Current Trends in Network Optimization

Abstract

Some current trends in automated network design optfilzation which, it is believed, will play a significant role in the computer-aided design of lumped-distributed and microwave networks are reviewed and discussed. In particular, the adjoint network approach due to Director and Rohrer for evaluating the gradient vector of suitable objective functions related to network responses that are to be opttilzed is presented in a tutorial manner. The advantage of this method is the ease with which the required partial derivatives with respect to variable parameters, such as electrical quantities or geometrical dimensions, can be obtained using at most two network analyses. Least pth and minimax approximation in the frequency domain are considered. Networks consisting of linear time-invariant elements are treated, including the conventional lumped elements, transmission lines, RC limes, coaxial lines, rectangular waveguides, and coupled lines. TO illustrate the application of the adjoint network method, an example is given concerning the optimization in the least #th sense using the Fletcher-Powell method of a transmissionline tilter with frequency variable terminations previously considered by Carlin and Gupta.

Adjoint Techniques for Sensitivity Analysis in High-Frequency Structure CAD

“…Comprehensive reviews can be found, for example, in [9], [12], and [44]. Reference [12] also provides a useful comparison between the adjoint network method based on Tellegen's theorem on the one hand and adjoint-based methods such as the direct method and the transpose-matrix methods on the other.…”

“…We refer to as the component sensitivity. The substitution of (7) in the right-hand side of (8) leads to [9] (9)…”

“…In microwave circuit design, we may be interested in minimizing the reflection at this port [9], assuming that the loads of all other ports are known. The reflection coefficient (25) is, in general, a complex number.…”

Computer-aided design of RF and microwave circuits and systems

“…The essential features are the simple relation between the original circuit and an auxiliary or "adjoint" circuit (e.g., transpose of the nodal admittance matrix [36]) and the need to derive simple element level sensitivity expressions. As a result, the computational effort to evaluate the first-order derivatives of any response with respect to all design parameters corresponds essentially to two circuit analyses [37].…”

Feasible adjoint sensitivity technique for EM design optimization

“…It is referred to as the adjoint network method (ANM). The first applications of the ANM to microwave circuit problems were published in the early 1970s when network sensitivities were calculated on both voltage-current [3]- [5], and S-parameter bases [6], [8], [9]. Later, Alessandri et al [10] applied the ANM to the analysis of microwave circuits whose subnetworks are represented by Yparameters.…”