The correct answer is option 'D' - Relaxation oscillators.

Relaxation oscillators are a type of oscillator that does not use a feedback network for its oscillation. Unlike LC oscillators, RC oscillators, and crystal oscillators, relaxation oscillators generate a periodic waveform through the charging and discharging of a capacitor or an inductor.

Relaxation oscillators work based on the principle of charging and discharging a capacitor or an inductor at a specific rate. The charging and discharging process creates a waveform with a specific frequency and shape. This waveform is then used as an output signal.

Here is a detailed explanation of the other oscillator types mentioned in the question:

a) LC Oscillator:
LC oscillators use a combination of inductors (L) and capacitors (C) to generate oscillations. The feedback network in an LC oscillator consists of an LC tank circuit, which is responsible for generating the desired frequency. The LC tank circuit is connected in a feedback loop to sustain oscillations.

b) RC Oscillator:
RC oscillators use resistors (R) and capacitors (C) to generate oscillations. The feedback network in an RC oscillator is typically an RC circuit. The resistor and capacitor values are chosen such that the RC circuit provides the required phase shift and gain for sustained oscillations.

c) Crystal Oscillator:
Crystal oscillators use a crystal resonator as a feedback network. The crystal resonator is a highly stable and precise component that vibrates at a specific frequency when an electric field is applied to it. The crystal resonator is connected in a feedback loop with an amplifier or an inverter to sustain oscillations at the desired frequency.

d) Relaxation Oscillators:
Relaxation oscillators, as mentioned earlier, do not use a feedback network for their oscillation. Instead, they rely on the charging and discharging of a capacitor or an inductor to generate a periodic waveform. The charging and discharging process is usually controlled by a timing element, such as a resistor-capacitor (RC) network or a resistor-inductor (RL) network.

In summary, while LC oscillators, RC oscillators, and crystal oscillators utilize feedback networks to generate oscillations, relaxation oscillators rely on the charging and discharging of a capacitor or an inductor without the need for a feedback network.