Optimization of full‐wave EM models by low‐order low‐dimension polynomial surrogate functionals

Abstract

A practical formulation for EM‐based design optimization of high‐frequency circuits using simple polynomial surrogate functionals is proposed in this paper. Our approach starts from a careful selection of design variables and is based on a closed‐form formulation that yields global optimal values for the surrogate model weighting factors, avoiding a large set of expensive EM model data, and resulting in accurate low‐order low‐dimension polynomials interpolants that are used as vehicles for efficient design optimization. Our formulation is especially suitable for EM‐based design problems with no equivalent circuital models available. The proposed technique is illustrated by the EM‐based design optimization of a Ka‐band substrate integrated waveguide (SIW) interconnect with conductor‐backed coplanar waveguide (CBCPW) transitions, a low crosstalk PCB microstrip interconnect structure with guard traces, and a 10–40‐GHz SIW interconnect with microstrip transitions on a standard FR4‐based substrate. Three commercially available full‐wave EM solvers are used in our examples: CST, Sonnet, and COMSOL. Copyright © 2015 John Wiley & Sons, Ltd.

Polynomial-Based Surrogate Modeling of RF and Microwave Circuits in Frequency Domain Exploiting the Multinomial Theorem

“…A similar approach to develop polynomial surrogate models is proposed in [32]; however, our new approach differs in three aspects: the surrogate model formulation, the calculation of weighting factors, and the surrogate order determination. For the surrogate model formulation, [32] implements the Nth order surrogate model by using an element-wise power operator, which creates some redundant terms, while our new formulation exploits the multinomial theorem, allowing us to expand a polynomial raised to an arbitrary power including all cross terms and no redundant terms. For the weighting factors calculation, the approach in [32] calculates simultaneously all weighting factors available for each surrogate model order.…”

“…For the surrogate model formulation, [32] implements the Nth order surrogate model by using an element-wise power operator, which creates some redundant terms, while our new formulation exploits the multinomial theorem, allowing us to expand a polynomial raised to an arbitrary power including all cross terms and no redundant terms. For the weighting factors calculation, the approach in [32] calculates simultaneously all weighting factors available for each surrogate model order. In contrast, the proposed approach in this work automatically calculates the weighting factors by assuming that lower-order surrogates are fixed or by calculating all weighting factors simultaneously, and the selection between both manners is based on the conditional number of the system matrix.…”

“…In contrast, the proposed approach in this work automatically calculates the weighting factors by assuming that lower-order surrogates are fixed or by calculating all weighting factors simultaneously, and the selection between both manners is based on the conditional number of the system matrix. Finally, the order of the surrogate model can be different for each simulated frequency point, while in [32] and [33] the same surrogate model order is used for all simulated frequency points.…”

Post-Silicon Receiver Equalization Metamodeling by Artificial Neural Networks

“…Additionally, the required time to evaluate and even to train any metamodel becomes, for practical purposes, insignificant as compared to the time required to collect the measurement data. On the other hand, it has been demonstrated [13], [14] that both ANN and polynomial functional surrogates perform better than SVM and Kriging surrogates in cases with a very limited amount of training data, while polynomial surrogates exhibit better performance than ANN only in cases with low-dimensionality and small regions of interest, Then, we propose a neural modeling approach to efficiently approximate the effects of a HSIO post-silicon receiver equalizer with a very reduced set of testing and training data, and possibly a large number of knobs. The resultant metamodel, obtained from the proposed inexpensive method, could later be used as a fast coarse model in a space mapping approach [7], [8] to find the optimal equalizer settings that maximize the actual HSIO performance.…”

Editorial for the special issue on advances in simulation‐driven modeling and optimization of microwave/RF circuits

“…In particular, application of space mapping methodology is considered in Rodrigues et al for automated design of microwave filters, whereas Hassan et al describe space mapping for low‐cost design centering of microwave circuits. In Rayas‐Sanchez et al, EM‐based optimization of microstrip and SIW interconnects is presented using low‐order polynomial surrogates. Application of adaptively adjusted design specification technique and sequential approximate optimization is considered in Bekasiewicz and Koziel in the context of design optimization of photonic directional couplers.…”