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

Square Wave Generator using Op-Amp

jojo

September - 21 - 2009

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op amp astable multi vibrator

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 compa­rator 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 an­other 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 Z₁ and Z₂ connected back-to-back and is limited to either  V_{Z 2} or –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 - β 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  β 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 β 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 -βV_{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+β)]e^-T/2τ

Where τ = R_fC

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 = +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+ (2R₃/R₂)]

The frequency, f = 1/T , of the square-wave is independent of output voltage V_out. This circuit is also known as free-running or astable multivibrator because it has two quasi-stable states. The output remains in one state for time T₁ and then makes an abrupt transition to the second state and re­mains in that state for time T₂. The cycle repeats itself after time T = (T₁ + T₂) 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 Z₁ and Z₂. The unsymmetrical square-wave (T₁ not equal to t₂) can be had by using different constants for charging the capacitor C to +V_out and -V_out