Nonlinear behavior and Nonlinear behavior and intermodulationintermodulation suppression suppression
in a TWT amplifierin a TWT amplifier
Aarti SinghAarti Singh
University of Wisconsin - MadisonUniversity of Wisconsin - Madison
Acknowledgments: J. Wöhlbier, J. Scharer and J. BooskeAcknowledgments: J. Wöhlbier, J. Scharer and J. Booske
OutlineOutline
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.
f f 2f 3f
Nonlinear distortionsNonlinear distortions
Single-tone case: Generation of harmonics
Nonlinear system
f1 f2 f1 f2
…
2f22f1
Nonlinear system
Multi-tone case: Generation of IMPs (intermodulation products)
Nonlinear distortions Nonlinear distortions (contd..)(contd..)
Multi-tone case: Generation of IMPs (intermodulation products)
Order relevant freqs Order relevant freqs
1 f1, f2
3 2f2-f1, 2f1-f2 (IM3s)
5 3f2-2f1, 3f1-2f2 (IM5s)
2 2f1, 2f2, f1+f2
4 3f2-f1, 3f1-f2
f1 f2
2f2-f12f1-f2
3f2-2f13f1-2f2
f1+f2
2f1 2f2
3f2-f13f1-f2
m+n mf1±nf2
~f ~2f
…………
TWT amplifier operationTWT amplifier operation
Bunch formation Exponential gain Saturation
collectorHelix (slow-wave structure)
RF input RF output
e- beam
Electron bunches
Circuit Voltage
Nonlinear behavior characterizationNonlinear behavior characterization
AM-AM curve AM-PM curve
Pout
Pin Pin
( ) ( )trtV cin ωcos=
( ) ( ) ( )[ ]rtrAtV cout ΔΦ+= ωcos
A(r)
r
Φ(r)
r
Nonlinear behavior characterizationNonlinear behavior characterization( ) , cos tar mω= ( )cm ωω <<
( ) ( ) ( ) coscos ttatV cmin ωω=
A(r)
rr
Φ(r)
( ) ( )( ) ( )( )[ ]tattaAtV mcmout ωωω coscoscos ΔΦ+=
Odd-order terms
Even-order terms
0.9 0.95 1 1.05 1.1
x 109
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Frequency (Hz)
Normalized Magnitude
0.9 0.95 1 1.05 1.1
x 109
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Frequency (Hz)
Normalized magnitude
Vin(f) Vout(f)fc-fm fc+fmfc+fmfc-fm
fc-3fm fc+3fm
fc-5fm fc+5fm
A(r) = acos(mt)
(r) = 0+a2cos2(mt)
Nonlinear behavior characterization Nonlinear behavior characterization (contd…)(contd…)
Harmonics arise due to non-sinusoidal e- bunching, not only at saturation but also in the “linear” gain region.
Cir
cuit
volt
ag
e
z=0 z=LAxial position
Axial position z=Lz=0
Beam
cu
rrent
Motivation for Multi-tone analysisMotivation for Multi-tone analysis
High data rate communications
Data rate bandwidthN simultaneous users - efficient use of available bandwidth.
Covert communications
Spread Spectrum Techniques (CDMA or pseudo-noise signaling)
TDMA
time
bandw
idth
1 2 … N
FDMA
time
bandw
idth
1 2
… N
Why suppress Intermods ?Why suppress Intermods ?
CHANNEL A CHANNEL B CHANNEL C
CHANNEL SPACING
Spectral regrowth around the fundamentals leads to:
In-band distortions
Adjacent channel interference
Limitation on Power efficiency – need back off
~f ~f~f ~f
10
15
20
25
30
35
40
45
-7 -2 3 8 13 18 23 28 33
Pin (dBm)
Pout (dBm)
Why suppress Intermods? (contd…)Why suppress Intermods? (contd…)
Newer modulation schemes aggravate these problems:
The closer the carrier spacing, the more pronounced is the effect of the IMPs.
Saturation occurs earlier with multiple carriers – more power limitations.
High PAR (Peak to Average Ratio) of modulation schemes like OFDM and CDMA requires more OBO (Output Back Off).
