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Electrical resonance occurs in an
electric circuit An electrical network is an interconnection of electrical components (e.g., batteries, resistors, inductors, capacitors, switches, transistors) or a model of such an interconnection, consisting of electrical elements (e.g., voltage sources, ...
at a particular '' resonant frequency'' when the impedances or
admittance In electrical engineering, admittance is a measure of how easily a circuit or device will allow a current to flow. It is defined as the reciprocal of impedance, analogous to how conductance & resistance are defined. The SI unit of admittance ...
s of circuit elements cancel each other. In some circuits, this happens when the impedance between the input and output of the circuit is almost zero and the
transfer function In engineering, a transfer function (also known as system function or network function) of a system, sub-system, or component is a function (mathematics), mathematical function that mathematical model, theoretically models the system's output for ...
is close to one. Resonant circuits exhibit ringing and can generate higher voltages or currents than are fed into them. They are widely used in
wireless Wireless communication (or just wireless, when the context allows) is the transfer of information between two or more points without the use of an electrical conductor, optical fiber or other continuous guided medium for the transfer. The most ...
(
radio Radio is the technology of signaling and communicating using radio waves. Radio waves are electromagnetic waves of frequency between 30 hertz (Hz) and 300 gigahertz (GHz). They are generated by an electronic device called a transmit ...
) transmission for both transmission and reception.


LC circuits

Resonance of a circuit involving
capacitor A capacitor is a device that stores electrical energy in an electric field by virtue of accumulating electric charges on two close surfaces insulated from each other. It is a passive electronic component with two terminals. The effect of ...
s and
inductor An inductor, also called a coil, choke, or reactor, is a passive two-terminal electrical component that stores energy in a magnetic field when electric current flows through it. An inductor typically consists of an insulated wire wound into a c ...
s occurs because the collapsing magnetic field of the inductor generates an electric current in its windings that charges the capacitor, and then the discharging capacitor provides an electric current that builds the magnetic field in the inductor. This process is repeated continually. An analogy is a mechanical
pendulum A pendulum is a weight suspended from a pivot so that it can swing freely. When a pendulum is displaced sideways from its resting, equilibrium position, it is subject to a restoring force due to gravity that will accelerate it back toward the ...
, and both are a form of
simple harmonic oscillator In mechanics and physics, simple harmonic motion (sometimes abbreviated ) is a special type of periodic motion of a body resulting from a dynamic equilibrium between an inertial force, proportional to the acceleration of the body away from the ...
. At resonance, the series impedance of the two elements is at a minimum and the parallel impedance is at maximum. Resonance is used for
tuning Tuning can refer to: Common uses * Tuning, the process of tuning a tuned amplifier or other electronic component * Musical tuning, musical systems of tuning, and the act of tuning an instrument or voice ** Guitar tunings ** Piano tuning, adjusti ...
and filtering, because it occurs at a particular
frequency Frequency is the number of occurrences of a repeating event per unit of time. It is also occasionally referred to as ''temporal frequency'' for clarity, and is distinct from ''angular frequency''. Frequency is measured in hertz (Hz) which is eq ...
for given values of
inductance Inductance is the tendency of an electrical conductor to oppose a change in the electric current flowing through it. The flow of electric current creates a magnetic field around the conductor. The field strength depends on the magnitude of the ...
and
capacitance Capacitance is the capability of a material object or device to store electric charge. It is measured by the change in charge in response to a difference in electric potential, expressed as the ratio of those quantities. Commonly recognized are ...
. It can be detrimental to the operation of
communications Communication (from la, communicare, meaning "to share" or "to be in relation with") is usually defined as the transmission of information. The term may also refer to the message communicated through such transmissions or the field of inquir ...
circuits by causing unwanted sustained and transient oscillations that may cause
noise Noise is unwanted sound considered unpleasant, loud or disruptive to hearing. From a physics standpoint, there is no distinction between noise and desired sound, as both are vibrations through a medium, such as air or water. The difference arise ...
, signal
distortion In signal processing, distortion is the alteration of the original shape (or other characteristic) of a signal. In communications and electronics it means the alteration of the waveform of an information-bearing signal, such as an audio signal ...
, and damage to circuit elements. Parallel resonance or near-to-resonance circuits can be used to prevent the waste of electrical energy, which would otherwise occur while the inductor built its field or the capacitor charged and discharged. As an example, asynchronous motors waste inductive current while synchronous ones waste capacitive current. The use of the two types in parallel makes the inductor feed the capacitor, and ''vice versa'', maintaining the same resonant current in the circuit, and converting all the current into useful work. Since the inductive reactance and the capacitive reactance are of equal magnitude, :\omega L = \frac~, so :\omega = \frac~, where \omega = 2\pi f\,, in which is the resonance frequency in
hertz The hertz (symbol: Hz) is the unit of frequency in the International System of Units (SI), equivalent to one event (or cycle) per second. The hertz is an SI derived unit whose expression in terms of SI base units is s−1, meaning that on ...
, is the inductance in
henries The henry (symbol: H) is the unit of electrical inductance in the International System of Units (SI). If a current of 1 ampere flowing through a coil produces flux linkage of 1 weber turn, that coil has a self inductance of 1 henry.‌ The un ...
, and is the capacitance in
farad The farad (symbol: F) is the unit of electrical capacitance, the ability of a body to store an electrical charge, in the International System of Units (SI). It is named after the English physicist Michael Faraday (1791–1867). In SI base unit ...
s, when standard
SI unit The International System of Units, known by the international abbreviation SI in all languages and sometimes pleonastically as the SI system, is the modern form of the metric system and the world's most widely used system of measurement. E ...
s are used. The quality of the resonance (how long it will ring when excited) is determined by its factor, which is a function of resistance: Q = \tfrac\sqrt\,. An idealized, lossless circuit has infinite , but all actual circuits have some resistance and finite , and are usually approximated more realistically by an circuit.


