Impedance matching is the electronics design practice of setting the
input impedanceThe input impedance, load impedance, or external impedance of a circuit or electronic device is the Thévenin equivalent impedance looking into its input.-Audio systems:...
(
ZS) of an electrical load equal to the fixed
output impedanceThe output impedance is the impedance on the output of a circuit. This is sometimes also referred to as the internal resistance of the circuit....
(
ZL) of the signal source to which it is ultimately connected, usually in order to
maximize the power transferIn electrical engineering, the maximum power theorem states that, to obtain maximum external power from a source with a finite internal resistance, the resistance of the load must be made the same as that of the source...
and minimize
reflectionsSignal reflection occurs when a signal is transmitted along a transmission medium, such as a copper cable or an optical fiber, some of the signal power may be reflected back to its origin rather than being carried all the way along the cable to the far end. This happens because imperfections in the...
from the load. This only applies when both are linear devices.
The concept of impedance matching was originally developed for
electrical powerElectric power is defined as the rate at which electrical energy is transferred by an electric circuit. The SI unit of power is the watt.When electric current flows in a circuit, it can transfer energy to do mechanical or thermodynamic work...
, but can be applied to any other field where a form of energy (not just electrical) is transferred between a source and a load.
Matching is obtained when
ZL =
ZS*.
Terminology
Sometimes the term "impedance matching" is used loosely to mean "choosing impedances that work well together" instead of "making two impedances
complex conjugateAs found in mathematics, a complex conjugate is most simply defined as one of a pair of complex numbers, each having the same real parts but with imaginary parts that differ in sign; e.g. 3 + 4i and 3 - 4i are complex conjugates...
". The looser interpretation includes
impedance bridgingIn electronics, especially audio and sound recording, a high impedance bridging, voltage bridging, or simply bridging connection is one which maximizes transfer of a voltage signal to the load...
, where the load impedance is much larger than the source impedance. Bridging connections are used to maximize the voltage transfer, not the power transfer.
With modern
audio electronics, impedance matching degrades audio performance;
impedance bridgingIn electronics, especially audio and sound recording, a high impedance bridging, voltage bridging, or simply bridging connection is one which maximizes transfer of a voltage signal to the load...
is used instead.
Explanation
The term impedance is used for the resistance of a system to an energy source. For constant signals, this resistance can also be constant. For varying signals, it usually changes with frequency. The energy involved can be electrical, mechanical, magnetic or even thermal. The concept of
electrical impedanceElectrical impedance, or simply impedance, describes a measure of opposition to a sinusoidal alternating current . Electrical impedance extends the concept of resistance to AC circuits, describing not only the relative amplitudes of the voltage and current, but also the relative phases...
is perhaps the most commonly known. Electrical impedance, like electrical resistance, is measured in ohms. In general, impedance has a
complexA complex number, in mathematics, is a number comprising a real number and an imaginary number; it can be written in the form a + bi, where a and b are real numbers, and i is the standard imaginary unit, having the property that i
2 = −1...
value, which means that loads generally have a
resistanceThe electrical resistance of an object is a measure of its opposition to the passage of a steady electric current. An object of uniform cross section will have a resistance proportional to its length and inversely proportional to its cross-sectional area, and proportional to the resistivity of the...
to the source that is in
phaseThe phase of an oscillation or wave is the fraction of a complete cycle corresponding to an offset in the displacement from a specified reference point at time t = 0. Phase is a frequency domain or Fourier transform domain concept, and as such, can be readily understood in terms of simple harmonic...
with a sinusoidal source signal
and reactance that is out of phase with a sinusoidal source signal. The total impedance (symbol:
Z) is the vector sum of the resistance (symbol:
R; a
real numberIn mathematics, the real numbers include both rational numbers, such as 42 and −23/129, and irrational numbers, such as pi and the square root of two; or, a real number can be given by an infinite decimal representation, such as 2.4871773339..., where the digits continue in some way; or, the real...
) and the reactance (symbol:
X; an
imaginary numberfrom blue area)|-||-||-||-| style="background:#cedff2;" | |-|style="background:#cedff2;" | |-|style="background:#cedff2;" | |-|style="background:#cedff2;" | |-||-||-||-| |-|}...
).
