If all resistors are equal in value, then the output voltage can be derived by using superposition principle.

**Subtractor:**

A
basic differential amplifier can be used as a subtractor as shown in the above
figure. If all resistors are equal in value, then the output voltage can be
derived by using superposition principle.

To
find the output V_{01} due to V_{1}
alone, make V_{2} = 0.

Then
the circuit of figure as shown in the above becomes a non-inverting amplifier
having input voltage V_{1}/2 at
the non-inverting input terminal and the output becomes

V_{01}
= V_{1}/2(1+R/R) = V_{1} when all resistances are R in
the circuit.

Similarly
the output V_{02} due to V_{2} alone (with V_{1} grounded) can be written simply
for an inverting amplifier as

V_{02}
= -V_{2}

Thus
the output voltage Vo due to both the inputs can be written as

V_{0}
=V_{01} - V_{02} = V_{1} - V_{2}

It
is possible to perform addition and subtraction simultaneously with a single
op-amp using the circuit shown in figure 2.16.

The
output voltage Vo can be obtained by using superposition theorem. To find
output voltage V_{01} due to V_{1}
alone, make all other input voltages V_{2}, V_{3} and V_{4}
equal to zero.

The
simplified circuit is shown in figure 2.17. This is the circuit of an inverting
amplifier and its output voltage is, V_{01}= -R/(R/2) * V_{1}/2=
- V_{1} by Thevenin‘s equivalent
circuit at inverting input terminal).

Similarly,
the output voltage V_{02} due to V_{2} alone is,

V_{02}=
- V_{2}

Now,
the output voltage V_{03} due to the input voltage signal V_{3}
alone applied at the (+) input terminal can be found by setting V_{1}, V_{2} and V_{4}
equal to zero.

V_{03}=V_{3}

The
circuit now becomes a non-inverting amplifier as shown in fig.(c).

So,
the output voltage V_{03} due to V_{3} alone is

V_{03}
= V_{3}

Similarly,
it can be shown that the output voltage V_{04} due to V_{4}
alone is

*V*_{04} = *V*_{4}

Thus,
the output voltage Vo due to all four input voltages is given by

*V _{o}
*=

*Vo *= -* V _{1}* -

*V _{o} = *(

So,
the circuit is an adder-subtractor.

Tags : Applications of Operational Amplifier , Linear Integrated Circuits : Applications of Operational Amplifier

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