FeedForward Linearization of L-Band Power Amplifier

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LINEARIZATION OF AN L-BAND POWER AMPLIFIER
BY Maj. Eng. Ahmad Seleem Mahmoud
Under Supervision of
Maj. Gen. Assoc. Prof. Alauddeen Hussein Assisi
Military Technical College Brig. Gen.
Assoc. Prof. Khairy Abd Elnabi El-Barbary
Military Technical College Col. Dr. Mustafa
Mohamed Ibrahim
Military Technical College
3
Outlines

• Introduction
• Background
• Analysis, Simulation and Measurement of RF
  Amplifier Nonlinearity
• Simulation, Design and Implementation of FF
  Linearization
• Conclusions and Suggestions for Future Work

• Mathematical Analysis of a Fifth Degree
  Nonlinear Amplifier Model
• Gain Capture as a Measure of Amplifier
  Nonlinearity
• Approaches to Extract the Nonlinear Amplifier
  Model
• Nonlinearity Case Studies

• Linearization Techniques
• Selection of a Suitable Linearization Technique
• Linearization Case Studies

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• INTRODUCTION

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Motivation

• RF and microwave PA are used in a wide variety of
  applications

• Jamming
• Radar
• Imaging
• Missile Guidance

• Amplifiers are nonlinear to some degree
• Nonlinearities cause imperfect reproduction of
  the amplified signal
• Desensitization (Gain Capture) important effect
  that degrades the overall system performance
  (wide band signal repeaters / EW systems)

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• The need for linearity is one of the principal
  targets in the design of modern amplifiers
• Back-Off technique is a traditional way
• Limitation Reduces the efficiency
  waste of energy
• (Unattractive linearization method )
• Another choice is to use external linearization
  circuit

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Objectives

• To investigate the nonlinear behavior of
  amplifiers using common measures of nonlinearity
  Focusing on the gain capture phenomena
• Design and implementation of Feedforward
  linearization circuit
• To Evaluate the performance of amplifiers with
  and without the linearization circuit.

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Outlines

• Introduction
• Background
• Analysis, Simulation and Measurement of RF
  Amplifier Nonlinearity
• Simulation, Design and Implementation of FF
  Linearization
• Conclusion and Suggestions for Future Work

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• BACKGROUND

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Linearity Vs Efficiency

•  linear    linearis which
  means Created by Lines
• A system is considered a linear system
• if the output is linearly proportional
• to the input

• Efficiency

Drain Efficiency Power-Added Efficiency (PAE)

• Efficiency and linearity are opposite
  requirements in amplifiers design

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Nonlinear Distortion in Power Amplifiers

• Harmonic Distortion

Fundamental signal
2nd Harmonic
3rd Harmonic
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• Inter-modulation Distortion IMD

Fundamental signal
IMD 3
IMD 5
Mixing frequency
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Gain Capture (Desensitization)

• Gain Compression

• Phase Distortion

The small signal gain degradation due to the
presence of large signal on a close frequency at
the PA input
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Common Measures of Nonlinearity

• 1 dB Compression Point (P1dB)
• Third Order Intercept Point (PIP3)

PIP3 P1dB 9.6 dB

• Adjacent Channel Power Ratio
• Spur Free Dynamic Range
• Output Intermodulation to Signal Ratio (IMSR)

SFDR 2/3 (PIP3 - MDS)
IMSR dBc 2 (Pout dBm IP3 dBm )
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Outlines

• Introduction
• Background
• Analysis, Simulation and Measurement of RF
  Amplifier Nonlinearity
• Simulation, Design and Implementation of FF
  Linearization
• Conclusions and Suggestions for Future Work

16

• ANALYSIS, SIMULATION AND MEASUREMENT
• OF AMPLIFIER NONLINEARITY

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Mathematical Analysis of a Fifth Degree Nonlinear
Amplifier Model
1. Single Tone Input-output Characteristics
Amplifier
(1)
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2. Two-Tone Input-output Characteristics
Amplifier

• In Case of equal signals

(2)
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• The voltage gain for each of the two equal input
  signals is

(3)
G1 G2

• In case of Gain Capture ( A1 ltlt A2 )

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• And the two gains become
• The gain of the amplifier is not equally
  distributed on the two signals
• G2 seems smaller than G1, but usually a3 and /or
  a5 are negative.
• G1 is really smaller than G2
• We now understand how the PA gain is captured by
  the strong signal

(4)
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Gain Capture as a Measure of Amplifier
Nonlinearity

• The degradation of small signal gain due to the
  presence of large signal is used to propose a
  measure of PA nonlinearity called
• Gain Capture Point PGC The minimum total
  input power level at which the gain difference
  between two unequal input signals reaches 6 dB

PGC Linearity
A more linear amplifier has a higher PGC
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• we are going to analyze the measured input-output
  characteristics of an amplifier to extract the
  coefficients of a fifth degree polynomial
  representing its nonlinear behavior to predict
  different nonlinear phenomena
• The IMD of the amplifier is analyzed to extract a
  set of 5th degree polynomial coefficients that
  can be used to predict the I/O characteristics of
  the same amplifier.
• The developed set of coefficients represent the
  measured characteristics at each input power
  independently. This gives a model that follows
  the amplifier characteristic point by point.

