Square Wave Generator or Astable Multivibrator

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Astable Multivibrator is also called as Free running multivibrator or relaxation oscillator with no stable states. It is a square wave generator and has two unstable states.It oscillates back and forth between these two states when the circuit is given power supply.

Circuit Diagram

Astable Multivibrator

Astable Multivibrator









Design equations

The Time period of Square wave 

     T = 2*R*C*ln((1+β)/(1-β))

Assume R1=R2 then T= R*C*ln(3), in which the values of R and C can have any combination based on availability of capacitor and resistor but should satisfy the time period equation.

Circuit analysis

The output of opamp is +Vccif V2 >> V1 and is –Vcc if V2<< V1.Assume that the output initially is at positive saturation value of +Vcc. By voltage divider rule the voltage at non inverting terminal of opamp is Vcc*R1/(R2+R1). The capacitor starts charging through R with time constant R*C and the voltage across capacitor is given by Vc = Vcc*(1-exp(-R*C*t)). When the voltage across the capacitor is just more than Vcc*R1/(R2+R1), at that instant the output of opamp changes to –Vcc .Now the Vc = -Vcc*R1/(R2+R1),the capacitor has to discharge through R till it reaches to a value less than          -Vcc* R1/(R2+R1). At that instant when V1 << -Vcc* R1/(R2+R1),  output will be +Vcc. During the charging and discharging time voltage across the capacitor will be Vc=-Vcc*exp(-R*C*t)). Hence the voltage across capacitor switches between -Vcc* R1/(R2+R1) and +Vcc* R1/(R2+R1) and output switches between +Vcc and -Vcc. The voltage acroos the capacitor during charging time is given by Vc = Vcc*(1-(1+β)exp(-t/(R*C)) where β = R1/(R2+R1).

Let us assume that the voltage across capacitor at t= 0 s is equal to -Vcc..At = T/2  output transits from -Vcc to +Vcc.

Hence at t=T/2 Vc=β*Vcc, substituting in Vc = Vcc*(1-(1+β)exp(-t/(R*C)) we get
                                   β*Vcc= Vcc*(1-(1+β)exp(-T/(2*R*C)))

                                               T = 2*R*C*ln((1+β)/(1-β))

Hence the frequency of oscillation of square wave is f=1/T.


This circuit can be used for generating square waves with frequencies of the Kilo hertz order. The slew rate of opamp poses a limitation in generating still higher frequency square waves.

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