This document discusses various applications of operational amplifiers (OP-AMPs), including as an inverting amplifier, non-inverting amplifier, adder, subtractor, differentiator, and integrator. It provides circuit diagrams and mathematical equations to describe the functionality of each application. Specifically, it explains that an inverting amplifier inverts the input signal phase and its closed-loop gain is determined by the ratio of the feedback and input resistors. A non-inverting amplifier does not invert the phase and has no virtual ground. An OP-AMP can also be used as an adder by applying multiple inputs to the inverting terminal, as a subtractor by applying inputs to both terminals, as a differentiator by connecting the input

1. Department of Physics
B.SC.III
Sem-V.Paper-XII
DSE-E4- Digital and Analog Circuits and Instrumentation
Topic-Applications of OP-AMP

2. • Applications of Op-4mps
Inverting Amplifier : Fig. 2.14(a) shows the circuit
diagram Op-Amp as inverting amplifier. If only one input
is applied to the a input terminal, then it is called as
inverting amplifier.
The positive input terminal is grounded and
input voltage V1 is applied to the negative
input terminal of amplifier through resistor
R1. The negative feedback is applied through
Ro from output terminal to input terminal.
The feedback resistor R0 and input resistor R1
determines the inverting operation. For an ideal Op-
Amp open loop gain is infinite. Hence, potential
difference between the input terminal must be zero.
Hence, Vs = 0, by negative feedback around the
amplifier. Again input impedance of an ideal Op-Amp is
infinite, hence input current to the amplifier will be
zero. The voltage Vs = 0 indicates that terminal 1, has
same potential as terminal 2. Since terminal 2 is
grounded, terminal 1 is also virtually grounded. Thus,
current II flowing through R1, must be flowing through
R. Hence we have

3. Inverting Amplifier :
Hence
𝐼1= 𝐼0
𝑉1−𝑉𝑠
𝑅1
=
𝑉𝑠−𝑉0
𝑅0
But 𝑉
𝑠 = 0
∴
𝑉1 − 0
𝑅1
=
0 − 𝑉0
𝑅0
𝑉1
𝑅1
=
−𝑉0
𝑅0
𝑉0
𝑉1
=
−𝑅0
𝑅1
AcL =
𝑉0
𝑉1
=
−𝑅0
𝑅1
= is closed loop gain of
inverting amplifier.
It is negative because closed loop amplifier
reverses the sign of input signal. That is
output is out of phase with input. The closed
loop gain depends upon the ratio Ro/Ri
• Non-inverting Amplifier :
Fig.2.15(a) shows the circuit diagram of an ideal Op-Amp
in non-inverting mode. The equivalent circuit of non-
inverting mode is shown in Fig. 2.15(b). The input signal
is applied to the non-inverting terminal (+). The feedback
is applied to the inverting input terminal (—) through Rf.
The resistors Rf and R1 from the feedback voltage divider
circuit. In this case also Vs = 0.
The voltage V1 from the negative terminal to ground is
equal to the input voltage V2. In this case V1 is not equal
to zero i.e. non-inverting circuit has no virtual ground at
either one of its input terminals.

4. Non-inverting Amplifier :
• Since

5. 2.7.3 : Op-Amp as Adder : An adder is a circuit whose output is
proportional to the algebraic sum of the input voltages. It is same
as the inverting amplifier except that it has several input terminals.
Consider an inverting amplifier with 3 inputs at inverting terminal
as shown in Fig. 2.16.
The inverting terminal is virtually ground by the feedback resistor
R0. Hence, sum of currents through R1, R2, R3 is equal to the
current through R0.
• Thus, we obtain the sum of the voltages at the output.
Hence Op-Amp works as an adder

6. The Op-Amp as subtractor is also
known as difference amplifier. The function of a
subtractor is to give output which is proportional or
equal to the difference of the two input signals. The
input signals are applied at the both inverting and non-
inverting terminals as shown in Fig. 2.17.
• Both inverting and non-inverting operations take place
simultaneously. Applying principle of superposition output
voltage Vo is given as, Vo = Vo1 +V02
• V01 and V02 are outputs due to V1 and V2, simultaneously.
The output V01 due to V1 alone with the other input earthed
is same as that of inverting circuit.
∴ 𝑉01 = −(
𝑅𝑓
𝑅1
)𝑉1
• The output V02 due to V2 alone with the other input earthed
is the same as that of non-inverting circuit.
• Thus the output voltage is the difference between two input
voltages.

7. • 2.7.5: Op-Amp as Differentiator : Fig. 2.18(a) shows a
circuit used to study Op-Amp as differentiator. Its
equivalent circuit is shown in Fig. 2.18(b).
• Fig. 2.18 : (a) Op-Amp as differentiator, (b) Equivalent
circuit.
• The input signal source of voltage V(t) is connected to the
inverting input terminal through a capacitor C. The non-
inverting input terminal is earthed. Negative feedback is
given through a resistance R. Let V(t) be the signal voltage
given as input which gives varying current through the
capacitance C. From equivalent circuit we have
I=C
𝑑𝑉(𝑡)
𝑑𝑡
Output voltage 𝑉0 = −𝐼𝑅 = −𝑅𝐶
𝑑𝑉(𝑡)
𝑑𝑡
Thus output voltage is time derivative of
input voltage. Hence Op-Amp work as
differentiator.

8. • Op-Amp as Integrator : Fig. 2.19(a) shows a circuit
diagram of Op-Amp as an integrator. Here the output
voltage is proportional to the time integral of the input
voltage. Fig. 2.19(b) shows an equivalent circuit of an
Op-Amp as a integrator.
• (a) Op-Amp as Integrator, (b) Equivalent circuit.
Here input current to the ideal Op-Amp is zero and the
feedback through the capacitor C forces the virtual ground
to exist at the inverting input terminal. Hence output
voltage is the voltage across C.
• ∴ 𝑉0 = −
1
𝐶
𝐼𝑑𝑡 = −
1
𝑅𝐶
𝑉𝑑𝑡
• Therefore, the amplifier provides an output voltage
proportional to the integral of the input voltage.