HYBRID CHIREIX/DOHERTY AMPLIFIERS POWER WAVEFORM SYNTHESIS

Abstract: Two amplifiers that are driven using outphasing modulation are coupled to one another so that the amplifiers affect each other's effective load line. The two amplifiers can maintain efficiency over a wider dynamic range than in a conventional amplifier. Amplifiers according to the invention amplify an AC input signal of varying amplitude and varying phase using a DC power supply. A converter converts the AC input signal into a first signal having constant amplitude and a first phase angle and into a second signal having constant amplitude and a second phase angle. The first amplifier amplifies the first signal, and the second amplifier amplifies the second signal. A coupler couples the first and second amplifiers to one another and to a load impedance, such that voltages or currents in the first amplifier become linearly related to voltages or currents in the second amplifier. The coupler may include at least one transformer that serially couples the first and second amplifiers to one another and to the load impedance. The coupler may also include first and second quarter wave transmission lines that couple the first and second amplifiers to one another and to the load impedance. The amplifiers preferably use bilateral devices, such that current flows from the first and second amplifiers to the DC power supply during a part of a signal cycle, and thereby returns energy to the DC power supply. Each of the more than two signals of constant amplitude and controlled phase is then separately amplified in separate amplifiers. The separately amplified more than two signals of constant amplitude and controlled phase are then combined to produce an output signal that is an amplification of the input signal at the desired power level. When converting the input signal into more than two signals, the phase of each of the more than two signals of constant amplitude and controlled phase is controlled to produce the output signal that is an amplification of the input signal at the desired power level. According to another aspect, a signal of varying amplitude and varying phase is generated from a plurality of constant amplitude varying phase signals, the sum of which is the signal of varying amplitude and varying phase. An IQ waveform generator generates a cosine carrier modulation waveform I(t) and a sine carrier modulation waveform Q(t) from the signal of varying amplitude and varying phase. A function generator generates a complementary waveform Q'(t) from the cosine carrier modulation waveform I(t) such that the sum of squares of I(t) and Q'(t) is constant. A first modulator modulates a cosine carrier signal with I(t) to obtain a first modulated cosine carrier. A second modulator modulates a sine carrier signal with Q'(t) to obtain a first modulated sine carrier. A circuit such as a butterly circuit forms the sum and difference of the first modulated cosine carrier and the first modulated sine carrier to obtain the constant amplitude varying phase signals.

Description: HYBRID CHIREIX/DOHERTY AMPLIFIERS POWER WAVEFORM SYNTHESIS Field of the Invention This invention relates to power amplifiers and amplifying methods, and more particularly to high-efficiency power amplifiers and related methods Background of the Invention Power amplifiers are widely used in communication systems, for example in radiotelephone base stations and radiotelephones. In radiotelephone communication systems, power amplifiers typically amplify high frequency signals for transmission. A major consideration in the design of power amplifiers is the efficiency thereof. High efficiency is generally desirable so as to reduce the amount of power that is dissipated as heat. Moreover, in many applications, such as in satellites and portable radiotelephones, the amount of power that is available may be limited. An increase in efficiency in the power amplifier is therefore important, in order to allow an increase the operational time or capacity for the satellite or portable radiotelephone. A conventional power amplifier such as a class-B amplifier generally only provides maximum efficiency at or near to its maximum saturated power output level. In order to accurately reproduce a signal of varying amplitude, the peak output signal level should be equal to or less than that maximum saturated power level. When the instantaneous signal output level is less than the peak, a conventional class-B power amplifier generally operates at less than maximum efficiency. The efficiency generally reduces as the square root of the output power. This is because, using the class-B example, the output power reduces as the square of the output current but the power consumption from the battery or other DC supply reduces only proportional to the output current. Therefore, the efficiency, which is - 2 - the ratio of output power to battery power, reduces proportional to the current, i.e., proportional to the square root of the output power. Accordingly, a power amplifier that has 60% efficiency at a peak output of 2 watts will generally have no more than 42% efficiency at an output of 1 watt (3dB reduced output). Moreover, when amplifying a signal of varying amplitude, a conventional amplifier may not produce an output signal amplitude proportional to the input signal amplitude, thereby causing nonlinear distortion and intermodulation. With a varying output signal power P(t) = A (t), the average efficiency can be estimated to be: average of (P(t)/Pmax) Max efficiency x average of square root (P(t)/Pmax) or -_ . average of (A(t)/Amax) ' Max efficiency x - — - average of (A(t)/Amax) Nonlinearities in conventional amplifiers can be reduced by various techniques, such as by an inverse predistortion of the input signal, or by feedback including Cartesian feedback in radio frequency power amplifiers for linearly amplifying signals with a bandwidth much less than the center frequency. Unfortunately, linearization generally does not alter the above efficiency formula, which in fact already assumes that the output amplitude can be made to faithfully follow the desired varying amplitude waveform. In effect, the average efficiency calculated above already assumes perfect linearization. The loss of efficiency comes about because current I(t) is drawn from the battery at a constant voltage Vcc, but is supplied to the load at a varying voltage I(t) RL which is less than Vcc. The voltage difference Vcc-I(t)-RL is lost across the output device (e.g. collector junction), causing power dissipation in the device. In U.S. Patent No. 2,210,028 to Doherty (August 1940), an arrangement of two vacuum tube power amplifiers coupled by a single quarter-wave line is described. The first amplifier is operated up to an output level of Pmax/4, at which it achieves maximum practical class-B efficiency. For powers above this level, the second amplifier is caused to contribute. The second amplifier affects the load impedance of - 3 - the first amplifier one quarter wave away such that the first amplifier can increase its power up to Pmax/2, while the second amplifier also contributes up to Pmax/2, making Pmax in total, at which point both amplifiers are once more achieving maximum practical class-B efficiency. Thus, efficiency is preserved over a 6dB range of output levels from Pmax/4 to Pmax. A semiconductor version of the Doherty amplifier is described in a more recent U.S. patent no. 5,420,541 entitled 'Microwave Doherty amplifier" to Upton et al. In the prior art Doherty amplifier, the "normal" power amplifier amplifies a signal from 0 power to 1/4 the peak power level, achieving maximum class-B efficiency at that power level. The peak power amplifier then begins to contribute to the output power and by reducing the effective load impedance seen by the "normal" power amplifier, enables it to generate a greater power output up to half the peak power level. The peak power amplifier also generates half the peak power level so that the two amplifiers jointly produce the desired peak power level. The "peak" power amplifier in this prior art is not operated in antiphase so as to detract from the output power level, and thereby increasing the effective load impedance seen by the "normal" power amplifier and allowing it to generate less power efficiently. Thus the "peak" power amplifier does not operate symmetrically as a "trough" power amplifier. In Proc. IRE, Vol. 23 No. 11 (1935), pages 1370-1392, entitled "High Power Outphasing Modulation ", Chireix describes producing a transmitter giving a modulated amplitude output signal by combining two constant output amplitude amplifiers with a variable phase difference so that their outputs can be varied in relative phase from additive to subtractive. The Chireix and Doherty techniques were not combined to obtain an amplifier of good linearity and high efficiency, as the Doherty amplifier relied on the two constituent amplifiers being co-phased while the Chireix amplifier relied upon them being out-of-phase. When two amplifiers are out- of-phase, they were in the prior art, preferably isolated from one another using a hybrid coupler or directional coupler to combine them. The directional coupler combines the two amplifier's output signals to produce a sum signal and a difference signal, the sum signal being used as the desired output and the difference signal being terminated in a dummy load. Since all the amplifier power ends up at either the sum - 4 - or the difference port and is not reflected to either amplifier, the amplifiers are isolated from one another and do not affect each other's load line. In U.S. Patents No.'s 5,568,088, 5, 574, 967, 5,631,604, and 5,638,024 to applicant Dent, all entitled "Waste Energy Control and Management in Power Amplifiers", various arrangements of coupled power amplifiers are disclosed in which a varying amplitude signal may be produced using constant amplitude power amplifiers. In one arrangement, two constant power amplifiers are driven with a relative phase shift as in Chireix such that their outputs add more or less constructively or destructively to produce a varying output. The amplifiers were coupled at their outputs using a hybrid coupler or directional coupler which forms both a sum signal and a difference signal. An improvement over the prior art described therein comprises recovering the normally wasted energy at the difference port using a rectifier circuit. The Doherty patent, the Chireix paper and the above referenced Dent patents are hereby incorporated by reference herein. In applicant's 1964 graduate thesis project, an amplifier was built and reported in which the value of Vcc was selected to be either Vcc or 0.7 Vcc based on whether the desired output amplitude was greater or less than 0.7 Vcc. With a pure sine wave drive, this raised the peak efficiency from the theoretical value of π/4 (-78.5%) for a class-B amplifier to 85.6% for the new amplifier, termed class-BC. The efficiency at half maximum output power was now 78.5% instead of 55% for class-B. The Vcc selection was effected by using a first pair of transistors connected to the 0.7 Vcc supply to supply load current when the output amplitude was less than 0.7 Vcc, and a second pair of transistors connected to the full Vcc supply for supplying the load current for amplitudes between 0.7 Vcc and Vcc. Diodes were used to protect the first pair of transistors by preventing reverse current flow when the output amplitude was driven above their supply voltage. The above arrangement worked well for audio frequencies where diodes turn on and off sufficiently fast, but may not be effective for microwave frequencies. Also in the 1960's, many so called "class-D" or pulse-width modulation amplifiers were proposed and manufactured. Pulse-width modulation amplifiers switched the output devices on and off at a high frequency with a mark-space ratio proportional to the instantaneous desired signal waveform. A low-pass output filter - 5 - smoothed the switching signal to reject the high switching frequency and to produce the mean of the varying mark-space ratio signal as the desired output signal waveform. A disadvantage of the class-D amplifier was the need to switch the output devices at a very much higher frequency than the desired signal to be amplified, which may not be practical when the desired signal is already a high frequency signal such as a microwave signal. The above survey indicates that many techniques have been used in order to improve the efficiency of power amplifiers. However, notwithstanding these techniques, there continues to be a need for power amplifiers that can operate at high efficiencies at maximum output, and also at outputs that are below maximum output. Moreover, it is desirable for high efficiency power amplifiers to operate with high frequency signals, such as are used in wireless communication systems. Conventional DC-to-AC power converters include square wave inverters, modified sinewave inverters and true sinewave inverters. Square wave inverters convert DC-to-AC power, but their square- wave output signal waveform may contain large amounts of odd harmonic energy. Certain electronic devices do not operate efficiently when large harmonic content is present in the output waveform. For example, radio or audio interference may occur when attempting to power a radio or TV set from such an inverter. An additional problem with square wave inverters is that the peak and rms values of the waveform generally do not have the same ratio of v2 as in a conventional sinewave supply. Certain loads, such as lamps, only require that the RMS value of a power source should be correct. However, other loads including transformer-rectifier arrangements, may operate correctly only if the peak voltage level is correct. Therefore, all loads may not operate correctly from a square waveform. The above problems may be partly overcome by using a modified sinewave inverter. A modified sinewave inverter is generally a modified square wave inverter, modified to produce a 3 -level output waveform of levels +Vpeak, 0, -Vpeak, 0...in repetitive sequence. Introduction of the 0-level for a properly chosen proportion of the time allows the waveform to have the same peak-to-rms ratio as a sinewave, thus extending the range of apparatus designed for sinewave operation that can be correctly powered by the inverter. However, the odd harmonic content of the - 6 - waveform may increase in this case, and loads such as motors that are less efficient when large harmonic content is present may still not function efficiently. Thus, there was still a need in the prior art for "true sinewave" inverters. A true sinewave inverter can be made using a class-B linear amplifier to amplify a sinewave signal to a high power level. However, such an amplifier may achieve a maximum DC-to-AC power conversion efficiency of π/4 or 78.5% even using ideal components. Another prior art means to produce a true sinewave inverter comprises using square-wave switching devices in conjunction with inductor- capacitor filtering to remove harmonics, thereby converting the square switching