Exact analysis of class E tuned power amplifier at any Q and switch duty cycle

Previous analytical descriptions of a Class E high-efficiency switching-mode tuned power amplifier have been based on the assumption of an infinite
Q
or the minimum possible value of
Q
. This paper presents an exact analysis of the Class E amplifier at any
Q
and any switch duty cycle
D
, along with experimental results. The basic equations governing the amplifier operation are derived analytically using Laplace-transform techniques and assuming a constant current through the dc-fed choke. The following performance parameters are determined for optimum operation: the current and voltage waveforms, the peak collector current and collector-emitter voltage, the output power, the power-output capability, the load-network component values, and the spectrum of the output voltage. It is shown that all parameters of the amplifier are functions of
Q
. Therefore, the high-
Q
assumption used in previous analyses leads to considerable errors. For example, for
Q < 7
at
D = 0.5
, some errors are up to 60 percent. The results can be used for designing Class E stages at any
Q
and switch duty cycle
D
. The measured performance shows excellent agreement with the design calculations. The collector efficiency was over 96 percent at 2 MHz for all tested values of
Q
from 0.1 to 10.