Fli';;" HEWLETT~ftIj PACKARD

Efficient.Linear RF Power Amplification withConstant Envelope Output Stages

Tom Hornak, Bill McFarlandInstruments and Photonics LaboratoryHPL-95-54May, 1995

linear power amplifier;line, constant envelope,power efficient, phasemodulation, amplitudemodulation

There is a scarcity of RF spectrum available for wirelessvoice and data communications. To utilize spectrumefficiently, the transmitted information is best encoded inboth the amplitude and phase of the RF carrier.Transmission of amplitude modulated carriers requireslinear power amplifiers. Conventional linear poweramplifiers use power inefficient class A, AB or B outputstages. In battery operated mobile radios powerefficiency of the transmitter is of utmost importance.More efficient power amplifiers using class C or E outputstages are suitable only for amplifying constant envelopecarriers because of their large envelope distortion. Thereport describes several new methods of generating anamplitude and phase modulated carrier from two phasemodulated constant envelope carriers. The carriers areproduced by efficient class C or E output stages and thencombined in a power combiner. The report describes alsoa new inherently lossless power. combiner whichmaintains unity input power factors at all modulationlevels.

© Copyright Hewlett-Packard Company 1995

Internal Accession Date Only

1. Introduction

Wide-spread use of mobile wireless communication requires two conditions to be met:

a) Due to the general shortage ofavailable spectrum, the RF carrier modulationby whichinformation is transmitted must demandthe smallest possible bandwidth . This means thatthe transmitted information shouldbe encoded in both the amplitude and the phase(frequency) ofthe carrier. In order to keep the transmittedsignal withinthe allottedbandwidth, the modulated carrier must be transmittedwith minimum distortion.

b) Because a mobileradio is powered from a battery, its power consumptionis verycritical. Ifthe transmitter's output amplifier is the largest power consumer in the radio,then a high efficiency power amplifier is an important designgoal.

Conventional linear power amplifiers ofphase and amplitude modulatedcarriershave class A, AB or class B output stages, whichare power inefficient. There are moreefficient output stages, such as class C, or E. Their higherefficiency occurs because theamplitude ofthe voltage swingon the transistor collector is equal to the power supplyvoltage. This leaves only a small voltage across the output transistor when it carriesmaximum current and thus minimizes the power dissipated in the transistor. To maintainhigh efficiency these output stages must be drivenby a fixed amplitude input signalsufficient for the full swing output voltage. An attempt to achievean amplitudemodulatedoutput by drivingthese stages with an alreadyamplitude modulatedinput signal leads togross envelopedistortion and loss ofefficiency. Class C and E stages are therefore mostsuitablefor amplifying constant envelope, only phase or frequency modulated carriers.

An attractive method ofamplifying phase and amplitude modulatedsignalslinearly butefficiently is to amplify a phase modulatedconstant envelopecarrier in a high efficiencyclass C or E output stage and to achieveamplitude modulationin a subsequent operation.

One method to accomplish the above is called "EnvelopeElimination and Restoration"[2]. Here the input signalis processed in parallel by an amplitude detector and a limiter.The envelopeproduced by the detector is amplified in a low frequency power amplifierand the amplifier's output is used as the power supplyofa, say, class C output stage. Theclass C stage is driven by the limited, but stillphase or frequency modulated input signal.The amplitude ofthe class C stages' output signalfollows the enveloperepresented by thevaryingoutput ofthe low frequency amplifier. The voltage across the output transistor,when the transistor carries maximum current, remains small regardlessofthe amplitudemodulation; power dissipation in the transistor thus remains low. The disadvantageofthismethod is the need for the low frequency power amplifier.

Another method ofachieving linear power amplification whileusing class C or E outputstages is known as "HighPower OutphasingModulation" [1] or "LINC - LinearAmplification with NonlinearComponents" [6]. In this method a phase and amplitudemodulatedcarrier v=q(t)Vmaxsin[mt+tp(t)] is being produced. Here Vmax is the carrier's

1

amplitude at its envelopepeak, q(t) is the fractional amplitude modulation, and rp(t) is thecarrier'sdesired phase modulation. To achieve highefficiency, two constant envelope,phase modulated components v}=Vsin[wt+q(t)+a] and sin[wt+qJ(t)-a] are suppliedbytwo constant envelopeoutput stages and then vectorially combined in a power combiner.The additional phase modulation a of vj and V2 is introducedto achievethe desiredamplitude modulationq(t). [In this report the explicit signoftime dependence (t) is usedto distinguish independent, externally imposedtimevarying values from internallygenerated time varyingvalues, suchas a.] If the power combiner generates the outputsignalv by vectorially adding V} and V2 (see Fig.1a), then Vmax=2V If the powercombinergenerates the output signal v by generating a vector average of vj and V2

(Fig.9), then Vmax = V In both cases the amplitude modulation will be q(t)=cosa. Ifvj andv2 are in phase, i.e. a=O, the resulting output has its maximum amplitude Vmax. When VI

and V2 are in antiphase, i.e. a=90o, the resultingoutput has zero amplitude. But the powercombinercould also be designed to vectorially subtract V] from V2 (see Fig.lb), in thiscase q(t)=sina. (phase modulation q(t) ofoutput v is achieved by rotating both V] and V2

in the same direction. This can be easily visualized by imagining the phase modulationrotating the entire referenceplane.)

One subject of this report is a new method ofgenerationofcarriers V] and V2. Anothersubject ofthis report is a new power combiner combining the outputs VI and V2 ofthe twoconstant envelope output stages. Both subjectsare protected by U.S. patents granted toHP [3],[4].

In all of the following discussion we willassumethat the bandwidthof the phasemodulation q(t) and ofthe amplitude modulation q(t) is much smallerthan the carrierfrequency OJ.

