Astable Multivibrator using Op-amp

Astable Multivibrator using Op-amp.

In this section we are going to study astable multivibrator operation using op-amp. Fig. 3.15.1 shows astable multivibrator circuit using op-amp. It looks like a comparator with Hysteresis (Schmitt trigger), except that the input voltage is replaced by a capacitor. The circuit has a time dependent elements such as resistance and capacitor to set the frequency of oscillation.

As shown in the Fig. 3.15.1 the comparator and positive feedback resistors R1 and R 2 form an inverting Schmitt trigger. 

When V_o is at +V_sat, the feedback voltage is called the upper threshold voltage V_UT and is given as

V_UT = R₁. (+V_sat) / R₁ + R₂  ... (3.15.1)

When V_o is at -V_sat, the feedback voltage is called the lower-threshold voltage V_LT and is given as

V_LT  = R₁. (- V_sat) /           R₁ + R₂  ... (3.15.2)

When power is turn ON, V_o automatically swings either to +V_sat or to -V_sat  since these are the only stable states allowed by the Schmitt trigger. Assume it swings to +V_sat. With V_o = +V_sat we have V_p = V_UT nnd capacitor starts charging towards +Vsat through the feedback path provided by the resistor R_f to the inverting (-) input. This is illustrated in Fig. 3.15.2 (a). As long as the capacitor voltage V_C is less than V_UT the output voltage remains at +V_sat.

As soon as V_C charges to a value slightly greater than V_UT / the (-) input goes positive with respect to the (+) input. This switches the output voltage from +V_sat to -V_sat and we have     V_p = V_LT , which is negative with respect to ground. As V_o switches to -Vsat, capacitor starts discharging via Rf, as shown in the Fig. 3.15.2 (b).

The current I ^- discharges capacitor to 0 V and recharges capacitor to Finally V_C V_LT. When V_C becomes slightly more negative than the feedback voltage V_LT, output voltage V_o switches back to +V_sat. As a result, the condition in Fig. 3.15.2 (a) is reestablished except that capacitor now has a initial charge equal to V_LT. The capacitor will discharge from V_LT to 0 V and then recharge to V_UT, and the process is repeating. Once the initial cycle is completed, the waveforms become periodic, as shown in the Fig. 3.15.2(c).

1. Frequency of Oscillation

The frequency of oscillation is determined by the time it takes the capacitor to charge from V_UT to V_LT and vice versa. The voltage across the capacitor as a function of time is given as

V_C(t) = V_max + (V_initial - V_max)e^(-t/T)       ... (3.15.3)

Where V_C(t) is the instantaneous voltage across the capacitor.

V_initial is the initial voltage

V_max is the voltage toward which the capacitor is charging.

Let us consider the charging of capacitor from V_LT to V_UT, where V_LT is the initial voltage, V_UT the instantaneous voltage and +V_sat is the maximum voltage. At t = T₁, voltage across capacitor reaches VUT and therefore equation (3.15.3) becomes

The time taken by capacitor to charge from V_UT to V_LT is same as time required for charging capacitor from V_LT to V_UT. Therefore, total time required for one oscillation is given as

The frequency of oscillation can be determined as f_o = 1/T, where T represents the time required for one oscillation.

Substituting the values of T we get,

Substituting the values of V_UT and V_LT we get,

2. Non-symmetrical Square Wave Generation

The astable multivibrator can be used to obtain non-symmetrical square wave by modifying the circuit as shown in the Fig. 3.15.3.

When V_o = + V_sat, the C will charge through R₃ due to forward biasing of D₁. When V_o = - V_sat, the C will discharge R₄ due to forward biasing of D₂. Selecting different values of R₃ and R₄, charging and discharging time of C can be varied and hence nonsymmetrical square wave can be obtained.

Variable duty cycle : To vary duty cycle from say d₁ % and d₂ % then divide R₃ + R₄ resistance in the ratio of the variable duty cycle required.

For example if it is to be varied from 30 % to 70 % then divide R₃ + R₄ in the ratio 3 : 4 : 3 a shown in the Fig. 3.15.4.

For varying duty cycle from 10 % to 90 %, R₃ + R₄ to be divided in the ratio 1:8:1 and so on.

Example 3.15.1 In the square wave oscillator shown, calculate the frequency of oscillations if R₂ = 10 kΩ, R₁ = 8.6 kΩ, R_f = 100 and C = 0.01 µF.

Solution : This is astable multivibrator using op-amp. Its time period is given by,

Review Question

1. Draw the circuit of an astable multivibrator using operational amplifier and derive an expression for its frequency of oscillation.