Patent Publication Number: US-2005134377-A1

Title: Doherty amplifier

Description:
BACKGROUND OF THE INVENTION  
      The present invention relates generally to amplifiers and more particularly to an efficient linear amplifier circuit for amplifying radio frequency (RF) signals of varying amplitude.  
      Linear power amplifiers are widely used in wireless communication systems to amplify signals transmitted between a base station and a mobile terminal. Because power is at a premium in wireless communication systems, particularly in the mobile terminals, it is desirable for the power amplifiers to provide highly efficient linear amplification. However, because most highly efficient amplifiers operate in saturation, there is a trade-off between high efficiency and linearity.  
      U.S. Pat. No. 2,210,028 to Doherty describes a vacuum tube amplification system that provides efficient linear amplification for input signals. The Doherty amplifier comprises two vacuum tube amplifiers connected in parallel at their outputs with a quarter wavelength transmission line. Each amplifier is driven with a varying amplitude drive signal. The primary amplifier, which is furthest in line length from an output load, provides an output current proportional to the current of the input drive signal until the primary amplifier reaches saturation.  
      As the primary amplifier approaches saturation, an auxiliary drive signal begins driving the auxiliary amplifier, which is a quarter wavelength nearer the load than the primary amplifier. Because of the impedance inversion property of the quarter wavelength transmission line, the current provided by the auxiliary amplifier reduces the apparent impedance of the load as seen by the primary amplifier. As a result, the primary amplifier can supply more current, and therefore, can supply more power to the load. For example, assume the primary amplifier alone provides P max /4 of output power at saturation. Further, assume that the auxiliary amplifier can also provide up to P max /4 of output power. According to the Doherty amplification system, driving both amplifiers into saturation causes the total output power at the load to increase from P max /4 to P max .  
      The efficiency curve of a Doherty amplification system has two efficiency peaks. Assuming the primary amplifier provides P max /4 of output power at saturation, the efficiency peaks occur at P max /4, when the first amplifier alone saturates, and again at P max , when both amplifiers saturate. Further, the efficiency is maintained at a high value between the two efficiency peaks. In contrast, the efficiency of a conventional power amplifier at P max /4 is half the efficiency provided by the same power amplifier at P max . Consequently, the Doherty amplification system significantly improves the average efficiency associated with linearly amplifying signals of varying amplitude.  
      Another prior art amplification system is described by Chireix in Proc. IRE, Vol. 23 No. 11 (1935), pages 1370-1392, entitled “High Power Outphasing Modulation.” Chireix describes a transmitter that provides a modulated amplitude output signal by combining two constant output amplitude amplifiers with a variable phase difference such that the amplifiers may be varied in relative phase from additive to subtractive. Unlike the Doherty amplification system, the Chireix system relies on the primary and auxiliary amplifiers being out-of-phase.  
      U.S. Pat. No. 6,133,788 to Applicant entitled “Hybrid Chireix/Doherty Amplifiers and Methods” discloses a combination of the techniques of Chireix and Doherty. According to the &#39;788 patent, an advantageous way to construct a Doherty amplifier using modern technology is to use a digital signal processor to generate two quadrature modulating waveforms with two separate quadrature modulators in order to form out-of-phase amplifier drive signals for the primary and auxiliary amplifiers. The &#39;788 patent also teaches that efficient linear amplification may be performed using two constant amplitude amplifiers as compared to the two linear amplifiers used in the Doherty amplification system.  
      Another variation is described in a CIP to the above &#39;788 patent, now issued as U.S. Pat. No. 6,359,506. According to the &#39;506 patent, the primary amplifier operates in saturation, so that it produces a constant amplitude output voltage. The auxiliary amplifier is driven to generate an amplitude modulated signal output. By coupling the primary and auxiliary amplifiers through the quarter wavelength transmission line, the drive signal of the auxiliary amplifier modulates the effective load impedance seen by the primary amplifier, and therefore, provides efficient amplifier coupling.  
     SUMMARY OF THE INVENTION  
      The present invention comprises a method and apparatus to provide efficient linear amplification of radio frequency (RF) signals. An amplifying circuit according to an exemplary embodiment of the present invention comprises a primary amplifier for providing power to a load and an auxiliary amplifier for generating an artificial reflection signal. The artificial reflection signal has a predetermined phase difference as compared to the output signal supplied to the load. The amplifying circuit also comprises a coupler connecting the primary amplifier to the load. The coupler includes a load port connected to the load, a primary port connected to an output of the primary amplifier, and an auxiliary port connected to an output of the auxiliary amplifier such that the artificial reflection signal changes an apparent impedance of the load as seen by the primary amplifier. According to exemplary embodiments of the present invention, the coupler may be a circulator or a quadrature coupler.  
