# LM741 summing amplifier and its applications

The LM741 operational amplifier is a popular operational amplifier (op-amp) that has been in use for over four decades. It is widely used in electronic circuits due to its simplicity, reliability, and versatility. One of its common applications is the summing amplifier or adder circuit, which is used to add multiple input signals and provide a single output signal. In this blog post, we will discuss the LM741 summing amplifier and its applications.

### LM741 Summing Amplifier

The LM741 summing amplifier is a op amp differential amplifier circuit that combines multiple input signals and produces a single output signal. It is used in applications such as audio mixers, voltage regulators, and power supplies. The summing amplifier is based on the principle of superposition, which states that the output of a linear system is the sum of the individual outputs produced by each input signal.

#### Types of Summing Amplifier

Since operational amp has two terminals inverting and non-inverting we can have two types of summing amplifier circuits:

1. Inverting Summing Amplifier

2. Non-Inverting Summing Amplifier

1. Inverting Summing Amplifier

The circuit diagram of inverting LM741 summing amplifier is shown below:

The inverting LM741 summing amplifier has two input terminals(inverting and non-inverting) and one output terminal. The LM741 op-amp is powered by a dual power supply, which provides both positive and negative voltage rails. One can also use single supply see how to operate LM741 with single supply.The input signals Vin1 and Vin2 are applied through a separate resistor, R1 and R2 at the inverting terminal. The two input signals are added or sum and the added signal appears at the output terminal. A feedback resistor, RF is connected from the output to the inverting terminal.

The inverting terminal 2 is at virtual ground because the non-inverting 3 is at virtual ground. This means that,

$$V1 = V2 = 0$$ ------->(1)

The input currents are given by,

$$I_1 = \frac{V_{in1}-V_2}{R_1} = \frac{V_{in1}}{R_1}$$  ------->(2)
$$I_2 = \frac{V_{in2}-V_2}{R_2} = \frac{V_{in2}}{R_2}$$   ------->(3)

Applying KCL at the inverting terminal we have,

$$I=I_1+I_2$$   ------->(4)

or, $$I=\frac{V_{in1}}{R_1}+\frac{V_{in2}}{R_2}$$   ---->(5)

From the output side, we have,

$$I = \frac{V_2 - V_{out}}{R_F} = \frac{-V_{out}}{R_F}$$   ---->(6)

And therefore we have,

$$\frac{-V_{out}}{R_F}=\frac{V_{in1}}{R_1}+\frac{V_{in2}}{R_2}$$

Therefore the output voltage is,

$$V_{out} = -[\frac{R_F}{R_1}V_{in1}+\frac{R_F}{R_2}V_{in2}]$$   ---->(7)

If the resistances are equal $$R_1=R_2=R_F$$ the output is,

$$V_{out} = -(V_{in1}+V_{in2})$$   ---->(8)

Thus from the above equation we can see that if the resistors area properly selected the output is the weighted addition of two inputs signals. Thus this circuit is summing amplifier circuit.

Example of inverting summing amplifier

Consider two input signals of 1V amplitude and frequency of 5KHz. Let all the resistor value be 10KOhm. The following shows the signal waveform of the two inputs and the output signal. As can be seen the output signal waveform has twice the amplitude compared to either of the two inputs. Also the output signal waveform is 180 degree out of phase with the input signal because this is inverting summing amplifier. This illustrates addition of the two input signals.

2. Non-inverting Summing Amplifier

The circuit diagram of non-inverting LM741 summing amplifier is shown below:

In case of non-inverting summing amplifier, the two inputs Vin1 and Vin2 are connected to the non-inverting input of the operational amplifier via resistors R1 and R2. A feedback resistor RF is connected from the output back to the inverting input. A resistor R is connected to the inverting input and the other side of this resistor is grounded.

In this case, the voltage at the inverting terminal V1 is equal to the voltage at the non-inverting terminal V2. That is,

$$V1 = V2$$ ---->(9)

The current I1 and I2 from the input sides are;

$$I_1 = \frac{V_{in1}-V_1}{R_1}$$    ---->(10)
$$I_2 = \frac{V_{in2}-V_1}{R_2}$$    ---->(11)

Since the input current of op-amp is zero we have,

$$I_1 + I_2 = 0$$    ---->(12)
or,  $$\frac{V_{in1}-V_1}{R_1} +\frac{V_{in2}-V_1}{R_2}=0$$

or,  $$\frac{V_{in1}}{R_1} +\frac{V_{in2}}{R_2}= V_1[\frac{1}{R_1}+\frac{1}{R_2}]$$   ---->(13)

So the voltage at the non-inverting node is,

$$V_1 = \frac{R_1 V_{in2}+R_2 V_{in1}}{R_1+R_2}$$    ---->(14)

At the inverting node we have,

$$I=\frac{V_2}{R}=\frac{V_1}{R}$$     ---->(15)

and $$I=\frac{V_{out}-V_2}{R_F}=\frac{V_{out}-V_1}{R_F}$$    ---->(16)

From equation (15) and (16), we have,

$$\frac{V_1}{R}=\frac{V_{out}-V_1}{R_F}$$

or, $$\frac{V_{out}}{R_F}=V_1[\frac{1}{R}+\frac{1}{R_2}]$$

or,  $$V_{out}=V_1[\frac{R+R_F}{R}]$$   ---->(17)

Substituting eqn(14) into eqn(17) we get,

$$V_{out} = \frac{(R_2 V_{in1}+R_1 V_{in2})[R+R_F]}{R(R_1+R_2)}$$

that is,

$$V_{out} = \frac{R_2(R+R_F)}{R(R_1+R_2)}V_{in1} + \frac{R_1(R+R_F)}{R(R_1+R_2)}V_{in2}$$   ---->(18)

This is the equation for non-inverting summing op-amp amplifier. If all the resistors are equal, $$R_1=R_2=R_F$$ the output is,

$$V_{out}=V_{in1}+V_{in2}$$  ---->(19)

Since this non-inverting summing amplifier, there is no phase difference between the input and output signal. Compare this with the inverting summing amplifier output given in equation (8).

Example of non-inverting summing amplifier

Consider two input signals of 1V amplitude and frequency of 5KHz. Let all the resistor value be 10KOhm. The following shows the signal waveform of the two inputs and the output signal. As can be seen the output signal waveform has twice the amplitude compared to either of the two inputs. This illustrates addition of the two input signals.

### Applications of LM741 Summing Amplifier

The LM741 summing amplifier has a wide range of applications in electronic circuits. Some of its common applications include:

• Audio Mixers: The LM741 summing amplifier is used in audio mixers to combine multiple audio signals and provide a single output signal. It is used in recording studios, concert halls, and other venues where multiple audio sources need to be mixed together. See Audio Amplifier with LM741.
• Voltage Regulators: The LM741 summing amplifier is used in voltage regulators to provide a stable output voltage. The input signals are the reference voltage and the error signal, and the output signal is the corrected voltage.
• Power Supplies: The LM741 summing amplifier is used in power supplies to regulate the output voltage. It is used in electronic devices such as computers, televisions, and mobile phones.
• Signal Conditioning: The LM741 summing amplifier is used in signal conditioning circuits to amplify, filter, and process input signals. It is used in instrumentation operational amplifier systems, medical equipment, and control systems.

Conclusion

The LM741 summing amplifier is a versatile operational amp circuit that is widely used in electronic circuits. Its ability to combine multiple input signals and provide a single output signal makes it an important component in many applications, such as audio mixers, voltage regulators, and power supplies. With its simple construction and reliable performance, the LM741 op-amp continues to be a popular choice among engineers and hobbyists alike.