RECEIVER

INPUT

MUX

CHANNEL AMP #1

CHANNEL AMP #2

OUTPUT

MUX

Versus

Single Amplifier

SSPSSPSSPSSPSSPA LinearizationA LinearizationA LinearizationA LinearizationA Linearizationby Allen Katz

Linearizer Technology Inc.

ABSTRACT

Many new communications services require highlylinear high power amplifiers (HPAs). This paperis an extension of an earlier paper, which discussedthe merits of linearization and its application toTraveling Wave Tube Amplifiers (TWTAs). Inthis paper the emphasis is on solid state poweramplifiers, SSPAs. Various methods of lineariza-tion are compared and found to offer significantbenefit when used with both bipolar and Si/GaAsFET power amplifiers. Problems unique to SSPAsare highlighted. Predistortion is shown to be thepreferred linearization approach for many appli-cations.

INTRODUCTION

The growth of the cellular telephone service andother forms of personal communications have cre-ated a demand for highly linear amplifiers. In thecase of cellular telephony, it is often more conve-nient and cost effective to transmit several carriersthrough a common amplifier rather than to usemultiple amplifiers and a lossy multiplexer, as isillustrated in Figure 1. To avoid unacceptably highintermodulation distortion (IMD), the commonamplifier must be highly linear.

Figure 1. In cellular telephony transmitting several carriers through a common amplifier ismore cost effective than using multiple amplifiers.

For the transmission of a single carrier, IMD isusually not a limitation. However with digitallymodulated signals, spectral regrowth (SR) can bea serious problem, and manifests itself in a formequivalent to IMD. SR is not unique to digital sig-nals, but an aspect of angle modulation (FM andPM). Angle modulated signals have a theoreti-cally infinite bandwidth; for example, the spectrumof a sinusoidal modulated FM signal,

n=∞Ac cos(ωct + M cos[ωmt]) = Ac Σ Jn(M)cos([ωc+nωm]t) (1)

n=-∞

contains an infinite number of sidebands. In prac-tice the bandwidth is limited to a finite frequencyband, beyond which sideband amplitude drops offrapidly. Analogue-FM has an approximate band-width given by Carson’s rule.2

BW = 2 (∆f + fm) (2)

where ∆f is the peak deviation and fm is the modu-lation frequency. The effective bandwidth of anglemodulated digital signals can be much greater thanpredicted by (2), due to the high frequency com-ponents of the modulating waveform. To reducetheir bandwidth to a more acceptable value, digi-tal waveforms are normally low-pass filtered be-fore modulation. Because of the mechanics of mostdigital modulators, (which are not true angle modu-lators), the amplitude of the carrier is also modu-lated by this process. In addition any “band limit-ing” (filtering) of an angle modulated signal willintroduce amplitude modulation. It is primarilythis incidental amplitude modulation which causesthe SR when a digital signal is passed through anon-linear amplifier. The distortion of the inducedamplitude waveform produces IMD products,which increase the signal’s spectrum.

In practical amplifiers there is usually a substan-tial change in signal phase angle with power level.

θ = f(Pin) (3)

This change in phase with amplitude converts thevariations in signal level to angle modulation side-bands. These new sidebands further broaden thesignal bandwidth. Amplitude and phase inducedspectral products add vectorally and are classifiedin general as IMD.

SR is a major concern in personal communicationssince transmission often occurs on a channel adja-cent to one in which reception of a much weakerdistant signal may be taking place. To ensure free-dom from interference, transmitter IMD productsmust be below the carrier (C/I ratio) by anywherefrom 35 to greater than 65 dB, depending on theapplication.3

The summation of the IMD terms in the adjacentchannel is referred to as the adjacent channel power(ACP).

ACP = Σ IMDs in the adjacent channel (4)

These levels of linearity are considerably higherthan had been required of communications ampli-fiers in the past, except for some very special ap-plications.

SATURATED POWER

All amplifiers have some maximum output powercapacity, referred to as saturated power or simplysaturation (SAT) - see Figure 2. Many SSPAs aresensitive to overdrive and can be easily damagedby operation at or beyond saturation. In addition,SSPAs tend to approach saturation exponentially.These factors make engineers reluctant to measureand use saturated power as a reference for com-parison of SSPA performance. They prefer to usethe power at which an amplifier’s gain compressesby 1 dB as the reference (REF) for amplifier com-parison.

