# LM741 phase shift oscillator design

The LM741 is a popular operational amplifier (op-amp) that is commonly used in electronic circuit design. One of the applications of the LM741 op-amp is in the design of phase shift oscillators. In this blog post, we will discuss the design of a phase shift oscillator using the LM741 op-amp.

A phase shift oscillator is a type of oscillator that generates a sine wave output by using a feedback network. The feedback network produces a 180-degree phase shift at the frequency of oscillation, and the op-amp provides the necessary gain to sustain oscillation. The feedback network can be constructed using passive components- resistors, capacitor and inductors. For example in the LM741 op amp oscillator circuit we use inductor(L) and capacitor(C) as feedback network. If the phase shift feedback network is build with resistor(R) and capacitors(C) then such oscillator is called RC phase shift oscillator. In this tutorial we will show how to design RC phase shift oscillator with LM741 as the amplifying component required in the oscillator design.

Below is the schematic diagram of the LM741 phase shift oscillator:

The circuit consist of three equal capacitors(C=C1=C2=C3) and three equal resistors(R=R1=R2=R3). These three RC filter produces a net 180 degree phase difference between the operational amplifier output and operational amplifier input at inverting terminal. The LM741 inverting amplifier circuit itself produces 180 degree phase shift between its input and output. Thus around the loop there is 360 degree phase shift. The RC feedback network produces energy loss of the signal while traveling through it. To compensate the energy loss, the op amp provides the necessary gain using the feedback resistor RF.

Here are the steps to design a phase shift oscillator using the LM741 op-amp:

• Frequency of oscillation:

The frequency of oscillation is determined by the feedback network of resistors and capacitors. The frequency can be calculated using the following formula:

f = 1 / (2Ï€RC√6)    ------------>(1)

Where f is the frequency of oscillation, R is the resistance of each feedback resistor, and C is the capacitance of each feedback capacitor.

In this example, we will consider frequency of oscillation(f) of 100KHz.

• Choose the values of R and C:
The values of R and C can be chosen to produce the desired frequency of oscillation. The values of R and C should be chosen to satisfy the following conditions:

1. The feedback network should produce a 180-degree phase shift at the frequency of oscillation.

2. The op-amp should have sufficient gain to sustain oscillation.

From equation(1), we can solve either for R or C. Since it is easier to pick resistor value than capacitor value because capacitor comes in less standard values, we will solve for resistor R. Thus from (1) the resistor value can be calculated by using the following equation,

R = 1 / (2Ï€fC√6)    ------------>(2)

Let us choose C=10nF and since f=100KHz we have,

R =  1 / (2Ï€*100KHz*10nF*√6)

That is, R=65Ohm

• Calculate the required gain:

The gain required for sustained oscillation can be calculated using the following formula:

A = - Rf / R   ----->(3)

Where A is the required gain, R is the resistance of each feedback resistor, and Rf is the resistance of the feedback resistor between the output and the non-inverting input of the op-amp. The equation(3) is because the operational amplifier is in the inverting configuration.

• Choose the value of Rf:
The value of Rf can be chosen to produce the required gain. The value of Rf should be chosen to satisfy the following condition:

- The gain should be greater than or equal to the required gain for sustained oscillation.

For RC phase shift oscillator it can be deduced that the feedback fraction is 1/29 and from Barkhausen criteria for sustained oscillation we have,

$$A \beta \ge 1$$    ----->(4)

Therefore, since $$\beta = \frac{1}{29}$$

$$A \ge 29$$

Using (3) we can calculate the value of Rf,

$$\frac{R_f}{R} \ge 29$$

or.  $$R_f \ge 29R$$

or,  $$R_f \ge 29 \times 65\Omega$$

That is,  $$R_f \ge 1.88k \Omega$$

The component values can be also be computed using the online phase shift oscillator design calculator.

Construct the circuit

The circuit can be constructed by connecting the feedback network to the inverting input of the op-amp and connecting the output of the op-amp to the input of the feedback network. The capacitors values and resistors values were calculated above.

The LM741 operational amplifier here is be powered using a dual power supply of +9V and -9V. The circuit can also be modified to operate LM741 with single supply

Video demonstration

The following video demonstrates how the LM741 op-amp based RC phase shift oscillator works.

Summary

In summary, the LM741 op-amp can be used to design a phase shift oscillator that generates a sine wave output. By choosing the appropriate values of R and C, and the value of Rf, the frequency of oscillation and the required gain can be achieved. The LM741 phase shift oscillator is a simple and effective design that is commonly used in electronic circuit design.

See other oscillator designs:

[3] Hartley Oscillator Design with Enhancement MOSFET