Zero-voltage-switching contour based outphasing power amplifier

A zero-voltage-switching contour based outphasing power amplifier having two class-E power amplifiers connected in an out-phasing architecture coupled on opposite sides of a load being driven. The pair of class-E power amplifiers receive separate digital drive signals with an amount of phase difference that is adjusted based on the load. Variable capacitor arrays are coupled in parallel on the class-E power amplifiers and controlled in response to system parameters including duty cycle of the input signal. Efficiency of the power amplifier is maintained despite variation in output loading.

Not Applicable

NOTICE OF MATERIAL SUBJECT TO COPYRIGHT PROTECTION

BACKGROUND OF THE INVENTION

1. Field of the Invention

This invention pertains generally to power amplifiers, and more particularly to a zero voltage switching (ZVS) contour based switching power amplifier having a wide dynamic range.

2. Description of Related Art

There are two types of power amplifiers; linear and switching. Linear power amplifiers (PAs), such as class A, B, and AB amplifiers, are biased for peak output power and consequently suffer from poor efficiency at backed-off power levels. A common design approach used to obtain the desired linearity for a PA is to design the PA to handle more power than the level at which it will be operating. This is called “power back-off”, and the differential between design output and operating output is typically expressed in dB. There are also techniques that have improved the efficiency of linear PAs, such as found in transformer combiner based PAs and envelope tracking PAs. However, a transformer combiner based PA is limited by die size constraints, and envelope tracking PAs suffer from supply regulator bandwidth and efficiency problems.

Architectures used in switching PAs, such as supply modulation (e.g., polar, polar loop), theoretically offer high efficiency even at very low output power levels. Yet, these architectures suffer from supply regulator inefficiency, particularly while handling wide bandwidth envelope variations. Recently developed digital PA architectures, such as the digital envelope modulator and the switching mixer PA architectures, all suffer from efficiency degradation at backed-off power levels. Duty cycle modulation and dynamic load modulation, such as used for class-E PAs, can achieve high peak efficiency but results in poor efficiency at low output power levels. In fact, class-E PAs operate sub-optimally at low output power levels when zero voltage switching (ZVS) conditions are not satisfied, thus resulting in significant losses and poor efficiency. It will be appreciated that ZVS is intended to maximize efficient operation of class-E PAs.

BRIEF SUMMARY OF THE INVENTION

The present invention is an outphasing zero voltage switching ZVS contour based power amplifier (PA) with a wide dynamic range. By way of example, and not of limitation, an embodiment of the inventive amplifier comprises a pair of separate power amplifiers (PAs) connected in an out-phasing architecture and coupled to opposite ends of a load, or a power combiner, (e.g., a transformer), coupled to a load. In the preferred embodiment, the pair of PAs are configured for zero voltage switching (ZVS), and arrays of variable capacitors are controlled in response to the duty cycle of the input drive signals whose relative phase is also changed based on the duty cycle. This inventive amplifier architecture provides a number of advantages over prior amplifier systems, including wide dynamic range.

DETAILED DESCRIPTION OF THE INVENTION

Our inventive outphasing ZVS contour based power amplifier (PA) architecture is based on the ZVS contour based PA. In a ZVS contour based PA, peak efficiency is maintained even under back-off conditions by a circuit configuration with select component values, such that ZVS conditions are met at varying duty cycles. Specifically, this involves varying the drain capacitance C and the equivalent resistance Reqfor a fixed zero voltage switching transistor drain inductance Lzvsalong with duty cycle D according to the following relation:

ω0⁢LZVSReq=g1⁡(D)andω0⁢CReq=g2⁡(D)
in which g1(D) and g2(D) are determined, such as analytically or empirically to ensure ZVS switching. The resultant output power varies with the duty cycle D according to the following relation:

Pout⁡(D)=g3⁡(D)·VDD2Req
The functions g1(D) and g2(D) and g3(D) can be found as solutions to a set of equations that can be analytically derived, or empirically determined as described in a later section.