waveform to a sinusoidal output waveform. However, inverters based on filtering may require very large filtering components and may suffer from poor voltage regulation when loaded by different amounts. Other prior art true sinewave inverters have been reported in which several square- wave inverters operating at, for example the line frequency, 3 x the line frequency, 5 x the line frequency, etc. have their outputs combined such that the odd harmonic content cancels. Such converters can achieve high efficiency but may be limited in the accuracy of the waveform. They are also generally adapted to convert DC-to-AC power only for a particular waveform, and not for a general waveform such as an audio or radio signal. It is also known to use a digital-to-analog (D/A) converter as a waveform synthesizer, where the input waveform is a digital waveform. A well known type of D/A converter is a weighted-resistor D/A converter. The weighted resistor D/A converter uses resistor values that are weighted, so that their resistances are inversely proportional to the numerical significance of the corresponding binary digit. The resistors are coupled to a load by a corresponding plurality of switches. The switches may be field effect transistors or complementary bipolar transistors. See pages 494- 516 of "Digital Integrated Electronics" by Taub and Schilling, 1977. Notwithstanding all of the above approaches, there continues to be a need for waveform synthesizers that can synthesize waveforms at high efficiency. - 7 - Summary of the Invention It is therefore an object of the invention to provide improved power amplifiers and amplifying methods. It is another object of the present invention to provide power amplifiers and amplifying methods that are capable of high efficiency. It is yet another object of the present invention to provide power amplifiers and amplifying methods that are capable of high efficiency at high frequencies. It is still another object of the present invention to provide power amplifiers and amplifying methods that are capable of high efficiencies at levels below their maximum output power. These and other objects are provided, according to the present invention, by coupling two amplifiers that are driven using Chireix outphasing modulation to one another, so that the amplifiers affect each other's effective load line. The two amplifiers can thereby maintain efficiency over a wider dynamic range than in a conventional Doherty amplifier. More specifically, the invention provides apparatus that amplifies an AC input signal of varying amplitude and varying phase using a DC power supply. The apparatus includes a converter that converts the AC input signal into a first signal having constant amplitude and a first phase angle and into a second signal having constant amplitude and a second phase angle. A first amplifier amplifies the first signal, and a second amplifier amplifies the second signal. A coupler couples the first and second amplifiers to one another and to a load impedance, such that voltages or currents in the first amplifier become linearly related to voltages or currents in the second amplifier. In one embodiment, described in detail below, the coupler comprises at least one transformer that serially couples the first and second amplifiers to one another and to the load impedance. In another embodiment, the coupler comprises first and second quarter wave transmission lines that couple the respective first and second amplifiers to one another and to the load impedance. According to another aspect of the present invention, the first and second amplifiers are first and second bilateral amplifiers, such that current flows from the first and second amplifiers to the DC power supply during part of the signal cycle of - 8 - the AC input signal, to thereby return energy to the DC power supply. Further increases in efficiency may thereby be obtained. Accordingly, two coupled amplifiers driven using the outphasing modulation of Chireix can operate identically and can symmetrically affect each other's effective load line so as to efficiently generate both peak and trough power levels and maintain efficiency over a wider dynamic range than in a Doherty amplifier. When the two amplifiers that are not in phase affect each other's load line, current flows from the DC source to the load during part of the signal waveform cycle and flows to the source for another part of the cycle. The mean power consumption from the source can be reduced in the same ratio as the load power is reduced, thus maintaining efficiency. In the Chireix and Doherty disclosures, vacuum tubes of that era were not able to conduct in the reverse direction to return current to the source. In contrast, in the present invention, two amplifiers constructed using bilateral devices are driven by two, separate, preferably digitally synthesized waveforms and their outputs are combined, for example using transformers or two quarter wave lines connected to a harmonic short circuit. Using the invention, the linearity advantage of Chireix may be obtained together with an even greater efficiency improvement than Doherty' s technique. A first embodiment of a power amplifier according to the present invention, amplifies an AC input signal of varying amplitude and varying phase, to produce an amplified output signal voltage and an output current in a load impedance using a DC power supply. The power amplifier includes means for converting the AC input signal into a first signal having constant amplitude and a first phase angle and into a second signal having constant amplitude and a second phase angle. The power amplifier also includes first means for amplifying the first signal, to produce a first output signal voltage of constant voltage amplitude. The first amplifying means includes bilateral amplifier devices that draw current from the DC power supply and supply current to the DC power supply. Second means for amplifying the second signal to produce a second output signal voltage of constant voltage amplitude is also included. The second amplifying means includes bilateral amplifier devices that draw current from the DC power supply and supply current to the DC power supply. - 9 - Means for serially coupling the first and second output signal voltages to the load impedance are also provided, such that the sum of the first and second output signal voltages produces the amplified output signal voltage across the load impedance, and produces the output current through the load impedance, and such that an amplifier current that is linearly related to the output current flows into the bilateral amplifier devices of both the first and second amplifying means. Preferably, during part of the signal cycle of the AC input signal, current flows from the first and second amplifying means to the DC power supply, to return energy to the DC power supply. The converting means preferably comprises a quadrature oscillator and first and second quadrature modulators that are coupled to the quadrature oscillator, to produce the first and second signals, respectively. The converting means also preferably comprises a quadrature signal generator that is coupled to the first and second quadrature modulators, and that is responsive to the AC input signal to generate in-phase and quadrature signals. The quadrature signal generator may be a digital signal processor. Moreover, the converting means itself may be implemented using a data processor. Alternatively, the converting means may be implemented using a digital frequency synthesizing circuit including phase modulation capability, such as a direct digital frequency synthesizer. In the above-described embodiment, the serial coupling means preferably comprises at least one transformer. The at least one transformer comprises a first transformer including a first primary and a first secondary, and a second transformer including a second primary and a second secondary. The first output signal voltage is coupled to the first primary, and the second output signal voltage is coupled to the second primary. The first and second secondaries are serially connected across the load impedance. In another embodiment of the present invention, means for coupling the first and second output signal voltages to the load impedance is provided, such that a voltage proportional to the sum of the first and second output signal voltages produces the amplified output signal voltage across the load impedance and produces the output current through the load impedance, and such that an amplifier current that is linearly - 10 - related to the output current flows in the bilateral amplifier devices the first and second amplifying means. In contrast with the coupling means described above, the coupling means of this embodiment need not serially couple the two amplifiers to the load impedance. Rather, the coupling means preferably comprises a first quarter wavelength transmission line that couples the first output signal voltage to the load impedance, and a second quarter wavelength transmission line that couples the second output signal voltage to the load impedance. The load impedance preferably includes an input node and the coupling means preferably comprises means for coupling the first output signal and the second output signal to the input node via the first and second quarter wavelength transmission lines. Thus, the same current may be forced to flow in both power amplifiers, scaled by any impedance differences between the quarter wavelength transmission lines. According to another aspect of the present invention, an input signal of varying amplitude and varying phase is converted into more than two signals of constant amplitude and controlled phase. Each of the more than two signals of constant amplitude and controlled phase is then separately amplified in separate amplifiers. The separately amplified more than two signals of constant amplitude and controlled phase are then combined to produce an output signal that is an amplification of the input signal at the desired power level. When converting the input signal into more than two signals, the phase of each of the more than two signals of constant amplitude and controlled phase is controlled to produce the output signal that is an amplification of the input signal at the desired power level. In a preferred embodiment, the more than two signals of constant amplitude and controlled phase are four signals of constant amplitude and controlled phase. The four signals of constant amplitude and controlled phase preferably are a first pair of signals of constant amplitude and controlled phase that combine to produce a first complex part of the output signal and a second pair of signals of constant amplitude and controlled phase that combine to produce a second complex part of the output signal. The phases of the first pair of signals of complex amplitude and controlled phase preferably are controlled to vary in a counter-rotating manner to produce the first complex part of the output signal. The phases of the second pair of signals of - 11 - complex amplitude and controlled phase preferably are controlled to vary in a counter-rotating manner to produce the second complex part of the output signal. Saturated power amplifiers are preferably used to separately amplify each of the more than two signals of constant amplitude and controlled phase. In one embodiment, combining takes place by series-combining the separately amplified more than two signals of constant amplitude and controlled phase to produce an output signal that is an amplification of the input signal at the desired power level. Series-combining may take place by using more than two transformers each having a primary winding and a secondary winding. A respective primary winding is coupled to a respective one of the more than two amplifiers. The secondary windings are serially coupled to produce an output signal that is an amplification of the input signal at the desired power level. Alternatively, more than two quarter wavelength transmission lines may be used to combine the signals from the more than two amplifiers. Each transmission line has first and second ends. A respective first end is coupled to a respective one of the more than two amplifiers. The second ends are coupled together to produce an output signal that is amplification of the input signal at the desired power level. Quarter wavelength transmission line equivalent networks also may be used. For example, Pi-networks including capacitors and inductors may be used. The phase of each of the more than two signals may be controlled by phase modulating, and preferably by quadrature modulating, each of the more than two signals of constant amplitude and controlled phase to produce the output signal that is an amplification of the input signal at the desired power level. Phase modulating preferably takes place using a separate phase locked loop for each of more than two signals of constant amplitude. According to another aspect of the present invention, a signal of varying amplitude and varying phase is generated from a plurality of constant amplitude varying phase signals, the sum of which is the signal of varying amplitude and varying phase. An IQ waveform generator generates a cosine carrier modulation waveform I(t) and a sine carrier modulation waveform Q(t) from the signal of varying amplitude and varying phase. A function generator generates a complimentary waveform Q'(t) from the cosine carrier modulation waveform I(t) such that the sum of - 12 - squares of I(t) and Q'(t) is constant. A first modulator modulates a cosine carrier signal with I(t) to obtain a first modulated cosine carrier. A second modulator modulates a sine carrier signal with Q'(t) to obtain a first modulated sine carrier. A circuit such as a butterfly circuit forms the sum and difference of the first modulated cosine carrier and the first modulated sine carrier to obtain the constant amplitude varying phase signals. A second function generator generates a complimentary waveform I'(t) from the sine carrier modulation waveform Q(t) such that the sum of squares of I'(t) and Q(t) is constant. A third modulator modulates a cosine carrier signal with I'(t) to obtain a second modulated cosine carrier. A fourth modulator modulates a sine carrier signal with Q(t) to obtain a second modulated sine carrier. A second circuit such as a second butterfly circuit forms the sum and difference of the second modulated cosine carrier and the second modulated sine carrier to obtain a second set of constant amplitude varying phase signals. Accordingly, the present invention combines more than two constant amplitude, varying phase vectors to obtain a given resultant vector, the combined vectors being of more slowly varying phase. In one aspect, four constant amplitude power vectors are combined. A first pair of signal vectors is generated, amplified and combined to produce a constant phase, varying amplitude vector, representing the real part of the desired resultant. A second pair of signal vectors is generated, amplified and combined to produce a second, constant phase, varying