1

LINEARIZATION:LINEARIZATION:

BY: DR. ALLEN KATZ, MAY 2004 04.16.04

REDUCING DISTORTION IN POWER AMPLIFIERS

• WHY LINEARIZE• TYPES OF LINEARIZERS• THEORY/IDEAL LIMITER• PREDISTORTION LINEARIZERS• PERFORMANCE EVALUATION• RESULTS• CONCLUSIONS

OUTLINE

2

IN PAST MOST AMPS USED FOR SC FM MOD SIGNALS

- NL PRODUCTS ELIMINATED WITH LP FILTER-OPERATER AT SATURATION (MAX PWR & EFF)

INPUT

MUX

CHANNEL AMP #1

CHANNEL AMP #2

OUTPUT

MUX

TODAY MULTI-CARRIER AND COMPLEX MODULATED SIGNALS COMMON WHEN MORE THAN ONE CARRIER - DISTORTION PRODUCED (IM)

DISTORTION PRODUCTS

f1 f2AMPLIFIERf1 f2

TO REDUCE DISTORTION TO AN ACCEPTABLE LEVEL

-MUST OPERATE AMPLIFIER AT REDUCED POWER LEVEL(BACKOFF FROM SATURATION)

3

Pin 2.5 dB/DIV

TWTA PHASE

TWT POUT

PHASE 5.0 deg/DIV

PHASE

OUT

Ac cos(ωct + M cos[ωmt]) = Ac ΣJn(M) cos([ωc+nωm]t)n= 8

n= - 8

DISTORTION ALSO PRODUCED BY CHANGE IN PHASE WITH POWER LEVEL

FOR A DIGITALLY MODULATED CARRIERDISTORTION PRODUCES SPECTRAL REGROWTH

FREQ 20 MHz/

10 dB/

FREQ 20 MHz/

10 dB/2.5dB OPBO

4

SYSTEMATIC PROCEDURE FOR REDUCING DISTORTIONS

USUALLY EXTRA COMPONENTS ADDED TO AN AMPLIFIER

WHEN CONFIGURED IN A SUBASSMBLY OR BOX KNOWNAS A LINEARIZER

THREE COMMON FORMS:1) FEEDFORWARD2) FEEDBACK3) PREDISTORTION

+ TECHNIQUES TO IMPROVE EFFICIENCY USING NL PAs

LINEARIZATION --

CHOICE OF LINEARIZATION

• LEVEL OF LINEARITY (DISTORTION REDUCTION) NEEDED.

• BANDWIDTH REQUIRED (SIGNAL AND OPERATIONAL).

• COST/COMPLEXITY CONSTRAINTS.

5

LINEARIZERS HAVE BEEN USED WITH

•FET SSPAs (GaAs, MOS, LDMOS)

•TWTAs and KLYSTRONS

• BIPOLAR SSPAs (CLASS A, AB, B)

AMP LAMP AMP LAMP

AMP LAMP AMP LAMP

“SAME” Distortion

“SAME” Distortion

POWER OUT

Greater Ouput Power

Efficiency

Greater Efficiency

LINEARIZERS ALLOW HPAs TO OPERATE CLOSER TO SAT

6

WANT TO OPTIMIZE EFFICIENCY AND SATURATED POWER, NOT LINEARITY

EXCELLENT RESULTS CAN BE OBTAINED WITH CLASS A-B AND B AMPS BOTH FET AND BIPOLAR

YOU CAN’T LINEARIZE AN AMPLIFIERTHAT IS ALREADY LINEAR!

FIRST RULE:

IDEAL AMPLIFIER CHARACTERISTIC

φ

Pout

inP

WANT CONSTANT GAIN AND PHASE

7

SATELLITE --•IMD PRODUCTS ADD TO THERMAL NOISE IF C/I = CNR THEN CNR DEGRADES BY 3 dB

•WANT C/I > CNR + 10 dB FOR NEGLIGIBLE DEG. (< .5 dB)IF CNR = 16 dB THEN C/I = 26 dB

•IF C/I = CNR + 6 THEN CNR = CNR DEG. BY 1 dB

CELLULAR --•INTERFERENCE FROM TX TO ADJACENT RX A PROBLEM --CAN NEED C/I > 35 ~ 70 dB.