In simple cases, such as low-frequency or direct-current power transmission, the reactance is
negligibleIn engineering, mathematics, physics and similar disciplines, the term negligible refers to the quantities so small that they can be ignored when studying the larger effect...
or zero and the impedance can be considered a pure resistance, expressed as a real number. In the following summary, we will consider the general case when the resistance and reactance are both significant, and also the special case in which the reactance is negligible.
Reflectionless or broadband matching
Impedance matching to minimize reflections and maximize power transfer over a (relatively) large bandwidth (also called
reflectionless matching or
broadband matching) is the most commonly used. To prevent all reflections of the signal back into the source, the load (which must be totally resistive) must be matched exactly to the source impedance (which again must be totally resistive). In this case, if a transmission line is used to connect the source and load together, it must also be the same impedance:
Zload =
Zline =
Zsource, where
Zline is the
characteristic impedanceThe characteristic impedance or surge impedance of a uniform transmission line, usually written , is the ratio of the amplitudes of a single pair of voltage and current waves propagating along the line in the absence of reflections. The SI unit of characteristic impedance is the ohm...
of the transmission line. Although source and load should each be totally resistive for this form of matching to work, the more general term 'impedance' is still used to describe the source and load characteristics. Any and all reactance actually present in the source or the load will affect the 'match'.
Complex conjugate matching
This is used in cases in which the source and load are reactive. This form of impedance matching can only maximize the power transfer between a reactive source and a reactive
loadIf an electric circuit has a well-defined output terminal, the circuit connected to this terminal is the load....
at a
single frequency. In this case,
Zload =
Zsource*
(where * indicates the
complex conjugateAs found in mathematics, a complex conjugate is most simply defined as one of a pair of complex numbers, each having the same real parts but with imaginary parts that differ in sign; e.g. 3 + 4i and 3 - 4i are complex conjugates...
).
If the signals are kept within the narrow frequency range for which the matching network was designed, reflections (in this narrow frequency band only) are also minimized. For the case of purely resistive source and load impedances, all reactance terms are zero and the formula above reduces to
Z
load = Z
source
as would be expected.
Power transfer
Whenever a source of power
with a fixed output impedance, such as an electric signal source, a
radioRadio is the transmission of signals by modulation of electromagnetic waves with frequencies below those of visible light. Electromagnetic radiation travels by means of oscillating electromagnetic fields that pass through the air and the vacuum of space...
transmitterA transmitter is an electronic device which, usually with the aid of an antenna, propagates an electromagnetic signal such as radio, television, or other telecommunications.-Transmitter types:...
, or even mechanical sound (e.g., a
loudspeakerA loudspeaker is an electroacoustic transducer that converts an electrical signal into sound. The speaker pulses in accordance with the variations of an electrical signal and causes sound waves to propagate through a medium such as air or water.Loudspeakers are the most variable elements in a...
) operates into a
loadIf an electric circuit has a well-defined output terminal, the circuit connected to this terminal is the load....
, the maximum possible
powerIn physics, power is the rate at which work is performed or energy is converted. It is an energy per unit of time. As a rate of change of work done or the energy of a subsystem, power iswhere P is power, W is work and t is time....
is delivered to the load when the impedance of the load (load impedance) is equal to the
complex conjugateAs found in mathematics, a complex conjugate is most simply defined as one of a pair of complex numbers, each having the same real parts but with imaginary parts that differ in sign; e.g. 3 + 4i and 3 - 4i are complex conjugates...
of the impedance of the source (that is, its internal impedance). For two impedances to be complex conjugates, their resistances must be equal, and their reactances must be equal in magnitude but of opposite sign.
In low-frequency or DC systems, or in systems with purely resistive sources and loads, the reactances are zero, or small enough to be ignored. In this case, maximum power transfer occurs when the resistance of the load is equal to the resistance of the source (see
maximum power theoremIn electrical engineering, the maximum power theorem states that, to obtain maximum external power from a source with a finite internal resistance, the resistance of the load must be made the same as that of the source...
for a proof).
Impedance matching is not always desirable. For example, if a source with a low impedance is connected to a load with a high impedance, then the power that can pass through the connection is limited by the higher impedance, but the electrical voltage transfer is higher and less prone to corruption than if the impedances had been matched. This maximum voltage connection is a common configuration called
impedance bridgingIn electronics, especially audio and sound recording, a high impedance bridging, voltage bridging, or simply bridging connection is one which maximizes transfer of a voltage signal to the load...
or
voltage bridging and is widely used in signal processing. In such applications, delivering a high voltage (to minimize signal degradation during transmission and/or to consume less power by reducing currents) is often more important than maximum power transfer.
