### Sinusoidal Oscillators

• Amplification that has positive feedback causes the signal to become stronger and provides an output that is in phase with the input. Degenerative feedback and direct feedback are other names for positive feedback. A feedback amplifier becomes an oscillator with this type of feedback.

• A feedback amplifier with positive feedback has a closed-loop gain that is higher than the open-loop gain. In addition to being unstable, it functions as an oscillating circuit. An oscillating circuit produces an output signal that is continuously changing and amplified at any specified frequency.

## The Oscillatory Circuit

• Electrical oscillations with the desired frequency are generated by oscillatory circuits. Tank circuits is another name for them.

• An inductor L and a capacitor C make up a straightforward tank circuit, and they work together to set the circuit's oscillation frequency.

• Let's look at the circuit below to better comprehend the idea of an oscillatory circuit. A dc source has previously been used to charge the capacitor in this circuit. In this case, the capacitor's upper plate has an overabundance of electrons while the bottom plate is deficient. There is a voltage across the capacitor, which contains some electrostatic energy.

• The capacitor discharges and current passes via the inductor when switch S is closed. The current gradually increases to a maximum value because of the inductive effect. The magnetic field surrounding the coil reaches its maximum once the capacitor has fully discharged.

• Let's proceed to the next phase right away. The magnetic field starts to collapse and create a counter EMF once the capacitor is fully depleted, in accordance with Lenz's law. Positive charge is now present on the upper plate of the capacitor while negative charge is present on the bottom plate.

• The following circuit diagram illustrates how the capacitor creates a magnetic field surrounding the coil by beginning to discharge once it is fully charged.

• The continued charging and discharging causes oscillatory currents or alternating electron motion. Continuous oscillations are produced by the energy transfer between L and C.

• The oscillations would continue forever in a perfect circuit with no losses. Losses like resistive and radiation losses in the coil and dielectric losses in the capacitor happen in a real tank circuit. Damped oscillations are the result of these losses.

Frequency of Oscillations:

The tank circuit's L and C components, which cause oscillations, control the frequency of those oscillations. The resonant frequency (or natural frequency) of the tank circuit, which is determined by, is the actual frequency of oscillations.

$F_r=\frac1{2\pi\sqrt{L_c}}$