TWTA Linearizationby Dr.Allen Katz

Linearizer Technology, Inc.www.lintech.com

ABSTRACT

New communications services have created ademand for highly linear high power amplifiers(HPA's). TWTA's continue to offer the bestmicrowave HPA performance in terms of power,efficiency, size and cost, but lag behing solidstate power amplifiers (SSAPs) in linearity. Thispaper discusses techniques for improving TWTAlinearity. The significance and methods forevaluation of linearity are reviewed, and themerits of various linearization methods com-pared. The use of predistortion linearization isshown to provide TWTA performance compa-rable or superior to conventional SSPA's.

INTRODUCTION

Technological developments are rapidly chang-ing the communication business. These changeshave created a demand for highly linear HPA's.In the past, the bulk of satellite transmissionshave been single carrier video signals. Digitalcompression now allows several televisionsignals to be transmitted in the frequency spacepreviously occupied by a single signal. Non-video, multiple signal VSAT (very small satelliteterminals) and mobile telephone services arealtering traditional satellite loading. New terres-trial microwave services for the transmission ofvideo, data and personal communications areappearing daily. Virtually all these servicesinvolve the transmission of multiple signals and /or large quantities of information at high datarates. For such signals, whether transmitted byfrequency division multiple access (FDMA) ortime division multiple access (TDMA), amplifierlinearity is a major consideration.

NEED FOR LINEARITY

Distortion can be thought of as the creation ofundesired signal energy at frequencies notcontained in the original signal. Distortion isproduced by a loss of linearity. Amplitudelinearity can be considered a measure of howclosely the input-output transfer response of anamplifier resembles a straight line. When anamplifier's input level increases by a certainpercent, its output level should increase by thesame percent. A deviation from a straight linecan be represented by a power series.

Vout=K1 Vin + K2 Vin2 + K3 Vin3...Kn Vinn (1)

When a single carrier input signal, representedby a sine wave, is substituted into this expressionthe output waveform will contain the originalsine wave and harmonic distortion products. Forall but the most wide band communicationsapplications (bandwidths of an octave orgreater), these harmonics can be eliminated byfiltering and do not pose a problem. However,when more than one carrier is present, beatproducts are produced in the vicinity of the inputsignals. These new signals are known as inter-modulation distortion (IMD) products. They arelocated at frequencies above and below the inputcarriers, and at frequency intervals equal to theseparations of the input carriers. This is illus-trated in Figure 1. IMD products can not beeasily eliminated by filtering as they are locatedon the same frequency or near to the desiredinput signals.

DISTORTION PRODUCTS

f1 f2AMPLIFIERf1 f2 Figure 1. When two or more

signals are amplified, distor-tion products appear in thevicinity of the desired signals.

Modulation of a carrier can also result in theproduction of IMD products.When a single carrier is ampli-tude modulated (AM) with amodulation index (M), multiplesignals are produced.

[1+M cos(ωmt)] Ac cos(ωct) = Accos(ωct) + M Ac cos([ωc+ωm]t)

+ M Ac cos([ωc-ωm}t) (2)

Even pure frequency modulation(FM) results in an effectivemulti-carrier signal when thesignal is filtered. Band-limitingan FM signal introduces AMmodulation which in turn pro-duces multiple signals andconsequent IMD.

All real amplifiers have somemaximum output power capac-ity. This is referred to as anamplifier's saturated power. Driving the ampli-fier with a greater input signal will not producean output above this level. Generally anamplifier's greatest efficiency will occur at ornear saturation. As an amplifier is driven closerto saturation, its deviation from a straight lineresponse will increase. Its output level willincrease by a smaller amount, for a fixed in-crease in input signal as shown in Figure 2.Thus, the closer an amplifier is driven to satura-tion, the greater the amount of distortion itproduces.Distortion is also produced by phase non-linear-

Figure 2. As an amplifier is driven closer to saturation, itsoutput level will increase by a smaller amount, for a fixedincrease in input signal.

ity. The shift in phase angle that a signal encoun-ters in passing through an amplifier is a measureof the time delay. Ideally this phase shift, or timedelay, should be constant for all power levels.