Figure 2. Saturated output power is approached exponentially by a typical Class A SSPA.

Pout

Pin

Pout

Pout

PinPin

(SATURATION)

REF = 1 dB CP = SAT - D (5)

For SSPAs with reasonable linearity, the differ-ence (D) in output level between SAT and the 1dB compression point (CP) is about 1 dB. Unfor-tunately D varies from amplifier to amplifier.Amplifiers with high linearity will have a smallerdifference (D < .25 dB), while amplifiers with poorlinearity can have a difference of several dB (D >2 dB). For this reason, in this paper, relative am-plifier performance will be referenced to (singlecarrier) saturated power. Output power backoff(OPBO) will be relative to an amplifier’s singlecarrier saturated power. (For most SSPAs, SATcan be safely determined using a network analyzerin a rapid power sweep mode. For amplifiers thatare especially thermal sensitive, pulsed powersweep techniques may be used.)4 When compar-ing the data presented here with that of SSPAsbased on a 1 dB CP reference, an appropriatecorrection factor should be assumed.

Generally an SSPA’s greatest efficiency will oc-cur at or near saturation. Similarly the closer to

saturation a linear amplifier, (class A and to a largeextent class AB), is driven, the greater the amountof distortion it produces. This means that typi-cally a (class A) SSPA will have to be backed-offabout 5.5 dB (for a C/I = 35 dB), and by more than15 dB (for a C/I = 65 dB) to satisfy cellular/PCadjacent channel IMD requirements. These arehuge reductions in usable output power, and applyfor both FET and bipolar devices.

LINEARIZATION

Linearization is a systematic procedure for reduc-ing an amplifier’s distortion. There are many dif-ferent ways of linearizing an amplifier. Usuallyextra components are added to the design of a con-ventional amplifier. Often these extra componentscan be configured into a subassembly or box thatis referred to as a linearizer. Linearization allowsan amplifier to produce more output power andoperate at a higher level of efficiency for a givenlevel of distortion. Feed-forward, Feedback andPredistortion are some common forms of linear-ization.

MAIN AMP

AUX AMP

Sin Sout 1 Sout 2

Scor

IMD

Feed-Forward Linearization

For SSPAs, Feed-forward (FF) techniques havereceived much attention in recent years. A blockdiagram of a basic FF system is shown in Figure3. This system consists of two loops. The firstloop subtracts samples of the input signal (Sin)from the output signal (Sout1) to produce a sampleof the main amplifier’s distortion. Sout1 consistsof the amplified input signal plus any distortionintroduced by the amplifier (IMD).

Figure 3. Feed-forward linearization employs two loops for the cancellation of IMD.

Sout1 = G Sin ∠Φamp + IMD (6)

G is the gain and ∠Φamp is the phase shift intro-duced by the main amplifier. The samples of Sin(SSin) and Sout1 (SSout1) are respectively

SSin = K0 Sin and SSout1 = K1 Sout1

K0 and K1 are the coupling coefficients of the di-rectional couplers used to sample Sin and Sout1respectively. If SSin is attenuated and delayed inphase such that

A0 SSin ∠Φ0 = - SSout1or

A0 K0 Sin ∠Φ0 = G K1 Sin ∠(Φamp + 180°) (7)

then Sin is canceled and the output of loop 1 is K1IMD. A0 and Φ0 are respectively the attenuationand phase shift introduced in loop 1 for adjustmentof the carrier cancellation.

The second loop subtracts the amplified sampleddistortion of loop 1 from a delayed Sout1 to pro-duce ideally a distortion free output signal (Sout2).The loop 1 output signal is amplified by an auxil-iary (aux) amplifier of gain GA and phase shiftΦaux to provide a correction signal (Scor) of suf-ficient level to cancel the distortion introduced bythe main amplifier. Scor is combined with the mainamplifier signal at a final directional coupler ofcoefficient K2.

IfScor = A1 GA K1 K2 IMD ∠(Φaux + Φ1) = IMD ∠(Φm + 180°) (8)

then the SSPA output will be distortion free. A1and Φ1 are respectively the attenuation and phaseshift introduced in loop 2 for adjustment of the dis-tortion cancellation. Φm is a delay added after themain amplifier to equalize the delay introduced bythe aux amplifier.

Sout2 = Sout1 ∠Φm + Scor (9)

From this discussion it may appear that undistortedoutput can be obtained from a FF amplifier rightup to SAT. Saturated output power can never beobtained from a FF amplifier because of the lossesin the phase shifter and couplers, which must belocated after the main amplifier.

