1

Delayed Feedback and GHz-Scale Chaos on the

Driven Diode-Terminated Transmission Line

Steven M. Anlage, Vassili Demergis, Renato Moraes, Edward Ott, Thomas Antonsen

Thanks to Alexander Glasser, Marshal Miller, John Rodgers, Todd Firestone

Research funded by the AFOSR-MURI and DURIP programs

AFOSR MURI Final Review

2

HPM Effects on Electronics

What role does Nonlinearityand Chaos play in producing

HPM effects?

3

OVERVIEWHPM Effects on Electronics

Are there systematic and reproducible effects?Can we predict effects with confidence?

Evidence of HPM Effects is spotty: Anecdotal stories of rf weapons and their effectiveness---Commercial HPM devicesE-Bomb (IEEE Spectrum, Nov. 2003)etc.

Difficulty in predicting effects given complicated coupling,interior geometries, varying damage levels, etc.

Why confuse things further by adding chaos?New opportunities for circuit upset/failureA systematic framework in which to quantify and

classify HPM effects

4

Overview/Motivation“The Promise of Chaos”

• Can Chaotic oscillations be induced in electronic circuits through cleverly-selected HPM input?

• Can susceptibility to Chaos lead to degradation of system performance?

• Can Chaos lead to failure of components or circuits at extremely low HPM power levels?

• Is Chaotic instability a generic property of modern circuitry, or is it very specific to certain types of circuits and stimuli?

These questions are difficult to answer conclusively…

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ChaosClassical: Extreme sensitivity to initial conditions

Manifestations of classical chaos:Chaotic oscillations, difficulty in making long-term predictions, sensitivity to noise, etc.

10 15 20 25 30

0.2

0.4

0.6

0.8

1

x

Iteration Number

101.00 =x

100.00 =xThe Logistic Map:

)1(41 nnn xxx −=+ μ0.1=μ

DoublePendulum later

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Chaos in Nonlinear Circuits

Many nonlinear circuits show chaos:Driven Resistor-Inductor-Diode series circuitChua’s circuitCoupled nonlinear oscillatorsCircuits with saturable inductorsChaotic relaxation circuitsNewcomb circuitRössler circuitPhase-locked loops…Synchronized chaotic oscillators and chaotic communication

Here we concentrate on the most common nonlinear circuit elementthat can give rise to chaos due to external stimulus: the p/n junction

7

V D

I(V D)

V D

C (V D)

B attery

Cor H unt

N L C RV D

I(V D)

V D

C (V D)

B attery

Cor H unt

N L C R

The p/n Junction

The p/n junction is a ubiquitous feature in electronics:Electrostatic-discharge (ESD) protection diodesTransistors

Nonlinearities:Voltage-dependent CapacitanceConductance (Current-Voltage characteristic)Reverse Recovery (delayed feedback)

HPM input can induce Chaos through several mechanismsRenato Mariz de Moraes and Steven M. Anlage, "Unified Model, and Novel Reverse Recovery Nonlinearities, of the Driven Diode Resonator," Phys. Rev. E 68, 026201 (2003).

Renato Mariz de Moraes and Steven M. Anlage, "Effects of RF Stimulus and Negative Feedback on Nonlinear Circuits," IEEE Trans. Circuits Systems I: Regular Papers, 51, 748 (2004).

8

Electrostatic Discharge (ESD) Protection CircuitsA New Opportunity to Induce Chaos at High Frequencies

in a distributed circuit

Circuit tobe protected

ESD Protection

Delay T

Schematic ofmodern integratedcircuit interconnect

The “Achilles Heel” of modern electronics

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Rg

Vref

VincVg(t)

+V(t)-

Transmission Line

Chaos in the Driven Diode Distributed Circuit

Z0

delay T

A simple model of p/n junctions in computersNew

Time-Scale!

mismatch

Delay differential equations for the diode voltage

)()2()()3

)()()()2

))(()()(2)1 0

TtVTtVtV

tVtVtV

tVQdtdgVZtVtV

grefinc

incref

inc

−+−=

−=

⎥⎦⎤

⎢⎣⎡ ++=

))(cos())((

)2())2(())((

)2())((

)1()(

))(()1()(

00

0

0

0 TttVCZ

VTtV

dtd

TtVCtVC

TtVtVCZgZ

tVtVCZgZtV

dtd gggg −+−

−−

+−−

++−

= ωτρρ

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Vg = .5 V Period 1

Vg = 2.25 V Period 2

Vg = 3.5 V Period 4

Vg = 5.25 V Chaos

V(t)

(Vol

ts)

