LC oscillations

As soon as we connect a charged capacitor to an inductor, the electric current and charge on that capacitor go through the LC oscillation process. No matter what happens, the LC Oscillations will continue endlessly if the LC circuit has no resistance in it. An LC oscillator is the name given to this circuit. Two components: a capacitor and an inductor are needed to complete the circuit.It is common practice that the order is equal to the number of L and C elements in the circuit, and it cannot exceed this number in any case.

Definition- LC oscillations

When the electric charge flows through the circuit before the device’s output, it forms an LC oscillator circuit that further carries out the process. When the connection of the capacitor and inductor undergoes the passage of electric charge, it performs the LC oscillations. In this type of circuit, the conversion of the signal from DC to AC takes place. This special oscillator circuit converts the signals and electric charge into waveforms. The LC oscillations can generate many types of waveforms:

• Sawtooth waveforms 

• Sinusoidal waveform

• Triangular waveform

• Square waveform etc

Circuit

The LC oscillator circuit is a very simple circuit that follows minimal devices and variations. The only special property of this circuit is that it performs a rare conversion of direct current (DC) to alternate current (AC). The circuit of the LC oscillations follows the tank circuit format, which consists of an inductor and a capacitor. A capacitor with a complete charge connects to an inductor with no charge in this circuit. This connection results in an output with a positive format.

Working

The process of LC oscillations is straightforward. When the connection of these electric circuit types is established, the attachments and their charging condition play a key role. The circuit functions like an electrical resonator, storing energy and oscillating at the circuit’s resonant frequency. These circuits are used to select a signal at a specific frequency using a compound signal or generate signals at a specific frequency using a signal generator. These circuits function as significant components in various electronic devices, including radio equipment, filters, tuners, and oscillators. When the capacitor with a complete charge position connects to the inductor with no charge in a low resistance, the inductor takes charge from the capacitor. 

When the inductor comes to a full charge position, the capacitor becomes empty, taking charge from the inductor. This process goes on, and these transfers of energies from the capacitor to the inductor and vice versa form the LC oscillations. The capacitor stores the energy and transfers it into the inductor in a uniform time interval. This continuous to and fro movement of energies converts the DC form of current to the AC form of current.

Let consider a circuit in which an inductor L and a capacitor C are connected in series. Differential equation for circuit is given as follow:

d²q/dt²+q/LC=0

Here q is charge flowing is circuit

L = inductance

C = capacitance

dt = small time duration.

Above equation is similar to SHM equation so it solution can be written as

q(t)= q0sin(ωt +Ø)

Here = 1/√LC is natural frequency and is the initial phase.

Total energy of LC circuit

U = q²/2C+Li²/2

In the above equation the first term defines the energy of the capacitor and the second term tells the energy of the inductor.

Types

The oscillations in the electric circuit bring the electric charge in form, as per the device’s need. The LC oscillations convert the direct to alternate current using the minimum amount of charge. The types of LC oscillations help circuits function better. Here is the description:

• Tuned collector oscillator:

This is a tune format of oscillators useful in the transistors. In this type of circuit, the LC transistor oscillation occurs between the base and ground of the transistor. The tune circuit formation takes place between the transformer coil and the capacitor. 

•  Hartley oscillator:

This type of tank circuit for the LC oscillations consists of two inductors and a single capacitor. In this type of circuit, both the inductors are connected in a series, while the capacitor is connected parallel to the combination. This circuit needs a maximum 20KHz to 20MHz of charge.

•  Colpitts oscillators:

This is one of the tank circuits that perform LC oscillations with two inductors and a single capacitor. This circuit also has a similar combination of two inductors in a series and the capacitor in parallel form as the Hartley oscillator. The energy consumption is also the same, but the frequency’s better stability improves the performance.

• Clapp oscillators:

A Clapp oscillator is an LC electrical oscillator with a frequency set by a specific combination of an inductor and three capacitors. In this type of tank circuit, the capacitor combines with the inductor in a series to improve frequency stability. When the additional capacitors move the other two capacitors to the isolation state, it reduces transistor parameters like the junction capacitance. This reduction during the LC oscillations brings the stable frequency in a better way. 

Conclusion

Because it implies no energy is lost through resistance, an LC circuit is a simplification. Small but non-zero resistance in the components and connecting wires of an LC circuit is always present in any practical implementation. With minimal damping in mind, the resistance of an LC circuit should be kept as low as feasible. In spite of the fact that a practical circuit will always have some losses, this ideal version of the circuit is nevertheless useful for understanding and physical intuition.