2. Generation of Carrier v1 and Carrier V2

2.1 Previously Published Methods

Severalmethods ofgeneratingthe two carriers in LINC power amplifiers have beenpublished in the past.

In [5] the two carriers VI and V2 are produced startingwith a low carrier frequency(rol<<CO) and low power version ofthe desired phaseand amplitude modulated outputsignalv, i.e. with Yin =q(t)Vjnmaxsin[OJ't+q(t)]. This signal is digitized and digital signalprocessingis used to generate Cartesiancomponents 1],Q], representing V], and h,Q2,representingV2, both at the lower frequency OJ'. Then,with an RF oscillator, a phaseshifter and mixersthe two sets ofI and Q components are upconverted to frequency OJ.Next the related I and Q components are combined into the constant envelope

2

components vj and V2. Those are then driving two highly efficient constant envelopeoutput stageswhich, in turn, feed the power combiner.

In [6] the angle a=arcsinq(t) is producedin the following way. Similarly to [5], thestarting point is a low power versionvt«= q(t)Vinmaxsin[mt+q.(t)] ofthe desiredultimatephase and amplitude modulated signal, but in contrastto [5], at the final frequency «J. Thissignal is processed by a limiter to generatea constant envelope, phase only modulatedsignal u=Usin[lVt+q.(t)], and in an envelope detector to generate a baseband replicaoftheamplitude modulation q(t). Then a feedback loop is created whichincludes a phasemodulatorfeeding a phase detector. The phasemodulator modulates the signalu=Usin[mt+q.(t)] fromthe limiter by an amplified error signal causing the phase detectoroutput to follow q(t). This implements an inverse sinefunction so that the signal at theinput ofthe phasemodulator, when reproduced by the constant envelope output stage, isvj=Vsin[mt+q.(t)+a], where a=arcsinq(t). Signal V2 is derived in a similar way.

The subjectof [7] is essentially the samemethod as described in [6], except frequencymultiplication is used in order to decreasethe phasemodulator's operatingrange. Thephase modulatoris driven by a frequency equalto one third ofthe operatingfrequency(iii3), its output frequency is then multiplied by 3 to (j) in a frequency multiplier. Becausephase changes are multiplied by frequency multiplication, this operates the phasemodulatorover a third ofthe ultimate phase angle range a and thus improves its linearity.

In [8] the amplifier first separatesthe input signal Vin = q(t)JlinmaxCOs[lVt+q.(t)] by limitingand amplitude detectioninto a fixed amplitude phasemodulated signal u=Ucos[mt+q.(t)]and a baseband envelope signal Vb=q(t)Jlinmax (similar to [6]). The envelopesignal is thenmodified by analog signal processing whichincludes squaring and square rooting circuitry.The limited signal is phase shifted by 900 to u' =Usin[lVt+q.(t)] and then amplitudemodulated by the modified envelope signal. The original signal Yin and the amplitudemodulated signal u' and its inverse -u' constitutethe respective I and Q components ofvj

and V2. The final step is then generating vj and V2 by proper summing and subtractingtheirI and Q components.

Finally, in [9], the startingpoint are the baseband I and Qcomponents ofthe desiredoutput signal v=q(t)VmaxCOs[lVt+q.(t)] and a carrieroffrequency (i). In this amplifier, lowpower versions ofvj and V2 are generatedby two voltagecontrolledoscillators (YCOs)and then amplified in two constant envelope output stages. The vector-summed outputsignal ofthe two stages is then decomposed bytwo mixers and the carrier (j) into I and Qbaseband components. Finally these I and Q components are comparedwith the originalinput I and Q signals. Anyerror betweenthemis amplified and drivesthe VCO frequencycontrol inputs, forcing the error to zero.

The disadvantage ofthe previously published methods are that any potentialphaseor amplitude error in someofthe processing circuits, in the constant envelopeoutputstages and the combiner appear as distortionin the ultimate output signal (except in [9]).A further disadvantage of some above amplifiers is that they cannot simply substitute a

3

conventional RF power amplifier because the input is either in baseband I,Q·fonn [9] orthe input frequency is lower than the output frequency to either match the limited speed ofthe digitizer and the digital signal processor [5] or to decrease the analog processingerrors [7]. Some amplifiers require complex and error prone open loop analog signalprocessing such as squaring and square rooting [8]. The disadvantage ofthe approach in[9] is that for a continuous >180° range of phase modulation q(t) ofthe final outputsignal, the amplifier must be complemented by a switching matrix operating on the input Iand Q components. This matrix is not described in [9].

2.2 The Proposed New Method

The new method includes the advantage of [6], i.e. the input signal is a low power versionofthe desired output signal, so that the method can easily substitute conventional linearpower amplifiers. It also includes the advantage of [9], i.e. the constant envelope outputstages and the power combiner are part ofa feedback loop and their error is beingattenuated by the loop gain. However, the proposed new method shares the disadvantageof[2], [6], [7], [8], in that it is suitable only for modulation schemes such as Offset-QPSKor 7tl4-QPSK in which the carrier amplitude never drops below a specified minimum.Below certain input level the limiter would lose its output signal and phase referencewould be lost. A block diagram ofthe new method is shown in Fig.2. The apparentcomplexity ofFig.2 is misleading; many ofthe blocks shown can be merged into relativelysimple circuits. For example, addition can be implemented by summing signal currents,inversion can be done by crossing wires in differential circuits.

The new method first separates the phase modulation and amplitude modulation ofthelow power input signal V;n =q(t)Vinmaxsin[a>t+q(t)], as in [6],[7] and [8], by Limiter 1 andEnvelope Detector 1.