Conventional class-E power amplifiers can utilize dynamically programmable reactive termination of outphasing PAs, but do not guarantee ZVS and hence lack efficiency and wide dynamic range. In addition, although the driving waveforms of a conventional ZVS contour based PA can have some phase modulation, its envelope dynamic range or power back-off range is also limited by the achievable load modulation. To overcome these problems, the single ZVS contour based class-E PA is replaced by two ZVS contour based class-E PAs, connected in an out-phasing architecture.

FIG. 1illustrates a simplified schematic10of an outphasing PA architecture. The embodiment shown comprises two identical, parallel class-E PA networks PA1 and PA2 with a phase difference of 2φ between their input voltages Vejφand Ve−jφ. The output from the PA networks is directed to a power combiner circuit PCOM, which can take various forms such as a transformer, that drives load RL. It will be noted that the inputs are said to have phases of φ and −φ, thus the difference between them is 2φ. It should be appreciated that in conventional outphasing, the PA does not have to be a class E amplifier; whereby the amplifier could be a class A/B/AB or even a class D amplifier. This phase difference between the input voltages presents an effective impedance of Z1and Z2to the two PAs, which are found to be:

Hence as can be seen, a varying output load can be supported by merely varying the phase difference φ between these input voltages Veφand Ve−jφ. It will be noted that j refers to a so-called imaginary number as the square root of negative one. Imaginary numbers allows the real number system R to be extended to the complex number system C, which in turn provides at least one root for every polynomial P(x), and is noted herein by j. In mathematics, the term “imaginary” was used because there is no real number having a negative square, but the use of these numbers is common and necessary in solving many system problems.

FIG. 2AandFIG. 2Bshow these equivalent impedances for Z120aand Z220bafter a series-to-parallel transformation. These equivalent impedances are seen for Z120ainFIG. 2Aas a parallel combination of capacitor and resistor, with contributions RL/sin 2φ, and RL/2 sin2φ, respectively. Similarly, the equivalent impedances are seen for Z220binFIG. 2Bas a parallel combination of inductor and resistor, with contributions RL/sin 2φ, and RL/2 sin2φ, respectively. It should be noted that if φ is allowed to become negative, the capacitor and inductor have to be interchanged.

In the present invention, for every duty cycle D, the drain capacitance value C(D), the relative phase (2φ), and the tunable networks are chosen such that ZVS conditions are satisfied for both class E PAs. The variable drain capacitor values, C(D), are chosen to satisfy the ZVS conditions as specified by the function g2(D). The relative phase (2φ) is chosen such that the resistance seen by the PAs, namely the real parts of Z1and Z2, satisfy the ZVS conditions as specified by the function g1(D). The tunable reactive networks are chosen, such that the imaginary parts of Z1and Z2are resonated out at the PA's center frequency. In effect, for each duty cycle value D, a different and unique output power, as specified by g3(D), is delivered while maintaining ZVS conditions and hence high efficiency. The relation between the duty cycle D and the output power can be derived analytically or empirically and used to map desired output power level (or desired back-off from nominal peak output power) to a required duty cycle value.

It is important to realize that a key aspect of the invention is operating the out-phasing PA along ZVS contours within its design space. ZVS conditions ensure that just as the transistor turns ON during each carrier period, the drain voltage is at zero, thereby avoiding any wasted power in discharging the drain. The ZVS contour PA is based on meeting ZVS conditions toward reaching optimal efficiency in a parallel class-E PA, not only at a particular power level, but also at backed-off power levels by a simultaneous modulation of the duty cycle, drain capacitance and load.

