Q. With a neat circuit diagram explain the working of a Hartley oscillator using an npn transistor and obtain the expression for oscillation frequency and for minimum gain for sustained oscillation.

                   The Hartley oscillator is widely used as a local oscillator in radio receivers. Hartley oscillator is the same as colpitt's oscillator except that phase shift network consists of two inductors L1 and L1 and a capacitor instead of two capacitors and one inductor. The output of the amplifier is applied across the inductor L1 and the voltage across inductor L2 is the feedback voltage. The coil L1 is inductively coupled to the coil L2, the combination functions as an autotransformer. However, because of direct connection, the junction of L1 and L2 cannot be directly grounded. Instead another capacitor is CL is used. The collector supply voltage Vcc is applied to the collector through a radio frequency choke, which permits an easy flow of direct current but at the same time, it offers very high impedance to the high frequency currents. The presence of the coupling capacitor Cc in the output circuit does not permit the dc currents to got to the tank circuit. The radio frequency energy developed across RFC is capacitively coupled to the tank tank circuit through the capacitor Cc. The output of the phase shift network is coupled from the junction of  L2 and C to the amplifier input at base through coupling capacitor Cc, which blocks dc but provides path to ac. Transistor itself produces a phase shift of 180 degree and another phase shift of 180 degree is provided by the feedback. Thus a total phase shift of 360 degree is obtained which is an essential condition for developing oscillations. The output voltage derived from a secondary winding L' coupled to the inductance L1.