historyFclass

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History of
Class-F and Inverse
Class-F Techniques
©istockphoto.com/gzaleckas
Andrei Grebennikov
and Frederick H. Raab
T
oday, class-F amplification is a well-established technique for increasing the efficiency of RF power amplifiers (PAs). The increase in efficiency afforded by class
F reduces power consumption and increases talk time,
both of which are driving forces in the design of RF
PAs. The operational efficiency of radio transmitters was of great
interest right at the dawn of the development of high-power radiotransmission systems. Many if not most readers will be surprised
to learn that the basic concepts of class-F amplification were
Andrei Grebennikov ([email protected]) is with Sumitomo Electric Europe Ltd., Elstree, Hertfordshire, United Kingdom.
Frederick H. Raab ([email protected]) is with Green Mountain Radio Research Company, Boone, Iowa.
Digital Object Identifier 10.1109/MMM.2018.2862838
Date of publication: 12 October 2018
November/December 2018
1527-3342/18©2018IEEE
99
“Those who cannot remember the past are condemned
to repeat it.”
This article endeavors to trace the history of the
class-F (and inverse class-F) RF PAs from their origins
in the 1910s to the early days of the solid-state era in the
1950s and then up to the beginning of the 1980s. It is
organized by decades, and all figures are taken directly
from the best available copies of the corresponding
papers. This shows the presentation style of that time
period and demonstrates retrospectively how the new
technology was visualized.
+VDD
Idc
RF Circuit
Z1 = R
Ze = 0 or ∞
Zo = ∞ or 0
FL1
iD
Drive
Q1
io
+
+
vD
vo
–
–
R
Class F
Figure 1. A generic single-ended RF PA.
discovered at the end of the 1910s, just a few years after
the first vacuum tube transmitters were developed.
We have often seen new amplifier techniques
using transistors that are actually resurrections of
long-forgotten techniques using vacuum tubes. Sometimes, those who originally pioneered the techniques
have been overlooked, especially if the development
occurred almost a century ago. In many cases, it is
difficult to access old and obscure periodicals written
in a variety of different languages, leaving the techniques unknown to most readers. It is both interesting
and useful to know how, where, and when these techniques first appeared. Many readers will be familiar
with the quotation by philosopher George Santayana:
A generic circuit for a single-ended RF PA is depicted
in Figure 1, and waveforms for both class-A and classF operations are shown in Figure 2. In ideal class-A
operation, no harmonics are present, and the drainvoltage and drain-current waveforms are raised sinusoids of opposite phases. The drain voltage is high
while the drain current is low and vice versa. However, both are nonzero almost all of the time, resulting
in significant power dissipation and a maximum dcto-RF conversion efficiency of 50%. The power-output
capability is 0.125 times the product of the peak voltage
and peak current.
Class-F amplification improves efficiency and
increases the power output by using harmonics to
shape the drain voltage and current waveforms [1],
[2]. The addition of a third harmonic to the drain voltage shapes the voltage into the first approximation
of a square wave; the addition of a second harmonic
to the drain current shapes the current into a first
3
4
n = 1 (Class A)
m = 1 (Class A)
3
iD
vD
2
1
2
1
0
0
3
4
n = 3 (Class F)
m = 2 (Class F)
3
iD
vD
2
1
2
1
0
0
3
4
n = ∞ (Class F)
iD
1
m = ∞ (Class F)
3
vD
2
vDD = 1 V
2
1
0
idc = 1 A
0
0
π
2π
0
π
2π
Figure 2. The waveforms in class-A and class-F PAs.
100
November/December 2018
November/December 2018
Ia
Anode
Grid
Increasing
Va
Cathode
O
–Vg
(a)
(b)
Ia
Temperature Saturation
Vg
Increasingly
Positive
=0
The development of the thermionic vacuum tube revolutionized radio, changing it from a mechanical technology to an electronic technology [3]. Edison discovered
that an additional element inserted into a light bulb
could allow it to rectify. The Fleming valve exploited
the Edison effect to make a detector. The de Forest
audion added a third element (a grid) that controlled
the current flow. Armstrong then discovered how
to properly use the audion for oscillation, high-gain
amplification, and detection.
It is interesting to note that in 1911 Lee de Forest built
a first vacuum tube amplifier based on three audions
after filing his patent for an oscillation detector based
on a three-electrode device representing a vacuum
tube called an audion in January 1907. He managed to
do this with his pioneering innovation by inserting
a third electrode (grid) in between the cathode (filament) and the anode (plate) of the previously invented
diode [4]. Reviewing his earlier arc-transmitter efforts,
he wrote in his autobiography that he had been “totally
unaware of the fact that in the little audion tube, which
I was then using only as a radio detector, lay dormant
the principle of oscillation which, had I but realized it,
would have caused me to unceremoniously dump into
the ash can all of the fine arc mechanisms which I had
ever constructed, a procedure which a few years later
actually took place all over the world” [5].
The original audion was capable of slightly amplifying received signals, but at this stage could not be used
for more advanced applications, such as radio transmitters. Beginning in 1912, various researchers discovered that, properly constructed according to scientific
and engineering principles, vacuum tubes could be
employed in electrical circuits that made radio receivers and amplifiers thousands of times more powerful
and could also be used to make compact and efficient
radio transmitters; this, for the first time, made radio
broadcasting practical.
In 1914, the first vacuum tube radio transmitters
began to appear, representing a key technical development that then resulted in the introduction of
widespread broadcasting. Both amateurs and commercial firms started to experiment with the new vacuum tube transmitters, employing them for a variety
of purposes.
The schematic symbol for a three-electrode vacuum
tube (triode) is shown in Figure 3(a). Its basic operating principles are very close to the three-electrode
solid-state device called a transistor invented later.
Figure 3(b) demonstrates the transfer characteristic of
the vacuum tube when the anode current I a increases
with increasing grid voltage V g, whereas Figure 3(c)
demonstrates the output characteristics of the vacuum
tube (anode current I a versus anode voltage Va) for
different grid voltage V g .
The amount of current that flows between the plates
to the cathode is controlled by the voltage applied to
g
Vacuum Tubes
Today, class-F amplification is a wellestablished technique for increasing
the efficiency of RF power amplifiers.
V
approximation of a half sine wave. As a result, the efficiency of an ideal amplifier is increased to 81.65%, and
the power-output capability is increased to 0.1443 times
the peak voltage-current product.