•FOR DIGITAL MOD, 16QAM … 8PSK NEED HIGH C/I TO KEEP BER DOWN.

IMPROVEMENT DEPENDS ON ACCEPTABLE DIST LEVEL

FEEDFORWARD

•RELATIVELY COMPLEX

•NOT WORKABLE AS STAND-ALONE UNIT

•NOT EFFECTIVE FOR OPBOs < 6 dB

•MOST USEFUL FOR VERY HIGH LINEARITY APPLICATIONS

Sin Sout 1 Sout 2

MAIN AMP

AUX AMP Scor

IMD

8

MINIMUM FEEDFORWARD OPBO FOR IMD CANCELATION (20 dB)

1) AUX AMP SIZE, 2) OUTPUT COUPLER COEF.

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

. OPB

O fo

r IM

D C

ance

llatio

n in

dB K2 3 dB

K2 10 dBK2 6dB

DEPENDS ON: 1) AUX AMP SIZE, 2) OUTPUT COUPLER COEF.

FEEDBACK LINEARIZATION

*FEEDBACK (NETWORK)NET-

WORK

AMP

- NARROW BAND- STABILITY PROB- REDUCED GAIN- DIFF TO ADJ

*INDIRECT FEEDBACK

-OPERATES ON ENVELOPE-VERY LIMITED BW < 1/(4∆tS)-CAN BE POLAR OR CARTESIAN

AMP

+

9

CARTESIAN FEEDBACK ELIMINATES THE NEED FOR PHASE CORRECTION CIRCUITRY

•RELATIVELY SIMPLE CIRCUITRY

PREDISTORTION

•WIDE BAND (>20% BW)

•MOST POPULAR FOR MICRO/MILLIMETER WAVE

•EASILY IMPLEMENTED AS A STAND-ALONE UNIT

10

LINEARIZER GAIN DEPENDS ON INPUT TO HPA

• THE GAIN OF THE LINEARIZER (GL) MUST INCREASE BY THE SAME AMOUNT THE HPA’s GAIN (GA) DECREASES.

• GL(PoutL) - GLss = - [GA(PinA) - GAss] PoutL = PinA

• ΦL(PoutL) - ΦLss = - [ΦA(PinA) - ΦAss] PoutL = PinA

• GL(PinL) = GLss+ GAss - GA(PinL + GL(PinL))

• ΦL(PinL) = ΦLss+ ΦAss - ΦA(PinL + GL(PinL))

• ΦL DEPENDS ON THE GL AND CANNOT BE SET IDENPENDENTLY

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 GAIN

PHA

SE IN

DEG

REE

S

45

-4.5

-3.5

-3.0

-2.5

-4.0

-2.0

-1.5

-1.0

-0.5

0

GAI

N IN

dB

AN IDEAL LINEARIZER MUST PROVIDE A GAIN EXPANSION THAT APPROACHES INFINITY NEAR SATURATION

dG/dP =>∞ as Pin => Sat

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FORMS OF PREDISTORTION LINEARIZERS

Vout (HIGH)

Vin

Vout (LOW)

Vnl

1. TRANSMISSIONLIN

NL

F

2. REFLECTIVE

NL

F

3. IN LINE

TECHNIQUES TO IMPROVE EFFICIENCY USING NL PAs

• MANY WAYS TO ACCOMPLISH.

• CLASSICAL “KHAN METHOD” DEMODS ENVELOPE AND LIMITS SIGNAL. THEN REMODULATES AT OUTPUT PA.

• LINC SYSTEMS USE OBTAIN LINEAR AMPLIFICATION BY COMBINING TWO NON-LINEAR PAs.

• LOAD MODULATION AND OUTPHASING (DOHERTY – ONE EXAMPLE)

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EER – ENVELOPE ELIMINATION AND RESTORATION

IF ELIMINATE ENVELOPE, SIGNAL CAN BE AMPLIFIED IN NL PA OPERATED AT OR NEAR SATURATION.

