Oscillator Circuits
Frontiers in Design, Analysis and Applications

Edited by Yoshifumi Nishio
Cloth: 978 1 78561 057 8 / $175.00
Published: December 2016  

Publisher: The Institution of Engineering and Technology
344 pp., 6 1/8" x 9 1/5"
This book fills the need for a comprehensive volume on the most recent research on oscillator circuit design, analysis and application. It highlights developments in the analysis of synchronization and wave phenomena, new analytical and design methods and their application, and novel engineering applications of oscillator circuits.

Topics covered include various oscillatory circuits and their synchronization; bifurcation analysis of oscillatory circuits; synchronization phenomena of hysteresis oscillators; recent research on memristor based relaxation oscillators; theory and design of fractional-order oscillators; piecewise-constant oscillators and their applications; multimode oscillations in hard oscillators; wave propagation of phase difference in coupled oscillator arrays; coupled oscillator networks with frustration; fundamental operation and design of high-frequency high-efficiency tuned power oscillator; graph comparison and synchronization in complex networks; experimental studies on networks of coupled chaotic oscillators; ring oscillators and applications in random bit generation; attacking on-chip oscillators.

Oscillator Circuits: Frontiers in Design, Analysis and Applications is essential reading for researchers, students and designers working in circuit theory, analysis, design and application.