The output ofLimiter 1, i.e. signal u;=Ucos[lD/+q(t)] carries the same phase modulationas the input signal V;n but has a constant envelope. Two-quadrant multiplier M2 multipliessignal U; with single polarity baseband signal vy and feeds the product, VM2, to the firstinputs ofsumming circuits S1 and S2. Signal U; is also advanced by the 900 phase shifter.Its output signal uq is multiplied by MI with Vx and fed as VMl to the second input ofsumming circuit SI. Signal VMl is also fed to the second input ofsumming circuit S2 viaunity gain inverting amplifier II -1". The outputs ofthe summing circuits drive the twoconstant envelope output stages OSI and OS2 via Limiter 2 and Limiter 3 respectively.These limiters guarantee that the output stages are driven by constant amplitude signals.The constant envelope outputs vj and V2 ofOS1 and OS2 are combined in the PowerCombiner into a single amplitude and phase modulated output signal v feeding the antennaor some other load. Output signal v ofthe Power Combiner is fed also via the Attenuatorto Envelope Detector 2 which generates a baseband signal Vb2 equal to the amplitudemodulation envelope of the attenuated output signal v. The attenuation of the Attenuatoris equal to the circuit's desired overall voltage gain G, i.e. G = VmdVinmax. Similar toEnvelope Detector 2, Envelope Detector 1 generates a baseband signal Vb] equal to the

4

amplitudemodulation envelope of the input signalVin. The two baseband signals arecompared in high gain differential amplifier OAI with complementary outputs X and Y.

In case v is generated as the vector sum or vector average of v I and V2 (as shown inFig.2), the voltages on outputs X and Y are described as:

(1)

In case v is generated as the vector difference ofvI and V2, the voltages on outputs X andY are described as:

(2)

where A] »1 is the gain ofamplifier OAl, Va a common mode voltage, and Va =Vbl­

Vb2, i.e. the differential input voltage ofamplifier OAl,

It follows from (1) and (2) that for any Va the sum ofvx and Vy is vx+vy=2Va. Voltage Vx isdrivingthe baseband input ofmultiplierMj, voltage vy drives the baseband input ofmultiplier M2.

The common mode voltage Va is chosen so that even the smallest rfvoltages VSI and VS2

passed by summingcircuits Sl and S2 (i.e. when Va= 0 and Vx= Vy= Va), are stillsufficiently large to drive Limiters 2 and 3 into saturation.

We will now describe the operation ofthe amplifier in Fig.2 using the vector diagramshown in Fig.2a. We assume again that the input signalvt« is only amplitude modulated,and has no phase modulation. Vector Ui represents the fixed amplitude output ofLimiter1. Vector Uq represents the output of the phase shifter, i.e. Ui advanced by 90°. VectorsVMI and -VMI are the voltages on the first inputs ofsumming circuits Sl and S2, andvector VM2 is the voltage on the second inputs of S1 and S2. With the two inputs ofsummingcircuits S1 changingwith Vx and Vy in a quasi-complementary fashion, the end­point ofvector VSI will move along the locus [OCvSI. The same applies for summing circuitS2 and locus IOCvS2. However, the outputs of Limiters2 and 3 have constant amplitude,and are amplified by the output stages OS1and OS2that have fixed, matched gains. Theloci ofthe end-points ofvectors VI and V2 are IOCvl and IOCv2.

As mentioned above, in Fig.2 output voltage v results from vector addition or vectoraveraging ofVI and V2 in the Power Combiner. The amplitudemodulation loop works asfollows. Ifthe envelope ofthe output carrier v is smallerthan G-times the envelope oftheinput signal Vin, baseband voltage Vb2 will be lower than vst- This will increase vy anddecrease Vx at the outputs ofamplifierOAI [see equation (1)]. As the result the magnitudeofvector VM2 in Fig.2a will increase, and the magnitudeofvectors VMI and -VMI willdecrease. Phase angles a will decrease, and the envelopeofoutput voltage v will increase'until the differencebetween Vbl and Vb2 is negligibly small. The opposite will happen if theenvelope ofoutput signal v increases above G-times the envelope of input signalVin.

5

If the Power Combiner generates output voltage v as the difference between vt and V2, theoperation ofamplifier OAl follows equation (2), and a too small envelope of output signalv will cause a decrease of vy and an increase ofvx, again correcting the envelope error.

We shall now examine the open loop gain in the amplitude control loop represented byFig.2. Again, in Fig.2 voltage v is the vector sum or the vector average ofvj and V2. Inboth cases the maximum amplitude ofv, i.e. for a=O, is denoted as Vmax. From Fig.2a:

(3)

and if multipliers Mj and M2 are linear, then from (1):

(4)

It was stated above that for generating v by vector summing or averaging the fractionalamplitude modulation is q(t)=cosa.

Using the trigonometric identity cosr = ~1 + (tanx)2 we get for q(t):

Ifwe write for brevity p=AjvaIVo, then:

q(t) = 1I~1 +[(1- p)/(l + p)f

The dependence ofq(t) onp is depicted on Graph 1.

(5)

(6)

To guarantee stability and accuracy of the amplitude modulation loop it is important tocheck the variation ofits open loop gain Ha over the amplitude modulation range q(t). Ifwe test the loop by cutting it at the negative input ofamplifier OAl, the open loop gain isHa=dvb2Idva. The signal Vb2 at the output ofEnvelope Detector 2 is Vb~ q(t)VmaxlG,where as before, Vmax is the output voltage v with a=O and G is the attenuation oftheAttenuator. When checking only the relative variations ofHa vs. q(t), we can neglect theconstants Vmax, G, A] and Vo and write Ha=dq(t)/dp.

The following table gives Ha normalized to its maximum value which occurs at q(t)=O.5.

