BELL TELEPHONE SYSTEM TECHNPI”CBAULC ATlONS B-93 1 A NEW HIGH-EFFICIENCY POWER AMPLIFIER FOR MODULATED WAVES W; H. DOHERTY Bell Telephone Laboratories DESCRIPTION OF A NEW FORM OF LINEAR POWER AMPLIPIER DESIGNED FOR EFFICIENT OPERATION OF HIGH-POWER TRANSMITTERS A New High-Efficiency Power Amplifier for Moclulated Waves By W. H. DOHERTY Bell Telephone Laboratories, Whippmy, N. J. This paper introduces a new form of linear power amplifier for modu- lated radio-frequency waves. Plate circuit efficiencies of 60 to 65 per cent independent of modulation are obtained by means of the combined action of varying load distribution among the tubes and varying circuit impedance over the modulation cycle. The theory of operation is developed and detailed observations on the behavior of tubes in the new circuit are given in the paper. The use of stabilized feedback in connection with this circuit is discussed and significant measurements on a laboratory model of a SO-kilowatt transmitter are shown. T. HE trend toward increasingly higher power levels in broadcasting III the last few years has attached new importance to the matter of more economical gperation of radio transmitters. Most of the opportunity for improvement in this direction lies in increasing the efficiency of the high-power stages to reduce the cost of power, the size of high-voltage transformers and rectifier, and the water-cooling requirements. With power levels of 50 kilowatts and higher these items account for an important part of the operating expense of a broadcast station, and the development of practical methods for in- creasing the efficiency should provide considerable stimulus to the use of higher power. Methods hitherto employed for reducing power consumption include the high-level Class B modulation system, such as is used at WLW,’ and the ingenious method of “outphasing modulation” 2 invented by Chireix and employed in a number of European installations. The development of these schemes was occasioned by the fact that the linear radio-frequency power amplifier, in the form in which it has been used for years in radio transmitters, may not be operated at an efficiency of more than about 33 per cent, for unmodulated carrier, if it is to supply the peak power output of a completely modulated wave. With this efficiency the d-c power input to B SO-kilowatt ampli- ’ Chz&nbers, Jones, Fyler Williamson, Leach, and Hutcheson, “The WLW 500. Kilowatt Broadcast Transmhter,” Proc. I. R. E., Vol. 22, p. 1151; October, 1934. z Chireix, “High Power Outphasing Modulation,” Proc. I. R. E., Vol. 23, p. 1370; November, 1935. 1 fier, for example, is 150 kilowatts, of which 100 kilowatts must be dissipated at the anodes of the water-cooled tubes. 03 The new form of linear power amplifier to be described in this paper removes this iumfatmn of the conventmnal crcut, permitting effi- . &n&s of 60 to 65 per cent to be realized, while retaining the advan- tages which account for the widespread use of linear amplifiers in broadcasting. These advantages include, notably, the elimination of high-power audio equipment, since modulation may be accomplished at a low power level; and the ease with which linear amplifiers may be added to an existing transmitter to increase its power output. Linear amplifiers, moreover, are suitable not only for the carrier-and-double- sideband signal enlployed in present-day broadcasting, but for any other type of transmission, such as the single-sideband system now in use in the transoceanic radio telephone circuit and frequently sug- gested as a remedy for the congestion in the broadcast spectrum. A brie? consideration of the mode of operation of the conventional linear power amplifier will show the reason for its low average efficiency and will afford a clew as to how, by the application of a new principle in power amplifier design, this efficiency may be approximately doubled. &‘ERilTION OF CONVENTIONAL LINEAR POWER hCPLIFIERS The tubes are usually biased nearly to the cut-off point, so that the plate current flows in a series of pulses having approximately the shape of half sine waves, as shown in Fig. 1. The output circuit is @-resonant to the fundamental and has a low impedance to the harmonic components of the plate current, so that the plate voltage wave is nearly sinusoidal and opposite in phase to the plate current and grid voltage. With a peak value of plate current of i,,, and a peak amplitude of emnl in the plate voltage wave, the power output of the tube is e,“,G”,, P out = 4 (1) Since the average value of the half-sine wave of plate current is t/~ times the maximum value, we have for the d-c input power to the tube pi” = s+, (2) The efficiency is accordingly If one were able to utilize a value of e,, equal to the d-c plate 0 voltage, the efficiency as given by (3) would be VT/~, or 78:.5 per cent. In practice, with a tube working close to its full output capacity, the plate swing is usually limited to a value of 0.85 to 0.9 times Eg, since ‘the output will be decreased if the plate potential swings down to a value lower than the maximum grid voltage. Under these conditions, Fig. l--Operating conditions in B linear power amplifier. and allowing for a 5 per cent loss in the tuned output circuits of the amplifier, expression (3) will give a value of 63 to 67 per cent as the maximum overall plate circuit efficiency obtainable. Now with a modulated wave applied to the