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Extracting Odd Terms Coefficients

• Extracting Odd Coefficients From Single
  Sinusoidal Input Measurement
• The input signal power is given by
• P ( v )2 / Rc
• 
  P ( Am )2 / 2Rc
  (5)
• where Rc is the system characteristic impedance.
  For a 50 Ohm RF system
• P w ( Am ) 2 / 100 w
• 
  Am 10 ( Pw ) 1/2
  (6)
• Since P dBm 10 log ( Pw ) 30
• Then P w 10 ( Pi dBm 30) / 10 10 ( P
  dBm / 10 3) (7)
• and Am 10 ( Pw ) 1/2 10
  (Pi dBm / 20 ½ )
  (8)

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If we measure the input-output characteristics we
get the power of each output harmonic Pok at a
certain input signal power Pi
Vo
The 5th harmonic output amplitude is
(9)
and
(10)
Equating the measured and calculated values of Ao5
(11)
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Similarly, we can estimate the third harmonic
output power as
(12)
(13)
The fundamental output amplitude is
(14)
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Extracting Odd Coefficients from a Two-Tone input
measurement
When a two-tone sinusoidal signal is input the
5th order terms of the output spectrum will be
(15)

• The amplitude of the (3?2-2?1) term is

(16)
(17)
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The amplitude of the 3th term (2?2- ?1 ) is
(18)
(19)
The amplitude of the fundamental output tone is
(20)
(21)
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First Case Study Mini-circuits ZHL- 42 PA

• Broadband amplifier
• Frequency 700 MHz to 4.2 GHz
• Output power 1 watt
• Gain 30 1dB

• Input Output Characteristics (L -Band)

1-dB compression point of the PA at 1.5 GHz 28
dBm
The Gain compression chst.
P1dB
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From the I/O characteristics, the coefficients of
the nonlinear model of the ZHL-42 PA are
extracted
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• Two-Tone Intermodulation Characteristics

Using 2-tone Harmonic balance with a test signal
of frequency spacing of 1 MHz

1. Two-Equal Input Tones

As the level of the input equal two-tone signal
increases the levels of the fundamental output
and the generated IMD products increase equally
IMSR
1 GHz 1.5 GHz 2 GHz
Input Signal (dBm) each tone 2 2 2
Fundamental Output (dBm) 26.9 26.8 26.7
IM3 (dBm) 14.9 14.6 14.2
IMSR (dBc) 12 12.2 12.5
The PA gain is divided equally between the two
tones
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Substituting with the extracted coefficients
values at each of the different input power
levels in the PA output formula to characterize
its IMD
Third order intercept point
Comparison between the measured and the modeled
IMD characteristics of the ZHL-42 PA
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2. Two Unequal Input Tones
Level of the lower frequency tone (m11) is kept
constant at (-30 dBm) while the level of the
higher frequency tone (m10) is increased from -30
to 10 dBm.

• Levels of Fundamental output tones and generated
  IMD are not equally increased
• The PA gain is unequally divided between the two
  input tones

-30, 5 dBm
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3. PA Gain Capture

• Simulation ensures that the lower frequency tone
  gain G1 decreases as the level of the higher
  frequency tone m10 increases

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• Gain capture point PGC of the ZHL-42 PA

The gain difference between the two signals
increase rapidly from 0 dB at initial input and
reaches 6 dB at total input power of
PGC ( 1 GHz ) 9.2 dBm PGC (1.5 GHz) 9.66
dBm
due to the gain variation with frequency of
operation.
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Second Case Study Three-stages VHF 1W PA
First and Third stage HELA-10D, 8-300 MHz band
of operation, typical gain of 11 dB, 1 W maximum
output power Second stage ERA-5, DC-4 GHz band
of operation, typical gain of 20.2 dB at 100 MHz,
18.4 dBm output power at P1-dB

• Input Output Characteristics

P1-dB at 100 MHz 25.5 dBm
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• Harmonic Distortion

From the I/O characteristics, the coefficients of
the nonlinear model of the VHF PA have been
extracted
Harmonic distortion at input power level of 3 dBm
I/O characteristics
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a1
a3
a5
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• Two-Tone Intermodulation Characteristics