amplitude vector representing the desired imaginary part of the resultant, i.e. a vector at right angles to the real part. Each of the four constant amplitude vectors therefore may be limited in the rate of its required phase variation, allowing the use of lower phase locked loop bandwidths. A preferred implementation uses a first quadrature modulator comprising a cosine and a sine or I and Q modulator to generate an amplitude modulated cosine carrier signal and an amplitude modulated sinewave carrier signal. The modulated cosine and sine signals are then both added and subtracted to generate two counter- rotating, constant-amplitude vectors whose resultant sum is a cosine signal of amplitude equal to a desired real part. The desired real part is the I-modulation applied to the cosine modulator. The Q-modulation is the square root of (l-I 2 ), which - 13 - ensures constant amplitude for both I+jQ and I-jQ. A second quadrature modulator modulates a sine carrier with the desired imaginary or Q part of the desired resultant signal while modulating a cosine carrier with the square root of (1-Q 2 ), thus ensuring that, after forming jQ+I and jQ-I, they are both counter-rotating constant amplitude vectors the sum of which is the desired imaginary part. The four constant-amplitude vectors are then power-amplified, for example by using four phase locked loops to transfer the four varying phases to the output of respective power amplifiers at a desired final frequency for transmission. Any number of constant-amplitude, varying-phase vectors greater than two, for example three, may be generated in such a way that their resultant sum is a desired varying amplitude, varying phase vector. The desired varying amplitude, varying phase vector has two components specified, being the real and the imaginary part respectively. However, the combination of more than two constant amplitude vectors provides excess degrees of freedom, which may be used according to the invention to choose a solution which can reduce and preferably minimize the maximum rate of change of phase of any vector. This solution may be computed by digital signal processing, either in real time, or alternatively, for digital modulations, can be computed off-line for various combinations of successive modulation symbols and stored in a look-up table for use later in generating signals in real time. Amplification systems and methods may be provided. According to another aspect of the invention, waveform synthesizers represent an input waveform as a sequence of numerical codes in a number base, each numerical code comprising a plurality of digits ordered by place significance. A plurality of bilateral amplifiers is provided, a respective one of which is associated with a respective one of the digits. The bilateral amplifiers consume current from the DC power supply and return current to the DC power supply based on the value of the associated digit, to thereby generate an output voltage level that is proportional to the value of the associated digit. The output voltage levels of the plurality of bilateral amplifiers are serially coupled to the load, with a weighting that is based upon the place significance of the associated digit. Waveform synthesizers that are so constructed are capable of theoretical efficiencies of 100% for any signal waveform. These waveform synthesizers may be used efficiently to amplify to a transmit power - 14 - level a radio signal that varies in amplitude as well as phase. These waveform synthesizers may also be used as a DC-to-AC converter having a sinusoidal output waveform. In a preferred embodiment of the present invention, the output voltage levels of the plurality of bilateral amplifiers are serially coupled to the load using a plurality of transformers, each having a primary and a secondary. A respective primary is coupled to a respective one of the bilateral amplifiers. The secondaries are serially coupled to the load. The primary-to-secondary turns ratios of the plurality of transformers are proportional to the place significance of the associated digit. As described above, the present invention preferably uses bilateral amplifiers. The bilateral amplifiers may use field effect transistors that conduct bilaterally from source-to-drain and from drain-to-source. Alternatively, bipolar transistors including reverse conduction diodes may be used. These bipolar transistors conduct in a forward direction through the bipolar transistor and in a reverse direction through the reverse conduction diodes. Other bilateral amplifying devices may also be used. The input waveform may be a DC input waveform to provide a DC-to-AC power converter, the output waveform of which is approximately sinusoidal. Alternatively, the input waveform may be an AC input waveform, to provide a power amplifier that is capable of high efficiency. A digital input waveform may also be used. The present invention is not confined to base 2 input waveform representations. The number base may be binary, so that the plurality of bilateral amplifiers can comprise a plurality of square wave inverters. However, the number base may also be ternary, wherein the plurality of binary amplifiers comprise a plurality of square wave inverters with zero clamping, to generate positive, zero and negative output voltage levels. According to yet another aspect of the present invention, at least one linear amplifier is also included that is associated with at least two of the least significant digits. The linear amplifier generates a linear output voltage that is proportional to the combined values of the at least two of the least significant digits. The linear output voltage is also serially coupled to the load along with the remaining bilateral amplifiers. - 15 - Brief Description of the Drawings Figure 1 graphically illustrates vector addition of two constant envelope signals. Figure 2 is a block diagram of a conventional power amplifier using quadrature modulators and a pair of isolated power amplifiers. Figure 3 is a block diagram of a first embodiment of power amplifiers according to the present invention. Figure 4 is a block diagram of a second embodiment of power amplifiers according to the present invention. Figure 5 is a block diagram of a third embodiment of power amplifiers according to the present invention. Figure 6 is a circuit diagram of current and voltage relations in a power amplifier that uses bilateral devices. Figure 7 is a block diagram of a fourth embodiment of power amplifiers according to the present invention. Figure 8 is a block diagram of a fifth embodiment of power amplifiers according to the present invention. Figure 9 graphically illustrates synthesis of a complex vector using four constant magnitude vectors according to the present invention. Figure 10 is a block diagram of systems and methods for defining an input signal of varying amplitude and varying phase to a desired power level using more than two signals of constant amplitude and controlled phase according to the present invention. Figure 11 is a block diagram of a four-phasor modulator of Figure 10. Figure 12 is a block diagram of systems and methods for filtering a phase modulated signal using phase locked loops according to the present invention. Figure 13 is a block diagram of another embodiment of systems and methods for defining an input signal of varying amplitude and varying phase to a desired power level using more than two signals of constant amplitude and controlled phase according to the present invention. - 16 - Figures 14a and 14b are circuit diagrams of bilateral devices that can be used with the present invention. Figure 15 is a circuit diagram of waveform synthesis by series connection of bit weighted, square wave inverters according to the invention. Figure 16 graphically illustrates synthesis of a sinewave using 8-bit waveforms. Figure 17 is a schematic of a ternary synthesis stage according to the present invention. Figure 18 is a circuit diagram of waveform synthesis using a square wave inverter for the most significant bit and a linear amplifier for the remaining bits, according to the invention. Detailed Description of Preferred Embodiments The present invention now will be described more fully hereinafter with reference to the accompanying drawings, in which preferred embodiments of the invention are shown. This invention may, however, be embodied in many different forms and should not be construed as limited to the embodiments set forth herein; rather, these embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the scope of the invention to those skilled in the art. Like numbers refer to like elements throughout. Moreover, each embodiment described and illustrated herein includes its complementary conductivity type embodiment as well. Figure 1 shows how a varying amplitude vector can be constructed by adding two constant amplitude vectors with correct relative phasing, as first proposed by Chireix in his 1935 paper. The inner circle indicates maximum amplitude for one power amplifier, and the outer circle indicates maximum amplitude for two equal power amplifiers. As shown, the desired amplitude is A(t) and the desired phase is φ(t). This may be obtained using first in-phase and quadrature signals II and Ql and second in-phase and quadrature signals 12 and Q2, where Il=COS(φ- ), Ql=SIN(φ-α), I2=COS(φ+α), and Q2=(φ+α), where α=arcos(A/2). In that era, Chireix did not have the benefit of modern digital signal processing technology to accurately generate the two out-phased signals. A modern - 17 - implementation using two quadrature modulators 202, 204 driven by digitally synthesized vector waveforms II, Ql, 12, Q2 and a quadrature oscillator 206 is shown in Figure 2. The output of the two power amplifiers 212, 214 each being for example, a class-C amplifier of power Pmax/2, can be added using a hybrid or -3dB directional coupler 220 (coupling factor "k" = 0.7071). A hybrid or directional coupler 220 effectively produces a sum and difference signal. Terminating the difference port and the sum port with like impedances gives isolation between the two power amplifiers so that power (voltage or current) from one does not reach the other. The sum signal rises to Pmax when both amplifiers are driven in phase, and falls to zero when they are driven 180 degrees out of phase. In between, the power is Pmaχ-cos 2 (α) where ' ' is the relative phasing. The difference output is Pmax-sin (α) and the sum of the outputs is thus always Pmax. When the desired output P(t) is less than Pmax, the difference Pmax-P(t) comes out the difference port and is normally lost. The average efficiency in this case may be even worse than that calculated above for class-B, as the battery current does not reduce when the output is less than Pmax. On the other hand, there is a possibility that constant envelope amplifiers can be constructed in practice with higher efficiency (at Pmax) than amplifiers with a linearity requirement, so that in practice an advantage may be obtained. However, even if a class-C efficiency of 100% could be obtained, the arrangement would only give 50% efficiency with a peak- to-mean power ratio of 3dB, and 25% with a peak-to-mean ratio of 6dB. To help the efficiency, applicant proposed in the above-incorporated Dent patents to recover the energy normally dissipated at the difference port of the output coupler. A waste energy recovery rectifier 222 is used to rectify the dissipated energy and feed the DC current back to the battery. It is known that very efficient rectifiers can be made even at microwave frequencies, as research on wireless power transmission using microwaves has demonstrated. For digital modulation signals, it is known that the number of different I and Q waveforms that are needed over a data bit interval can be limited to two to the power of a small number of bits surrounding the current bit, because data bits further removed from a current data bit have negligible effect. Thus the waveforms II, Ql, 12 - 18 - and Q2 may be precomputed for all two to the power N combinations of nearby bits and stored in memory, and recalled when needed. In that way, the need to compute arc-cosines in real time may be avoided. Referring now to Figure 3, a power amplifier 300 according to the present invention is described. Power amplifier 300 amplifies an AC input signal 332 of varying amplitude and varying phase to produce an amplified output signal voltage and an output current in a load impedance R 326 using a DC power supply VCC 328. It will be understood that the load impedance 326 may be an antenna and the DC power supply 328 may be a battery. Still referring to Figure 3, the power amplifier 300 includes converting means 330 for converting the AC input signal 332 into a first signal 306 having constant amplitude and a first phase angle and into a second signal 308 having constant amplitude and a second phase angle. Converting means 330 may be formed by a digital signal processor (DSP) 334 that generates II, Ql, 12 and Q2 signals. First and second quadrature modulators 302, 304 respectively, are responsive to a quadrature oscillator 310 and to the in-phase and quadrature signals II, Ql, 12, Q2 to produce the first signal 306 and second signal 308. The design and operation of converting means 330, and the individual components thereof, are well known to those having skill in the art and need not be described further herein. Still referring to Figure 3, a first amplifier 312 amplifies the first signal 306, to produce a first output signal voltage SI (316) of constant voltage amplitude. As will be described in detail below, the first amplifier 312 preferably includes bilateral amplifier devices that draw current from the DC power supply, but that also supply current to the DC power supply. Accordingly, the connection between first amplifier 312 and DC power supply 328 is shown to be bidirectional. Still referring to Figure 3, a second amplifier 314 amplifies the second signal 308 to produce a second output signal voltage of constant voltage amplitude S2 (318). As was described above, the second amplifier 314 also preferably includes bilateral amplifier devices that draw current from the DC power supply and supply current to the DC power supply. Amplifiers 312 and 314 may be class-C power amplifiers, although other classes of power amplifiers may also be used. Still referring to Figure 3, a coupler 320 couples the first and second - 19 - amplifiers 312 and 314 to each other and to the load impedance 326 such that the voltage or current in the first amplifier become linearly related to the voltage or current in the second amplifier. Coupler 320 may be contrasted from a directional coupler that was used in a conventional Chireix circuit. In particular, the coupler 320 does not isolate the first and second amplifiers from one another. Rather, it interactively couples the first and second amplifiers to one another, so that each affects the other's load line. In Figure 3, the coupler 320 comprises a first transformer 322 and a second transformer 324. Their respective secondaries 322b and 324b are serially coupled across