An operational amplifier (op-amp) is an electronic device that amplifies the difference between two input voltages. It has very high gain, very high input impedance, and very low output impedance. Op-amps can perform mathematical operations like addition, subtraction, integration, and differentiation. Key characteristics of an ideal op-amp include infinite input impedance, zero output impedance, infinite voltage gain, and zero offset voltage. Practical op-amps have finite characteristics. Op-amps can be configured as inverting or non-inverting amplifiers to produce output signals that are inverted or non-inverted versions of the input. Common op-amp applications include adders, subtractors, and active filters.

1. Operational Amplifier
1. An amplifier is an electronic device for increasing the amplitude of electrical signals.
2. An amplifier with high gain and high input impedance (usually with external
feedback), used especially in circuits for performing mathematical operations on an
input voltage.
3. Gain is the ratio of output voltage to input voltage.
4. Op-amps can be used to perform various mathematical operations like addition,
subtraction, differentiation and integration etc.
5. Basic diagram of an op-amp is shown in below figure:

2. Terminal Characteristics of an Op-amp
• Op-amps is also called as IC741.
• The pin diagram of an op-amp is shown in below figure:
• Pin 1 and Pin 5 are called as offset null, because they removes the offset voltage
and balances the input voltage.
• Pin 2 is the inverting signal input and Pin 3 is the non-inverting signal input.
• Pin 4 is the ground or negative voltage supply input and Pin 7 is the positive
voltage supply input.

3. Ideal characteristics of an op-amp:
• Pin 6 is the output terminal.
• Pin 8 is not connected, this terminal is only used when two op-amps are required to
connected in series.
• The open loop voltage gain (AOL) without any feedback for an ideal op-amp is infinite.
• The input impedance (RIN)of an ideal op-amp is infinite, so there is no current flowing
in the input circuit.
• The output impedance (ROUT)of an ideal op-amp is zero.
• An ideal op-amp has an infinite bandwidth, so it can amplify any signal from DC to
the highest AC frequency without any losses.
• The offset voltage of an ideal op-amp is zero, which means that the output voltage
will be zero if the difference between the inverting and non-inverting terminal is zero.

4. Op-amp as an Differential amplifier:
AOL = Open-loop voltage gain
• The basic formula for output voltage of an op-amp
VOUT = AOL (V+ -V-)
• From above equation , it is clearly seen that the output voltage amplifying the
difference between two input signals, so an op-amp is also called the differential
amplifier.

5. Practical Characteristics of an Op-amp:
• The open loop voltage gain (AOL) without any feedback for an op-amp is 105
.
• The input impedance (RIN) of an op-amp is 2MΩ, so there is a small offset current
flowing in the input circuit in the range of 20nA.
• The output impedance (ROUT) of an op-amp is 75Ω.
• An op-amp has an bandwidth 1MHz.
• The offset voltage of an op-amp is 2mV.
Virtual Ground concept in op-amp:
• In op-amps the term virtual ground means that the voltage at that particular
node is almost equal to ground voltage (0V).
• This concept is very useful in analysis of op-amp circuits and it will make a lot of
calculations very simple.
• We already know that the voltage gain of an ideal op-amp is infinite.

6. • Gain = Vo/Vin
• As gain is infinite, Vin = 0
• Vin = V2 – V1
• In the above circuit V1 is connected to ground, so V1 = 0. Thus V2 also will be at
ground potential.
• V2 = 0
• All the derivation of op-amps are based on this concept only.

7. Op-amp as an inverting amplifier:
• The operational amplifier as an inverting operational amplifier or an inverting op-
amp when the op-amp circuit produces the output which is out of phase with
respect to its input by 180o. This means that if the input pulse is positive, then the
output pulse will be negative and vice versa.
Applying KCL at node V2,

8. V2
–Vin
R1
+
V2
–Vout
Rf
= 0 … … … … … … … … … ( 𝑖)
But from figure V1=0, so from virtual ground concept V2=0. Hence putting the value
of V2 in equation (i), we get
0–Vin
R1
+
0–Vout
Rf
= 0
–Vin
R1
−
Vout
Rf
= 0
−Vin
R1
=
Vout
Rf
−Vin x
Rf
R1
=
Vout
−Rf
R1
Vin =
Vout

9. Av=
Vout
Vin
= −Rf
R1
So from above equation, it is seen that the closed loop voltage gain Av in an inverting
op-amp is the ratio of its feedback resistance to the input resistance and negative sign
(-) shows that the output voltage is 180º out of phase with respect to input.
Op-amp as an non-inverting amplifier:
• The operational amplifier as an non-inverting operational amplifier or an non-
inverting op-amp when the op-amp circuit produces the output which is in phase
with its input. This means that if the input pulse is positive, then the output pulse
will be positive and vice versa.

10. Applying KCL at node V2
V2
−0
R1
+
V2
–Vout
Rf
= 0 … … … … … … … … … 𝑖
But from figure V1= Vin, so from virtual ground concept V2= Vin. Hence putting the
value of V2 in equation (i), we get
Vin
R1
+
Vin
–Vout
Rf
= 0
Vin
R1
+
Vin
Rf
−
Vout
Rf
= 0
Vin(
1
R1
+
1
Rf
) =
Vout
Rf
Vin(
Rf
R1
+
Rf
Rf
) =
Vout

11. Vin(
Rf
R1
+ 1) =
Vout
Av=
Vout
Vin
= (
Rf
R1
+ 1)
From above equation it is clear that the output voltage will be in phase with respect to
input voltage, so it follows the same waveform as the input voltage, hence in non-
inverting configuration the op-amp is called voltage follower circuit.
Applications of an op-amp:
(i) As an adder circuit:
• It is possible to apply more than one input signal to an inverting amplifier. This
circuit will add all these input signals and produce their addition to output
terminals. Such a circuit called as an Adder Circuit.
• The diagram for an adder circuit is shown in below figure: