Optimization Algorithms for Designing a Two-Section Dual-Band Transformer

In this paper, we focus on designing an impedance transformer with two sections and capable of achieving matching at two arbitrary frequencies. Specifically, the problem is formulated as minimizing the reflection coefficient by finding the optimal value of characteristic impedance and line length for the two section transmission line under the constraints of limited value for characteristic impedance. Using Convex Optimization and Steepest Descend Algorithm, we successfully find the optimal parameters for the transmission line. Simulation result shows that this algorithm can achieve reflection coefficient lower than 0.001 at the transmission frequency in GSM system while still guaranteeing a promising bandwidth of 70.6MHz.