a load impedance 326. Their respective primaries 322a and 324a are coupled to the outputs 316 and 318 of first and second amplifiers 312 and 314 respectively. Accordingly, the sum of the first and second output signal voltages SI and S2 produces the amplified output signal voltage across the load impedance 326 and also produces the output current through the load impedance. An amplifier current that is linearly related to the output current flows in the bilateral amplifier devices of both the first and second amplifiers 312 and 314. The transformers 322 and 324 facilitate the series coupling of outputs that are relative to ground. The series coupling can ensure that the same current, equal to the load current or a scaled value thereof, flows in the output circuits of both amplifiers 312 and 314. By omitting the output coupler of Figure 2, which isolated the two amplifiers from each other, the amplifiers are now allowed to affect or interact with each other. In particular, when the two amplifiers are driven out of phase so that output signal SI equals -S2, the sum of their outputs into load impedance RL will be zero and there will be no load current. Therefore, the current flowing in the amplifier devices will also be zero due to the series connection, which ensures that both amplifier currents and the load current are the same. If no current flows in the amplifier devices, the current consumed from the DC supply voltage Vcc will also be zero. Thus in contrast to the coupled power amplifiers of Figure 2, which consume a constant amount of power from the supply even when the instantaneous load power is zero, the arrangement of Figure 3 can reduce its current consumption as the instantaneous output power is reduced. - 20 - Referring now to Figure 4, a second embodiment of power amplifiers according to the present invention is shown. As shown in Figure 4, power amplifier 400 is similar to power amplifier 300 of Figure 3. However, the interactive coupler 320' that couples the first and second amplifiers 312 and 314 to the load impedance 326 is embodied by first and second quarter wavelength transmission lines 422 and 424 respectively. The load impedance includes an input node 440, and the first and second quarter wavelength transmission lines 422 and 424 are preferably coupled to the input node 440. As illustrated in Figure 4, series connection at microwave frequencies may be more practically achieved by parallel connection a quarter wave distant, using the two quarter wave lines 422 and 424. When the outputs of the two quarter wave lines are paralleled, the output voltages are forced to be the same (Vo) at the input node 440. This forces the currents to be the same quarter- wave away at the power amplifiers 312 and 314, if the lines are of equal impedance, creating the same conditions as in the series connection of Figure 3. If the transmission lines are of different impedance 201, 202, the power amplifier output currents II and 12 are forced to be scaled in the inverse ratio of the impedances. The power amplifiers ideally each generate an output swing of Vcc at their ends of their quarter wave lines. Since the voltages are the same at that end, the currents at the other end one quarter wave away must be equal with equal lines. With unequal line impedances, the currents will be respectively Vcc/Zol and Vcc/Zo2 at the junction of the lines. The total output current is thus Io = Vcc (1/Zol + l/Zo2) or 2Vcc/Zo for equal lines. If the power amplifiers generate relatively phased currents Vcc-EXP(j ) and VccΕXP(-jα), then the total output current is: /' / (TE;YXPPC(;j«α , )I + C EYXPP/('--j;«α\)\ Io = VCC Zo Zo = 2Vcc - Cos(α)/Zo, assuming equal impedance Zo lines. The voltage Vo is thus given by: τ „ 2VCC - R I Cos(α) Io - R, = - ^ L L Zo - 21 - This in turn forces the power amplifier currents to be: 2Vcc - R L Cos(α) Zo 1 showing that the peak current in each power amplifier has reduced by Cos(α), which it did not do in the case of hybrid coupling. When α=90 degrees, the power amplifiers are antiphased, the output signals Vo, Io are zero, but so is the power amplifier current even though they are still driven to full Vcc output swing. It is as if the load impedance had been increased to infinity. Thus, by modulating a (in the DSP code), the effective load impedance seen by the power amplifiers is also modulated so that they generate only the instantaneously desired output power To obtain maximum efficiency, it is desirable to avoid harmonic currents flowing in the power amplifier output circuits. This may be obtained using a series resonant circuit in series with the power amplifier output terminal to present a low impedance to the fundamental and a high impedance to harmonics. However, a single shunt resonant circuit 550 may instead be connected one quarter wave away at the node of the two quarter wave lines, as shown in amplifier 500 of Figure 5. The shunt resonator forces the voltage waveform to be sinusoidal at the junction of the lines (node 440), and therefore one quarter wave away the current at the power amplifier devices is forced to be sinusoidal. As described above, the first and second amplifiers 312 and 314 respectively preferably include bilateral amplifier devices that draw current from the DC power supply 326 and supply current to the DC power supply. Accordingly, during part of the signal cycle of the AC input signal 332, current flows from the first and second amplifiers to the DC power supply to return energy to the DC power supply. Figure 6 illustrates a power amplifier including bilateral amplifier devices according to the present invention. As shown in Figure 6, power amplifier 312 includes a P-type field effect transistor 602 and an N-type field effect transistor 604 that are respectively coupled between positive and negative power supplies 328a and 328b respectively. Input signal 332 is coupled to the P-type field effect transistor 602 and the N-type field effect transistor 604. These field effect transistors produce an output signal that is provided to the quarter wavelength line 422. Similar considerations apply to second - 22 - amplifier 314. When α is between 0 and 90 degrees, the sinusoidal current in the power amplifier devices is not in phase with the switching of the devices on and off, as illustrated in Figure 6. As also shown in Figure 6, the mean current from the power supplies is reduced by a further factor of cos( ) relative to the peak current Ipk. Since Ipk also reduces with cos( ), the net supply current reduces as cos 2 ( ), which is the same factor by which the output power is reduced by modulating . The supply power and load power both therefore track, maintaining the same theoretical efficiency when backed off as when not. This relies on the use of bilateral power amplifier devices which can pass current in the reverse direction during part of the input signal cycle, returning energy to the battery. That the theoretical efficiency using ideal bilateral devices is 100% may be understood in the context of a single ended push-pull output stage, as shown in Figure 6. In region "a" from 0 to (π-α), the current flows from -Vcc/2 to the load, while the N-type device is on, pulling down. This is delivering energy from -Vcc/2 source 328b to the load. In region "b", current is still negative, but the P-type device is on. That means current and energy are flowing back towards the +Vcc/2 source 328a. In region "c", current is flowing from the Vcc/2 328a source to the load while the P-type device is on, and in region "d", current is still negative when the N-type device comes on, sending current and energy back to the -Vcc/2 source 328b. The mean currents are thus: Ipk j sin(θ )δθ - Jsin(θ )δθ I pk cos(α)/π 2π o o from each of the -Vcc/2 and +Vcc/2 supplies, that is reduced by the factor cos( ) compared to an in-phase current. In Figure 6, the mean supply currents from the split supplies -Vcc/2 and +Vcc/2 are computed to be Ipk/π when α=0. The total power from both supplies is therefore: Ipk-Vcc/π. (1) The square-wave voltage swing at the single-ended power amplifier output is -Vcc/2 to I-Vcc/2 i.e. Vcc/2 peak, so the current at the end of a quarter wave line of impedance Zo must be a square wave of peak current +/- Vcc/2Zo. The fundamental - 23 - component of a square wave is 4/π times the peak, so the fundamental current driving the resonator of Figure 5 is: 2Vcc ... — —peak (2) π - Zo The current induces a peak load voltage of: 2Vcc.R L (3) π - Zo The load power is thus 1/2 x peak current x peak voltage: _ 2Vcc 2 - R L (4) (π • Zo) 2 Equation (3) gives the sinusoidal voltage swing on the resonator at the end of the quarter wave line. Thus, the current at the power amplifier device end of the line is this divided by Zo, i.e.: 2Vcc - R, Ipk = 7 2 L (5) π - Zo Substituting for Ipk from equation (5) into equation (1) gives the total DC input power as: 2Vcc 2 - R τ = 7 L (6) (π • Zo) 2 which is the same as equation (4), showing that the efficiency is 100% It is well known that a switch-mode inverter with lossless filtering to convert a square- wave to a sine-wave output gives theoretical 100% efficiency. However, in the arrangement of Figures 3 to 6, which is encapsulated in the transmitter of Figure 7, the efficiency is maintained even for signals of varying amplitude, or when the transmitter is backed off to less than full output. In Figure 7, amplifier 700 can use switch-mode (class-D) power amplifiers. The load 326 is an antenna. Thus, the present invention, which has no theoretical limitations to efficiency, is a better starting point than prior art power amplifiers, the theoretical efficiency of which is already less than 100% even with ideal devices. The present invention uses means, such as a digital signal processor (DSP) 334, to convert a complex modulation signal having a varying amplitude and a varying phase into two modulation signals having constant amplitude and differently - 24 - varying phases. It then uses means to produce two signals modulated by respective phase modulation signals. One means has been illustrated in Figure 2, namely the use of two quadrature modulators 302, 304 driven respectively by the cosine and sine of their respective phase modulation signals. Another technique is shown in Figure 8 wherein two frequency synthesizers, each modulatable in phase, such as modulatable fractional-N synthesizers 802 and 804 are used. A modulatable fractional-N synthesizer comprises an accumulator whose value determines the phase of an oscillator 812, 814 controlled by the synthesizer. Normally in a fractional-N synthesizer, the accumulator augments continuously (with wraparound) by the repeated addition of a slope value, which provides a frequency offset. To change the phase, the accumulator may be additionally augmented by adding once only a value equal to the change of phase desired. This arrangement is shown in Figure 8. Using two separate fractional-N synthesizers 802, 804, the cumulative nature of the delta-phase values added may get out of step. In practice therefore, the need to maintain synchronism suggests that the two synthesizers should be combined into a single chip. Moreover, the type of synthesizer called a "reciprocal fractional-N" disclosed by applicant in U.S. Patent Application No. 08/902,836, filed July 30, 1997, assigned to the assignee of the present application, the disclosure of which is hereby incorporated herein by reference, may be advantageous, as it modulates the reference divider controlled by a fixed reference frequency, which is then easier to synchronize when two modulated synthesizers are required. Another directly phase-modulatable synthesizer technique is the Direct Digital Synthesizer or DDS, in which an accumulator computes the value of (ωt+φ) continuously and converts the most significant part to a sine wave using a sine look-up table. Any other conventional method of producing phase modulated signals can also be used with the present invention. Accordingly, a transmit power amplifier for linearly amplifying signals of varying amplitude and phase comprises a signal generator for generating a first amplifier drive signal of constant amplitude and first phase angle and a second amplifier drive signal of constant amplitude and second phase angle such that the combined signals have the desired instantaneous amplitude and phase angle of a signal to be transmitted. The first drive signal is amplified by a first power amplifier - 25 - using first active amplifier devices and the second drive signal is amplified by a second power amplifier using second active amplifier devices, the first and second amplifier devices preferably being driven to saturation. The outputs of the first and second power amplifiers are connected using two quarter wave lines each connected to respective active devices at one end and connected to a common junction at their other end. Alternatively, transformers may be used. A shunt resonant circuit at the common junction can constrain the voltage at the junction to be sinusoidal and proportional to the cosine of half the difference between the first and second phase angle. The shunt circuit can thereby constrain the peak current in the amplifier devices to be sinusoidal and proportional to the same cosine. The sinusoidal currents in the devices are also out of phase with their respective drive wave forms by plus and minus half the difference between said first and second waveform such that power is taken from a DC supply source during part of the cycle and returned by reverse conduction through an amplifier device during another part of the cycle. The mean current consumed from the DC supply source can thereby be reduced by a further factor equal to the cosine. The net power consumed from the DC source therefore can reduce in proportion to the square of the cosine and in the same ratio as sinusoidal power delivered to the load, thus maintaining the same efficiency at all reduced instantaneous amplitudes as at peak output amplitude, within the limits of practical devices. The theoretical efficiency of the present linear amplifier using ideal devices is 100% even when backed-off to reduced output levels and thus can be a better starting point for obtaining high efficiency than a prior art amplifier. For example, a class-B type has a theoretical efficiency using ideal devices of only 78.5% at full output. When the invention is to be used to generate signals that vary both in amplitude and phase, the two constant envelope amplifiers generate signals that vary in phase by the sum and difference respectively of the desired phase variation and an amplitude determining phase component. When the variation of both phase components is in the same direction, the sum phase varies faster; otherwise the difference phase varies faster. One phase thus varies faster than the other and the rate - 26 - of phase variation can become very large when the desired signal vector has a trajectory that passes close to the origin (0,0) of the complex plane. If the signal vector passes exactly through the origin, i.e. the signal amplitude goes to zero, both phase variations have finite