θ (P) = constant (3)

(2)

Pout

Pin

Pout

Pout

PinPin

(SATURATION)

Linearization

A linearizer is a device which reduces anamplifier's distortion. Use of a linearizer allowsan amplifier to produce more output power andoperate at a higher level of efficiency for a givenlevel of distortion.

Linearizers have been used in video broadcastingfor years. Microwave applications generallyrequire a different approach than broadcastingbecause of their wider bandwidths. There aremany different ways of linearizing an amplifier.Feedforward, feedback and predistortion aresome common methods. Figure 3 shows blockdiagrams and lists the characteristics of theseapproaches. Instead of operating a backoff of 7dB for FDMA, a linearized TWTA may beoperated at 3 dB. Likewise with digital modula-tion only a 4 dB backoff may be required.

Figure 3a. Feedforward is relatively complex,but can provide wide-band and excellent distor-tion reduction.

In practical amplifiers there can be a substantialchange in phase with power level. This change inphase with amplitude converts variations insignal level to phase/frequency modulation.

For a sinusoidal signal envelope,

P(t) = M cos[ωmt]

the resulting spectrum resembles that of a sinu-soidal modulated FM signal

n = ∞Ac cos(ωct + Mcos[ωmt]) = AcΣJ

n(M) cos([ωc + nωm]t)

n = -∞ (4)

Thus, phase non-linearity produces IMD prod-ucts in a similar fashion to amplitude non-linearity. In some systems, phase non-linearity isthe principal cause of distortion.

When multiple signals are sent through a com-munications system, an amplifier must be oper-ated at a reduced power level (backed off) inorder to keep distortion at an acceptable level.The acceptable IMD level usually depends onthe carrier-to-noise ratio (CNR) required at thereceiver. IMD products are consider to add to thereceiver noise level. For a carrier to IMD ratio

C/I = CNR the resultant CNR = CNR -3 dB

C/I = CNR + 6 dB → CNR = CNR-1 dB

C/I=CNR+10 dB → CNR = CNR-.05dB (5)

tions TWTA's are typically backed-off 5 to 7 dB,and sometimes more to keep distortion at anacceptable level. This is about a 4 to 1 reductionin usable power. For TDMA applications theback-off is less, usually 2 to 4 dB, to keepdistortion in the form of spectral regrowth frominterfering with adjacent channel communica-tions.

If a CNR of 16 dB (10 dB FM threshold + 6 dBfor rain fading) is required, and the IMD prod-ucts are to have a negligible effect, a C/I > 26 dBis required.

Multiple signals may be present due to the use ofFDMA transmission, or the result of digitalmodulation of single carrier. For FDMA applica-

MAIN AMP

AUX AMP

(+)(-)

(+) (-)

Network

Amplifier

Figure 3b. Feedback is relatively narrow bandand has potential stability problems.

Amplifier

Figure 3c. Predistortion is relatively simple toimplement, can provide wide bandwidth and iswidely used with TWTA's.

In feedforward, the input signal is subtractedfrom a sample of the main amplifier's outputsignal. This leaves only the amplifier's distortionproducts. This distortion signal is amplified andthen subtracted from the main amplifier's outputsignal to produce an ideally distortion freesignal. Feedforward has been extensively usedwith solid state amplifiers, and functions well

with TWTA's, but is considerably more complexthan the other two methods. It requires an auxil-iary amplifier, approximately 20 percent of thesize of the amplifier to be linearized. A phaseshifter and combiner must be added after theHPA. These components introduce loss and mustbe capable of handling the peak output signallevel. Consequently feedforward is not easilyadded to an existing amplifier. When comparingfeedforward with other linearization techniques,the power of the auxiliary amplifier should beadded to the power capacity of the main ampli-fier to establish a common point for reference.