Harmonics are added to the voltage waveform
by configuring the output filter to produce an open
circuit at the harmonic frequency. Similarly, harmonics are added to the current waveform by providing
short circuits. The roles of voltage and current can be
reversed to produce inverse class-F operation. The
efficiency and output capability increase with the
number of harmonics. As the number of harmonics
is increased toward infinity, the voltage waveform
approaches a square wave, and the current waveform
approaches a half sine wave. In this case, current
flows only when the voltage is (ideally) zero, resulting
in an efficiency of 100%. The power-output capability is increased to 0.159 times the product of the peak
voltage and current.
O
(c)
Vg
Increasingly
Negative
Va
Figure 3. A vacuum tube and its electrical characteristics.
(a) The schematic symbol for a three-electrode vacuum
tube, (b) the transfer characteristic, and (c) the output
characteristics of the vacuum tube.
101
0.5
1
1.5
(a)
the grid. Electrons are made mobile by a heater, which
can serve as the cathode or be separate. The anode
(plate), grid, and cathode are thus analogous to the
drain, gate, and source of a field-effect transistor (FET)
or to the collector, base, and emitter of a bipolar transistor. The reader can, in fact, think of the vacuum tube
as a junction FET with a heater that operates at significantly higher voltages (hundreds of volts) and significantly lower currents (hundreds of milliamps). The
high-impedance nature of vacuum tubes allowed their
circuits to be more spread out than the corresponding
circuits of transistor amplifiers.
2
(b)
Late 1910s–1920s
(c)
Figure 4. The waveforms and multiresonant load
networks [7]. (a) The meander-like form of an anode
current or voltage waveform; the load network (b) designed
as a ladder-type high-pass circuit and (c) with multiple
resonators, each tuned to the corresponding harmonic.
R
C
L1
L2
–
B
+
(a)
I
II
JS
I
EA
JA
VA
II
VR
PV
0
0
0
0.5
1
Period
(b)
1.5
2
Figure 5. The single-resonant vacuum tube oscillator
and anode waveforms [8]. (a) The circuit schematic and
(b) significant power loss as a result of both the sinu­soidal
voltage and sinusoidal current appearing at the anode of the
vacuum tube.
102
One commercial company that played a significant
role in the development of high-efficiency radio transmitters was Telefunken (initially Gesellschaft für
Drahtlose Telegraphie) in Germany, where the first
vacuum tube transmitters of small power up to 15 W
were built at the beginning of 1915. To provide high
transmitter operating efficiency, the special waveform
should be produced on the anode of the vacuum tube
(proposed by Hans Rukop); as an alternative, an auxiliary voltage of triple frequency should be impressed
on the grid (proposed by Alexander Meissner) [6]. In
both cases, the tube losses are greatly reduced because, during the tube’s operation, the time required
to apply the highest voltages to the tube is reduced;
furthermore, because at the time when the highest
voltages are applied to the tube, the passage of current is prevented.
The possibility for maximizing efficiency was first
demonstrated by a suitable choice of grid voltage with
a corresponding anode arrangement to produce an
anode current or voltage waveform, composed principally of the fundamental frequency and the third
harmonic and having a meander-like form, as shown
in Figure 4(a) [7]. The third harmonic is added to the
fundamental-frequency component, and both amplitudes are correctly dimensioned by suitable values of
high resistances. As a result, such a combining of the
fundamental and third-harmonic components, being
180° out of phase at the center point, results in a flattened voltage or current waveform with depression in
its center. This means that the power loss on the device
is partly compensated for by the reactive power the
harmonic resonator provides.
What is shown for the fundamental frequency and
the third harmonic is equally valid for the other harmonics. The load network can be designed as a laddertype high-pass circuit [Figure 4(b)], or with multiple
resonators, each tuned to the corresponding harmonic
[Figure 4(c)]. It was concluded that the power loss must
be zero and the efficiency equal to 100% if either the
tube current or voltage is always zero with meandertype shapes. Producing such curves involves employing resonators in the anode circuit to include not only
November/December 2018
the fundamental frequency but also a considerable
number of higher-order harmonic components. The
shapes of the anode voltage and current waveforms
can be significantly flattened with increasing fundamental voltage amplitude by adding even one additional harmonic component that is properly phased.
Figure 5(a) shows the circuit schematic of a singleresonant vacuum tube oscillator, where inductive feedback coupling is provided to the resonant circuit tuned
to the fundamental frequency. In this case, both sinusoidal voltage V A and sinusoidal current J A appear at
the anode of the vacuum tube, resulting in a significant
power loss [Figure 5(b)], where the power loss PV is calculated as an integral of the product of anode current
and anode voltage over period [8].
However, the power loss can be substantially reduced
for the multiple-resonator circuit in the vacuum tube
oscillator with multiple inductive feedback couplings
and resonant circuits tuned to the fundamental, third,
VII
V
III
The development of the thermionic
vacuum tube revolutionized radio,
changing it from a mechanical
technology to an electronic
technology.
fifth, and seventh harmonics, as shown in Figure 6(a),
to provide the meander-type voltage waveforms simultaneously, both at the anode and at the grid of the tube
[8]. As a result, the anode voltage and anode current
will represent both meander-type waveforms [Figure 6(b)], thus minimizing overlapping between each
other and the resulting power loss.
Independently, it was suggested by Henry Round,
based on his experiments with a variety of different
aspects of radio transmitter technology at Marconi and
RCA, to use a square-voltage-driving waveform and
an additional resonator tuned to the fifth harmonic
for efficiency improvement of vacuum tube amplifiers
(Figure 7) [9]. Consequently, the basic theoretical background and potential circuit solutions to increase efficiency of vacuum tube amplifiers and oscillators were
generally understood almost 100 years ago.
Figure 8 shows the push–pull configuration of the
vacuum tube amplifying circuit, where two tubes
I
B
–
H. J. ROUND
Wireless Telegraph and Telephone Transmission
Filed 31 March 1920
+
(a)
F
F3
F5
I
II
JS
I
EA
JA
VA
II
Figure 7. A schematic of a vacuum tube amplifier with
harmonic traps [9].
VR
PV
0
0
–
0
0.5
1
1.5
+
2
Period
(b)
Figure 6. The multiple-resonant vacuum tube oscillator
and anode waveforms [8]. (a) The circuit schematic and
(b) the substantially reduced power loss and the anode
voltage and anode current representing both meander-type
waveforms.
November/December 2018
Figure 8. A push–pull vacuum tube amplifier with
harmonic traps [10].
103
+
Radio
Choke
Harmonic
Trap
Fundamental
Oscillating
Circuit
(a)
Figure 9. A schematic of a vacuum tube oscillator with a
harmonic trap [11].
