Homotopy Optimization and ANN Modeling of Millimeter-Wave SIW Cruciform Coupler

Abstract

The development of millimeter-wave and terahertz (THz) passive components such as couplers and filters is an intimidating task because of underlying ultrasensitivity of electrical performances to geometric dimensions and processing tolerances. It is a common practice for us to use an integrated optimizer of commercial electromagnetic (EM) software packages for the design and optimization of such geometric parameters. However, those optimizers may fail to achieve a desired performance if initial variables are not in a range close enough to the optimal solution. In this article, we introduce an homotopy approach to optimizing the geometric parameters of a <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$D$ </tex-math></inline-formula> -band cruciform coupler based on substrate integrated waveguide (SIW) technique in conjunction with an artificial neural network (ANN) model. Starting from a set of initial variables, a homotopy optimization is set to search for an optimum solution. The ANN technique is adopted as the surrogate in place of a usual time-consuming EM model to accelerate the homotopy optimization process of the cruciform coupler. We propose a feed-forward computational formulation inspired by the fundamental transmission line impedance equation. Such a transmission line knowledge-based feedforward network results in a faster convergence with better accuracy than its conventional counterpart. To demonstrate the homotopy optimization method based on the ANN model, an example of multiparameterized cruciform coupler design is detailed. This cruciform coupler with optimized geometric dimensions is simulated, fabricated, and measured. Measured and simulated results validate the combined ANN model and homotopy method. An equivalent lumped-element circuit model of the cruciform coupler is also proposed in this work. An ANN model development technique is described how to extract the equivalent circuit parameters for given coupler specifications. Extracted circuit parameters in connection with the desired coupler performance are then compared with published results which verify the ANN model development algorithm.