      The present invention may be implemented by supplying power to a load using a primary amplifier, generating an artificial reflection signal with an auxiliary amplifier, and connecting the primary amplifier to the load with a coupler. The coupler connects the primary amplifier to the load by connecting a load port to the load, connecting a primary port to an output of the primary amplifier, and connecting an auxiliary port to an output of the auxiliary amplifier such that the artificial reflection signal changes an apparent impedance of the load as seen by the primary amplifier at the primary port. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
       FIG. 1  illustrates an exemplary amplifier circuit according to the present invention.  
       FIG. 2  illustrates a first exemplary embodiment of the amplifier circuit of  FIG. 1 .  
       FIG. 3A  illustrates an exemplary efficiency plot where a =0.5 for the amplifier circuit of  FIG. 2 .  
       FIG. 3B  illustrates an exemplary amplifier drive signal plot associated with the exemplary efficiency plot of  FIG. 3A .  
       FIG. 4A  illustrates another exemplary efficiency plot where a =1 for the amplifier circuit of  FIG. 2 .  
       FIG. 4B  illustrates an exemplary amplifier drive signal plot associated with the exemplary efficiency plot of  FIG. 4A .  
       FIG. 4C  illustrates an exemplary drive circuit for the amplifier circuit of  FIG. 2 .  
       FIG. 5A  illustrates another exemplary “Buck and Boost” efficiency plot for the amplifier circuit of  FIG. 2 .  
       FIG. 5B  illustrates an exemplary amplifier drive signal plot associated with the exemplary efficiency plot of  FIG. 5A .  
       FIG. 6  illustrates a second exemplary embodiment of the amplifier circuit of  FIG. 1 .  
       FIG. 7  illustrates an exemplary amplifier drive signal plot for the amplifier circuit of  FIG. 6 .  
       FIG. 8  illustrates an exemplary auxiliary amplifier configuration for the amplifier circuit of  FIG. 2 .  
       FIG. 9  illustrates an exemplary auxiliary amplifier configuration for the amplifier circuit of  FIG. 6 .  
       FIG. 10  illustrates an exemplary signal generator for the auxiliary amplifier of  FIG. 1 .  
       FIG. 11  illustrates an exemplary RF signal generator for the auxiliary amplifier of  FIG. 1 .  
       FIG. 12  illustrates an exemplary transceiver that uses the amplifier circuit of  FIG. 1 . 
    
    
     DETAILED DESCRIPTION OF THE INVENTION  
      In each of the above described amplification systems, the auxiliary amplifier is directly connected to the output of the primary amplifier, even when the auxiliary amplifier does not contribute any power to the load. The auxiliary amplifier increases the total losses associated with the amplifier circuit. To minimize these losses, the auxiliary amplifier may be tuned to present a high output impedance at the junction between the primary and auxiliary amplifiers so that the auxiliary amplifier looks like an open circuit to the primary amplifier when the auxiliary amplifier is not contributing any power to the load. However, when used in systems operating at microwave frequencies, the high output impedance may be difficult to achieve.  
       FIG. 1  illustrates a block diagram for an exemplary amplifier circuit  100  according to the present invention. Amplifier circuit  100  is applicable to any wireless transmitter, such as the base station and/or mobile terminal transmitter. The term “mobile terminal” may include a cellular radiotelephone with or without a multi-line display; a Personal Communication System (PCS) terminal that may combine a cellular radiotelephone with data processing, facsimile, and data communications capabilities; a Personal Digital Assistant (PDA) that can include a radiotelephone, pager, Internet/intranet access, web browser, organizer, calendar, and/or a global positioning system (GPS) receiver; and a conventional laptop and/or palmtop receiver or other appliance that includes a radiotelephone transceiver. Mobile terminals may also be referred to as “pervasive computing” devices.  
      Amplifier circuit  100  includes a primary amplifier  110 , an RF coupler  130 , a load  140 , and an auxiliary amplifier  150 . RF coupler  130  connects primary amplifier  110  to the load  140  and has at least three ports: a load port  132 , an auxiliary port  134 , and a primary port  136 . The load  140  connects to the RF coupler  130  at the load port  132 , the output of the auxiliary amplifier  150  connects to the RF coupler  130  at the auxiliary port  134 , and the output of the primary amplifier  110  connects to the RF coupler  130  at the primary port  136 .  
      Initially, auxiliary amplifier  150  does not provide any current to load  140 , and therefore, is effectively disabled while primary amplifier  110  provides power to the load  140 . Primary amplifier  110  provides power up to a saturation output power level to the load  140 . As the primary amplifier  1 O approaches saturation, the auxiliary amplifier  150  is enabled and injects an artificial reflection signal into the output of primary amplifier  110  via the RF coupler  130 . As with the Doherty amplifier, the reflection signal changes the apparent impedance of the load  140  as seen by primary amplifier  1   10 , which enables the primary amplifier  110  to provide more current, and therefore, more power to the load  140 . However, unlike the Doherty amplifier, auxiliary amplifier  150  is not directly connected to load  140 , and therefore, does not contribute to the overall losses associated with the amplifier circuit  100 . Further, because auxiliary amplifier  150  is not directly connected to load  140 , the phase of the artificial reflection signal input into the RF coupler  130  may differ by a predetermined phase difference from the phase of the output signal supplied to the load  140 .  