FIG. 3AandFIG. 3Billustrate plots of g1and g2as a function of duty cycle D for a given configuration of the amplifier. From these plots the following curve fitting equations were determined:
g1(D)=218.3D6−431.1D5+355.3D4−148.3D3+33.45D2−2.677D+0.105
g2(D)=0.4752D−1.596−0.7232

FIG. 3Csimilarly illustrates a plot of g3as a function of duty cycle D for a given configuration of the amplifier, from which curve fitting arrives at the following equation for g3(D):
g3(D)=2.714D

The above equations for g1(D), g2(D) and g3(D) are valid, to the first order, for a general class-E PA design (with a finite drain inductance) assuming: (a) instantaneous switching, (b) zero switch ON resistance, and (c) disregarding higher order switching harmonics.

Although values of g1(D), g2(D) and g3(D) will vary for any specific implementation, a useful design would still result, however, with somewhat less efficiency. While not necessary, for any specific configuration, a designer can analytically, or from circuit simulations, derive and plot these functions in response to duty cycle and create a set of equations expressing optimum values of g1(D), g2(D) and g3(D) for that configuration.

FIG. 4illustrates an example embodiment30of the inventive ZVS contour based outphasing power amplifier network with PA132and PA234configured for receiving variable duty cycle drive signals shown in block36. The output of PA132and PA234is coupled to a load, represented as RL, through transformer T1. It should be noted that other forms of power coupling can be alternatively utilized, without departing from the teachings of the present invention, including transmission lines, lumped element networks, and so forth which are forms of power combiner.

Driving signals Vejφand Ve−jφhave variable duty cycles and relative phase, and are seen generated by a phase control circuit (PCC). In addition, the driving signals Vejφand Ve−jφcan provide phase modulation To those versed in outphasing PA art, the block that generates the two waveforms is generally referred to as “signal component separator”. In original outphasing art, this block was implemented using some kind of analog amplifier control; while in more modern implementations a digital signal processing block is generally followed by, or accompanied with, a frequency/phase synthesizer or a digital-to-phase converter. However, in addition to providing relative phase difference, the duty cycle of both waveforms in the present invention is also changed, and thus the phase control circuit shown differs significantly from the “signal component separator” of conventional outphasing designs.

Signals Vejφand Ve−jφwith variable duty cycles are received by first and second switching circuits, herein represented by transistors M1and M2, with respective drain inductors Lzvs1and Lzvs2, preferably of the same fixed value. Output from the switching stage is received by the variable drain capacitances C1(D) in PA1 and C2(D) PA2, as controlled by signals A and B from the phase control circuit. These signals are received by tunable networks TN1and TN2, whose respective resistances are shown given by RL/2 sin2φ, and whose impedance is controlled by signals C and D respectively from the phase control circuit PCC. According to at least one embodiment these tunable networks comprise at least a series and parallel LC network, or equivalent, an example of which is seen inFIG. 5.

The desired output power level (or desired back-off from nominal peak output power) is mapped appropriately to a chosen duty cycle D according to g3(D). The chosen duty cycle D is mapped appropriately according to g1(D) and g2(D) in controlling the value of the tunable networks, which preferably include variable capacitors. It should be noted that the load is typically not sensed in modern implementations to determine φ, although sensing is not precluded. It should be appreciated that the duty cycle dynamically changed to achieve the desired envelope modulation. Furthermore, it should be appreciated that in at least one embodiment, the various component values, can also be changed dynamically to achieve the desired envelope modulation.

FIG. 5illustrates an example embodiment40of a wide dynamic range zero voltage switching (ZVS) contour based switching power amplifier having PA142and PA244in like manner asFIG. 4, yet showing the inductive and capacitive contributions within the tunable networks, and outputting to a power combiner (PCOM)46connected to a load, represented as RL. For the sake of simplicity of illustrationFIG. 5does not depict the waveforms and phase control circuits shown inFIG. 4, although they are presumed to be utilized with this figure as well.

