How it works
The Hartley oscillator uses an LC tank with a tapped coil: the total inductance (L1 + L2 + 2M for coupled coils) resonates with C to set frequency. The transistor provides voltage gain; the tap on the inductor feeds back a fraction of the output voltage V_feedback = V_out × L2/(L1+L2) to the base. For sustained oscillation, the Barkhausen criterion requires loop gain ≥ 1: |A_v| × β_feedback ≥ 1. The feedback is 180° out of phase from the tank, and the common-emitter stage adds another 180°, making total phase shift 360° — positive feedback. Mutual inductance M between L1 and L2 (when they are wound on the same core) increases effective total inductance.
Key points to remember
Oscillation frequency f_0 = 1/(2π√(L_T·C)) where L_T = L1 + L2 + 2M. Feedback fraction β = L2/(L1+L2) for uncoupled coils; minimum transistor gain needed is A_v = L1/L2 to satisfy |Aβ| = 1. The Hartley oscillator is identified by its tapped inductor — replace the inductor tap with a capacitor tap and the circuit becomes a Colpitts oscillator. Frequency stability is moderate — better than RC oscillators but worse than crystal oscillators. Loading the output affects the tank Q and shifts frequency; a buffer amplifier stage is used to isolate load from the tank in precision applications.
Exam tip
The examiner always asks you to derive the frequency of oscillation and explain how the tapped inductor provides the 180° feedback phase shift — draw the tank circuit, label L1, L2, and C, and show the feedback voltage division explicitly.