Abstract:
An envelope feedforward technique is described that provides efficient, variable-power, linear amplification of an input signal. An input signal having phase and amplitude components is separated (decomposed) into an FM portion and an envelope portion. The FM portion contains the high frequency phase and frequency information from the input signal. The envelope portion contains the low frequency amplitude information from the input signal. An envelope combiner uses the envelope signal to amplitude-modulate the FM signal to produce an output signal. Spectral regrowth of the output signal is reduced by adjusting the relative time delays in the signal path of the envelope signal and the FM signal such that the FM signal and the envelope signal arrive at the envelope combiner at the same time. The envelope feedforward technique may be used to increase battery life in a handheld mobile RF unit such as a cellular telephone. An efficient Class D switching amplifier is constructed using a dual-gate FET by applying the envelope signal to the first gate to vary the transconductance of the FET and by applying the FM signal to the second gate to switch the FET on and off.

Description:
BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     The disclosed invention relates to efficient power amplifiers and more particularly to efficient RF power amplifiers. 
     2. Description of the Related Art 
     Radio Frequency (RF) transmitters, such as cellular telephones, use an RF Power Amplifier (PA) to provide the RF signal strength needed for radio communications over a distance. The output of the PA is typically provided to a transmitting antenna, and thus the power output of the PA is proportional to the transmitted power. As the output power of the PA increases, the power radiated by the transmitting antenna increases and the useable range of the transmitter increases. 
     In most RF transmitters, the PA handles the largest power within the transmitter and inefficiency in the PA typically accounts for much of the wasted power in the transmitter. Unfortunately, in many applications, the PA does not perform the task of power amplification efficiently, consuming much more power than is actually transmitted. This excess power generation can be costly, especially in battery operated devices, because it often necessitates the use of larger-capacity batteries, and/or shorter battery recharging intervals. 
     A PA may be designed to amplify an RF signal with a constant envelope or an RF signal with a non-constant envelope. A PA designed for constant envelope signals is typically more efficient than a PA designed for a non-constant envelope signal because the biasing circuits in the constant envelope PA can be optimized to deliver the constant power level. Moreover, if perfect envelope magnitude fidelity is not required, the PA circuits can be driven slightly into compression (nonlinearity), which offers even further efficiency gains. Unfortunately, as the PA is driven into compression, the signal spectrum tends to widen, due to nonlinear distortions. These nonlinear distortions produce intermodulation products, which arise when signals of differing frequencies pass through a nonlinearity. This spectral widening is called spectral regrowth, and is undesirable because it spills RF energy into adjacent frequency channels. The energy spilled into other channels is known as Adjacent Channel Power (ACP) emissions and is often undesirable because it may cause interference with communication systems operating in the other channels. Thus, tradeoffs exist between efficiency and ACP emissions, even for constant-envelope PAs. Typically, regulations on RF transmitters and communication systems specify an acceptable Adjacent Channel Power Ratio (ACPR). The ACPR is the ratio of the average power in the active channel passband to the average power spilled into an adjacent channel passband or some fraction of the adjacent channel passband. 
     Non-constant envelope signals, such as π/4 DQPSK (Differential Quadrature Phase Shift Keying) and spread spectrum signals, make the PA efficiency problem even more difficult because the modulation may cause the amplitude of the envelope to vary by 14 dB or more. Moreover, the peak-to-average power values may run from 3 dB, as in π/4 DQPSK, to 17 dB for some CDMA systems. Peak-to-average power is important because clipping occurs when the peak-power capabilities of the PA are exceeded, and clipping introduces much distortion. Most systems are biased so that the PA runs at near saturation when the amplitude of the envelope is at a maximum, corresponding to peak power output. To become even more efficient, some systems push the peak power output into saturation, but this can result in unacceptable ACP emissions. This push into saturation can also cause distortions in the in-band modulation accuracy, which is called EVM (error-vector modulation) accuracy, and is specified in terms of RMS error from an ideally modulated signal. To realize good ACP and EVM figures, transmitters that drive the PA into saturation often pre-distort those sections of the input envelope which would be compressed during saturation, so that the resulting output is an undistorted facsimile of the input. Unfortunately, most saturation regions are narrow (often less than the 3 dB peak-to-average criterion given above for π/4 DQPSK), and thus only allow modest pre-distortion (and efficiency) improvements. 
     Prior art PA designs are particularly inefficient when operating at less than full output power, as is common in systems that use adaptive power control. With adaptive power control the system controls the output power of the PA such that the PA provides only as much output power as is needed to provide good communications. Adaptive power control is useful because it extends battery life, by transmitting with no more power than needed, and, at the same time, increases a communication system&#39;s capacity, by reducing the interference among users. However, many of the desired gains promised by adaptive power control have not been realized because the power saved by transmitting at reduced power is lost because the PA is less efficient at reduced power. In one prior implementation, a typical prior art PHS (Personal Handy phone System) transmitter is typically 25% efficient at full power but only 3% efficient at a nominal power reduction of 10 dB. Similar performances have been observed for other modulation schemes and communication systems. 
     SUMMARY 
     The present invention solves these and other problems by providing an envelope feedforward PA design that improves the efficiency of a PA. Efficient operation is provided for signals with a non-constant, as well as constant, envelope. Efficient operation is also provided when operating the PA at reduced power levels. The PA may advantageously be used with many wireless communications systems because power control and high efficiency are universally desired features in subscriber units, as well as base stations. Even though battery life is not generally a problem in a base station, base stations benefit from a more efficient PA because the PA can be made relatively smaller, and the PA can be connected to circuits with lower power delivery ratings. 
     Virtually all communication systems employing a non-constant envelope modulation scheme, including, for example Personal Handy System (PHS) telephones, CDMA and spread spectrum telephones such as the Rockwell Spread Spectrum Telephone (SST), IS-95 [Electronic Industries Association/Telecommunications Industry Association; 1993] telephones, IS-136 telephones, and Personal Digital Cellular (PDC) telephones will benefit from the envelope feedforward PA. In one embodiment, the envelope feedforward PA is advantageously applied to PHS transmitters to increase PA efficiency to 70% or more. 
     Even communications standards employing constant envelope modulation schemes, such as Advanced Mobile Phone Service (AMPS), Global System for Mobile Communications (GSM), and Digital European Cordless Telephone (DECT) systems benefit from the power control feature provided by the envelope feedforward PA. The envelope feedforward transmitter is also useful with wideband systems such as CDMA and spread spectrum systems (e.g., IS-95, etc.). 
     In another embodiment, the feedforward transmitter provides higher efficiency over a range of nominal power output settings. Higher efficiency over a range of power output settings is desirable to support adaptive power control. 
     In one embodiment, an input signal having phase and amplitude components is separated (decomposed) into a phase and frequency modulated (FM) portion and an envelope portion. The FM portion has a constant envelope (no amplitude modulation) and contains the phase and frequency information from the input signal. The envelope portion contains the amplitude information from the input signal. In a multistage amplifier, the FM portion is amplified by a first amplifier to produce an amplified FM signal, and the envelope portion is optionally amplified by a second amplifier. In some embodiments, “amplification” of the envelope portion may be accomplished by adjusting the reference voltage in a digital-to-analog converter. The envelope signal is combined with the amplified FM signal by an envelope combiner to produce a combined signal having FM and amplitude components. The envelope combiner uses the envelope signal to amplitude-modulate the FM signal to produce the combined signal. 
