Inductive Coupled Transfer Functions for Four Major Topologies, and their Relevant Design Equations

The four major topologies for inductive couplers (such as transformers with air gaps used for wireless power transfer), are discussed in many articles widely available. In this article all the relevant transfer functions and design equations for all four topologies are given and derived. It contains Bode plots showing gain and phase characteristics against frequency with different load resistances, demonstrating clearly that each topology has its own specific characteristics so that the best one for a particular application can be selected. The author used the Laplace s-parameter in all derivations, and only convert later to the frequency domain when required. The concept of reflected impedances due to the transformer in all the designs is used, because it simplifies the derivations significantly, though care must be taken to apply it correctly. Therefore, the basic der-ivation of reflected impedances is also given. A novel set of formulas is derived for calculating the capacitance of the capacitor on the secondary side of the transformer. It is demonstrated to give satisfactory results even though the resultant formulas are relatively simple