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 (grandrei@ieee.org) is with Sumitomo Electric Europe Ltd., Elstree, Hertfordshire, United Kingdom. Frederick H. Raab (f.raab@ieee.org) 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