     The feedforward PA also provides precise and efficient power control to allow the transmitter to be operated at reduced power levels without sacrificing efficiency. Over a certain range of power outputs, adjusting the nominal (average) power at the PA output is accomplished by level shifting the envelope component. One method of accomplishing this is by intelligently changing the output range of the DAC (Digital-to-Analog Converter) responsible for the envelope component at baseband. Alternatively, a bias voltage associated with the envelope control input is adjusted. One skilled in the art will recognize that a combination of the above techniques may be used. 
     In one embodiment, the envelope combiner uses a gain-controlled amplifier having a signal input and a control input. The gain of the gain-controlled amplifier is a function of a signal provided to the control input. The amplified FM signal is provided to the signal input and the amplified envelope signal is provided to the control input. An output of the gain-controlled amplifier is the combined signal. 
     In another embodiment, the envelope combiner uses a mixer with conversion gain to combine the amplified FM signal and the amplified envelope signal. The amplified FM signal is provided to one input of the mixer and the amplified envelope signal is provided to another input of the mixer. An output of the mixer is provided to a filter, and an output of the filter is a combined signal. 
     In yet another embodiment, the envelope combiner uses a voltage-controlled switch in combination with a variable gain element to combine the FM signal and the envelope signal. The FM signal is provided to a control input of the switch. The amplified envelope signal is used to alter the transconductance of a variable gain element, such as a FET operating in its linear (saturation) region. The envelope is superimposed on the FM signal by altering the gain of the variable gain element. In one embodiment, the combination of a voltage-controlled switch and a variable gain element is provided by a dual gate FET. 
     In one embodiment, the relative time delays in the signal path of the envelope signal and the FM signal are matched such that the amplified non-constant signal and the amplified FM signal arrive at the envelope combiner at the same time. The delay in the envelope signal path is tuned to the delay in the FM signal path. Proper adjustment of the relative time delay in the two paths reduces spectral regrowth associated with the constant envelope signal input. Real-time adjustment of the delay (tuning) is typically not needed. However, real-time adjustment of the delay may be advantageously provided for transmitters that are not sufficiently stable over time and temperature. Temperature sensors and a control algorithm are used to adjust the delay timing. 
     In one embodiment, an input signal having FM and envelope components is produced by an encoder that produces a modulated signal represented by an I channel output and Q a channel output. The modulated signal is separated (decomposed) into an FM portion and an envelope portion by using a lookup table having cells arranged as rows and columns. A cell is selected (addressed) by using I channel and Q channel values ad row and column addresses. Each cell in the lookup table provides data corresponding to the envelope signal, the I portion of the FM signal (IC), and the Q portion of the FM signal (QC). In one embodiment, the IC and QC portions are combined by a quadrature mixer to produce the FM signal. 
     In one embodiment, an input signal is separated into a first signal and a second signal, the second signal having an envelope amplitude maximum and an envelope amplitude minimum. The first signal is modified to produce a first modified signal, the first modified signal being delayed by a first propagation delay. The second signal is modified to produce a second modified signal, the second modified signal being delayed by a second propagation delay. The first modified signal and said second modified signal are combined to produce an output signal. The lesser of the first propagation delay and the second propagation delay are adjusted to reduce spectral regrowth of the output signal. In one embodiment, an absolute value of a difference between the first propagation delay and the second propagation delay is less than one microsecond. In one embodiment, an absolute value of a difference between the first propagation delay and the second propagation delay is less than one tenth of a time bandwidth of the input signal. In one embodiment, the propagation delay adjustment includes increasing said lesser of said first propagation delay and said second propagation delay. 
     In one embodiment,. the envelope minimum is not less than 75% of the envelope maximum 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     The advantages and features of the disclosed invention will readily be appreciated by persons skilled in the art from the following detailed description when read in conjunction with the drawings listed below. 
     FIG. 1A is a block diagram of prior art PA showing an input signal, several gain stages, and an output signal. 
     FIG. 1B is a frequency-domain representation of the spectrum of the input and output signals shown in FIG.  1 A. 
     FIG. 2 is a block diagram of an envelope feedforward PA in accordance with one aspect of the present invention, that uses an envelope combiner to combine an envelope signal with an FM signal. 
     FIG. 3 is a block diagram of an envelope combiner that uses a mixer with conversion gain to combine an FM signal and an envelope signal. 
     FIG. 4A is a block diagram of an envelope combiner that uses a switch with double-ended (push-pull) inputs to combine an FM signal and an envelope signal. 
     FIG. 4B is a block diagram of an envelope combiner that uses a switch with single-ended inputs to combine an FM signal and an envelope signal. 
     FIG. 4C is a block diagram of an envelope combiner that uses a switch and a variable gain element to combine an FM signal and an envelope signal. 
     FIG. 5 is a circuit schematic of an envelope combiner switch that uses a dual gate FET. 
     FIG. 6 is a block diagram of a prior art transmitter that uses an I-Q encoder and a quadrature mixer, and a conventional PA. 
     FIG. 7A is a block diagram of an improved transmitter that uses an I-Q encoder, a quadrature mixer, and an envelope feedforward PA. 
     FIG. 7B is a block diagram of an improved transmitter that uses an FM modulator to convert a phase signal into an FM signal for an envelope feedforward PA. 
     FIG. 8A is a block diagram of an envelope extractor that uses a lookup table to separate a signal, represented by I and Q channels, into an envelope portion and an FM portion, where the FM portion is represented by two new I and Q channels labeled IC and QC. 
     FIG. 8B is a block diagram of an envelope extractor that uses separate envelope and FM lookup tables to separate a signal, represented by I and Q channels, into an envelope portion and an FM portion, where the FM portion is represented by two new I and Q channels labeled IC and QC. 
     FIG. 9 is a plot showing Adjacent Channel Power Ratio (ACPR) in dBc (Decibels above the carrier) versus the feedforward envelope delay mismatch in microseconds for a typical PHS system using the transmitter shown in FIG.  7 A. 
     FIG. 10 is a plot showing Error Vector Magnitude (EVM) in percent versus the feedforward envelope delay mismatch in microseconds for a typical PHS system using the transmitter shown in FIG.  7 A. 
     In the drawings, the first digit of any three-digit number generally indicates the number of the figure in which the element first appears. Where four-digit reference numbers are used, the first two digits indicate the figure number. 
    
    
     DETAILED DESCRIPTION 
     FIG. 1A is a block diagram of a typical prior art Radio Frequency (RF) Power Amplifier (PA)  100  having an input  102  and an output  104 . The input  102  is provided to an input of a first gain stage  106 . An output of the first gain stage  106  is provided to an input of a second gain stage  107 . An output of the second gain stage  107  is provided to an input of a third gain stage  108  and an output of the third gain stage  108  is provided to the output  104 . The first and second gain stages  106  and  107  are shown as having a gain of 10 dB each, and the gain stage  108  is shown as having a gain of 8 dB. 