       FIG. 2  illustrates an exemplary embodiment of the amplifier circuit  100  of  FIG. 1 . According to the exemplary embodiment, primary amplifier  10  comprises a first primary amplifier  112  and a second primary amplifier  114  driven in quadrature by a quadrature splitter  102 . RF coupler  130  comprises a quadrature coupler  130 , where primary port  136  comprises a first primary port  136 a and a second primary port  136   b . The first and second primary ports  136   a ,  136   b  couple the outputs of the first and second primary amplifiers  112 ,  114  to load  140 .  
      As shown in  FIG. 2 , a primary drive signal input to a first input port of quadrature splitter  102  is equally split between two output ports of the quadrature splitter  102 . Therefore, the primary drive signal is equally split between the first and second primary amplifiers  112 ,  114 . However, due to the properties of the quadrature splitter  102 , there is a 90° phase difference between the signal input to the first primary amplifier  112  and the signal input to the second primary amplifier  114 . For simplicity, it is assumed that the phase of the primary drive signal is arbitrarily set to 0°. Therefore, the phase of the signal input to first primary amplifier  112  is 0°, while the phase of the signal input to second primary amplifier  114  is −90°. A load  104  is connected to the second input of quadrature splitter  102  to absorb any signals present at this port. However, it will be appreciated by those skilled in the art that a signal may be input to the second input port of quadrature splitter  102 . As with the first input port, a signal input to the second input port of quadrature splitter  102  is equally split between the inputs to the first and second primary amplifiers  112 ,  114 . However, the phasing of the signal input to the second input port is reversed from the phasing of the signal input to the first input port, e.g., 0° at the input to the second primary amplifier  114  and −90° at the input to the first primary amplifier  112 .  
      Quadrature coupler  130  behaves in exactly the same manner as quadrature splitter  102 . Therefore, the signal from the first primary amplifier  112  and the signal from the second primary amplifier  114  both arrive at the load with the same phase, and add constructively at the load  140 . Further, the signal from the first primary amplifier  112  and the signal from the second primary amplifier  114  arrive 180° out of phase at auxiliary port  134 , and therefore, add destructively at the auxiliary port  134 .  
      As discussed above, auxiliary amplifier  150  is effectively disabled while primary amplifier  110  operates below its saturation point. However, as primary amplifiers  112 ,  114  approach saturation, the auxiliary amplifier  150  is enabled. The enabled auxiliary amplifier  150  generates an artificial reflection signal with a phasing of −180°, based on the auxiliary drive signal, and injects the artificial reflection signal into auxiliary port  134 . The artificial reflection signal is split at first and second primary ports  136   a ,  136   b  to produce an artificial reflection signal of phase −180° traveling backwards into the output port of the first primary amplifier  112 , and an artificial reflection signal of phase −270 degrees traveling backwards into the output port of the second primary amplifier  114 . The phase of these artificial reflection signals are both 180° offset from the phase of the output signals generated by the respective amplifiers  112 ,  114 . Therefore, the artificial reflection signals appear to primary amplifiers  112 ,  114  as a load impedance mismatch to the low impedance side. Because of this “apparent” change in load impedance, the primary amplifiers  112 ,  114  increase their output current and deliver more power to the load  140 .  
      It will be appreciated that, whatever the line length between first and second primary amplifiers  112 ,  114  and ports  136   a ,  136   b , and whatever the line length between auxiliary amplifier  150  and auxiliary port  134 , a suitable phasing of the auxiliary drive signal may be found to produce the above situation. Therefore, when auxiliary amplifier  150  has an appropriately phased drive signal, auxiliary amplifier  150  can change the apparent impedance of the load  140  as seen by primary amplifiers  112 ,  114 , and therefore, increase the output power provided by amplifier circuit  100  to load  140 .  
      To illustrate the above embodiment, consider the following example. Assume that auxiliary amplifier  150  produces an artificial reflection signal with an output voltage having a wave amplitude of {square root}{square root over (2)}aV o where “a” is an auxiliary constant that may be set to any desired number to produce a desired power output from auxiliary amplifier  150 , as discussed further below. Further, assume that primary amplifiers  112 ,  114  are each modeled as voltage sources of wave amplitude V o  when saturated. When the auxiliary drive signal begins driving auxiliary amplifier  150 , quadrature coupler  130  splits the artificial reflection signal generated by auxiliary amplifier  150  into equal waves, each having an amplitude aV o , traveling backwards into the output of the primary amplifiers  112 ,  114 . The artificial reflection signals reach the outputs of the primary amplifiers  112 ,  114  with a phase 180° offset from the phase of the amplifier output voltages. Due to conservation of energy, the sum of the forward voltage waves (from the primary amplifiers  112 ,  114 ) and the reverse voltage waves (from the auxiliary amplifier  150 ) at the outputs of the primary amplifiers  112 ,  114  equals V o . Therefore, at the outputs of the primary amplifiers  112 ,  114 , the forward voltage wave amplitudes are (1+a) V o  and the reverse voltage wave amplitudes due to the artificial reflection signals are -aV o .  