Signals Vejφand Ve−jφwith variable duty cycles, are received by first and second switching circuits, herein represented by transistors M1and M2. Inductors Lzvs1and Lzvs2, preferably of the same fixed value, are again seen in the drain connection to VDDpower, with output waveforms VS1and VS2shown in the schematic. Output from the switching stage is received by the variable drain capacitances C1(D) in PA1 and C2(D) PA2 prior to reaching the bandpass filters BPF148and BPF252, which are shown comprising capacitor C1in series with inductor L1in BPF1 and C2in series with inductor L2in BPF2. Output from the bandpass filters is input to an inductive lead circuit Llead(φ)50in PA1 comprising parallel fixed inductor Lfixand variable capacitor CL1(D), while in PA2 a capacitive lag circuit Clag(φ)54is seen comprising parallel fixed inductor Lfixand variable capacitor CL2(D). The output is directed to the load RLthrough a circuit here exemplified as a power combiner (PCOM)46.

It should be appreciated that since the tunable network also provides overcoming stray parasitic capacitance and/or inductance, it requires more than a bandpass filter in combination with a variable load capacitance. It will be noted that in the absence of any stray parasitics, Z1and Z2would be capacitive and inductive (or vice versa). Since CL1(D) and CL2(D) are used to tune out the reactive portions of Z1and Z2, they both can't be implemented as simple capacitor arrays. At least one of them has to include an inductor in parallel. In the presence of stray parasitics, such as from the transformer, then both CL1(D) and CL2(D) preferably comprise capacitor arrays in parallel with fixed inductors.

The following sections refer generally toFIG. 4andFIG. 5. The variable capacitors of these inventive amplifiers can be implemented in any desired manner, such as comprising varactors, digital capacitor banks or combinations thereof. These digital capacitor banks are preferably implemented as parallel banks of capacitors of various sizes with series switches that could be turned ON or OFF, thus selecting or deselecting the capacitors. Digital circuits (e.g., dedicated logic circuits and/or memory blocks such as lookup tables) preferably map the digital duty cycle value D to a set of controls from which buffers/drivers accordingly drive the state of these switches. In at least one embodiment, the dedicated logic circuits and/or lookup tables themselves employ intelligence to overcome inevitable errors in the component values of the capacitor banks. Varactor-based implementations preferably employ additional control circuits, such as digital-to-analog converter circuits, to generate the appropriate control waveforms for the varactors. In either case, timing synchronization circuits (e.g., flip-flops) may be used in one or more embodiments to “time” the change of the capacitor value, which is an important consideration on providing a proper output.

Signals Vejφand Ve−φarrive as digital inputs to the two PA circuits which are generated out of phase with one another by a time value t given by t=φT/180°, which is seen in the leftmost dashed block ofFIG. 4, while T is the period of these first and second drive signals that drives the gates of switching stages in the PA circuits, exemplified by MOSFET transistor devices M1and M2, although other forms of electrical switching elements may be utilized without departing from the teachings of the present invention. It will be noted that the switching stages of these PA circuits may alternatively comprise multiple transistors without departing from the teachings herein. The drain supplies of the switching stages, such as on the drain of transistors M1and M2, are coupled to VDDpower through preferably fixed inductors with value Lzvs, which are shown inFIG. 4andFIG. 5as Lzvs1and Lzvs2for the respective PAs. It will be noted that the inductor itself does not assure zero voltage switching, but operates in combination with the transformer combiner, the device capacitances, and the additional passive components (e.g., drain cap array and load cap array) so that the dynamics of the resultant network assures ZVS for a specific duty cycle D. The sources of these switching stages are coupled to ground, exemplified as the source lead of transistors M1and M2connected to ground. The outputs of the switching stages each have a parallel variable drain capacitor array C(D), which are shown inFIG. 4andFIG. 5as C1(D) and C2(D) for the respective PAs, preceding a tunable network, shown with parameters controlled by signals C and D, respectively for the first and second PA.