     A time domain plot  110  shows a typical input signal provided to the input  102  and a time-domain plot  120  shows a typical output signal provided by the output  104 . The plot  110  shows the input signal as a curve  112  having an envelope  111 . The amplitude of the envelope  111  varies with time, having a relatively low amplitude region  114  and a relatively high amplitude region  118 . As illustrated, the amplitude envelope has an envelope amplitude minimum and an envelope amplitude maximum. The plot  120  shows the output signal and its envelope as being very similar to the curve  112  and envelope  11 I respectively, except that the amplitudes in the plot  120  are much larger owing to the amplification provided by the gain stages  106 - 108 . FIG. 1B is a frequency-domain representation of the spectrum of the input and output signals shown in FIG.  1 A. The spectrum shown in FIG. 1B shows a bandwidth B and a center frequency ω c . 
     FIG. 1A shows three gain stages because typical solid state amplifier cannot produce enough power gain in a single stage. If the signal at the input  102  has an average power level of −10 dBm (where dBm is the power in decibels referenced to one milliwatt), then the output of the first gain stage  106  will have an average power level of 0 dBm, the output of the second gain stage  107  will have an average power level of 10 dBm, and the output of the third gain stage  108  will have an average power level of 18 dBm (74.0 milliwatts). Thus, the total power amplification provided by the PA  100  is 28 dB. 
     However, just because each gain stage provides approximately the same gain does not mean that each stage is operating at the same power level. Each successive gain stage operates at a higher power level than the previous gain stage. In the above example, the first stage  106  can be designed to operate at a maximum output power level of just over 0 dBm without distorting the signal being amplified. Thus, even if the first gain stage  106  is only 50% efficient at full power (e.g. a Class A amplifier), the total power dissipated by the first gain stage  106  is only about 0 dBm (1.0 milliwatts). The second stage can be designed to operate at a maximum output power level 10 dBm. Continuing with the same assumption of 50% efficiency, the power dissipated by the second gain stage  107  is approximately 10.0 milliwatts. Finally, the third gain stage  108  can be designed to operate at a maximum output power level of approximately 18 dBm, corresponding to a power dissipation of approximately 63.0 milliwatts. Thus, the total power dissipated by the PA  100  is approximately 74.0 milliwatts (1.0+10.0+63.0), corresponding to an overall efficiency of 50%. 
     The above analysis shows that the greatest potential for improving the efficiency of the PA  100  lies in improving the efficiency of the third gain stage  108 . Even if the efficiency of the first two stages could be increased to 100%, the total power dissipation would still be 63 milliwatts, corresponding to an overall efficiency of 54%. 
     The efficiency of the gain stages  106 - 108  is determined largely by the mode (or class) in which the gain stages operate. Class A amplifiers are know to have a theoretical maximum efficiency of 50%, and this maximum efficiency is achieved only when operating at full output power. Class A amplifiers are less efficient when operating at lower power levels. A pure sine wave can drive a Class A amplifier at full power continuously. A more common signal, such as a music signal or human voice signal, will typically drive a Class A amplifier to full power during some time periods and less than full power during other time periods such that the overall efficiency is typically closer to 25%. The Class A amplifier is least efficient when operating in the quiescent (idle) state wherein the output power is zero. In the quiescent state, the efficiency of the Class A amplifier is 0% and the Class A amplifier dissipates twice its maximum output power level as heat. Thus, in the above example, the third gain stage dissipates approximately 126.0 milliwatts in the quiescent state. 
     Other amplifiers, such as Class AB, Class D, etc., which provide higher efficiencies are known in the art. Class AB amplifiers are commonly used in audio power amplifiers and can provide a theoretical maximum efficiency of approximately 75% (when operated in Class B mode) and, perhaps more importantly, dissipate very little power in the quiescent state. Class D amplifiers provide a theoretical maximum efficiency of 100% and dissipate very little power in the quiescent state. Other types of amplifiers are known as well. However, due to the characteristics of solid-state devices, solid-state RF power amplifiers, especially amplifiers that operate at 0.5 GHz and higher, are typically based on Class A or Class AB designs for non-constant envelope modulation schemes. 
     The maximum output power that can be delivered by a Class A amplifiers is largely determined by the power supply voltage provided to the amplifier, the output impedance of the amplifier, and the characteristics of the active devices (e.g. transistors, FETs, etc.) used in the amplifier. Reducing the power supply voltage provided to a Class A amplifier will reduce the maximum output power that the amplifier can produce, and thus will also reduce the power dissipated by the amplifier. However, reducing the power supply voltage does not make the amplifier more efficient. Moreover, the theoretical 50% efficiency of a Class A amplifier is not achieved in a solid state RF power amplifiers (PA), again because of characteristics of solid state devices. A typical low distortion RF PA with a Class A input stage and a Class AB output stage has an efficiency closer to 25-28% at full power and 3% when operating at 10 dB below full power. 
     Since a Class A RF PA operates more efficiently at full power, it would seem prudent to design RF communications systems to use modulation schemes that provided a modulated signal with a constant envelope so that the PA could operate at full power (peak efficiency at all times). For example, the curve  112  shown in FIG. 1A corresponds to a modulation scheme that does not provide a constant envelope, as shown by the envelope  111 . Modulation schemes that do produce a constant envelope (e.g., an envelope such that the curve  111  is a horizontal line) are known, including, for example, Frequency Shift Keying (FSK), Minimum Shift Keying (MSK), Gaussian Minimum-Shift Keying (GMSK), Frequency Modulation (FM), and Tamed-FM. Unfortunately, such modulation schemes use more bandwidth than many of the modulation schemes that produce a non-constant envelope. If the constant envelope is viewed as a constraint on the modulated signal, then it can be said that the constant envelope modulation schemes use more bandwidth because the constant envelope signal is constrained in one dimension as compared to (i.e., has fewer degrees of freedom than) the non-constant envelope (unconstrained) scheme. The constant amplitude modulator overcomes the constraint on amplitude by using more bandwidth. The spectrum  150  shown in FIG. 1B shows a bandwidth B corresponding to the frequency bandwidth of the curve  112 . If the curve  112  were re-modulated using a modulation scheme that provided a constant envelope  111 , then the value of B shown in FIG. 1B would increase. Increasing the bandwidth B for a communication channel is undesirable because it limits the number of channels that can be provided within a given frequency band. Thus, communications systems designers, such as the designers of cellular telephone systems, are often forced to balance transmitter efficiency (and thus battery life) against the number of channels that can be provided. 
     FIG. 2 is a block diagram of a feedforward PA  200 , in accordance with one aspect of the present invention, that simultaneously provides some of the efficiency of constant envelope modulation and the system benefits of non-constant envelope modulation. In FIG. 2, an input signal  202 , having a non-constant envelope, is provided to an input of an envelope extractor  206 . The envelope extractor  206  decomposes the input signal  202  into two signals: an envelope signal having a non-constant envelope, and an FM signal having a constant envelope. In one embodiment, an AM (Amplitude Modulation) detector is used to extract the envelope signal, and an FM detector is used to extract the FM signal. The envelope signal carries the envelope (AM) portion of the input signal  202 , and the FM signal carries the phase and frequency modulated (FM) portion of the input signal  202 . The envelope signal is provided to an input of a delay block  208 . An output of the delay block  208  is provided to an input of an envelope amplifier  212 . An output of the envelope amplifier  212  is provided to an envelope input of an envelope combining PA shown as an envelope combiner  216 . 