The main signal, Sout1, is reduced in amplitudeby a factor (R1) due to passing through the K1coupler.

In dBR1 = 10 LOG( 1- 10-(k1/10) ) + L1 (10)

where L1 is the dissipation loss of the coupler indB. K1 can be made very small, provided the mainamplifier has sufficient gain. (A K1 of -30 dB isnot unusual). The K2 of the final directional cou-pler must also be relatively small to minimize theloss of output power (R2). Since the two signals,(carriers and distortion), being combined are notat the same frequency, power will be split betweenthe load and the coupler’s dump port. The R2power loss in dB as function of K2 is described byequation (10) with 2 substituted for 1 in the vari-able names. The overall loss in saturated power(∆SAT) is

∆SAT = 10 LOG( 1- 10-(k1/10) ) + 10 LOG( 1- 10-(k2/10) ) + L1 + L2 + Lm

(11)

where Lm is the loss of the delay line (Φm). Inpractice it is very difficult to achieve a ∆SAT ofless than 1 dB.

∆SAT can be considered the minimum OPBO of aFF amplifier. In actuality, ∆SAT must be addedto the difference between the saturated power ofan amplifier with single and multi-carrier signals.1

This factor can vary from about .5 to >1 dB forSSPAs. Further more, the amplifier’s true SATpower should not be considered only that of themain amplifier. A FF amplifier combines both thepower of the main and the aux amplifier. The sumof the saturated power of both these amplifiersshould be considered when comparing the relativeOPBO performance of different methods of lin-earization.

Practical considerations limit the size of the auxamplifier. This limits Scor and in turn theundistorted FF output level. The smaller K2 isset, the larger in power the aux amplifier must besized. The aux amplifier must also be operatedrelatively linear so as not to distort the distortionsignal, and thus introduce distortion of its own.Figure 4 shows the relationship between minimumOPBO (from single carrier SAT of the main am-plifier) and size of the aux amplifier (relative tothe main amplifier), for cancellation of IMD. Mini-mum OPBO is given for different values of outputcoupler coefficient K2. These results depend onthe linearity of the main and aux amplifiers and onthe resistive loss of the couplers and the delay line.Linear characteristics typical of a class A GaAsFET SSPA were assumed for both amplifiers, andresistive losses of 1 dB were assumed for the pas-sive output components. Figure 4 shows that withan aux amplifier of size equal to the main ampli-fier (0 dB), cancellation of IMD can be achievedup to only -4.2 dB from single carrier SAT.

9

8

7

6

5

4

3

2

1

00 1 2 3 4 5 6 7 8 9 10

Aux Amp Size Relative to Main Amp in dB

Min

. OP

BO

for

IMD

Can

cella

tion

in d

B K2 3 dBK2 10 dBK2 6dB

8

7

6

5

4

3

2

1

00 1 2 3 4 5 6 7 8 9 10

Aux Amp Size Relative to Main Amp in dB

Min

. OP

BO

for

IMD

Can

cella

tion

in d

B K2 3 dBK2 10 dBK2 6dB

Figure 4. The mnimum OPBO for cancellation of IMD by a feed-forward amplifier depends onauxiliary amplifier size and output coupler coefficient.

If the combined saturated output power levels ofthe main and aux amplifiers are used as the refer-ence for OPBO, then IMD cancellation is limitedto OPBOs of less than -6.3 dB. The relationshipbetween minimum OPBO (from single carrier SATof the main plus aux amplifiers) and size of theaux amplifier is shown in Figure 5. When overallamplifier power capacity is considered, the mini-

mum corrected OPBO occurs for an aux amplifiersized approximately 3 dB smaller than the mainamplifier, and a K2 of about 6 dB. (A minimumIMD cancellation of 20 dB was assumed. If only10 dB of cancellation is acceptable, an additional1 to 2 dB increase in output level can be achieved.)In practice other factors limit IMD reduction andperfect cancellation can never be achieved.5,6,7

Figure 5. Additional OPBO is required for cancellation of IMD when the output power of theauxiliary amplifier and the main amplifier are used as the reference.

Figures 4 and 5 reveal why FF is not a good choicefor linearization of amplifiers near SAT. Otherlinearization methods can provide superior IMDcancellation with considerably less complexity.However FF becomes competitive for OPBOsgreater than 6 ~ 7 dB, and for high linearity re-quirements may be the system of choice.

