Complex Impedance Transformation using Symmetric Coupled Microstrip Lines of Adjusted Electrical Lengths

This paper describes a systematic design method for complex impedance transformation using a single pair of symmetric coupled microstrip lines of suitably selected electrical length. Unlike the single line transformer, there are no forbidden regions in the Smith chart for this transformer and any complex/real impedance could be theoretically transformed into a complex/real impedance. The regions in the smith chart where average of the even and odd mode electrical lengths of the coupled lines is less than or greater than 90° have been derived. The coupled microstrip line transformer has a low profile as no cascading of line sections or shunt stubs are required for matching and both the coupled and through ports of the transformer are left open circuited. Therefore, this is an attractive solution for complex impedance transformation in microwave circuits where there are space constraints. Firstly, a number of coupled line transformers were designed at 2 GHz and simulated to validate the proposed methodology and secondly, three (12 + j31.5 Ω to 21 + j30 Ω, 33.2 + j10 Ω to 50 Ω and 27 + j50 Ω to 50 Ω ) such impedance transformers were fabricated for experimental validation of the method. The simulation results and measurements are in excellent agreement with high return losses at the design frequency.