      As a result, the voltage reflection coefficient “r” is -a/(l+a), and the load impedance seen by primary amplifiers  112 ,  114  is R L (1+r)/(1−r) =R L (1+2a). The current output by primary amplifiers  112 ,  114  into load  140  may therefore be represented by (1 +2a) V o /R L . Because the current normally produced by each primary amplifier  112 ,  114  alone is V o /R L , the current produced by each primary amplifier  112 ,  114 , as influenced by auxiliary amplifier  150 , has increased by a factor of 1+2a. The resulting output power into the load from each primary amplifier  112 ,  114  is therefore (1 +2a) V o   2 /R L , which is also higher than the power provided by primary amplifiers  112 ,  114  alone by the factor 1+2a.  
      The forward voltage waves from primary amplifiers  112 ,  114  combine at the load  140  via quadrature coupler  130  to produce a voltage wave amplitude into load  140  of 29 {square root over (2)}(1+a)·V o . When combined with the voltage wave amplitude from auxiliary amplifier  150  ({square root}{square root over (2)}aV o ), the delivered power into load  140  is 2(1+a)  2 V o   2 /R L . It may be verified that this delivered power is the sum of the powers (1 +2a) V o   2 /R L  from each of the primary amplifiers  112 ,  114  and the power 2a  2 V o   2 /R L  from auxiliary amplifier  150 . Thus, all the power generated by the three amplifiers  112 ,  114 ,  150  is transferred to load  140 .  
      For example, suppose each of primary amplifiers  112 ,  114  saturate at a power level of P max , given by:  
         P   max     =         V   o   2       R   L       .         
 
      Further, suppose auxiliary amplifier  150  is designed to saturate at a level of P max /2 (by choosing a =0.5). When auxiliary amplifier  150  is disabled, the power output into load  140  is simply 2P max . However, when auxiliary amplifier  150  is enabled and saturated, the power output into the load is 2(1+a) 2 P max= 4.5P max . By generating a power level varying from zero to P max / 2, auxiliary amplifier  150  causes the total output power at the load  140  to vary from 2P max  to 4.5P max , with the primary amplifiers  112 ,  114  generating the majority of the power at maximum saturated efficiency.  
       FIG. 3A  plots the efficiency vs. instantaneous output power of the amplifier circuit  100  (when a =0.5) over the instantaneous output power range of 0 to 4.5P max . For comparison,  FIG. 3A  also includes the maximum theoretical efficiency of a conventional class-B amplifier. The efficiency of the conventional class-B amplifier is computed assuming ideal class-B amplifier operation. Those skilled in the art will appreciate that while practical losses will reduce these efficiencies, the relative advantage of the invention is maintained.  
      In  FIG. 3A , power outputs below 2P max  are obtained using primary amplifiers  112 ,  114  below saturation, with auxiliary amplifier  150  disabled. Because auxiliary amplifier  150  is disabled, the efficiency curve from power level 0 to 2P max  exhibits the class-B efficiency curve shape, with a peak at 2P max  of instantaneous output power. After auxiliary amplifier  150  is enabled, the efficiency peaks again at a power level of 4.5P max , when primary amplifiers  112 ,  114  each operate with an output power of 2P max , and auxiliary amplifier  150  operates with a saturated output power of 0.5P max . Between the levels of 2P max  and 4.5P max , auxiliary amplifier  150  operates below saturation on its own efficiency versus power output curve. However, because auxiliary amplifier  150  contributes only a small proportion of the output power, the overall efficiency of the amplifier circuit  100  drops only slightly while auxiliary amplifier  150  is unsaturated.  
      Above their saturation points, primary amplifiers  112 ,  114  generate an output current proportional to 1 +2a; the output current of auxiliary amplifier  150  increases linearly with “a” above the saturation point of the primary amplifiers  112 ,  114 . As a result, the output amplitude of the entire amplifier circuit  100  increases proportionally to 1+a, as described above. Because drive signals of linear amplifiers track the output signals of the linear amplifiers, the primary and auxiliary drive signals also increase proportionally to 1 +2a and a, respectively.  
       FIG. 3B  plots exemplary primary and auxiliary amplifier drive signals used to operate the amplifier circuit  100  of  FIG. 2  as a function of a desired output amplitude for the case of a =0.5. Before primary amplifiers  112 ,  114  reach saturation, the ratio of the amplifier drive amplitude to the desired output amplitude is {square root}{square root over (2/2)}. Once the primary amplifiers  112 ,  114  reach saturation (at point A in  FIG. 3B ), auxiliary amplifier  150  is enabled and the drive current changes in proportion to the new output current provided by the amplifier circuit  100 . Once auxiliary amplifier  150  is enabled, it can be shown that the ratio of the amplifier drive amplitude to the desired output amplitude is {square root}{square root over (2)}.  
