Op-Amp can be used in variety of application such as signal processing and waveform generator. We can classify waveform generator in two broad classes- sinusoidal waveform generator and non-sinusoidal waveform generator(relaxation oscillator). Relaxation oscillator produce waveform like sawtooth, triangle and square wave. A family of oscillator called Multivibrator oscillators are relaxation oscillators which has used for generating timing signal in circuits. Again there are two classes of multivibrator called monstable multivibrator and astable multivibrator. In this tutorial astable multivibrator using op-amp is illustrated. A astable multivibrator has two unstable state and the circuit oscillates between these two states and thereby generates square waves. Because of the oscillation between the two unstable states, the astable multivibrators are also called free-running multivibrator. Thus here we will design a free running op-amp multivibrator.
Op-Amp Multivibrator Circuit Diagram
The following shows circuit diagram of a free running Op-Amp Multivibrator.
The circuit has a timing circuit \(R_1\) and \(C_1\) which sets the oscillation frequency of the output square wave signal(\(V_o\)). It has a positive feedback circuit made up of the resistor divider circuit \(R_2\) and \(R_3\). The voltage feedback at the positive terminal of the op-amp is \(V_p\).
Operation of Op-Amp Multivibrator
When power is applied to the circuit, the output signal \(V_o\) either swings to \(+V_{sat}\) or \(-V_{sat}\) as these are the only two allowed stables states. Let say that the output signal \(V_o\) swings towards \(+V_{sat}\) of the op-amp. In this case, current from the output flows into the \(R_1\) resistors into the capacitor \(C_1\) and therefore the capacitor starts charging towards \(+V_{sat}\). But it cannot reach \(+V_{sat}\), instead it charges upto a upper threshold voltage limit \(V_{UT}\). The \(V_{UT}\) is the fraction of \(V_o\) feedback voltage going into the positive terminal of the op-amp from the voltage divider circuit. The waveform graph shown below shows the output signal \(V_o\), the charging voltage \(V_c\) and the \(+V_{UT}\) voltage level.
When the capacitor voltage \(V_c\) reaches a value slightly greater the \(+V_{UT}\), the magnitude of the signal \(V_c\) at the inverting terminal becomes greater the signal \(V_p=+V_{UT}\) at the non-inverting terminal. Since the op-amp is operates as a comparator which compares the voltages magnitude at the inverting and non-inverting terminal, the output signal \(V_o\) switches from \(+V_{sat}\) to \(-V_{sat}\). Now this also changes signal amplitude \(V_p\) polarity going into the non-inverting terminal from \(+V_{UT}\) to \(+V_{LT}\). Because of the voltage difference developed by this switching, the capacitor starts to discharge via the \(R_1\) resistor. The discharging continues towards the \(V_{LT}\). The \(V_{LT}\) is the lower magnitude of the signal \(V_p\) going into non-inverting terminal of the op-amp. When the voltage \(V_c\) becomes slightly more negative than the feedback signal \(V_p=V_{LT}\), then the output switches back to \(+V_{sat}\). Then the process repeats generating a square wave with amplitude between \(+V_{sat}\) and \(-V_{sat}\).
Upper & Lower feedback voltages
The upper feedback voltage(\(V_{UT}\)) is the feedback voltage(\(V_p\)) from the voltage divider circuit going into the non-inverting terminal of the op-amp during the output is \(+V_{sat}\) and hence,
\(V_{UT}=\frac{R_2(+V_{sat})}{R_2+R_3}\)
Let, \(\beta=\frac{R_2}{R_2+R_3}\)
And so we can rewrite,
\(V_{UT}=\beta(+V_{sat})\)
Similarly, the lower feedback voltage (\(V_{LT}\)) is the feedback voltage(\(V_p\)) from the voltage divider circuit going into the non-inverting terminal of the op-amp when the output is \(-V_{sat}\) and therefore,
\(V_{UT}=\frac{R_2(-V_{sat})}{R_2+R_3}\)
Using \(\beta\) as defined above, we can rewrite,
\(V_{LT}=\beta(-V_{sat})\)
Frequency of Oscillation
By derivation, the frequency of oscillation of op-amp astable multivibrator is,
\(f=\frac{1}{2R_1C_1 ln\frac{+V_{sat}-V_{LT}}{+V_{sat}-V_{UT}}}\)
Using the relation, \(V_{UT}=\beta(+V_{sat})\) and \(V_{LT}=\beta(-V_{sat})\) we can rewrite the frequency of oscillation as,
\(f=\frac{1}{2R_1C_1 ln(\frac{1+\beta}{1-\beta})}\)
And the time period for one oscillation is,
\(T=\frac{1}{f}\)
Substituting f,
or, \(T=2R_1C_1 ln(\frac{1+\beta}{1-\beta})\)
where, \(\beta=\frac{R_2}{R_2+R_3}\)
From the above frequency equation we can see that the frequency is set by the capacitor and the 3 resistors.
Single Supply Op-Amp Multivibrator
Two supply Op-Amp Multivibrator circuit was illustrated above but one may not have two supply voltages and many op-amp now supports single supply interface. In such case, one can use the following single supply op-amp multivibrator circuit diagram.
Op-Amp Multivibrator Design Example
In this op-amp multivibrator design example we will TL072 op-amp which supports single power supply interface. One can equivalently use LM358N op-amp. For the two biasing resistors \(R_4\) and \(R_5\) we will use 10KOhm resistor. For achieving output square wave with 50% duty cycle we will use \(R_3\) equal to biasing resistors \(R_4\) and \(R_5\.
So, \(R_3\)=\(R_5\)=\(R_4\)=10KOhm and let \(R_1\)=100KOhm and \(C_1\)=10nF.
The \(\beta\) can be calculated as,
\(\beta=\frac{R_2}{R_2+R_3}=\frac{0}{0+10K\Omega}=0\)
Using the frequency equation of the op-amp multivibrator above, we have,
\(f=\frac{1}{2R_1C_1 ln(\frac{1+\beta}{1-\beta})}\)
that is, \(f=\frac{1}{2R_1C_1}\)
\(f=\frac{1}{2\times 100K\Omega \times 10nF}\)
calculating we get, \(f=500Hz\)
The time period is,
\(T=\frac{1}{f}=\frac{1}{500Hz}=2ms\)
Single supply op-amp multivibrator with the calculated component value is shown below.
Op-Amp Multivibrator on breadboard
The following picture shows single supply op-amp multivibrator implemented using TL072 op-amp on breadboard.
The following video demonstrates TL072 op-amp based free running multivibrator on breadboard which generates square wave signal of 500Hz.
Simulation of Free-Running Op-Amp Multivibrator
Below is video that shows a simulation of how the free running TL072 op-amp Multivibrator works.
So in this tutorial it was explained how a free running op-amp multivibrator works and how it can be built and tested on breadboard. For the construction of the oscillator op amp we used TL072 op-amp but similar op-amp like LM358 can also be used. The op-amp multivibrator generated a square wave due to the charging and discharging of capacitor which is connected to the inverting input of the operational amplifier. Such signal can be used for generating timing signal in electronics circuit.