Uma2
Ea
ωt
Uma1
(a)
(b)
Figure 10. The anode voltage waveform and modulation
characteristics [14]. (a) The provided symmetrical anode
voltage waveform and minimum level of its depression for
a biharmonic mode. (b) The modulation properties of a
vacuum tube amplifier.
are coupled back to back and each grid is periodically and alternatively made positive by applying a
rectangular wave to the grid of each vacuum tube
[10]. The harmonic resonant circuits connected to the
common anode circuit are tuned to the third, fifth,
and seventh harmonics and have as low a decrement
as possible.
Figure 9 depicts a type of load network with a harmonic trap that was discussed and first published in
1923 as a journal paper on the topic of vacuum tube
oscillators [11]. In this case, the third or fifth harmonic can be added to the fundamental-frequency
component with proper amplitude and phase so that
the resulting waveform has a flattened peak [12]. To
further approximate the rectangular waveform, both
third- and fifth-harmonic traps can be introduced in
104
(b)
Figure 11. A vacuum tube amplifier with second-harmonic
control and an anode voltage waveform [15]. (a) The
circuit schematic with the parallel resonant circuit tuned
to the second harmonic and located in series to the anode
and (b) the anode voltage waveform resulting from the
corresponding combination of the fundamental frequency
and second harmonic.
series into the anode circuit of vacuum tube oscillators
to approximate the rectangular voltage waveform [13].
1930s–1940s
During the 1930s, some Russian papers were published
stating an efficiency improvement of 25–30% in broadcasting radio transmitters by using a biharmonic mode
for vacuum tube amplifiers [14]–[16]. It was shown that
the symmetrical anode voltage waveform and minimum level of its depression for a biharmonic mode
[Figure 10(a)], can be provided with opposite phase conditions between the fundamental frequency and third
harmonic and an optimum value of the ratio between
their voltage amplitudes [14]. It was also noted that high
efficiency can be achieved, even when the impedance
of the third-harmonic resonator is equal to or slightly
greater than the impedance of the fundamental tank
circuit. Such an approach could slightly improve the
modulation properties of a vacuum tube amplifier using
either grid or anode modulation techniques because
saturation at the fundamental frequency as a part of the
November/December 2018
flattened anode voltage waveform occurs later than that
for the sinusoidal anode voltage [Figure 10(b)] [14].
The effect of including the parallel resonant circuit
tuned to the second harmonic (n = 2) and located in
series to the anode [Figure 11(a)], was first described
and analyzed in the very early 1940s [15], [16]. It was
shown that the symmetrical anode current waveform and level of its depression can be provided with
the opposite phase conditions bet ween the fundamental frequency and second-harmonic components (i 2 100c for anode current) and an optimum
value of the ratio between their amplitudes. It was
also noted that high efficiency can be achieved, even
when the impedance of the parallel circuit to the second harmonic is equal to or slightly greater than the
impedance of the tank circuit to the fundamental frequency. In addition, such an approach could improve
the modulation properties of vacuum tube amplifiers when the phase of the second voltage harmonic
becomes negative compared to that of the fundamental frequency [15]. Figure 11(b) portrays the anode
voltage waveform resulting from the corresponding
combination of the fundamental frequency and second harmonic.
To i ncrease the eff iciency of t he bi harmon ic
vacuum tube amplifier, a biharmonic driving signal consisting of the fundamental frequency and
second-harmonic component was introduced. The
simple solution to realize 180° out-of-phase conditions between the voltage fundamental frequency and
second-harmonic components at the device output is
to use a second-harmonic tank resonator connected in
series to the device input [Figure 12(a)] [15]. Such an
approach flattens the anode current waveform in the
active region, avoiding the device saturation mode.
Due to the diode-type input of the vacuum tube, the
resulting grid current pulse will contain a strong
second-harmonic component, resulting in a secondharmonic voltage component across the input resonator. The loaded quality factor of the second-harmonic
resonator must be high enough to neglect the voltage
drop at the fundamental frequency. As a result, the
second-harmonic resonator has no effect on the fundamental frequency voltage component. However, it
provides a phase shift of 180° for the second harmonic,
because an increase in the voltage drop across the resonator results in a decrease of the voltage drop across
the grid–cathode terminals.
Figure 12(b) shows the combination of the fundamental frequency and second-harmonic components
shifted by 180° [15]. In this case, the grid voltage waveform is characterized by its top flattening when the
second harmonic has its minimum value at the maximum point of the fundamental frequency component.
Choosing the grid bias point that is equal to the device
pinchoff voltage (the selection of which corresponds
to class-B mode with the conduction angle of 180° for
November/December 2018
During the 1930s, some Russian
papers were published stating an
efficiency improvement of 25–30%
in broadcasting radio transmitters by
using a biharmonic mode for vacuum
tube amplifiers.
2ω
2ω
ω
(a)
ωt
(b)
ia
ωt
θ
(c)
Figure 12. A vacuum tube amplifier with secondharmonic resonators in its anode and grid circuits and
waveforms [15]. (a) The circuit schematic with a secondharmonic tank resonator connected in series to the device
input; (b) the combination of the funda­mental frequency
and second-harmonic components shifted by 180°; and (c)
the anode biharmonic current pulses.
105
At very high frequencies, a series of
parallel-tuned harmonic traps can
be replaced by a series quarter-wave
transmission line.
sine-wave operation) will result in anode biharmonic
current pulses with i 2 90c [Figure 12(c)]. At the same
time, using a second-harmonic resonator in the load
network contributes to the anode voltage waveform
[Figure 11(b)]. For the practical circuit of a vacuum tube
amplifier with second-harmonic resonators in the grid
and anode circuits, an output power of 446.5 W was
achieved with an anode efficiency of 85%.
Figure 13 shows the final-stage schematic of a
push–pull vacuum tube amplifier with second-harmonic resonators in each amplifying path [16]. In this
case, to eliminate the phase shifts at the fundamental
that affect the linearity under modulation, the inductive paths in the second-harmonic resonators are
tuned to the series resonances at the fundamental. In
this case, to achieve series resonance at the fundamental and parallel resonance at the second harmonic, the
value of the capacitor connected in series to the inductance should be greater by three times that of the parallel capacitor.
2ω
ω
2ω
Figure 13. A push–pull vacuum tube amplifier with a
second-harmonic control [16].
+
f
Output
– +
Figure 14. A schematic for third-harmonic voltage
injection into an anode circuit [17].
f2
– +
Ec
+
Auxiliary
Tube
f1
M
f2
Main Tube
3f
Auxiliary
Tube
f1
Output
Main Tube
Input
To
Exciter
Main
Tube
106
Comprehensive research presented in [17] confirmed that the second- or third-harmonic voltage
introduced into the anode and grid circuits in the
proper phase can improve vacuum tube performance.