derivatives. However, for a vector that passes infinitesimally close to the origin, the phase derivatives can be arbitrarily large. It is a potential advantage that constant amplitude signals varying only in phase can be produced using modulated phase locked loops. However, the rate of change of phase produced by a phase locked loop generally is limited by its loop bandwidth. It is desired to avoid using excessively wide loop bandwidths so that the phase locked loop helps to filter out unwanted noise and prevent wideband noise from being transmitted. However, the use of narrow phase locked loops may limit the ability to accurately reproduce complex signal vector trajectories that pass close to the origin. The present invention can resolve this design conflict and can permit the use of more desirable phase locked loop parameters without impacting the accuracy with which complex signal trajectories can be reproduced. A first aspect is described with the aid of Figure 9. Figure 9 shows synthesis of a complex vector Z by separately synthesizing its real part I and its imaginary part Q. These are each in turn synthesized by adding pairs of constant-amplitude, counter- rotating, variable-phase vectors. Thus, Figure 9 shows addition of four constant amplitude vectors, VI, V2 (which combine to yield the real part I) and V3, V4 (which combine to yield the imaginary part Q). An advantage of using a pair of vectors to synthesize only the real or the imaginary part is that the trajectory of the real or imaginary part alone must pass through the origin exactly upon changing sign. The rate at which the value passes through zero is limited by the finite bandwidth of the complex signal being synthesized. Thus, the rate of rotation of each of the four vectors VI, V2, V3 and V4 may be guaranteed to be finite when synthesizing a finite bandwidth signal. Moreover, each of the vectors only ever has to rotate through +/-90 degrees relative to a mean phase, in order to produce a real or imaginary part varying between plus the maximum and minus the maximum signal amplitude. Thus the design of phase locked loops may be eased compared to the use of only two constant amplitude - 27 - vectors, where the phase of each vector can need to rotate through the full 360 degrees and continue rotating through any multiple of 360 degrees. Figure 10 shows an arrangement of four, coupled, constant-amplitude power amplifiers 1011a, 1011b, 1011c, and lOlld according to the invention. A four- phasor modulator 1010 is fed with information on the desired signal to be transmitted, which can for example be described by the waveform of the real part I (cosine carrier component) of the complex signal and the waveform Q of the imaginary part (sine carrier component). Modulator 1010 produces four, constant amplitude, varying phase signals denoted by: e (iwt * ,) e (jwt+φ2) e 0wt+φ3) and e 0wt+φ4) where φl = ARCCOS(I); φ2 = - φl ; φ3 = 90-ARCCOS(Q) and φ4 = 180 - φ3, and "w" is the frequency of the carrier frequency signal which may be supplied at another input. Because the ARCCOS function is undefined for arguments greater than unity, the desired signal Z=I+jQ is properly scaled so that its peak amplitude never exceeds unity, and is preferably just less than unity. Scaling to a desired power level is accomplished by amplifiers 1011a lOlld. The outputs of amplifiers 1011a,1011b, corresponding to vectors VI, V2 of Figure 9, are added in series using transformers 1012a and 1012b to produce the real part I. The real part I will consist of a cosine carrier component only that is modulated in amplitude from positive amplitudes to negative amplitudes, i.e. Double-SideBand, Suppressed Carrier modulation (DSBSC). Likewise, the outputs of amplifiers 1011c, 101 Id corresponding to vectors V3, V4 of Figure 9 are added in series using transformers 1012c, 1012d to produce the imaginary part Q, which is a DSBSC modulated sine carrier component. The outputs of all transformers are then coupled in series to add I and Q to obtain the desired complex signal modulation Z = I+jQ. As disclosed in the parent application, series coupling causes the same output or load current to flow in all amplifier devices, irrespective of their voltage contribution to the total output signal. When that current is in phase with an - 28 - amplifier's voltage contribution, that amplifier is delivering power from the DC source to the load. When the amplifier's voltage contribution is in antiphase with the load current, that amplifier acts as a synchronous rectifier and returns current to the DC source, providing bilateral output devices are used. When an amplifier's voltage contribution is 90 degrees out of phase with the load current, current is consumed from the DC source during part of the AC signal cycle and returned to the DC source during the other part of the cycle, consuming no net current from the source in the mean. Thus the only mean power consumed by amplifiers 1011a.... lOlld from their common DC source (not shown) corresponds to power delivered to the output circuit or load, which therefore corresponds only to the desired signal waveform Z. The theoretical efficiency of the amplifier with ideal bilateral amplifier devices is therefore 100%, in contrast to prior art linear amplifiers that have lower theoretical efficiencies even with ideal devices. For very high frequency and microwave operation, it was disclosed in the parent application that a more practical form of series coupling can be to use parallel coupling one quarter wavelength away from the amplifiers, using quarter wave transmission lines of appropriate impedance. The choice of impedance is made to match the amplifiers to the load impedance, e.g. an antenna, for generating the desired total output power. The length of the quarter- wave coupling lines should also be shortened as necessary to compensate for the output capacitance of the amplifier devices. Quarter-wave line equivalent circuits may also be constructed with discrete inductors and capacitors, for example in a Pi-network configuration 1302, as shown in Figure 13. The first capacitor Cl of each Pi network Cl, L, C2 can absorb the output capacitance of the amplifier devices while the second capacitors C2 can be combined into a single capacitance 4C2. Such networks preferably should be designed to reflect a high impedance at the amplifiers at as many odd harmonics as possible, using additional LC components, and the amplifiers should preferably be push-pull amplifiers that suppress even harmonics of the carrier frequency. Figure 11 shows more detail of one implementation of a four-phasor modulator 1010 of Figure 10. The I signal is fed to a first balanced modulator 1101a where it multiplies a cosine carrier component to produce Icos(wt). The I signal is also fed to function generator 1100a that derives a signal Q' from I such that the sum - 29 - of the squares of I and Q' is a constant. This is achieved if the function f(x) implemented by the function generator 1100a is a vl - x 2 function. Q' is fed to a second balanced modulator 1101b where it multiplies a sine carrier component to obtain Q'sin(wt). Butterfly circuit 1102a forms both the sum and the difference of the outputs of modulators 1101a,1101b to obtain: Icos(wt) + Q'sin(wt) and Icos(wt) - Q'sin(wt), both of which have the constant amplitude Λ / TQ 7 . These two constant-amplitude drive signals correspond to vectors VI and V2 of Figure 9 and drive amplifiers 1011a and 1011b of Figure 10. The desired Q signal component feeds a similar circuit except that Q multiplies the sine carrier component in balanced modulator 1101c and the derived signal I', derived using function generator 1100b, multiplies the cosine carrier in balanced modulator llOld. Butterfly circuit 1102b then forms the sum and difference of the outputs of modulators 1101c and llOld to obtain the two constant amplitude signals Qsin(wt) + I'cos(wt) and Qsin(wt) - I'cos(wt), which correspond to vectors V3 and V4 of Figure 9, and drive amplifiers 1011c and lOlld of Figure 10. It is common to encode information for transmission and to convert coded information to baseband modulating signals I and Q using digital signal processing. I and Q may first be produced using digital signal processing as a sequence of numerical samples, which are then converted to analog waveforms by means of digital to analog (DtoA) convertors. A technique for eliminating the DtoA convertors is described in U.S. Patent Number 5,530,722 to the present inventor, the disclosure of which is hereby incorporated by reference herein. The technique involves converting the numerical I/Q sample streams to high bitrate, sigma-delta modulation, which can then be converted to analog signals by low-pass filtering. The balanced modulators 1101a, 1101b, 1101c and llOld can, for example, be of the type known as Gilbert Cells, which are easy to fabricate in semiconductor processes. The output signal from a Gilbert Cell is a balanced (i.e. push-pull) current and the output of two Gilbert cells can therefore be added by paralleling their outputs to add their output currents. Reversal of the connections of one Gilbert cell then - 30 - causes subtraction. Thus the Butterfly circuits 1102a, 1102b may be obtained by parallel coupling the outputs of Gilbert cells, using a reversal of connections to one Gilbert cell for the difference output. The current outputs from a Gilbert cell may be duplicated using current mirrors in order to obtain one balanced output for forming the sum and a similar balanced output for forming the difference. It is also known from the incorporated references that, for modulating data signals, the entire sigma- delta bitstream may be precomputed and stored in a look-up table for different, finite- length data symbol sequences and recalled by addressing the table with modulating data sequences to obtain the correct sigma-delta waveforms. One of the potential benefits of synthesizing a signal for transmission using only phase-modulated signals is that the phase modulation may be applied to an oscillator running directly at the output frequency and with a power output that is higher than that achievable from prior art quadrature modulators. Thus the power amplifier may need less gain to amplify the oscillator output and thus amplifies wideband noise less. Preventing the power amplifier from amplifying wideband noise can help avoid interference from the transmitter to a receiver in the same or in a nearby apparatus, such as a cellular telephone. The technique of first generating a phase modulated signal at a transmit intermediate frequency and then transferring that phase modulation by means of a phase locked loop to a transmit frequency VCO is further described in U.S. Patent No. 5,535,432 to the present inventor, the disclosure of which is hereby incorporated by reference and has been used in cellular phones conforming to the GSM digital cellular standard manufactured by L.M. Ericsson and sold in Europe since 1992. An application of this scheme with the present invention is shown in Figure 12. Referring now to Figure 12, the four-phasor modulator 1010' produces phase modulated signals at a transmit intermediate frequency (TXIF). A transmit frequency voltage controlled oscillator 1215a produces a signal at transmit frequency Ftx which is amplified by power amplifier 1211a. A portion of the output of oscillator 1215a is fed to downconverting mixer 1214a where it is heterodyned with a local oscillator signal of frequency Flo, which is offset from the desired transmit frequency Ftx by the TXIF, i.e. Flo = Ftx +/- TXIF. - 31 - In a cellular telephone, the local oscillator signal often is the same as already used in the receiving section, which is ensured by choosing TXIF correctly so that the transmit frequency is displaced from the receive frequency by an amount known as the "duplex spacing". The difference frequency output from heterodyne downconvertor (mixer 1214a) at a frequency TXIF is phase compared in phase detector 1213a with the phase-modulated TXIF signal from modulator 1010'. If the compared phases do not match, a phase error signal is generated by phase detector 1213a which is integrated in loop filter 1216a to produce a correcting control signal to VCO 1215a, thus controlling the phase and frequency of VCO 1215a to follow the phase modulation from modulator 1010'. The entire Phase Locked Loop phase-transfer circuit 1220a comprising elements 1213a, 1214a, 1215a and 1216a and power amplifier 1211a is replicated as 1220b, 1220c and 1220d for the other three phasor channels. Four-phasor modulator 1010' is shown in Figure 12 having a single data input rather than I and Q inputs. Thus, 4-phasor modulator 1010' is assumed to incorporate the conversion of data symbol sequences to I,Q waveforms, using, for example, precomputed look-up tables as discussed above. When the transmit output frequency is to be changed between different channels, it now suffices to change the local oscillator frequency Flo, and the generated transmit signal will change to the new channel in step with the change to Flo. A benefit of using phase locked loops to transfer the phase modulation to the output frequency is that the phase locked loop bandwidth determined by loop filters 16a....l6d need only have a bandwidth sufficient to pass the modulation accurately, and thus can help to reject wideband noise which could otherwise be amplified by power amplifiers 1211a....l211d, potentially interfering with a receiver. Another aspect of the invention will now be described that corresponds to the more general inventive principle of synthesizing a vector of variable phase and amplitude by combining more than two vectors of constant amplitude. One special case of combining four vectors was discussed in detail above with the aid of Figures 9 to 13. In that example, the vectors were combined in pairs to produce the real and the imaginary parts of the desired complex signal vector. An objective was to eliminate 32 the likelihood of large rate-of-change of phases being needed on any vector. The excess degrees of freedom available in using more than two constant amplitude vectors to synthesize a complex vector may be more generally targeted to reduce the maximum rate-of-change of phase needed for any vector. The minimum rate-of- change of phase solution would not necessarily turn out to combine two vectors to generate the real part and two vectors to generate the imaginary part, and this would not be the solution if three of five vectors were used. The general problem may be formulated mathematically as follows: Find N phase waveforms φ( 1 ) ....φ(N) such that N JΦC jT e = Z(t), a desired complex waveform k=l and the largest | φ (k) | is minimized. An alternative goal is to minimize the sum of the squares of the phase derivatives, i.e. Find N phase waveforms φ(l)....