Radio Frequency Integrated Circuit Design - Webs

Figure 10.24 Class E waveforms.
Power Amplifiers
The fundamental frequency component of vC (� )isv 1(� ). This is applied
to R + jX to determine output current, voltage, and power. Here jX is the
residual impedance of the series combination of L o and C o , which are tuned
to be slightly away from resonance at f 0.
For lossless components (as in the assumptions), the only loss is due to
the discharge of C when the switch turns on. If the components are selected
so that vC just reaches zero as the switch turns on, no energy is lost and the
efficiency is 100%. In practice, because the assumptions do not strictly hold
and because components will not be ideal, the voltage will not be at zero and
so energy will be lost. However, with careful design, efficiencies in the 80%
range are feasible.
10.7.2 Class E Equations
It is necessary to choose B and X for the correct resonance to make sure vC = 0
as the switch turns on, and to make sure that d [vC (� )]/d� = 0 so that there
is no current flowing into the capacitor.
Setting vC (� ) and d[v C (� )]/d� to0at� = �/2 + y results in
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