By David Herres
A resonant circuit is formed when a capacitor and inductor (coil) are in parallel or in series. The two circuit elements will block or pass a single specific frequency out of a divers mix. For this reason, resonant circuits make possible radio and TV transmission and reception and perform many other useful tasks.
Capacitors and coils share the property that they are both capable of storing electrical energy. When voltage is applied to the plates of a capacitor, C, an electrostatic charge is established in the thin dielectric layer that separates the two plates. If a load is connected to the capacitor’s leads, the capacitor discharges through the load at a rate that is determined by the circuit’s time constant, which depends on the resistance and capacitance.
An inductor, L, is also capable of storing electrical energy and subsequently dissipating it through a load. The mechanism is different. When voltage is applied to a coil (or to any conductor, which always has some degree of inductance), a magnetic field is established in the surrounding space. The act of establishing the magnetic field requires energy, which is stored in the magnetic field as opposed to being dissipated in the form of heat as in a resistive load. If the inductor now connects to a load, the magnetic field collapses, its energy being released into the circuit.
In a parallel LC resonant circuit, the impedance is maximum at the resonant frequency, so the current is minimum at this point. In a series LC resonant circuit, the impedance is minimum at the resonant frequency, so the current is maximum at this point. Either of these LC circuits can be placed in either shunt or series configuration to produce band pass or band rejection.
Accordingly, the resonant circuit can be used to pass or tune out any desired signal. If you examine a graph of the resonant circuit output, you will see a peak or dip in amplitude (Y axis) plotted against frequency (X axis). This is the frequency domain well known by Fourier Transform students. The sharpness of this curve corresponds to the Q (for quality) of the circuit, but keep in mind that the appearance of the curve will depend also upon how the graph is scaled.
For a resonant circuit to work, that is to say for it to be in a condition of resonance, inductive reactance and capacitive reactance must be equal. As long as they are the same, they can be any practical value. As the frequency increases, capacitive reactance becomes lower and inductive reactance becomes higher. For this reason, those values will be equal at one particular frequency, and that is the resonant frequency.
After a pulse of energy has been injected into a resonant circuit, this energy is alternately stored as an electrostatic charge in the capacitor and as a magnetic field surrounding the inductor. An oscilloscope connected to the plates of the capacitor will display a sine wave. Ideally, the resonant circuit would ring indefinitely, but in the real world a small amount of resistance causes the output to gradually diminish to zero. The waveform as seen in an oscilloscope display is known as a damped wave. This situation arises often in nature and in electronic circuits.
If electrical energy is fed into the circuit continuously, there is a condition known as oscillation. An oscillator is an essential part of the superheterodyne used in virtually all modern radio and TV equipment. A subsequent article will discuss some of the varieties and uses of oscillators in all sorts of electrical equipment.
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