In older audio systems, reliant on transformers and passive filter networks, and based on the
telephoneThe telephone is a telecommunications device that transmits and receives sound, most commonly the human voice. It is one of the most common household appliances in the developed world, and has long been considered indispensable to business, industry and government...
system, the source and load resistances were matched at 600 ohms. One reason for this was to maximize power transfer, as there were no amplifiers available that could restore lost signal. Another reason was to ensure correct operation of the
hybrid transformersA hybrid coil is a transformer that has three windings, and which is designed to be configured as a circuit having four branches, that are conjugate in pairs....
used at central exchange equipment to separate outgoing from incoming speech so that these could be amplified or fed to a
four-wire circuitIn telecommunication, a four-wire circuit is a two-way circuit using two paths so arranged that the respective signals are transmitted in one direction only by one path and in the other direction by the other path...
. Most modern audio circuits, on the other hand, use active amplification and filtering, and they can use voltage bridging connections for best accuracy.
Impedance matching devices
Adjusting the source impedance or the load impedance, in general, is called "impedance matching".
There are a variety of devices that are used between some source of energy and some load that perform "impedance matching".
To match electrical impedances, engineers use combinations of
transformerA transformer is a device that transfers electrical energy from one circuit to another through inductively coupled conductors—the transformer's coils. A varying current in the first or primary winding creates a varying magnetic flux in the transformer's core, and thus a varying magnetic field...
s,
resistor|- align = "center"||width = "25"|| |- align = "center"||| Potentiometer|- align = "center"| || |- align = "top"| Resistor|| Variable
resistor|- align = "center"||width = "25"|| |- align = "center"||| Potentiometer|- align = "center"...
s,
inductorAn inductor or a reactor is a passive electrical component that can store energy in a magnetic field created by the electric current passing through it. An inductor's ability to store magnetic energy is measured by its inductance, in units of henries...
s and
capacitorA capacitor or condenser is a passive electronic component consisting of a pair of conductors separated by a dielectric. When a voltage potential difference exists between the conductors, an electric field is present in the dielectric. This field stores energy and produces a mechanical force...
s.
These passive and active impedance matching devices are optimized for different applications, and are called
balunA balun, , is a type of electrical transformer that can convert electrical signals that are balanced about ground to signals that are unbalanced and vice versa. They are also often used to connect lines of differing impedance.Baluns can take many forms and their presence is not always obvious...
s,
antenna tunerAn antenna tuner, transmatch, or antenna tuning unit matches a transceiver with a fixed impedance to a load impedance which is unknown, complex or otherwise does not match...
s (sometimes called ATUs or roller coasters because of their appearance), acoustic horns, matching networks, and
terminatorsElectrical termination of a signal involves providing a terminator at the end of a wire or cable to prevent an RF signal from being reflected back from the end, causing interference...
.
Transformers are sometimes used to match the impedances of circuits with different impedances. A transformer converts
alternating currentIn alternating current the movement of electric charge periodically reverses direction. An electric charge would for instance move forward, then backward, then forward, then backward, over and over again...
at one
voltageVoltage is commonly used as a short name for electrical potential difference. Its corresponding SI unit is the volt...
to the same waveform at another voltage. The power input to the transformer and output from the transformer is the same (except for conversion losses). The side with the lower voltage is at low impedance, because this has the lower number of turns, and the side with the higher voltage is at a higher impedance as it has more turns in its coil.
Resistive impedance matches are easiest to design. They limit the power deliberately, and are used to transfer low-power signals, such as unamplified audio or radio frequency signals in a radio receiver. Almost all digital circuits use resistive impedance matching which is usually built into the structure of the switching element.
Some special situations, such as radio tuners and transmitters, use tuned
filtersElectronic filters are electronic circuits which perform signal processing functions, specifically to remove unwanted frequency components from the signal, to enhance wanted ones, or both...
, such as stubs, to match impedances at specific frequencies. These can distribute different frequencies to different places in the circuit.