     The FM signal from the envelope extractor  206  is provided to an input of an up-converter  210  and an output of the up-converter  210  is provided to an input of an amplifier  214 . The up-converter  210  is optional and may be omitted. If the up-converter is omitted, then the FM output from the envelope extractor  206  is provided to the input of amplifier  214 . An output of the amplifier  214  is provided to an FM input of the envelope combiner  216 . An output of the envelope combiner  216  is provided to an output  204 . The output  204  is the output of the PA. The amplifiers  212  and  214  are optional. 
     In one embodiment, the envelope combiner  216  is a gain-controlled amplifier  218  as shown in FIG.  2 . The envelope input of the envelope combiner  216  is provided to a gain control input of the amplifier  218  and the FM input of the envelope combiner  216  is provided to a signal input of the amplifier  218 . An output of the amplifier  218  is provided to the output of the envelope combiner  216 . 
     FIG. 2 also shows various plots corresponding to waveforms in the feedforward PA  200 . A frequency-domain plot  220  shows a frequency spectrum  224  corresponding to the spectrum of the input signal  202 . A time-domain plot  222  shows a curve  224  corresponding to the input signal  202 , a curve  223  corresponding to the positive portion of envelope of the waveform  224 , and a curve  221  corresponding to the negative portion of envelope of the waveform  224 . 
     A frequency-domain plot  230  shows a frequency spectrum  232  corresponding to the spectrum of the envelope signal at the envelope output of the envelope extractor  206 . A time-domain plot  240  shows a curve  242  corresponding to the envelope signal. The envelope shown in the curve  242  is approximately the same as the curve  223 . 
     A time-domain plot  250  shows a waveform  252  corresponding to the FM signal at the FM output of the envelope extractor  206 . The waveform  252  has an envelope that is approximately constant. A frequency-domain plot  270  shows a curve  272  corresponding to the spectrum of the FM signal. The bandwidth of the spectrum  272  is broader than the bandwidth of the spectrum  224  because the spectrum  272  is a constant envelope whereas the spectrum  272  is a non-constant envelope. However, the center frequency of the spectrum  272  is approximately the same as the center frequency of the spectrum  224 . 
     A time-domain plot  280  shows a waveform  282  corresponding to the output signal on the line  204 . A frequency-domain plot  260  shows a spectrum  262  corresponding to the spectrum of the output signal. The output spectrum  262  is approximately the same as the input spectrum  224  to within a constant gain factor. Likewise, the output curve  282  is approximately the same as the input curve  224  to within a constant gain factor. 
     The envelope extractor  206  decomposes the input signal into an envelope signal and an FM signal. In general, the input signal has a time-varying amplitude component and a time-varying FM component. The FM signal has a constant envelope, and thus it is the envelope signal that contains the time-varying envelope component from the input signal. By contrast, the envelope signal is at a lower frequency than the input signal, and thus the time-varying FM component of the input signal is carried by the FM signal. Mathematically, the FM and envelope portions of a signalf(t) may be described as: 
     
       
           f ( t )= Re[a ( t ) Ke   j[ω     c     t+γ(t)] ]  (1) 
       
     
     where a(t) is the envelope portion and Ke j[ω     c     t+γ(t)]  is the FM portion (where ω c  is the carrier frequency, K is a constant gain factor, and γ(t) is the time-varying angle with respect to the carrier. The time dependence provided by the term γ(t) is sufficient to describe both frequency modulation and phase modulation. The envelope portion a(t) is positive and real valued such that a(t)=|a(t)|. For a pure frequency-modulated signal (e.g., an FM broadcast signal) the envelope portion a(t) is a constant. 
     Stated differently, if the input signal is viewed as an amplitude-modulated signal, then the envelope signal is the baseband component and the FM signal is the RF component. Accordingly, the FM signal may be up-converted by the up-converter  210  without affecting the envelope signal  209 , in the same way that up-converting an amplitude-modulated signal from an Intermediate Frequency (IF) to RF does not change the envelope of the up-converted signal. Thus, the FM signal provided by the envelope extractor  206 , may be up-converted to RF. The FM signal has a constant envelope, and up-converting to RF will not change the nature of the envelope. This is clear from Equation (1) because a up-conversion merely changes the value of the carrier ω c  and thus has no effect on the envelope a(t). 
     After up-conversion, the output of the up-converter  210  will be a constant envelope FM signal. The constant envelope FM signal is provided by the up-converter  210  to the optional amplifier  214 . Since the signal provided to the amplifier  214  has a constant envelope, the amplifier  214  may operate at full power (e.g., at or near saturation) at all times. The amplifier  214  may be a Class D amplifier. Even if the amplifier  214  is a Class A amplifier, it will operate near its region of maximum efficiency because it operates at full power. However, the amplifier  214  need not operate at high power levels. In one embodiment, the amplifier  214  is a single stage amplifier, corresponding approximately to the first gain stage  106  shown in FIG.  1 . In another embodiment, the amplifier  214  is a two-stage amplifier, corresponding approximately to the first gain stage  106  and the second gain stage  107  shown in FIG.  1 . In general, the amplifier  214  is an n-stage amplifier. The number of stages is determined by the signal output level of the up-converter  210 , the drive signal requirements of the combiner  216 , and the amount of gain that can be provided by each gain stage. 
     The amplifier  212  amplifies the envelope signal, but since the envelope signal is operating at baseband, the amplifier  212  is typically not an RF amplifier. In a cellular telephone application, the amplifier  212  is a baseband frequency amplifier. Techniques for building efficient solid-state amplifiers are known in the art, and thus the amplifier  212  may be made to operate in a power efficient manner. Even if the amplifier  212  is a Class A amplifier, it will still typically operate more efficiently than an RF Class A amplifier because solid-state devices typically operate more efficiently at lower frequencies. The amplifier  212  may be omitted when the output of the delay  208  is sufficient to drive the envelope input of the envelope combiner  216 . Typically, the FM signal is amplified more than the envelope signal. 
     The envelope signal propagates along an envelope signal path from the envelope output of the envelope extractor  206  to the envelope input of the envelope combiner  216 . The FM signal propagates along an FM signal path from the FM output of the envelope extractor  206  to the FM input of the envelope combiner  216 . The envelope combiner  216  recombines the envelope signal and the FM signal to produce an output signal. The envelope combiner  216  effectively amplitude-modulates the FM signal according to the amplitude of the envelope signal. If the up-converter  210  is not provided, then the output signal will be an amplified replica of the input signal. If the up-converter  210  is provided, then the output signal will be an up-converted and amplified replica of the input signal. 
     If the envelope signal and the FM signal are properly recombined, then the bandwidth of the output signal will be approximately the same as the bandwidth of the original input signal  202 . If the envelope signal and the FM signal are not properly recombined, then the bandwidth of the output signal will be broader than the bandwidth of the original input signal  202 . The increase in the bandwidth is known a spectral regrowth. Proper recombination depends, in part, on matching the time delay in the FM signal path to the time delay in the envelope signal path. Proper recombination also depends on the envelope depth being appropriate for the output power level. In other words, the peak-to-average envelope output power should be faithfully reproduced. Since the time delay in the FM signal path is often longer than the time delay in the envelope signal path, the time delay  208  is added to the envelope signal path. 