In at least one embodiment, the tunable networks comprise a series connected band-pass filter which determines the fundamental frequency and a parallel load inductance and variable load capacitor array CL1(D) and CL2(D) as clearly shown inFIG. 5. An inductive load Lload, and different variable load capacitor arrays CL1(D) and CL2(D) are preferably connected in parallel with the output of the bandpass filters, within the respective tunable networks. Output from the respective tunable networks drives the load, preferably through a power combiner, such as transformer T1which drives RL.

The variable elements exemplified inFIG. 4andFIG. 5, are controlled by an external circuit, with C1(D) and C2(D) variable capacitances controlled by a circuit such as exemplified by the phase control circuit PCC depicted inFIG. 4outputting signals A and B in response to duty cycle. Additionally, signals C and D, of that figure are output for controlling characteristics of the respective tunable networks, such as controlling the tunable networks TN1and TN2, and more specifically the value of variable capacitances CL1(D) and CL2(D) as seen inFIG. 5that are part of tunable stages (networks). The value of variable capacitances CL1(D) and CL2(D) are controlled in response to selecting impedance values for the first and second PAs, these being determined for example using the equations for Z1and Z2. In at least one embodiment, the signals A, B, C and D comprise digital buses controlling the respective capacitor arrays. It should be appreciated that the drain and load capacitor arrays may be of different sizes, whereby the number of control signals on the digital bus would also be different. In other words, the mappings from D to C(D), CL1(D) and CL2(D) can be different as required. These variable capacitances are preferably controlled digitally by a digital circuit, herein exemplified as being part of the phase control circuit (PCC) shown inFIG. 4.

It will be noted that the exemplified phase control circuit shown inFIG. 4, provides means for generating the first drive signal and the second drive signal at a desired duty cycle and varying the phase difference between the first drive signal and the second drive signal to maintain efficiency of the power amplifier apparatus in response to a varying output load. The phase control circuit also preferably includes pre-distortion logic in the control signals as is common in most PA circuits to correct linearity errors in the inventive power amplifier. In addition, the exemplified phase control circuit of this embodiment provides means for varying capacitances of the first variable drain capacitor array and the second variable drain capacitor array in response to duty cycle. Still further, the exemplified phase control circuit of this embodiment provides means for differentially varying capacitances of the first variable load capacitor array and the second variable load capacitor array in response to the duty cycle, the equations on Z1and Z2and the functioning of g1(D) and g2(D) as described. Said another way, for each output power level, there would be a corresponding set of relative phase, 2φ, duty cycle, D, C(D), CL1(D) and CL2(D). The interoperational relationship between these parameters is given by equations Z1and Z2and the functioning of g1(D) and g2(D) and g3(D).

One of ordinary skill in the art will appreciate that these control signals can be generated by a wide range of circuits, including computer processors (e.g., digital signal processor (DSP) chips), processor controlled devices, logic circuits and arrays (fixed & programmable), application specific integrated circuits (ASICs), and so forth.

In the embodiments shown, the drain capacitor bank C(D) (depicted as C1(D) and C2(D)) comprises a digitally controlled capacitance which is varied as a function of duty cycle D. The minimum value of this drain capacitance is determined by transistor sizing considerations. The inductor Lzvs(depicted as Lzvs1and Lzvs2) is preferably fixed and its value determined using the function g1(D) for a 50% duty cycle. In order to eliminate the unwanted inductive and capacitive components of Z1and Z2a tunable impedance network consisting of two load capacitor banks, CL1(D) and CL2(D) and a fixed inductor Lloadare preferably utilized. Ideally, this architecture would yield upwards of 100% efficiency due to its ZVS contour based design and out-phasing arrangement. However, it is limited by the finite Q of the Lloadinductor, which presents a resistance Rstray=QLloadω in parallel with the effective load resistance, (RL/2 sin2φ). This effect becomes dominant only when Rstraybecomes comparable to (RL/2 sin2φ). The load capacitor banks, CL1(D) and CL2(D), have almost negligible losses and hence have practically no effect on overall efficiency.