Confusingly, there are 3 possible ways to improve an impedance mismatch, all of which are called "impedance matching":
- devices intended to present an apparent load to the source of Rload = Rsource* (complex conjugate matching). Given a source with a fixed voltage and fixed source impedance, the maximum power theorem
In electrical engineering, the maximum power theorem states that, to obtain maximum external power from a source with a finite internal resistance, the resistance of the load must be made the same as that of the source...
says this is the only way to extract the maximum power from the source.
- devices intended to present an apparent load of Rload = Rline (complex impedance matching), to avoid echoes. Given a transmission line source with a fixed source impedance, this "reflectionless impedance matching" at the end of the transmission line is the only way to avoid reflecting echoes back to the transmission line.
- devices intended to present an apparent source resistance as close to zero as possible, or presenting an apparent source voltage as high as possible. This is the only way to maximize energy efficiency, and so it is used at the beginning of electrical power lines. Such an impedance bridging
In electronics, especially audio and sound recording, a high impedance bridging, voltage bridging, or simply bridging connection is one which maximizes transfer of a voltage signal to the load...
connection also minimizes distortionA distortion is the alteration of the original shape of an object, image, sound, waveform or other form of information or representation. Distortion is usually unwanted...
and electromagnetic interferenceElectromagnetic interference is a disturbance that affects an electrical circuit due to either electromagnetic conduction or electromagnetic radiation emitted from an external source. The disturbance may interrupt, obstruct, or otherwise degrade or limit the effective performance of the circuit...
, and so it is also used in modern audio amplifiers and signal processing devices.
In addition, there is the closely related idea of
- power factor correction devices intended to cancel out the reactive and nonlinear characteristics of a load at the end of a power line. This causes the load seen by the power line to be purely resistive. For a given true power required by a load, this minimizes the true current supplied through the power lines, and so minimizes the power wasted in the resistance of those power lines.
For example, a
maximum power point trackerA maximum power point tracker is a high efficiency DC to DC converter which functions as an optimal electrical load for a photovoltaic cell, most commonly for a solar panel or array, and converts the power to a voltage or current level which is more suitable to whatever load the system is...
is used to extract the maximum power from a solar panel, and efficiently transfer it to batteries, the power grid, or other loads.
The maximum power theorem applies to its "upstream" connection to the solar panel, so it emulates a load resistance equal to the solar panel source resistance.
However, the maximum power theorem does not apply to its "downstream" connection, so that connection is a
impedance bridgingIn electronics, especially audio and sound recording, a high impedance bridging, voltage bridging, or simply bridging connection is one which maximizes transfer of a voltage signal to the load...
connection -- it emulates a high-voltage, low-resistance source, to maximize efficiency.
"L" section
One simple electrical impedance matching network requires one capacitor and one inductor. One reactance is in parallel with the source (or load) and the other is in series with the load (or source). If a reactance is in parallel
with the source, the effective network matches from high impedance to low impedance. The "L" section is inherently a
narrowbandNarrowband refers to a situation in radio communications where the bandwidth of the message does not significantly exceed the channel's coherence bandwidth...
matching network.
The analysis is as follows. Consider a real source impedance of and real load impedance of . If a reactance is in parallel with the source impedance, the combined impedance can be written as:
If the imaginary part of the above impedance is completely canceled by the series reactance, the real part is
Solving for
If the above equation can be approximated as
The inverse connection, impedance step up, is simply the reverse, e.g. reactance in series with the source. The magnitude of the impedance ratio is limited by reactance losses such as the
QIn physics and engineering the quality factor or Q factor is a dimensionless parameter that describes how under-damped an oscillator or resonator is, or equivalently, characterizes a resonator's bandwidth relative to its center frequency....
of the inductor. Multiple "L" sections can be wired in cascade to achieve higher impedance ratios or greater bandwidth.
Transmission lineA transmission line is the material medium or structure that forms all or part of a path from one place to another for directing the transmission of energy, such as electromagnetic waves or acoustic waves, as well as electric power transmission....
matching networks can be modeled as infinitely many "L" sections wired in cascade. Optimal matching circuits can be designed for a particular system with the use of the
Smith chartThe Smith chart, invented by Phillip H. Smith , is a graphical aid or nomogram designed for electrical and electronics engineers specializing in radio frequency engineering to assist in solving problems with transmission lines and matching circuits...
.
