An operational amplifier is an amplifier which has high open loop gain, very high input impedance, very low output impedance and large bandwidth. This amplifier is a direct coupled device with differential inputs and a single ended output. The amplifier responds only to the difference voltage between the two input terminals. Fig.1(a) shows the most widely used symbol for a circuit with two inputs and one output. For simplicity, power supply and other pin connections are omitted. Since the input differential amplifier stage of the op-amp is designed to be operated in the differential mode, the differential inputs are designated by the (+) and (-) notations. The (+) input is the non-inverting input. An ac signal (or dc voltage) applied to this input produces an in phase (or same polarity) signal at the output. On the other hand, the (-) input is the inverting input because an ac signal (or dc voltage) applied to this input produces an 180" out-of-phase (or opposite polarity) signal at the output.

InFig. 1(a),
V_b = Voltage at the non-inverting input (volts)
V_a = Voltage at the inverting input (volts)
V_o = Output voltage (volts)
All these voltages are measured with respect to ground.
A = Large-signal voltage gain, which is specified on the data sheet for an op-amp

Fig. 1(b) shows an equivalent circuit of an op-amp. This circuit includes important values from the data sheets: A, Rin, and Rout. Here AV_in is an equivalent Thevenin voltage source, and Rout is the Thevenin equivalent resistance looking back into the output terminal of an op-amp. The equivalent circuit is useful in analyzing the basic operating principles of op-amps and in observing the effects of feedback arrangements. For the circuit shown in Fig. 1(b), the output voltage is

V_o = AV_in = A(V_b – V_a)

where
V_in = Difference input voltage
Above equation indicates that the output voltage Vo is directly proportional to the algebraic difference between the two input voltages. The output signal is single ended and is referred w.r.t. the ground.

The op-amp is a versatile device that can be used to amplify d.c. as well as a.c. input signals and was originally designed to perform mathematical operations such as addition, subtraction, multiplication, division, integration and differentiation. Thus the name operational amplifier stems from its original use for these mathematical operations and is abbreviated to op-amp.

IC 741 usually called as op-amp 741 is 8 pin dual in line package (DIP) integrated circuit consists of 8 pins as shown in Fig. 2. Terminals 2 and 3 are called input terminals. Signal applied to terminal 2 is arrived at the output terminal with the negative sign hence it is called inverting terminal while the signal applied to the terminal 3 is arrived with same sign at the output hence it is called non-inverting terminal. Power supplies of +15 V and -15 V are applied at terminals 7 and 4 respectively. The output is obtained at the terminal 6. Terminal 1 is offset null because it has no use in general operations. The name op-amp 741 is given to this integrated circuit as it is clear from its pin configuration that 7 active pins have 4 input terminals(2, 3, 4 and 7) and one output terminal (6th terminal).

Adder

Fig. 3 shows the inverting configuration with three inputs V₁, V₂ and V₃. Depending on the relationship between the feedback resistance R_f and the input resistors R₁, R₂ and R₃, which can be used as a summing amplifier. The circuit’s function can be verified by examining the expression for the output voltage. In this configuration of op-amp when the three inputs V₁, V₂ and V₃ are applied at the inverting terminal then they produce currents I₁, I₂ and I₃ respectively. Using the concept of infinite impedance and virtual ground, we can see that inverting input of the op-amp is at virtual ground (0 V) and there is no current to the input. This means that the three input currents I₁, I₂ and I₃ combine at the summing point A and form the total current I_f which goes through R_f as shown in Fig. 3.

I₁ + I₂ + I₃ = I_f

When all the three inputs are applied, the output voltage is

V_o1 = –I_f R_f = –R_f ( I₁ + I₂ + I₃ )

V_o1 = −R_f ( V₁/R₁ + V₂/R₂ + V₃/R₃ )

If R₁ = R₂ = R₃ =R,then

V_o1 = −R_f / R ×( V₁+V₂+V₃ )

It means that the output voltage is equal to the negative sum of all the inputs times the gain of the circuit R_f/R; hence the circuit is called a summing amplifier. An interesting case results when the gain of the amplifier is unity, in this case R₁ = R₂ = R₃ = R_f and output voltage is

V_o1 = –( V₁ + V₂ + V₃ )

Thus, when the gain of summing amplifier is unity, the output voltage is the algebraic sum of the input voltages.

Subtractor

A basic differential amplifier can be used as a subtractor when input signals are applied at the two input terminals of op-amp i.e. one at inverting and other at non-inverting terminal, then output is given by the difference of two input signals. The practical circuit of the op-amp as subtractor is given in Fig. 4. It is a combination of inverting and non-inverting amplifiers. If terminal B is grounded, the circuit operates as an inverting amplifier and input V₁ is amplified by –R_f/R₁. With terminal A grounded, R_f and R₁ function as the feedback components of a non-inverting amplifier. Input voltage V₂ is divided across resistors R₂ and R₃ to give V_R3 and then V_R3 is amplified by (R_f + R₁)/R₁.
With V₂ = 0,

V_o1 = (−R_f/R₁ )×V₁

With V₁ = 0,

V_R3 = { R₃/( R₃ + R₂ )}×V₂

and

V_o2 = {( R_f + R₁ )/ R₁}×VR₃

or

V_o2 = {( R_f + R₁ )/ R₁}×{ R₃/( R₃ + R₂ )}×V₂

With R₃ = R_f and R₂ = R₁

V_o2 = ( R_f/R₁ )×V₂

With both signals present,

V_o1 = V_o2 + V_o1

V_o1 = {( R_f/R₁ )×V₂} − {( R_f/R₁ )×V₁}

V_o1 = R_f / R₁ ×(V₂ − V₁)

When R_f and R₁ are equal value resistors, the output is the direct difference of the two inputs i.e.

V_o1 = V₂ – V₁

Multiplication/Division by a constant

The practical circuit of the op-amp as multiplication is given in Fig. 5. When the feedback resistance R_f and input resistance R₁ are so chosen to give a constant value K_m = (−R_f /R₁) then the input given to the inverting terminal of op-amp is multiplied at the output by this constant K_m, therefore the output at the terminal 6 is given by

V_o1 = −(R_f/R₁) × V_in

V_o1 = K_m × V_in

where K_m =( −R_f/R₁ )

When the feedback resistance R_f and input resistance R₁ are so chosen that the ratio R_f/R₁ give a fractional value then the input voltage given to inverting terminal of op-amp is divided at the output by this division factor K_d = (−R₁/R_f). The circuit for this operation is shown in Fig. 5. The output is obtained at terminal 6 of op-amp by D.M.M. with respect to ground.

V_o1 = −(R_f / R₁) × V_in

V_o1 = V_in/K_d

where K_d =( −R₁/R_f )