Broadband Impedance Matching

Abstract

This chapter examines in detail the common broadband impedance matching subcircuits, and detailed derivations of the design equations are provided. The discussion starts with an analysis of the Bode–Fano inequalities that impose restrictions on the gain and bandwidth of broadband impedance matching subcircuits. However, applying the Bode–Fano inequalities for designing and implementing practical real-world broadband impedance matching subcircuits is very difficult. To circumvent the fact that Bode–Fano inequalities arise from the frequency dependency of the reactances of both a capacitor and an inductor, two (Zobel transform, negative impedance converter) extremely efficient and powerful techniques to neutralize the reactive part of a complex impedance are examined in detail, and the design equations are derived. By neutralizing the reactive part of a complex impedance, the impedance is “converted” into a pure resistor, forcing the gain to remain constant over the entire operating frequency range. Even after the reactive part of a complex impedance is neutralized, the issue of unequal source and load resistors remains. To tackle that, the Norton subnetwork or transform scheme is examined in detail, and design equations are derived. The use of an ideal transformer as an impedance matching device, as well as a transmission line impedance transformer (Guanella and Ruthroff), is examined in detail, along with the real frequency impedance matching technique.