Summing Amplifier Using Op-Amp | Adder Using Op-Amp

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Summing amplifiers or adders are the amplifier circuits which can add more than one input signal. It is possible to apply more than one input signal to an inverting or non-inverting terminal of op-amp.

The summing amplifier then add all these input signals to produce their addition at the output.

Depending on the polarity of the output voltage the adder circuit can be classified into two categories as

Inverting summing amplifier
Non-inverting summing amplifier

Inverting Summing Amplifier Using Op-Amp

The summing amplifier is same as that inverting amplifier except that is has several input terminals. The negative feedback applied through resister R_f from the output to the input terminal.

Following figure shows the circuit diagram of an inverting configuration of summing amplifier (Inverting adder) using op-amp.

As shown in figure, the input voltages V₁, V₂ and V₃ are applied through resistance R₁, R₂ and R₃ respectively to the inverting terminal of op-amp.

Let the current flowing through resistance R₁, R₂ and R₃ be I₁, I₂ and I₃ respectively.

Let V_A is the voltage at non-inverting terminal and V_B is the voltage at inverting terminal respectively.

Applying Kirchhoff’s current law (KCL) at node B,

(KCL: Sum of current going toward node is equal to sum of currents going away from the node.)

${I_1} + {I_2} + {I_3} = {I_f}$

$\therefore \frac{{{V_1} - {0}}}{{{R_1}}} + \frac{{{V_2} - {0}}}{{{R_2}}} + \frac{{{V_3} - {0}}}{{{R_3}}} = \frac{{{0} - {V_O}}}{{{R_f}}}$ …(1)

According to the concept of virtual ground, as node A is grounded, node B is also grounded, i.e., V_A= V_B= 0,

Putting V_B= 0 in equation (1) we get

$\frac{{{V_1} - 0}}{{{R_1}}} + \frac{{{V_2} - 0}}{{{R_2}}} + \frac{{{V_3} - 0}}{{{R_3}}} = \frac{{0 - {V_O}}}{{{R_f}}}$ …(2)

Therefore, equation (2) will become

$\frac{{{V_1}}}{{{R_1}}} + \frac{{{V_2}}}{{{R_2}}} + \frac{{{V_3}}}{{{R_3}}} = \frac{{ - {V_O}}}{{{R_f}}}$

$\therefore {V_O} = - {R_f}(\frac{{{V_1}}}{{{R_1}}} + \frac{{{V_2}}}{{{R_2}}} + \frac{{{V_3}}}{{{R_3}}})$ …(3)

Where R₁≠R₂≠R₃

It is known as “scaling amplifier” or “Weighted amplifier”.

If R_f=R₁=R₂=R₃=R then,

we get,

${V_O} = - R\left( {\frac{{{V_1}}}{R} + \frac{{{V_2}}}{R} + \frac{{{V_3}}}{R}} \right)$

$\therefore {V_O} = - R\left( {\frac{{{V_1} + {V_2} + {V_3}}}{R}} \right)$

$\therefore {V_O} = - ({V_1} + {V_2} + {V_3})$

This circuit is called as “Inverting Adder” or “Inverting Summing Amplifier”.

If R₁=R₂=R₃=R and R_f=Ri/3

Equation (3) becomes,

${V_O} = - \frac{R}{3}\left( {\frac{{{V_1}}}{R} + \frac{{{V_2}}}{R} + \frac{{{V_3}}}{R}} \right)$

$\therefore {V_O} = - \frac{R}{3}\left( {\frac{{{V_1} + {V_2} + {V_3}}}{R}} \right)$

$\therefore {V_O} = - \left( {\frac{{{V_1} + {V_2} + {V_3}}}{3}} \right)$

Thus, the magnitude of output voltage is equal to the average of three input voltages. This is called “Averaging amplifier”.

Non-inverting Summing Amplifier Using Op-Amp

Non-inverting Summing Amplifier or non-inverting adder is the circuit in which the output is proportional to the sum of the input and also the output is in phase with input.

The negative feedback applied through resister R_f from the output to the input terminal. Following figure shows the circuit diagram of non-inverting configuration of summing amplifier (non-inverting adder) using op-amp.

As shown in figure, the input voltages V₁, V₂ and V₃ are applied through resistance R₁, R₂ and R₃ respectively to the non-inverting terminal of op-amp.

Let the current flowing through resistance R₁, R₂ and R₃ be I₁, I₂ and I₃ respectively.

Let V_A is the voltage at non-inverting terminal.

Applying Kirchhoff’s current law (KCL) at node A,

(KCL: Sum of current going toward node is equal to sum of currents going away from the node.)

${I_1} + {I_2} + {I_3} = 0$

$\therefore \frac{{{V_1} - {V_A}}}{{{R_1}}} + \frac{{{V_2} - {V_A}}}{{{R_2}}} + \frac{{{V_3} - {V_A}}}{{{R_3}}} = 0$

Also,

$\frac{{{V_1}}}{{{R_1}}} - \frac{{{V_A}}}{{{R_1}}} + \frac{{{V_2}}}{{{R_2}}} - \frac{{{V_A}}}{{{R_2}}} + \frac{{{V_3}}}{{{R_3}}} - \frac{{{V_A}}}{{{R_3}}} = 0$

Above equation can be rearranged as

$\frac{{{V_1}}}{{{R_1}}} + \frac{{{V_2}}}{{{R_2}}} + \frac{{{V_3}}}{{{R_3}}} = \frac{{{V_A}}}{{{R_1}}} + \frac{{{V_A}}}{{{R_2}}} + \frac{{{V_A}}}{{{R_3}}}$ …(4)