Q.Explain virtual ground concept and also derive an expression for output of an inverting adder.

Virtual ground means the inverting input of an op-amp sits at 0 V (ground potential) without being physically connected to ground, because the non-inverting input is grounded and the differential input voltage is essentially zero. …

[!TLDR]

Because the op-amp gain is infinite, its inverting input is held at ground potential without a physical connection (virtual ground); applying KCL at that node gives the inverting adder output $V_O = -R_f\left(\tfrac{V_1}{R_1}+\tfrac{V_2}{R_2}+\tfrac{V_3}{R_3}\right)$.

Virtual ground concept: For an ideal op-amp the open-loop gain $A=\infty$ and the input impedance $Z_i=\infty$. The differential input voltage is

Since $A=\infty$ and $V_O$ is finite, $V_B - V_A = 0$, i.e. $V_A = V_B$. In an inverting configuration the non-inverting input (node B) is grounded, so $V_B = 0$ and therefore $V_A = 0$. Thus the inverting input node sits at 0 V (ground potential) even though it is not physically connected to ground — this is called a virtual ground. Also, because $Z_i=\infty$, no current enters the op-amp input ($i_b = 0$).

Derivation of the inverting-adder output: In the summing amplifier, inputs $V_1$, $V_2$, $V_3$ are applied through resistors $R_1$, $R_2$, $R_3$ to the inverting node A; $R_f$ is the feedback resistor and the non-inverting input is grounded.

Using $V_A = 0$ (virtual ground) and $i_b = 0$, apply KCL at node A:

Since $V_A = 0$:

$\boxed{V_O = -R_f\left(\frac{V_1}{R_1} + \frac{V_2}{R_2} + \frac{V_3}{R_3}\right)}$ …