Hartley Oscillator

HARTLEY OSCILLATOR

Hartley oscillator shown in Fig. 4.13, Z₁ and Z₂ are inductors and Z₃ is a capacitor. resistors R₁, R₂ and R_E provide the necessary dc bias to the transistor.

C_E is a bypass capacitor C_C1 and C_C2 are coupling capacitors. The feedback network consisting of inductors L₁ and L₂, and capacitor C determines the frequency of the oscillator.

When the supply voltage +V_CC is switched ON, a transient current is produced in the tank circuit and consequently, damped harmonic oscillations are set up in the circuit.

The oscillatory current in the tank circuit produces ac voltages across L₁ and L₂. As terminal 3 is earthed, it is at zero potential. If terminal 1 is at a positive potential with respect to 3 at any instant, terminal 2 will be at a negative potential with respect to 3 at the same instant.

Thus the phase difference between the terminal 1 and 2 is always 180°. In the CE mode, the transistor provides the phase difference of 180° between the input and output. Therefore the total phase shift is 360°. Thus at the frequency determined for the tank circuit, the necessary condition for sustained oscillation is satisfied. If the feedback is adjusted so that the loop gain Aβ = 1, the circuit acts as an oscillator.

The frequency of oscillation is f_o = 

Where

L = L₁ + L₂ + 2M

M - Mutual inductance between the coils L₁ and L₂.

The condition for sustained oscillation is

Analysis

In the Hartley oscillator Z₁ and Z₂ are inductive reactances and Z₃ is the capacitive reactance. If M is the mutual inductance between the inductors, then

Substituting these values in oscillator equation, h_ie (Z₁ + Z₂ + Z₃) + Z₁ Z₂ (1+ h_fe) + Z₁ Z₃ = 0 and simplifying, we get

0

The frequency of oscillation f_o = ω_o/2π can be determined by equating the imaginary part to zero

The condition for maintenance of oscillation is