φ(N) such that N JΦC T e = Z(t), a desired complex waveform k=l N and | φ (k) | 2 is minimized. k=l The above can be restated as a standard Lagrange multiplier problem as: N . N JΦ(O Minimize ∑ | φ (k) | 2 subject to T je φ(k) = Z(t) k=l k=l Splitting the above complex equation involving Z into its real and imaginary constituent waveforms I and Q, and defining the 2 x N matrix A as: [A] = _ I cos(φl)cos(φ2) cos(φn) sin(φl) sin(φ2) sin(φ N ) the Lagrange multiplier problem has the solution: ( • \ φ l ( φ 2 Q(t) A [A.A # ]-' - /(/) Φ π - 33 The above equation is a set of N, non-linear differential equations which can in principle be solved for the N phase waveforms, given the desired complex signal waveform Z(t), in terms of its real part 1(f) and its imaginary part Q(t). Such a solution may be onerous to perform in real time, but as digital processors become ever more powerful and the real-time solution method may soon, if not already, be an economically practical implementation. The problem can be stated in discrete time steps of dt to obtain phase waveform samples in steps of dt, given the values of Z(t) at discrete steps dt as Zl=Il+jQl; Z2=I2+jQ2....etc. The values of the phases at time step number "i" can then be derived from the above differential equation to be: ^φl^j φl^ φ2 f Q ( j) -Q ( i - Ϋ φ2 = A # [A.A"]- 1 + 7(,- _i) _ /(0) y Φ N -1 where I , Q are the previously achieved values given by _ N JΦMi-1) ϊ(I-l) +j Q (I-l) = ∑e k=l The use of the previously achieved I,Q values at timestep (i-1) as the stepping-off point from which to reach the new desired I,Q values at timestep "i" can ensure that computational errors such as rounding errors in the previously achieved values are compensated by computing the step change in the phase values necessary to move from the previously achieved values, including error, to the new desired values. Thus, computational errors may be prevented from accumulating. In the above, the matrix A is computed again from the new phase values after every step. Also after every step, the new phase values are applied to a phase modulator, which can include any or all of digital to analog conversion of the phase values, filtering of the converted phase values, phase locked loops for transferring phase modulation to a desired transmitter output frequency, phase modulatable frequency synthesizers such as fractional-N synthesizers or Direct Digital Synthesizers (DDS), or alternatively reconversion of phase values to I,Q values using a Cosine/Sine function or table followed by the use of quadrature modulators to modulate each pair of I and Q values on to a desired radio frequency carrier signal to - 34 - obtain N constant amplitude signals whose sum will be the desired phase and amplitude modulated signal. When the desired modulation arises from a digital information signal, the computation can often be simplified, by utilizing the fact that the complex modulation waveform Z(t) is at each time a function of only a limited number L of past and future digital information symbols. Thus there are at each time only a limited number M of possible values of Z(t) that can arise, where M is the size of the alphabet of possible information symbols. All possible waveforms of Z(t) can thus be precomputed for all possible sequences of M symbols. Likewise, using the above equations, all possible sets of N phase waveforms can be precomputed and associated with symbol sequences in a waveform look-up table. Actual information symbol sequences are then applied to address the table to extract the precomputed phase waveforms or equivalent I,Q waveforms, thus saving on real-time computation required. One advantage of precomputation is to detect and then avoid any tendency of the matrix A. A to become singular by taking an alternative route between successive points that may temporarily depart from the minimum rate-of-change of phase solution in order to avoid the need for a greater rate of change of phase later. Accordingly, an amplitude and phase-varying signal may be generated efficiently at a power level for transmission, based on series combining (or the equivalent) more than two amplified signals of constant power level. General methods and systems for computing the required phase variations of each of the constant amplitude signals have been presented which may be used for three or more signals. Specific methods and systems for generating and combining four signals have also been presented, which may be simpler and may be a preferred solution. All variations based on the above teachings which may be made by a person skilled in the art are considered to fall within the spirit and scope of the invention as described by the following claims. The present invention uses bilateral amplifier devices that can be turned on and off, and which can pass current in either direction when turned on. Figures 14a and 14b illustrate the circuit symbols of conventional bilateral devices that are suitable for use in the invention. Figure 14a shows an N-type FET 102 including its incidental substrate diodes 104. The FET 102 becomes a low impedance to currents - 35 - flowing from either drain to source or vice versa. By connecting substrate to source, the incidental drain-substrate diode also assists in reverse current flow from source to drain. However, this connection is not necessary with an FET. Figure 14b shows a bipolar transistor 110 with a reverse conduction diode 112 added externally. When current attempts to flow in the reverse direction in a bipolar transistor, reversing the roles of emitter and collector, the reverse current gain is generally much lower than the forward current gain, such that the control current supplied to the base may have to be increased excessively in order to support the reverse current. The use of an external reverse conduction diode 112 allows reverse current to flow through the diode without relying upon the transistor's reverse current gain. Using any suitable bilateral device such as exemplified in Figures 14a and 14b, the invention may be constructed according to Figure 15. Referring to Figure 15, a synthesizing apparatus 200 according to the present invention, synthesizes an output waveform in a load R L 202 using a DC power supply Vcc 204 from an input waveform 206. Synthesizing apparatus 200 includes means, such as an analog-to-digital (A to D) converter 210 for representing the input waveform 206 as a sequence of numerical codes in a number base. Each numerical code comprises a plurality of digits ordered by place significance. In Figure 2, the representing means is a binary 8-bit analog-to-digital converter, so that the plurality of digits are bit 0-bit 7 and bit 0 - bit 7 , ordered by powers of two. Still referring to Figure 15, a plurality of bilateral amplifying means each includes a pair of bilateral devices 220a, 220a'-220n, 220n\ The bilateral amplifiers may comprise either of the bilateral devices shown in Figures la or lb or any other bilateral device. Each bilateral device 220a, 220a'-220n, 220n' consumes current from the DC power supply Vcc 204 and returns current to the DC power supply based on the value of the associated digit, to thereby generate an output voltage level that is proportional to the value of the associated digit. Finally, referring to Figure 15, means is provided for serially coupling the output voltage levels of the plurality of bilateral amplifying means to the load R L 202 with a weighting that is based upon the place significance of the associated digit. As shown in Figure 15, the serially coupling means preferably comprises a plurality of - 36 - transformers 230a-230n. Each transformer has a primary and a secondary. The secondaries are serially coupled to the load 202. A respective one of the primaries is coupled to a respective one of the bilateral amplifying means 220. The primary-to- secondary turns ratios of the plurality of transformers 230a-230n are proportional to the place significance of the associated digit. It will be understood that the designation primary and secondary is arbitrary and may be reversed. Additional description of waveform synthesizers of Figure 15 will now be provided. A signal waveform to be amplified to a high power level is fed to an 8-bit analog-to-digital (A/D) converter 210 to generate an 8-bit representation of the waveform at a plurality of sampling points in time. The sampling rate should conform to at least the Nyquist rate for the waveform of twice the maximum frequency obtained in the waveform. However, the sampling rate is preferably many times greater than the Nyquist rate to reduce the need for stringent filtering of the amplified signal to remove quantization noise. If the waveform is repetitive, as in a DC-to-AC power converter application, or comprises a limited number of variants, as in a radio transmitter for transmitting digital data, the numerical samples can be precomputed and stored in a memory, and the A/D converter 210 can then be omitted in favor of direct digital representation of an input waveform as a sequence of numerical codes. The numerical samples are a binary coded representation of the instantaneous signal voltage having a most significant bit (MSB) that represents ±0.5, a next most significant bit that represents ±0.25, a third most significant bit that represents ±0.125, etc., down to the least significant bit (LSB) which, in the case of an 8-bit converter, represents ± 1/256. When all the bits are of the same positive polarity, e.g. all binary Is, the voltage represented is 0.5+0.25+0.125....+1/256 = 255/256 which is nearly +1. Conversely, when all the bits are of negative polarity, i.e. 00000000, the voltage represented is -0.5-0.25....-1/256 = -255/256 which is nearly -1. These are normalized representations, relative to some maximum voltage. Scaling of the actual switched DC source voltage to an AC output voltage is effected with the aid of transformers 230a-230n. - 37 - The most significant bit, bit-7 is used to control a most significant inverter 220n-220n' connected to the load circuit via an N:l transformer 230n. The value of the turns ratio N is chosen to be the reciprocal of the bit weight (1/0.5 = 2 for the most significant bit) times the ratio of the DC supply voltage to the desired peak AC output voltage. The turns ratio N thus successively doubles for bits of progressively lower bit weight as shown in Figure 15 by the ratios N: 1 , 2N: 1 , 4N: 1....128N: 1 for the transformers of successively lower significance. Figure 16 shows the unfiltered output waveform and the waveforms of the individual bits when synthesizing a sinewave output using 32 time samples per cycle. In these waveforms, quadrential symmetry has been enforced by computing the 8-bit representations for the first 8 sample points and time-reversing them for the next 8. The second 16 samples are then given the code complementary to the first 16 samples. Each bit waveform thereby possesses ± symmetry, so that it will pass through a transformer. The weighted sum of the bits, i.e. the load voltage, showing the purity of the synthesized sinewave, is also shown in Figure 16, as SUM. It may be seen that the most significant bit, which can be thought of as a sign bit, changes in a square-wave fashion at the fundamental frequency. The bits of lower significance, as well as being of progressively half the voltage significance, change at a faster rate. Thus, the amount of magnetic material or copper in the output transformers of lower significance may be reduced due to both the reduced voltage and power level they have to handle and also due to the higher alternation frequency. It will be noted in Figure 16 that, while the most significant bit is always positive during the first (positive) half cycle of the sinewave output, bits of lower significance are often negative, which means that their contribution is being subtracted from the net output voltage. The inverters associated with bits that are subtracting from the magnitude of the output voltage thus have an output current flow which is in the opposite direction to the output voltage. This means that the output device of that inverter which is in the ON state is not absorbing power from the DC supply, but is returning current to the DC supply by virtue of the bilateral inverter device conducting current in the reverse direction. The operation of synthesizer 200 of Figure 15 as an audio amplifier or medium frequency radio transmitter output stage is similar to its operation as a DC- 38 AC power converter. The transformers should be properly designed to operate efficiently in the desired frequency range. Using the invention, very linear and efficient single-sideband (SSB) transmitters may be constructed, for example in the 1- 30MHz radio frequency range. It is also possible to synthesize a sinusoidal output waveform based on a sampled and ternary coded representation. A ternary coded representation comprises, for each sample, a multi-digit code, the digits of which represent either +1, 0 or -1. Digits of lower significance then have one third the weight of digits of the next highest significance. Since 3 is 243 and 2 is 256, five ternary digits can represent approximately the same purity as an 8-bit version of the invention using only 5 ternary stages. A ternary bilateral amplifier 420 is shown in Figure 17. An extra transistor 420c is connected between the ends of the transformer primary 230, compared to Figure 15. When this extra transistor is turned ON after ensuring that the other two transistors 420a and 420b are OFF, it will short circuit the primary of the transformer 230 ensuring that the voltage contribution to the output is zero; i.e. the third ternary state. The third, shorting transistor 420c should preferably be a completely symmetrical device having the same voltage handling capability and transconductance upon reversal of the roles of source and drain electrodes. The gate control voltage enabled by the control signal T2 should be greater than Vcc+V threshold in order to turn the device ON, and should be less than V t h re shoid in order to turn the device OFF. The relation between the three control signals Tl, T2, T3 and the selected ternary level is shown in the Table below, with a binary " 1 " indicating that the control voltage is at the ON level and a "0" indicating the OFF level. Table LEVEL: -1 0 +1 Tl 1 0 0 T2 0 1 0 T3 0 0 1 - 39 - Apart from reduction of the number of stages for the same waveform accuracy, ternary systems may also prevent flux build-up in transformers due to slight asymmetries (center tap position for example). In addition, the relative scaling of 3:1 in voltage between successive stages can allow a more rapid reduction in transformer size for the lower significant digits. A set of ternary control signals Tl, T2, T3 may be generated by a ternary A/D converter for an arbitrary signal to be amplified in real time. A ternary A/D converter may comprise a binary A/D converter followed by a binary-to-ternary code converter, which may be a look-up table. For a repetitive waveform, or for a limited number of waveforms such as encountered when modulating a radio signal with digital data streams, sequences of control signals Tl, T2, T3 may be precomputed and stored in memory, being recalled from memory in the proper sequence when needed using conventional Read Only Memory modulation generators. According to another aspect of the invention, all of the inverters below