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