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A New High-Efficiency, Linear Power Amplification Design Technique Derived from

Nonlinear Dynamical Systems

Dr. Chance M. Glenn, Sr.

Associate Professor – Department of Electrical Computer and Telecommunications Engineering Technology

Director – The Laboratory for Wireless Networks and Advanced Communications Technology

Rochester, New York USA

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Overview

•This talk describes the basis and implementation of a new concept in power amplifier design.

•This work represents a collaborative effort between the Laboratory for Wireless Networks and Advanced Communications Technology at RIT, and Syncrodyne Systems Corporation.

•The ongoing research effort has also been supported by DARPA, ARO, and MDA

•The goal is the commercial application of this technology in various forms of wireless telecommunications.

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Syncrodyne Power AmpBlock Diagram

Chaotic Oscillator

DC Power

Adaptive Power Control&

Output Stabilization

Coupling Control

Input x(t) Output y(t)

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Chaotic Dynamics

• The heart of the Syncrodyne Power Amplifier is the chaotic oscillator

• Chaos is a type of behavior that occurs in nonlinear systems.

• While chaos tends to elude specific definition, there are properties that define its behavior:

1. Broad-band frequency spectra2. Sensitivity to small changes3. Tendency towards synchronization4. Capable of efficient operation (nonlinearity)

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Chaotic Dynamics

1 evc ei

whereVe

Vc

R

Re

L

Ce

C

+

Vee

Q

+

Vcc

Circuit diagram:

cLec

e

EEeL

ee

LLcCCL

iidt

dvC

dt

dvC

R

Vvi

dt

dvC

iRRvVdt

diL

• A typical chaotic oscillator is the Colpitts system.

• The Colpitts circuit is a typical circuit topology used in the engineering design of oscillators.

Equations of motion:

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Chaotic Dynamics

State-space plot:

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The term Syncrodyne derives from the concept of amplification using synchronous dynamics. Dynamically matched devices are used which lock to a signal of similar dynamics.

The green (applied) and blue (output) signals in this schematic representation come together (synchronize) and the error (red) goes to zero rapidly when the input is coupled.

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Syncrodyne Amplification

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Adaptive Nature of Synchronization

•We first reported that a chaotic system was adaptable, or conformed to, non-chaotic waveforms.

•That is, a chaotic system, properly coupled, will take on the nature of an arbitrary waveform, depending on some conditions.

•This realization was critical to the implementation of this technique on typical information bearing signal formats like GSM and CDMA.

•We first showed this adaptive conformity using phase modulated sinusoidal waveforms coupled to a Colpitts oscillator operating in the chaotic regime.

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0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.50.0 6.0

-80

-60

-40

-20

0

-100

20

freq, GHz

dB(F

Vin

)

0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.50.0 6.0

-80

-60

-40

-20

0

-100

20

freq, GHz

dB(F

Vo)

0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.50.0 6.0

-100

-80

-60

-40

-20

0

-120

20

freq, GHz

dB

(FV

o)

CouplingSpectral content of the free-runningchaotic oscillator.

Spectral content of the generated GSM signal.

Spectral content of the amplified GSMwaveform using the Syncrodyne Power Amplifier Series-3 prototype simulation.

Syncrodyne AmplificationR I TRochester Institute of Technology

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Syncrodyne Amplification

The extent and effectiveness of Synchronization depends on the factors below: dc bias voltages of the source signal and the chaotic signal (Vsdc and Vcdc)

peak to peak voltage range of the two signals (Vsr and Vcr) fundamental frequencies of the two signals Value of coupling impedance in the coupling circuit

The factors mentioned above need to be properly matched to obtain maximum amplification of the source signal.

Increase in the extent of coupling would increase the gain and the efficiency of the signal produced.

1.284 1.286 1.288 1.290 1.292 1.294 1.296 1.298 1.300 1.302 1.3041.282 1.306

-1

0

1

2

-2

3

time, usec

Vin

, V

1.068 1.070 1.072 1.074 1.076 1.078 1.080 1.082 1.084 1.0861.066 1.088

-1

0

1

2

3

-2

4

time, usec

Vo,

VVsdc VcdcVsr

Vcr

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The power amplifier system comprises of the following components: The dc power source (5 volts dc) – V_DC The chaotic oscillator The coupling network The modulated input source (GSM modulation at 800 MHz) The load impedance

Vin

VoVdc

modulatorX3

Modulated Source

I_ProbeIinSPA-S3-C2-BJ T-CPL

X2

CouplingNetwork

21

SPA-S3-C2-BJ T-OSCX1

sig outsig in

CODC in

2

1

3I_ProbeIdc I_Probe

Io

RRloadR=50 OhmV_DC

SRC1Vdc=5.0 V

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© The Laboratory for Wireless Networks and Advanced Communications Technology

ADS Simulation Diagram

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The circuit has three ports, the functions are as below

Port1 – dc supply (input) Port2 – Amplified signal (output) Port3 – Modulated signal (input)

The other components are varied to obtain the desired output.