Table of Contents:
1 Introduction
Yoshifumi Nishio
2 Analysis of bifurcations in oscillatory circuits
Hiroyuki Asahara, Takuji Kousaka and Tetsushi Ueta
2.1 Introduction
2.2 Analysis of bifurcations of autonomous systems
2.2.1 Stability of equilibrium point
2.2.2 Bifurcation at equilibrium point
2.2.3 Stability of fixed point
2.2.4 Bifurcation of fixed point
2.3 Example of bifurcation analysis applied to an autonomous system
2.3.1 Single BVP oscillator
2.3.2 Coupled BVP oscillators
2.4 Conclusions
3 Fractional-order oscillators
Ahmed G. Radwan, Brent J. Maundy and Ahmed S. Elwakil
3.1 Fractional-order sinusoidal oscillators
3.1.1 Fractional-order linear time invariant systems (FLTI)
3.1.2 Stability analysis
3.1.3 Stability analysis examples
3.1.4 General theorems of fractional-order LTI systems
3.2 Fractional-order relaxation oscillators
3.2.1 The fractional multivibrator
3.2.2 Verification via simulation and experimentation
3.2.3 Multivibrator with biological tissues
3.3 Conclusion
4 Memristive and memcapacitive astable multivibrators
Dongsheng Yu, Herbert Ho-Ching Iu, Tyrone Fernando and Jason Eshraghian
4.1 Introduction
4.2 Circuit schematic of floating memristor emulator
4.3 Theoretical analysis of memristive astable multivibrator
4.3.1 Discharging interval
4.3.2 Charging interval
4.4 Simulation validation for memristive astable multivibrator
4.4.1 Testing the memristor emulator
4.4.2 Observing the oscillation of memristive astable multivibrator
4.5 Memcapacitor-based astable oscillator circuit
4.6 Simulation validation for memcapacitive astable multivibrator
4.7 Conclusion
5 Piecewise-constant oscillators and their applications
Tadashi Tsubone, Keisuke Suzuki and Takahiro Aoki
5.1 Basic concept of piecewise-constant oscillations
5.2 Example 1: a piecewise-constant chaotic spiking oscillator
5.2.1 Circuit and dynamics
5.2.2 Embedded return map
5.3 Example 2: coupled systems of piecewise-constant oscillators
5.3.1 A piecewise-constant oscillator exhibiting limit cycle
5.3.2 Coupled system of piecewise-constant oscillators
5.3.3 Analysis of PWC oscillators
5.4 Conclusions
6 Master–slave synchronization of hysteresis neural-type oscillators
Kenya Jin’no, Takuya Kurihara and Toshimichi Saito
6.1 Introduction
6.2 Relaxation oscillator with a time-variant threshold
6.2.1 Periodic fluctuation threshold
6.2.2 Period adjustment capability
6.3 The response to non-periodic external force
6.3.1 Without external force
6.3.2 Periodic external force
6.3.3 Uniform random period external force
6.4 Conclusions
7 Multimode oscillations in coupled hard oscillators
Kuniyasu Shimizu and Tetsuro Endo
7.1 Introduction
7.2 Two inductor-coupled hard oscillators
7.2.1 Weakly nonlinear oscillators
7.2.2 Strongly nonlinear oscillators
7.3 Propagating waves in a coupled hard-oscillator ring
7.4 Conclusions
8 Wave propagation of phase difference in coupled oscillator arrays
Masayuki Yamauchi, Yoshihito Todani and Syohei Fujimoto
8.1 Introduction
8.2 Circuit model
8.3 Phase-inversion waves
8.3.1 Basic synchronization phenomena
8.3.2 Sample of phase-inversion waves
8.3.3 Characteristics of the phase-inversion waves
8.3.4 Propagation velocity of phase-inversion waves
8.3.5 Mechanisms
8.4 Conclusion
9 Coupled oscillator networks with frustration
Yoko Uwate and Yoshifumi Nishio
9.1 Introduction
9.2 Frustration in ring van der Pol oscillators with different frequencies
9.2.1 Circuit model
9.2.2 Synchronization phenomena
9.3 Frustration in coupled polygonal oscillatory networks
9.3.1 Weakly coupled oscillators
9.3.2 Strongly coupled oscillators
9.4 Conclusions
10 Graph comparison and synchronization in complex networks
Hui Liu, Ming Cao and Chai Wah Wu
10.1 Introduction
10.2 Network model and preliminaries
10.3 Tools of graph comparison
10.4 Synchronization in an undirected network
10.4.1 Graph comparison with the complete graph
10.4.2 Graph comparison with the star graph
10.4.3 Illustrative examples
10.5 Synchronization in a directed network
10.5.1 Graph comparison with the complete graph
10.5.2 Illustrative examples
10.6 Conclusions
Appendix A: Comments on Assumption
Appendix B: Numerical simulation
11 Experimental studies on reconfigurable networks of chaotic oscillators
Massimiliano de Magistris, Carlo Petrarca and Soudeh Yaghouti
11.1 Introduction
11.2 Realization of a network of nonlinear oscillators with linear coupling
11.2.1 Designing a reconfigurable complex network of nonlinear oscillators
11.2.2 Chua’s circuits as system nodes
11.2.3 A reconfigurable linear N-pole as interconnection network
11.2.4 The actual system implementation
11.3 Collective behaviours and relative analysis tools
11.3.1 Synchronization
11.3.2 Clustering
11.4 Experimental results and validation of theoretical predictions
11.4.1 Experiments on synchronization with diffusive links
11.4.2 Experiments on synchronization with dynamic links
11.4.3 Experiments on clustering
11.4.4 Observation of patterns and waves
11.5 Concluding remarks
12 Fundamental operation and design of high-frequency high-efficiency tuned power oscillator
Hiroo Sekiya
12.1 Introduction
12.2 Power amplifiers
12.2.1 Class-D amplifier
12.2.2 Class-E amplifier
12.2.3 Driver circuit
12.3 Tuned power oscillator
12.3.1 Free-running class-E oscillator
12.3.2 Injection-locked class-E oscillator
12.3.3 Class-EM oscillator with second harmonic injection
12.4 Design of free-running class-E oscillator
12.4.1 Design strategies
12.4.2 Numerical design procedure
12.4.3 Design examples and experimental measurements
12.5 Conclusion
13 Ring oscillators and self-timed rings in true random number generators
Viktor Fischer, Patrick Haddad and Abdelkarim Cherkaoui
13.1 Introduction
13.2 Design of TRNGs
13.3 Electric noise and clock jitter as a source of randomness
13.3.1 Electric noise in clock generators
13.3.2 Jitter of the generated clock signal
13.4 Harvesting the entropy from jittery clock signals
13.5 Single-event ring oscillators as sources of jittery clocks
13.5.1 Modelling the jitter of clocks generated in ring oscillators
13.6 Multi-event ring oscillators with signal collisions
13.6.1 Modelling number of oscillations in TERO
13.7 STR oscillators
13.7.1 Clock jitter in STRs
13.8 Examples of oscillator-based TRNGs
13.8.1 Elementary ring oscillator-based TRNG
13.8.2 Multiple ring oscillator-based TRNG
13.8.3 TERO-based TRNG
13.8.4 STR-based TRNG
13.9 Conclusions
14 Attacking on-chip oscillators in cryptographic applications
Lilian Bossuet, Pierre Bayon and Viktor Fischer
14.1 Introduction
14.2 Background
14.2.1 TRNG model and implementation
14.3 Figures
14.3.1 Attack scenario
14.4 Retrieving information on the RO-TRNG: passive electromagnetic attack
14.4.1 Electromagnetic analysis platform
14.4.2 Frequency analysis
14.4.3 Differential frequency analysis
14.4.4 Experiments
14.4.5 Experimental results
14.5 Modifying the RO-TRNG behavior: active electromagnetic attack
14.5.1 Injection platform
14.5.2 Experiments
14.5.3 Attack description
14.5.4 Effect of the electromagnetic waves on the ROs—Target #1
14.5.5 Effect of the electromagnetic waves on the TRNG—Target #2
14.5.6 Discussion
14.6 Conclusion