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.