# Sinusoidal Oscillators - Basic Concepts

Tutorial on sinusoidal oscillators
2020-11-20 02:58:39
# Sine Oscillators - Basic Concepts

An amplifier with positive feedback produces its output to be in phase with and increases signal strength. Positive feedback is also referred to as ** degenerative feedback ** or ** direct feedback **. This type of feedback makes a feedback amplifier, an oscillator.

The use of positive feedback results in a feedback amplifier having a higher closed loop gain than the open loop gain. This results in ** instability ** and functions as an oscillatory circuit. An oscillating circuit provides a constantly varying amplified output signal of any desired frequency.

## The oscillatory circuit

An oscillatory circuit produces electrical oscillations of a desired frequency. They are also known as ** tank circuits **.

A simple tank circuit cincludes an inductance L and a capacitor C which together determine the frequency of oscillation of the circuit.

To understand the concept of an oscillatory circuit, consider the following circuit. The capacitor in this circuit is already charged using a DC source. In this situation, the upper plate of the capacitor has an excess of electrons while the lower plate has a deficit of electrons. The capacitor contains electrostatic energy and there is a voltage across the capacitor.

When the ** S ** switch is closed, the capacitor discharges and current flows through the inductor. Due to the inductive effect, the current slowly builds up to a maximum value. After the capacitor is fully discharged, the magnetic field around the coil is maximum.

Now let's move on to the next step. Once the capacitor is completely discharged, the magnetic fie ld begins to collapse and produces a counter-EMF according to Lenz's law. The capacitor is now charged with a positive charge on the top plate and a negative charge on the bottom plate.

Once the capacitor is fully charged, it begins to discharge to create a magnetic field around coil, as shown in the following circuit diagram.

This continuation of charge and discharge results in a reciprocating motion of 'electrons or an ** oscillating current **. The exchange of energy between L and C produces continuous ** oscillations **.

In an ideal circuit , where there are no losses, the oscillations would go on indefinitely. In a practical tank circuit, losses such as ** resistive ** and ** radiation losses ** in the coil and ** dielectric losses ** occur. in the capacitor. These losses result in damped oscillations.

## Frequency of oscillations

The frequency of oscillations produced by the tank circuit is determined by the components of the tank circuit, ** the L ** and ** the C **. The actual frequency of the oscillations is the ** resonant frequency ** (or natural frequency) of the tank circuit which is given by

$$ f_r = frac {1} {2 pi sqrt { LC}} $$

### Capacitance of the capacitor

The oscillation frequency f _{ o } is inversely proportional to the square root of the capacitance of a capacitor. Thus, if the value of the capacitor used is large, the periods of charge and discharge time will be larges. Therefore, the frequency will be lower.

Mathematically, the frequency,

$$ f_o propto 1 sqrt {C} $$

### Self- Inductance of the coil

The frequency of the oscillation f _{ o } is proportional to the square root of the self-inductance of the coil. If the value of the inductance is large, the opposition to the change of current flow is greater and therefore the time required to complete each cycle will be longer, which means that the period of time will be longer and the frequency will be lower.

Mathematically, the frequency,

$$ f_o propto 1 sqrt {L} $$

Combining the two equations above,

$$ f_o propto frac {1} {sqrt {LC}} $$

$$ f_o = frac {1} {2 pi sqrt {LC}} $$

The above equation, although it indicates the output frequency, is the ** natural frequency ** or ** resonant frequency ** of the tank circuit.