     The time delay  208  adds enough additional delay to the envelope signal path such that the time delay of the envelope signal path matches the time delay of the FM signal path. 
     The time delay  208  is added to the envelope signal path because the envelope signal path is usually shorter than the FM signal path. In transmitters where the reverse is true, then the time delay  208  is moved to the FM signal path. The time delay  208  is a fixed time delay when the other components of the transmitter  200  are sufficiently stable with time and temperature to maintain the desired synchronization between the envelope and FM signal paths. In many systems, the travel time required for a signal to traverse the system is a function of the temperature of the system. This variation in travel time versus temperature can be reduced by increasing the bandwidth of the signal path. Moreover, it is the differential variation (i.e., the difference between the travel time through the envelope signal path and the FM signal path) that is adjusted by the time delay  208 . Common mode variations (i.e., changes that occur in both signal paths) are less important. In a preferred embodiment, the envelope signal path and the FM signal path are provided with sufficient bandwidth such that the differential variation in the signal travel time through the two paths is relatively small, and the time delay  208  is a fixed time delay. 
     In an alternative embodiment, the time delay  208  is an adaptive variable time delay that adjusts the amount of time delay provided by the time delay  208  in order to reduce spectral regrowth in the output signal. The time delay  208  is configured as a variable time delay when the other components of the transmitter  200  are not sufficiently stable with time and temperature to maintain the desired synchronization. In one embodiment, the variation of an adaptive time delay is controlled by a sensor (such as a temperature sensor) that detects instabilities in the other components and/or a filter that detects spectral regrowth in the output signal. 
     If these envelope and FM signals are not properly synchronized, the resulting spectral regrowth can be large. The time delay block  208  can be implemented using analog devices or digital devices. Digital delay compensation provides a relatively easy way to control the delay in the envelope path and thus ensure that the delay in the envelope path matches the delay in the FM path. Specific examples of the effect of delay mismatch between the envelope signal path and the FM signal path are shown in FIGS. 9 and 10 in connection with the quadrature feedforward transmitter  700  shown in FIG.  7 . 
     The envelope combiner amplitude modulates the FM signal by multiplying the FM signal with the envelope signal. The gain-controlled amplifier  218  shown in FIG. 2 is one embodiment of an envelope combiner. Since the amplitude of the envelope of the FM signal is constant, it is the envelope signal that carries the amplitude variations in the envelope of the output waveform. The gain-controlled amplifier  218  shows, very simply, how the amplitude of the FM signal can be varied according to the envelope signal. 
     The FM signal is, in some embodiments, an RF signal, and thus the amplifier  218  in these embodiments is an RF amplifier. FIG. 3 is a block diagram of an envelope combiner  316  that avoids the use of an amplifier, and instead, uses a mixer  310  to combine the FM signal and the envelope signal. The envelope combiner  316  has an envelope input  304 , an FM input  302 , and a combined output  308 . The envelope combiner  316  may be used in place of the envelope combiner  216 . The envelope input  304  is provided to a first input of the mixer  310  and the FM input  302  is provided to a second input of the mixer  310 . An output of the mixer  310  is provided to an input of a bandpass filter  312  and an output of the bandpass filter  312  is provided to the output  308 . 
     Mathematically, the gain controlled amplifier  218  used in the envelope combiner  216  multiplies the FM signal by a gain factor that is provided by the envelope signal. The mixer  310  used in the envelope combiner  316  performs the same mathematical operation, but without the use of an amplifier. In fact, the mixer  310  may be a passive device (many mixers use diodes). One skilled in the art will recognize that a passive mixer cannot provide more power out than power in, whereas an active device, such as the amplifier  218  can provide gain. The envelope combiner  316  relies on the gain provided by the amplifier  212  and  214 . In other words, when comparing FIG.  1  and FIG. 2, the gain provided by the amplifiers  106 - 108  in FIG.  1 . is provided by the amplifiers  212  and  214  in FIG. 2 (when using a passive envelope combiner). 
     The mixer  316  multiplies the envelope signal by the FM signal and, mathematically, in terms of the power in the output signal, it matters little whether most of the gain is provided by the amplifier  212  or the amplifier  214 . Since the amplifier  212  is typically more efficient than the amplifier  214 , it is typically desirable to provide relatively more power (e.g., gain) from the amplifier  212  and relatively less power (e.g., gain) from the amplifier  214 . 
     Since the envelope and FM signals have different frequency components, the multiplication produces sum and difference products of the various frequencies in the two signals. The filter  312  selects the desired frequencies and provides these frequencies at the output  308 . 
     FIG. 4A is a block diagram of yet another envelope combiner  416  based on a solid state Single-Pole Double-Throw (SPDT) switch  417 . The switching envelope combiner  416  may be used in place of the envelope combiner  216 . The envelope combiner  416  shows an envelope input  404 , an FM input  402 , and a combined output  408 . The envelope input  404  is provided to an input of a non-inverting amplifier  410  having a gain K and to an input of an inverting amplifier  412  having a gain −K. An output of the non-inverting amplifier  410  is provided to the first throw of the SPDT switch  417  and an output of the inverting amplifier  412  is provided to the second throw of the SPDT switch  417 . The pole of the SPDT switch  417  is provided to an input of a filter  418  and an output of the filter  418  is provided to the output  408 . The FM input  402  is provided to a control input of the SPDT switch  417 . 
     One skilled in the art will recognize that other embodiments of the envelope combiner  416  are possible. The non-inverting amplifier  410  may be removed (replaced by a short) if the inverting amplifier has no power gain (K=1). Both the non-inverting amplifier  410  and the inverting amplifier  412  may be removed if the amplifier  212  provides inverted and non-inverted outputs, in which case the inverting output is provided to the first throw and the non-inverting output is provided to the second throw (or vice versa). 
     In yet another embodiment, the functions of the switch  417  and the amplifiers  410  and  412  are combined into a single power amplifier-switch. The amplifier-switch may provide sufficient power amplification such that the amplifiers  212  and  214  are relatively low-power amplifiers. 
     FIG. 4B is a block diagram of yet another envelope combiner  426  based on the solid state Single-Pole Double-Throw (SPDT) switch  417 . The switching envelope combiner  426  may be used in place of the envelope combiner  416 . The envelope combiner  426  shows an envelope input  404 , an FM input  402 , and a combined output  408 . The envelope input  404  is provided to an input of the non-inverting amplifier  410  having a gain K. An output of the non-inverting amplifier  410  is provided to the first throw of the SPDT switch  417  and the second throw of the SPDT switch  417  is provided to ground. The pole of the SPDT switch  417  is provided to an input of a filter  418  and an output of the filter  418  is provided to the output  408 . The FM input  402  is provided to a control input of the SPDT switch  417 . 
