Question

Find the input resistance for the given circuit

(a) RIF = Ri*[1+(A*R4+R5)/(2* R4+R5)].

(b) RIF = Ri*[1+(A*R4)/(2* R4+R5)].

(c) RIF = Ri*[1+(A*R4+R5)/(R4+R5)].

(d) None of the mentioned

I have been asked this question in a dream while sleeping

This is a very interesting question from Differential Amplifiers with Multiple Op-Amp in section Operational Amplifier Characteristics of Linear Integrated Circuits

Answer 1

The correct answer is:

(a) RIF=Ri⋅[1+A⋅R4+R52⋅R4+R5]R_{IF} = R_i \cdot \left[ 1 + \frac{A \cdot R_4 + R_5}{2 \cdot R_4 + R_5} \right]RIF​=Ri​⋅[1+2⋅R4​+R5​A⋅R4​+R5​​]

Explanation:

The input resistance (RIFR_{IF}RIF​) for the given differential amplifier circuit depends on the internal resistance (RiR_iRi​), the amplifier's gain (AAA), and the resistances R4R_4R4​ and R5R_5R5​ in the feedback network. The formula accounts for the effect of the amplifier's gain and the resistive network configuration on the effective input resistance.

1. The A⋅R4+R5A \cdot R_4 + R_5A⋅R4​+R5​ term reflects the effect of the gain and the resistances in the feedback path.
2. The denominator 2⋅R4+R52 \cdot R_4 + R_52⋅R4​+R5​ adjusts for the division of voltage and current in the resistive network.

Why not the other options?

• (b) RIF=Ri⋅[1+A⋅R42⋅R4+R5]R_{IF} = R_i \cdot \left[ 1 + \frac{A \cdot R_4}{2 \cdot R_4 + R_5} \right]RIF​=Ri​⋅[1+2⋅R4​+R5​A⋅R4​​]: This misses the R5R_5R5​ term in the numerator, which is essential for accurate calculation.
• (c) RIF=Ri⋅[1+A⋅R4+R5R4+R5]R_{IF} = R_i \cdot \left[ 1 + \frac{A \cdot R_4 + R_5}{R_4 + R_5} \right]RIF​=Ri​⋅[1+R4​+R5​A⋅R4​+R5​​]: The denominator should be 2⋅R4+R52 \cdot R_4 + R_52⋅R4​+R5​, not R4+R5R_4 + R_5R4​+R5​.
• (d) None of the mentioned: Incorrect, as option (a) is valid.

This formula is derived by analyzing the feedback and input resistances in the context of the differential amplifier circuit.