Fourth- and higher-order harmonics were, at best, of a
little value in improving the operation efficiency. The
proper phasing can be accomplished by various means
(including an auxiliary tube), and the power output
and overall efficiency of the main tube acting as a
class-C PA are increased. Proper phasing can be easily
obtained by introducing the third-harmonic voltage
180° out of phase with the fundamental voltage into
the anode circuit, as shown in Figure 14.
However, while this circuit arrangement can generate the third harmonic in the correct phase with respect
to the fundamental for efficient operation, it will not
work for the second harmonic. A reversal in the fundamental voltage as fed to the auxiliary tube will reverse
the phase of the third harmonic in the anode circuit
but not the phase of the second harmonic. Figure 15
shows the circuit with two main amplifiers and one
auxiliary amplifier that will work efficiently for the
second harmonic but not the third. When the third
harmonic is adjusted in phase to give the most favorable path for one of the main tubes, it will be in the
wrong phase for the other. For the second harmonic,
however, this is not the case, and the main tubes mutually benefit each other.
In view of the parasitic anode–cathode capacitance
comprising the interelectrode, case capacitances, and
series plate inductance, the entire anode circuit should
be tuned to the third harmonic, not only a single resonator. Such an anode circuit may include a parallel
third-harmonic resonator (is slightly mistuned in this
case, e.g.) and an additional series LC circuit connected
in parallel to the tube (Figure 16), which has capacitive
reactance at the fundamental frequency and inductive
reactance at the third harmonic; this is tuned to the
resonance with other elements in the anode circuit [18].
The parallel resonators tuned to the third- and fifthharmonic components can be replaced by a low-pass
filter with three sections (see Figure 17), the elements
–
+
+
Figure 15. A schematic for second-harmonic voltage
injection into an anode circuit [17].
November/December 2018
+
+
+
–
+
–
Figure 16. A biharmonic vacuum tube push–pull
amplifier [18].
of which are designed to pass the third and fifth harmonics of the fundamental frequency, terminating in a
parallel resonant circuit tuned to the fundamental [19].
November/December 2018
+
Figure 17. The load network with third- and fifthharmonic control [19].
δ
k
3ω
1950s–1960s
Figure 18(a) shows the first implementation of the
bipolar-transistor biharmonic PA with an additional
resonant tank in the load network tuned to the third
harmonic [20]. Because the third-harmonic current
coefficient r3 (i) is positive for the half-conduction
angle i 1 90c, the PA was operated in a slightly saturated mode to obtain r3 (i) 1 0. Due to device inertia
at high frequencies when the collector current pulse
increases, higher efficiency can be achieved by reducing i, which can be easily provided by the emitter
resistor–capacitor circuit. As a result, an output power
of about 300 mW with a collector efficiency of 88% was
achieved at the operating frequency of 106 kHz.
Figure 18(b) shows the biharmonic bipolar-transistor PA with an additional resonant tank in the load
network tuned to the second harmonic: a collector efficiency of 92% and an output power of about 400 mW
were achieved at an operating frequency of 106 kHz
[21]. The required phase shift between the fundamental and second voltage harmonics at the collector was
obtained due to the device inertia provided by its
input capacitance and operation in a slightly saturated
mode. However, in this case, the collector voltage peak
factor is higher compared to that for a PA with the thirdharmonic resonator.
An additional resonator tuned to the fourth harmonic can be connected in series with the second-harmonic resonator [Figure 19(a)] to maximize the anode
efficiency of the vacuum tube amplifier exhibiting an
anode voltage waveform with substantially flat valleys
–
δ
2ω
k
ω
ω
mA
mA
B
B
((a))
(b)
Figure 18. The basic circuits of a bipolar-transistor
amplifier with a third-harmonic resonator [20] and secondharmonic resonator [21]. (a) The first implementation of
the bipolar-transistor biharmonic PA with an additional
resonant tank in the load network tuned to the third
harmonic and (b) the biharmonic bipolar-transistor PA
with an additional resonant tank in the load network tuned
to the second harmonic.
corresponding in time to the substantially flat peaks of
the anode current waveform with rectangular driving
and sinusoidal load currents [Figure 19(b)] [22], [23].
An infinite number of even-harmonic resonators can
maintain a half-sinusoidal anode voltage waveform,
whereas odd-harmonic resonators can maintain a rectangular anode current waveform.
At lower frequencies, aperiodic drive a­ mplifiers
can be designed, providing good approximations of
ideal rectangular waveforms. However, at higher
frequencies, tuned drive amplifiers become necessary
to provide a one- or two-harmonic complex grid or
base waveforms with suitable bias arrangements.
107
At lower frequencies, aperiodic drive
amplifiers can be designed, providing
good approximations of ideal
rectangular waveforms.
Impedance matching without waveform distortion
is possible by using complex tank circuits, which are
electrical equivalents of the series arrangements of
harmonic resonators. The required arrangement of
poles and zeroes in a two-terminal reactive network
can be realized either by series arrangements of parallel resonators and reactances or by parallel arrangements of series resonators and reactances [Figure 20(a)]
[22]. In this case, the parallel-capacitor complex tank
has two advantages.
At very high frequencies, the shunt capacitor may
largely (or entirely) represent the internal tube capacitance and can be split to give voltage division, and
hence impedance matching, between the anode and
the load. A typical application of a complex tank is
shown in Figure 20(b) [22]. Here, the ratio between C 1
and C 2 determines the degree of impedance transformation. The tap in the split capacitor is grounded so
that the anode voltage is antiphase with the output.
This makes it possible to neutralize the driven stage
with a very small capacitor C n connected between the
two anodes.
To obtain high efficiency in a class-C operation
using the third-harmonic resonator in the anode circuit, it is convenient to provide a grid-driving waveform of an approximately 120°-wide pulse [24]. The
voltage waveform that appears on the anode (or collector, in the case of bipolar transistors) is a mixture of the
V.J. Tyler
A New High-Efficiency, High-Power
Amplifier
4f
2f
(a)
Load
f
f and 3f C
n
(a)
C1
3f
C2
AV
f
Load
(b)
AC
Figure 20. Two-terminal reactive tank networks and
a typical application of a reactive tank [22]. (a) Twoterminal reactive networks and (b) a typical application of
a complex tank.
OV
(b)
Figure 19. The load network with second- and fourthharmonic control and corresponding current and voltage
waveforms [22], [23]. (a) The vacuum tube amplifier with
an additional resonator tuned to the fourth har­monic
connected in series with the second-har­monic resonator
and (b) an anode voltage waveform with substantially flat
valleys corresponding in time to the substantially flat peaks
of the anode current waveform with rectangular driving
and sinusoidal load currents.
