linear nonlinear amp

7/28/2019 Linear Nonlinear Amp

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Linear and Nonlinear Power Amplifier

EE542 Microwave Engineering Class

The material is from the book, Solid-State Microwave Amplifier Design, Tri T. Ha

Nov. , 2011, Fall , KAIST1EE542 Microwave Engineering,

Park, 2012. Fall, KAIST


2/29

Characterizing Nonlinear Behavior

Power amplifiers require additional measurements tocharacterize nonlinear behavior

power sweeps (using network analyzer)Gain com ression

H ACTIVECHANNEL

RESPONSE

STIMULUS

ENTRY

INSTRUMENTSTATE RCHANNEL

NETWORKANALYZER50MHz-20GHz

AM to PM conversionsingle-tone harmonic

RL

T

S

HP-IBSTATUS

PORT 2PORT 1

secon armon cthird harmonic

multi-tone intermodulationthird-order intercept using two toneshigh-order intermodulation using many carriers

di ital modulationadjacent-channel power

g )

Lower Adjacent Channel

Upper Adjacent Channel

Nov. , 2011, Fall , KAIST2

frequency

p o w e r

( l Carrier Channel

EE542 Microwave Engineering,



3/29

Power Sweep Compression (AM-to-AM Conversion)

Saturatedoutput power

r ( d B m

)

u t P o w Compression

region

O u

t

Linear region(slope = small-signal gain)


EE542 Microwave Engineering,



4/29

Measured Gain Compression

CH1 S 21 log MAG 1 dB/ REF 25 dB

CH2 B log MAG REF 26 dBm5 dBm/

1_: 25.018 dB

-12.6 dBm

1_ -12.418 dBm

1 dB compression :input power resulting in

C2

PRm

1

1

2_: 23.933 dB

1 dB drop in gainratioed measurementoutput power available (non-

2

_ 3.7 Bm

2

use power-meter calibrationfor best accuracy

PRm

2

2_ 27.633 dBm3.7 dBm

1

CH1 START -15.0 dBm STOP 9.0 dBmCW 1.880 000 000 GHz CH2 START -15.0 dBm STOP 9.0 dBmCW 1.880 000 000 GHz


1dB Compression Results:Input power: 3.7 dBm Output power: 27.633 dBm Gain,1dB : 23.933 dB

EE542 Microwave Engineering, Park, 2012. Fall, KAIST


5/29

Single Frequency Input Test (AM-to-AM Conversion)

Single Frequency Input Testingle Frequency Input Test 1( ) cos x t A t

2 2 3 3

2 31 2 3( ) ( ) ( ) ( ) y t k x t k x t k x t

1 1 2 1 3 1

2 31 1 2 1 3 1 1

1 1 3 12 3

2 2 4 4cos ( cos ) ( cos cos )k A t k A t k A t t

2 3 2 32 1 3 1 2 1 3 12 32 4 2 4

( )cos cos cosk A k A k A t k A t k A t

)3

log(2043

log20 231

331

Ak k Ak Ak

GThe gain at the fundamental frequency 1 is given by

11

0 log20log20 k A Ak G

dBGG dB 101 12

31 891.03

k Ak k

As compared to the linear gain G0 defined as

1-dB gain compression point is defined as the signal level where

0,145.0 33

12 k k k

AHence at the 1-dB compression point the amplitude of is limited as

The input and output powers P 1 and P 0 at the fundamental frequency 1 is given in dBm as

dBm A

Pi 32 10

log10 Ak Ak

3

23

31 1043

Nov. , 2011, Fall , KAIST5dBmPG

R

i

02



6/29

Single Frequency Input Test (AM-to-AM Conversion)

The output power at 1dB gain compression point P 1dB is

1 1 0 1dB dB i iP G P G P dBm

dBm Rk

k GP dB

3

3

101

102145.0

log101

dBm Rk

k Rk k

3

3

3

1

3

3

1 1033.17

1log1070.57log10

Nov. , 2011, Fall , KAIST6EE542 Microwave Engineering, Park, 2012. Fall, KAIST


7/29

Example

Consider a two port with the following transfer characteristic (assumingR=50 )

3( ) 15 ( ) 2 ( ) y t x t x t

Linear gain G 0 =23.5dB and 1dB gain compression point is G 1dB =22.5dB. Atthis point the amplitude is limited to

1/ 2

10.145 , 1.044k

A V

Saturatedoutput power

and the output power is

3

e r ( d B m

)

P 1dB =32.89dB

u t p u

t P o Compression

region

O

Linear region= -

Nov. , 2011, Fall , KAIST7EE542 Microwave Engineering,

Park, 2012. Fall, KAISTInput Power (dBm)


8/29


9/29

Nonlinearity of Power Amplifiers

Input(x(t)) output (y(t))