Using the setup and a two-tone test signal with
frequency spacing of 1 MHz

1. Two-Equal Input Tones

100 MHz 200 MHz 300 MHz
Fundamental Output 26.9 25.5 25.5
IM3 (dBm) 15.5 14.2 13.3
IM5 (dBm) 9.2 8.3 7.3
IMSR (dBc) 11.4 11.3 12.2
Output spectrum at input power level 0 dBm
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The modeled two-tone I/O characteristics of the
PA are compared with the measured characteristics
Third order intercept point
PIP3 33.3 dBm
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2. Two Unequal Input Tones
Two-tone I/O spectra of the PA
f1 constant at (-20 dBm) f2 sweep level
from -20 to 0 dBm.

• Levels of the fundamental output tones and the
  generated IMD products are not equally increased.
  
• The PA gain is unequally divided between the two
  input tones

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3. PA Gain Capture
we can compute the two tone gains G1 and G2 in
(dB) at each simulation step
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• we can determine the gain capture point PGC of
  the VHF PA

Gain difference reaches 6 dB at total input power
of
PGC ( 100 MHz ) 0 dBm PGC (300 MHz) -0.5 dBm
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Third Case Study ERA-5 Two Stage RF Amplifier
wideband (DC to 4 GHz)
Nonlinearity is investigated in the UHF band at
350 MHz

• Input Output Characteristics

1-dB compression point P 1dB (350 MHz) 16 dBm
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• Harmonic Distortion

The test signal Un-modulated carrier CF 350
MHz Level sweeping from -60 to -8 dBm
Harmonic distortion at input power level of -8 dBm
I/O Characteristics
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• Two-Tone Intermodulation Characteristics

CF 350 MHz and frequency spacing of 1 MHz
350 MHz
Fundamental Output 15.67
IM3 (dBm) 4.77
IM5 (dBm) -2.11
IMSR (dBc) 10.9

1. Two-Equal Input Tones

PA i/o spectra at 350 MHz. at input tones power
level of -10, -10 dBm
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Third order intercept point
Two-tone I/O characteristics at 350 MHz
IM3 level at an input level of -40 dBm (each
tone) is -58 dBc and increases as the input
signal level increases until it reaches -10.9 dBc
when the amplifier is excited with the maximum
input signal specified for no damage (-7 dBm
total input power)
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2. Two Unequal Input Tones
Gain Capture of the at 350 MHz
weak signal gain decreases from the linear gain
of 39 dB as the level of the strong signal
increases, until it reaches 20 dB at total input
power of -7 dBm
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• The gain capture point PGC of the ERA 5
  amplifier

Gain difference reaches 6 dB at total input power
of
PGC ( 350 MHz ) -7 dBm
PGC
Gain difference between weak and strong signals
of the ERA 5 amplifier at 350 MHz
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Outlines

• Introduction
• Background
• Analysis, Simulation and Measurement of RF
  Amplifier Nonlinearity
• Simulation, Design and Implementation of FF
  Linearization
• Conclusions and Suggestions for Future Work

50

• Simulation, Design And Implementation Of
  Feedforward Linearization

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Linearization Techniques

• Since the reason of problems is amplifier
  nonlinearity
• The solution is to linearize the amplifier
  characteristics using external circuit.
• Several linearization techniques exist
  Linearization techniques can be roughly
  classified into three groups

• Feedback techniques
• Predistortion techniques
• Feedforward techniques

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• Feedback Techniques (FB)
• Simplest technique
• Invented by Harold S. Black1 in 1927
• A portion of the RF output signal is fed back to
  and subtracted from the input

• Classification

1 Harold Stephan Black (1898 - 1983)
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Predistortion (PD) Techniques

• PD simply involves the creation of a distortion
  characteristic (FA) that is opposite to the
  distortion characteristic of the PA

• Classification

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Feedforward Technique

• One of the most effective and popular techniques
  for improving the linearity of power amplifiers,
  due to its potential for excellent distortion
  suppression

• Applications

• Very wide bandwidth systems
• Multi-carrier applications
• Base station applications

• Circuit Configuration

• Signal Cancellation Loop
• Error Cancellation Loop

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Comparison Between Linearization Techniques
Feedback Feedforward Predistortion
Bandwidth Narrow Wide Wide
Efficiency Low medium High
Complexity Low High Intermediate
Stability There are stability problems Unconditionally stable Can overcome stability problems
Cost Low High Intermediate

• Unfortunately, Predistortion need a priori
  knowledge of the input signal and can not be used
  in application such as EW receivers, or jammers
• we select the classical feed-forward
  linearization

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Principle of Operation of Feedforward
Linearization
Reference branch

• Sample of the PA output is compared with the
  reference signal producing error signal
  proportional power amplifier nonlinearities.
• Error signal is amplified by the highly linear
  auxiliary amplifier and subtracted from the main
  PA output
• The result is an distortion free amplified signal
  at the linearizer output.