It should be understood that Z1and Z2are the respective impedances seen by the two power amplifiers, one is dominantly capacitive, and the other is dominated by inductance. The reactive components of Z1and Z2are tuned out by CL1(D) and CL2(D). By picking the relative phase 2φ, according to the duty cycle, it is assured that ZVS is maintained because the resistive portion changes with changes in φ.

For instance, suppose Z1is capacitive and Z2is inductive. Then, the reactive part of Z2is tuned out simply by using a capacitor array, CL2(D). However, to tune out the reactive part of Z1, a variable inductor is needed; which is generally not practical. So, instead, the combination of an inductor and a capacitor array CL1(D) is used to tune out capacitive Z1.

In addition, the capacitor arrays can also be chosen to simultaneously tune out any unwanted inductive and capacitive components, which primarily comprise stray parasitics, for example parasitic capacitance of the transformer primary coils.

It should be appreciated that ZVS conditions may not be maintained for large values of back-off, in view of the practical limitations on how small a duty cycle can be realized. However, these larger back-off values are still attainable in response to reducing the relative phase 2φ, and accordingly changing the tunable networks as in a conventional outphasing PA with programmable termination. It will be appreciated, however, that ZVS conditions are no longer satisfied and efficiency drops for further back-off. Therefore, below the lowest achievable duty cycle, the architecture of the invention then operates in a manner more similar to a conventional outphasing PA, thus in this trade-off the present invention provides even further dynamic range as a trade-off with efficiency.

The advantages of the inventive PA circuit are multifold and readily apparent, as a solution which maintains constant drain efficiency over a wide dynamic range. The design offers not only constant efficiency but also improves upon the dynamic range. It will be noted that the inventive PA architecture allows wide modulation bandwidths and is free from many of the problems faced by traditional PA architectures, such as envelope-phase mismatch common to polar architectures that is significantly alleviated by the absence of an explicit envelope filter.

The inventive circuit has been verified using realistic transistor level circuit simulation in 0.13 μm CMOS. Realistic models for passives have been obtained from ASITIC which stands for Analysis and Simulation of Spiral Inductors and Transformers for ICs, which were used in the simulations. The architecture has also been verified (without modulation) using measurements on 100 MHz discrete PAs. The relative phase 2φ was swept in a static sense and the duty cycle D and the variable components were changed accordingly and was shown that efficiency remains high and relatively constant.

The increasing sophistication of wireless communication technologies, particularly in power conscious portable devices, has made efficient, wide bandwidth, linear power amplifiers (PAs) that handle high peak-to-average signal power ratios (PAR) critically important. In any transmitter chain, the power amplifiers are the major source of power consumption, and alone account for about 70-80% of total power consumption in any transmitter chip. The inventive power amplifier maintains close to peak efficiency over the wide dynamic range of modulation schemes and achieves significant battery power conservation. The invention makes it possible to efficiently generate high power, wide bandwidth modulated radio frequency signals from low voltage supplies with a high degree of linearity The invention can be utilized in great benefit in power control applications where high speed modulation is not required (e.g., no modulation or very low modulation) but simple back-off is desired. For example, the invention would be particularly well-suited for use in cellular and other wireless transceivers.

From the discussion above it will be appreciated that the invention can be embodied in various ways, including the following:

