Basic Oscillatory Circuits
Basic Oscillator Circuit
The oscillatory circuit, also called the L-C circuit or tank circuit, consists of an inductive coil of inductance L connected in parallel with a capacitor of capacitance C. The frequency of oscillations produced by the circuit depends upon the values of L and C. The worth noting point is that both inductor and capacitor are capable of storing energy—the inductor stores energy in its magnetic field whenever current flows through it while the capacitor stores energy in its dielectric field whenever a pd exists across its plates.
For understanding the operation of an oscillatory circuit, let the capacitor be charged from a dc source with the polarity as shown in figure.a. The negative terminal of the supply battery supplies electrons to the lower plate of the capacitor and because of accumulation of electrons on the lower plate the capacitor gets charged and a pd is developed across the plates of the capacitor. Thus the energy is introduced in the capacitor in the form of electric potential energy. Now when the capacitor is fully charged and the switch S is opened, as shown in fig. (b), the capacitor cannot discharge through L.
Now let the switch S be thrown in position ‘b’, current starts flowing in the circuit but the self induced emf in the coil opposes the current flow. Thus the rate of rise of current is slow. Maximum current flows in the circuit when the capacitor is fully discharged. Due to flow of current, magnetic field is set up which stores the energy given by the electric field,as shown in fig. (c). Thus, at the instant the capacitor gets completely discharged, the electrostatic energy stored in the capacitor gets converted into the magnetic field energy associated with the inductor L.
When the capacitor is completely discharged, the magnetic field begins to collapse and a counter or back emf is developed which, according to Lenz’s law, keeps the current flowing in the same direction. The capacitor now starts getting charge but with opposite polarity, as shown in fig.(d). In this case, the energy associated with the magnetic field is again converted into electrostatic energy. In an ideal case (that is, both the L and C are loss-free), the capacitor is charged to the value it had initially while the magnetic field energy reduces to zero.
After the collapsing field has recharged the capacitor, the capacitor now begins to discharge with a current flow in the opposite direction. The electric field starts collapsing whereas magnetic field starts building up again but in opposite direction. Fig. (e) shows the condition when the capacitor gets fully discharged. The sequence of charging and discharging continues, that is, the process of transformation of dielectric energy into magnetic energy and vice-versa is repeated again and again. This situation is similar to an oscillating pendulum, in which the energy keeps on interchanging between potential and kinetic energy. Thus the charge and discharge of a capacitor through inductor results in oscillating current and hence electrical oscillations are set up in the L-C or tank circuit. The frequency of oscillation is the same as the resonant frequency of the tank circuit and it is given as fo = 1/2∏√LC
If there were no losses in the tank circuit, the interchange of energy between L and C would continue indefinitely. However, this is not factual position – some energy is lost in the form of heat generated in the coil resistance, capacitor leakage resistance and connecting wires and some energy is also lost in the form of electro-magnetic waves that are radiated out from the circuit through which an oscillatory current is flowing. As a result, the oscillating current goes on decreasing with time and eventually becomes zero when the total energy is consumed in overcoming the losses.
Thus for sustaining the oscillations it is imperative that energy is supplied to the L-C circuit at the same rate at which it is dissipated. In case of electronic oscillators, the transistor and power supply source are provided to feed energy to the for meeting the losses at right time. Thus sustained or undamped oscillations are produced by electronic oscillator circuits.
