Passive Components 41
Figure 2.16: The parallel resonant circuit. The voltage V across this circuit is a maximum at the resonant frequency
A resonant circuit can act like a selective transformer, delivering an output which is at a much larger voltage or current than the input, for one particular frequency (in practice, a small range or band of frequencies centered around one frequency). This is the effect that allows a radio or television to be tuned to one of a set of transmitting stations, using the selective transformer effect of the resonant circuit. Resonant circuits are also important for timing and for transmitting signals. A piece of quartz, made in the form of a capacitor that uses the quartz as an insulator, will behave like a resonant circuit, with a step-up ratio at resonance that is much higher than can be achieved by any combination of inductor and capacitor, so that these quartz crystals are used to control the frequency of transmitters and also in clocks and watches. Summary When an inductor and a capacitor are used in the same circuit, their phase shifts are in opposite directions. When the sizes of the reactances are equal, the effects cancel so that for alternating signals, the only effect is of resistance. For a series circuit, this causes the current to be a maximum at the resonant frequency and for a parallel circuit the voltage is a maximum at resonance. The resonance effect is used for selecting a frequency or a small range (a narrow band) of frequencies for purposes such as radio tuning. A quartz crystal can be made to resonate, and is more efficient than any inductor/capacitor combination, so that quartz crystals are widely used for timing and frequency setting.