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Analysis and Design of Autonomous Microwave Circuits
Almudena Suarez
ISBN: 978-0-470-05074-3
Hardcover
704 pages
January 2009, Wiley-IEEE Press
Analysis and Design of Autonomous Microwave Circuits provides microwave designers and oscillator designers with a sound understanding of the free-running oscillation mechanism, the start-up from the noise level, and the establishment of the steady-state oscillation. It deals with the operation principles and main characteristics of free-running and injection-locked oscillators, coupled oscillators, and parametric frequency dividers. It covers techniques for the efficient simulation of the most common autonomous regimes as well as those used to eliminate common types of undesired behavior, such as spurious oscillations, hysteresis, and chaos.
Chapter 1: General concepts on oscillator dynamics. 1 General concepts on oscillator dynamics. 1.1 Introduction. 1.2 Operation principle of free-running oscillators. 1.3 Impedance/admittance analysis of the oscillator. 1.4 Frequency-domain formulation of the oscillator circuit. 1.5 Oscillator dynamics. 1.5.1 Equations and steady-state solutions. 1.5.2 Stability analysis. 1.5.2.a Stability analysis of a DC solution. 1.5.2.b Stability analysis of a periodic solution. 1.6 Phase noise. Chapter 2: Phase noise. 2.1 Introduction. 2.2 Generalities about random variables and random processes. 2.2.1 Random variables and probability. 2.2.2 Random processes. 2.2.3 Correlation functions and power-spectral density. 2.2.4 Stochastic differential equations. 2.3 Types of noise sources in electronic circuits. 2.3.1 Thermal noise. 2.3.2 Shot noise. 2.3.3 Generation-recombination noise. 2.3.4 Flicker noise. 2.3.5 Burst noise. 2.4 Derivation of the oscillator noise spectrum with a time-domain analysis. 2.4.1 Oscillator with white-noise sources. 2.4.1.a Stochastic differential equations. 2.4.1.b Phase-noise sensitivity. 2.4.1.c Derivation of the oscillator spectrum due to phase noise. 2.4.2 White and colored noise sources. 2.5 Frequency-domain analysis of the noisy oscillator. 2.5.1 Frequency-domain representation of the noise sources. 2.5.2 Carrier-modulation analysis . 2.5.3 Frequency-domain calculation of the variance of the phase deviation. 2.5.4 Comparison between the two techniques for the frequency-domain analysis of phase noise. 2.5.5 Amplitude noise. Chapter 3: Bifurcation analysis. 3.1 Introduction. 3.2 Representation of solutions. 3.2.1 Phase space. 3.2.2 Poincar‚ map . 3.3 Bifurcations. 3.3.1 Local bifurcations. 3.3.1.1 Bifurcations from a DC solution. 3.3.1.2 Bifurcations from a periodic solution. 3.3.2 Transformations between solution poles. 3.3.3 Global bifurcations. 3.3.3.1 Saddle connection. 3.3.3.2 Saddle-node bifurcations of local/global type. Chapter 4: Injected oscillators and frequency dividers. 4.1 Introduction. 4.2 Injection-locked oscillators. 4.2.1 Analysis based on a linearization about the free-running solution. 4.2.2 Nonlinear analysis of the synchronized-solution curves. 4.2.3 Stability analysis. 4.2.4 Bifurcation loci. 4.2.5 Phase variation along the periodic curves. 4.2.6 Analysis of a FET-based oscillator. 4.2.7 Phase-noise analysis. 4.3 Frequency dividers. 4.3.1 General characteristics of a frequency-divided solution. 4.3.2 Harmonic-injection frequency dividers. 4.3.3 Regenerative frequency dividers. 4.3.4 Parametric frequency dividers. 4.3.5 Phase noise in frequency dividers. 4.4 Subharmonically and ultra-subharmonically injection-locked oscillators. 4.5 Self-oscillating mixers. Chapter 5: Nonlinear circuit simulation. 5.1. Introduction. 5.2. Time-domain integration. 5.2.1 Time-domain modeling of distributed elements. 5.2.2 Integration algorithms. 5.2.3 Convergence considerations. 5.3. Fast time-domain techniques . 5.3.1 Shooting methods . 5.3.2 Finite differences in time domain. 5.4. Harmonic balance. 5.4.1 Formulation of the harmonic balance system. 5.4.2 Nodal harmonic balance. 5.4.3 Piecewise harmonic balance. 5.4.4 Continuation techniques. 5.4.5 Algorithms for the calculation of the discrete Fourier transforms. 5.4.5.1 DFT of periodic signals . 5.4.5.2 DFT of quasi-periodic signals. 5.5 Harmonic-balance analysis of autonomous and synchronized circuits. 5.5.1 Mixed harmonic-balance formulation. 5.5.2 Auxiliary-generator technique. 5.5.2.1 Free-running oscillators. 5.5.2.2 Synchronized regime. 5.5.2.3 Self-oscillating mixer regime. 5.6 Envelope transient. 5.6.1 Expression of the circuit variables. 5.6.2 Envelope-transient formulation. 5.6.3 Extension of the envelope transient method to the simulation of autonomous circuits. 5.6.3.1 Analysis of free-running oscillations. 5.6.3.2 Analysis of injected oscillators. 5.6.3.3 Analysis of self-oscillating mixers. 5.7 Conversion-matrix approach. Chapter 6: Stability analysis using harmonic balance. 6.1 Introduction. 6.2 Local stability analysis. 6.2.1 Small-signal regime. 6.2.2 Large-signal regime. 6.3 Stability analysis of free-running oscillators. 