LINC – LINEAR AMPLIFICATION WITH NON-LINEAR COMPONENTS

CAN OBTAIN ANY AMPLITUDE FROM THE SUM OF 2CONSTANT AMPLITUDE SIGNALS OF VARIABLE PHASE

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DIGITAL PREDISTORTION

• CAN PRODUCE CURVES OF ANY SHAPE• NORMALLY PROCESS AT BASEBAND• CAN USE EITHER G AND Φ OR I AND Q• MUST SAMPLE AT > 2 X CORRECTION BW FOR G AND Φ• BUT ONLY > CORRECTION BW FOR I AND Q• CORRECTION BW (CBW) ≥ 3 x BW OF SIGNAL• MUST USE MANY BITS FOR HIGH CANCELATION (<6 dB/)

MIX DOWN TO BB MIX UP TO IFIF RF

BW

0 3 ω0 6ω0

A/DSIGNAL

INTERPOLATE

II~

cos 3 ω0t(1, 0, -1, 0)

Q~

sin 3ω0t(1, 0, -1, 0)

CALCULATE

cos 3 ω0t

sin 3ω0tIY+QX

D/A FIL

IX-QY

smoothing

HPA

ω1+3ω0

~ ω1

R

X (R)LUT

Y (R)LUT

Q

COMPUTE

UPDATED

VALUES

FOR

X(R), Y(R)

UPDATEX(R), Y(R)

R'

INTERPOLATE

A/D

I~

Q~

cos 3 ω0t

sin 3ω0t

LUT = Look Up Table

T= sampling period

3w0 (4∆T) = 2 π3f0 (4∆T) = 1

fs = 1/ ∆T

fs = 12 f 0 = 6BW

SPECTRUM

DIGITAL ADAPTIVE PREDISTORTION

ADAPTIVE SYSTEMS CORRECT AT << ENVELOPE RATE

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• ADVANTAGES:* ACCURATE CORRECTION OVER WIDE DYNAMIC

RANGE AND FOR IRREGULAR NON MONOTONIC CHARACTERISTICS

* EASY TO MODIFY AND UPDATE * SIMPLE TO IMPLEMENT AS ADAPTIVE SYSTEM

• DISADVANTAGES:* CORRECTION BANDWIDTH LIMITED BY

SAMPLING RATE: SR = CBW = N X BW* COST CAN BE HIGHER THAN ANALOG * POWER CONSUMPTION CAN BE HIGH* WIDE BW SYSTEMS DIFFICULT TO IMPLEMENT

DIGITAL PREDISTORTION

PERFORMANCE EVALUATION

MAGNITUDE & PHASE IMPORTANT INDICATORS OF PERFORMANCE

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

** OBTAIN WITH POWER SWEEP

SEPARATION OF 1 dB COMPRESSION AND SATURATIONPROVIDES GAGE FOR COMPARISON

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C/I (CARRIER TO IMD) MEASUREMENT

• MANY DIFFERENT STANDARDS MAKE COMPARISON DIF.

• DATA USUALLY PRESENTED REL TO BACKOFF FROM SAT.

• SAT POINT SHOULD BE SINGLE CARRIER SAT.2 CARRIER SAT ABT 1 dB LOWER, NOISE ABT 1.5 dB.

• CAN NOT USE COMPRESSION POINT FOR REFERENCE.1 dB = SAT - D

• BOTH IPBO AND OPBO USED … IPBO CAN BE MISLEADING.BEST TO REFER TO OPBO- OUTPUT LEVEL IS WHAT’S IMPORTANT!

OFTEN RESULTS PRESENTED FOR C/I3 ONLY

7 73 3

5th 5th

th thrd rd

With Linearizers, not uncommon for 5th order terms to be greater than 3rds or of same order

Total C/I preferred to C/I3

C/Imin is a good compromise

C/I total = C/ Ι3 2 + Ι5 2 + Ι7 2 + ...Σ

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IMD TERMS CAN BE NON-SYMMETRICAL

UPPER & LOW ODD ORDER AM/AM TERMS IN PHASE

UPPER & LOW ODD ORDER AM/PM TERMS OUT OF PHASE

DUE TO MEMORY EFFECTS (AM/AM AND AM/PM)