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General Advantages and Limitations
Limitations
Advantages

• The matching between the circuit elements in both
  amplitude and phase must be maintained to a very
  high degree over the correction bandwidth of
  interest.
• Circuit complexity is generally greater than that
  of a feedback and PD systems. This usually
  results in greater size and cost.
• Low overall efficiency. (May be only 10-15 for
  typical multi-carrier signals)
• The BW of the combiners and the phase shifters
  limits the cancellation BW

• It can be used with wide BW, typically 10-100
  MHz, and hence is Commonly used with wide band
  multi-carrier base-station amplifiers
• Correction is independent of the magnitude of the
  amplifier delays within the system.
• Correction is not based on past events.
• unconditionally stable.
• Low overall system noise figure

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First Case Study Linearization of the LBand
(ZHL-42) PA
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Simulated output spectrum for equal two-tone
input of 2 dBm each at CF 1 GHz.
PA Output
Linearizer Output
The linearization circuit is capable of
decreasing the level of
IMD3 by at least 54 dB IMD5 by at least 53 dB
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Simulations show that a gain reduction of 2.2 dB
occurs at the output of the linearization circuit
2 dB Reduction in gain due to linearization
circuit components losses
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Raising of the IP3 level from 38.75 dBm to 62.5
dBm
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Correction of the Gain Capture Problem
dBm Small Signal Small Signal Large signal Large signal
dBm Level Gain Level Gain
Input Signal dBm -30 - 9 -
PA output -13.8 16.2 31.1 22.1
linearizer output -11.3 18.7 27.7 18.7
both small and large signals have equal gains
linearization system is capable of completely
correcting the gain capture effect for a certain
total input power when the attenuators are set to
cancel the two-equal tone IMD for the same total
input power
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Second Case Study Linearization of ERA-5
Amplifier
The SCL board implemented on 8 x 5 cm FR4 board
The ECL board implemented on 7.5 x 12 cm FR4
board
Amplifier
Output
Input
JSPHS-42 phase shifter implemented on a 4.5 x 4
cm board
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Schematic Diagram of SCL Board
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Phase Shifter
Attenuator
Error Amp
Schematic Diagram of The ECL board
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PA Output
Input two tone signal of level of -11 dBm.
The linearization circuit is able to decrease the
levels of the generated IMD3 by 31.6 dB
IMD5 by 10.5 dB
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Stand alone amplifier Linearized amplifier Effect
Pi dBm -11 -11 -
PodBm 15.6 13 2.6 dB Loss
IMSR dBc - 11 - 40 29 dB Enhancement
IP3 dBm 25.8 37.8 12 dB increase
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Effect of Amplitude and Phase Unbalance on
Cancellation Performance of the Linearization
Circuit
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Correction of the Gain Capture Problem
Linearizer is capable of dividing the amplifier
gain equally between the two signals
Maximum of 0.4 dB difference in gain Can be
eliminated by using high accuracy digital
controls instead of analog controls
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• Conclusions And Suggestions For Future Work

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Conclusions
Conclusion

• Amplifying simultaneous signals with the same
  gain is an essential requirement in repeater
  systems
• The gain capture point PGC is proposed as a
  measure of amplifiers nonlinearity. The higher
  the PGC the more linear the amplifier.
• Amplifier nonlinearity problems can be treated
  independent of the carrier frequency and signal
  power
• Complex Feedforward is the most suitable
  linearization technique for communication
  repeaters and repeater jammer applications

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Conclusion

• Careful control over the phase and amplitude
  balance of the FF circuit must be maintained to
  obtain a high cancellation performance
• The attenuation and phase settings used in the
  equal two-tone case for a certain total input
  power can completely correct the gain capture
  effect for the same total input power
• Simulation results show that FF circuit was
  capable of decreasing the level of the IM3 by 52
  dB and increasing the PIP3 by 24 dB for the price
  of 2 dB gain loss
• A prototype FF linearization circuit was able to
  decrease the level of the IM3 by 31 dB ,
  increasing the PIP3 by 12 dB for the price of 2.6
  dB gain loss
• FF linearization technique is capable of
  correcting the gain capture problem

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Suggestions for Future Work

• Simultaneous enhancement of efficiency and
  linearity
• Appropriate use of DSP to adapt the FF circuit
  parameters (amplitude and phase balance)

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Thank you Any Questions