Mumbai University > COMPS > Sem 3 > Digital Logic Design and Analysis

Marks: 5 M

Year: Dec 2013

• An As table or free running multi vibrator is a square wave generator. The As table multi vibrator using op-amp is as below:

• The circuit above is a compactor circuit with a combination of Rf and C is used to integrate the output voltage $V_{out}$ and the voltage across the capacitor, C is applied to the inverting input terminal in place of the external signal.
• The compactor uses positive feedback that increases the gain of the amplifier. In a comparator circuit this offer two advantages. First, the high gain causes the op-amp’s output to switch very quickly from one state to an¬other and vice-versa. Second, the use of positive feedback gives the circuit hysteresis. In the op-amp square-wave generator circuit given in figure, the output voltage Vout is shunted to ground by two Zener diodes $Z_1$ and $Z_2$ connected back-to-back and is limited to either $V_{Z \ 2}$ or $–V_{Z \ 1}$. A fraction of the output is feedback to the non-inverting (+) input terminal. Combination of IL and C acting as a low-pass R-C circuit is used to integrate the output voltage $V_{out}$ and the capacitor voltage $V_O$ is applied to the inverting input terminal in place of external signal. The differential input voltage is given as $v_{in} = V_O- β V_{out}$
• When $V_{in}$ is positive, $V_{out} = – V_{z1}$ and when $V_{in}$ is negative $V_{out} = – V_{z2}$. Consider an instant of time when Vin< 0. At this instant Vout = + VZ 2 , and the voltage at the non-inverting (+) input terminal is $β V_{Z 2}$ , the capacitor C charges exponentially towards $V_{Z 2}$, with a time constant Rf C. The output voltage remains constant at $V_{Z 2}$ until $V_O$ equal $β V_{Z 2}$.

• When it happens, comparator output reverses to $– V_{Z 1}$. Now $V_O$ changes exponentially towards $– V_{Z 1}$ with the same time constant and again the output makes a transition from $– V_{Z 1}$ to + $–V_{Z 2}$. whenVOequals $-β V_{Z 1}$

  Let $V_{Z 1} = V_{Z 2}$

• The time period, T, of the output square wave is determined using the charging and discharging phenomena of the capacitor C. The voltage across the capacitor, $V_O$ when it is charging from $– B V_Z$ to + $V_Z$ is given by

  $V_O= [1-(1+β)]e^{-T/2τ}$

  Where $τ = Rf C$

• The waveforms of the capacitor voltage $v_c$ and output voltage $V_{out}$ (or $V_Z$) are shown in figure.

  When t = t/2

  $V_O= +β V_{Z \ or} + β V_{out}$

  Therefore $β V_Z = V_Z[1-(1+β)e^{-T/2τ}]$

  Or $e^{-T/2τ} = 1- β/1+ β$

  Or $T = 2τ log_e 1+β/1- β = 2R_f C log_e [1+ (2R_3/R_2)]$