Transcript Nonlinear behavior and intermodulation suppression in a

Nonlinear behavior and
intermodulation suppression in a
TWT amplifier
Aarti Singh
University of Wisconsin - Madison
Acknowledgments: J. Wöhlbier, J. Scharer and J. Booske
Outline
 Characterization of Nonlinearity in terms of distortion
products (Identify harmonics and intermods).
 Nonlinear behavior description of a TWT amplifier.
 Why suppress intermods?
 Intermodulation suppression techniques and Experimental
results.
Nonlinear distortions
Nonlinear
system
f
f
2f
3f
Single-tone case: Generation of harmonics
Nonlinear
system
f1 f2
…
f1 f2
2f1 2f2
Multi-tone case: Generation of IMPs (intermodulation products)
Nonlinear distortions (contd..)
Multi-tone case: Generation of IMPs (intermodulation products)
f1
f2
2f1
2f1-f2
2f2-f1
3f1-2f2
3f2-2f1
…
…
3f1-f2
2f2
3f2-f1
…
…
~2f
~f
m+n
Order
f1+f2
relevant freqs
mf1±nf2
Order
relevant freqs
1
f1, f2
2
2f1, 2f2, f1+f2
3
2f2-f1, 2f1-f2 (IM3s)
4
3f2-f1, 3f1-f2
5
3f2-2f1, 3f1-2f2 (IM5s)
TWT amplifier operation
Helix (slow-wave structure)
collector
e- beam
RF output
RF input
Circuit Voltage
Electron bunches
Bunch formation
Exponential gain
Saturation
Nonlinear behavior characterization
Pout
DF
A(r)
DΦ(r)
Pin r
AM-AM curve
Pin r
AM-PM curve
V in t   r cos  c t 
V out t   A r  cos  c t  DF  r 
Nonlinear behavior characterization
r  a cos  m t  ,
 m
A(r)
  c 
DΦ(r)
r
r
V in t   a cos  m t  cos  c t 
V out t   A a cos  m t  cos  c t  DF  a cos  m t 
Odd-order terms
1
Vin(f)
fc-fm
0.9
0.8
Vout(f)
fc+fm
0.7
0.6
0.5
0.4
0.3
0.5
0.4
0.3
0.1
0.1
0.95
1
Frequency (Hz)
1.05
0
1.1
9
x 10
fc+3fm
0.6
0.2
0.9
fc+fm
fc-3fm
0.7
0.2
0
fc-fm
0.9
0.8
Normalized magnitude
Normalized Magnitude
A(r) =
acos(mt)
DF(r) = 0+a2cos2(mt)
1
Even-order terms
fc-5fm
0.9
0.95
fc+5fm
1
Frequency (Hz)
1.05
1.1
9
x 10
Circuit voltage
Nonlinear behavior characterization (contd…)
Axial position
z=L
Beam current
z=0
z=0
Axial position
z=L
Harmonics arise due to non-sinusoidal e- bunching, not only
at saturation but also in the “linear” gain region.
Motivation for Multi-tone analysis
 High data rate communications
Data rate  bandwidth
N simultaneous users - efficient use of available bandwidth.
2
…
N
2
bandwidth
1
bandwidth
1
…
N
time
time
TDMA
FDMA
 Covert communications
Spread Spectrum Techniques (CDMA or pseudo-noise signaling)
Why suppress Intermods ?
~f
~f
~f
~f
Spectral regrowth around the fundamentals leads to:
 In-band distortions
CHANNEL
SPACING
 Adjacent channel interference
CHANNEL A
 Limitation on Power efficiency – need back off
CHANNEL B
CHANNEL C
Why suppress Intermods? (contd…)
Channel BW
Newer modulation schemes aggravate these problems:
 The closer the carrier spacing, the more pronounced is
the effect of the IMPs.
f
OFDM spectra
45
Two tone
2GHz
35
Pout (dBm)
 Saturation occurs earlier with multiple carriers
– more power limitations.
Single tone
2GHz
40
30
25
20
15
10
-7
-2
3
8
13
18
23
Pin (dBm)
 High PAR (Peak to Average Ratio) of modulation schemes like OFDM and
CDMA requires more OBO (Output Back Off).
28
33
Research Objective
 To investigate intermodulation suppression techniques
that achieve:
f
f
1
- maximum suppression for IM3
IM3IM5-
…
2
IM3+
IM5+
…
- reduction of higher (5th, 7th) order intermods
or have no effect on them
- easy implementation
Techniques for IM3 suppression
Input spectra
 Harmonic injection
Output spectra
f1 f2
f1 f2
2f2
 IM3 injection
f1 f2
f1 f2
f1 f2
f1 f2
IM3+
IM3+
IM3-
IM3+
 Two frequency
(harmonic + IM3)
injection
IM3+
IM3-
2f2
IM3-
IM3+
Mechanism of IM3 suppression by injection
Mechanism of IM3 suppression by injection
Impressed and Nonlinear modes have different growth rates and wavelengths.