6

q(t) Ha

0 64%0.2 83%0.4 96%0.5 100%0.6 94%0.8 74%0.9 50%0.97 26%1 0%

Graph 2 depicts Ha vs. q(t) in more detail. The open loop gain Ha remains within acomfortable 2:1 ratio for a modulation range q(t) from zero to 0.9. This corresponds to arange of phase angles a from 900 to approx. 26°. It is desirable to extend the range of ato the lowest possible values to achieve the largest Vmax from a given output amplitude Vofthe constant envelope output stages. With a lower range edge of a=26°, Vmar1.8Vand Vmax=O.9Vwith vector summing and averaging respectively, while the variation inmodulation open loop gain Ha is 2:1 worst case. The modulation range of a is limited atthe high end [i.e. at low q(t)] by Limiter 1 which does not tolerate an input envelope levelbelow a certain minimum.

2.2.0 Phase Correction

When describing the amplifier operation in 2.2.1, we assumed that input voltage V;n is onlyamplitude modulated, i.e. that it has zero phase modulation. Ifwe now allow that V;n isalso phase modulated, i.e. v;n=q(t)Pjnmaxsin[aJt+~t)], then the whole vector diagram inFig.2a rotates with ~t) and nothing in Fig.2a needs to be changed. A phase differencebetween input voltage V;n and output voltage v, caused for example by a fixed or slowlyvarying delay in all circuits between Limiter 1 and the output of the combiner, is also ofno concern. However, any modulation dependent dynamic parasitic phase shift in thecircuit elements ofFig.2 would distort the power amplifier's output spectrum.

2.2.1 Phase Correction Version 1

Amplifier performance can be improved by adding to amplifier shown in Fig.2 a phasecorrection loop, see Fig.3. This loop, in contrast to the amplitude control loop, has tocorrect only phase errors, in an ideal case non-existent. Again the complexity ofFig.3 ismisleading, all functions are shown explicitly for clarity.

The amplifier in Fig.3 differs from the amplifier in Fig.2 by the following. A phase detectorPD is driven at one ofits inputs from the Attenuator via Limiter 4. Limiter 4 erases theamplitude modulation q(t) but maintains the desired phase modulation ~t) as well as anyparasitic phase modulation ofoutput voltage v. The other input of phase detector PD is

7

driven via a voltage controlled Delay Circuit from Limiter 1. The Delay Circuit's range is>360° of the rfcycle and it is controlled by the output ofthe Integrator. The integrator isdriven by the output of phase detector PD. The resulting control loop drives the staticphase difference between the two inputs of phase detector PD to zero. Because the DelayCircuit tracks only slowly changing phase difference and both inputs of phase detector PDinclude the desired phase modulation qi."t), the phase difference ¢i...t) seen by phase detectorPD consists only of fast dynamic phase errors, ifany. Phase difference ¢i...t) includes alsothe phase errors of Limiters 1 and 4 which must be held negligibly small for properoperation of the phase correction. The output of phase detector PD is also applied to theLow Pass Filter and results in an error voltage Ve following ¢i...t). The bandwidth of'v, is inthe worst case a low multiple ofthe bandwidth of the desired amplitude and phasemodulation q(t) and qi."t), i.e. much lower than the operating rffrequency e. Thus toimplement the Low Pass Filter that passes Ve but blocks the rf ripple at the output of phasedetector PD is easy. Voltage Ve is amplified by error amplifier OA2 with complementaryoutputs W and Z carrying voltages Vw and Vz respectively. Signals Vw and Vz are bothsummed with voltage Vx in summing circuits S3 and S4. Multiplier MI ofFig.2 has beendivided in Fig.3 into two multipliers, MI and M3. The baseband input ofmultiplier MI isdriven by output voltage Vs3 of summing circuit S3. Similarly, the baseband input ofmultiplier M3 is driven by output voltage Vs4 ofsumming circuit S4. Inverting amplifier"-I II has been relocated from the output ofmultiplier MI to the input ofmultiplier M3.Multiplier M2 is operating as in Fig.2, its baseband input is vy, its output VM2 is driving thesecond inputs ofsumming circuits SIand S2.

In Fig.3 a difference between the input and output envelopes will increase phasor VM2 anddecrease both phasors VMJ and VM3, or vice versa. This is causing, similarly to Fig.2, acorrecting change in q(t). But in Fig.3 a voltage Ve caused by a phase error (J will changeVMJ and VM2 in opposite ways, thus rotating both v J and V2 in a direction counteractingthe phase error (J. This is illustrated in Fig.3a, where the assumption ofvw<vz leads toVMJ<VM3. Since the phase correcting rotation will not be necessarily the same for vectorsvJ and V2, a second order change in amplitude ofv will result. It will be corrected by theamplitude control loop. The phase correction split angle a ofFig.2a into two unequalangles aJ and a2 in Fig.3a.

We need again to calculate the phase correction loop's change in open loop gain Hp toassess the difficulty ofkeeping the loop both effective and stable over the expected rangeofphase error (J and amplitude modulation range q(t). We will assume that the phasemodulation ~t) of input signal Vin is zero.

Let us denote the gain ofamplifier OA2 as A2. Then the voltage Vw at output W ofamplifier OA2 will be A2Ve. This voltage is added to vx=Vo-AJva from amplifier OAI insumming circuit S3. The sum applied to multiplier MI will be Vo-AJva+A2Ve. Similarly, thevoltage at output Z ofamplifier OA2 will be Vz=-A2Ve. This voltage is added to vx=Vo­A/Va from amplifier OAI in summing circuit 84. The sum applied to multiplier M3 will be

. Vo-A/Va-A2Ve. Because ofthe difference between the control voltages ofmultipliers MI

8

and M3, the magnitude ofvectors vM/and VM3 in Fig.3awill not be the same anymore.The voltage vyat input ofmultiplier M2 is still vy=Vo+A/va.

From Fig.3a:

(7)

and:

By recalling that A/valVo=P and by introducing A2Ve/Vo=b we get:

(8)

I-p+ba/ =arctan 1+p

andI-p-b

a2 = arctan 1+p(9)

Withvector vi leading by phaseangle a/ and vector v2laggingby phaseangle a2, thevoltage v at the output ofthe Power Combiner will havea phase shift e inducedby errorvoltageVe:

a -a ( I-p+b I- P-b]e = 1 2 = arctan -arctan /22 l+p l+p

This phase shifte willcounteract the phaseerror (J.