RLC circuit

An RLC circuit (or LCR circuit) is an
electrical circuit An electrical network is an interconnection of electrical components (e.g., batteries, resistors, inductors, capacitors, switches, transistors) or a model of such an interconnection, consisting of electrical elements (e.g., voltage sources, ...
consisting of a
resistor A resistor is a passive two-terminal electrical component that implements electrical resistance as a circuit element. In electronic circuits, resistors are used to reduce current flow, adjust signal levels, to divide voltages, bias active el ...
, an inductor, and a capacitor, connected in series or in parallel. The RLC part of the name is due to those letters being the usual electrical symbols for resistance,
inductance Inductance is the tendency of an electrical conductor to oppose a change in the electric current flowing through it. The flow of electric current creates a magnetic field around the conductor. The field strength depends on the magnitude of the ...
and
capacitance Capacitance is the capability of a material object or device to store electric charge. It is measured by the change in charge in response to a difference in electric potential, expressed as the ratio of those quantities. Commonly recognized are ...
respectively. The circuit forms a harmonic oscillator for current and resonates similarly to an
LC circuit An LC circuit, also called a resonant circuit, tank circuit, or tuned circuit, is an electric circuit consisting of an inductor, represented by the letter L, and a capacitor, represented by the letter C, connected together. The circuit can ac ...
. The main difference stemming from the presence of the resistor is that any oscillation induced in the circuit decays over time if it is not kept going by a source. This effect of the resistor is called
damping Damping is an influence within or upon an oscillatory system that has the effect of reducing or preventing its oscillation. In physical systems, damping is produced by processes that dissipate the energy stored in the oscillation. Examples in ...
. The presence of the resistance also reduces the peak resonant frequency of ''damped'' oscillation, although the resonant frequency for ''driven'' oscillations remains the same as an LC circuit. Some resistance is unavoidable in real circuits, even if a resistor is not specifically included as a separate component. A pure LC circuit is an ideal that exists only in
theory A theory is a rational type of abstract thinking about a phenomenon, or the results of such thinking. The process of contemplative and rational thinking is often associated with such processes as observational study or research. Theories may be s ...
. There are many applications for this circuit. It is used in many different types of oscillator circuits. An important application is for
tuning Tuning can refer to: Common uses * Tuning, the process of tuning a tuned amplifier or other electronic component * Musical tuning, musical systems of tuning, and the act of tuning an instrument or voice ** Guitar tunings ** Piano tuning, adjusti ...
, such as in
radio receivers In radio communications, a radio receiver, also known as a receiver, a wireless, or simply a radio, is an electronic device that receives radio waves and converts the information carried by them to a usable form. It is used with an antenna. The ...
or
television set A television set or television receiver, more commonly called the television, TV, TV set, telly, tele, or tube, is a device that combines a tuner, display, and loudspeakers, for the purpose of viewing and hearing television broadcasts, or using ...
s, where they are used to select a narrow range of frequencies from the ambient radio waves. In this role the circuit is often referred to as a tuned circuit. An RLC circuit can be used as a
band-pass filter A band-pass filter or bandpass filter (BPF) is a device that passes frequencies within a certain range and rejects (attenuates) frequencies outside that range. Description In electronics and signal processing, a filter is usually a two-por ...
,
band-stop filter In signal processing, a band-stop filter or band-rejection filter is a filter that passes most frequencies unaltered, but attenuates those in a specific range to very low levels. It is the opposite of a band-pass filter. A notch filter is a ...
,
low-pass filter A low-pass filter is a filter that passes signals with a frequency lower than a selected cutoff frequency and attenuates signals with frequencies higher than the cutoff frequency. The exact frequency response of the filter depends on the filter des ...
or
high-pass filter A high-pass filter (HPF) is an electronic filter that passes signals with a frequency higher than a certain cutoff frequency and attenuates signals with frequencies lower than the cutoff frequency. The amount of attenuation for each frequency d ...
. The tuning application, for instance, is an example of
band-pass filter A band-pass filter or bandpass filter (BPF) is a device that passes frequencies within a certain range and rejects (attenuates) frequencies outside that range. Description In electronics and signal processing, a filter is usually a two-por ...
ing. The RLC filter is described as a ''second-order'' circuit, meaning that any voltage or current in the circuit can be described by a second-order
differential equation In mathematics, a differential equation is an equation that relates one or more unknown functions and their derivatives. In applications, the functions generally represent physical quantities, the derivatives represent their rates of change, an ...
in circuit analysis. The three circuit elements can be combined in a number of different
topologies In mathematics, topology (from the Greek words , and ) is concerned with the properties of a geometric object that are preserved under continuous deformations, such as stretching, twisting, crumpling, and bending; that is, without closing ho ...
. All three elements in series or all three elements in parallel are the simplest in concept and the most straightforward to analyse. There are, however, other arrangements, some with practical importance in real circuits. One issue often encountered is the need to take into account inductor resistance. Inductors are typically constructed from coils of wire, the resistance of which is not usually desirable, but it often has a significant effect on the circuit.


