Design of Nonuniform Transmission Line Impedance Transformers Using Convex Optimization

The design of nonuniform transmission line impedance transformers is demonstrated by applying a convex optimization method. A constrained convex semidefinite relaxation problem is defined by minimizing the input reflection coefficient magnitude squared at a number of frequency values. Additional constraints on the minimum and maximum transmission line impedance values along the length of the line are imposed. The optimization process is demonstrated for real and complex loads. Such impedance transformers find broad applications in broadband impedance matching and balun design for antenna and amplifier circuits or rectifier circuits, for example in energy harvesting and wireless power transmission applications.