Op amp circuit output

[abhishek046]

What's the output of this op amp circuit? Consider the 1V source as just V. Could someone give me the working & description of this circuit with relevant expressions?

 

[Doug Tao]

The output of the circuit is 1.22 Vin.

Inverting op-amp configuration, positive and negative feedback. Looking at positive terminal, we can see the voltage is the output voltage through the voltage divider, or 1/11 Vout. Ideal conditions, no current flows into the inputs, thus Vn = Vp, node equations give Vin - Vn = Vn - Vout.

The final expression is Vout = -1.22 Vin. Note the negative output, we can confirm because we have an inverting op-amp configuration.

 

[albbg]

Solution by Doug Tao is correct. However we can also apply the blocks algebra to analyze the circuit, also taking into acccount the finite gain A=100 kV/V of the amplifier.

The block diagram is the following:



where α is the input divider, β the positive feedback ratio and γ the negative feedback

We can call R1 from in+ to gnd, R2 from in+ to Vout, R3 from Vi to in- and R4 from in- to Vout so the parameters will be given by:

α=R4/(R3+R4)
β=R1/(R1+R2)
γ=R3/(R3+R4)

applying the blocks rules:

(-α*Vi+β*Vo-γ*Vo)*A=Vo then

Vo=(-α*A*Vi)/[1+A*(γ-β)]

numerically, in your circuit α=0.5, β=1/11, γ=0.5, A=100000, Vi=1 thus

Vo=(-0.5*100000*1)/[1+100000*(0.5-1/11)]≈-1.222 V

since A is very large:

Vo≈(-α*Vi)/(γ-β)