Example

A series circuit has resistance of 4 Ω, and inductance of 500 mH, and a variable capacitance. Supply voltage is 100 V alternating at 50 Hz. At resonance ~X_\mathsf ~=~ X_\mathsf~. The capacitance required to give series resonance is calculated as: :X_\mathsf ~=~ X_\mathsf ~=~ 2 \pi f L ~=~ 2\pi \times 50\ \mathsf \times 0.5\ \mathsf ~=~ 157.1 \text ~ :C ~=~ \frac ~=~ \frac = 20.3 \text ~ Resonance voltages across the inductor and the capacitor, ~V_\mathsf~ and ~V_\mathsf, will be: :I ~=~ \frac ~=~ \frac ~=~ 25\ \mathsf ~ :V_\mathsf ~=~ V_\mathsf ~=~ I X_\mathsf ~=~ 25\ \mathsf \times 157.1 \text ~=~ 3927.5\ \mathsf ~. As shown in this example, when the series circuit is at resonance, the magnitudes of the voltages across the inductor and capacitor can become many times larger than the supply voltage.


See also

*
Antiresonance In the physics of coupled oscillators, antiresonance, by analogy with resonance, is a pronounced minimum in the amplitude of an oscillator at a particular frequency, accompanied by a large, abrupt shift in its oscillation phase. Such frequencies ...
*
Antenna theory In radio engineering, an antenna or aerial is the interface between radio waves propagating through space and electric currents moving in metal conductors, used with a transmitter or receiver. In transmission, a radio transmitter supplies a ...
*
Cavity resonator A resonator is a device or system that exhibits resonance or resonant behavior. That is, it naturally oscillates with greater amplitude at some frequencies, called resonant frequencies, than at other frequencies. The oscillations in a resonator ...
*
Electronic filter Electronic filters are a type of signal processing filter in the form of electrical circuits. This article covers those filters consisting of lumped electronic components, as opposed to distributed-element filters. That is, using components ...
* Resonant energy transfer - wireless energy transmission between two resonant coils


References

{{FS1037C Electronic circuits Filter theory Synthesizers