard-de Hoop method to each term of the series, we can derive the time-domain Green's function. It is demonstrated that this series converges rapidly and there are two contributing waves from each source image if the observation point is beyond the total internal refraction location. The two waves are the direct wave from the image and the head wave from the image to the critical point, and then laterally along the surface to the observer. Each contribution is a definite integral that is evaluated for each point in space and time. Therefore, the derived Green's function is efficient for time-domain simulations compared with conventional approach, in which for each point in space and frequency a Sommerfeld type integral is involved and then the frequency-domain data is converted into time-domain by discrete Fourier transform. This rigorous Green's function can also be used to check the accuracy of other approximate methods such as those using the discrete complex image theory.