## How to make an Astable or Free running Multi vibrator using 741 Op-Amp ?

The non-sinusoidal waveform generators are also called relaxation oscillators. The op-amp relaxation oscillator shown in figure is a square wave generator. In general, square waves are relatively easy to produce. Like the** UJT relaxation oscillator**, the circuit’s frequency of oscillation is dependent on the charge and discharge of a capacitor C through feedback resistor R,. The “heart” of the oscillator is an **inverting op-amp comparator **

The compaÂrator 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 anÂother 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 v_{out} 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 â€“V_{Z }_{1}. A fraction of the output is fedback 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_{c} is applied to the inverting input terminal in place of external signal. The differential input voltage is given as **v**_{in }**= v**_{c }**– Î² v**_{out}

When v_{in} is positive, v_{out} = – V_{z1} and when v_{in} is negative v_{out} = + V_{z }2. Consider an instant of time when v_{in} < 0. At this instant v_{out} = + V_{z 2} , and the voltage at the non-inverting (+) input terminal is Î² V_{z 2} , the capacitor C charges exponentially towards V_{z 2}, with a time constant R_{f} C. The output voltage remains constant at V_{z 2 }until v_{c} equal Î² V_{z 2}.

When it happens, comparator output reverses to – V_{z} _{1}. Now v_{c} changes exponentially towards -V_{z1} with the same time constant and again the output makes a transition from -V_{z1 }to + V_{z 2. }when v_{c } equals -Î²V_{z 1}

**Let V**_{z1}** = 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_{c} when it is charging from – B V_{z} to + V_{z} is given by

**V**_{c }**= [1-(1+Î²)]e**^{-T/2Ï„}

Where Ï„ = R_{f}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**_{c }**= +Î² V**_{z or }**+ Î² V**_{out}

Therefore Î² V_{z} = V_{z }[1-(1+Î²)e^{-T/2Ï„}]

**Or e**^{-T/2Ï„ }**= 1- Î²/1+ Î²**

**Or T = 2Ï„ log**_{e }**1+Î²/1- Î² = 2R**_{f }**C log**_{e }**[1+ (2R**_{3}**/R**_{2}**)]**

** The frequency, f = 1/T **, of the square-wave is independent of output voltage V

_{out}.

**. The output remains in one state for time T**

*This circuit is also known as free-running or astable multivibrator because it has two quasi-stable states*_{1}and then makes an abrupt transition to the second state and reÂmains in that state for time T

_{2}. The cycle repeats itself after time

**T = (T**

_{1}

**+ T**

_{2}

**)**where T is the time period of the square-wave.

The op-amp square-wave generator is useful in the frequency range of about 10 Hz -10 kHz. At higher frequencies, the op-amp’s slew rate limits the slope of the output square wave. The symmetry of the output waveform depends on the matching of two Zener diodes Z_{1} and Z_{2}. The unsymmetrical square-wave (T_{1} not equal to t_{2}) can be had by using different constants for charging the capacitor C to +V_{out} and -V_{out}

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