A Generalized Approach for Multifrequency Transmission Line Transformer With Frequency-Dependent Complex Source and Load

In this paper, a generalized approach to design a multifrequency transformer with frequency-dependent complex source and load is proposed. By introducing an equivalent transformation between the perfectly matched complex-to-complex (a complex source impedance transformed to another complex load impedance) and unmatched real-to-real transformers (a real source impedance transformed to another real load impedance), the modified small reflection theory once limited to the design of the real-to-real transformer is further extended to that of the complex-to-complex transformer with more than two operating bands. Moreover, it is very useful to the design of multifrequency cascaded power amplifiers or low-noise amplifiers with compact size since its forward-stage output can be directly matched to the next-stage input. To validate the presented method, several multifrequency transformers are designed, simulated, and measured. Good agreement among the calculated, simulated, and measured results is achieved.