# Op-Amp Adder and Subtractor

## Applications of Operational Amplifiers in Tamil

## Op-Amp Adder

- Op-amp is used to design a circuit whose output is the sum of several input signals. Such a circuit is called a summing amplifier or a summer or adder.
- If the input resistors are equal in value (R
_{1}= R_{2}= R) then the summed output voltage is as given and the gain is +1. If the input resistors are unequal then the output voltage is a weighted sum and becomes:

## Inverting Summing Amplifier

- A typical summing amplifier with three input voltages V
_{1}, V_{2}and V_{3}three input resistors R_{1}, R_{2}, R_{3}and a feedback resistor R_{f}. - The following analysis is carried out assuming that the op-amp is an ideal one, AOL= ∞. Since the input bias current is assumed to be zero, there is no voltage drop across the resistor R
_{comp}and hence the non-inverting input terminal is at ground potential.

To find R_{comp}, make all inputs V_{1} = V_{2} = V_{3} = 0.

So the effective input resistance R_{i} = R_{1} || R_{2} || R_{3}. Therefore, R_{comp} = R_{i} || R_{f} = R_{1} || R_{2} || R_{3} || R_{f}.

## Non-Inverting Summing Amplifier

Non-Inverting Summing Amplifier

- A summer that gives a non-inverted sum is the non-inverting summing amplifier. Let the voltage at the (-) input terminal be Va which is a non-inverting weighted sum of inputs.

Let R_{1} = R_{2} = R_{3} = R = R_{f}/2, then V_{0} = V_{1}+V_{2}+V_{3}

## Op-Amp Subtractor

Op-Amp Subtractor

- The Subtractor also called a differential amplifier, uses both the inverting and non-inverting inputs to produce an output signal which is the difference between the two input voltages V
_{1}and V_{2}allowing one signal to be subtracted from another. - If resistances are equal (R = R
_{3}and R_{A}= R_{4}) then the output voltage is as given and the voltage gain is +1. - If the input resistance are unequal the circuit becomes a differential amplifier producing a negative output when V
_{1}is higher than V_{2}and a positive output when V_{1}is lower than V_{2}.

## Adder/Subtractor:

- It is possible to perform addition and subtraction simultaneously with a single op-amp using the circuit.
- The output voltage V
_{o}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.

Adder Subtractor Circuit

- This is the circuit of an inverting amplifier
and its output voltage is, V
_{1}= -R/(R/2) * V 1/2= - V_{1} - 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}

Non-inverting Amplifier

- The circuit now becomes a non-inverting amplifier. 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} = V_{01} = V_{02} = V_{03} = V_{04}

V_{o} = -V_{1} -V_{2} +V_{3}+ V_{4}

V _{o} = (V _{3} +V _{4}) – (V_{1} +V _{2})

So, the circuit is an adder-subtractor.

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