      The efficiency associated with the amplifier circuit  100  may be altered to suit particular applications by choosing the maximum value, a max , of the scaling factor “a”. If a max= 1, for example, auxiliary amplifier  150  has a saturated output power twice that of each of primary amplifiers  112 ,  114  into a load  140 . The resulting efficiency curve, shown in  FIG. 4A , exhibits a first maximum efficiency at a power output of 2P max , where P max  is the saturation power level of each of primary amplifiers  112 ,  114  into load  140 . After auxiliary amplifier  150  is enabled, the apparent impedance of the load  140  as seen by primary amplifiers  112 ,  114  decreases due to the artificial reflection signal. When saturated, auxiliary amplifier  150  provides 2P max  and each primary amplifier  112 ,  114  provides 3P max  to load  140 . Therefore, a second maximum efficiency peak occurs at 8P max .  
      The amplifier circuit  100  used to generate the efficiency curve of  FIG. 4A  (a max= 1) operates with substantially maximum efficiency over a 6dB range of instantaneous output power. This amplifier circuit  100  is suitable for efficient linear amplification of signals with a 6dB peak to mean ratio, or of signals that may be clipped at 6dB above the root mean square value (rms). For example, the sum of many signals is amplified in cellular base station transmitters using code division multiple access (CDMA). The sum of these signals has a Gaussian amplitude distribution, according to the Central Limit Theorem. However, the Gaussian distribution has theoretically infinite peak values, which are almost never reached. The probability of a Gaussian signal exceeding its rms value by 6dB is sufficiently small that values greater than this may be limited to that value while producing only a tolerable increase in out-of-band spectral energy. In that case, the amplifier circuit  100  corresponding to the efficiency curve of  FIG. 4A  may be operated at an rms level coincident with the maximum efficiency point at output power 2P max .  
       FIG. 4B  illustrates the amplitude drive signals vs. the desired output amplitude for a max= 1. As shown in  FIG. 4A , the combined output power at the load  140  of the primary amplifiers  112 ,  114  when saturated is 2P max  before auxiliary amplifier  150  is activated, which corresponds to a desired output amplitude of {square root}{square root over (2)} units. Thus, for each of primary amplifiers  112 ,  114 , the amplifier drive amplitude ranges linearly from 0 to 1 unit for the desired output amplitude range of 0 to {square root}{square root over (2)} units, as shown in  FIG. 4B .  
      As the power output is increased beyond 2P max , auxiliary amplifier  150  is enabled. As with the primary amplifiers  112 ,  114 , the output power associated with auxiliary amplifier  150  for a max= 1 ranges from 0 to 2P max  and requires an amplifier drive signal ranging linearly from 0 to 2 units. Because gain is an arbitrary scaling, the input drive amplitude of the auxiliary amplifier  150  would also range from 0 to 2 units if the gain of the auxiliary amplifier  150  was 3dB lower than the gain of the primary amplifiers  112 ,  114 . Therefore, the amplifier drive signal for amplifier circuit  100  may be the result of generating a linearly proportional drive signal for primary amplifiers  112 ,  114  over the entire range, ending at 2 units of amplifier drive amplitude, and adding some appropriate fraction, e.g., 0.5, of the auxiliary drive signal when auxiliary amplifier  150  is enabled.  
       FIG. 4C  provides an exemplary drive circuit  200  for achieving the above-described amplifier drive signal when a max= 1.  FIG. 4C  only shows the I-parts of the drive circuit  200  for generating the primary and auxiliary amplifier drive signals. Apart from being fed with balanced Q signals, the Q-parts of the drive circuit  200  would be identical. The I, Q outputs would be connected in parallel to generate the primary and auxiliary amplifier drive signals.  
      The exemplary circuit of  FIG. 4C  comprises a primary modulator  210 , a supplemental circuit  220 , and an auxiliary modulator  230 . Primary modulator  210  is a Gilbert-cell type balanced modulator comprising a principal transistor pair  212 , driven by the primary signal I p  and its inverse {overscore (I)} p , and two switching transistor pairs  214 , driven by a cosine carrier signal. The emitter voltages generated by principal transistor pair  212  appear across resistor R 1 , causing an imbalance in the collector currents of principal transistor pair  212 . Switching transistor pairs  214  switch the imbalanced collector currents such that the imbalanced collector currents are modulated by cos(ωt) to produce the In-phase part (or real part) of the primary drive signal.  
