## Fast Analysis and Optimization of Substrate Integrated Waveguide (SIW) Antennas Using the Contour Integral Method (CIM)

With the powerful simulations tools from TET, we want to develop a fast simulation method to calculate the inside-, near- and far- field of a standard SIW horn antenna. First, the excitation inside-field and the aperture-field of the SIW horn will be calculated by using the CIM. Then the Huygens’ equivalence principle will be used to calculate the radiation field. Thus, the approach is a combined method of the CIM and Huygens’ Principle as shown in Fig. 1.

Fig. 1. Illustration of the proposed method to calculate SIW horn antennas.

First, this combined method needs to be implemented on the basis of the existing codes of the host. Next, the accuracy of the radiation pattern, gain, side-lobe level and back radiation will be compared to results from commercial full-wave software and measured results. If the results don’t agree well, we will revise the port conditions at the horn aperture for the CIM to take initially neglected effects into account. A preliminary study on the CIM approach to calculate the excitation and inner-field inside the SIW horn has already been conducted to check the feasibility of the proposed hybrid CIM-MoM approach. The electric-field results are shown in Fig. 2, which agree well with full-wave simulation results from commercial software. This CIM approach is more efficient by a speed-up of one to three orders of magnitude.

Fig. 2. Field calculation example of SIW horn antennas with CIM approach (electric fields are shown).

Apart from applying CIM, we are also going to fully integrate the Polynomial Chaos Expansion (PCE) into CIM for e.g. analysis of model variations in an efficient manner. It will be very interesting to study how robust the radiation patterns are with respect to uncertainties in the dielectric. Alternatively, it will be used to identify the right ‘tuning screws’ in a design because PCE allows to identify variables that have a high impact on performance.

**Funding:** Alexander-von-Humbodt Foundation

**Contact:** Ph. D. Lei Wang