Feedback linearization can take a variety offorms. All these approaches tend to have alimited bandwidth and potential stability prob-lems. There has been little application of feed-back linearization to TWTA's.

Of various types, predistortion linearizers havebeen favored for microwave and satellite ser-vices because of their relatively wide bandcharacteristics and ability to function as a standalone unit. Predistortion linearizers generate atransfer characteristic that is the opposite of thepower amplifier's saturation characteristic inboth magnitude and phase. The gain of thelinearizer increases by the same amount theamplifier's gain decreases. Likewise, the phaseshift introduced by the linearizer increases by thesame amount the amplifier's phase decreases.The desired result is the composite linear transfercharacteristic shown in Figure 4. This is theresponse of a so called ideal limiter.

φ

Pout

inP

Pout Pout

inPinP

PREDISTORTION

LINEARIZER

HPA OUTPUT

Figure 4.Predistortion linearizers

generate a responseopposite to a TWTA'scharacteristics in bothmagnitude and phase.

LINEAR

NON-LINEAR

+

-Φ

V in

Vout (Low)

Vout (High) Vnl

÷

Attn.

Σ PoutPin

Once a TWTA has saturated, it is impossible toobtain more output power by driving the ampli-fier harder. Thus, the best a predistortion linear-izer can do is to produce an ideal limiter charac-teristic. Despite this limitation, it is possible for alinearizer to provide large benefits in signalquality, especially as output power is reducedfrom saturation. Some improvement is possibleeven at saturation and beyond as the linearizercan correct for post-saturation phase distortionand power slump.

An alternate way of thinking about a predistor-tion linearizer, is to view the linearizer as agenerator of IMD products. If the IMD's pro-duced by the linearizer are made equal in ampli-tude and 180 degrees out of phase with theIMD's generated by the amplifier, the IMD's willcancel.

Predistortion linearizers can be produced bysubtracting the output signals from parallel linearand nonlinear paths. This results in gain expan-sion as illustrated by the vector diagram ofFigure 5.

The gain of the linear path (Vlin) remainsconstant with increasing drive level, while thegain of the nonlinear path (Vnl) decreases assaturation is approached. Thus, the overall gain(Vout) increases. Adjustment of the angle (Φ)between the two paths allows the change ofphase with level to be controlled.

Recently design advances have greatly simpli-fied predistortion linearizers. Past linearizerswere complex and difficult to adjust. Newdesigns use in line networks. They are muchsmaller in size and offer wider bandwidths - fullC, X and Ku-band coverage, enhanced perfor-mance, easy alignment and excellent stability.

Figure 5. Gain expansion can be produced by subtracting a linear path from a nonlinear path.

(6)

Vout = Vlin - Vnl

LINEARIZER ADVANTAGE

Figure 6 shows the transfer characteristics of atypical TWTA and the corrected response pro-vided by a contemporary predistortion linearizer.Note how the shape of the linearized Pout/Pincurve approaches the desired ideal limiter char-acteristic of Figure 4. The separation of the 1dBcompression point (CP

1dB point where the gain

has dropped by 1dB) from saturation is a goodindicator of linearizer performance. Ideally theCP

1dB is located 1dB in input power beyond

saturation. It is not unusual for TWTA's to havethe CP

1dB occur 10 to 12 dB before saturation. In

Figure 6 the CP 1dB

is moved from 6.25 dBbefore saturation for the TWTA, to just aboutsaturation for the linearized TWTA. The linear-izer also reduces the change in phase with powerlevel from more than 40 degrees for the TWTAalone to a near flat line.

Figure 6. Transfer characteristics of TWTA and linearized TWTA.

Some authors have tried to define the point ofsaturation in terms of gain compression. Theyhave suggested using 6 dB compression as anindicator of saturation. This approach clearlywill not work in the case of a linearized ampli-fier. Figure 6 shows that saturation occurs atabout 6 dB compression for the unlinearizedTWTA, but only at 2 dB for the linearized case.

