Example - 1

The Schmitt trigger circuit of fig. 1 uses 6V zener diodes with V_D = 0.7 V. if the threshold voltage V₁ is zero and the hysteresis is V_H = 0.2V. Calculate R₁ / R₂ and V_R.

Fig. 1

Solution:

The normal output voltage of Schmitt trigger circuit will be either +V_O or –V_O,
Where, V_O = V_Z + V_D
                     = 6.7 V

Let the output voltage be +V_O. The voltage V₁ can be obtained from the voltage divider circuit consisting of R₁ and R₂.

When v_in > V₁ then v_o = -V_O
Therefore, upper trigger point voltage will be given by,

Similarly, the lower trigger point voltage will be given by,

Therefore, the hysteresis voltage is

Since, the threshold voltage v₁ is zero,

Therefore,

Relaxation Oscillator:

With positive feedback it is also possible to build relaxation oscillator which produces rectangular wave. The circuit is shown in fig. 2.

Fig. 2

In this circuit a fraction R₂/ (R₁ +R₂) = b of the output is feedback to the non-inverting input terminal. The operation of the circuit can be explained as follows:

Assume that the output voltage is +V_sat. The capacitor will charge exponentially toward +V_sat. The feedback voltage is +bV_sat. When capacitor voltage exceeds +bV_sat the output switches from +V_sat to -V_sat. The feedback voltage becomes -V_sat and the output will remain –V_sat. Now the capacitor charges in the reverse direction. When capacitor voltage decreases below –bV_sat (more negative than –bV_sat ) the output again switches to +V_sat.This process continues and it produces a square wave. Under steady state conditions, the output voltage and capacitor voltage are shown in fig. 2. The frequency of the output can be obtained as follows:

The capacitor charges from -β V_sat to +β V_sat during time period T/2. The capacitor charging voltage expression is given by

This square wave generator is useful in the frequency range of 10Hz to 10KHz. At higher frequencies, the slew rate of the OPAMP limits the slope of the output square wave.

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