grid this efficiency is obtained only at the maximum instantaneous output of the amplifier, and since the amplitude of the radio-frequency plate voltage wave, in a transmitter capable of 100 per cent modulation, is only half as great for the unmodulated condition as for the peaks of modulation, the efficiency with zero modulation does not exceed 33 per cent. Even during complete modulation the effective efficiency over the whole 3 audio cycle is only 50 per cent, and for the average percentage modu. lation of broadcast programs the all-day efficiency is scarcely in excess of the value for unmodulated carrier. The weakness, then, of the conventional method of amplifying a modulated wave is that the amplitude of the radio-frequency plate voltage is too small during most of the operating time, and in order to improve the situation it is necessary to devise a system in which a larger amplitude is employed. HIGH-EFFICIENCY OPERATION The method of attack on this problem is to consider an amplifier operating, arbitrarily, with a high plate voltage swing and conse- quently high efficiency at the carrier output, and then to find what must be done to permit an increase in output. We shall see that a simple and fundamental means is available for doing this. A tube will operate at high efficiency at any desired output power, however small, provided the alternating plate, voltage is high, i.e., provided the load impedance is high enough to require a large voltage output from the tube. To take a concrete example, a tube capable of delivering 100 kilowatts at high efficiency into an impedance of R ohms will deliver 50 kilowatts into 2R ohms at the same voltage output and consequently the same efficiency. We should find, how- ever, upon modulating the radio-frequency grid voltage, that the tube could not respond to the upward swings of modulation because the alternating plate voltage had already reached its maximum value at the SO-kilowatt output. Suppose now that an additional source of voltage could be inserted in series with the load, as represented by the generator of Fig. 7.. If (isz”X Fig. Z-Insertion of a hypothetical source of additional voltage. the voltage of this generator increases from zero to a value equal to the output voltage of the original tube, we shall obtain the necessary increased voltage for modulation peaks. The tirrent in the circuit will increase to twice its original value and the power in the load, which was originally 50 kilowatts, will increase to the necessary peak power of 200 kilowatts, or four times the carrier power, 100 kilowatts being furnished by the tube and the other 100 kilowatts by the generator. 4 The sensation experienced by the original tube as the added generator c~me.s into play is a gradual lowering of the impedance into which it 0 works, since its output current increases without any increase in its output voltage, and when the added generator has a voltage equal to - that of the tube this impedance has effectively been reduced from 2R to R ohms. The increase in current occasioned by the activity of the generator of course tends to reduce the output voltage of the * original tube because of the greater internal drop, but since the grid excitation on the tube is continuing to increase in accordance with the modulation the tube is able to maintain its output voltage in spite of the increase in load current. We now have the problem of replacing this added generator vith a tube. Obviously we cannot replace it directly, because while a generator would offer no impedance to the flow of current from the original tube, an inactive tube would offer an infinite impedance. The solution is to interpose, as shown in Fig. 3, a network having a certain 0 Fig. 3-Fundamental form of a high-efficiency circuit. property, namely, that the impedance at the sending end is inversely proportional to the terminating impedance. This is a familiar prop- erty of quarter-wave transmission lines and their equivalent networks. As long as the second tube does not conduct, the network is terminated in an open circuit. Its input impedance is therefore zero and the first tube works into an impedance of 2R ohms. When the second tube is permitted to conduct, the terminating impedance of the network is reduced, and since the grid excitation on the tube causes the plate current to be opposite in phase to the plate potential, this terminating impedance provided by the tube is a negative shunt resistance; 3 that is, the tube delivers power to the circuit. As the contribution of the second tube increases, lowering the negative terminating resistance of the network, the input impedance of the network, which was originally zero, increases. This input impedance is a negative series resistance which reduces the impedance presented to Tube No. 1 from its original value of 212 ohms, and when, at the peak of modulation, Tube No. 2 n is contributing half the total power, the load impedance to No. 1 is R ohms, and No. 1 is able to supply twice the carrier power at the same radio-frequency plate potential as at the carrier. We may revert to the generator analogy by recalling an associated property of impedance-inverting networks, namely, that any definite current at one pair of terminals is associated with a definite coexisting voltage at the other pair, entirely without regard to the terminating impedances; the supplying of current to the circuit by Tube No. 