Introduction:
The Hartley oscillator is a type of LC oscillator that generates sinusoidal waveforms at a specific frequency. It is widely used in radio frequency (RF) applications. The oscillator consists of an LC tank circuit and an active element, typically a transistor or an operational amplifier, which provides the required gain and feedback to sustain oscillations. In the Hartley oscillator, the active element introduces a phase shift between the input and output signals.

Explanation:
The phase difference produced by the active element in the Hartley oscillator is 180 degrees. This means that the output signal is inverted with respect to the input signal. Let's understand why this phase difference occurs.

Working principle of Hartley oscillator:
The Hartley oscillator works on the principle of positive feedback. The LC tank circuit, consisting of an inductor (L) and a capacitor (C), provides the necessary energy storage and frequency-selective properties. The active element, connected in a feedback configuration, amplifies the signal and provides the required phase shift.

Phase shift in the active element:
The active element in the Hartley oscillator, typically a transistor, introduces a 180-degree phase shift between the input and output signals. This phase shift occurs due to the transistor's inherent characteristics and the biasing arrangement.

When the input signal is applied to the base/emitter of the transistor, it undergoes amplification. During this amplification process, the transistor introduces a phase shift of 180 degrees. This means that the output signal is in reverse phase compared to the input signal.

Effect on the LC tank circuit:
The inverted output signal from the active element is fed back to the LC tank circuit. This feedback signal combines with the input signal and reinforces the oscillations. The LC tank circuit, being a frequency-selective network, allows only the desired frequency to oscillate.

Importance of 180-degree phase shift:
The 180-degree phase shift introduced by the active element is crucial for sustaining oscillations in the Hartley oscillator. It provides the necessary positive feedback required to maintain a constant amplitude and frequency of oscillation. Without this phase shift, the oscillator would not be able to generate sustained oscillations.

Conclusion:
In summary, the active element in the Hartley oscillator introduces a phase shift of 180 degrees between the input and output signals. This phase shift is essential for sustaining oscillations and generating sinusoidal waveforms at the desired frequency.