Mathematical Formula for given circuit ?

1. Mathematical Formula for given circuit ?

Hi,

Can somebody give me the mathematical formula for the following circuit.

Where R1≠R2≠R3≠R4, R5 is variable. Calculate Vout for any V1 value.

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2. Re: Mathematical Formula for given circuit ?

To make it a simple network calculation problem you have to assume an ideal OP with infinite input resistance and gain. Then Vout will be always controlled so that the input OP difference voltage becomes zero. This gives you the oportunity to apply a basic network calculation method of your choice.

3. Re: Mathematical Formula for given circuit ?

Hi FvM,

I simulated the circuit under LTSpice with the following values.
Ideal OpAmp:
.subckt ideal-opamp 1 2 3
G1 0 3 1 2 100Meg
.ends ideal-opamp

R1=10K, R2=270, R3=1K5, R4=560 and R5=27.5, V1=1Vpk-1KHz, Vout=0.198133

Calculation Used:
Non-Inverting Vninv = V1×[R2/(R2+R1)]×[1+(R4/R5)], So Vninv = 0.561649
Inverting Vinv = V1×-(R4/R3), So Vinv = -0.373333
Therefore Vout = Vninv + Vinv, Vout = 0.188316

What I am missing ?

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4. Re: Mathematical Formula for given circuit ?

Vninv = V1×[R2/(R2+R1)]×[1+(R4/R5)]
You are using a superposition method to calculate the output voltage. In this case R3 has to be connected parallel to R5 for the noninverting case.

Your "ideal OpAmp" is an OTA, by the way. You should use a voltage controlled voltage source to model an OP. But both can work in this circuit.

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5. Re: Mathematical Formula for given circuit ?

Thank you so much FvM

Vninv = V1×[R2/(R2+R1)]×[1+{R4/(R5||R3}]

---------- Post added at 16:16 ---------- Previous post was at 15:51 ----------

May I know why we put R3 parallel to R5 ?

6. Re: Mathematical Formula for given circuit ?

Superposition method involves that you're supplying input voltage to +ve and -ve branche seperately. The other input is connected to zero input voltage. Zero input voltage means paralleling both resistors.

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Thanks

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