The *Operational Amplifier* or **Op-amp** for short, is a very versatile device that can be used in a variety of different electronic circuits and applications, from voltage amplifiers, to filters, to signal conditioners. But one very simple and extremely useful op-amp circuit based around any general purpose operational amplifier is the Astable Op-amp Multivibrator.

We saw in our tutorials about Sequential Logic that multivibrator circuits can be constructed using transistors, logic gates or from dedicated chips such as the NE555 timer. We also saw that the astable multivibrator switches continuously between its two unstable states without the need for any external triggering.

But the problem with using these components to produce an astable multivibrator circuit is that for transistor based astables, many additional components are required, digital astables can generally only be used in digital circuits, and the use of a 555 timer may not always give us a symmetrical output without additional biasing components. The *Op-amp Multivibrator* circuit however, can provide us with a good rectangular wave signal with the use of just four components, three resistors and a timing capacitor.

The **Op-amp Multivibrator** is an astable oscillator circuit that generates a rectangular output waveform using an RC timing network connected to the inverting input of the operational amplifier and a voltage divider network connected to the other non-inverting input.

Unlike the monostable or bistable, the astable multivibrator has two states, neither of which are stable as it is constantly switching between these two states with the time spent in each state controlled by the charging or discharging of the capacitor through a resistor.

In the op-amp multivibrator circuit the op-amp works as an analogue comparator. An op-amp comparator compares the voltages on its two inputs and gives a positive or negative output depending on whether the input is greater or less than some reference value, V_{REF}.

However, because the open-loop op-amp comparator is very sensitive to the voltage changes on its inputs, the output can switch uncontrollably between its positive, +V(sat) and negative, -V(sat) supply rails whenever the input voltage being measured is near to the reference voltage, V_{REF}.

To eliminate any erratic or uncontrolled switching operations, the op-amp used in the multivibrator circuit is configured as a closed-loop *Schmitt Trigger* circuit. Consider the circuit below.

### Op-amp Schmitt Comparator

The op-amp comparator circuit above is configured as a Schmitt trigger that uses positive feedback provided by resistors R1 and R2 to generate hysteresis. As this resistive network is connected between the amplifiers output and non-inverting (+) input, when Vout is saturated at the positive supply rail, a positive voltage is applied to the op-amps non-inverting input. Likewise, when Vout is saturated to the negative supply rail, a negative voltage is applied to the op-amps non-inverting input.

As the two resistors are configured across the op-amps output as a voltage divider network, the reference voltage, Vref will therefore be dependant upon the fraction of output voltage fed back to the non-inverting input. This feedback fraction, β is given as:

Where +V(sat) is the positive op-amp DC saturation voltage and -V(sat) is the negative op-amp DC saturation voltage.

Then we can see that the positive or upper reference voltage, +Vref (i.e. the maximum positive value for the voltage at the inverting input) is given as: +Vref = +V(sat)β while the negative or lower reference voltage (i.e. the maximum negative value for the voltage at the inverting input) is given as: -Vref = -V(sat)β.

So if Vin exceeds +Vref, the op-amp switches state and the output voltage drops to its negative DC saturation voltage. Likewise when the input voltage falls below -Vref, the op-amp switches state once again and the output voltage will switch from the negative saturation voltage back to the positive DC saturation voltage. The amount of built-in hysteresis given by the Schmitt comparator as it switches between the two saturation voltages is defined by the difference between the two trigger reference voltages as: V_{HYSTERESIS} = +Vref – (-Vref).

## Sinusoidal to Rectangular Conversion

One of the many uses of a Schmitt trigger comparator, other than as an op-amp multivibrator, is that we can use it to convert any periodic sinusoidal waveform into a rectangular waveform providing the value of the sinusoid is greater than the voltage reference point.

In fact the Schmitt comparator will always produce a rectangular output waveform independent of the input signal waveform. In other words, the voltage input does not have to be a sinusoid, it could be any wave shape or complex waveform. Consider the circuit below.

### Sinusoidal to Rectangular Converter

As the input waveform will be periodical and have an amplitude sufficiently greater than its reference voltage, Vref, the output rectangular waveform will always have the same period, T and therefore frequency, ƒ as the input waveform.