a given bit significance may be replaced with a linear class-B amplifier or other amplifier that generates the same contribution to the voltage waveform, albeit with lower efficiency. The loss of efficiency may be small if confined to generating the lower significant parts. For example, as shown in Figure 18, synthesizing apparatus 500 replaces all inverters except for that of greatest bit significance by a class-B amplifier 504 that is coupled to A/D converter 210 by a D/A converter 502. Transformer 230a has a turns ratio of MN:1, where M is the number base of the digital signal representation (e.g. 2 for binary and 3 for ternary). It may be shown that the theoretical efficiency drops from 100% to π/2 V3 , which is of the order of 90%. Thus, a trade-off may be made between maximum theoretical efficiency and the number of transformer-coupled stages, i.e. cost. Many variations may be made by persons skilled in the art, such as, for example, the use of single-ended push-pull amplifiers, having their outputs connected in series with the aid of transformers. Accordingly, power amplifiers for linearly amplifying a signal waveform include a signal generator for generating a sampled, digital representation of the signal to be amplified, each sample being represented by a numerical code having a number of significant bits from most significant to least significant. - 40 - Each bit of the numerical code drives the input of an associated, saturated push-pull amplifier such that the amplifier generates an output of one polarity when the control bit is a binary " 1 " and an output of the opposite polarity when the control bit is a binary "0". Each amplifier is connected to a prime power source, such as a DC or battery supply. The outputs of the amplifiers are coupled in series with a load into which the amplified signal waveform is to be delivered, such that their respective output voltages are summed in proportion to the significance of their associated code bits and such that the same load current flows in the output terminals of each amplifier. A preferred series coupling comprises, at the output of each amplifier, a transformer having a primary winding and a secondary winding with turns ratios of N: 1 , 2N: 1 , 4N: 1...etc., with an increase of two in the ratio for each bit of lower significance. The amplifiers are constructed using bilateral devices that pass current in either direction when biased to the ON state. When an associated control bit is of such a polarity as to cause the associated amplifier output to subtract from the voltage sum and to thus be of opposite polarity to the direction of load current flow, the current flow in the amplifier devices is reversed, returning energy to the prime power source that is not needed to sustain the load current. It may be shown that amplifiers according to the invention can have a theoretical efficiency, using ideal bilateral devices, of 100% for any signal waveform, and is thus a better starting point for obtaining practically efficient amplifiers than prior art amplifiers that had less than 100% efficiency even in theory. The invention may be used efficiently to amplify to a transmit power level a radio signal that varies in amplitude as well as phase. Alternatively, the invention may be used as a DC-to- AC converter having a sinusoidal output waveform. In the drawings and specification, there have been disclosed typical preferred embodiments of the invention and, although specific terms are employed, they are used in a generic and descriptive sense only and not for purposes of limitation, the scope of the invention being set forth in the following claims.

Claims: - 41 - What is Claimed is: 1. A power amplifier that amplifies an AC input signal of varying amplitude and varying phase to produce an amplified output signal voltage and an output current in a load impedance using a DC power supply, comprising: means for converting the AC input signal into a first signal having constant amplitude and a first phase angle and into a second signal having constant amplitude and a second phase angle; first means for amplifying the first signal to produce a first output signal voltage of constant voltage amplitude, the first amplifying means including bilateral amplifier devices that draw current from the DC power supply and supply current to the DC power supply; second means for amplifying the second signal to produce a second output signal voltage of constant voltage amplitude, the second amplifying means including bilateral amplifier devices that draw current from the DC power supply and supply current to the DC power supply; and means for serially coupling the first and second output signal voltages to the load impedance, such that the sum of the first and second output signal voltages produces the amplified output signal voltage across the load impedance and produces the output current through the load impedance, and such that an amplifier current that is linearly related to the output current flows in the bilateral amplifier devices of both the first and second amplifying means. 2. A power amplifier according to Claim 1 wherein during part of the signal cycle of the AC input signal, current flows from the first and second amplifying means to the DC power supply, to return energy to the DC power supply. 3. A power amplifier according to Claim 1 wherein the converting means comprises a quadrature oscillator and first and second quadrature modulators that are coupled to the quadrature oscillator to produce the first and second signals respectively. - 42 - 4. A power amplifier according to Claim 3 wherein the converting means further comprises a quadrature signal generator that is coupled to the first and second quadrature modulators and that is responsive to the AC input signal to generate in- phase and quadrature signals. 5. A power amplifier according to Claim 4 wherein the quadrature signal generator is a digital signal processor. 6. A power amplifier according to Claim 1 wherein the converting means comprises a data processor. 7. A power amplifier according to Claim 1 wherein the converting means comprises a digital frequency synthesizing circuit including phase modulation capability. 8. A power amplifier according to Claim 7 wherein the digital frequency synthesizing circuit comprises a direct digital frequency synthesizer. 9. A power amplifier according to Claim 1 wherein the serial coupling means comprises at least one transformer. 10. A power amplifier according to Claim 9 wherein the at least one transformer comprises a first transformer including a first primary and a first secondary, and a second transformer including a second primary and a second secondary, the first output signal voltage being coupled to the first primary and the second output signal voltage being coupled to the second primary, the first and second secondaries being serially connected across the load impedance. 11. A power amplifier that amplifies an AC input signal of varying amplitude and varying phase to produce an amplified output signal voltage and an output current in a load impedance using a DC power supply, comprising: - 43 - means for converting the AC input signal into a first signal having constant amplitude and a first phase angle and into a second signal having constant amplitude and a second phase angle; first means for amplifying the first signal to produce a first output signal voltage of constant voltage amplitude, the first amplifying means including bilateral amplifier devices that draw current from the DC power supply and supply current to the DC power supply; second means for amplifying the second signal to produce a second output signal voltage of constant voltage amplitude, the second amplifying means including bilateral amplifier devices that draw current from the DC power supply and supply current to the DC power supply; and means for coupling the first and second output signal voltages to the load impedance, such that a voltage proportional to the sum of the first and second output signal voltages produces the amplified output signal voltage across the load impedance and produces the output current through the load impedance, and such that an amplifier current that is linearly related to the output current flows in the bilateral amplifier devices of both the first and second amplifying means. 12. A power amplifier according to Claim 11 wherein during part of the signal cycle of the AC input signal, current flows from the first and second amplifying means to the DC power supply, to return energy to the DC power supply. 13. A power amplifier according to Claim 11 wherein the converting means comprises a quadrature oscillator and first and second quadrature modulators that are coupled to the quadrature oscillator to produce the first and second signals respectively. 14. A power amplifier according to Claim 13 wherein the converting means further comprises a quadrature signal generator that is coupled to the first and second quadrature modulators and that is responsive to the AC input signal to generate in-phase and quadrature signals. - 44 - 15. A power amplifier according to Claim 14 wherein the quadrature signal generator is a digital signal processor. 16. A power amplifier according to Claim 11 wherein the converting means comprises a data processor. 17. A power amplifier according to Claim 11 wherein the converting means comprises a digital frequency synthesizing circuit including phase modulation capability. 18. A power amplifier according to Claim 17 wherein the digital frequency synthesizing circuit comprises a direct digital frequency synthesizer. 19. A power amplifier according to Claim 11 wherein the coupling means comprises: a first quarter wavelength transmission line that couples the first output signal voltage to the load impedance; and a second quarter wavelength transmission line that couples the second output signal voltage to the load impedance. 20. A power amplifier according to Claim 19 wherein the load impedance includes an input node and wherein the coupling means comprises means for coupling both the first output signal and the second output signal to the input node. 21. A method for amplifying an AC input signal of varying amplitude and varying phase using a DC power supply, the amplifying method comprising the steps of: converting the AC input signal into a first signal having constant amplitude and a first phase angle and into a second signal having constant amplitude and a second phase angle; amplifying the first signal in a first amplifier; amplifying the second signal in a second amplifier; and - 45 - coupling the first and second amplifiers to one another and to a load impedance, such that voltages or currents in the first amplifier become linearly related to voltages or currents in the second amplifier. 22. A method according to Claim 21 : wherein the step of amplifying the first signal further comprises the step of returning energy from the first amplifier to the DC power supply during part of the signal cycle of the AC input signal; and wherein the step of amplifying the second signal further comprises the step of returning energy from the second amplifier to the DC power supply during part of the signal cycle of the AC input signal. 23. A method according to Claim 21 wherein the coupling step comprises the step of coupling the first and second amplifiers to the load impedance using at least one transformer. 24. A method according to Claim 21 wherein the coupling step comprises the step of coupling the first and second amplifiers to the load impedance using respective first and second quarter wave transmission lines. 25. An apparatus that amplifies an AC input signal of varying amplitude and varying phase using a DC power supply, comprising: a converter that converts the AC input signal into a first signal having constant amplitude and a first phase angle and into a second signal having constant amplitude and a second phase angle; a first amplifier that amplifies the first signal; a second amplifier that amplifies the second signal; and a coupler that couples the first and second amplifiers to one another and to a load impedance, such that voltages or currents in the first amplifier become linearly related to voltages or currents in the second amplifier. 26. An apparatus according to Claim 25: - 46 - wherein the first and second amplifiers are first and second bilateral amplifiers such that current flows from the first and second amplifiers to the DC power supply during part of the signal cycle of the AC input signal, to thereby return energy to the DC power supply. 27. An apparatus according to Claim 25 wherein the coupler comprises at least one transformer that serially couples the first and second amplifiers to the load impedance. 28. An apparatus according to Claim 25 wherein the coupler comprises first and second quarter wave transmission lines that couple the respective first and second amplifiers to the load impedance. 29. A method for amplifying an input signal of varying amplitude and varying phase to a desired power level, the method comprising the steps of: converting the input signal of varying amplitude and varying phase into more than two signals of constant amplitude and controlled phase; separately amplifying each of the more than two signals of constant amplitude and controlled phase; and combining the separately amplified more than two signals of constant amplitude and controlled phase to produce an output signal that is an amplification of the input signal at the desired power level; wherein the converting step comprises the step of controlling the phase of each of the more than two signals of constant amplitude and controlled phase to produce the output signal that is an amplification of the input signal at the desired power level. 30. A method according to Claim 29 wherein the more than two signals of constant amplitude and controlled phase are four signals of constant amplitude and controlled phase. 31. A method according to Claim 30 wherein the four signals of constant amplitude and controlled phase are a first pair of signals of constant amplitude and - 47 - controlled phase that combine to produce a first complex part of the output signal and a second pair of signals of constant amplitude and controlled phase that combine to produce a second complex part of the output signal. 32. A method according to Claim 31 wherein the controlling step comprises the steps of: controlling the phases of the first pair of signals of complex amplitude and controlled phase to vary in a counter-rotating manner to produce the first complex part of the output signal; and controlling the phases of the second pair of signals of complex amplitude and controlled phase to vary in a counter-rotating manner to produce the second complex part of the output signal. 33. A method according to Claim 29 wherein the step of separately amplifying comprises the step of separately amplifying each of the more than two signals of constant amplitude and controlled phase in separate saturated amplifiers. 