Transmission lines
Impedance bridging is unsuitable for RF connections because it causes power to be reflected back to the source from the boundary between the high impedance and the low impedance. The reflection creates a
standing waveA standing wave, also known as a stationary wave, is a wave that remains in a constant position. This phenomenon can occur because the medium is moving in the opposite direction to the wave, or it can arise in a stationary medium as a result of interference between two waves traveling in opposite...
, which leads to further power waste. In these systems, impedance matching is essential.
In electrical systems involving
transmission lineA transmission line is the material medium or structure that forms all or part of a path from one place to another for directing the transmission of energy, such as electromagnetic waves or acoustic waves, as well as electric power transmission....
s, such as radio and fiber optics, where the length of the line is large compared to the wavelength of the signal (the signal changes rapidly compared to the time it takes to travel from source to load), the impedances at each end of the line must be matched to the transmission line's
characteristic impedanceThe characteristic impedance or surge impedance of a uniform transmission line, usually written , is the ratio of the amplitudes of a single pair of voltage and current waves propagating along the line in the absence of reflections. The SI unit of characteristic impedance is the ohm...
, to prevent reflections of the signal at the ends of the line from causing echoes. In radio-frequency (RF) systems, a common value for source and load impedances is 50 ohms. A typical RF load is a quarter-wave ground plane
antennaAn antenna is a transducer designed to transmit or receive electromagnetic waves. In other words, antennas convert electromagnetic waves into electrical currents and vice versa. Antennas are used in systems such as radio and television broadcasting, point-to-point radio communication, wireless...
(37 ohms with an ideal ground plane but can be matched to 50 ohms by using a modified ground plane or a coaxial matching section, ie part or all the feeder being of higher impedance).
In a transmission line, a wave travels from the source along the line. Suppose the wave hits a boundary (an abrupt change in impedance). Some of the wave is reflected back, while some keeps moving onwards. (Assume there's only one boundary.)
At the boundary, the two waves on the source side of the boundary (with impedance ) will be equal to the waves on the load side (with impedance ). The derivatives will also be equal. Using that equality, we solve for all wave functions, getting a
reflection coefficientThe reflection coefficient is used in physics and electrical engineering when wave propagation in a medium containing discontinuities is considered. A reflection coefficient describes either the amplitude or the intensity of a reflected wave relative to an incident wave...
:
The purpose of a transmission line is to get the maximum amount of energy to the other end of the line, or to transmit information with minimal error, so the reflection should be as small as possible. This is achieved by matching the impedances and so that they are equal .
An electromagnetic wave consists of energy being transmitted down the transmission line. This energy is in two forms, an electric field and a magnetic field, which fluctuate constantly, with a continuing exchange between electrical and magnetic energy. The electric field is due to the voltage over the cross section of the line, perpendicular to the direction the wave is flowing. The magnetic field is due to the current flowing parallel to the direction of the wave.
Assume that voltage and current vary as sine waves. Inside the transmission line, the law of conservation of energy applies: the sum of magnetic and electric energy must always be the same (ignoring the effect of the small amount of energy converted to
heatIn physics and thermodynamics, heat is the process of energy transfer from one body or system due to thermal contact, which in turn is defined as an energy transfer to a body in any other way than due to work performed on the body....
). This means that if the voltage is changing rapidly, the current must also change rapidly.
Now consider two moments: 1). when the current is zero and the voltage is maximum; 2). when the current is maximum and the voltage is zero. The amount of energy stored in the electric field at 1). must be exactly the same as the amount of energy stored in the magnetic field at 2). The ratio between voltage and current at 1). and 2). determines the impedance (Z) of the line:
At a boundary, for example, where the line is connected to the receiver, the law of conservation of charge applies. The current just before the boundary must be the same as just after. However, if the circuit at the receiver has a different impedance, , than the line, the voltage will be at the receiver, which is not the same as the original incident voltage .