6.4. Solution curves versus a circuit parameter. 6.5 Global stability analysis. 6.5.1 Bifurcation detection from the characteristic determinant of the harmonic-balance system. 6.5.1.1 Bifurcations from a DC regime. 6.5.1.2 Bifurcations from a periodic regime. 6.5.2 Bifurcation detection using auxiliary generators. 6.6 Bifurcation control. Chapter 7: Noise analysis of oscillator circuits using harmonic balance. 7.1 Introduction. 7.2 Noise in semiconductor devices. 7.2.1 Noise in field-effect transistors. 7.2.2 Noise in bipolar transistors. 7.2.3 Noise in varactor diodes. 7.3 Decoupled analysis of phase and amplitude perturbations in the harmonic balance system. 7.3.1 Perturbed oscillator equations. 7.3.2 Phase noise. 7.3.2.a Phase-sensitivity functions. 7.3.2.b Phase-noise spectrum. 7.3.3 Amplitude noise. 7.4 Coupled phase and amplitude noise calculation. 7.5 Carrier-modulation approach. 7.6 Conversion matrix approach. 7.7 Noise in synchronized oscillators. 7.7.1 Conversion matrix approach. 7.7.2 Semi-analytical formulation. Chapter 8: Harmonic-balance techniques for oscillator design. 8.1. Introduction. 8.2. Oscillator synthesis. 8.2.1 Oscillation start-up conditions. 8.2.2 Steady-state design, with one harmonic accuracy. 8.2.3 Multi-harmonic steady-state design. 8.3 Design of voltage-controlled oscillators. 8.3.1 Technique for increasing the oscillation bandwidth. 8.3.2 Technique to preset the oscillation band. 8.3.3 Technique to linearize the VCO characteristic . 8.4 Maximization of the oscillator efficiency. 8.4.1 Class-E design. 8.4.2 Class-F operation. 8.4.3 General load-pull system. 8.5 Control of the oscillator transients. 8.5.1 Reduction of Oscillator Start-Up Time. 8.5.2 Improvement of the modulated response of a voltage-controlled oscillator. 8.6 Phase-noise reduction. Appendix. Chapter 9: Stabilization techniques for phase-noise reduction. 9.1 Introduction. 9.2 Self-injection topology. 9.2.1 Steady state solution. 9.2.2 Stability analysis. 9.2.3 Phase-noise analysis. 9.3 Use of high Q resonators. 9.4 Stabilization loop. 9.5 Transistor-based oscillators. 9.5.1 Harmonic balance analysis. 9.5.2 Semi-analytical formulation. 9.5.3 Application to a 5 GHz MESFET-based oscillator. Chapter 10: Coupled-oscillator systems. 10.1 Introduction. 10.2 Oscillator systems with global coupling. 10.2.1 Simplified analysis of oscillation modes. 10.2.2 Applications of globally-coupled oscillators. 10.2.3 Stability analysis of the steady-state periodic regime. 10.2.4 Phase noise. 10.2.5 Analysis and design using harmonic balance. 10.2.5.1 Push-push oscillator. 10.2.5.2 Quadruple-push oscillator. 10.3 Coupled-oscillator systems for beam steering. 10.3.1 Analytical study of the oscillator-array operation. 10.3.2 Harmonic-balance analysis . 10.3.3 Semi-analytical formulation. 10.3.4 Determination of coexisting solutions. 10.3.5 Stability analysis. 10.3.6 Phase Noise Analysis . 10.3.7 Comparison between weak and strong oscillator coupling. 10.3.8 Forced operation of the coupled-oscillator array. Chapter 11: Simulation techniques for frequency-divider design. 11.1 Introduction. 11.2 Types of frequency dividers. 11.3 Design of transistor-based regenerative frequency dividers . 11.3.1 Frequency-divided regime. 11.3.2 Control of the operation bands in frequency dividers by 2. 11.3.3 Control of the divider settling time. 11.4 Design of harmonic-injection dividers. 11.4.1 Semi-analytical estimation of the synchronization bands. 11.4.2 Full harmonic-balance design. 11.4.3 Introduction of a low-frequency feedback loop. 11.4.4 Control of turning points. 11.5 Extension of the techniques to subharmonic-injection oscillators. Chapter 12: Circuit stabilization. 12.1 Introduction. 12.2 Unstable Class AB amplifier using power combiners. 12.2.1 Oscillation modes. 12.2.2 Analytical study of the mechanism for frequency division by two. 12.2.3 Global stability analysis with harmonic balance. 12.2.4 Amplifier stabilization. 12.3 Unstable Class E/F amplifier. 12.3.1 Brief description of the Class E/F operation. 12.3.2 Anomalous experimental behavior in a Class-E/Fodd power amplifier. 12.3.3 Stability analysis of the Class-E/Fodd power amplifier. 12.3.4 Stability analysis with pole-zero identification. 12.3.5 Hopf-bifurcation locus. 12.3.6 Analysis of the undesired oscillatory solution. 12.3.7 Circuit Stabilization. 12.4 Unstable Class-E amplifier. 12.4.1 Amplifier measurements. 12.4.2 Stability analysis of the power amplifier. 12.4.3 Analysis of the noisy precursors. 12.4.3.a Mathematical model. 12.4.3.b Application to the Class-E amplifier. 12.4.4 Elimination of the hysteresis phenomenon from the power-transfer curve Pin-Pout . 12.4.5 Elimination of the noisy precursors . 12.5 Stabilization of oscillator circuits. 12.5.1 Stability analysis of the oscillator circuit. 12.5.2 Stabilization technique for fixed bias voltage. 12.5.3 Stabilization technique for the entire tuning-voltage range. 12.6 Stabilization of multifunction MMIC chip.
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