      Similarly, auxiliary modulator  230  is a Gilbert-cell type balanced modulator comprising a principal transistor pair  232 , driven by the auxiliary signal I a1  and its inverse {overscore (I)} a1 ,an and two switching transistor pairs  234  driven by the cosine carrier signal. Switching transistor pairs  234  modulate the imbalanced collector currents from principal transistors  232  to generate the In-phase (or real) part of the auxiliary drive signal.  
      I a1 and {overscore (I)} a1  have zero amplitude until primary amplifier  110  approaches saturation. As primary amplifier  110  approaches saturation, the amplitude of I a1  begins increasing, causing auxiliary amplifier  150  to boost the output capability of the primary amplifier  110 , as described above. As shown in  FIG. 4B , after auxiliary amplifier  150  is enabled primary amplifier  110  requires a drive signal that rises 50% faster. This additional rise in the primary drive signal is implemented in the drive circuit  200  of  FIG. 4C  by supplemental circuit  220 . Supplemental circuit  220  includes a supplemental principal transistor pair  222  driven by auxiliary drive signals I a2  and its inverse {overscore (I)} a2 . Note, the auxiliary signal I a2  has been distinguished by a suffix “2” when applied to supplemental transistor pair  222 , as opposed to a suffix “1” when applied to auxiliary modulator  230  because the contribution of I a2  to the primary amplifier  110  may have to be independently phased as compared to I a1 , for the auxiliary amplifier  150  to obtain the proper phase relationships.  
      Assuming the amplitude of the primary drive signal rises linearly over the range 0 to 2 while the primary amplifier  110  actually requires a peak drive amplitude of 3, and assuming the auxiliary drive signals also peak at an amplitude of 2, the contribution from supplemental principal transistors is scaled by one half and added to the contribution from principal transistors  212 . Thus, the emitter resistance for supplemental transistor pair  222  is double the resistance of the principal transistor pair  212 . The current sources in supplemental circuit  220  may also be scaled down from I o , to I o /2 to conserve current. As a result, the exemplary drive circuit  200  generates the primary and auxiliary drive currents shown in  FIG. 4B .  
      Turning now to  FIG. 5A , an alternate embodiment that improves the efficiency of the amplifier circuit  100  below 2P max , where primary amplifiers  112 ,  114  are operating unsaturated, will be described. When primary amplifiers  112 ,  114  operate below saturation, auxiliary amplifier  150  may be used to reduce the output power (instead of increasing it) by inverting the auxiliary constant “a”. By switching the phase of auxiliary amplifier  150  by 180°, the sign of the constant “a” is inverted. As a result, the reverse voltage wave amplitude reaching the output ports of primary amplifiers  112 ,  114  is “+a” instead of “−a,” and the forward voltage wave amplitude is 1− a instead of 1+a. Therefore, the reflection coefficient, “r,” is a/(1−a) and the apparent impedance of load  140  as seen by the primary amplifiers  112 ,  114  is R L /(1−2a). When a =0.5, the apparent impedance of load  140  as seen by primary amplifiers  112 ,  114  is infinite. As a result, while primary amplifiers  112 ,  114 , in principle, still operate in voltage saturation, no output current is provided to the load. Because the primary amplifiers  112 ,  114  do not provide any output current to the load  140 , the output current provided by auxiliary amplifier  150  is the only contribution to the load  150 . Thus, a third point on the efficiency curve exists at the saturation power level of auxiliary amplifier  150 , i.e., 0.5P max  when a =0.5. Providing that the outputs of primary amplifiers  112 ,  114  are effectively open circuits, the efficiency curve below 0.5P max  is completed by modulating auxiliary amplifier  150  down to zero.  
      The modulation of auxiliary amplifier  150  used to obtain the efficiency curve at output powers below 0.5P max  is, however, non-linear; auxiliary amplifier  150  is therefore amplitude modulated in the range a =0 to a =0.5. Primary amplifiers  112 ,  114  are enabled just as auxiliary amplifier  150  reaches saturation. At this point, auxiliary amplifier  150  is modulated downwards from a =0.5 to 0, causing now-driven primary amplifiers  112 ,  114  to contribute to the total power at the load  140  between the power range of 0.5P max  to 2P max . Auxiliary amplifier  150  is then linearly amplitude modulated in the negative (−a) direction, which completes the power range from 2P max  to 4.5P max .  FIG. 5A  shows the resulting efficiency curve obtained by this “Buck and Boost” mode of operation. The higher efficiencies at the lower power levels are, however, only obtained at the expense of some complexity in generating the amplifier drive signals (shown in  FIG. 5B ), as compared to amplifier drive signals for the “Boost only” cases of  FIGS. 3B and 4B , for which the drive signals are more straightforward to generate.  