By replacing either resistor R1 or R2 with a potentiometer we could adjust the feedback fraction, β and therefore the reference voltage value at the non-inverting input to cause the op-amp to change state anywhere from zero to 90^{o} of each half cycle so long as the reference voltage, Vref remained below the maximum amplitude of the input signal.

## Op-amp Multivibrator

We can take this idea of converting a periodic waveform into a rectangular output one step further by replacing the sinusoidal input with an RC timing circuit connected across the op-amps output. This time, instead of a sinusoidal waveform being used to trigger the op-amp, we can use the capacitors charging voltage, Vc to change the output state of the op-amp as shown.

### Op-amp Multivibrator Circuit

So how does it work. Firstly lets assume that the capacitor is fully discharged and the output of the op-amp is saturated at the positive supply rail. The capacitor, C starts to charge up from the output voltage, Vout through resistor, R at a rate determined by their RC time constant.

We know from our tutorials about RC circuits that the capacitor wants to charge up fully to the value of Vout (which is +V(sat)) within five time constants. However, as soon as the capacitors charging voltage at the op-amps inverting (-) terminal is equal to or greater than the voltage at the non-inverting terminal (the op-amps output voltage fraction divided between resistors R1 and R2), the output will change state and be driven to the opposing negative supply rail.

But the capacitor, which has been happily charging towards the positive supply rail (+V(sat)), now sees a negative voltage, -V(sat) across its plates. This sudden reversal of the output voltage causes the capacitor to discharge toward the new value of Vout at a rate dictated again by their RC time constant.

### Op-amp Multivibrator Voltages

Once the op-amps inverting terminal reaches the new negative reference voltage, -Vref at the non-inverting terminal, the op-amp once again changes state and the output is driven to the opposing supply rail voltage, +V(sat). The capacitor now see’s a positive voltage across its plates and the charging cycle begins again. Thus, the capacitor is constantly charging and discharging creating an astable op-amp multivibrator output.

The period of the output waveform is determined by the RC time constant of the two timing components and the feedback ratio established by the R1, R2 voltage divider network which sets the reference voltage level. If the positive and negative values of the amplifiers saturation voltage have the same magnitude, then t1 = t2 and the expression to give the period of oscillation becomes:

Where: R is Resistance, C is Capacitance, ln( ) is the Natural Logarithm of the feedback fraction, T is periodic time in seconds, and ƒ is oscillation Frequency in Hz.

Then we can see from the above equation that the frequency of oscillation for an **Op-amp Multivibrator** circuit not only depends upon the RC time constant but also upon the feedback fraction. However, if we used resistor values that gave a feedback fraction of **0.462**, (**β = 0.462**), then the frequency of oscillation of the circuit would be equal to just 1/2RC as shown because the linear log term becomes equal to one.

## Op-amp Multivibrator Example No1

An **op-amp multivibrator circuit** is constructed using the following components. R1 = 35kΩ, R2 = 30kΩ, R = 50kΩ and C = 0.01uF. Calculate the circuits frequency of oscillation.

Then the frequency of oscillation is calculated as 1kHz. When β = 0.462, this frequency can be calculated directly as: ƒ = 1/2RC. Also when the two feedback resistors are the same, that is R1 = R2, the feedback fraction is equal to 3 and the frequency of oscillation becomes: ƒ = 1/2.2RC.

We can take this op-amp multivibrator circuit one step further by replacing one of the feedback resistors with a potentiometer to produce a variable frequency op-amp multivibrator as shown.

### Variable Op-amp Multivibrator

By adjusting the central potentiometer between β1 and β2 the output frequency will change by the following amounts.

Potentiometer wiper at β1

Potentiometer wiper at β2

Then in this simple example we can produce an operational amplifier multivibrator circuit that can produce a variable output rectangular waveform from 100Hz to 1.2kHz, or any frequency range we require just by changing the RC component values.

We have seen above that an **Op-amp Multivibrator** circuit can be constructed using a standard operational amplifier, such as the 741, and a few additional components. These voltage controlled non-sinusoidal relaxation oscillators are generally limited to a few hundred kilo-hertz (kHz) because the op-amp does not have the required bandwidth, but nevertheless they still make excellent oscillators.