Mechanism of IM3 suppression by injection
Impressed and Nonlinear modes have different growth rates and wavelengths.
γ
NetIM 3  a
Sum
imp
e
imp
γ
z
a
np
e
np
z
impressed nonlinear product
Normalized voltage
Mechanism of IM3 suppression by injection
Axial distance
Suppression occurs only at the output of the tube.
Experimental Set-up
f1
1.95 GHz
f2
Variable
Attenuator
2.00 GHz
x2 2f2
(4.00GHz)
Phase
shifter
Variable
Attenuator
Solid State
Amplifiers
Semi Rigid
Coax
Isolator
Combiners
TWT
Gated Spectrum Analyzer
Experimental TWT
XWING (eXperimental Wisconsin Northop Grumman) TWT
Broadband (1.5-6 GHz gain bandwidth)
Maximum gain 30dB at ~ 4 GHz
RF sensor array along helix
Harmonic injection
f1 = 1.90 GHz
2f2-f1 = 2(1.95)-1.90 = 2.00 GHz (nonlinear product)
f2 = 1.95 GHz
2f2-f1 = 3.90-1.90 = 2.00 GHz
2f2 = 3.90 GHz
Harmonic Injection (15 dBm/tone)
Harmonic Injection (18dBm/tone)
40
30
30
20
20
Power (dBm)
Power (dBm)
40
D IM3
-29.5 dB
10
0
(impressed product)
D IM3
-32.4 dB
10
0
-10
-10
-20
-20
IM5-
IM3-
f1
f2
IM3+
IM5+
2f1
2f2
IM5-
IM3-
f1
f2
IM3+
IM5+
Spectral frequency
Spectral frequency
without injection
optimum injection
2f1
2f2
Harmonic injection Sensitivity
(18 dBm/tone)
IM3 Power w/o inj
13.53 dBm
IM3 injection
f1 = 1.90 GHz
2f2-f1 = 2(1.95)-1.90 = 2.00 GHz (nonlinear product)
f2 = 1.95 GHz
2f2-f1 = 2.00 GHz
2f2-f1 = 2.00 GHz
(15dBm/tone)
40
40
30
30
20
20
D IM3
-26.6 dB
10
Power (dBm)
Power (dBm)
IM3 Injection
(impressed product)
(18dBm/tone)
D IM3
-30.0 dB
10
0
0
-10
-10
-20
IM3 Injection
-20
IM5-
IM3-
f1
f2
IM3+
IM5+
2f1
2f2
Spectral frequency
IM5-
IM3-
f1
f2
IM3+
IM5+
Spectral frequency
without injection
optimum injection
2f1
2f2
Two Frequency (Harmonic+IM3) injection
Concept:
Voltage Phasor diagram at z=L
IM3 voltage components at output:
Resultant IM3
 Naturally produced IM3
 IM3 due to injected harmonic
 Injected IM3
IM3 due to
injected harmonic
Injected IM3
Naturally produced IM3
Experimental challenge: Keeping phase fixed as amplitude is varied.
Two Frequency (Harmonic+IM3) injection
Two frequency (Harmonic + IM3) injection
(15dB m/ to ne)
40
Power (dBm)
30
20
D IM3
30.7 dB
10
0
-10
-20
-30
IM5- IM3- f1
f2 IM3+ IM5+
Spectral frequency
2f1 2f2
Spatial evolution of IM3 with optimum injection
IM3 Power (dBm)
Spatial evolution (15dBm/tone)
5
0
-5
-10
-15
-20
-25
-30
sensor 1
sensor 4
sensor 5
Two frequency injection
(Harmonic + IM3)
sensor 6
output
Harmonic injection
Summary
 The nonlinear behavior of TWTs gives rise to harmonics and intermods.
 Minimization of these nonlinear products is important for reliable
communications.
 IM3 suppression techniques were investigated that employ injecting an
amplitude and phase adjusted harmonic, IM3 or simultaneous injection
of both with only amplitude adjustment.
 Strong suppression of ~26-32 dB was measured.
 It was observed that harmonic injection may lead to reduction in IM5s
and harmonics too, while IM3 injection may enhance these. The two
amplitude (harmonic+IM3) suppression technique offers possibly better
implementation issues.
 Understanding the theoretical details underlying the nonlinear behavior
is a topic of current research.
Ref - M. Wirth, A. Singh, J. Scharer and J. Booske, "Third-Order Intermodulation
Reduction by Harmonic Injection in a TWT Amplifier", IEEE Trans. on Electron Devices,
pp. 1082-84, vol. 49, No. 6, June 2002.