“…The paper describes for the first time an implementation of a comprehensive simulation model of an OEO under injection by an external source using the Simulink™ block diagram environment. The paper demonstrates the expressiveness of the new injection-locking theory 4 as illustrated by the Simulink simulations. It also provides a service to researchers in this field through the full disclosure of the simulation methods, The new theory coupled with the simulation results has value in aiding the design of low phase noise OEOs and the optimization of their performance metrics.…”
Section: Introductionmentioning
confidence: 85%
“…However, the frequency interval between adjacent oscillation modes decreases in inverse proportion to the delay (40 kHz for 5 km), and a practical RF resonator cannot provide sufficient selectivity to suppress the multitude of sidemode resonances. Multimode operation is an artefact of an OEO with profound consequences on its behaviour 3 , 4 . Figure 1 Schematic of a single-loop OEO.…”
Section: Introductionmentioning
confidence: 99%
“…A new delay integral/differential equation (DDE) formulation of an OEO under external injection is presented in a prior work 4 that removes the implicit assumption of a single-mode oscillator under weak injection made in previous treatments that apply classical injection locking theory to OEOs. The emphasis of the prior work is on the theory and the correct prediction of the experimentally observed phase noise spectrum; simulation results were precluded by space considerations.…”
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.
“…The paper describes for the first time an implementation of a comprehensive simulation model of an OEO under injection by an external source using the Simulink™ block diagram environment. The paper demonstrates the expressiveness of the new injection-locking theory 4 as illustrated by the Simulink simulations. It also provides a service to researchers in this field through the full disclosure of the simulation methods, The new theory coupled with the simulation results has value in aiding the design of low phase noise OEOs and the optimization of their performance metrics.…”
Section: Introductionmentioning
confidence: 85%
“…However, the frequency interval between adjacent oscillation modes decreases in inverse proportion to the delay (40 kHz for 5 km), and a practical RF resonator cannot provide sufficient selectivity to suppress the multitude of sidemode resonances. Multimode operation is an artefact of an OEO with profound consequences on its behaviour 3 , 4 . Figure 1 Schematic of a single-loop OEO.…”
Section: Introductionmentioning
confidence: 99%
“…A new delay integral/differential equation (DDE) formulation of an OEO under external injection is presented in a prior work 4 that removes the implicit assumption of a single-mode oscillator under weak injection made in previous treatments that apply classical injection locking theory to OEOs. The emphasis of the prior work is on the theory and the correct prediction of the experimentally observed phase noise spectrum; simulation results were precluded by space considerations.…”
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.
“…In respect of injection locking the models reduce to the differential equations of Adler (weak injection) [9] or Paciorek (strong injection) [10] valid only for classical single mode oscillator. Recently, a delay integral/differential equation formulation of injection locking theory for a time delay oscillator has been introduced [11] that fully accounts for the multimode character of the oscillator and the distinct physical roles of the delay line and RF bandpass filter. It is long established that injection locking has an equivalent representation as a type-I PLL [12], i.e., a proportional controller, so these architectures may be viewed from the perspective of self-referenced phase locked loops, which has been applied to the study of self-injection locked electronic oscillators and a short loop OEO [3].…”
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 −𝟖𝟎 𝒅𝑩𝒄⁄𝑯𝒛 𝐚𝐭 𝟏𝟎 𝑯𝒛 and −𝟏𝟒𝟓 𝒅𝑩𝒄⁄𝑯𝒛 𝐚𝐭 𝟏𝟎 𝒌𝑯𝒛, 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.
“…In respect of injection locking the models reduce to the differential equations of Adler (weak injection) 9 or Paciorek (strong injection) 10 valid only for classical single mode oscillator. Recently, a delay integral/differential equation formulation of injection locking theory for a time delay oscillator has been introduced 11 that fully accounts for the multimode character of the oscillator and the distinct physical roles of the delay line and RF bandpass filter. It is long established that injection locking has an equivalent representation as a type-I PLL 12 , i.e., a proportional controller, so these architectures may be viewed from the perspective of self-referenced phase locked loops, which has been applied to the study of self-injection locked electronic oscillators and a short loop OEO 3 .…”
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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