IMD data are also sometimes presented in termsof input-power-backoff (IPBO). IPBO is moredifficult to interpret, and in some cases can bemisleading as it depends on the gain transfercharacteristics of the amplifier. Definition of theexact point of saturation is also more criticalwhen IPBO is used. The use of OPBO is recom-mended since the distortion at a required level ofoutput power is the real parameter of concern.

Distortion is most often evaluated in terms of theratio of carriers to third order IMD products(C/I3)- IMD terms closest to the carriers. Withlinearizers it is not uncommon to find the fifthorder IMD terms equal to or even greater thanthe thirds. This is illustrated in Figure 7.

EVALUATION OF MULTI-CARRIERDISTORTION

Many different standards have been used for theevaluation of distortion. This makes comparisondifficult. IMD data are usually presented as afunction of output-power-backoff (OPBO)relative to saturation. The reference saturatedpower should be for single carrier saturation.Two-carrier saturation is typically about 1 dBlower. Noise saturation can be even lower.

Pin 2.5 dB/DIV

TWTA PHASE

LTWTA PHASE

TWT POUT

LTWTA POUT

PHASE 5.0 deg/DIV

Pin 2.5 dB/DIV

LTWTA GAIN

TWTA GAIN

LTWTA POUT

TWTA POUT

GAIN 0.5 dB/DIV Pout 2.5 dB/DIV

Pin 2.5 dB/DIV

TWTA PHASE

LTWTA PHASE

TWT POUT

LTWTA POUT

PHASE 5.0 deg/DIV

a. Upper & lower odd order AM/PM terms outof phase.

b. Upper & lower odd order AM/AM terms inphase.

Figure 8. IMD terms can be non-symmetrical.

IMD terms can also be non-symmetrical. Thisimbalance is due to the presence of both ampli-tude and phase induced IMD products. Upperand lower frequency IMD terms generated bygain compression (AM/AM) are in phase. How-ever, upper and lower frequency IMD termsgenerated as a result of phase change with power

(AM/PM) are 180 degrees out of phase as illus-trated in Figure 8. This phase difference is aresult of the properties of the Bessel function inequation (4). When the AM/AM and AM/PMinduced terms combine, the result is a non-symmetrical IMD spectrum.

Figure 7. Linearizers can produce 5th order IMD terms equal or greater than 3rd order terms.

7th 5th 3rd 3 rd 5th 7th

A preferred C/I measure is to use the ratio of thecarrier power to the total IMD power (C/It),

C/It = N ∞ ½Σ Cn2 / Σ Im2

n=1 m=1 (7)

where N is the total number of carriers. Becauseof the calculation involved in the measurementof C/It, C/I is often evaluated as the ratio ofcarrier power to the power of the largest IMDproduct, regardless of its order. This method isused for the C/I data presented in this paper.

The two-tone output spectrum of a typicalTWTA at 4 dB OPBO with and without linear-ization is shown in Figure 9. A reduction in IMDof greater than 15 dB is common at this OPBOlevel.

although a higher level of back-off will berequired for the same C/I level as the number ofcarriers is increased.

The data shown in Figure 10 is typical for twocarriers spaced 10 MHz apart at the top, centerand bottom of a satellite band. It representsStatic bandwidth, the ability of a linearizer toequalize an amplifier over frequency with thecarriers relatively closely spaced. There isanother type of bandwidth which needs to alsobe considered. This is the Dynamic bandwidthand measures the ability of the linearizer/ampli-fier to function with a rapidly changing signalenvelope. It can be measured by increasing thefrequency spacing of a two-tone test signal.TWTA's generally have superior dynamicbandwidths than SSPA's and can be linearized tocarrier spacings of 300 to 500 MHz.