2 at the far end of the network is, accordingly, identical in its effect to the injection of a voltage at the near end, in series with the voltage of Tube No. 1, after the fashion of our original hypothetical generator. Considering now the dynamic characteristic of the amplifier as a whole, the operation is as follows: The grids of both tubes are excited by the modulated output of the preceding stage, but for all instan- taneous outputs from zero up to the carrier level Tube No. 2 is pre- vented by a high grid bias, or some other means, from contributing to the output, and the power is obtained entirely from Tube No. 1, which is working into twice the impedance into which it is to work when delivering its peak output. In consequence, the radio-frequency plate voltage on this tube at the carrier is nearly as high as is per- missible and the efficiency is correspondingly high. Beyond this point the dynamic’characteristic of Tube No. 1, unassisted, would flatten off very quickly because the plate voltage swing could not be appre- e ciably increased. The second tube, however, is permitted to come into play as the instantaneous excitation increases beyond the carrier point. In coming into play the second tube not only delivers power of itself, but through the action of the impedance-inverting network causes an effective lowering of the impedance into which the first tube works, so that the first tube may increase its power output without increasing its plate voltage swing, which was already a maximum at the carrier point. At the peak of a 100-per-cent modulated wave each tube is working into the impedance R most favorable to large output and delivering twice the carrier power, so that the total instantaneous out- put is the required value of four times the carrier power. Thus the required tube capacity is the same as in a conventional linear power amplifier. What we have, then, is a two-tube amplifier in which the contribu- tion of the second tube is delayed until the first tube has reached an efficient operating condition; whereupon there ensues a supplementary action between the tubes, to which the impedance-inverting network is a necessary adjunct. 6 6 The arrangement of Fig. 3 is one of the two fundamental forms of the high-efficiency circuit. The other form is shown in Fig. 4. In this case the physical load impedance used is R/2, which is the same as would be employed if the tubes were to be connected in parallel in the conventional type of amplifier. The impedance-inverting net- work is then interposed between the load and Tube No. 1, which is to deliver the carrier power. As long as Tube No. 2 is inactive the network is terminated in R/2 ohms, and the network is so designed that the impedance presented to Tube No. 1 under this condition is 2X ohms, the impedance necessary for attaining high efficiency at the carrier output. As the second tube comes into action in parallel with the load it raises the effective terminating impedance of the network, with a consequent lowering of the impedance presented to Tube No. 1; Fig. 4-Second fundamental form of high-efficiency circuit. and again we have each tube, at the instantaneous peak of modulation, working into the desired effective load impedance of R ohms. Fig. 4 may be said to show a shunt-connected load, as contrasted with the series-connected load of Fig. 3. The shunt connection ap- pears to be more advantageous for most practical purposes because the load circuit is grounded, while in the s&es arrangement the load is nelther grounded nor balanced to ground. GENERAL OBSERVATIONS The voltage and current relations in the two tubes as the amplitude of the grid excitation is varied are shown by Figs. 5 (a) and 5 (b), and the corresponding shapes of the envelopes of radio-frequency plate currents and voltages during complete modulation are shown in Fig. 6. If we denote by k the ratio of the instantaneous amplitude of the envelope to the peak amplitude reached during 100 per cent modu- lation, then for amplitudes between zero and the carrier point, where k = l/Z, the total output of the amplifier comes from Tube No. 1, T- 7 and is given by the expression P tota, = PI = (2kL,)(kL”ax) (4) = 2k=E“ l&XI mnx, where E,,, and I,, are the root-mean-square values of radio-frequency plate voltage and plate current which are to exist when the tube is delivering its maximum power, i.e., when k = 1. The factor 2 above is reouired because the voltage on Tube No. 1 reaches the value Em, when k = l/2. Between k = l/7. and k = 1 the voltage on No. 1 remains at E,, volts while the current in No. 1 and the voltage across No. 2 continue to rise linearly; meanwhile the current in No. 2 commences and rises twice as fast in order to reach the value I,, at k = 1. The total power between these two values of k is the sum of the outputs of the two tubes: P totn* = PI + Pz = Em&L& + (5) (kEmJ(2k - 1)Lm = 2k2E rn%IX m sx, which is the same as expression (4) above, showing that the current and voltage relations of Fig. 5 are consistent with continuity in the dynamic characteristic of the amplifier. By assuming k to vary sinuso.idally about its carrier value of l/2, in accordance with the modulation, and integrating the values of PI and PZ as given by (4) and (5) over the appropriate half-cycles of modulation, the average output of each tube during modulation may be determined. This integration gives for the average output of 8