The frequency of oscillation of a Hartley Oscillator is given as :

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  1. \(\rm \omega_O=\frac{L_1+L_2}{L_1L_2C}\)
  2. \(\rm \omega_O=\frac{1}{\sqrt{(L_1+L_2)}C}\)
  3. \(\rm \omega_O=\sqrt{\frac{L_1+L_2}{L_1L_2C}}\)
  4. \(\rm \omega_O=\frac{2\pi}{\sqrt{(L_1+L_2)}C}\)

Answer (Detailed Solution Below)

Option 2 : \(\rm \omega_O=\frac{1}{\sqrt{(L_1+L_2)}C}\)
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Detailed Solution

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Concept:-

 Hartley oscillator consists of a common emitter or common source amplifier which provides a phase shift of 180º.

F1 Madhu Engineering 09.06.2022 D6

In LC feedback network of 3 impedance which together provide an additional phase shift of 180º at the resonant frequency.

Thus total phase shift becomes 360° and oscillation occurs at f0.

X1 + X2 + X3 = 0

WoL1 + WoL2 - 1/WoC = 0

Wo( L1 + L) = 1/WoC

Wo = \(\frac{1}{\sqrt{( L_1 + L_2 ) C}}\)

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