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Phase noise-induced single coherence resonance (CR) has been reported in previous studies. It is reported here that double CRs can be induced in the FitzHugh–Nagumo (FHN) model by phase noise when the oscillation period of phase noise is much larger than the firing period of the FHN model. By analyzing peaks in the power spectrums for the fast voltage variable and the coefficient variations (CVs) of interspike interval (ISI) series, we find that double CRs corresponding to the frequency of phase noise and the firing frequency of the FHN model respectively appear at small and large noise intensities. This implies that there are double chances for the FHN model to take advantage of the benefits of phase noise. Possible causes of the single CR are also discussed.

Coherent population trapping (CPT) cesium frequency standard plays a significant role in precision guidance of missile and global positioning system (GPS). Low noise 4.596 GHz voltage controlled oscillator (VCO) is an indispensable part of microwave signal source in cesium frequency standard. Low-phase noise is also the most important and difficult performance indicator of VCO. Starting from phase noise analysis method proposed by Leeson, the formulas about the relationship between phase noise of output signal of oscillator feedback model and phase fluctuation spectrum of amplifier, phase noise of oscillator are derived in this paper. Finally, the asymptote model of microwave oscillator is proposed based on the formula derivation. The experiment shows that when the reverse bias voltage of variode is 1.8 V, the designed oscillation frequency of VCO is 4.596 GHz, the power is −1 dBm and the DC power consumption is 19.6 mW. The tendency of phase noise simulation curve and actual test curve conform to asymptote model. The phase noise in 1 and 10 kHz is, respectively, −60.86 and −86.58 dBc/Hz. The significance of the paper lies in determining the main factors influencing oscillator phase noise and providing guiding direction for the design of low-phase noise VCO.

Nowadays, some countries have already invented chip-scale atomic clock (CSAC) based on coherent population trapping (CPT), and it has been applied in every areas. According to its working principle, the microwave signal source is one of the decisive factors affecting its stability. Usually the microwave signal source is a phase-locked loop circuit, it mainly includes a frequency synthesizer, a voltage controlled oscillator (VCO) and a loop filter. This paper aims to develop a microwave signal source for Cs CSAC. First, a VCO should be designed, in order to validate the characteristic of the designed VCO, the VCO needs to be tested at high and low temperatures, and the results show that it has good stability of high and low temperatures. Second, for the purpose of verifying that the design and production consistency of the VCO are in good condition, 1000 VCOs are test, respectively. The statistical distribution of the phase noise at 1 kHz offset would be painted a curve. Finally, the designed VCO (PN: 61.01dBc/Hz@1kHz) will be applied in phase-locked loop, the test results show that the phase noise is −83.57dBc/Hz@300Hz, it is much better than −43dBc/Hz@300Hz which is the spec of CSAC. If the microwave signal source would be used in CSAC, its stability would be greatly improved.

The influences of phase noise together with autapse on the resonance dynamics in a modified FitzHugh–Nagumo (FHN) neuron are investigated by numerical simulation, where the neuronal model is in the environment of electromagnetic induction. First, it is found that phase noise can induce double coherence resonances, which is further confirmed to be robust to the feedback gain of induction current. Surprisingly, by individually changing the period of phase noise and the feedback gain, a resonance-like behavior also appears. Subsequently, the significant phenomenon of autapse-induced multiple coherence resonances is discovered. Moreover, the phenomenon of multiple coherence resonances can emerge at a broad parameter range of autaptic strength and autaptic delay.

Through introducing the ingredients of electromagnetic induction and coupled time delay into the original Fitzhugh–Nagumo (FHN) neuronal network, the dynamics of stochastic resonance in a model of modified FHN neuronal network in the environment of phase noise is explored by numerical simulations in this study. On one hand, we demonstrate that the phenomenon of stochastic resonance can appear when the intensity of phase noise is appropriately adjusted, which is further verified to be robust to the edge-added probability of small-world network. Moreover, under the influence of electromagnetic induction, the phase noise-induced resonance response is suppressed, meanwhile, a large noise intensity is required to induce stochastic resonance as the feedback gain of induced current increases. On the other hand, when the coupled time delay is incorporated into this model, the results indicate that the properly tuned time delay can induce multiple stochastic resonances in this neuronal network. However, the phenomenon of multiple stochastic resonances is found to be restrained upon increasing feedback gain of induced current. Surprisingly, by changing the period of phase noise, multiple stochastic resonances can still emerge when the coupled time delay is appropriately tuned to be integer multiples of the period of phase noise.