Feedback Linearization

There has been considerable work on feedback forthe linearization of RF and microwave amplifiers.Feedback techniques can be divided into severaldistinct branches. The use of linear networks forfeedback is well documented, but has seen littleapplication at microwave frequencies.8 The rea-son for this reluctance is probably concern withamplifier stability and the difficulty in making net-works with non-ideal components function overwide frequency bands.

HPA

Pin Pout

PHASEGAIN

DETECTORF

COUPLERCOUPLER

+-

F

Indirect feedback (IFB) techniques have been morewidely applied.9,10 In these approaches anamplifier’s input and output signals are detected,and the resulting baseband signals compared. Theerror signal (Ve) is used to modify the amplifier’scharacteristics so as to minimize distortion.

Ve = |DSout - DSin| (12)

where DSout and DSin are respectively the de-tected output and input signals. Ve can be used tocontrol the gain of the amplifier by means of avoltage variable attenuator. Superior linearity isobtained by correcting both gain and phase. Themagnitude and phase of Ve can be determined asillustrated in Figure 6. The resulting error signalsare used to respectively control an attenuator anda phase shifter so as to minimize the error.

Figure 6. The difference in magnitude and phase between input and output signals is detectedand the error signals used to control amplifier gain and phase.

A variation of IFB, know as Cartesian feedback,separates the signal into in-phase and quadraturecomponents. This eliminates the need for the phasedetectors and shifters, and still allows the correc-tion of gain and phase by adjusting the amplitudesof two orthogonal components. Figure 7 showsan example of a Cartesian feedback system in

which the input and output signals are separatedinto orthogonal components and detected. The re-sulting baseband in-phase and quadrature compo-nents are compared and used to control the attenu-ators in a vector modulator. Cartesian feedback ismost often used with QPSK modulation. In thiscase the detected components are subtracted fromthe in-phase and quadrature modulation signals asshown in Figure 8.

Figure 7. Cartesian feedback eliminated the need for phase correction by using the differencebetween in-phase and quadrature signals to control attenuators in a vector modulator.

Today correction is done at baseband using digitalsignal processing techniques. Very high linearitycan be achieved with IFB. The resulting system isself-correcting for changes due to environmentaland aging effects. IFB’s principal limitation is aninability to handle wideband signals. It is “practi-cally” very difficult to make a feedback systemresponds to signal envelope changes much greaterthan a few MHz due to the inherent time delay builtinto the system.10

Figure 8.Cartesian feedback is usedwith QPSK modulation todirectly correct the in-phase and quadraturemodulation signals.

Schemes in which amplifier bias is changed in re-sponse to Ve have been referred to as DynamicElectronic Bias Systems (DEBS). However, mostDEBS use the input signal as the reference with-out comparison to produce an indirect form of FFlinearization.11

Predistortion Linearization

Predistortion (PD) linearizers have been used ex-tensively in microwave and satellite applicationsbecause of their relative simplicity, and their abil-ity to be added to existing amplifiers as separatestand alone units. PD linearizers, unlike FF, canprovide a viable improvement in linearity near satu-

ration, but can be difficult to apply in applicationsrequiring very high linearity (C/I > 50 dB). PDlinearizers generate a non-linear transfer charac-teristic, which is the reverse of the amplifier’s trans-fer characteristics in both magnitude and phase –see Figure 9. An alternate way of thinking of a PDlinearizer is to view the linearizer as a generator ofIMD products. If the IMDs produced by thelinearizer are made equal in amplitude and 180

f

Pout

inP

Pout Pout

inPinP

PREDISTORTION

LINEARIZER

HPA OUTPUT

degrees out phase with the IMDs generated by theamplifier, the IMDs will cancel. This conditionoccurs when the gain and phase of the linearizedamplifier remain constant with change in powerlevel.

Figure 9. Ideally the gain and phase of a linearized amplifier should remain constant up tosaturation.

In dB, the gain of the linearizer (GL) must increaseby the same amount the amplifier’s gain (GA) de-creases.

GL(PoutL

) - GLss = - [GA(P

inA) - GA

ss] P

outL = P

inA (13)

where GLss and GA

ss are respectively the small sig-

nal gains of the linearizer and the amplifier, andGL(P

outL) and GA(P

inA) are respectively these gains

as a function of linearizer output and amplifier in-put levels. Likewise the phase shift introduced bythe linearizer must increase by the same amountthe amplifier’s phase decreases, (or vice-verse de-pending on the direction of phase change by theamplifier).