(10)

We will now calculate the relative changeofopen loop gainHp ofthe phase correctionloop over the modulation range ofq(t)=O.1 to q(t)=O.9. Let k be the sensitivity ofphasedetector PD and the Low Pass Filter (in volts!A(J). Cuttingthe loop at the input ofamplifier OA2, the open loop gain isHp=kde/dve. Withk, A2 and Vo beingconstants, wecan substitutefor relative changes Hp=de/db.

Graph 3 depictse vs. b with q(t) as a parameter. The rangeofb is from -1 to 1. The slopeofe vs. b is a strong function ofq(t). Graph4 depictsloop gainHp=de/db vs. b, againwith q(t) as a parameter. We can see that over the rangeof-1<b<1 the largest variationofloop gainHp does not exceed 25% at anyfixed q(t). Graph 5 depictsthe range ofe for bchanging from b=-1 to b=1 vs. q(t) whichis a linearized measureofHp . The graph showsthat the range ofe is approximately proportional to q(t) up to q(t)=O.8 with a maximumrange of64° (i.e, ±320) at q(t)=O.9.

In the amplifier ofFig.3 the open loop gainHp as wellas the range ofachievable phasecorrectione is a very strong function ofamplitude modulation q(t). It is possiblethat forsome modulation schemes the sensitivity to or the range ofpotential phase errors willbedirectly dependent on output signal amplitude. In that case an almostdirect proportionalityof phasecorrection loop gainHp on q(t) would not be a problem. However, if this is not

9

the case, the dependence ofHp on q(t) could be compensated by making the gain A2 ofamplifier OA2 inversely proportional to q(t), for example, by using voltage Vb2 orpreferably vblas a gain control signal.

2.2.2 Phase Correction Version 2

Another way ofmaking phase correction loop gain Hp less dependent on q(t) is bychanging both inputs ofboth summing circuits SI and S2 by output voltages vwand Vz ofamplifier OA2. This is shown in Fig.4.

In Fig.4 the multiplier M2 ofFig.3 is divided into two multipliers, M2 and Ma. MultiplierM2 is driving summing circuit SI, and multiplier Mt is driving summing circuit S2. Thebaseband input ofM2 is now the voltage vy+vz supplied by summing circuit S6, thebaseband input ofMa is the voltage vy+vw supplied by summing circuit S5. Thisconnection is chosen so that the output voltages vx, Vy and the output voltages vw, Vzchange the magnitude of input voltages of summing circuits S1 and S2 according to thefollowing table:

vM2 VM4 VMl VM3vy-vx>O + +vy-vx<O + +vw-vz>O + +vw-vz<O + +

Fig.4a illustrates a situation where vw-vz<O leads to VM~VM2and VM1<VM3.

From Fig.4a:

and:

By recalling that A1Va1Vo=p and A2velVo=b we get:

I-p+bal = arctan 1 b+p-

andI-p-b

a2 = arctan 1 b+p+(13)

The change e in the phase ofoutput voltage v will be:

a -a ( I-p+b I- P-b)e = 1 2 = arctan arctan 122 l+p-b l+p+b

10

(14)

Graph6 depicts again e vs. b with q(t) as a parameter. The range ofb is from -1 to 1,which for values of O. 1<q(t)<O.9 givesa range ofe ofat least ±26°. Graph 7 depicts openloop gainHp=de/db vs. b, againwith q(t) as a parameter. We can see that over the rangeof -I <b<1 and the rangeof0.1<q(t)<0.9 the worst case variation ofopen loop gainHp is3:1. This variation of gain is compatible with keeping the phase correction loop effectivebut stable.

Graph 8 depicts the rangeofe for b changing from b=-I to b=I vs. q(t) which is alinearized measure of Hp. The graph shows that the range ofe changesfrom 52° (i.e.±26°) at q(t)=O.I to 90° (i.e.±450) at q(t)=O.7, a less than 2:1 variation.

2.2.3 Crosstalk Between the Loops

To keep the phasecorrection loop from interfering with the amplitude modulation loop,q(t) as a function ofp=A]va/Vo should be independent ofb=A2Ve!Vo.

To keep the amplitude modulation loop from interfering with the phasecorrection loop, eas a function ofb=A2Ve/Vo should be independent ofp=Ajva!Vo.

The two loops would be free ofcrosstalkif the multipliers MI to M4 were drivenwithbaseband control voltagesproportional to the sineand cosineof cq and az. But becausethe voltagescontrolling the multipliers are derived in a simplified way in Fig.3 and in asomewhat less simplified way in Fig.4, it is important to checkthe amountofcrosstalkbetweenthe amplitude modulation and phase correctionloop.

2.2.3.1 Influence ofAmplitude Modulation on Phase Correction Loop

We will derivehow much changewill be required in phase loop error voltage Ve to maintain agivenphase correctione as the modulation q(t) is changing. The requiredchange in Ve can beread off Graphs3 (for amplifier in Fig.3) and Graph6 (for amplifier in Fig.4) by observingatany fixed valueofe the changein b=A2Ve/Vo as parameter q(t) is variedfrom q(t)=O.l toq(t)=O.9. As couldbe expected, in the amplifier ofFig.3 the interaction is very strong at lowvaluesofq(t), where the phasecorrectionloop's open loop gain is at its minimum.

In the amplifier ofFig.4 the situationis muchbetter, the worst case occurs at e-±26° with avariation ofq(t) between0.1 and 0.7. This requiresa 1:2 changein b and thus in error voltageVe. But becausegainA2 ofamplifier OA2 must be highenoughto generatee=±26° at q(t)=O.lwith a negligibly small Ve, the influence ofamplitude modulation onthe phase correctionaccuracyin the amplifier ofFig.4 is also negligible.

