A real relay exhibits a dead zone as shown in the figure that follows:

               

The corresponding analytic expression is:

y\left ( t \right )=\left\{\begin{matrix} -\alpha ;\, x\left ( t \right ) \textless{} -\beta \\ 0;\, -\beta \, \textless{} x\left ( t \right )\, \textless{} \, \beta \\\alpha;\, \beta \, \textless{}\, x\left ( t \right ) \end{matrix}\right.

It can easily be seen that the value will be \alpha to the right of \beta and - \alpha to the right of - \beta .

The simulation is performed using as the input function a sinusoid, x(t)=A\, sen(\omega \, t) , where \omega = 2 \pi f .

It is necessary to choose A , f and both the initial and the final times of the simulation.

A = , 0 \textless{} A \leq 10
   f = Hz, 0 \textless{} \omega \leq 50


\:Inicial \:time = s, \: \geq 0.

\:Final \:time = s, \: \leq 50.

For the relay with dead zone, it is necessary to choose the values of the dead zone \beta and the fixed value \alpha .

\alpha = 0 \: \textless{} \alpha \: \leq 5.

\beta = 0 \: \textless{} \: \beta \: \leq 10.