V(t)

(Vol

ts)

V(t)

(Vol

ts)

V(t)

(Vol

ts)

Time (s)

Time (s)

Time (s)

Time (s)

Chaos in the Driven Diode Distributed CircuitSimulation results

f = 700 MHzT = 87.5 psRg = 1 ΩZ0 = 70 ΩPLC, Cr = Cf/1000

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Vg (Volts)

Stro

be P

o in t

s (V

o lts

)

Period 2

Period 1

Period 4

Chaos

Chaos in the Driven Diode Distributed Circuit

f = 700 MHzT = 87.5 psRg = 1 ΩZ0 = 70 ΩPLC, Cr = Cf/1000

Simulation results

http://arxiv.org/abs/nlin.cd/0605037

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Experiment on the Driven Diode Distributed Circuit

1 23

Signal Generator

Amplifier

CirculatorDirectional

Coupler

50ΩLoad Oscilloscope Spectrum Analyzer

TransmissionLine (Z0)

DiodeL

70001N5400

1601N5475B

41N4148

4BAT 86

Reverse Recovery Time (ns)Diode

13

Experimental Bifurcation DiagramBAT41 Diode @ 85 MHz

T ~ 3.9 ns, Bent-Pipe

0 20 40 60 80 100Frequency HMHzL-80

-60

-40

-20

0

rewoPHmBdL

17. dBm

0 20 40 60 80 100Frequency HMHzL-80

-60

-40

-20

0

rewoPHmBdL

19. dBm

0 20 40 60 80 100Frequency HMHzL

-80

-60

-40

-20

0

rewoPHmBdL

20.5 dBm

0 20 40 60 80 100Frequency HMHzL-80

-60

-40

-20

0

rewoPHmBdL

21.6 dBm

0 20 40 60 80 100Frequency HMHzL-80

-60

-40

-20

0

rewoPHmBdL

21.85 dBm

0 20 40 60 80 100Frequency HMHzL

-80

-60

-40

-20

0

rewoPHmBdL

22.2 dBm

Driving Power (dBm)

140 200 400 600 800 1000 1200

Frequency HMHzL-25

-20

-15

-10

-5

0

rewoPHmBdL

21. dBm

0 200 400 600 800 1000 1200Frequency HMHzL-25

-20

-15

-10

-5

0

rewoPHmBdL

19. dBm0 200 400 600 800 1000 1200Frequency HMHzL

-25

-20

-15

-10

-5

0

rewoPHmBdL

17. dBm

NTE519785 MHzT ~ 3.5 nsDC Bias=6.5 Volts

Distributed Transmission Line Diode Chaos at 785 MHz

17 dBm input

21 dBm input

19 dBm input

http://arxiv.org/abs/nlin.cd/0605037

Power Combiner

SourceCirculator

Oscilloscope

T-Line

1 23

1 23

50Ω Load

Length - 2

Length - 1

OptionalDC Source

& Bias TeeMatched to 50Ω

Directional Coupler

Spectrum Analyzer

Diode

Circulator Power Combiner

SourceSourceCirculator

Oscilloscope

T-Line

1 23

1 23

50Ω Load50Ω Load

Length - 2

Length - 1

OptionalDC Source

& Bias TeeMatched to 50Ω

Directional Coupler

Spectrum Analyzer

Diode

Circulator

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Chaos and Circuit DisruptionWhat can you count on?

Bottom Line on HPM-Induced circuit chaosWhat can you count on? → p/n junction nonlinearityTime scales!

Windows of opportunity – chaos is common but not present for all driving scenarios

ESD protection circuits are ubiquitous

Manipulation with “nudging” and “optimized” waveforms.Quasiperiodic driving lowers threshold for chaotic onset

D. M. Vavriv, Electronics Lett. 30, 462 (1994).Two-tone driving lowers threshold for chaotic onset

D. M. Vavriv, IEEE Circuits and Systems I 41, 669 (1994).D. M. Vavriv, IEEE Circuits and Systems I 45, 1255 (1998).J. Nitsch, Adv. Radio Sci. 2, 51 (2004).

Noise-induced Chaos:Y.-C. Lai, Phys. Rev. Lett. 90, 164101 (2003).

Resonant perturbation waveformY.-C. Lai, Phys. Rev. Lett. 94, 214101 (2005).

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What needs further research?

Are nonlinearity and chaos the correct organizing principles forunderstanding HPM effects?