108
L1
3F
c1
L2
3F
c2
F
+E
F
–Eg
Figure 21. A vacuum tube amplifier with third-harmonic
resonators in the anode and cathode circuits [25].
November/December 2018
November/December 2018
Ls
Load
Cs
λ /6
λ /4
(a)
λ /4
Ls
L
Cs
C
Load
λ /4
(b)
Figure 22. The simplified schematics of vacuum tube
amplifiers with third-harmonic and even-harmonic control
[22]. (a) The short-circuited quarter-wave line develops
high impedances at the fundamental and odd harmonics
simultaneously, and (b) the open-circuited inner line
produces poles at every even-harmonic frequency up to
the cutoff frequency.
Third-Harmonic
Resonators
L1
C3
L4
C2
C1
C4
L2
Fundamental
RF Output
Fundamental
RF Input
L3
(a) Basic Circuit
Arrangement for Class-D Operation
Fundamental Power
in Output Circuit
kW, Third-Harmonic Circuit
to Output Circuit
Power (kW)
fundamental frequency and third harmonic, with the
amplitude and phase relationships so arranged as to
result in an almost flat-topped wave. During the early
and late parts of the current pulse, energy is stored
in the third-harmonic tank circuit. However, during
the middle of the pulse, this energy is transferred to
the fundamental tank circuit. In the operation of such
an amplifying stage, the peak voltage across the fundamental tank circuit is approximately 1.2 times the
peak anode or collector voltage swing, whereas the
peak voltage across the third-harmonic tank circuit is
about 0.2 times the anode or collector voltage swing.
In practice, it was suggested that the grid or base can
be driven with a waveform composed of a mixture of
the fundamental frequency and third harmonic and
biased well beyond cutoff so that the current flows for
approximately 120° [24].
Figure 21 shows the simplified schematic of a highefficiency anode-modulated PA using a single tube
to deliver the nominal 5 kW at 90–92% power conversion [25]. Here, the circuit arrangement is very similar
to a conventional class-C PA except for the presence
of two third-harmonic resonators: L 1 C 1 in the anode
circuit and L 2 C 2 in the cathode circuit. This approach
provides a corrective means for maintaining a flat
waveform near peak. When the cathode resonator is
adjusted to resonate at the third harmonic, the instantaneous grid-to-cathode potential modifies the cathode
emission to approximate a rectangular pulse. However,
there is an alternative approach with the second-harmonic resonator in the cathode circuit that can provide
the flattened grid voltage waveform even without grid
currents to achieve high efficiency of about 85–88%
under optimum conditions [26].
At very high frequencies, it was suggested that the
transmission-line analog having the multiple-resonance characteristic be used instead of the lumpedconsta nt load net work [22]. The short-circuited
quarter-wave line shown in Figure 22(a) develops
high impedances at the fundamental and odd harmonics simultaneously if the line is terminated nonreactively at both ends. In this case, the stray anode
capacitance C s must be compensated for, e.g., by the
series inductance L s , so that their combination represents an artificial extension of the real line. This extension involves a finite upper cutoff frequency above
which clean resonances cannot be obtained, but this
is enough because the only harmonic pole required
for a third-harmonic amplifier is the third. The load
is connected to the inner conductor at a point that represents two-thirds of the electrical line length from
the short circuit: this point is a voltage node for the
third-harmonic resonance. The open-circuited inner
line shown in Figure 22(b) produces poles at every
even-harmonic frequency up to the cutoff frequency of
L s C s, and the short-circuited outer line, electrically in
series with the inner line, produces one significant
kVA, Valve to
Third-Harmonic Circuit
Valve Power Output
0°
60° 120° 180°
(b) Energy Transfer in Class-D Operation
Figure 23. A schematic of a vacuum tube amplifier
with third-harmonic resonators and its anode voltage
waveform [27]. (a) The circuit arrange­ment of the
vacuum tube amplifier where the third-harmonic
resonator is also a part of the input tuned circuit and
(b) the phase of the harmonic energy reversed and ­
trans­ferred into the fundamental angle.
109
Final Amplifier for 750-kW Medium-Frequency Transmitter
C19
X
L3
X Heater Supply
Three Phase
R4
C4
C7
R1
X
L4
L2
C1
R5
Tl
L9
C18
Wide-Band
Neutralizing
C5
L6
R10
C12
L7
C10
C8
RF Input
C3
from π C2
Circuit
Thirdof Driver
Harmonic
Stage
Resonator
CH1
LI
R7
C17
Tuned
Harmonic
Filters
C11
R2
R8
X
L5
R6
ThirdHarmonic
Resonator
C6
C9
RI1
CH2
R3
100-Ω
Output
Feeder
L8
C13C14
C15 C16
R9
Bias Supply
Screen Supply
Anode Supply
Figure 24. A simplified circuit diagram of a 750-kW RF PA for a medium-frequency broadcast transmitter [27].
C3
F3
C2
F1
C1
(a) Circuit for High-Efficiency Operation
Lead Inductance
Ls
C3
C2
C1
(b) Effective Output Circuit at Higher Frequencies
Figure 25. The load networks with third-harmonic control
[27]. (a) The load network of the bipo­lar-transistor PA with
a low-pass, two-section load network providing thirdharmonic control for high-efficiency operation and (b) the
flattened collector voltage waveform provided as a result of
the low operating impedance, stray series inductance, and
relatively small collector capacitance.
pole that is at the fundamental frequency. All other
poles are lossy and off-tuned relative to the harmonic
spectrum, because the cutoff frequency of LC is only
barely above the fundamental frequency.
110
Applying the biharmonic driving signal containing the fundamental and third-harmonic components
can be very efficient because of the flattened driving
waveform [22]. The detailed mathematical explanation
of the effect of the biharmonic driving signal consisting of the fundamental and third-harmonic components is given in [26]. Figure 23(a) shows the circuit
arrangement of the vacuum tube amplifier where the
third-harmonic resonator is also a part of the inputtuned circuit [27]. In this case, by the resonant action
of the third-harmonic resonator in the anode-tuned
circuit and from a fundamental angular position of
60–120°, the phase of the harmonic energy is reversed
and transferred into the fundamental [Figure 23(b)]. At
120°, the phase is again reversed, and, for the remainder of the conducting cycle, the third-harmonic circuit
again receives energy from the vacuum tube.