      As explained above for the a =0.5 case, reversing the phase of the auxiliary amplifier allows the power to be modulated lower than 2P max  while keeping primary amplifiers  112 ,  114  saturated. When a =1 however, an interesting effect occurs. Assume that primary amplifiers  112 ,  114  are built with bi-directional devices that can return current to a battery by acting as synchronous rectifiers, as explained further in U.S. Pat. Nos. 5,930,128; 6,097,615; 6,181,199; 6,201,452; 6,285,251; 6,311,046; 6,359,506; 6,369,651 and 6,411,655 to Applicant, which are hereby incorporated by reference herein. At maximum inverse contribution from auxiliary amplifier  150  with a =1, primary amplifiers  112 ,  114  receive the incident energy from auxiliary amplifier  150 , synchronously rectify it, and return the energy as DC current to the battery. At this exact level, the “rectifier” input impedance appears to be R L , so no energy is reflected from primary amplifiers  112 ,  114 , and the output power to the load  140  is zero, despite auxiliary amplifier  150  generating power.  
      Referring now to  FIG. 6 , another embodiment of the present invention will be described. In the embodiment of  FIG. 6 , a circulator  130  replaces the quadrature coupler  130 . In the circulator configuration, a single primary amplifier  110  feeds its output through circulator  130  to load  140 . When the primary amplifier  110  is driven, it produces an output power between 0 and the saturated power level of P max =V o   2 /R L . Beyond the saturation point, primary amplifier  110  remains saturated while auxiliary amplifier  150  is enabled and outputs an artificial reflectance signal with a voltage wave amplitude of a V o  to the auxiliary port  134  of circulator  130 . The circulator  130  transfers the artificial reflectance signal to the primary port  136 , where it travels backwards into the output of the primary amplifier  110  looking like a reflected wave from load  140 . With the proper phasing, the artificial reflected signal changes the apparent impedance of the load  140  as seen by primary amplifier  110  from R L  to R L /(1+2a). For example, when a =1, i.e. auxiliary amplifier  150  has the same power level as primary amplifier  110 , and the impedance of the load  140  as seen by the primary amplifier  110  is R L /3. Due to the artificial reflection signal, primary amplifier  110  contributes three times its normal saturated output power level of P max  into the load  140  while auxiliary amplifier  150  contributes P max , resulting in a total of 4P max  at the load  140 . When suitably scaled, the efficiency curve of this arrangement is exactly the same as  FIG. 4A . The drive amplitudes for this embodiment are shown in  FIG. 7 . It will be appreciated by those skilled in the art that, after some slight modifications, the above described efficiency curves and drive signals are also applicable to the circulator configuration.  
      While  FIG. 2  shows auxiliary amplifier  150  as a single amplifier, there are a number of ways to construct auxiliary amplifier  150  according to the present invention. For example, auxiliary amplifier  150  may, if desired, be constructed identically to the primary amplifier  110 , using a pair of quadrature coupled amplifiers  152  in place of the single auxiliary amplifier of  FIG. 2 , as shown in  FIG. 8 . In this scenario, the juxtaposition of the auxiliary amplifier  150  and the primary amplifiers  112 ,  114  is completely symmetrical. Therefore, either may serve as the auxiliary or the primary amplifier. For example, if a signal input is fed into the unused input port of the auxiliary amplifier input quadrature splitter  154 , the amplified output appears at the terminated port of the auxiliary amplifier output coupler  156 , which is now the load for this mode. The primary amplifiers  112 ,  114  may then be used as an auxiliary amplifier  150  for this mode by feeding the desired auxiliary amplifier drive signal into the unused input port of the primary amplifier&#39;s input quadrature splitter  102 . This raises the possibility that both modes may be used at the same time to amplify two signals and deliver them to two loads.  
      Alternatively, the construction of the auxiliary amplifier  150  may be extended by recursive applications of the inventive principle to arrive at a chain coupling of auxiliary amplifiers  150 , which become progressively smaller, as shown in  FIG. 9 . The gain in efficiency is however small, and merely obviates the efficiency dip to 75% shown in  FIG. 4A  between 2P max  and 8P max , and flattens it to a constant 78% across this range. Auxiliary amplifier  150  may also deliver higher efficiencies than conventional class B amplifiers when driven hard into saturation using harmonic filtering to select only the wanted fundamental component, as described in more detail in U.S. patent application Ser. No. 09/730,791 to Applicant filed 7 Dec. 2000 and entitled “Harmonic Matching Network Design for a Saturated Amplifier,” which is hereby incorporated by reference herein. It will be appreciated by those skilled in the art that the auxiliary amplifier configurations of  FIGS. 8 and 9  are also applicable to the amplifier circuits  100  of  FIGS. 6 and 2 , respectively.  
       FIG. 10  shows an exemplary signal generator  160  that generates the desired drive signals for the amplifier circuit  100 . Signal generator  160  comprises an input RF sampler  162 , a signal modulator  164 , an output RF sampler  166 , a signal demodulator  168 , comparators  170 , loop filters  172 , and error modulator  174 . Input I, Q waveforms are applied to signal modulator  164 , i.e., a quadrature modulator, as is well known. The modulated signal then drives primary amplifier  110 , which may comprise the pair of quadrature coupled amplifiers  112 ,  114  as in  FIG. 2 , or a single amplifier  110 , as in  FIG. 6 . Primary amplifier  110  faithfully amplifies the modulated signal until the primary amplifier i  10  approaches saturation, at which point the output of primary amplifier  110  may start to under represent the desired amplitude due to the saturation.  
