Radio Frequency Integrated Circuit Design - Webs

370 Radio Frequency Integrated Circuit Design
added capacitor C A . Thus, it is possible to obtain close to 100% efficiency
even in the presence of parasitics.
10.7.1 Analysis of Class E Amplifier
Several simplifying assumptions are typically made in the analysis [4]:
1. The radio frequency choke (RFC) is large, with the result that only dc
current I dc flows through it.
2. The Q of the output circuit consisting of L o and C o is high enough
so that the output current io and output voltage vo consist of only the
fundamental component. That is, all harmonics are removed by this
filter.
3. The transistor Q 1 behaves as a perfect switch. When it is on, the
collector voltage is zero, and when it is off the collector current is zero.
4. The transistor output capacitance co , and hence C, is independent of
voltage.
With the above approximations, the circuit can now be analyzed. Waveforms
are shown in Figure 10.24. When the switch is on, the collector voltage
is zero, and therefore the current iC through the capacitor C is zero. In this
case, the switch current is = I dc − i o . When the switch is off, i s = 0. In this
case, iC = I dc − io . This produces an increase of collector voltage vC due to
the charging of C. Due to resonance, this voltage will rise and then decrease
again. To complete the cycle, as the switch turns on again, C is discharged and
collector voltage goes back to zero again. If the component values are selected
correctly, then the collector voltage will reach zero just at the instant the switch
is closed, and as a result, there is no power dissipated in the transistor.
We cannot explicitly solve for voltage and current waveforms over the
entire cycle. We can, however, determine the collector voltage waveform when
the switch is off:
vC (� ) =� I dc �
B � y − 2� + Vom BR sin (� − y) + I dc
B � + Vom BR
cos (� + �)�
(10.21)
where I dc is the dc input current, I om is the magnitude of the output current
io , Vom is the magnitude of the output voltage and is given by the product of
Iom and R, � is the phase of v o measured from the time the switch opens, 2y
is the switch-off time in radians (e.g., y = �/2 for 50% duty cycle), and B is
the admittance of the capacitance C.