Discussion
The frequency of the following phase shift oscillator :
The figure shows a transistor RC phase shift oscillator in which three RC sections, each a series capacitor C with a resistor R to ground, feed the collector output back to the base; C = 13 × 10\(^{-9}\) F and R = 1 kΩ.
is nearly equal to :
Answer: B
The frequency is nearly 5 kHz.
For the three-section RC phase shift oscillator, using the standard formula:
\[ f = \frac{1}{2\pi RC\sqrt{6}} \]
\[ \begin{aligned} 2\pi RC\sqrt{6} &= 2\pi(10^{3})(13 \times 10^{-9})(2.449) \\ &\approx 2.0 \times 10^{-4}\ \text{s} \end{aligned} \]
so \(f \approx 5000\) Hz. The \(\sqrt{6}\) arises because the three RC sections must together give 180° of phase shift. Leaving it out gives about 12 kHz, and none of the other options follows from these values.
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