Q1Analog Circuits

Question

How the oscillations are maintained in Hartley oscillator? Also obtain the expression for the frequency of oscillation.

Answer 1

A Hartley Oscillator is an LC electronic oscillator whose tuned tank circuit consists of two inductors ( $L_{1}$ and $L_{2}$ , often a single tapped coil) in series and a single capacitor ( $C$ ) in parallel with them.

When power is applied, transient noise charges the capacitor, which then discharges through the inductors, initiating damped oscillations. To sustain these oscillations (undamped), positive feedback is required.

The amplifier (typically a CE transistor) provides a $18 0^{\circ}$ phase shift. The tank circuit's tapped inductor acts as an auto-transformer. The ground is connected between $L_{1}$ and $L_{2}$ . The feedback voltage developed across $L_{2}$ is $18 0^{\circ}$ out of phase with the voltage across $L_{1}$ . This provides an additional $18 0^{\circ}$ phase shift, resulting in a total phase shift of $36 0^{\circ}$ , satisfying the Barkhausen criterion to maintain continuous oscillations.

The resonant frequency is determined by the total equivalent inductance and the capacitance of the tank circuit.

The equivalent inductance of the two series inductors (including mutual inductance $M$ if they share a core) is: $L_{e q} = L_{1} + L_{2} + 2 M$

The frequency of oscillation $f$ is given by the standard LC resonance formula:

Q1Analog Circuits

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