A simplified circuit diagram of the high-efficiency
750-kW RF PA designed for a medium-frequency
(525–1,625 kHz) broadcast transmitter is shown in
Figure 24 [27]. In this case, the type of tube used is
the vapor-cooled tetrode with a maximum anode dissipation of 180 kW. Because it would not be possible
to obtain 180 kW from one of these tubes operating in
class C without exceeding the permitted anode dissipation at 100% modulation, the simplest possibility
to provide a 750-kW rating with these tubes is to use
an amplifier circuit with third-harmonic resonators.
November/December 2018
Here, the RF drive is fed directly from the pi circuit of
the driving amplifier into the final-stage tuned-input
circuit, which includes a third-harmonic resonator
circuit L 2 C 1 C 2 . It then passes the three power tubes
via their individual antispurious circuits, L 3 R 1, L 4 R 2,
and L 5 R 3 . The tube anodes are directly paralleled
and feed the pi-type output circuit via the third-harmonic resonator circuit L 6 C 10 C 11 . The series capacitor C 17 in the anode circuit used for neutralization is
adjusted to give the correct feedback voltage to the
grids of the tubes via the wide-band phase reversal
transformer T1 (where the circuit L 9 R 10 is included
for antispurious purposes). The maximum RF drive
required for full output power is only 6 kW, which
was obtained from a single tetrode amplifier with
only 15 W of drive.
Figure 25(a) shows the load network of the bipolar-transistor PA with a low-pass, two-section load
network providing third-harmonic control for highefficiency operation [24]. When tuned correctly, the
resulting flattened collector waveform provides an
obvious improvement in efficiency compared with the
class-C waveform. With transistor amplifiers, as the
frequency increases, the need for the external thirdharmonic resonator diminishes because the flattened
collector voltage waveform is provided as a result of
the low operating impedance, stray series inductance
L s, and relatively small collector capacitance C 3, as
illustrated in Figure 25(b).
1970s–Early 1980s
At very high frequencies, including microwaves, a
series of parallel-tuned harmonic traps can be replaced
by a series quarter-wave transmission line [Figure 26(a)],
where the parallel-tuned output circuit provides a
short circuit to all harmonics, resulting in the squarewave voltage and half-wave rectified sine-wave current
+VDD
iDC
rf Choke
T1:R0
iD
L
C
RL
(a)
Ideal Drain
Voltage vD
FET
Off
2VDD
FET
On
VDD
t
0
(4/π)VDD
Load
Voltage
vL
t
0
–(4/π)VDD
2vLP/R
Drain
Current
iD
0
t
(b)
Figure 26. The load network with a series quarter-wave
line and output waveforms of a class-F amplifier [29]. (a)
A series of parallel-tuned harmonic traps replaced at very
high frequencies by a series quarter-wave transmission line
and (b) the parallel-tuned output circuit producing a short
circuit to all harmonics and resulting in a square-wave
voltage and half-wave rectified sine-wave current.
24
01
Signetics
SD–200
+16
vL
λ /4
vD
0
–16
+4
001
T1
T2
100
001
T3
Signetics
SD-200
–4
100 k
.01
.01
L2
C1
330
C2
T8
50
L1
+Vdd = 12 V
Figure 27. The circuit schematics of a high-efficiency class-F MOSFET RF PA with a series quarter-wave transmission
line [28].
November/December 2018
111
L7
R3
1 MEG
R4
100 k
C8
C5
L4
Line 1
Line 2
G2
C1
D
Secondary
R1
100
C6
Q1
L1
Primary
LA
G1
C7
S
C3
L5
R2
100 K
U1
C4
C2
C9
L2
L3
U2
L8
L6
Figure 28. A circuit schematic of a high-efficiency UHF dual GaAs FET oscillator with a quarter-wave transmission line
[32]. LA: lead and bonding wire inductance.
3
1
2
4
En
Figure 29. A circuit schematic of a high-efficiency class-F
bipolar PA with a shunt quarter-wave line [33].
shown in Figure 26(b) [28], [29]. The first prototype of
such a class-F PA using two metal–oxide–semiconductor FETs (MOSFETs) in parallel (Figure 27) produced
an output power of 300 mW with 73% efficiency at
25 MHz [28].
These types of multiply tuned RF PAs with oddharmonic control have been given different names,
such as biharmonic, polyharmonic, optimum-efficiency
112
class B, multiple-resonator class C, single-ended class D, or
even class E [28], [30]. However, all were assigned by
Raab to class F, which introduced the high-frequency
PA with a quarter-wave transmission line and paralleltuned output circuit immediately following the introduction of the class-E PA by Sokals in 1975 [31].
A high-efficiency oscillator circuit with a shorted
quarter-wave line to improve operating efficiency by
approximating the square drain-voltage waveform is
shown in Figure 28 [32]. Here, U1 is a phase shifter, U2
is a delay line, and the total length of coaxial line one
and microstrip line two constitutes the shorted quarterwave line. To minimize the reactive loading effects of
the device output capacitance and parasitic packaging
series inductance LA, the length of the quarter-wave
line was adjusted to 82.6° for optimum reactance cancellation at the ninth harmonic (3,600 MHz) to sustain
a square-voltage waveform at 400 MHz. The impedance matching of the 50-W load with the device output impedance at fundamental to provide the desired
output power can be conveniently done by tapping off
the required voltage from the shorted line through the
series resonant circuit C 7 L 5 to reject harmonics. In this
case, the position of the tap was chosen to be approximately one-eighth of the overall line length from the
shorted end, which is the length of line two.
November/December 2018
Matching Circuit
at Fundamental Frequency
FET 1
λ /4
Cb
FET 2
Output
Input
λ2
4
Matching Circuit at
Fundamental Frequency
+VCC
io
Zo
iC
Lo
vCE
Co
RL vo
Reactive Termination at
Even Harmonics
(a)
iC
Figure 30. A circuit schematic of a high-efficiency class-F
FET PA with an even-harmonic short [34].
0
π
–
2
λ /4
0
π
2
0
π
2
π
3π
2
ωt
3π
2
ωt
vCE
R
0
π
–
2
(a)
π
vo
π
–
2 0
ωo
2ωo
2
(b)
3π
2
0
π
2
π
ωt
(b)
Figure 31. The load network and impedances of a vacuum
tube amplifier with second-harmonic control [35]. (a) The
peak output power and anode efficiency increased with
second-har­monic control using a quarter-wave transmission
line connected between the two parallel resonant circuits. (b)
The short-circuited bottom part of the inductor connected
to the anode and the top part tuned to resonance with the
shunt capacitance at the second harmonic.
Figure 32. The load network with a series quarter-wave
line and output waveforms of an inverse class-F amplifier
[36]. (a) A circuit representation of an inverse class-F PA
with a series quarter-wave transmission line loaded by the
series-resonant cir­cuit tuned to the fundamental frequency.
