SR in the circuits with trigger and cubic nonlinearity
M.V.Davidovich
M.V. Davidovich
Saratov Technical University,
Saratov, Russia
The stochastic resonance (SR) in the circuits with nonlinear
element (NE) which represented as ideal trigger or element with
cubic current per voltage dependence have investigated. All circuits
was represented as contour with series resistor R, nonlinear element
(NE) and voltage source which was the additive signal S(t) and noise
N(t) influence. The trigger NE was modeled by system of inequalities
and conditions for threshold of switching 
and total voltage
S(t) + N(t). For cubic NE we have the following algebraic equation:
where 
and 
are the current and voltage on the working point,
e is the constant voltage to provide this point thus 
, 
is the module of negative differetial resistance for curve I(U) and
is the voltage distance between two extremal points on the curve.
There is the simple signal amplification at the point when the
noise is absent and 
for cubic NE and no output signal for
trigger type NE. When the big noise is present then there are
switchings between two stable states for both cases which can cause
the amplification of the small regular signal ( 
).
This amplification and signal to noise ratio (SNR) increase when
stochastic resonance (SR) occur or when the frequency of switching
by noise is equal to the main frequency of the modulated signal
[1]. In this work the amplification of amplitude and frequency
modulated signals have explored for above mentioned circuits. As (1)
have zero relaxation time, the single Kirhgoff procedure have been
developed to solve it. For each time realization of the solutions
the spectrum have been computed by use the fast Fourier integral
tramsform based upon pulse-constant time discreditation of thise
solution. The such transform for solitary pulse between moments 
and 
with amplitude V and duration 
is
To compute the SNR the stochastic averaging by use the several tens of the spectral realizations have used. The investigations show the strong (in order of several tens of decibel) wide band (about 20%) signal and noise amplification. The SNR increase when SR occur.