Question

Design an operational amplifier circuit to form the weighted sum V0 = – (2V1+V2).

Answer 1

Assume : Op-amp is ideal, so the virtual ground is applicable

$V^+$ (non inverting) = $V^-$ (Inverting)=0

By KCL at (Inverting terminal)

$\frac{V_1}{R_1}+\frac{V_2}{R_2}=\frac{0-V_{out}}{2K}$

So, $V_{out}=-2K[\frac{V_1}{R_1}+\frac{V_2}{R_2}]=-[\frac{V_1}{\frac{R_1}{2K}}+\frac{V_2}{\frac{R_2}{2K}}]$ .........(1)

Now comparing with given equation

$V_{out}=-[\frac{V_1}{\frac{1}{2}}+\frac{V_2}{\frac{1}{2}}]$ .....................(2)

Comparing 1 and 2

$\frac{R_1}{2K}=\frac{1}{2}; \frac{R_1}{2K}=2 \implies R_1=1K \Omega; R_2=4K \Omega$