34. A method according to Claim 29 wherein the step of combining comprises the step of series-combining the separately amplified more than two signals of constant amplitude and controlled phase to produce an output signal that is an amplification of the input signal at the desired power level. 35. A method according to Claim 29 wherein the step of combining comprises the step of combining the separately amplified more than two signals of constant amplitude and controlled phase in more than two quarter wavelength transmission lines, to produce an output signal that is an amplification of the input signal at the desired power level. 36. A method according to Claim 29 wherein the step of combining comprises the step of combining the separately amplified more than two signals of constant amplitude and controlled phase in more than two quarter wavelength - 48 - transmission line equivalent networks, to produce an output signal that is an amplification of the input signal at the desired power level. 37. A method according to Claim 36 wherein the more than two quarter wavelength transmission line equivalent networks are more than two Pi-networks comprising inductors and capacitors. 38. A method according to Claim 37 wherein the capacitors include output capacitors that are combined in parallel. 39. A method according to Claim 37 wherein the capacitors include input capacitors that include the output capacitance of the associated separate amplifiers. 40. A method according to Claim 29 wherein the step of controlling comprises the step of phase modulating each of the more than two signals of constant amplitude and controlled phase to produce the output signal that is an amplified version of the input signal at the desired power level. 41. A method according to Claim 29 wherein the step of controlling comprises the step of quadrature modulating each of the more than two signals of constant amplitude and controlled phase to produce the output signal that is an amplification of the input signal at the desired power level. 42. A method according to Claim 29 wherein the step of controlling comprises the step of phase modulating each of the more than two signals of constant amplitude and controlled phase using a separate phase locked loop, to produce the output signal that is an amplification of the input signal at the desired power level. 43. A transmitter for producing an output signal of varying amplitude at a desired power level and at a desired carrier frequency, from an input signal of varying amplitude and varying phase, the transmitter comprising: - 49 - means for converting the input signal of varying amplitude and varying phase into more than two signals of constant amplitude and controlled phase at the desired carrier frequency; means for separately amplifying each of the more than two signals of constant amplitude and controlled phase to obtain more than two amplified signals; and means for combining the more than two amplified signals to produce the output signal of varying amplitude at the desired power level and at the desired carrier frequency; wherein the means for converting comprises means for controlling the phase of each of the more than two signals of constant amplitude and controlled phase to produce the output signal of varying amplitude at the desired power level and at the desired carrier frequency. 44. A transmitter according to Claim 43 wherein the more than two signals of constant amplitude and controlled phase are four signals of constant amplitude and controlled phase. 45. A transmitter according to Claim 44 wherein the four signals of constant amplitude and controlled phase are a first pair of signals of constant amplitude and controlled phase that combine to produce a first complex part of the output signal and a second pair of signals of constant amplitude and controlled phase that combine to produce a second complex part of the output signal. 46. A transmitter according to Claim 45 wherein the controlling means comprises: means for controlling the phases of the first pair of signals of complex amplitude and controlled phase to vary in a counter-rotating manner to produce the first complex part of the output signal; and means for controlling the phases of the second pair of signals of complex amplitude and controlled phase to vary in a counter-rotating manner to produce the second complex part of the output signal. - 50 - 47. A transmitter according to Claim 43 wherein the means for separately amplifying comprises more than two saturated amplifiers. 48. A transmitter according to Claim 43 wherein the means for combining comprises means for series-combining the separately amplified more than two signals of constant amplitude and controlled phase to produce the output signal of varying amplitude at the desired power level and at the desired carrier frequency. 49. A transmitter according to Claim 43 wherein the means for combining comprises more than two quarter wavelength transmission lines. 50. A transmitter according to Claim 43 wherein the means for combining comprises more than two quarter wavelength transmission line equivalent networks. 51. A transmitter according to Claim 50 wherein the more than two quarter wavelength transmission line equivalent networks are more than two Pi-networks comprising inductors and capacitors. 52. A method for generating from a signal of varying amplitude and varying phase, a plurality of constant amplitude varying phase signals, the sum of which is the signal of varying amplitude and varying phase, comprising the steps of: generating a cosine carrier modulation waveform I(t) and a sine carrier modulation waveform Q(t) from the signal of varying amplitude and varying phase; generating a complementary waveform Q'(t) from the cosine carrier modulation waveform I(t) such that the sum of the squares of I(t) and Q'(t) is constant; modulating a cosine carrier signal with I(t) to obtain a first modulated cosine carrier; modulating a sine carrier signal with Q'(t) to obtain a first modulated sine carrier; and forming a sum and difference of the first modulated cosine carrier and the first modulated sine carrier to obtain the constant amplitude varying phase signals. - 51 - 53. A method according to Claim 52 further comprising the steps of: generating a complementary waveform I'(t) from the sine carrier modulation waveform Q(t) such that the sum of the squares of I'(t) and Q(t) is constant; modulating a cosine carrier signal with I'(t) to obtain a second modulated cosine carrier; modulating a sine carrier signal with Q(t) to obtain a second modulated sine carrier; and forming a sum and difference of the second modulated cosine carrier and the second modulated sine carrier to obtain a second set of constant amplitude varying phase signals. 54. A system for generating from a signal of varying amplitude and varying phase, a plurality of constant amplitude varying phase signals, the sum of which is the signal of varying amplitude and varying phase, the system comprising: means for generating a cosine carrier modulation waveform I(t) and a sine carrier modulation waveform Q(t) from the signal of varying amplitude and varying phase; means for generating a complementary waveform Q'(t) from the cosine carrier modulation waveform 1(f) such that the sum of the squares of I(t) and Q'(t) is constant; means for modulating a cosine carrier signal with 1(f) to obtain a first modulated cosine carrier; means for modulating a sine carrier signal with Q'(t) to obtain a first modulated sine carrier; and means for forming a sum and difference of the first modulated cosine carrier and the first modulated sine carrier to obtain the constant amplitude varying phase signals. 55. A system according to Claim 54 further comprising: - 52 - means for generating a complementary waveform I'(t) from the sine carrier modulation waveform Q(t) such that the sum of the squares of I'(t) and Q(t) is constant; means for modulating a cosine carrier signal with I'(t) to obtain a second modulated cosine carrier; means for modulating a sine carrier signal with Q(t) to obtain a second modulated sine carrier; and means for forming a sum and difference of the second modulated cosine carrier and the second modulated sine carrier to obtain a second set of constant amplitude varying phase signals. 56. Apparatus for synthesizing from an input waveform, an output waveform in a load using a DC power supply, the synthesizing apparatus comprising: means for representing the input waveform as a sequence of numerical codes in a number base, each numerical code comprising a plurality of digits ordered by place significance; a plurality of bilateral amplifying means, a respective one of which is associated with a respective one of the digits, for consuming current from the DC power supply and for returning current to the DC power supply based on the value of the associated digit, to thereby generate an output voltage level that is proportional to the value of the associated digit; and means for serially coupling the output voltage levels of the plurality of bilateral amplifying means to the load, with a weighting that is based upon the place significance of the associated digit. 57. Apparatus according to Claim 56 wherein the serially coupling means comprises a plurality of transformers, each having a primary and a secondary, the secondaries being serially coupled to the load, a respective primary being coupled to a respective one of the bilateral amplifying means, the primary-to-secondary turns ratios of the plurality of transformers being proportional to the place significance of the associated digit. - 53 - 58. Apparatus according to Claim 56 wherein the bilateral amplifying means are at least one of field effect transistors that conduct from source to drain and from drain to source, and bipolar transistors including reverse conduction diodes that conduct in a forward direction through the bipolar transistor and in the reverse direction through the reverse conduction diodes. 59. Apparatus according to Claim 56 wherein the input waveform is a DC input waveform, to provide a DC to AC power converter. 60. Apparatus according to Claim 58 wherein the output waveform is an approximately sinusoidal output waveform. 61. Apparatus according to Claim 56 wherein the number base is binary and wherein the plurality of bilateral amplifying means comprises a plurality of square wave inverters. 62. Apparatus according to Claim 56 wherein the number base is ternary and wherein the plurality of bilateral amplifying means comprises a plurality of square wave inverters with zero clamping to generate positive, zero and negative output voltage levels. 63. Apparatus according to Claim 56 further comprising at least one linear amplifier that is associated with at least two of the least significant digits to generate a linear output voltage that is proportional to the combined values of the at least two least significant digits, the serially coupling means also serially coupling the linear output voltage to the load. 64. Apparatus for synthesizing from an input waveform, an output waveform in a load using a DC power supply, the synthesizing apparatus comprising: a numerical code generator that represents the input waveform as a sequence of numerical codes in a number base, each numerical code comprising a plurality of digits ordered by place significance; and - 54 - a plurality of bilateral amplifiers, a respective one of which is associated with a respective one of the digits, the bilateral amplifiers consuming current from the DC power supply and returning current to the DC power supply based on the value of the associated digit, to thereby generate an output voltage level that is proportional to the value of the associated digit, the output voltage levels of the plurality of bilateral amplifiers being serially coupled to the load, with a weighting that is based upon the place significance of the associated digit. 65. Apparatus according to Claim 64 further comprising a plurality of transformers, each having a primary and a secondary, the secondaries being serially coupled to the load, a respective primary being coupled to a respective one of the bilateral amplifiers, the primary-to-secondary turns ratios of the plurality of transformers being proportional to the place significance of the associated digit. 66. Apparatus according to Claim 64 wherein the bilateral amplifiers are at least one of field effect transistors that conduct from source to drain and from drain to source, and bipolar transistors including reverse conduction diodes that conduct in a forward direction through the bipolar transistor and in the reverse direction through the reverse conduction diodes. 67. Apparatus according to Claim 64 wherein the input waveform is a DC input waveform, to provide a DC to AC power converter. 68. Apparatus according to Claim 66 wherein the output waveform is an approximately sinusoidal output waveform. 69. Apparatus according to Claim 64 wherein the number base is binary and wherein the plurality of bilateral amplifiers comprise a plurality of square wave inverters. 70. Apparatus according to Claim 64 wherein the number base is ternary and wherein the plurality of bilateral amplifiers comprise a plurality of square wave - 55 - inverters with zero clamping to generate positive, zero and negative output voltage levels. 71. Apparatus according to Claim 64 further comprising at least one linear amplifier that is associated with at least two of the least significant digits to generate a linear output voltage that is proportional to the combined values of the at least two least significant digits, the linear output voltage also being serially coupled to the load. 72. A method for synthesizing from an input waveform, an output waveform in a load using a DC power supply, the synthesizing method comprising the steps of: representing the input waveform as a sequence of numerical codes in a number base, each numerical code comprising a plurality of digits ordered by place significance; bilaterally amplifying the value of each of the digits, to consume current from the DC power supply and return current to the DC power supply based on the value of the associated digit, and thereby generate a plurality of output voltage levels each of which is proportional to the value of the associated digit; and serially coupling the plurality of output voltage levels to the load, with a weighting that is based upon the place significance of the associated digit. 73. A method according to Claim 72 wherein the input waveform is a DC input waveform, to provide a DC to AC power converting method. 74. A method according to Claim 72 wherein the output waveform is an approximately sinusoidal output waveform. 75. A method according to Claim 72 further comprising the step of: linearly amplifying at least two of the least significant digits to generate a linear output voltage that is proportional to the combined values of the at least two least significant digits; and -56- serially coupling the linear output voltage to the load.

Inventors: DENT PAUL WILKINSON, DENT, PAUL, WILKINSON
Applicants: ERICSSON INC, ERICSSON, INC.
Application year: 1999
Main classification: H03F3
IPC codes: H03F1, H03F3, H03G3, H04L27