The improvement in two-tone C/I as a functionof OPBO achieved by using a linearizer with aTWTA is depicted in Figure 10. For the C/I of26 dB of equation (5), a greater than 3 dB in-crease in output power is provided. If a C/I ratioof 30 dB is required, the TWTA would have tobe backed-off at least 10 dB, but with thelinearizer it need only be backed-off 4 dB. Thisis a 6 dB increase in output power. A compa-rable or superior output power increase can beachieved for signals of more than 2 carriers,

( )

Figure 9.A two-tone C/Iimprovementof greater than15 is commonat 4 dB OPBO.

10

15

20

25

30

35

C/I

in d

B

OUTPUT POWER BACKOFF IN dB

40

45

>3dB

LTWTA

TWTA

High Band

Mid Band

Low Band

6dB

Figure 10.Two-tone C/Iof TWTA andimproved C/Iof linearizedTWTA.

Figure 11 shows how efficiency is related toOPBO for a modern high efficiency TWTA. Fora C/I of 26 dB, the use of a linearizer can providegreater than a 70 percent efficiency increase.

10

30

%

EFFICIENCY

OUTPUT BACKOFF IN dB

50

70

26 dB C/I WITH LIN

26 dB C/I TWTA ALONEFigure 11.A 70 percentincrease inefficiency canbe achieved fora C/I of 26 dB.

NOISE POWER RATIO

The performance of a linearized TWTA withmany carriers (>10) is normally tested using anoise power ratio (NPR) measurement. In thistest white noise is used to simulate the presenceof many carriers of random amplitude and phase.The white noise is first passed through abandpass filter to produce an approximatelysquare spectral pedestal of noise of about thesame bandwidth as the signals being simulated.This signal is then passed through a narrowband-reject filter to produce a deep notch at thecenter of the noise pedestal as shown in Figure12.

The width of the notch should be about 1 percentor less of the width of the noise pedestal. Thisnoise signal is used to excite the test amplifier.Amplification will produce IMD products whichtend to fill in the notch. The depth of the notch atthe output of the amplifier can be observed witha spectrum analyzer, and is the measure of theNPR. NPR test signals are usually generated atIF and upconverted to the microwave band ofinterest. Care must be taken to insure the notchdepth is not degraded by this process. The notchdepth of the test signal should be at least 10 dBgreater than the maximum NPR to be measured.The NPR's of a typical TWTA and a linearizedTWTA are shown in Figure 13.

NoisePedestal

Notch

Noise BPF Notch

Figure 12. An NPR test generator consists of a white noise source connected in cascade with abandpass filter and a notch filter. Notch depth can be measured with a spectrum analyzer.

10

15

20

25

30

35NPR

IN

dB

OUTPUT BACKOFF IN dB

40

5

0

LTWTA

TWTA

Figure 13.NPR predicts theimprovementprovided bylinearization of aTWTA withmany carriers.

SINGLE CARRIER SIGNALS

Even with single carrier signals, a linearizer canoften be of benefit. For example, HPA's trans-mitting single carrier QPSK (quadrature phase-shift-keyed) and OQPSK (offset QPSK) signalsare usually operated at a reduced output level.They are backed off to prevent spectral regrowth,caused by amplifier non-linearity, which caninterfere with adjacent channel signals. Linear-ization can reduce this spreading to an accept-able level (> 25 dB for OPBOs of ~ 0.5 dB fromsaturation, > 30 dB for OPBOs of ~ 2 dB fromsaturation). Figure 14 shows an illustration ofthe improvement provided by a linearizer for aQPSK satellite signal. At 4 dB OPBO, about a10 dB decrease in interference level is achieved.Figure 15 shows the reduction in sprectral

Figure 15. Reduction in spectral regrowth provided by linearization of a TWTA.

regrowth achieved by linearization as a functionof OPBO. If a 2-tone C/I > 25 dB can beachieved, the spectral regrowth will be > 30 dBdown. Linearization also improves the bit-error-rate (BER) of digital modulated signals. Ingeneral the greater the required BER, the greaterthe improvement provided by linearization.

