National Conference on Nonlinear Systems & Dynamics, Saha Institute of Nuclear Physics, Kolkata, India, 5-7 March 2009
Noise induced resonance effects in UJT relaxation oscillator
Md. Nurujjaman, P.S. Bhattacharya, and A.N. Sekar Iyengar ∗
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In this poster, the constructive role of noise, which is generally termed as coherence resonance (CR) has been studied in the
threshold based system. The basic characteristic of such system
is that it shows fixed point and limit cycle attractors below and
above the threshold respectively. When the system resides at
fixed point, it reacts to an external perturbations in two different
ways depending upon the perturbation amplitude and when the
amplitude is small to cross the threshold, the system remains at
stable state and if large enough to cross, produces a large amplitude excursion in the output through limit cycle before settling
back to the fixed point. Application of the time dependent external stochastic perturbation produces coherent limit cycle oscillations depending upon the amplitude of the perturbation and
maximum coherency has been observed for the optimum noise
and coherency decreases for higher noise level.
The experiment has been carried out in an UJT relaxation oscillator (UJT-ROs) whose schematic circuit diagram has been
shown in Figure 1. For the present experiments, the emitter (E)
voltage (VE ) was modulated with the noise and the output was
recorded at two points E (VE O) and B1 (VB1 O) respectively.
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Figure 2: Emergence of coherence resonance for the output
recorded at emitter (VE O): The right panel shows the NV as
a function of noise amplitude for the experiments performed at
VE = 3.142V . Left panel: The time series of the output for (a)
low, (b) optimum and (c) high-level noise.
tion of noise amplitude D. It shows that the appearance of the
minimum in the NV curve is not always necessary for CR.
Direct modulation of the strong noise distorts the limit cycles particularly its peaks and as the excursion time is almost
independent of noise amplitude, the increase in NV in Fig 2(d)
at higher noise comes from the increase in the variation of the
inter-peak distances of the distorted limit cycle at high level of
noise but that does not happen in the later case [Fig 3(d)]. In this
case, the noise is blocked by UJT to be transmitted to the other
side.
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Figure 1: Circuit Description of the UJT Relaxation Oscillator
Figures 2(a)−2(c) (left panel) show the time series of the output recorded at output VE O of the oscillator for different noise
levels and Fig. 2 (d) is the experimental NV curve as a function of noise amplitude D. The appearance of minimum in NV
curve 2(d) indicates CR.
Figures 2(a)−2(c) (left panel) show the time series of the output recorded at output VE O of the oscillator for different noise
levels and Fig. 2 (d) is the experimental NV curve as a func∗ The authors are with P.P.D., Saha Institute of Nuclear Physics, 1/AF,
Bidhannagar, Kolkata-700064, email: jaman nonlinear@yahoo.co.in and
ansekariyengar@saha.ac.in
Figure 3: Emergence of coherence resonance for the output
recorded at base1 (VB1 O): The right panel shows the NV as
a function of noise amplitude for the experiments performed at
VE = 3.142V . Left panel: The time series of the output for (a)
low, (b) optimum and (c) high-level noise.
In conclusion, the effect of noise has been studied experimentally in UJT-ROs. We have also shown that depending upon
system properties, coherency may or may not be significantly
destroyed at high amplitude noise.