Discussion
What is the oscillator frequency of a transistor phase shift oscillator, if the value of \(R = 5\ \mathrm{k\Omega}\), \(C = 10\ \mu\mathrm{F}\), \(R_C = 10\ \mathrm{k\Omega}\) (for a single transistor stage)?
Answer: A
For a transistor phase shift oscillator the frequency of oscillation is
\[ f = \frac{1}{2\pi RC\sqrt{6 + 4\,(R_C/R)}} \]
With \(R = 5\ \text{k}\Omega\), \(C = 10\ \mu\text{F}\) and \(R_C = 10\ \text{k}\Omega\), so that \(R_C/R = 2\):
\[ \begin{aligned} 2\pi RC \\ &= 2\pi \times 5000 \times 10 \times 10^{-6} \\ &= 0.3142 \end{aligned} \]
\[ \begin{aligned} f = \frac{1}{0.3142 \times \sqrt{6 + 8}} \\ &= \frac{1}{0.3142 \times 3.742} = 0.85\ \text{Hz} \end{aligned} \]
The answer is 0.85 Hz, option A. The larger values would need a capacitance a hundred times or more smaller.
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