ΦL(PoutL

) - ΦLss = - [ΦA(P

inA) - ΦA

ss] P

outL = P

inA (14)

When these conditions are met, the result is thecomposite linear transfer characteristic shown inFigure 9. This is the response of a so-called ideallimiter. Once an amplifier has saturated, it is im-possible to obtain more output power by drivingthe amplifier harder. Thus the best a predistortionlinearizer can do is produce an ideal limiter char-acteristic. Despite this limitation, it is possible fora linearizer to provide large benefits in signal qual-ity when output power is reduced from saturation.Some improvement is possible even at saturationand beyond as the linearizer can correct for post-saturation phase distortion and power slump – butthis improvement is usually very small.

Since the power out of the amplifier (in dB) is

PoutA

= PinA

+ GA = PoutL

+ GA = P

inL + GL + GA

Equations (13) and (14) can be rewritten referencedto the power into the linearizer (P

inL), and the de-

sired transfer characteristics of the linearizer ex-pressed as follows:

GL(PinL

) = GLss + GA

ss - GA(P

inL + GL(P

inL)) (15)

ΦL(PinL

) = ΦLss + ΦA

ss - ΦGA(P

inL + GL(P

inL)) (16)

Equations (15) and (16) can be solved iterativelyfor the ideal linearizer response needed to correcta given amplifiers transfer response. Figure 10shows the response needed to correct a typical classA MESFET SSPA. As saturation is approachedthe rate of gain and phase change become infinite.

0

-20 -18 -16 -14 -12 -10 -8 -6 -4 -2 0

10

15

20

5

PIN dB

25

30

35

40

LIN PHASE

LIN GAINPH

AS

E IN

DE

GR

EE

S

45

-4.5

-3.5

-3.0

-2.5

-4.0

-2.0

-1.5

-1.0

-0.5

0

GA

IN IN

dB

Figure 10. An ideal linearizer response requires the rate of gain and phase change to becomeinfinite as SAT is approached.

0

1 2 3 4 5 6 7 8 9 10

20

30

40

10

OUTPUT BACKOFF IN dB

50

60

70

802-TONE

MANY-TONE (NPR)

C/I

IN d

B

dGL /dPin = ∞ and dΦL /dP

in = ∞ as P

out => Sat

Such a characteristic can not be achieved in prac-tice. Often a small amount of gain expansion nearsaturation, due to the finite dGL /dP

in available, is

traded for superior C/I near saturation at the ex-penses of degraded C/I at higher OPBOs.

Figure 11. C/I of an ideal transfer characteristic for 2 and an infinite number of carriers.

Figure 11 shows the 2-tone C/I achievable by anideal transfer characteristic. The C/I goes to infin-ity for OPBO greater than 3 dB. This result oc-curs because the peak-envelope-power (PEP) of a2-tone signal is 3 dB greater than the averagepower. A signal backed-off by more than 3 dBnever experiences clipping at saturation, and issubject to only a linear response. However toachieve this same level of performance with a largernumber of carriers requires a greater level ofOPBO. This is a consequence of the increase inPEP with carrier number:

PEP = N Pav (17)

Where N is the number of carriers and Pav is theaverage power of the overall signal. For 4 carriersthe OPBO for no IMD increases to 6 dB. The C/Ifor an ideal limiter driven by an infinite number ofcarriers (of random phase) is also show in Figure11. The infinite carrier case is also known as noisepower ratio or NPR.1 Although the OPBO requiredfor a given C/I increases with N, the improvementprovided by PD linearization also increases withN.12

Figure 12 shows the transfer characteristics of aSSPA and the corresponding corrected responseresulting from linearization. The characteristicsare for a class A power MESFET amplifier. Nothow the shape of the linearized Pout/Pin curve ap-proaches the desired ideal limiter characteristic ofFigure 9. The separation of the 1 dB CP from SATis a good indicator of linearizer performance. Ide-ally the 1 dB CP is located 1 dB in input powerbeyond SAT. Although the change in 1 dB CP inthis case is not as great as for more non-linearamplifiers, the benefit can still be substantial.

Figure 12. Transfer characteristics of a Class A MESFET SSPA and linearized SSPA.

