Hartley Oscillator

The circuit diagram of Hartley Oscillator is as shown in figure below. It uses two inductors placed across common capacitor C and the center of two inductors ins tapped. The tank circuit is made up of L₁ , L₂ and C and is given by.

 where                L_T = L₁ + L₂ + 2M

         

                           M= Mutual inductance between L₁ and L₂

• When the circuit is turned ON, the capacitor is charged. When this capacitor is fully charged, it discharges through coils L₁ and L₂ setting up oscillations of frequency determined by expression 1. The output voltage of the amplifier appears across L₂ and feedback voltage across L₁. The voltage across L₁ is 180⁰  out of phase with the voltage developed across L₂.
• A phase shift of 180⁰ is produced by the transistor and a further phase shift of 180⁰ is produced by L₁-L₂ voltage divider circuit. In this way feedback is properly phased to produce continuous undamped oscillations.

Feedback fraction- In Hartley oscillator the feedback voltage is across L₁ and output voltage is across L_2.

Therefore  feedback fraction