Nonlinear Dynamics and Stability of Power Amplifiers

1
Nonlinear Dynamics and Stability of Power
Amplifiers

• Sanggeun Jeon, Caltech
• Almudena Suárez, Univ. of Cantabria
• David Rutledge, Caltech

May 19th, 2006
2
Outline

• Introduction
• Bifurcation detection techniques
• Stability analysis of power amplifiers
• Oscillation, chaos, hysteresis
• Noisy precursor, hysteresis in power-transfer
  curve
• Conclusion

3
Introduction

• Strong nonlinearity of power amplifiers
• Instabilities
• Performance degradation, interference, damage of
  circuit.
• Bifurcations
• Qualitative stability changes by varying a
  circuit parameter(s).
• Oscillators are also based on bifurcation
  phenomenon.
• Bifurcation detection
• Solve nonlinear differential equations
• difficult!
• Must harness circuit simulator techniques like HB.

4
Types of instabilities and bifurcations - I

• Many routes lead to chaos
• Quasi-periodic route
• Period-doubling route
• Torus-doubling route

5
Types of instabilities and bifurcations - II
6
Auxiliary generator
7
Pole-zero identification

• Identify poles and zeros of the large-signal
  operated system.
• Impedance function Zin(?)Vs/Is calculated thru
  the conversion-matrix approach in combination
  with HB.
• Detect bifurcations and pole evolution with a
  circuit parameter varied.

8
1.5kW, 29MHz Class-E/Fodd PA using a Distributed
Active Transformer
9
Evolution of measured output spectrum in Pin

• Self-oscillation at fa 4 MHz
• Chaos
• Hysteresis in the lower Pin boundary of
  bifurcation.

10
Local stability analysis using pole-zero
identification technique

• Change input-drive power Pin (5W 15W by 1W
  step).

• Good agreement with the measurement in terms of
  bifurcation points.

11
Bifurcation locus

• Auxiliary generator with the non-perturbation
  condition solved in combination with HB
• Delimit the stable and unstable operating regions.

12
Oscillating solution curve

• Auxiliary generator with the non-perturbation
  condition (fixed VDD)

13
Chaos prediction

• Two-tone based envelope-transient

14
7.4-MHz Class-E power amplifier

• Pout 360 W with 16 dB gain and 86 drain
  efficiency

15
Measured output spectrum
16
Stability analysis over solution curve

• Hysteresis in power-transfer curve.
• Pole-zero identification performed along the
  power-transfer curve.

?2
?1
17
Simulated noisy precursor spectrum

• Simulated by two different techniques
• Envelope-transient
• Conversion-matrix technique

18
Elimination of hysteresis in Pin-Pout curve

• The cause of hysteresis turning points in the
  curve.
• Elimination of turning points by varying a
  circuit parameter.

Cusp bifurcation

• At turning points, the Jacobian matrix for the
  non-perturbation equation YAG(VAG, fAG)0
  becomes singular.

19
Locus of turning points

• No hysteresis below 85pF.

20
Conclusion

• Bifurcation detection techniques are introduced.
• Linked to a commercial HB simulator.
• Application to the stability analysis of power
  amplifiers.
• Stabilization of power amplifiers by bifurcation
  control.
• Versatility of techniques
• General-purpose
• Design of self-oscillating and synchronized
  circuits