**Hartley Oscillator using Transistor Analysis:**

The transistor Hartley oscillator is as popular as Colpitt’s oscillator and is widely used as a local oscillator in radio receivers. The circuit arrangement is shown in Fig. 21.16. Hartley oscillator circuit is similar to Colpitt’s oscillator circuit, except that phase shift network consists of two inductors L_{1} and L_{2} and a capacitor C instead of two capacitors and one inductor. The output of the amplifier is applied across inductor L_{1} and the voltage across inductor L_{2} forms the feedback voltage. The coil L_{1} is inductively coupled to coil L_{2}, the combination functions as an auto-transformer. However, because of direct connection, the junction of L_{1} and L_{2} cannot be directly grounded. Instead, another capacitor C_{L} is used. The operation of the circuit is similar to that of the Colpitt’s oscillator circuit.

Considering the fact that there exists mutual inductance between coils L_{1} and L_{2} because the coils are wound on the same core, their net effective inductance is increased by mutual inductance M. So in this case effective inductance is given by the equation

and resonant or oscillation frequency is given by the equation

**Frequency of Oscillation:**

The general Eq. (21.10) derived in Art. 21.7 is reproduced here

Here Z_{1} = jÏ‰L_{1} + jÏ‰M; Z_{2} = jÏ‰L_{2} + jÏ‰M and

Substituting these values in general Eq. (21.10), we get

Equating the imaginary part of above Eq. (21.28) to zero, we have

The above Eq. (21.29) gives the frequency of oscillation. Equating the real component of Eq. (21.28) to zero, we get

As for other oscillator circuits, the loop gain must be greater than 1 to ensure that circuit oscillates.

**FET Hartley Oscillator:**

An FET Hartley oscillator circuit is shown in Fig. 21.17. The noteworthy point is that inductors L_{1 }and L_{2} have a mutual coupling M, which is to be taken into account in determination of the equivalent inductance for the resonant circuit. This circuit operates at a frequency given by Eq. (21.29).