A Study of a Driven Oscillator with FM Feedback by Use of a Phase-Lock-Loop Model

Couch, Leon W.

doi:10.1109/tmtt.1971.1127520

Cited by 6 publications

(3 citation statements)

References 13 publications

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“…10 b). The locking behavior is similar to a phase locked loop with proportional control 38 . In this example, an envelope model is used but a phase model provides identical results.…”

Section: Simulation Resultsmentioning

confidence: 71%

Simulation of optoelectronic oscillator injection locking, pulling & spiking phenomena

Banerjee,

Hall

2024

Sci Rep

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Complex envelope and reduced phase simulation models describing the dynamical behaviour of an optoelectronic oscillator (OEO) under injection by an external source are described. The models build on the foundations of a previously reported delay integral/differential equation (DDE) theory of injection locking of time delay oscillators (TDO) such as the OEO. The DDE formulation is particularly amenable to high precision simulation using the Simulink™ block diagram environment. The correspondence between the blocks and the oscillator components offers intuition and considerable freedom to explore different circuit architectures and design variations with minimal coding effort. The simulations facilitate the study of the profound effect the multimode nature of a TDO has on its dynamical behavior. The reduced phase models that make use of the Leeson approximation are generally successful in reproducing the results of complex envelope models for established oscillations except for spiking phenomena for which the Leeson approximation fails. Simulation results demonstrating phenomena not captured by classical injection theory are presented, including multimode oscillation, the appearance of sidemodes in the RF and phase noise spectrum, and persistent spike trains redolent of recent experimental observations of $$2\pi $$ 2 π phase pulse trains in a broadband OEO under injection.

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“…10 b). The locking behavior is similar to a phase locked loop with proportional control 38 . In this example, an envelope model is used but a phase model provides identical results.…”

Section: Simulation Resultsmentioning

confidence: 71%

Simulation of optoelectronic oscillator injection locking, pulling & spiking phenomena

Banerjee,

Hall

2024

Sci Rep

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show abstract

“…7. 35 The receiver consists of a simple shift register of which the first flipflop is used as a phase detector. When a phase shift is applied to the input, the data register will clock.…”

Section: Motor Torque T Oscmentioning

confidence: 99%

“…It is therefore intuitive to model them similarly [35,123]. In a PLL, the different building blocks help to understand the selective filtering of the noise coming from the reference of the oscillator itself.…”

Section: A Pll-based Noise Modelmentioning

confidence: 99%

Temperature- and Supply Voltage-Independent Time References for Wireless Sensor Networks

Smedt

Gielen

Dehaene

2015

Analog Circuits and Signal Processing

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On the stability & phase locking to a system reference of an optoelectronic oscillator with large delay

Hasan

Nicholls

Hall

2023

Sci Rep

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Delay line oscillators based on photonic components, offer the potential for realization of phase noise levels up to 3 orders of magnitude lower than achievable by conventional microwave sources. Fibreoptic-based delay lines can realize the large delay required for low phase noise systems whilst simultaneously achieving insertion loss levels that can be compensated with available microwave and photonic amplification technologies. Multimode operation is an artefact of the delay line oscillator and introduces modulational instability into phase-locked control loops. An optoelectronic oscillator (OEO) with large delay under proportional integral control by a phase-locked loop (PLL) is modelled, providing the first report of the location of all the infinity of poles of the PLL-OEO system function. The first experimental observation of giant phase modulated oscillation of a free OEO and spontaneous giant phase modulated oscillation of a PLL-OEO are also reported and explained respectively as a source and manifestation of modulational instability. Nevertheless, the analysis and experimental observations, including a prototype 10 GHz PLL-OEO phase noise spectral density achieving $$ - 80dBc/Hz {\text{at}} 10 Hz$$ - 80 d B c / H z at 10 H z and $$- 145dBc/Hz {\text{at}} 10 kHz$$ - 145 d B c / H z at 10 k H z , demonstrate that stable phase lock operation and optimum phase noise performance is achievable provided full account of the multimode nature of the OEO is taken in the phase lock analysis.

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A Study of a Driven Oscillator with FM Feedback by Use of a Phase-Lock-Loop Model

Cited by 6 publications

References 13 publications

Simulation of optoelectronic oscillator injection locking, pulling & spiking phenomena

Simulation of optoelectronic oscillator injection locking, pulling & spiking phenomena

Temperature- and Supply Voltage-Independent Time References for Wireless Sensor Networks

On the stability & phase locking to a system reference of an optoelectronic oscillator with large delay

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