To achieve the voltage difference, an electric field is needed over the boundary. However, energy is needed to form this field, for which a part of the energy of the original wave is used. The remaining energy cannot just 'disappear'; it must go somewhere. Due to the impedance and voltage difference, it cannot go to the other side of the boundary. There remains only one way to go for this energy: back into the transmission line, as a reflection. The voltage of this reflected wave, , is calculated from the incident voltage and the reflection coefficient, (from the formula above):
Electrical examples
Telephone systems
TelephoneThe telephone is a telecommunications device that transmits and receives sound, most commonly the human voice. It is one of the most common household appliances in the developed world, and has long been considered indispensable to business, industry and government...
systems also use matched impedances to minimise echoes on long distance lines. This is related to transmission lines theory. Matching also enables the telephone
hybrid coilA hybrid coil is a transformer that has three windings, and which is designed to be configured as a circuit having four branches, that are conjugate in pairs....
(2 to 4 wire conversion) to operate correctly. As the signals are sent and received on the same
two-wire circuitA two-wire circuit is characterized by supporting transmission in two directions simultaneously, as opposed to four-wire circuits, which have separate pairs for transmit and receive. In either case they are twisted pairs. Telephone lines are almost all two wire, while trunks and switching are...
to the central office (or exchange), cancellation is necessary at the telephone earpiece so that excessive
sidetone-Telephony:In telephony, sidetone is the effect of sound that is picked up by the telephone's mouthpiece and introduced into the earpiece of the same handset, acting as feedback...
is not heard. All devices used in telephone signal paths are generally dependent on using matched cable, source and load impedances. In the local loop, the impedance chosen is 600 ohm (nominal). Terminating networks are installed at the exchange to try to offer the best match to their subscriber lines. Each country has its own standard for these networks but they are all designed to approximate to about 600 ohms over the
voice frequencyA voice frequency or voice band is one of the frequencies, within part of the audio range, that is used for the transmission of speech.In telephony, the usable voice frequency band ranges from approximately 300 Hz to 3400 Hz...
band.
Loudspeaker amplifiers
Modern solid state audio amplifiers do not use matched impedances, contrary to myth. The
driver amplifierAn audio amplifier is an electronic amplifier that amplifies low-power audio signals to a level suitable for driving loudspeakers and is the final stage in a typical audio playback chain.The preceding stages in such a chain are low power audio amplifiers which perform tasks like...
has a low output impedance, such as < 0.1 ohm, and the
loudspeakerA loudspeaker is an electroacoustic transducer that converts an electrical signal into sound. The speaker pulses in accordance with the variations of an electrical signal and causes sound waves to propagate through a medium such as air or water.Loudspeakers are the most variable elements in a...
usually has an input impedance of 4, 8, or 16 ohms, which is many times larger than the former. This type of connection is
impedance bridgingIn electronics, especially audio and sound recording, a high impedance bridging, voltage bridging, or simply bridging connection is one which maximizes transfer of a voltage signal to the load...
, and it provides better
dampingIn audio system terminology, the damping factor gives the ratio of the rated impedance of the loudspeaker to the source impedance. Only the resistive part of the loudspeaker impedance is used. The amplifier output impedance is also assumed to be totally resistive...
of the loudspeaker cone to minimize distortion.
The myth comes from tube audio amplifiers, which required impedance matching for proper, reliable operation. Most of these had output transformer taps to approximately match the amplifier output to typical loudspeaker impedances.
Non-electrical examples
Acoustics
Similar to electrical transmission lines, the impedance matching problem exists when transferring sound energy from one medium to another. If the
acoustic impedanceThe acoustic impedance Z is a frequency f independent parameter and is very useful, for example, for describing the behaviour of musical wind instruments. Mathematically, it is the sound pressure p divided by the particle velocity v and the surface area S, through which an acoustic wave of...
of the two media are very different, then most of the sound energy will be reflected or absorbed, rather than transferred across the border.
The gel used in
medical ultrasonographyDiagnostic sonography is an ultrasound-based diagnostic imaging technique used to visualize subcutaneous body structures including tendons, muscles, joints, vessels and internal organs for possible pathology or lesions. Obstetric sonography is commonly used during pregnancy and is widely...
helps transfer acoustic energy from the transducer to the body and back again.
Without the gel, the "impedance mismatch" in the transducer-to-air and the air-to-body discontinuity reflects almost all the energy, leaving very little to go into the body.