SAT

AMP L/AMP

Rel

ativ

e P

ower

Out

put 0

.5 d

B/D

IV

SAT

AMP

L/AMP

GAIN

START -10.0 dBm CW 1.9500 GHz STOP 15.0 dBm

Phase

L/AMP

AMP

Gai

n G

hang

e 0

.5 d

B/D

IV

Phase C

hange 2 dB

/DIV

Figure 13 shows similar graphs for a class ABamplifier. Here the 1dB CP has been moved nearerto saturations by almost 5 dB. The improvementin two-tone C/I as function of OPBO achieved byusing a PD linearizer with class A and class ABMESFET SSPAs is depicted in Figures 14 and 15respectively. The advantage of of linearizeringSSPAs varies greatly with bias class and devicetype. The class A amplifier of Figure 14 showsonly about a 0.5 dB increase in output power for a

C/I of 26 dB, but a 2.5 dB power increase for a 50dB C/I. The calsses AB SSPA, Figure 15, showsabout a 1.5 dB increase in output power for a C/Iof 26 dB. Ordinarily the more linear a SSPA, theless the advantage of linearization. When design-ing an SSPA to be linearized emphasis should beplaced on optimizing parameters other than linear-ity.

Figure 13. Transrfer characteristics of a Class AB MESFET SSPA and linearized SSPA.

Figure 14. C/I vs. OPBO of a Class A SSPA and linearized SSPA.

GAIN 0.5 dB/ PHASE 5º/P

out 2

.5 d

B/

1

Pin 2.5 dB/

1

L/SSPA

SSPA

L/SSPA

SSPAL/SSPA

SSPA

70

65

60

55

50

45

40

35

30

25

20

15

10

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

OUTPUT BACKOFF IN dB

C/I

IN d

B

L/SSPA

SSPA

+

+

+

+

++

+

Figure 15. C/I vs. OPBO of a Class AB SSPA and linearized SSPA.

Design advances have greatly improved PDlinearizers. Past linearizers were limited in band-width and difficult to adjust. New designs can of-fer greater than octave frequency performance, andthe complex non-monotonic transfer responsesneeded by some SSPAs. They are much smallerin size and provide enhanced performance witheasy alignment and excellent stability.

ADAPTIVE LINEARIZATION

For high linearity application (C/I > 50 dB) ad-justment and maintenance of optimal linearizersettings become very critical. A change in phaseof less than a degree can move a linearized ampli-fier out of specification. As a result of this param-eter sensitivity, much effort has been devoted tothe development of linearizers that can automati-cally adapt to environmental and stimulus changes.These adaptive linearizers can be considered a form

of IFB linearization in which the feedback is ap-plied to PD and FF linearizers. A measure of thelinearizer’s performance is generated. This per-formance measure (V

PM) can be the error voltage

of equation (12), or a voltage proportional to theintegrated IMD present in an unoccupied portionof spectrum near the desired signal. A microcom-puter is normally used to analyze V

PM and deter-

mine the optimum linearizer settings.

In a FF linearizer, the microcomputer could be usedcontrol A0 and Φ0 in the signal loop and A1 andΦ1 in the cancellation loop – see respectively equa-tions (7) and (8), and Figure 3. Using a searchalgorithm the computer would vary these param-eters so as to keep V

PM at a minimum value.

In a PD linearizer the desired non-linearity can beproduced using a power series:

Vout = k1 Vin + k2 Vin2 + k3 Vin3 (18)

Vin2 and Vin3 can be generated using double bal-anced mixers. Vin is applied to both ports of themixer to obtain an output of Vin2. A second mixeris used to obtain to Vin3. If needed, additionalmixers can be used to obtain even higher powers.The values of coefficients k1, k2 and k3 could becontrolled by the microcomputer. As in the FFexample, the computer would use a search algo-rithm to vary these coefficients so as to keep V

PM

at a minimum value. Two non-linear PD elementscan be combined in an arrangement similar to theCartesian feedback system of Figure 7 to keep bothgain and phase optimal.

The adaptive linearizers just described do not havethe frequency response limitations of feedbacklinearizers, since they not attempt to correct forchanges in the signal’s envelope. These linearizersrespond slowly to gradual changes in the systemscharacteristics.