      Output RF sampler  166 , i.e., a - 30 dB directional coupler, samples the actual amplifier output to the load  140 . The output signal sample is then demodulated back to the complex baseband by signal demodulator  168 , i.e., a quadrature demodulator, to produce I′, Q′ signals. Signal demodulator  168  uses the same local oscillator signals (cos(wt), sin(wt)) as signal modulator  164  apart from a possible deliberate phase shift designed to match the phase shift through primary amplifier  110  and RF coupler  130 . Thus, the output of demodulator  168  (I′, Q′) should match the desired I, Q input signals if the output to the load  140  is a faithful amplification of the original I, Q input.  
      Comparators  170  subtract the demodulated I′, Q′ signals from samples of the original I, Q signals provided by input sampler  162  to obtain error signals ε Q  and ε I , which represent the error between the desired I, Q signals and the achieved I′, Q′ signals. Loop filters  172 , which may typically be integrators, filter the error signals and apply the error signals to error modulator  174 . Error modulator  174  generates a drive signal for auxiliary amplifier  150  that corrects the error by causing auxiliary amplifier  150  to contribute to the load  140  if the output power is too low due to the primary amplifier  110  either approaching saturation or arriving at saturation. With this feedback arrangement, no special waveform generation algorithm for the auxiliary amplifier  150  is needed; if desired however, the expected drive waveform for auxiliary amplifier  150  can be added to the output of filters  172 . As a result, the feedback loop only needs to generate a correction to the “guess” at the correct waveform rather than having to provide the full waveform.  
      The arrangement of  FIG. 10  is called a Cartesian loop because it resolves the controlled RF signal into X and Y (I, Q) or Cartesian coordinates. It is also possible to construct polar loops in which the RF signal is controlled in its amplitude or phase component or both.  
      A Cartesian loop may also be constructed without modulators and demodulators using the signal generator  180  shown in  FIG. 1l . Signal generator  180  includes an input RF sampler  182 , an output RF sampler  184 , a comparator  186 , and a loop filter  188 . In  FIG. 11 , comparator  186  subtracts a sample of the RF output taken by output RF sampler  184  from a sample of the desired signal, taken by input RF sampler  182 . Loop filter  188  then filters the error signal and auxiliary amplifier  150  corrects the error, as discussed above.  
      While the above uses comparators to generate the error signal(s), there are many alternative ways to obtain this error signal. For example, the sample of the desired signal may be input to a terminated port of output RF sampler  184  such that the desired difference signal is formed in and output from output RF sampler  184 . Other methods may include using a matched 180° hybrid junction to combine the input and output samples with the desired subtractive phase relationship. The line lengths between the units are set to achieve the correct subtractive phase relationship. Because this phase relationship is difficult to maintain over a very large band of frequencies, loop filter  188  reduces the gain outside the band of interest. In  FIG. 11 , this band limitation may be provided by making loop filter  188  a single pole, narrow bandpass filter, such as a high-Q resonator. The loop filter  188  allows errors within the band of interest to be amplified with high gain while reducing the loop gain out of band to less than unity before the phase relationships change from stable negative feedback to unstable positive feedback.  
      The present invention may be implemented in a radio transceiver of a wireless terminal in a wireless communication system. Exemplary wireless terminals include base stations, mobile terminals, etc. An exemplary transceiver  300  is shown in  FIG. 12 . Transceiver  300  includes a transmitter  310  for transmitting radio communication signals to one or more wireless terminals in the wireless communication system via antenna  320 , a receiver  330  for receiving radio communication signals from one or more wireless terminals via antenna  320 , and the amplifier circuit  100  of  FIG. 1 . As described above, amplifier circuit  100  provides efficient linear amplification of signals transmitted to one or more wireless terminals by transmitter  310 .  
      There are several advantages to the above described amplifier circuit  100 . For example, because the auxiliary amplifier  150  is not directly connected to the load  140 , auxiliary amplifier  150  does not contribute to the losses of the amplifier circuit  100 . This also obviates the need to tune auxiliary amplifier  150  to present a high impedance to the output of the primary amplifier  110 . As a result, the primary amplifier  110  may be readily used at microwave frequencies. Further, the amplifier circuit  100  may be designed for devices with, for example, normal  50  ohm outputs and inputs. As a result, the amplifier circuits  100  of the present invention may be tested using conventional test equipment.  
      The present invention may, of course, be carried out in other ways than those specifically set forth herein without departing from essential characteristics of the invention. The present embodiments are to be considered in all respects as illustrative and not restrictive, and all changes coming within the meaning and equivalency range of the appended claims are intended to be embraced therein.