2.2.3.2 Influence of Phase Correction on Amplitude Loop

In this sectionwe shall investigate how much changewill be required in input voltage Vaof amplifier OAl to maintain a givenmodulation level q(t) over the range of phasecorrectionangles e. The required changein Va can be r~d off from Graphs 9 (for amplifier

11

in Fig.3) and Graph 10 (for amplifier in Fig.4) by observing at any fixed value ofq(t) thechange inp=A]vaIVo as parameter b is varied from b=-1 to b=l. Graphs 9 and 10 weregenerated in the following way.

With the phase correction loop in action, the two voltages entering the Power Combinerare:

v]=Vsin[a>t+qJ(t)+aJ] and vrVsin[a>t+qJ(t)-a2] (15)

The phase angle between V] and V2 will be a] +a2 =2ae Thus the amplitude ofoutputvoltage v will be VmaxCosae or Vmaxsinae depending whether output v is derived byvectorially adding (averaging) or subtracting VJ and V2. In the following we will assumevector addition or vector averaging. With the phase correction loop in action:

q(t) =co~(al +a2 ) 12]=co{(arctan 1- p+b +arctan 1-P-b)/2] (16)I+p I+p

for amplifier in Fig.3 (Graph 9), and

q(t) =co~(al +a2 ) 12] =co{(arctan 1- p +b +arctan 1- p -b)/2] (17)I+p-b I+p+b

for amplifier in Fig.4 (Graph 10).

We see in both Graphs 9 and 10 that the change inp (and thus the change in va) at anylevel ofq(t) is small compared to the value ofVa required for changing q(t) from 0.1 to0.9. And because gain zlj must be high enough to guarantee a negligible Va for changingq(t) over its full range, the influence ofphase correction on amplitude modulation will benegligible too.

2.2.4 Phase Correction Version 3

A third possibility to achieve phase correction is shown in Fig.5. The amplitudemodulation function in Fig.5 is identical to Fig.2. A voltage controlled Delay Circuitsimilar to the one in Fig.3 and 4 is inserted into the amplifier's forward path. Contrary toFig.3 and 4, here the Delay Circuit operates fast enough to follow the dynamic phaseerror (J. Phase detector PD measures the phase difference between the output Uj ofLimiter I and output Uo ofLimiter 4 and keeps it negligibly small by controlling the DelayCircuit via the Low Pass Filter and amplifier OA2. As in Fig.3 and 4, phase detector PD,the Low Pass Filter and amplifier OA2 must pass the bandwidth of the dynamic phaseerror ¢ and, as in Fig.3 and 4, they do not see the desired phase modulation <At). In the

12

arrangement ofFig.5 the modulation control loop and the phasecorrectionloop have nofirst order interaction.

2.2.5 Phase Correction Version 4

In Fig.6 the voltagecontrolled DelayCircuit ofFig.5 is replaced by a voltagecontrolledoscillator YCO. It is now the YCO frequency which is controlled by phase detector PDvia the Low Pass Filter and amplifier OA2. The YCO's output phase is such that the phasedifference betweenoutput Uj ofLimiter 1 and output uo ofLimiter 4 is negligible.Contrary to Fig.5, phasedetector PD, the Low Pass Filterand amplifier OA2 must hereprocessnot onlythe dynamic phaseerror (J but also the desired phasemodulation rAt) .Thiscausesany phasetrackingerror to appearfirst order in the output voltage v. The loopmustbe also equipped by somefrequency control means (not shownin Fig.6) requiredtobringat start up the YCO frequency sufficiently closeto the carrierfrequency dor phaseloop capture. Again, in Fig.6 the modulation control loop and the phasecontrol loop haveno first order interaction.

The 900 phase shifter in Fig.6 can be often replaced by a conveniently available 900 tapfromthe YCO.

3. The Power Combiner

Thispart ofthe report addresses the Power Combiner required for changing the two constantenvelope phasemodulated carriersvj and V2 into the desired amplitude and phasemodulatedoutput carrierv=q(t)Vmaxeos[lllt+rAt)].

There are two conditions a Power Combiner mustmeet:

a) The Power Combiner must consist ofreactive components only, so that no power isdissipated in the combiner itself.

b) To maximize overall power efficiency, the combiner mustpresent a unitypower factor (i.e.a resistive only) load to the two constantenvelope output stagesat allq(t), i.e. at all phaseangles a. In case the constant envelope carriersvj and V2 are supplied by class C transistorstages, this guarantees that at allphaseangles a the voltagebetweenthe transistors' emitterand collectoris at its minimum valuewhenthe transistors conduct maximum current.Violation ofthis rule willcauseexcessive power dissipation in the transistors, thus reducingthe efficiency ofclassC output stages.

13

3.1 Previously Published Combiners

To our knowledge, no combiner satisfying the above conditions a) and b) was yet published.The closest is a combiner described in [1], depicted here in Fig.7. This combiner offers anacceptable unity power factor for a limited range of aonly, and the power factor rapidly faIlsto zero for a>72° (assuming v is generated by summation ofphasors VI and V2). This restrictsthe range ofoutput amplitudes that can be supplied by the amplifier and sacrifices efficiencyeven within that range. Resistor R in Fig.7 represents the load, inductors L I and L2 areuncoupled, the range ofacceptable power factor is optimized by choosing capacitors CI andC2.

3.2 The New Combiner

The new combiner in its most elementary form is depicted in Fig.S. It shows the voltagesources ofviand V2, a transformer Tr with a single center tapped winding, the desired load R(e.g. the antenna), and two reactive loads, Xj and X2. The currents loading the voltagesources are ts and i2, the current taken by the load is ts. the current through the reactive loadsare iXI and iX2 respectively. The-voltage across load R is VR. In all ofthe following discussionwe will assume again that the bandwidth of phase modulations a and rp(t) is only a smallfraction ofthe carrier frequency as. The new combiner generates the output voltage VR as thevector average ofvoltages VI and V2.

