# Electrical oscillations

The oscillations of the current within an electrical circuit are of fundamental importance in the generation of waveforms of a variety of shapes for radio, oscilloscopes, signal generators and so forth. One of the simplest circuits for producing these oscillations is a capacitor and an inductor connected as shown in Figure 1. In understanding these oscillations it is helpful to compare them with the mechanical oscillations in a spring.

The mass on the spring oscillates, transferring stored potential energy in the spring to kinetic energy of the mass and back again. The charge in the electrical circuit also oscillates, transferring stored energy in the electric field of the capacitor to energy in the magnetic field in the inductor.

(a) This diagram represents the initial zero energy situation for both Systems. The mass is at rest and the springs are in equilibrium and no energy exists as stored charge in the capacitor or current in the inductor.

(b) The mass is displaced from its rest position, and therefore potential energy is stored in the spring. The capacitor is charged, thus possessing potential energy.

(c) As soon as the mass is released it moves to the right, gaining kinetic energy. The capacitor begins to discharge through the inductor, producing a current in it.

(d) The mass is now at rest; all the energy is stored as potential energy in the spring. The charge has now stopped moving and all energy is stored in the capacitor, which is charged in the opposite sense from its original state.

(e) This process now repeats itself, the mass oscillating backwards and forwards and the charge continually charging and discharging the capacitor.
A continuous exchange of energy occurs from potential to kinetic energy in the springs ½Fe going to ½mv2and in the electrical circuit ½ QV going to ½ Li2

The amplitudes of the oscillations decrease with time, since energy is lost as other forms: (a) in the spring as heating in the coils and air resistance, (b) in the inductor and connecting wires as heat due to the flow of current within them.

## Filters and tuned circuits

The resonance effects in an L-C circuit maybe used to filter out selected regions of the frequency spectrum.
Figure 2(a) shows an acceptor filter where frequencies of 1/[2p(LC)1/2] will be passed by the filter. Figure 2(b) shows a rejector filter where all frequencies except those of frequency 1/2p(LC)1/2 will be passed by the filter.

If the capacitor (or inductor) is variable, then the circuit may be tuned to resonate at a particular frequency. This is used in the tuning of a radio set. The aerial receives a broad hand of frequencies and the capacitor is varied so that the circuit resonates at the frequency of the required station. A simple circuit for the tuner section of a radio receiver is shown in Figure 3(a). The response of the circuit with frequency is shown in Figure 3(b), in which R is the total series resistance of the tuned circuit.