A LINEARIZER IMPROVES LINEARITY OF A CLASS A SSPA

Rel

ativ

e Po

wer

Out

put 0

.5 d B/D

IV

START -10.0 dBm CW 1.9500 GHz STOP 15.0 dBm

Gai

nG

hang

e0 .5

dB

/DIV

SAT

AMPL/AMP

GAIN

PHASE

AMPSAT

AMP

L/AMP

L/AMP

17

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

LINEARIZATION OF A CLASS A SSPA PROVIDES ONLY

A 0.5 dB POWER INCREASE FOR A C/I OF 26 dB,BUT A 2.5 dB POWER INCREASE FOR A C/I OF 50 dB

45

40

35

30

25

20

15

101 2 3 4 5 6 7 8 9 10

C/I (MIN) IN dB

OUTPUT POWER BACKOFF IN dB

L/SSPA

SSPA26 dB

LINEARIZATION OF LESS LINEAR CLASS AB SSPA

PROVIDES > 1.5 dB POWER INCREASE FOR C/I OF 26 dB.

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WITH A TWTA A C/I = 26 dB CAN OBTAIN > 3 dB POWER INCREASE

WITH MULTIPLE CARRIERS THE IMPROVEMENT IS EVEN GREATER!

1 2 3 4 5 6 7 8 9 1010

15

20

25

30

35C

/I in

dB

OUTPUT POWER BACKOFF IN dB

40

45

>3dB

LTWTA

TWTA

High Band

Mid Band

Low Band

6dB

MULTIPLE CARRIERS (N>2)

• NO SIMPLE RELATIONSHIP BETWEEN C/I FOR 2 AND N CARRIER CASE

• EXERCISE OVER RANGE Ppk = 2NPav

14 16 18 20 22 24 26 28 30 32

1

2

3

4

5

6

0OPB

O R

EUC

TIO

N I N

dB

C/I IN dB

7

OPBO IMPROVEMENT

2-TONE

4-TONENPR

• GREATER IMPROVEMENT(REDUCTION IN OPBO) FOR A GIVEN C/I AS N INCREASES

19

NPR - NOISE POWER RATIO

NoisePedestal

Notch

Noise BPF Notch

MEASURE OF N-CARRIER C/I

WANT DEPTH OF GENERATOR NOTCH > 10 dB BELOW NPR OF INTEREST

NPR PREDICTS AMPLIFIER PERFORMANCEWITH MANY CARRIERS

1 2 3 4 5 6 7 8 9 10 11

10

15

20

25

30

35

5

LTWTA

TWTA

C/I

in d

B

OUTPUT POWER BACKOFF IN dB

4 dB

FOR C/I = 25 dB OBTAIN ALMOST 6 dB INCREASE IN POWER.

20

NPR OF CLASS AB SSPA

10

15

20

25

30

35

1 2 3 4 5 6 7 8 9 10 11OPBO in dB

NPR

in d

B

PROVIDES SIGNIFICANT REDUCTION IN SPECTRUM

REF LEVEL0.5 dBm

TWT ONLY

4.0 dB B.O.

4.0 dB B.O.WITH LINEARIZER

10 dB/

VBW 1 kHZ

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> 2 dB POWER INCREASE

EVEN NEAR SAT

REDUCTION IN SPECTRAL REGROWTH PROVIDED BY LINEARIZATION OF A TWTA

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

25

30

35

40

45

50

20

Car

rier t

o N

oise

Rat

i o

OPBO IN dB

15dB

LTWTA

TWTA

22

01 2 3 4 5 6 7 8 9 10

20

30

40

10

OUTPUT BACKOFF IN dB

50

60

70

80

C/I

IN d

B

IDEAL LINEARIZER PERFORMANCE IS LIMITED BY SIGNAL PEAK-TO-AVERAGE CHARACTERISTICS (PAC)

2-TONE

MANY-TONE (NPR)

PAC SETS MINIMUM BACKOFF OF PA!CANNOT IMPROVE BY LINEARIZATION.