A phasor diagram ofthe voltages ofthe combiner in Fig.S is shown in Fig.9. With phasemodulation rp(t) applied to both vI and V2 equally and expected to appear also in v, we canassume that the reference zero phase in Fig.9 is phase modulated by rp(t) and thus neglect rp(t)in all further discussion. Both voltages vI and V2 can be decomposed into two components.One is ofcommon mode phase (vertical in Fig.9) creating the same voltage on all three nodesof transformer Tr and acting as VR across load R The other is ofdifferential mode phase (vdiffand -vdiff in Fig.9) acting across transformer Tr. The amplitude ofthe common modecomponents acting across R will be VR = Vcosa, the magnitude ofeach of the differentialmode components will be VdifJ= Vsina. The two common mode components will generate acurrent iR ofamplitude Vcosa/R flowing in R The differential mode components will generatezero voltage across R and no current in the transformer because ofits assumed infiniteimpedance at frequency o: Each ofthe two voltage sources delivers halfof the currentthrough R, i.e. currents iRI=iR~iRI2 ofamplitude IRI2=Vcosal(2R) and ofcommon modephase. Thus, ifwe first neglect currents iXI and iX2 into reactances Xj and X2, the phaseangles between the voltages VI, v2 and currents ii, i2 are -a and a respectively. The powerfactor seen by voltage sources VI and V2 is cosa. For a approaching 900 the power factorapproaches zero.

We will now consider the reactances X I and X2. The phasor diagram in Fig. 10 shows thesituation for voltage source VI, the situation for source V2 is similar. Fig.10 shows VI, currenttm delivered by source VI (lagging VI by a), and current iXl that is also delivered by source

14

VI. As dictated by the reactive character of Xj, current iXI is in quadrature with VI. Vectoraddition ofcurrent iXI with current iRI results in a total current iI. Ifnow reactance XI isproperly chosen, iI will be in phase with VJ, thus ensuring a unity power factor. To maintainunity power factor for all values of a, current iXJ, and thus reactance XI must be a functionofa.

By observation of the phasor diagram in Fig. 10 we see that in order to keep iI and V I inphase, the amplitude IXJ ofcurrent iXI must follow the amplitude IR/2 ofcurrent iRI asfollows:

and with IR -_ V cos a .we can wnte:R

(18)

IV sin acosa V.

XI= =-sm2a2R 4R

(19)

To produce the desired current iXI in Fig. 10, reactance XI must be capacitive and itsmagnitude must depend on phase angle a as:

XI (a)=4R1sin2a (20)

Ifa changes from 0 to 90°, XI in Fig.8 is infinite for a=O, capacitive 4R for a=45°, andinfinite again for a=900.

Similarly, to produce the desired current iX2, reactance X2 must be inductive and itsmagnitude must depend on phase angle a as:

(21)

Ifa changes from 0 to 90°, X2 will be infinite for a=O, inductive 4R for a=45°, and infiniteagain for a=900.

A possible implementation of reactances X I and X2 allowing their magnitude to be changedbetween infinite and 4R is shown in Fig.II. Load R, transformer Tr, sources ofVI and V2 arethe same as in Fig.8. Reactance XI is implemented by tuned circuit LICI, reactance X2 bytuned circuit L2C2. In Fig.II we can assume LI=L2=L. Capacitors CI and C2 are tunable, forexample by using varactor diodes. When the circuits are tuned to resonate with the carrierfrequency liJ, they represent an infinite reactance. When capacitor C. is increased above itsresonance value Co, tuned circuit LIC. becomes a capacitive reactance. When capacitor C2 isdecreased below its resonant value Co. circuit L2C2 becomes an inductive reactance.We can write for capacitor C. and C2:·

15

The higher the aJRCo product, the smaller the required fractional change of capacity.

Other possible ways of implementing the variable reactances Xj and X2 is by tuning theinductances LI and L2.

Still another method is changing the voltage across Lj and/or Cl and across L2 and/or C2 to avarying percentage ofV] and V2 respectively.

3.2.1 Tuning for Unity Power Factor

As described above, to maintain for all values of aa unity power factor at the inputs ofthePower Combiner, the generation of the function sin2a is required. The following describesmeans for producing a voltage proportional to sin2a applicable to the amplifiers shown inFig.2,6 and 7. In those Figures, as a is changing from 0 to 90°, Vx is changing from zeroto 2Vo and vy is changing from 2Vo to zero. The sin2a function has zero value at a=O anda=90o and has its peak at a=45° when vx=vy=Vo. The sin2afunction can beapproximated, over the range of a=O to a=900, by a full wave rectifier consisting ofamatched differential pair Ql and Q2 (see Fig.12). The pair is connected as two emitterfollowers loaded by a common current sink. With the bases ofQl and Q2 driven byvoltages Vx and Vy properly scaled by resistor dividers Rl and R2, the common emittervoltage Vc approximates the function -sin2awith some de offset. Graph 11 depicts thematch. The dividers scaling Vx and vy are chosen so that the peak-to-peak swing on bothbases is approximately 200mV. The value ofcommon emitter current I and the emitterarea ofQ; and Q2 are first order not influencing the match. Ifa larger swing ofvc isdesired, the voltage swing at the bases of'Qj and Q2 can be increased with a propernumber ofdiodes connected in series with the transistor emitters.

The circuitry described above generates a signal proportional to sin2a. When combined withthe appropriate additional circuitry, the proper tuning ofthe reactive elements could beachieved. For example, additional linearizing circuitry would be required if the tuning weredone by varactors that are generally non-linear. This additional circuitry is not the subject ofthis report.

