The GATE Grind

GATE 2022 BM – Question 41

Analog and Digital Electronics · Operational Amplifiers · 2 marks · Multiple choice

The op-amp/resistor/capacitor filter shown uses ideal op-amps with infinite gain and bandwidth. What R₂ in kΩ makes Vₒ(s)/Vᵢ(s) all-pass?

Diagram for GATE 2022 BM question 41
  1. 1
  2. 10
  3. 5
  4. 2

Practise this question in The GATE Grind →

Show answer and explanation

Correct answer: (B) 10

Explanation

The upper unity inverter gives −Vᵢ; the bottom unity inverter gives −Vₒ. With τ=(1 kΩ)(100 pF), the integrator output is U=−(Vᵢ−Vₒ)/(sτ). The final summer gives Vₒ=(10 kΩ/R₂)Vᵢ−2U. Therefore H=[a sτ+2]/[sτ+2], a=10 kΩ/R₂. Its magnitude is constant when a=1, giving R₂=10 kΩ, B. In the printed ideal topology this reduces to the constant unity all-pass response.

More Operational Amplifiers questions

All Operational Amplifiers questions →