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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
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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
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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)
Nov. , 2011, Fall , KAIST3
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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
Nov. , 2011, Fall , KAIST4
1dB Compression Results:Input power: 3.7 dBm Output power: 27.633 dBm Gain,1dB : 23.933 dB
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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
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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
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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)
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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
Nov. , 2011, Fall , KAIST9
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
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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
Nov. , 2011, Fall , KAIST10
m Rww
)212(2
og
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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
Nov. , 2011, Fall , KAIST11
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
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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
Nov. , 2011, Fall , KAIST12
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
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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
Nov. , 2011, Fall , KAIST13
t t mCM 2coscos 331 4
3 Ak Ak E
CM 231 43
Ak k
M where
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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(
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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(
Nov. , 2011, Fall , KAIST15
M P )1log(20
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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
Nov. , 2011, Fall , KAIST16EE542 Microwave Engineering, Park, 2012. Fall, KAIST
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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)
Nov. , 2011, Fall , KAIST17EE542 Microwave Engineering, Park, 2012. Fall, KAIST
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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
Nov. , 2011, Fall , KAIST18
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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
Nov. , 2011, Fall , KAIST19
an w t
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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
Nov. , 2011, Fall , KAIST20
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Feedforward Linearization
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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
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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
Nov. , 2011, Fall , KAIST23EE542 Microwave Engineering, Park, 2012. Fall, KAIST
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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
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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
Nov. , 2011, Fall , KAIST25
- Isolator unnecessary
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Experimental results
PA out ut
Nov. , 2011, Fall , KAIST26Linearized PA
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Continued
Power = 44 dBm
Nov. , 2011, Fall , KAIST27IS97 Recommendation
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Pilot tone controller
nc us on o p o one
DownConv
BPF
A/DDownConv
PilotDSPA/DPilotDSP
BPF
Nov. , 2011, Fall , KAIST28
mon or on ro er
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Predistortion Linearizer
Pre-distortorHigh Power AMP
IN OUT
Gain GainGain-
Phase Phase Phase
AM-PM distortion
Nov. , 2011, Fall , KAIST29EE542 Microwave Engineering, Park, 2012. Fall, KAIST