MUST USE PA WITH HIGHER POWER/EFFICIENCY

DSP L/TWTA AT 3 dB OPBO – C/I > 50 dB

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TWO KINDS OF BANDWIDTH1) STATIC BANDWIDTH - ABILITY OF LIN MAG/PHASE TRANSFER RESP TO

EQUALIZE AMP AT ALL FREQ OF INTEREST

2) DYNAMIC BANDWIDTH - ABILITY OF LIN MAG/PHASE TRANSFER RESP TO FOLLOW ENVELOPE OF SIGNALS

- MEAS WITH 2 CLOSE SPACED TONES AT ALL FREQ OF INTEREST

- MEAS WITH 2-TONE SIGNAL IN WHICH THESPACING OF THE TONES IS INCREASED

THE LINEARITY OF AMPLIFIERS DEGRADE WITH INCREASING CARRIER SPACING

C/I5 LOWER

4 dB OPBO

40

35

30

25

20

15

10

1 2 3 4 5 6 7 8 9 10 20 30 40 50 60 70 80 90 100CARRIER SPACING (MHz)

C/I

(dB

)

C/I3 UPPER

C/I3 LOWER

C/I5 UPPER

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MAJOR CAUSE OF DEGRADATION --

ENVELOPE FREQUENCY Fe = F∆/2

TRANSFER CHARACTERISTICS CHANGE WITH Fe

INABILITY OF AMPLIFIERS TO FOLLOW RAPIDLY CHANGING ENVELOPE

MEMORY EFFECTSMEMORY EFFECTS

• Memory Effects are changes in a Power Amplifier’s (PA) non-linear characteristics resulting from the past history of the input signal.

Vo = f(Vin, time)

• Primary cause drain/collector and gate/base bias change.

• Thermal, device and frequency are also factors.

• Standard predistortion linearizers depend on a stable non-linear response, and can be particularly degraded by memory effects.

25

IMPROVEMENT IN C/I RESULTING FROM ADDED LOWINDUCTANCE DRAIN CAPACITORS (RESONATE AT 12 MHz)

40

35

30

25

20

15

10

Linearizer with CapsLinearizer without CapsNo Linearizer with CapsNo Linearizer without CapsLinearized (1MHz Average)Non-Linearized (1 MHz Average)

C/I

IN d

B

OUTPUT BACKOFF IN dB

30 MHz CARRIER SPACING

LINEARIZERS INCREASE HPA POWER CAPACITY AND EFFICIENCY FOR MULTI-CARRIER AND COMPLEX DIGITAL SIGNALS

NEW LINEARIZER DESIGNS HAVE GREATLY ENHANCED PERFORMANCE

SSPAs - BENEFIT GREATEST FOR CLASS B AND AB 2 X POWER INCREASE IN HIGH LIN APPLICATIONS

TWTAS - 4 X POWER INCREASE AND DOUBLE EFFICIENCY

SUMMARY

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PREDISTORTION:

ADVANTAGES SIMPLICITY, WIDEBAND, VIABLE BOTH LOW AND HIGH LIN. DSP CAN PROVIDE VERY HIGH LIN.

INDIRECT FEEDBACK:

WORKS WELL, BUT LIMITED IN BANDWIDTH.

FEEDFORWARD:

LINEARIZATION IS MOST VALUABLEWHEN VERY HIGH LIN REQUIRED.

SUMMARY

FOR MORE INFORMATION

1. A. Katz, “Linearization: Reducing Distortion in Power Amplifiers,” IEEE Microwave Magazine, pp. 37-49, December 2001.

2. Vuolevi and Rahkonen, “Distortion in RF Power Amplifiers”, Artech House, 2003.

3. S. Cripps, “Advanced Techniques in RF Power Amplifier Design”, Artech House, 2002.

4. A. Katz and R. Gray, “The Linearized Microwave Power Module,” MTT-S International Microwave Symposium Digest, June, 2003.

5. A. Katz, “Performance Of Multi-carrier 16QAM Over a Linearized TWTA Satellite Channel,” AIAA 20th International Communications Satellite Systems Conference Proceedings, Montreal, May 2002.

6. P. Kenington, “Methods Linearize RF Transmitters and Power Amps, Part 1, ”Microwaves & RF Magazine,” pp. 103-116, December 1998, Part 2, pp. 79-89, January 1999.