1 2 3

1 2

( ) ( ) ( ) ( )

( ) c o s c o s

y t k x t k x t k x t

x t A t A t

2 2 3

2 2 1 2 1 3 1

3 3 31 3 2 3 1 2 3 2 1

( ) cos( ) ( ) cos( )9

4 3 3( ) cos cos(2 ) cos(2 )

9 4 4

y t k A k A k A k A t

k A k A t k A t k A t

2 2 22 1 2 2 1 2 2cos( ) cos(2 ) cos 22 2

k A t k A t k A t

In-band and out-of-band distortion P y

B f f B N

a N

B N a BN a a a

d R f P y y

)2(4

32

)29

36(

)()(

22302

3022

023031

21

Distortion

gna

B f f B N

a N

B N a BN a a a

d R f P y y

)2(4

32

)29

36(

)()(

22302

3022

023031

21


B f B f B N

a 3)2(4

3 2023 B

f -B

B f B f B N

a 3)2(4

3 2023



10/29

Two Frequency Input Test (AM-to-AM Conversion)2 2 3 3

1 1 2 2 1 2 3 1 2

2 2 32 2 1 2 1 3 1

94

( ) (cos cos ) (cos cos ) (cos cos )

cos( ) ( )cos

y t k A t t k A t t k A t t

k A k A t k A k A t

3 31 3 2 3 1 2

3 2 2

9 32

4 43 1

( )cos cos( )k A k A t k A t

3 2 1 2 1 2 2 1

22

4 212

ck A

3 32 3 1 2 3 2 1

3 32 2 2

4 4os cos( ) cos( )t k A t k A t

3 33 1 3 21 13 34 4

cos cosk A t k A t

At hi her ower levels the res onse of P will be com ressed and will deviate from the res onse of P

dBm Ak

P 32

10

10log10

dBm R

Ak Ak P

w

3

23

31

)1(

10

249

log10

Ak

3

23

3 103


m Rww

)212(2

og



11/29

Harmonics and Conversion Gain Measurement

Harmonics

20Input : 3.4- 4.2 GHzOutput 950 ~ 1750 MHz

)

0

Stability : 25 KHzLO : 5.15 GHzGain : 65 dB

t p o w e r

( d B

-40

-

o u

t p

-80

-601st at 1350 MHz2nd at 2700 MHz3rd at 4050 MHz

Input power (dBm)

-120 -100 -80 -60 -40 -20-100

2 2 32 2 1 2 1 3 1

3 3 31 3 2 3 1 2 3 2 1

4( ) c o s ( ) ( ) c o s ( )

94 3 3

( ) c o s c o s ( 2 ) c o s ( 2 )9 4 4

y t k A k A k A k A t

k A k A t k A t k A t


2 2 22 1 2 2 1 2 2

1 1c o s ( ) c o s ( 2 ) c o s 22 2k A t k A t k A t

Park, 2012. Fall, KAISTEE542 Microwave Engineering,


12/29

Harmonics and Conversion Gain Measurement

SG : -80 ~ -10 dBm SA

RF Input

LNB

RF Input IF Output

RF = 3.8GHz, IF = 1.317 GHz RF = 4.2GHz, IF = 0.903 GHz

Parameter Specification


RF Input Frequency Range 3.7 ~ 4.2 GHz

IF Output Frequency Range 950 ~ 1750 MHz

Local Oscillator Frequency 5150 MHz Park, 2012. Fall, KAIST


13/29

Cross Modulation of PAs

1 21( ) ( cos )cos cosm y t A M t t A t

One modulated and the other initially unmodulated as follows;

1 1 1 2

2 21 22

1

1 1 1 1 1 11 2 2 2 2

( ) ( cos )cos cos

cos cos cos cos

m

m m

y t k A M t t k A t

M t M M t t t

2

1 2 1 2

3 2 3

1

1 1 3 1

cos cos( ) cos( )m M t t t

3 2

2 2 4 4m m

2 21 1

3 1 1 13 3 1 2 2

4 4 2 2( cos cos ) ( cos cos )

m

m mt t M t M M t

1 2 2 1 2 2

1 1 1 1 3 12 3 1 2 3

2 2 2 2 4 4( cos )cos ( cos )( cos )cos cos cos ]mt t M t t t t t

t t M Ak t Ak Ak e mCM

'

23

323

31 cos)cos3(cos)43

(

CM

2' 3 M Ak


t t mCM 2coscos 331 4

3 Ak Ak E

CM 231 43

Ak k

M where



14/29

t t M E

t t M Ak t Ak Ak e

mCM

mCM

2'

2332331

cos)cos1(

cos)cos3(cos)4(

])cos(21

)cos(21

[cos 2'

2'

2 t M t M t E e mmCM CM

2'

