Find v0 in the circuit in Fig P440 SolutionFrom the fig P440

Solution

From the fig P4.40 we can see two Op-amps.

the 1st op-amp is a non in verting amplifier.

the output of non-inverting amplifier is V₀₁= V₁(1+ R₁/R₁) = 2V₁

This output  2V₁ is the inverting input of 2nd op-amp.

But the second op-amp is a difference amplifier. where the inverting input is  2V₁ and the non-inverting input is  V2.

The output of the difference amplifier is V0 = V₀₂ - V₀₁

Here V₀₁ is the inverting output of the 2nd amplifier. then V₀₁ = 2V₁(-R₂/R₁)

V02 is the non-inverting output of 2nd amplifier, then V₀₂ =V₂( 1+ R₂/R₁)

The output of the difference amplifier is V0 = V₀₂ - V₀₁ = V₂( 1+ R₂/R₁) - 2V₁(-R₂/R₁) = V₂ +  R₂/R₁(V 2 + 2V1)