Single tone 2GHz
Two tone 2GHz
OFDM spectra
Channel BWChannel BW
f
Research ObjectiveResearch Objective
To investigate intermodulation suppression techniques that achieve:
- maximum suppression for IM3
- reduction of higher (5th, 7th) order intermods or have no effect on them
- easy implementation
f1 f2
IM3+IM3-
IM5+IM5-……
Techniques for IM3 suppressionTechniques for IM3 suppression
IM3 injection
Two frequency (harmonic + IM3) injection
Harmonic injection
Input spectra Output spectra
f1 f2
2f2
IM3+
f1 f2
IM3-
f1 f2
IM3+
f1 f2
2f2IM3+
IM3+
f1 f2
IM3-
IM3+
f1 f2
IM3-
Mechanism of IM3 suppression by Mechanism of IM3 suppression by injectioninjection
Mechanism of IM3 suppression by Mechanism of IM3 suppression by injectioninjection
Impressed and Nonlinear modes have different growth rates and wavelengths.
Mechanism of IM3 suppression by Mechanism of IM3 suppression by injectioninjection
Impressed and Nonlinear modes have different growth rates and wavelengths. z
npãe
npa
zimpãe
impaNetIM +=3
impressednonlinear product
Sum
Mechanism of IM3 suppression by Mechanism of IM3 suppression by injectioninjection
No
rmal
ized
vo
ltag
e
Axial distance
Suppression occurs only at the output of the Suppression occurs only at the output of the tube.tube.
Experimental Set-upExperimental Set-up
x2
f1 1.95 GHz f2 2.00 GHz
2f2 (4.00GHz)
Solid StateAmplifiers
Combiners
Semi RigidCoax
Phase shifter
Variable Attenuator
Isolator
TWT
Gated Spectrum AnalyzerVariable Attenuator
Experimental TWTExperimental TWT
XWING (eXperimental Wisconsin Northop Grumman) TWTXWING (eXperimental Wisconsin Northop Grumman) TWT
Broadband (1.5-6 GHz gain bandwidth)
Maximum gain 30dB at ~ 4 GHz
RF sensor array along helix
Harmonic injectionHarmonic injection
IM3 -29.5 dB
IM3-32.4 dB
without injection optimum injection
f1 = 1.90 GHz
f2 = 1.95 GHz
2f2 = 3.90 GHz
2f2-f1 = 2(1.95)-1.90 = 2.00 GHz (nonlinear product)
2f2-f1 = 3.90-1.90 = 2.00 GHz (impressed product)
Harmonic injection SensitivityHarmonic injection Sensitivity
(18 dBm/tone)(18 dBm/tone)
Relative Injected Harmonic Phase
(degrees)
Relative Injected Harmonic Amplitude (dBm)
IM3 Power w/o inj13.53 dBm
IM3 injectionIM3 injection
IM3-26.6 dB
IM3-30.0 dB
without injection optimum injection
f1 = 1.90 GHz
f2 = 1.95 GHz
2f2-f1 = 2.00 GHz
2f2-f1 = 2(1.95)-1.90 = 2.00 GHz (nonlinear product)
2f2-f1 = 2.00 GHz (impressed product)
Two Frequency (Harmonic+IM3) Two Frequency (Harmonic+IM3) injectioninjection
Concept:
Naturally produced IM3
Injected IM3IM3 due to injected harmonic
Resultant IM3
Experimental challenge: Keeping phase fixed as amplitude is varied.
Voltage Phasor diagram at z=L
IM3 voltage components at output:
Naturally produced IM3
IM3 due to injected harmonic
Injected IM3
Two Frequency (Harmonic+IM3) Two Frequency (Harmonic+IM3) injectioninjection
IM330.7 dB
Spatial evolution of IM3 with optimum Spatial evolution of IM3 with optimum injectioninjection
Spatial evolution (15dBm/tone)
-30
-25
-20
-15
-10
-5
0
5
sensor 1 sensor 4 sensor 5 sensor 6 output
IM3 Power (dBm)
Two frequency injection Harmonic injection(Harmonic + IM3)
SummarySummary
The nonlinear behavior of TWTs gives rise to harmonics and intermods.
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.
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.