231

3

43

Ak k M CM

233k Ak

CM

2

1

233log10log20)(k

Ak CM dBCM

At a lower level signal, CM can be approximated by

The relation between CM(dB) and the intermodulation distortion of the twounmodulated carriers at 1 and 2 with the same amplitude A

dBPPPP

dBPPdBCM

I w I

oww

12)(212)(2

12)(

)1(0

)212(



15/29

The amplitude modulated input signal can be expressed as

0

0

2 2cos cos( ) cos( )

i m

i ii o m o m

ME ME E t t t

The output signal of the system under test with small-signal gain K can becan be expressed as

2 21

( ) cos ( ) cos( )( ) cos( )( )[ cos ( )]cos ( )

i i

i o d o m d o m d

i m d o d

y t KE t t t t t t KE M t t t t

Where t d is the group delay of the system under test, assumed to be constantfrom c - m and c + m

p )/180(


M P )1log(20



16/29

AM-to-PM Conversion

Consider a system whose output phase shift is a function of theinstantaneous input amplitude of an amplitudemodulated signal as follows:

( ) (1 cos )ma t A M t ( ) cos ca t t

)()( 2 t caa

radianst M t M cAa mm )coscos21()(222

t

M t M cA

mPo

m

cos

1),cos21(2

The peak phase error K p is given by

dBreecA M

cMA M

cMAK P /deg2.1369.8

)/180(2)1log(20

)/180(2 222



17/29

Linearization of PAs

Back off re s or on

- Look up table based- Nonlinear component to compensate of PAnonlinearity

w Harmonic feedback Envelope feedback

LINC Cartesian Feedback- IF / Base band feedback)



18/29

Feedforward LPA

Advantage-

more than 30 dB IMD or ACPR- Wideband width

sa van age- Additional amplifier- Power loss in lossy delay line cable

- Low efficienc- Complexity- Hi h Cos




19/29

Linear Power Amplifier Issue

Linearity- Not a problem in Feedforward scheme=> Adaptive control with compact, low cost

- Marginal in only Predistortion scheme=> More study is needed for linearization algorithm=> Adaptive control

Adaptive control- Different component, Current setting- Environment variation (Temperature)

- Aging effects (slow response)- Mechanical impacts- No manual tuning => Low cost


an w t



20/29

Linearization technique

PhasePout

Operationat small out ut ower

AttenuatorPhase shifter

Pin

Amp

2f 0

In OutCombiner

out ut sam lin

Back off -low efficiency

Second HarmonicFeedback

Amp

GainControl

In Out

Phase shifter

PhOP

Ampdetector

Power divider Phasedetector

Envelop feedback


-



21/29

Feedforward Linearization



22/29

Designs of LPA

Amplifiers- near y , , c ency, a y, a nflatness

,

- Flatness, LinearityOne chi solution

Coupler,Delay Line,Power Divider (Combiner )

- Loss , Flatness,directivitMetal Cavity delay module

Housing

Nov. , 2011, Fall , KAIST22- Thermal dissipation, RF signal Isolation



23/29

RF Power and Gain Budgeting

Main Amp

Gain : 38+24 dB

Delay line

Output20dB

46 dBm avg / 23 dBc

44 dBm avg / 60dBc

3dBInput~ -12 dBm avg ~ 16 dBm / 60 dBc

10dB

~ 33 dBm av / 30 dBc

VM2

Error Amp50 + 20dB

Signal Amp ~ -10 dBm distortion only



24/29

Stability of LPA

L I DC GT lineVM comb MainAmp 1211

- Bias circuits optimization- cou ler ldirectionao Directivit : D

Amplifier of Gain:G

L DC DGT lineVM ErrorAmp

13212

Loop oscillation- Hi h ain of Am lifiers

Loss: L

coupler ldirectionaof Coupling:C

- Need of High directivityin directional coupler

- Inclusion of Isolato- Ground leak

3



25/29

High directivity directional coupler

V1(In)

V3(Coupled )

V2(Through)

V4(Isolated)

-20

Coupling (S31) )

-50

-40

-

Directivity

n i t u

d e ( d

Even-odd modecompensation

-70

-60

Isolation (S41)

M a

3

110PP

logCoupling

. . . . . . .

Frequency (GHz) 4310

Plog y Directivit


- Isolator unnecessary



26/29

Experimental results

PA out ut

Nov. , 2011, Fall , KAIST26Linearized PA



27/29

Continued

Power = 44 dBm

Nov. , 2011, Fall , KAIST27IS97 Recommendation



28/29

Pilot tone controller

nc us on o p o one

DownConv

BPF

A/DDownConv

PilotDSPA/DPilotDSP

BPF


mon or on ro er



29/29

Predistortion Linearizer

Pre-distortorHigh Power AMP

IN OUT

Gain GainGain-

Phase Phase Phase

AM-PM distortion


linear nonlinear amp

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