**Astable multivibrator**
is a type of multivibrator circuit that generates a continuous square
wave output signal without the need for an external trigger or input
signal. It is also known as a **free-running multivibrator** because
it does not require any external input to start or stop the
oscillations. One of the most commonly used methods to implement an
astable multivibrator is by using an operational amplifier (op-amp),
which is a versatile and widely used electronic component in various
applications. In this blog post, we will discuss the concept of astable
multivibrator using an op-amp and its applications.

### Introduction to Astable Multivibrator

An astable multivibrator is a type of electronic circuit that generates a continuous square wave output signal with a fixed frequency and adjustable duty cycle. The duty cycle is the ratio of the time the output is high to the time the output is low, and it determines the width of the square wave pulses. Astable multivibrators are used in a wide range of applications, such as timing circuits, frequency generators, pulse width modulators, and clock generators.

#### Op-Amp as a Building Block

An operational amplifier, commonly referred to as an op-amp, is a high-gain, voltage amplifying device that is widely used in electronic circuits for various purposes, such as amplification, filtering, and signal conditioning. Op-amps are versatile components that can be configured in different ways to perform different functions. They have two input terminals, an inverting (-) terminal and a non-inverting (+) terminal, and an output terminal. Op-amps can operate in different modes, such as inverting amplifier, non-inverting amplifier, voltage follower, integrator, differentiator, and astable multivibrator, among others.

### Astable Multivibrator using Op-Amp

The
basic configuration of an astable multivibrator using an op-amp
consists of time dependent capacitor(C), resistor(R) and feedback
resistors(R1,R2) as shown below.

The op-amp is connected as a comparator with two positive feedback resistors R1 and R2 which forms an inverting schmitt trigger. We have a capacitor C and negative feedback resistor RF connected as voltage divider on the inverting terminal. The resistor RF and capacitor C determine the frequency and duty cycle of the output square wave. When the circuit is powered up, the op-amp starts to oscillate, generating a continuous square wave output signal. The capacitor is charged and discharged periodically and therefore the output signal switches between high and low levels at a frequency determined by the time constants of the resistor RF and capacitor C.

The equation for frequency of oscillation for op-amp astable multivibrator is,

\(
f_o = \frac{1}{2R_F C ln(\frac{-V_{sat}-V_{LT}}{+V_{sat}-V_{UT}})}
\) ---->(1)

\(
V_{UT}=\frac{R_1 (+V_{sat})}{R_1+R_2}
\) ------->(2)

\(
V_{LT}=\frac{-R_1 (-V_{sat})}{R_1+R_2}
\) ----------->(3)

where,

\(V_{UT}\) and \(V_{UT}\) are upper and lower threshold voltages.#### Working Principle of Astable Multivibrator

The working principle of an astable multivibrator using an op-amp can be explained as follows:

**Initial State**

When
the circuit is powered up, the output of the op-amp automatically
switches to one of the saturation levels, either high \(+V_{sat}\) or
low \(-V_{sat}\) , depending on the initial conditions. This is because
these are the only two stable state allowed by the Schmitt trigger.

**Capacitor Charging**

Let's assume that the output is initially at the high level \(+V_{sat}\). The capacitor connected to the inverting terminal starts charging through the resistor RF as illustrated below.

The output voltage \(V_o\) is and remains \(+V_{sat}\) as long as \(V_c < V_{UT}\).

**Op-Amp Saturates at Upper Threshold Voltage**

The capacitor cannot be charged indefinitely. When capacitor voltage \(V_c\) at the inverting terminal reaches and gets slightly higher than the upper threshold voltage \(V_{UT}\) at the non-inverting terminal the voltage at the non-inverting becomes higher than at the inverting terminal. Therefore the op-amp eventually reaches its threshold level, and it switches its output to the low level.

**Capacitor Discharging**

The output switches to \(-V_{sat}\) and the voltage at the inverting terminal starts decreasing. The capacitor starts discharging through the resistor RF, and the voltage at the inverting terminal starts increasing. The output voltage \(V_o\) becomes and remains \(-V_{sat}\) as long as \(V_c > -V_{LT}\). This is illustrated by the picture below.

**Op-Amp Saturates at Lower Threshold Voltage**

The voltage at the inverting terminal continuous to increase until it reaches the lower threshold level \(V_{LT}\). When the capacitor voltage at the inverting terminal becomes slightly more negative than the feedback voltage \(V_{LT}\) at the non-inverting terminal then the op-amp saturates being a comparator it switches its output back\(V_o\) to the high level \(+V_{sat}\).

The capacitor starts charging again through the resistor R1, and the cycle repeats.

**Continuous Oscillations**

The cycle of charging and discharging of the capacitors continues indefinitely, generating a continuous square wave output signal.

#### Designing Operational Amplifier Astable Multivibrator

To design op-amp astable multivibrator we need to use the above equations(1), (2) and (3). For this we need the value of DC power supply, the desired frequency of the oscillator and provide values for resistors R1 and R2. Then we can set the value for capacitor C and solve for frequency.

Let Vcc=5V and Vee=-5V, R1=R2=10kOhm and capacitor C=10nF. Let the frequency be 10kHz. Then solving the above equation for op-amp astable multivibrator we get RF=4.55kOhm. The component value for given frequency of frequency for given component values can also be computed using the online op-amp astable multivibrator calculator.

The following video shows the circuit designed with the calculated values.

The
above video also shows how the op-amp astable multivibrator circuit can
be designed with single supply. The astable multivibrator here is
operated using single supply and
this two resistors R4 and R5 as shown below can be used to bias the
non-inverting terminal at the mid-way of the dc power supply, is Vcc/2
which here for power supply of +5V is 2.5V. See single supply op-amp tutorial to learn how this works.

**References**:

[1] Monostable Multivibrator using Transistors

[2] 555 Timer as Astable Multivibrator