Exercise 10.1 A Colpitts oscillator

For the harmonic oscillator circuits shown in the figure below you can assume that the current gain of the transistor is very large, i.e. $\mathit{\beta fe}\to \infty$.

a)

Draw a small-signal equivalent circuit.

b)

Derive the condition for oscillation for this circuit.

c)

Derive an expression for the (radian) frequency of oscillation.

d)

Derive an expression for the required value of $g_m$ to get stable oscillation.