Q.Write the expression for frequency of oscillations of a Hartley oscillator.

The Hartley oscillator is an LC oscillator that takes its feedback from a tapped (two-section) inductor — hence it is said to use inductive feedback. Its tank circuit is a single capacitor $C$ in parallel with two inductors $L_1$ and $L_2$ connected in series, the junction between them being the tapping point. The output is developed across $L_1$ and the feedback voltage across $L_2$.

A common-emitter transistor amplifier supplies the amplification. Resistors $R_1$, $R_2$ and $R_E$ set the DC bias, $C_E$ is the emitter bypass capacitor, $C_C$ is the coupling capacitor, and a radio-frequency choke (RFC) — a short circuit for DC but an open circuit for AC — isolates the DC supply from the collector oscillations.

Working: at switch-on the collector current charges $C$, which then discharges through $L_1$ and $L_2$, setting up tank oscillations. The voltages across the two inductor sections are in opposite phase, so the tank contributes $180^\circ$ and the transistor another $180^\circ$, giving the $360^\circ$ loop shift needed for oscillation. …