(b) The ideal drain-current and voltage waveforms
represented by the corresponding normalized square and
half-sinu­soidal waveforms.
It is worth noting that Raab’s scheme of a class-F
mode with a series quarter-wave line published in Electronics [29] was translated into Russian and served as a
series motivation for modified approaches to provide
high efficiencies of bipolar PAs at very-high-frequency
and ultrahigh-frequency (UHF) bands. Figure 29 shows
the simplified circuit schematic of a bipolar class-F
PA with a shunt quarter-wave line, the load network
for which consists of the 1) RF choke, 2) quarter-wave
transmission line, 3) series LC resonant circuit tuned
to the fundamental, and 4) load [33]. The matching circuit can be included between the series LC resonant
circuit and the load if the equivalent device output
impedance at the fundamental differs from the 50-Ω
load. Otherwise, it behaves similarly to the class F
with series quarter-wave line and shunt LC resonant
circuit without impedance transformation. Based on
this approach and using high-Q elements in the load
network, high collector efficiencies of about 90% were
achieved at operating frequencies and output powers
up to 250 MHz and 10 W, respectively.
Figure 30 shows the circuit schematic of a highefficiency class-F two-stage gallium arsenide (GaAs)
FET PA having a total efficiency of 70% and an output
power of 2 W designed to operate at 900 MHz [34]. A
drain efficiency of 80% was achieved at a low supply
voltage of 6 V. These high efficiencies were obtained
using even-harmonic tuning of an output ­m atching
circuit. In this case, the harmonic impedance was
short at the even harmonics, and impedance at the
odd harmonics was not considered from the point of
view of obtaining maximum output power. The output circuit was designed under the assumption that
the parasitic device parameters can be represented as a
November/December 2018
113
This new concept of high-efficiency
PAs with even-harmonic control was
ultimately termed the inverse class F
at the end of the 1990s.
transmission line, and the GaAs FET consists of a current source and an equivalent transmission line at harmonic frequencies so that, when seen from the current
source, a short circuit is observed for even harmonics.
In Figure 30, the transmission line between FET2 and
the open-circuited m 2 /4 microstrip line, where m 2 /4
is the wavelength of the second-harmonic frequency,
is a compensation line for the equivalent transmission
line of the GaAs FET. The circuit between the output
terminal and the open-circuited m 2 /4 microstrip line
is a matching network that converts the FET output
impedance containing the reactive component to 50 Ω.
In practical vacuum tube amplifiers intended for
operation at very high frequencies and with high output
power, the peak output power and anode efficiency
can conveniently be increased with second-harmonic
control using a quarter-wave transmission line connected between the two parallel resonant circuits
[Figure 31(a)] [35]. At the second harmonic, the input
impedance of the quarter-wave line loaded by the parallel tank tuned to the fundamental is close to zero.
In this case, the bottom part of the inductor connected
to the anode becomes short-circuited, and the top part
of this inductor is tuned to resonance with the shunt
capacitance at the second harmonic [Figure 31(b)], to
create an open-circuit condition for the second harmonic at the anode. As a result, for a 2-kW vacuum
tube amplifier operating at 85 MHz, the efficiency and
peak output power were increased by 1.15–1.2 times,
with anode efficiency of about 90%.
An infinite set of even-harmonic parallel resonant
circuits connected in series can be effectively replaced
by a quarter-wave transmission line with the same
operating capability. A circuit representation of an
inverse class-F PA with a series quarter-wave transmission line loaded by the series-resonant circuit
tuned to the fundamental frequency [Figure 32(a)], was
introduced in 1984 as a new concept for the class-F PA
[36]. The series-tuned output circuit presents to the
transmission line a load resistance at the frequency
of operation. At the same time, the quarter-wave
transmission line transforms the load impedance. For
even harmonics, the open circuit on the load side of
the transmission line is repeated, thus producing an
open circuit at the drain. However, the quarter-wave
TABLE 1. A summary of class-F and inverse class-F circuit development.
Author
Contribution
Figure
Technology
Year
Reference
Rukop
Odd-harmonic resonator at anode
4, 6
Vacuum tube
1917
[7], [8]
Round
Odd-harmonic resonator at anode
7
Vacuum tube
1920
[9]
Robinson
Odd-harmonic resonator, push–pull mode
8
Vacuum tube
1923
[10]
Kolesnikov
Second-harmonic resonator at grid and anode
11, 12
Vacuum tube
1940
[15]
Second-harmonic resonator, push–pull
13
Vacuum tube
1941
[16]
Third-harmonic injection into anode
14
Vacuum tube
1943
[17]
Second-harmonic injection into anode
15
Vacuum tube
1943
[17]
Royden
Ladder-type load network
17
Vacuum tube
1945
[19]
Berman
Third-harmonic resonator at collector
18(a)
Bipolar transistor
1957
[20]
Second-harmonic resonator at collector
18(b)
Bipolar transistor
1958
[21]
Even-harmonic resonator at anode
19
Vacuum tube
1956
[22], [23]
Third-harmonic transmission-line control
22(a)
Vacuum tube
1958
[22]
Even-harmonic transmission-line control
22(b)
Vacuum tube
1958
[22]
Series quarter-wave line with parallel tank
26, 27
MOSFET
1974
[28], [29]
Introduction of class F
–
–
1975
[31]
Borisov, Voronovich
Parallel quarter-wave line with series tank
29
Bipolar transistor
1983
[33]
Chiba, Kanmuri
Even-harmonic tuning at microwaves
30
GaAs FET
1983
[34]
Kazimierczuk
Series quarter-wave line with series tank
32
Bipolar transistor
1984
[36]
Sarbacher
Tyler
Raab
114
November/December 2018
transmission line converts the open circuit at the load
to a short circuit at the drain for odd harmonics with
resistive load at the fundamental frequency.
Consequently, for a purely sinusoidal current flowing into the load due to the infinite, loaded quality
factor of the series-fundamentally tuned circuit, the
ideal drain-current and voltage waveforms can be re­­
presented by the corresponding normalized square
and half-sinusoidal waveforms [Figure 32(b)]. A sum
of the fundamental and odd harmonics approximates
a square-current waveform, and a sum of the fundamental and even harmonics approximates a halfsinusoidal collector voltage waveform. As a result,
the shapes of the collector current and voltage waveforms provide a condition when the current and voltage do not overlap simultaneously. The quarter-wave
transmission line causes the output voltage across the
load resistor to be phase-shifted by 90° relative to the
fundamental-frequency components of the collector
voltage and current. The measured collector efficiency
for the bipolar-transistor PA corresponding to this new
class-F concept and operating at a supply voltage of
15 V with an output power of 3 W achieved 92.9% at
3 MHz [36]. This new concept of the high-efficiency
PAs with even-harmonic control, historically beginning from biharmonic mode, was ultimately termed
the inverse class F at the end of the 1990s.