     In both FIGS. 4A and 4B, the FM signal controls the switch  417 . When the FM signal is positive, then the switch  417  switches to the first throw, and when the FM signal is negative, then the switch  417  switches to the second throw. Most of the power gain comes from the switch  417  acting like a Class D amplifier. The envelope input  404  changes the output swing of the Class D amplifier. Efficiency is enhanced when the gain K is such that a small envelope control produces a large output swing. The amplifier  214  need only provide enough power to operate the switch  416 . The envelope combiner  416  operates as a sampled data system, with the switch  416 , as the sampler. Like most samplers, the signal on the output of the sampler (i.e., on the throw of the switch  417 ) will contain many sidebands. The filter  408  selects the desired sideband. In one embodiment, the filter  418  is a bandpass filter tuned to the same frequency band as the FM signal provided at the input  402 , but with a bandwidth that corresponds to the input signal provided at the input  202  in FIG.  2 . 
     FIG. 4C is a block diagram of yet another envelope combiner  436  based on a solid state Single-Pole Single-Throw (SPST) switch  432 . The switching envelope combiner  436  may be used in place of the envelope combiner  416 . The envelope combiner  436  shows an envelope input  404 , an FM input  402 , and a combined output  408 . The envelope input  404  is provided to a control input of a controlled current source  430  having a transconductance gm. A first terminal output of the current source  430  is provided to a first terminal of the SPST switch  432  and the second terminal of the SPDT switch  432  is provided to ground. The FM input  402  is provided to a control input of the SPST switch  432 . A second terminal of the current source  430  is provided to an input terminal of a filter  434  and an output terminal of the filter  434 -is provided to the combiner output  408 . The second terminal of the current source  430  is also provided to a first terminal of an inductor  438 . A power supply voltage VDD is provided to a second terminal of the inductor  438 . The power supply VDD is bypassed by a bypass capacitor  440  connected between the VDD supply and ground. 
     In FIG. 4C, the FM signal controls the switch  434 . When the FM signal is positive, then the switch  434  switch closes and the current source  430  delivers current to the filter  434 . When the FM signal is negative, then the switch  434  opens and the current flow stops. Most of the power gain comes from the switch  434  acting like a Class D amplifier that provides pulses of current to the filter  434 . The envelope input  404  changes the amplitude of the current pulses. Efficiency is enhanced when the transconductance g m  is such that a relatively small envelope control voltage produces relatively large current pulses. The amplifier  214  need only provide enough power to operate the switch  434 . The envelope combiner  436  operates as a sampled data system, with the switch  436 , as the sampler. Like most samplers, the signal on the output of the sampler will contain many sidebands. The filter  434  selects the desired sideband. In one embodiment, the filter  434  is a bandpass filter tuned to the same frequency band as the FM signal provided at the input  402 , but with a bandwidth that corresponds to the input signal provided at the input  202  in FIG.  2 . 
     FIG. 5 is a circuit schematic of a switching envelope combiner  500  that uses a dual gate FET  534  as a power amplifier-switch. The circuit shown in FIG. 5 functions according to the block diagram shown in FIG. 4C where the FET  534  is an active element used to provide the functions represented by the current source  430  and the switch  432 . In FIG. 5, an envelope input  502  is provided to a first terminal of a capacitor  510 . A resistor  509  is connected in parallel with the capacitor  510 . A second terminal of the capacitor  510  is provided to a first terminal of a resistor  518 , to a first terminal of an inductor  520 , to a first terminal of a capacitor  516 , and to a first terminal of a resistor  514 . A second terminal of the resistor  514  is provided to a power supply input VG 2   512 . A second terminal of the capacitor  516  is provided to ground. A second terminal of the resistor  518  is provided to ground, and a second terminal of the inductor  520  is provided to a second gate of the FET  534 . 
     An FM input  504  is provided to a first terminal of a DC-blocking capacitor  522 . A second terminal of the DC-blocking capacitor  522  is provided to a first terminal of an inductor  524  and to a first gate of the FET  534 . A second terminal of the inductor  524  is provided to a grounded resistor  526 , to a grounded capacitor  528 , and to a first terminal of a resistor  530 . A second terminal of the resistor  530  is provided to a grounded capacitor  532  and to a power supply input VG 1   522 . 
     A power supply input VDD  550  is provided to a first terminal of a grounded bypass capacitor  544  and to a first terminal of an inductor  546 . A second terminal of the inductor  546  is provided to a first terminal of an inductor  538 , to a grounded capacitor  542  and to a grounded capacitor  540 . In a preferred embodiment, the inductor  546  is a wire through a ferrite bead. A second terminal of the inductor  538  is provided to a first terminal of a DC-blocking capacitor  536  and to a drain of the FET  534 . A second terminal of the DC-blocking capacitor  536  is provided to a combined output  506 . A source of the FET  534  is provided to ground. 
     In a preferred embodiment for a PHS system, the FET  534  is a dual-gate MESFET. The ferrite bead of the inductor  546  is an F bead. The capacitors  522 ,  542 ,  536 ,  516  and  528  are each 15 pF (pico-Farad) capacitors. The capacitors  532  and  540  are 1000 pF capacitors. The capacitor  544  is a 4.7 μF (micro-Farad) capacitor and the capacitor  510  is a 1.0 μF capacitor. The inductors  524  and  538  are 15 nH (nano-Henry) inductors and the inductor  520  is a 75 nH inductor. The resistors  518  and  526  are 1.0 M-Ohm (Mega-Ohm) resistors and the resistor  530  is a 10 k-Ohm (kilo-Ohm) resistor. The power supply voltage VG 1   522  is 1.9 V (Volts) to 5 V, the power supply voltage VG 2   512  is −1.0 to −3.0 V, and the power supply voltage VDD  550  is 1.9 V to 5 V. The higher voltages generally provide more output power and the lower voltages generally provide lower output power, but this is load-line dependent. 
     When used with the component values above in a PHS system, the FM signal provided to the FM input  504  is a band-limited signal RF signal with a center (carrier) frequency of approximately 1.9 GHz, and the envelope signal provided to the envelope input  502  is a baseband signal with most of its spectral components below 300 kHz (kilo-Hertz). The output signal  506  after bandpass filtering by a bandpass filter, such as the filter  418  shown in FIG. 4, is a PHS transmitter signal having a bandwidth of approximately 300 kHz at a center frequency of approximately 1.9 MHz. 
     The dual-gate FET  534  operates as a common source amplifier, providing primarily current gain with little, if any, voltage gain. The first gate of the FET  534  is biased by a voltage divider using the resistor  530  and the resistor  526 . First gate is biased such that the FET  534  is in an “off” state (pinch-off) when there are no input signals to the input  504 . The FM signal, provided at the input  504 , is coupled through a DC-blocking capacitor  522  to the second gate. The FM signal operates to switch the FET  534  between the off state and a fully “on” (saturated) state in a manner similar to a Class-D switching amplifier. 
     The second gate of the FET  534  is biased by a voltage divider using the resistors  514  and  518 . An envelope signal provided at the input  502  is coupled through a bandpass filter (the series combination of the capacitor  510  and the RF blocking inductor  520 ) to the second gate of the FET  534 . The envelope signal provided to the second gate controls the g m  (transconductance) of the FET  534 . Thus, the RF signal applied to the first gate controls when the FET  534  is on and off, and the envelope signal applied to the second gate controls the current provided by the FET  534  when the FET  534  is in the on state. The linearity of the envelope combiner  500  depends, in part, on the linearity of the transconductance g m . The upper gate of the dual-gate FET  534  is preferably operating in its linear region to control g m . 