1. A zero-voltage-switching contour based outphasing power amplifier apparatus, comprising: (a) a first power amplifier configured to receive a first drive signal at an input and having an output configured for connection to a first side of a load, said first power amplifier comprising: a first transistor switching stage configured to be driven by said first drive signal; a first zero voltage switching inductance having a fixed value on the drain of said first transistor switching stage; a first variable drain capacitor array coupled in parallel to an output from said first transistor switching stage; a first bandpass filter in series with the output from said first transistor switching stage; a first variable load capacitor array coupled in parallel to an output from said first bandpass filter; and a first load inductance having a fixed value coupled in parallel to the output from said first bandpass filter; (b) a second power amplifier configured to receive a second drive signal at an input and having an output configured for connection to a second side of the load, said second power amplifier comprising: a second transistor switching stage configured to be driven by said second drive signal; a second zero voltage switching inductance having a fixed value on the drain of said first transistor switching stage; a second variable drain capacitor array coupled in parallel to an output from said second transistor switching stage and having capacitance which is varied as a function of duty cycle; a second bandpass filter in series with said output from said second transistor switching stage; a second variable load capacitor array coupled in parallel to an output from said second bandpass filter; and a second load inductance having a fixed value coupled in parallel to an output from said second bandpass filter; (c) means for generating said first drive signal and said second drive signal at a desired duty cycle and varying the phase difference between said first drive signal and said second drive signal to maintain efficiency of said power amplifier apparatus in response to a varying output load; (d) means for varying capacitances of said first variable drain capacitor array and said second variable drain capacitor array in response to duty cycle; and (e) means for differentially varying capacitances of said first variable load capacitor array and said second variable load capacitor array in response to determining impedance values for said first power amplifier and said second power amplifier.

2. The apparatus of any of the preceding embodiments, wherein said means for varying capacitances of said first variable drain capacitor array and said second variable drain capacitor array comprises a digital control circuit.

3. The apparatus of any of the preceding embodiments, wherein said means for differentially varying capacitances of said first variable load capacitor array and said second variable load capacitor array comprises a control circuit.

4. The apparatus of any of the preceding embodiments, wherein said means for generating said first drive signal and said second drive signal at a desired duty cycle and varying the duty cycle comprises a control circuit.

5. The apparatus of any of the preceding embodiments, wherein said phase difference results in a time difference between said first and second drive signals given by t=φT/180°, in which t is time between corresponding edges in said first and second drive signals, while T is wavelength period for these first and second drive signals.

6. The apparatus of any of the preceding embodiments, wherein said phase difference between said first drive signal and said second drive signal presents an effective impedance of Z1to said first power amplifier and Z2to said second power amplifier, given by,

7. The apparatus of any of the preceding embodiments, wherein said first drive signal and said second drive signal are out of phase with one another by a phase difference of 2φ.

8. The apparatus of any of the preceding embodiments, wherein peak efficiency is maintained even under back-off conditions in response to selection of component values assuring zero voltage switching (ZVS) conditions are met at varying duty cycles.

9. The apparatus of any of the preceding embodiments, wherein selecting component values involves varying the drain capacitance C and the equivalent resistance for a fixed Lzvsalong with variation of said duty cycle based on the load.

10. The apparatus of any of the preceding embodiments, wherein values of drain capacitance C and equivalent resistance Reqare selected for a fixed zero voltage switching transistor drain inductance Lzvswith duty cycle D according to

ω0⁢LZVSReq=g1⁡(D)andω0⁢CReq=g2⁡(D)
in which g1(D) and g2(D) are determined to ensure ZVS switching.

11. The apparatus of any of the preceding embodiments, further comprising a transformer, with a first winding having a first end coupled to the output of said first power amplifier and a second end coupled to the output of said second power amplifier, and a second winding, magnetically coupled to said first winding, configured for driving the load.

