Design Optimization of the Exponentially Tapered Microstrip Impedance Matching Sections Using a Cost Effective 3-D-SONNET-based SVRM with the Particle Swarm Intelligence

Abstract

Non uniform transmission lines are extensively used as impedance-matching sections in microwave circuits. Non uniform transmission lines are widely examined in the literature with the pioneering works [1-3]. In this work, exponential tapered microstrip line are realized by the microstrip lines with the exponentially tapered widths and a robust design optimization procedure is put forward to match a complex load to a given another complex impedance within a bandwidth. In the first stage of the design procedure, a cost effective 3-D SONNET-based Support Vector Regression Machine (SVRM) model of the microstrip line is completed. The 3D EM-based SVRM microstrip model provides the accurate and fast characterization of the equivalent transmission line in terms of the characteristic impedance Z(0) and the dielectric constant epsilon(eff) within the continuous domain of the microstrip width W, substrate parameters (epsilon, h) and in the work the input variable domain is defined by {0.1 mm <= w <= 4.6 mm, 2 <= epsilon(r) <= 10, 0.1 mm <= h <= 2.2 mm, 2 GHz <= f <= 14 GHz} in an efficient manner. In the modeling process, the substantial reduction (up to 64%) is obtained utilizing sparseness of SVRM in the number of expensive fine discretization training data with the negligible loss in the predictive accuracy using the quasi-TEM microstrip synthesis formulas as the coarse model that allow to identify the regions of the design space requiring denser sampling. The impedance transformation of anexponential tapered microstrip transmission segment in the differential length Delta l with the variable Z(0)(x) and epsilon(r)(x) is formulated in the second stage. The total length of the transmission line f, the governing parameter a of the exponential variation and maximum value of the width are determined as output of the Particle Swarm Optimization (PSO). The objective of the PSO is to minimize the magnitude of the difference between the desired and input impedances over a defined bandwidth. In the final stage of the work, a worked example is presented which is design of input matching network of a low-noise amplifier using the exponential tapered microstrip line.