SUMMARY

Linearizers are needed to increase TWTA'spower capacity and efficiency when handlingmulti-carrier and high data rate digitally modu-lated traffic. New linearizer designs have greatlyenhanced performance and bandwidth, madealignment easier, and provided excellent stabilityand reliability. These linearizers can deliver upto a four fold increase in TWTA power capacity,and more than double TWTA efficiency. Withthe increasing demand for greater data transmis-sion rates, it seems likely that in the near futurevirtually all TWTAs will be operated with alinearizer.

TWTA

L/TWTA

SPECTRUM10 dB/div

4 dB OPBO

SPAN 2 MHz/div

Figure 14.The bandwidth/noisereduction of QPSK signalachieved by linearizationof a TWTA.

REFERENCES

1. E. Ballesteros, and F. Perez. "Microwave Power Amplifiers Linearized By Active FeedbackNetworks IEEE MTT-S Symposium Workshop on Linearizers, June 1989.

2. C. Bremenson, etal, "Linearizing TWT Amplifiers in Satellite Transponders, Systems Aspectsand Practical Implementation." Proc. AIAA 8th Communications Satellite System Conference, pp.80-89, Ap 20-24, 1980.

3. D. Cahana, etal, "Linearized Transponder Technology for Satellite Communications, Part 1:Linearizer Circuit Development and Experimental Characterization," COMSTAT Technical Review,Vol. 15, No. 2A, pp. 277-308, Fall 1985

4. Ryuichi Inada, etal, "A Compact 4-GHz Linearizer for Space Use," IEEE Transactions on Micro-wave Theory and Techniques, Vol. MTT-34, No. 12, pp. 1327-1332, December 1986.

5. A. Katz, etal, R. Sudarsanam, and D. Aubert. "A Reflective Diode Linearizer for SpacecraftApplications," IEEE MTT-S International Microwave Symposium Digest, pp. 661-664, June 1985.

6. A. M. Khilla, etal, "Multi-Band Predistortion Linearizers for Satellite Transponders and GroundStations," American Institute of Aeronautics and Astronautics, pp. 927-937, 1992.

7. Y. S. Lee, etal, "Linearized Transponder Technology for Satellite Communications; Part 2:System Simulation and Performance Assessment," COMSTAT Technical Review, Vol. 15, No. 2A,pp. 309-341, Fall 1985.

8. Mahesh Kumar, etal, "Predistortion Linearizer Using GaAs Dual-Gate MESFET for TWTA andSSPA Used in Satellite Transponders," IEEE Transactions on Microwave Theory and Techniques,Vol. MTT-33, No. 12, pp. 1479-1484, December 1985.

9. Shabbir S. Moochalla, etal, "An Integrated Ku-Band Linearizer Driver Amplifier for TWTAsWith Gain and Bandwidth," American Institute of Aeronautics and Astronautics 14th InternationalCommunications Satellite Systems Conference, 1992.

10. A. Saleh, "Intermodulation Analysis of FDMA Satellite Systems Employing Compensated andUncompensated TWTAs," IEEE Trans. Commun., Vol. COM-30, No. 5, pp. 1233-1242, May 1982.

11. G. Satoh and T. Mizuno, "Impact of a New TWTA Linearizer Upon QPSK/TDMA Transmis-sion Performance." IEEE Journal on Selected Areas in Communications, Vol. SAC-1, No. 1, pp.39-45, January 1983.

12. J. Steck and D. Pham. "A New TWT Linearizer for Satellite-Communications Transmitters,"Microwave System News and Communications Technology, Vol. 17, No. 9, pp. 28-42, June 1987.

Linearizer Technology, Inc.3 Nami Lane, Unit C-9 Hamilton, NJ 08619 Tel: (609) 584-8424 Fax: (609) 631-0177 www.lintech.com

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