Similar Questions -

1. Explain how op-amp can be used as summing, calling and averaging amp in inverting configuration.

2. Explain how operational amp can be used for addition of two AC signals with one DC signal

3. Explain how op-amp can be used as a averaging amp in inverting configuration

4. Explain how operational amp can be used for taking average of three signals.

Inverting Adder/ Summing Amplifier:

$V_1,V_2,V_3→ 3 i/p$ signals simultaneously applied to inverting terminal of op-amp through $R_1,R_2$ and $R_3$

Voltages are measured w.r.t. grid. $R_f$ is feedback resistor connected between the o/p terminal and inverting i/p terminal of op-amp. The non – inverting i/p terminal →

KCL at node A.

$I_1+I_2+I_3=I_B2+I_f$

But $R_i$ of op-amp ideally $'∞',I_B2= 0$

$V_A=V_B=0$ due to virtual grid concept.

Hence, $I_1+I_2+I_3=I_f$

⇒ On i/p side, $I_1=\frac{V_1-V_A}{R_1} =\frac{V_1}{R_1}$ as $V_A=0$

Similarly, $I_2=\frac{V_2}{R_2} ,I_3=\frac{V_3}{R_3}$

⇒ On o/p side

$I_f=\frac{V_A-V_0}{R_f} =-\frac{V_0}{R_f}$

Substituting:-

$\frac{V_1}{R_1}+\frac{V_2}{R_2}+\frac{V_3}{R_3}=-\frac{V_0}{R_f}$

OR

$V_0=-\big[\frac{R_f}{R_1}V_1+\frac{R_f}{R_2}V_2+ \frac{R_f}{R_3}V_3 \big]$

If we substitute $R_f=R_1=R_2=R_3=R$ , then

$V_0= -(V_1+V_2+V_3)$

Averaging circuit:

The inverting adder circuit, can be used as an averaging circuit by setting $R_1=R_2=R_3=R$ and $R_f=R/3$

$∴V_0=\frac{-RF}{R} (V_1+V_2+V_3 )=\frac{-R/3}{R} (V_1+V_2+V_3 ) \\ ∴V_0=\frac{-(V_1+V_2+V_3 )}{3}$

Thus magnitude of o/p voltage is equal to the avg of 3 i/p voltages. This principle can be extended for n nos of i/ps by setting.

$R_f=\frac{R}{n}$ and $R_1=R_2…….=R_n=R$

Then o/p $V_0=\frac{-(V+V_2+V_3+⋯…..+V_n )}{n}$