HornsA horn is a tapered sound guide designed to provide an acoustic impedance match between a sound source and free air. This has the effect of maximising the efficiency with which sound waves from the particular source are transferred to the air...
are used like transformers, matching the impedance of the transducer to the impedance of the air. This principle is used in both
horn speakerA horn loudspeaker is a complete loudspeaker or loudspeaker element which uses a horn to increase the overall efficiency of the driving element, typically a diaphragm driven by an electromagnet. The horn itself is a passive component and does not amplify the sound from the driving element as such,...
s and
musical instrumentsThe horn is a brass instrument consisting of about of tubing wrapped into a coil with a flared bell. A musician who plays the horn is called a horn player ....
.
Most loudspeaker systems themselves contain impedance matching mechanisms, especially for low frequencies. Because most driver impedances are poorly matched to the impedance of free air at low frequencies, and because of out-of-phase cancellations between output from the front of a speaker cone and from the rear, loudspeaker enclosures serve both to match impedances and prevent the interference. Sound coupling into air from a
loudspeakerA loudspeaker is an electroacoustic transducer that converts an electrical signal into sound. The speaker pulses in accordance with the variations of an electrical signal and causes sound waves to propagate through a medium such as air or water.Loudspeakers are the most variable elements in a...
is related to the ratio of the diameter of the speaker to the wavelength of the sound being reproduced. That is, larger speakers can produce lower frequencies at higher levels than smaller speakers for this reason. Elliptical speakers are a complex case, acting like large speakers lengthwise, and like small speakers crosswise.
Acoustic impedance matching (or the lack of it) affects the operation of a
megaphoneA megaphone, speaking-trumpet, bullhorn, blowhorn, or loud hailer is a portable, usually hand-held, funnel cone-shaped device whose application is to amplify a person’s voice towards a targeted direction. This is accomplished by channeling the sound through a funnel, which also serves to match the...
, an
echoIn audio signal processing and acoustics, an echo is a reflection of sound, arriving at the listener some time after the direct sound. Typical examples are the echo produced by the bottom of a well, by a building, or by the walls of an enclosed room. A true echo is a single reflection of the sound...
, and
soundproofingSoundproofing is any means of reducing the sound pressure with respect to a specified sound source and receptor . There are several basic approaches to reducing sound: increasing the distance between source and receiver, using noise barriers to block or absorb the energy of the sound waves, using...
.
Optics
A similar effect occurs when
lightLight is electromagnetic radiation, particularly radiation of a wavelength that is visible to the human eye ....
(or any electromagnetic wave) transfers between two media with different
refractive indicesThe refractive index of a medium is a measure of how much the speed of light is reduced inside the medium. For example, typical soda-lime glass has a refractive index close to 1.5, which means that in glass, light travels at 1 / 1.5 = 2/3 the speed of light in a vacuum...
. An
optical impedance of each medium can be calculated, and the closer the impedances of the materials match, the more light is refracted rather than reflected from the interface. The amount of reflection can be calculated from the
Fresnel equationsThe Fresnel equations, deduced by Augustin-Jean Fresnel , describe the behaviour of light when moving between media of differing refractive indices...
. Unwanted reflections can be reduced by the use of an anti-reflection
optical coatingAn optical coating is one or more thin layers of material deposited on an optical component such as a lens or mirror, which alters the way in which the optic reflects and transmits light. One type of optical coating is an antireflection coating, which reduces unwanted reflections from surfaces, and...
.
Mechanics
If a body of mass
m collides elastically with a second body, the maximum energy transferred to the second body will occur when the second body has the same mass
m. For a head-on collision, with equal masses, the energy of the first body will be completely transferred to the second body. In this case, the masses act as "mechanical impedances" which must be matched. If and are the masses of the moving and the stationary body respectively, and
P is the momentum of the system, which remains constant throughout the collision, then the energy of the second body after the collision will be
E2:
which is analogous to the power transfer equation in the above "mathematical proof" section.
These principles are useful in the application of highly energetic materials (explosives). If an explosive charge is placed upon a target, the sudden release of energy causes compression waves to propagate through the target radially from the point charge contact. When the compression waves reach areas of high acoustic impedance mismatch (like the other side of the target), tension waves reflect back and create
spallSpall are flakes of a material that are broken off a larger solid body and can be produced by a variety of mechanisms, including as a result of projectile impact, corrosion, weathering, cavitation, or excessive rolling pressure...
ing. The greater the mismatch, the greater the effect of creasing and spalling will be. A charge initiated against a wall with air behind it will do more damage to the wall than a charge initiated against a wall with soil behind it.
External links