Noise induced resonance effects in UJT relaxation oscillator by gfi17626

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									   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 ∗


   In this poster, the constructive role of noise, which is gener-                                                    1 .0
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                                                                                                                                                                                                                (c )

                                                                                                                      0 .0                                                                                                                                                                                                                  (d )
ally termed as coherence resonance (CR) has been studied in the                                                      -0 .5
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                                                                                                                                                                                                                                     0 .7
                                                                                                                                                                                                                                                                                                                              (c )


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threshold based system. The basic characteristic of such system                                                      -1 .5
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                                                                                                                                                                                                                                     0 .6

                                                                                                                                                                                                                                     0 .5
                                                                                                                                                                                                                                                             (a )




                                                                               A m p litu d e ( V )
is that it shows fixed point and limit cycle attractors below and                                                      0 .0
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                                                                                                                                                                                                                              N V
                                                                                                                                                                                                                                     0 .3
                                                                                                                     -0 .5
above the threshold respectively. When the system resides at                                                         -1 .0
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                                                                                                                                                                                                                                     0 .1
                                                                                                                       0 .5                                                                                                                                                             (b )
                                                                                                                                                                                                                (a )
fixed point, it reacts to an external perturbations in two different                                                   0 .0
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                                                                                                                                                                                                                                    -0 .1


ways depending upon the perturbation amplitude and when the                                                          -0 .5

                                                                                                                     -1 .0
                                                                                                                                                                                                                                                         0               2                  4               6
                                                                                                                                                                                                                                                                                    N o is e A m p litu d e ( V )
                                                                                                                                                                                                                                                                                                                          8           1 0




amplitude is small to cross the threshold, the system remains at                                                              0 .0           0 .5              1 .0                      1 .5            2 .0
                                                                                                                                                     T im e ( s e c )
stable state and if large enough to cross, produces a large ampli-
tude excursion in the output through limit cycle before settling
back to the fixed point. Application of the time dependent ex-                Figure 2: Emergence of coherence resonance for the output
ternal stochastic perturbation produces coherent limit cycle os-             recorded at emitter (VE O): The right panel shows the NV as
cillations depending upon the amplitude of the perturbation and              a function of noise amplitude for the experiments performed at
maximum coherency has been observed for the optimum noise                    VE = 3.142V . Left panel: The time series of the output for (a)
and coherency decreases for higher noise level.                              low, (b) optimum and (c) high-level noise.
   The experiment has been carried out in an UJT relaxation os-
cillator (UJT-ROs) whose schematic circuit diagram has been                  tion of noise amplitude D. It shows that the appearance of the
shown in Figure 1. For the present experiments, the emitter (E)              minimum in the NV curve is not always necessary for CR.
voltage (VE ) was modulated with the noise and the output was                   Direct modulation of the strong noise distorts the limit cy-
recorded at two points E (VE O) and B1 (VB1 O) respectively.                 cles 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.
                                                                                                                         1 .5                                                                                          (c )
                                                                                                                         1 .0
                                                                                                                                                                                                                                            0 .4 5
                                                                                                                         0 .5                                                                                                                                                                                                               (d )
                                                                                                                                                                                                                                            0 .4 0
                                                                                                                         0 .0
                                                                                                                                                                                                                                            0 .3 5            (a )
                                                                                                                         1 .5                                                                                          (b )
                                                                                              A m p litu d e ( V )




                                                                                                                                                                                                                                            0 .3 0

                                                                                                                         1 .0                                                                                                               0 .2 5

                                                                                                                         0 .5
                                                                                                                                                                                                                                    N V




                                                                                                                                                                                                                                            0 .2 0

                                                                                                                         0 .0                                                                                                               0 .1 5

                                                                                                                         1 .5                                                                                          (a )                 0 .1 0
                                                                                                                                                                                                                                                                                                                                (c )
                                                                                                                         1 .0                                                                                                               0 .0 5                           (b )

                                                                                                                                                                                                                                            0 .0 0
                                                                                                                         0 .5                                                                                                                        0               2                  4               6             8         1 0
                                                                                                                                                                                                                                                                                      N o is e A m p litu d e ( V )
                                                                                                                         0 .0

                                                                                                                                0 .0 0   0 .0 1     0 .0 2                      0 .0 3          0 .0 4            0 .0 5
                                                                                                                                                             T im e ( s e c )



Figure 1: Circuit Description of the UJT Relaxation Oscillator
                                                                             Figure 3: Emergence of coherence resonance for the output
   Figures 2(a)−2(c) (left panel) show the time series of the out-           recorded at base1 (VB1 O): The right panel shows the NV as
put recorded at output VE O of the oscillator for different noise            a function of noise amplitude for the experiments performed at
levels and Fig. 2 (d) is the experimental NV curve as a func-                VE = 3.142V . Left panel: The time series of the output for (a)
tion of noise amplitude D. The appearance of minimum in NV                   low, (b) optimum and (c) high-level noise.
curve 2(d) indicates CR.
   Figures 2(a)−2(c) (left panel) show the time series of the out-              In conclusion, the effect of noise has been studied experimen-
put recorded at output VE O of the oscillator for different noise            tally in UJT-ROs. We have also shown that depending upon
levels and Fig. 2 (d) is the experimental NV curve as a func-                system properties, coherency may or may not be significantly
   ∗ The authors are with P.P.D., Saha Institute of Nuclear Physics, 1/AF,
                                                                             destroyed at high amplitude noise.
Bidhannagar, Kolkata-700064, email: jaman nonlinear@yahoo.co.in and
ansekariyengar@saha.ac.in

								
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