Design of Planar Complex Impedance Transformers With the Modified Coupled Line

Complex impedance transformers with the modified coupled line are provided in this paper. With the modified coupled line as proposed, the electrical length of the impedance transformer would be smaller than a quarter wavelength. In addition, analytic equations for the design of complex impedance transformers are derived; optimal characteristic impedance and impedance transformation are also calculated for successful power transfer. Simulation and measurement have demonstrated transformation efficiency and the potential for application of the proposed structure to radio frequency and microwave circuits.