Question

The required current gain in a transistor phase-shift oscillator is

• A. \[ h_{fe}>29+23\frac{R_C}{R}+4\frac{R}{R_C} \]
• B. \[ h_{fe}<29+23\frac{R_C}{R}+4\frac{R}{R_C} \]
• C. \[ h_{fe}>23+29\frac{R}{R_C}+4\frac{R_C}{R} \]
• D. \[ h_{fe}<23+29\frac{R}{R_C}+4\frac{R_C}{R} \]

Hint:

For equal RC sections, a phase-shift oscillator requires a minimum amplifier gain of approximately \[ 29. \] This is one of the most frequently used results in oscillator theory.

Answer 1

The Correct Option is A

Concept: For sustained oscillations, the Barkhausen criterion requires \[ A\beta=1. \] In a transistor RC phase-shift oscillator, the transistor must provide sufficient gain to compensate for the attenuation introduced by the RC feedback network.

Step 1: Recall the transistor phase-shift oscillator condition.
For a transistor phase-shift oscillator, \[ h_{fe}> 29+23\frac{R_C}{R} + 4\frac{R}{R_C}. \] This is the minimum current gain requirement for maintaining oscillations.

Step 2: Interpret the inequality.
The transistor gain must be greater than the above value. If the gain falls below this limit, oscillations die out.

Step 3: Match with the options.
The expression exactly matches \[ \boxed{ h_{fe}> 29+23\frac{R_C}{R} + 4\frac{R}{R_C} } \] Therefore option (A) is correct.