4. Summary

The report describes new linear power amplifiers that generate an amplitude and phasemodulated carrier by combining two constant envelope carriers in a power combiner. Thesignificance ofthis method is that the constant envelope carriers can be produced by efficientclass C or E output stages. The advantages of the described amplifiers over most of previouslypublished circuits is the inclusion of the output stages and ofthe power combiner intofeedback loops linearizing the amplifier's amplitude and phase response. The describedamplifiers are distinguished also by their simplicity.

16

A further contribution of the report is a new, inherently lossless power combiner offering onboth of its inputs a unity power factor at all times. This maintains the high efficiency oftheclass C or E output stages at all modulation levels.

References:

[I] H.Chireix, "High Power Outphasing Modulation", Proc.IRE, Vo1.23, Number II,November 1935, pp.1370-1392.

[2] H.L.Krauss, C.W.Bostian, F.H.Raab, "Solid State Radio Engineering", John Wiley andSons, 1980, pp.517-519.

[3] T.Hornak, W.J. McFarland, "Power Amplifier Utilizing the Vector Addition ofTwoConstant Envelope Carriers, U.S. Patent 5,365,187.

[4] T.Homak, W.J. McFarland, "Vectorial Signal Combiner for Generating an AmplitudeModulated Carrier by Adding Two Phase Modulated Constant Envelope Carriers", U.S.Patent 5,345,189.

[5] F.J. Casadevall, "The LINC Transmitter", RF Design, February 1990, pp.41-48.

[6] D.C. Cox, "Linear Amplification with Nonlinear Components", IEEE Transactions onCommunications, December 1974, pp.1942-1945.

[7] D.C.Cox, RP.Leck "Component Signal Separation and Recombination forLinear Amplification with Nonlinear Components", IEEE Transactions onCommunications, November 1975, pp.1281-1287.

[8] L.Couch, "A VHF Linc Amplifier", IEEE Southeastcon '82 Conference Proceedings, April4-7, 1982, pp.122-125.

[9] A Bateman, "The Combined Analogue Locked Loop Universal Modulator(CALLUM)", IEEE Vehicular Technology Conference Digest, 1992,pp.759-763.

17

---_.. ---,"'---._~------

:~axIII

Iocvf 'I

I,,tI

.: ---.

V" .--- - ............

" -,

'\'\ Iocip\

\\\,

•••••••••••••••••••••• 1

Fig.1a

-----v " "

locv, " " Ioc~I '\, \

t ,, \, . ,~---------_._---------~

maxv

Fig.1b

v

~f v~'---------l

~

Fig.2

exu·I1I

I

I

""/ I ,/ . ,

vsiooo / / 1M2: ',:'~..................... "52

r : .,/ : : ,

locv /",: '=.... , ISf / " • : ' ,IOCVS2

/ / : '" ,/ I : \ '"

/ I : \ ,

/ ,: \ '"/ t: \ ,Uq / locv,: »tocv. '

/ 1,: , 2 ,__ L ..... • • •••••••••L ••••••••••••,

Fig.2a

Fig.3

v

I1 II I

• ~-"'I I• IVI~ 1 ' •VS

1, : V

: _- -1__ : S2. - ,..... .,. .'" . I

/ , ",:/ I ~

.I I : ,I I ,

I , \I I \

Uq locv, " \/OC~______1 --.JL.----__•..... 1••••••••••••••

VM1 ~3

Fig.3a

Fig.4

v

u·I+

.~---i-_~

'",.,./

/ ," ~~ "

/ \

/oc~ " ~ /oc~U ' ,q - - - - - - - - - - - - - ~-...:....-_---~.....I

VMI

Fig.4a

Fig.5

PO

-VAl,

Fig.6

v

Fig.7

Fig.8

/OCV,//I

II

IIII

... ----1;----_- 11/-

'" ,. ,. II max - -.. '"/ '"I ,

:,j '\ /OC~: \: \: \: \: \

\\__----.111_---_. 1

ldiff

Fig.9

oFig.10

Tr

Fig.11

~c

o D

I

Fig.12

1.8

GRAPH 1

p

q<t> us. p

~r--

/./

//

v

//

./'

/v

a-1.8

1.8

q<t>

~r- --~-:

/' 1\\

\

188:<

Ha

OJ'.8

Open Anplitude Loop Gain Ha us. qCt>

q<t> 1.8

GRAPH 2

1.8

GRAPH 3

b

e us. b with q(t> as ParaMetero36 r--------r------.------r----:;;-r

e

o-38

-1.8

Hp us. h with q(t) as ParCllll8ter8.4 ,..-------------,--------------,

Hp

_-----..,-------___.--0.9

1-------------+-------iit.1-----f8-1.8 8 b 1.8

GRAPH 4

--»: '\-:./

V

.:-: v

./V

,/

o76

De

o8

8

De = [e for b=ll - [e for b=-ll us. q<t>

q(t) 1.8

GRAPH 5

1.8b8

8.98.5----_-G~

e us. b with q<t) as Paruetel'

o8 .-------------::2~---------__1

e

o48

o-48

-1.8

GRAPH ()

Hp us. h with q<t) as Paraaeter8.6 r------------,.-------------,

Hp

8-1.8 8 b 1.8

GRAPH ?

o188

De

o8

De =[e for b=-11 - [e for b=11 us. q<t)

~- -r-,.>

~

'\/ \

1.8

GRAPH 8

q<t> vs. p with b as ParaMeter

1.8p8-1.8

1.8 II-I-I-T-T-I---=G~;;;;;;-:=-r--I

q(t)

GRAPH 9

q(t) vs, p with b as ParaMeter

q(t)

8-1.4 -1 p 1.8

GRAPH 18

CoMbiner Control Voltage for Fig.Z.5.68r---------------------------:l

a(t)-1 '------------~--=--------------"'o

8 ~

GRAPH 11