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

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)

Pin 2.5 dB/DIVPin 2.5 dB/DIV

TWTA PHASE

TWT POUT

PHASE 5.0 deg/DIVPHASE 5.0 deg/DIV

PHASEPHASE

OUTOUT

Ac cos(wct + M cos[wmt]) = Ac SJn(M) cos([wc+nwm]t)n= 8n= - 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

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.

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

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 CANT LINEARIZE AN AMPLIFIERTHAT IS ALREADY LINEAR!

FIRST RULE:

IDEAL AMPLIFIER CHARACTERISTIC

f

Pout

inP

WANT CONSTANT GAIN AND PHASE

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

SinSin Sout Sout 11 Sout Sout 22

MAIN AMPMAIN AMP

AUX AMPAUX AMP ScorScor

IMDIMD

MINIMUM FEEDFORWARD OPBO FOR IMD CANCELATION (20 dB)

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

DEPENDS ON: 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

K2 3 dBK2 10 dBK2 6dB

Min

. OP

BO

for

IMD

Can

cella

tio

n in

dB

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/(4DtS)-CAN BE POLAR OR CARTESIAN

AMP

+

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

LINEARIZER GAIN DEPENDS ON INPUT TO HPA

THE GAIN OF THE LINEARIZER (GL) MUST INCREASE BY THE SAME AMOUNT THE HPAs GAIN (GA) DECREASES.

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

FFL(PoutL) - FFLss = - [FFA(PinA) - FFAss] PoutL = PinA

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

FFL(PinL) = FFLss+ FFAss - FFA(PinL + GL(PinL))

FFL 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

PH

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

I

N

dB

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

dG/dP => as Pin => Sat

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)

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

DIGITAL PREDISTORTION

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

BW

0 3 w0 6w 0

A/DSIGNAL

IINNTTEERRPPOOLLAATTEE

IIII~~

cos 3cos 3w 00 tt(1, 0, -1, 0)(1, 0, -1, 0)

QQ~~

sin 3sin 3w 00 tt(1, 0, -1, 0)(1, 0, -1, 0)

CCAALLCCUULLAATTEE

cos 3cos 3w 00 tt

sin 3sin 3w 00 ttIY+QXIY+QX

D/AD/A FILFIL

IX-QYIX-QY

smoothing

HPAHPA

w 11 +3+3w 00

~~ w 11

RR

X (R)X (R)LUTLUT

Y (R)Y (R)LUTLUT

QQ

COMPUTECOMPUTE

UPDATEDUPDATED

VALUESVALUES

FORFOR

X(R), Y(R)X(R), Y(R)

UPDATEUPDATEX(R), Y(R)X(R), Y(R)

R'R'

IINNTTEERRPPOOLLAATTEE

A/DA/D

II~~

QQ~~

cos 3cos 3w 00 tt

sin 3sin 3w 00 tt

LUT = Look Up TableLUT = Look Up Table

T= sampling periodT= sampling period

3w3w 00 (4 (4DDT) = 2T) = 2pp3f3f00 (4 (4DD T) = 1T) = 1

fs = 1/fs = 1/DD TT

fs = 12 ffs = 12 f00 = 6BW = 6BW

SPECTRUM

DIGITAL ADAPTIVE PREDISTORTION

ADAPTIVE SYSTEMS CORRECT AT

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

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 WHATS IMPORTANT!

OFTEN RESULTS PRESENTED FOR C/I3 ONLY

77 7733 33

55thth 55thth

thth ththrdrd rdrd

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/ 3 2 + 5 2 + 7 2 + ...SS

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

START -10.0 dBm CW 1.9500 GHz STOP 15.0 dBm

SAT

AMPL/AMP

GAIN

PHASE

AMPSAT

AMP

L/AMP

L/AMP

Gai

nG

hang

e0

.5 d

B/D

IVR

elat

ive

Pow

er O

utpu

t 0.

5 dB

/DIV

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

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

L/SSPA

SSPAC/I

IN d

B

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.

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

35

C/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

0OP

BO

R

EU

CT

IO

N

IN

d

B

C/I IN dB

7

OPBO IMPROVEMENT

22--TONETONE

44--TONETONENPRNPR

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

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 dB

OUTPUT POWER BACKOFF IN dB

4 dB

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

NPR OF CLASS AB SSPA

10

15

20

25

30

35

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

NP

R

in

dB

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

> 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

Ca

rr

i er

t o

N

oi s

e

Ra

t io

OPBO IN dB

15dB

LTWTA

TWTA

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

TWO KINDS OF BANDWIDTH

1) STATIC BANDWIDTH - ABILITY OF LIN MAG/PHASE TRANSFER RESP TOEQUALIZE 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

(d

B)

C/I3 UPPER

C/I3 LOWER

C/I5 UPPER

MAJOR CAUSE OF DEGRADATION --

ENVELOPE FREQUENCY Fe = FDD/2

TRANSFER CHARACTERISTICS CHANGE WITH Fe

INABILITY OF AMPLIFIERS TO FOLLOW RAPIDLY CHANGING ENVELOPE

MEMORY EFFECTSMEMORY EFFECTS

Memory Effects are changes in a Power Amplifiers (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.

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

40

35

30

25

20

15

10

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

C/I

IN

dB

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

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.