Effects of chaotic driving signals on nonlinear circuits (challenge – circuits are inside systems with a frequency-dependent transfer function)

Unify our circuit chaos and wave chaos research

Uncover the “magic bullet” driving waveform that causes maximum disruption to electronicsS. M. Booker, “A family of optimal excitations for inducing complex dynamics in planardynamical systems,” Nonlinearity 13, 145 (2000).

A. Hübler, PRE (1995): Aperiodic time-reversed optimalforcing function

Chaotic Driving WaveformsChaotic microwave sources

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Conclusions

The p/n junction offers many opportunities for HPM upset effectsInstability in ESD protection circuits (John Rodgers)Distributed trans. line / diode circuit → GHz-scale chaos

GHz chaos paper: http://arxiv.org/abs/nlin.cd/0605037

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Simple ExperimentPhase Diagram

400 500 600 700 800Frequency HMHzL-30

-20

-10

0

10

20

30

40

rewoPmBd

400 500 600 700 800Frequency (MHz)

1N4148 DiodeτRR = 4 ns

Z0 = 75 ΩT ~ 8.6 nsED ~ 2.3 ns (-0.7m)

Period 2 or more complicated

Rea

ctan

ce (5

0Ω)-

-Pow

er (d

Bm

)

40

30

20

10

0

-10

-20

-30

Data

19 HL

Simple Experiment & ModelPhase Diagram Comparison

21 dBm

21 dBm

Sim

ple Experim

entM

odel Predictions

400 500 600 700 800

40

30

20

10

0

40

30

20

10

Freq (MHz)

1N4148 Diode

Si Contact Potential

~0.6 Volts

T ~ 8.6 nsED ~ 2.3 nsCj(0) ~ 4 pF

ρ = -0.2, τ = 0.8

Numerical

V0 = 0.6 Volts

T = 10.9 nsCr = 3 pF

ρ = -0.35, τ = 0.80

20 HL

21 dBm

21 dBm

Sim

ple Experim

entM

odel Predictions

400 500 600 700 800

40

30

20

10

0

40

30

20

10

Freq (MHz)

1N4148 Diode

Si Contact Potential

~0.6 Volts

T ~ 17.3 nsED ~ 2.3 nsCj(0) ~ 4 pF

ρ = -0.2, τ = 0.8

Numerical

V0 = 0.6 Volts

T = 19.5 nsCr = 3 pF

ρ = -0.35, τ = 0.80

Simple Experiment & ModelPhase Diagram Comparison

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3.0, 3.5, 3.9, 4.1, 4.4, 5.5, 7.0Bent-Pipe0.02 - 1.2 GHz---Per 1 only

8.6, 17.3Part. Reflecting2.01005082-3081

3.0, 3.5, 3.9, 4.1, 4.4, 5.5, 7.0Bent-Pipe0.02 - 1.2 GHz---Per 1 only

8.6, 17.3Part. Reflecting0.7<155082-2835

3.0, 3.5, 3.9, 4.1, 4.4, 5.5, 7.0Bent-Pipe0.02 - 1.2 GHz---Per 1 only

8.6, 17.3Part. Reflecting66.630MV209

3.0, 3.5, 3.9, 4.1, 4.4, 5.5, 7.0Bent-Pipe0.02 - 1.2 GHz---Per 1 only

8.6, 17.3Part. Reflecting11635NTE588

0.5-1.2 GHz~16 dBmPD, Chaos*3.0, 3.5, 3.9, 4.1, 4.4, 5.5, 7.0Bent-Pipe

0.4–1.0 GHz periodically~25 dBmPD8.6, 17.3Part. Reflecting

1.14®NTE519

20-800 MHz---Per 1 only3.0, 3.5, 4.1, 4.4, 5.5, 7.0

85 MHz~ 17 dBm

43 MHz~ 25 dBmPD, Chaos3.9

Bent-Pipe

0.4-1.0 GHz---Per 1 only8.6, 17.3Part. Reflecting

4.65®BAT41

20-800 MHz---Per 1 only3.0, 3.5, 3.9, 4.1, 4.4, 5.5, 7.0Bent-Pipe

0.4–1.0 GHz periodically~ 35 dBmPD8.6, 17.3Part. Reflecting

11.54®BAT86

0.2–1.2 GHz~14 dBmPD, Chaos*3.0, 3.5, 3.9, 4.1, 4.4, 5.5, 7.0Bent-Pipe

0.4–1.0 GHz periodically~20 dBmPD8.6, 17.3Part. Reflecting

0.74®1N4148

~ƒ Range for Result

Min. Pow. to PDResultDelay Time T (ns)ExperimentCj0 (pf)τrr (ns)Diode

*With dc bias.Highest Frequency Chaos @ 1.1 GHz