Bilinear Transformations Applied to the Tuning of the Output Network of a Transmitter

The literature on the proper tuning of the output network of a class-C power amplifier inductively coupled to a load is surprisingly meager and, in general, there seems to exist considerable confusion concerning the relation between the following three conditions: (a) Resonance of the secondary circuit (b) Maximum-minimum point of average plate current (c) Maximum coupled circuit efficiency. This state of affairs is probably due in large part to the complexity of mathematics involved in a straightforward analysis of the circuits involved. In this paper we have employed the powerful theory of bilinear transformations in a complex plane, for which circles are transformed into circles, to determine the actual value of the secondary capacitance for a maximum-minimum of average plate current and for maximum coupled circuit efficiency. The results of this investigation show that (b) and (c) differ widely from (a)-except for the case of a series load in the secondary circuit. Moreover, although (b) may differ considerably from (c), these two conditions are indistinguishable if the Q of the primary coil is large, and the coefficient of coupling is very small.