Sample values are shown in the figure.

CC4C=C4o pF

CC5C=C5o pFL

L1

R=.707L=L1o nH

CC2C=C2o pF

CC1C=C1o pFR

R1R=R1o Ohm

RR2R=R2o Ohm

CC3C=C3o pF

RR4R=R4o Ohm

RR3R=R3o Ohm

CCLC=0.158 pF

RR5R=0 OhmPort

P3Num=3

PortP2Num=2

PortP1Num=1

pb_nec_NE68130_19921215Q3

P1

P3

P2

VAROscillator

L1o=10C5o=472C4o=156C3o=36C2o=4C1o=7.89R4o=10R3o=15466R2o=290R1o=5400

EqnVar

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ADS Simulation Diagram

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The system SPA-S3-C2-BJT-SYS2 was simulated and the results obtained are as shown below. Other such circuits were simulated and the results are have been tabulated in an excel sheet.

PAE (%) 52.301

Gain (dB) 18.129

Vo_avg (V) 0.654

Vo_range (V) 2.126

Pdc (W) 0.066

Po_rf (W) 0.130

Pin_rf (W) 0.002

Pin_rf_dBm 1.895

Po_rf_dBm 20.040

FVoFund (dB) 4.670

Fdown (dB) 28.143

FVoHarm (dB) -23.473

Lyapunov Exp 1.84370.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.50.0 6.0

-100

-80

-60

-40

-20

0

-120

20

freq, GHz

dB

(FV

o)

Synchronized output signal

0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.50.0 6.0

-80

-60

-40

-20

0

-100

20

freq, GHz

dB(F

Vo)

R I TRochester Institute of Technology

Results

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Conclusions

© The Laboratory for Wireless Networks and Advanced Communications Technology

•We’ve demonstrated Syncrodyne Power Amplification for GSM waveforms with PAE greater than 50% and gain approaching 20-dB

•We are implementing new techniques that should allow us to push the performance levels higher.

•The property of chaotic oscillators to adaptively conform to different waveform types is a key to this concept.

•We are able to achieve linear power amplification utilizing a nonlinear device, thus benefiting from the high efficiency capable in nonlinear operation.

•We intend to explore the benefit of this amplification concept in other technology settings.

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R I TRochester Institute of Technology

The Laboratory for Wireless Networks and Advanced Communications Technology

Goals

•Push the performance to PAE > 70%, gain > 30-dB

•Implement Series-3 design in hardware

•Design a SPA-S3 chip to meet commercial performance criteria

•Develop commercially viable testbed for performance evaluation

•Cultivate strategic partnerships for technology adoption.

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R I TRochester Institute of Technology

The Laboratory for Wireless Networks and Advanced Communications Technology

References

[1] E. Ott, C. Grebogi, J. A. Yorke, Phys. Rev. Lett. 64, 1196 (1990).[2] S. Hayes, C. Grebogi, E. Ott, Phys. Rev. Lett. 70, 3031 (1993).[3] H. Dedieu, M.P. Kennedy, and M. Hasler, “Chaos shift keying; Modulation and demodulation of a chaotic carrier using self-synchronizing Chua’s circuit,” IEEE Transactions on Circuits and Systems I, vol. 40, pp. 634-642, 1993.[4] C. M. Glenn, S. Hayes, Weak Signal Detection by Small-Perturbation Control of Chaotic Orbits, 1996 IEEE-MTT Symposium Digest (June 1996).[5] L. M. Pecora and T. L. Carroll, Synchronization in Chaotic Systems, Phys. Rev. Lett. 64, 821 (1990).[6] C. M. Glenn, Synthesis of a Fully-Integrated Digital Signal Source for Communications from Chaotic Dynamics-based Oscillations, Doctoral Dissertation, The Johns Hopkins University, January 2003.[7] C. M. Glenn, High-Gain, High-Efficiency Power Amplification for PCS, International Symposium on Advanced Radio Technology Digest, March 2003.[8] S. Cicarelli, Development of a Digital Wireless Communication System for Security Sensor Applications, Defense Nuclear Agency (Jan 1998)[9] Francis Moon, Chaotic Vibrations, Wiley & Sons, New York, 1987.[10] Edward Ott, Chaos in Dynamical Systems, Cambridge Univ. Press, Canada, 1993.