Table 1 summarizes the development and main
achievements of class-F and inverse class-F techniques for high-power amplification from a historical perspective.
References
[1] F. H. Raab, “Class-F power amplifiers with maximally flat waveforms,” IEEE Trans. Microw. Theory Techn., vol. MTT-45, pp. 2007–
2012, Nov. 1997.
[2] F. H. Raab, “Maximum efficiency and output of class-F power
amplifiers,” IEEE Trans. Microw. Theory Techn., vol. MTT-49, pp.
1162–1166, June 2001.
[3] T. K. Sarkar, R. J. Mailloux, A. A. Oliner, M. Salazar-Palma, and D.
L. Sengupta, History of Wireless. Hoboken, NJ: Wiley, 2005.
[4] L. de Forest, “The audion—Detector and amplifier,” Proc. IRE, vol.
2, pp. 15–29, Mar. 1914.
[5] T. H. White. (2018). United States early radio history, section 11.
[Online]. Available: http://earlyradiohistory.us
[6] A. Meissner, “The development of tube transmitters by the Telefunken Company,” Proc. IRE, vol. 10, pp. 3–23, Jan. 1922.
[7] J. Zenneck and H. Rukop, Lehrbuch der Drahtlosen Telegraphie. Stuttgart, Germany: Ferdinand Enke, 1925.
[8] Gesellschaft fur drahtlose Telegraphie, “An arrangement for minimising loss in the production of oscillations by means of vacuum
tubes,” (in German), German Patent 304360, Sept. 1919.
[9] H. J. Round, “Wireless telegraph and telephone transmission,” U.S.
Patent 1,564,627, Dec. 1925.
[10] E. Y. Robinson, “System of generation of alternating currents,”
Canada Patent 248810, Apr. 1925.
[11] D. C. Prince, “Vacuum tubes as power oscillators, part III,” Proc.
IRE, vol. 11, pp. 527–550, Sept. 1923.
November/December 2018
[12] D. C. Prince and F. B. Vogdes, Vacuum Tubes as Oscillation Generators. Boston, MA: General Electric Company, 1929.
[13] J. Slepian, “Electron tube system,” U.S. Patent 1,592,388, July
1926.
[14] I. N. Fomichev, “A new method to increase efficiency of the radio
broadcasting station,” (in Russian), Elektrosvyaz, pp. 58–66, June
1938.
[15] A. Kolesnikov, “A new method to improve efficiency and to increase power of the transmitter,” (in Russian), Master Svyazi, pp.
27–41, June 1940.
[16] A. Kolesnikov, “Tuning and operation of vacuum tube generator
with complicated voltage waveform,” (in Russian), Vestnik Svyazi,
pp. 34–41, Mar. 1941.
[17] R. I. Sarbacher, “Power-tube performance in class C amplifiers
and frequency multipliers as influenced by harmonic voltage,”
Proc. IRE, vol. 31, pp. 607–625, Nov. 1943.
[18] Z. I. Model, B. I. Ivanov, S. V. Person, and G. F. Soloviev, “Increasing the efficiency of a high power HF vacuum tube generator by
separating the third harmonic,” (in Russian), Radiotekhnika, vol. 2,
pp. 15–23, Apr. 1947.
[19] G. T. Royden, “High-frequency amplifier,” U.S. Patent 2,498,711,
Feb. 1950.
[20] L. S. Berman, “Increasing of useful power of the resonant semiconductor power amplifier by increasing its efficiency, part I,” (in
Russian), Radiotekhnika, vol. 12, pp. 62–65, Nov. 1957.
[21] L. S. Berman, “Increasing of useful power of the resonant semiconductor power amplifier by increasing its efficiency, part II,” (in
Russian), Radiotekhnika, vol. 13, pp. 70–73, Mar. 1958.
[22] V. J. Tyler, “A new high-efficiency high-power amplifier,” Marconi
Rev., vol. 21, no. 130, pp. 96–109, Fall 1958.
[23] V. J. Tyler, “Electron discharge device circuit arrangements,” U.S.
Patent 2,936,420, May 1960.
[24] J. R. Boykin, “Tuned amplifiers,” Amplifier Handbook, R. F. Shea,
Ed. New York: McGraw-Hill, 1966.
[25] I. R. Skarbek, “New high-efficiency 5-kW AM transmitter—
Unique class C amplifier operates with 90 percent efficiency,” RCA
Broadcast News, vol. 107, pp. 8–13, Mar. 1960.
[26] N. S. Fuzik, “Biharmonic modes of a tuned RF power amplifier,” Telecommun. Radio Eng. 2, Radio Eng., vol. 25, pp. 117–124,
July 1970.
[27] V. O. Stokes, Radio Transmitters: R.F. Power Amplification. New
York: Van Nostrand, 1970.
[28] F. H. Raab, “High-efficiency RF power amplifiers,” Ham Radio,
vol. 7, pp. 8–29, Oct. 1974.
[29] F. H. Raab, “FET power amplifier boosts transmitter efficiency,”
Electronics, vol. 49, pp. 122–126, June 1976.
[30] H. L. Krauss, C. W. Bostian, and F. H. Raab, Solid State Radio Engineering. New York: Wiley, 1980.
[31] F. H. Raab, “High efficiency amplification techniques,” IEEE Circuits and Systems (Newsletter), vol. 7, pp. 3–11, Dec. 1975.
[32] I. Leja and T. E. Parker, “High efficiency SAW oscillator using a dual gate GaAs FET,” in Proc. 1979 Ultrasonics Symp., pp.
865–869.
[33] V. A. Borisov and V. V. Voronovich, “Switching-mode generator,”
(in Russian), Russian Patent 2102832, Jan. 1983.
[34] K. Chiba and N. Kanmuri, “GaAs FET power amplifier module
with high efficiency,” Electronics Lett., vol. 19, pp. 1025–1026, Nov.
1983.
[35] E. S. Glazman, L. B. Kalinin, and Y. I. Mikhailov, “Improving VHF transmitter efficiency by using the biharmonic mode,”
Telecommun. Radio Eng. 1, Telecommun., vol. 31, pp. 46–51, July
1976.
[36] M. K. Kazimierczuk, “A new concept of class F tuned power amplifier,” in Proc. 27th Midwest Circuits and Systems Symp., 1984, pp.
425–428.
115
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