TIME DEPENDENTAMPLIFIER NON-LINEARITY

The linearity of HPAs can degrade when operatedwith signals of bandwidths greater than severalMHz. This degradation is referred to as Dynamicbandwidth and is a measure of the ability of thelinearizer/amplifier to function with a rapidlychanging signal envelope. It is particularly a prob-lem for class AB SSPAs, and is not normally cor-rected by conventional linearization techniques.Figure 12 shows the change in 2-tone C/I as a func-tion of carrier spacing, at 4 dB OPBO for a 40 watt,C-band, MESFET SSPA, designed for satelliteservice. (SSPAs used on satellites are normallyoperated class AB for greater efficiency.) The levelof both upper and lower, third and fifth order IMDproducts are shown. The non-symmetry of upperand lower products is an indicator of the relativelevels of AM/AM and AM/PM distortion.10 Ascarrier frequency spacing is increased, C/I de-creases noticeably. At a spacing of 30 MHz, C/Idegrades by more than 2.5 dB. At 60 MHz, C/I is

Figure 16. The linearity of SSPAs can degrade with increased carrier spacing

Cause of Degradation and Solutions

When the frequency separations of carriers is in-creased, the resulting signal’s time-envelopechanges more rapidly. For 2-carriers, the frequencyof this envelope is

Fe = F∆ /2 (19)

down by more than 6 dB. Some SSPAs have beenfound to degrade by more than 10 dB, for 100 MHzcarrier spacing. NPR displays the same phenom-enon. A similar effect is often observed for veryclose carrier spacing (< 50 kHz).

where F∆ is the carrier separation. Distortion ofthe envelope produces IMD. The time-envelope,and related linearity, are dependent on the shapeof the amplifier’s gain and phase transfer charac-teristics. Assuming an amplifier with a flat fre-quency response, these parameters are normallyconsidered time-invariant. When C/I changes withF∆, this indicates that the system is time-depen-dent. Time related change is particularly troubling

Figure 17. Two-Tone gain and phase transfer response of C-Band SSPA.

for linearized amplifiers. In such systems, theamplifier transfer characteristics are corrected toprovide a constant gain and phase, with input powerlevel. Change with F∆ will cause the linearizer tobe in alignment for one particular frequency, andout of alignment for another.

Figure 17 shows the 2-tone gain and phase trans-fer characteristics, as a function of carrier frequencyseparation, for the amplifier which produced theC/I performance of Figure 12.13,14 The shape ofthe two-tone gain curves, (at Fc < 10 MHz), werein very close agreement with the amplifier’s singlecarrier transfer response. The 1 dB compressionpoint is degraded at higher separation frequencies.More significant is the dramatic change in phasetransfer characteristics above 30 MHz; this is the

frequency where the non-symmetry of upper andlower C/I products increased abruptly. This changeis likely due to a resonance in the SSPAs bias cir-cuitry.

The principal cause of the SSPAs linearity degra-dation is believed due to changes in the bias cur-rents. The uniform gain characteristics and theslump in saturated power at higher carrier spac-

ing, indicates a problem in the drain circuitry. Asignificant induced voltage was found on the drainlines, when 2-carrier and NPR excitation waspresent. Induced voltages were also observed atthe gate, but at a much lower level. Evaluation ofthe drain capacitors (7 µf) revealed they resonatednear 0.5 MHz. Smaller low inductance capacitorswere added on the device side of the drain circuitry.This change enhanced the 2-carrier transfer char-acteristics and improved amplifier linearity at widercarrier spacing. The resultant C/I as a function ofOPBO for a 30 MHz carrier spacing is given inFigure 18. Performance of both the SSPA and alinearized SSPA, with and without the added ca-pacitors is shown. For reference, the C/I with a 1MHz carrier spacing is also included. Only onecurve is shown, as performance with and withoutcapacitors was essentially identical at 1 MHz.

Figure 18. Improvement in C/I resulting from added drain capacitors.

SUMMARY

Linearizers increase SSPA power capacity and ef-ficiency when high linearity is required for thetransmission of digitally modulated signals andmulti-carrier traffic. The greatest benefit is accruedwith class B and AB amplifiers of marginal lin-earity and in applications requiring a very high lin-earity. In these cases linearizers can deliver agreater than 3 dB increase in power capacity, andmore than double SSPA efficiency. Generallyfeedforward linearization is most valuable for ap-plications requiring very high linearity. Indirectfeedback also works well for these applications,but is limited to narrow bandwidth signals.Predistortion has the advantage of relative simplic-ity. It works over wideband widths and is viablefor applications requiring both low and high lin-earity.

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