     When the FET  534  is in the on state (saturated), current flows from the constant voltage power supply input VDD  550  and into the inductor  538 . The RF signal applied to the first gate switches the FET  534  on and off to produce a series of current pulses through the inductor  538 . The inductor  538  provides DC current to the FET  534  which converts the DC current to an RF current that is coupled through the DC-blocking capacitor  536  to the output  506 . 
     The Feedforward PA with a Quadrature Mixer 
     The signal to be amplified by the PA and transmitted may be decomposed into the envelope component and FM component at many stages before the PA. Many transmitters use a quadrature mixer in combination with a quadrature encoder. The quadrature encoder provides an in-phase (I) channel and a quadrature-phase (Q) channel to the quadrature mixer. A feedforward power amplifier, as discussed in connection with FIGS. 2-4 may advantageously be used in systems that have a quadrature encoder. 
     FIG. 6 is a block diagram of a conventional transmitter  600  that uses an I-Q encoder  610 , a quadrature mixer  620 , and a conventional PA  633 . A π/4 DQPSK (Differential Quadrature Phase Shift Keying) encoder is an example of an I-Q encoder. In FIG. 6, a data signal  602  is provided to a data input of the encoder  610 . The data signal may be data bits, such as digitized voice data in a digital cellular telephone, that are to be encoded and transmitted. An I channel output of the encoder  610  is provided to an input of a digital-to-analog converter  612  and an analog output of the digital-to-analog converter is provided to a first input of the quadrature mixer  620 . The I channel data is N bits wide. A Q channel output of the encoder  610  is provided to an input of a digital-to-analog converter  614  and an analog output of the digital-to-analog converter is provided to a second input of the quadrature mixer  620 . The Q channel data is M bits wide. In most systems, M=N. 
     The quadrature mixer  620  includes a first mixer  622 , a second mixer  624 , and an adder  626 . The first input of the quadrature mixer  622  is provided to a first input of the first mixer  622 . A Local Oscillator (LO) signal cos(ω c  t) is provided to a second input of the first mixer  622 . An output of the first mixer  622  is provided to a first input of the adder  626 . The second input of the quadrature mixer  622  is provided to a first input of the second mixer  624 . A Local Oscillator (LO) signal sin(ω c  t) is provided to a second input of the second mixer  624 . An output of the second mixer  624  is provided to a second input of the adder  626 . An output of the adder  626  is provided as an output of the quadrature mixer  620 . 
     The output of the quadrature mixer  620  is provided to an input of the PA  633 , and an output of the PA  633  is provided as an output of the transmitter  600 . The PA  633  is shown as a series of three gain stages  630 - 632  similar to the PA shown in FIG.  1 . 
     FIG. 7A is a block diagram of an improved transmitter  700  that uses the quadrature encoder  610  and the quadrature mixer  620  in a feedforward PA configuration. As in FIG. 6, FIG. 7A shows the data input  602  provided to the quadrature encoder  610 . The I and Q channel outputs from the quadrature encoder  610  are provided, respectively, to I and Q channel inputs of a quadrature envelope extractor  716 . The I channel is provided by an I bus  712  and the Q channel is provided by a Q bus  714 . The quadrature envelope extractor  716  decomposes the signal represented by the I and Q channels into an envelope portion (E), a constant envelope in-phase (IC) FM portion and a constant envelope quadrature (QC) FM portion. The envelope portion E is given by the equation E=sqrt(I 2 +Q 2 ), where sqrt is a square root. The IC portion is given by the equation IC=I/E and the QC portion is given by the equation QC=Q/E. 
     An envelope output (E) from the quadrature extractor  716  is provided by and E bus  718  to an input of a delay block  724 . An output from the delay block  724  is provided to an input of an envelope digital-to-analog converter  726 . An output of the envelope digital-to-analog converter  726  is provided to an input of an amplifier  728 . An output of the amplifier  728  is provided to an envelope input of a feedforward envelope combiner  740 . 
     As with the time delay  208 , the time delay  724  may be moved to the FM signal path, and the time delay is either fixed or variable as needed to maintain the desire synchronization between the envelope signal path and the FM signal path. 
     The IC FM portion from the quadrature envelope extractor  716  is provided by an IC bus  721  to an input of a first digital-to-analog converter  732 . The QC FM portion from the quadrature envelope extractor  716  is provided by a QC bus  722  to an input of a second digital-to-analog converter  734 . An analog output from the first analog converter  732  is provided to the I channel input of the quadrature mixer  620  and an analog output from the second analog converter  734  is provided to the Q channel input of the quadrature mixer  620 . An output of the quadrature mixer  620  is provided to an input of an amplifier  737 . An output of the amplifier  737  is provided to an FM input of the envelope combiner  740 . 
     An output of the envelope combiner is provided as an output  704  of the transmitter  700 , where the output signal O may be expressed as O=E(IC+QC ). The I bus  712  is NI bits wide, the Q bus  714  is NQ bits wide, E bus  718  is NE bits wide, the IC bus  721  is NIC bits wide, and the QC bus  722  is NQC bits wide. In one embodiment, NI=NQ and NIC=NQC. 
     Although the transmitter  700  is shown as a hybrid device having both digital and analog portions, one skilled in the art will recognize that the transmitter  700  may also be implemented using analog devices, digital devices, or software running on a digital processor. Power control inputs may be provided to the DACs, envelope combiner, and various gain elements in the system. 
     FIG. 7B is a block diagram of an improved transmitter  750  that uses the quadrature encoder  610  and an FM modulator  762  in a feedforward PA configuration. As in FIG. 6, FIG. 7B shows the data input  602  provided to the quadrature encoder  610 . The I and Q channel outputs from the quadrature encoder  610  are provided, respectively, to I and Q channel inputs of an quadrature envelope extractor  752 . The I channel is provided by an I bus  712  and the Q channel is provided by a Q bus  714 . The envelope extractor  152  decomposes the signal represented by the I and Q channels into an envelope portion and a phase portion. 
     An envelope output (E) from the extractor  752  is provided by an E bus  718  to an input of a delay block  724 . An output from the delay block  724  is provided to an input of an envelope digital-to-analog converter  726 . An output of the envelope digital-to-analog converter  726  is provided to an input of an amplifier  728 . An output of the amplifier  728  is provided to an envelope input of a feedforward envelope combiner  740 . 
     A phase output (P) from the extractor  752  is provided to an input of a digital-to-analog converter  760 . An analog output from the analog converter  760  is provided to a modulation input of the FM modulator  762 . A carrier frequency signal is provided to an FM reference input of the FM modulator  762 . An FM output of the modulator  762  is an FM signal. The FM output of the modulator  762  is provided to an input of a wideband filter  764 . An output of the filter  764  is provided to an input of an amplifier  737 . An output of the amplifier  737  is provided to an FM input of the envelope combiner  740 . 