12. A zero-voltage-switching contour based outphasing power amplifier apparatus, comprising: (a) a first power amplifier configured to receive a first drive signal at an input and having an output configured for connection to a first side of a load, said first power amplifier comprising: a first transistor switching stage configured to be driven by said first drive signal; a first zero voltage switching inductance having a fixed value on the drain of said first transistor switching stage; a first variable drain capacitor array coupled in parallel to an output from said first transistor switching stage; a first bandpass filter in series with the output from said first transistor switching stage; a first variable load capacitor array coupled in parallel to an output from said first bandpass filter; and a first load inductance having a fixed value coupled in parallel to the output from said first bandpass filter; (b) a second power amplifier configured to receive a second drive signal at an input and having an output configured for connection to a second side of the load, said second power amplifier comprising: a second transistor switching stage configured to be driven by said second drive signal; a second zero voltage switching inductance having a fixed value on the drain of said first transistor switching stage; a second variable drain capacitor array coupled in parallel to an output from said second transistor switching stage and having capacitance which is varied as a function of duty cycle; a second bandpass filter in series with said output from said second transistor switching stage; a second variable load capacitor array coupled in parallel to an output from said second bandpass filter; and a second load inductance having a fixed value coupled in parallel to an output from said second bandpass filter; (c) a digital control circuit for generating said first drive signal and said second drive signal at a desired duty cycle and varying the phase difference between said first drive signal and said second drive signal to maintain efficiency of said power amplifier apparatus in response to a varying output load; (d) a control circuit for varying capacitances of said first variable drain capacitor array and said second variable drain capacitor array in response to duty cycle; and (e) a control circuit for differentially varying capacitances of said first variable load capacitor array and said second variable load capacitor array in response to determining impedance values for said first power amplifier and said second power amplifier; (f) wherein peak efficiency of said power amplifier apparatus is maintained even under back-off conditions so that zero voltage switching (ZVS) conditions are met at varying duty cycles.

13. The apparatus of any of the preceding embodiments, wherein said phase difference results in a time difference between said first and second drive signals given by t=φT/180°, in which t is time between corresponding edges in said first and second drive signals, while T is the period of these first and second drive signals.

14. The of any of the preceding embodiments, wherein said phase difference between said first drive signal and said second drive signal presents an effective impedance of Z1to said first power amplifier and Z2to said second power amplifier, given by,

15. The apparatus of any of the preceding embodiments, wherein said first drive signal and said second drive signal are out of phase with one another by a phase difference of 2φ.

16. The apparatus of any of the preceding embodiments, wherein selecting component values involves varying the drain capacitance C and the equivalent resistance for a fixed Lzvsalong with variation of said duty cycle based on the load.

17. The apparatus of any of the preceding embodiments, wherein values of drain capacitance C and equivalent resistance Reqare selected for a fixed zero voltage switching transistor drain inductance Lzvswith duty cycle D according to

ω0⁢LZVSReq=g1⁡(D)
and ω0CReq=g2(D) in which g1(D) and g2(D) are determined to ensure ZVS switching.

18. The apparatus of any of the preceding embodiments, further comprising a transformer, with a first winding having a first end coupled to said first power amplifier and a second end coupled to said second power amplifier, and a second winding, magnetically coupled to said first winding, and configured for driving the load.

19. A zero-voltage-switching contour based outphasing power amplifier apparatus, comprising: a first power amplifier having a switching transistor with a drain inductor for zero voltage switching, said first power amplifier configured to receive a first drive signal at an input and having an output configured for connection to a first side of a load; a second power amplifier having a switching transistor with a drain inductor for zero voltage switching, said second power amplifier configured to receive a second drive signal at an input and having an output configured for connection to a second side of the load; a variable drain capacitor array coupled in parallel on an output of the switching transistor in each of said first and second power amplifier, wherein capacitance of said variable drain capacitor array is varied in response to duty cycle; a variable load capacitor array coupled in parallel at the output of said first and second power amplifier near the load, wherein capacitance of said variable load capacitor array are varied differently on said first and said second power amplifier in response to determining impedance values for said first power amplifier and said second power amplifier; and a band-pass filter within said first power amplifier and said second power amplifier coupled between said variable drain capacitor array and said variable load capacitor array; wherein efficiency of said power amplifier apparatus is maintained despite a varying output load, in response to receiving said first drive signal and said second drive signal with a phase difference that is responsive to load conditions.

20. The apparatus of any of the preceding embodiments, further comprising a digital control circuit for generating said first drive signal and said second drive signal, and adjusting the capacitance of said variable drain capacitor arrays in response to load, and separately adjusting the capacitance of said variable load capacitor array in response to determining impedance values for said first power amplifier and said second power amplifier.