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GATE 2014 EE (EE1) – Question 32

Analog and Digital Electronics · Oscillators and feedback amplifiers · 1 mark · Multiple choice

For the Wien-bridge oscillator shown, identify the bridge-balance conditions.

Diagram for GATE 2014 EE (EE1) question 32
  1. $R_3/R_4=R_1/R_2,\quad\omega=1/\sqrt{R_1C_1R_2C_2}$
  2. $R_2/R_1=C_2/C_1,\quad\omega=1/(R_1C_1R_2C_2)$
  3. $R_3/R_4=R_1/R_2+C_2/C_1,\quad\omega=1/\sqrt{R_1C_1R_2C_2}$
  4. $R_3/R_4+R_1/R_2=C_2/C_1,\quad\omega=1/(R_1C_1R_2C_2)$

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Correct answer: (C) $R_3/R_4=R_1/R_2+C_2/C_1,\quad\omega=1/\sqrt{R_1C_1R_2C_2}$

Explanation

The series arm is R1+1/(sC1), and the shunt arm is R2/(1+sR2C2). At zero phase, ω²=1/(R1C1R2C2). The feedback attenuation is1/[1+R1/R2+C2/C1], so the non-inverting amplifier gain1+R3/R4must equal its reciprocal. Hence **R3/R4=R1/R2+C2/C1and ω=1/√(R1C1R2C2),C**.