     The feedforward envelope extractors discussed in connection with FIGS. 2,  7 A and  7 B may be constructed as analog devices, digital devices, software running on a digital processor, or digital-analog hybrids. FIG. 8 is a block diagram of a power-efficient digital quadrature envelope extractor  800  that uses a lookup table  820  to “calculate” the envelope portion E and FM portions IC and QC from the I and Q input channels. In a digital envelope extractor, calculation of the E, IC, and QC portions may be accomplished by conventional mathematical operations (e.g., add, subtract, multiply, divide, etc). However, in some implementations, the lookup table  820  consumes less power than mathematical hardware (e.g., a hardware multiplier) and thus the lookup table  820  is relatively more power efficient. Moreover, the use of lookup tables reduces numerical errors, especially the numerical errors introduced by numerical calculations (e.g., round-off errors, numerical approximations, etc.). Such numerical errors can lead to poor ACPR performance. 
     In the envelope extractor  800 , NI bits of I channel data from an I channel input  802  are provided to a row decoder  812  that selects a row in a lookup table  820 . Similarly, NQ bits of Q channel data from a Q channel input  804  are provided to a column address decoder  812  that selects a column in the lookup table  820 . The lookup table  820  has  2   NI+NQ  cells arranged in  2   NI  rows and  2   NQ  columns. Each cell contains a E bit field  822  that is NE bits wide, an IC bit field  826  that is NIC bits wide, and a QC bit field  824  that is NIQ bits wide. 
     A particular cell is selected by using the input I bits to select a row of cells, and the input Q bits to select a cell in the selected row. The E bits from the selected cell are provided to an E output  806 , the IC bits from the selected cell are provided to an IC output  808  and the QC bits from the selected cell are provided to a QC output  810 . One skilled in the art will recognize that other lookup table arrangements can be used. For example, the single lookup table  820  can be decomposed into three lookup tables as an E table, an IC table, and a QC table. 
     Reductions in the size of the lookup table  820  are available by exploiting symmetries in the data stored in the table  820 . Data in the I and Q inputs  802  and  804  is typically generated by a quadrature encoder. For many types of quadrature encoding, data in the lookup table  820  will be symmetric when the table  820  is broken up into four quadrants (i.e., one fourth of the lookup table) needs to be stored. Making the assumption that all inputs and outputs are 7 bits wide (NI, NQ, NIC, NQC, and NE are all equal to 7) then (2 7 ×2 7 )/4=4096 7-bit words would be needed for each of the E, IC, and QC bit fields (either as one table where each cell is three 7-bit words, or three tables where each cell is one 7-bit word). The use of 7 bits for the inputs and outputs is typical of many voice-grade communication systems such as PHS, cellular telephones, etc. One skilled in the art will recognize that the assumption of 7 bits for the inputs and outputs is by way of example only and not intended as a limitation. 
     Further reductions in the size of the lookup tables are possible because the output E is unsigned, and the output values IC and QC carry the same sign bits as the input values I and Q, respectively. Thus, no sign bit is needed in addressing the E, I, and Q lookup tables, and no sign bit is necessary in the bit fields that contain E, IC and QC. The sign bits are simply removed from the I and Q inputs and appended to the IC and QC outputs as shown (for 7-bit I and Q channels) in FIG.  8 B. 
     In FIG. 8B, a 7-bit I input bus  802  and a 7-bit Q input bus  804  each have data bits  0 - 5  and a sign bit  7 . Bits  0 - 5  of the I bus  802  are provided to a row address decoder of an envelope (E) lookup table  822 . Bits  0 - 5  of the Q bus  804  are provided to a column address decoder of the envelope (E) lookup table  822 . A 7-bit output of the lookup table  822  is provided as an E output  806 . Bits  0 - 5  of the I bus  802  are provided to a row address decoder of an I/Q lookup table  821 . Bits  0 - 5  of the Q bus  804  are provided to a column address decoder of the I/Q lookup table  821 . A 6-bit Q output of the lookup table  821  is combined with the sign bit (bit  7 ) from the Q bus  804  to produce a QC output  810 . A 6-bit I output of the lookup table  821  is combined with the sign bit (bit  7 ) from the I bus  802  to produce an IC output  808 . Again it is emphasized that the use of 7-bit buses for E, I, Q, IC, and QC is by way of example only, and not as a limitation. 
     In the above example, for the purposes of addressing rows and columns in a lookup table, removing the sign bit effectively reduces the number of address bits in I and Q from 7 bits to 6 bits. Moreover, since the sign bits for IC and QC are obtained from I and Q, the number of bits in each IC and QC field of the lookup table may be reduced from 7 to 6. Thus, in the above example, a total storage of 4096 7-bit words (envelope table), and 8192 (2*4096) 6-bit words (IC and QC tables together) is possible. 
     FIG. 9 is a plot showing the computed Adjacent Channel Power Ratio (ACPR) in dBc (Decibels above the carrier) versus the feedforward envelope delay mismatch in microseconds for a simulated PHS system using the transmitter architecture shown in FIG.  7 A. The calculations shown in FIG. 9 are for a numerical simulation of a PHS system. A PHS system is used by way of example, and not as a limitation. The plot in FIG. 9 is computed for a PHS transmitter operating at a carrier frequency of approximately 1.9 GHz (GigaHertz) with a channel (frequency) bandwidth of approximately 300 kHz, corresponding to a time bandwidth of 3.0 μs (microseconds). A delay mismatch between the envelope signal and the FM signal will cause the bandwidth to increase due to spectral regrowth. Thus, at least to a first order, the required delay match is related to the time bandwidth. FIG. 9 shows that a 600 kHz ACPR (approximately twice the channel bandwidth) of −50 dBc requires that the envelope channel and the FM channel be matched to within approximately 0.25 ps, which is less than one tenth of the time bandwidth. A 600 kHz ACPR of −55 dBc requires that the envelope channel and the FM channel be matched to within approximately 0.05 μs, which is 60 times less than the time bandwidth. A 600 kHz ACPR of −55 dBc is typical of many PHS systems, and thus, in a typical PHS transmitter, it is preferred that the envelope channel and the FM channel be time matched to within approximately ±0.027 μs in order to meet ACPR requirements for the entire transmitter. 
     FIG. 10 is a plot showing a modulation Error Vector Magnitude (EVM) in percent versus the feedforward envelope delay mismatch in microseconds for a simulated PHS system using the transmitter architecture shown in FIG.  7 A. EVM is the RMS modulation error (i.e., the RMS of the desired modulation vector minus the actual modulation vector) in relation to the length of the desired modulation vector. An increase in the EVM increases the bit error rate of the communications system. Although a typical PHS transmitter is expected to have an EVM of approximately 12.5%, an EVM of about 2% is typically allowed in the PA (the remaining 10.5% comes from other elements of the system). As shown in FIG. 10, an EVM of 1% corresponds to a 0.1 μs mismatch between the envelope channel and the FM channel. Thus, the allowable time mismatch associated with the EVM is much larger than the allowable mismatch time delay associated with ACPR. In other words, the sensitivity of EVM to delay mismatch is seen to be less that the sensitivity of ACPR to delay mismatch. 
     Other Embodiments 
     Although the foregoing has been a description and illustration of specific embodiments of the invention, various modifications and changes can be made thereto by persons skilled in the art, without departing from the scope and spirit of the invention as defined by the following claims.