Impedance Match is the practice of attempting to make the output impedance Z_S of a source equal to the input impedance Z_L of the load to which it is ultimately connected, usually in order to maximize the power transfer and minimize reflections from the load. This only applies when both are linear devices.
The concept of impedance matching was originally developed for electrical power, but can be applied to any other field where a form of energy (not just electrical) is transferred between a source and a load. This article does not cite any references or sources. ... The input impedance or sometimes loading impedance of a circuit or electronic device is the impedance actually experienced by a signal which is connected to its input. ... In electrical engineering, the maximum power (transfer) theorem states that, to obtain maximum power from a source with a fixed internal resistance, the resistance of the load must be made the same as that of the source. ... When a signal is transmitted along a transmission medium, such as a copper cable or an optical fibre, there is the possibility that some of the signal power is reflected back to its origin, rather than being carried all the way along the cable to the far end. ... The word linear comes from the Latin word linearis, which means created by lines. ... For delivered electrical power, see Electrical power industry. ...

Image File history File links A simple source and load circuit. ...

Z_source = Z_load

Terminology

Sometimes the term "impedance matching" is used loosely to mean "choosing impedances that work well together" instead of "making two impedances complex conjugate". The looser interpretation includes impedance bridging, where the load impedance is much larger than the source impedance. Bridging connections are used to maximize the voltage transfer, not the power transfer. In mathematics, the complex conjugate of a complex number is given by changing the sign of the imaginary part. ... For the amplifier configuration, see bridged amplifier. ...

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 impedance is perhaps the most commonly known. Electrical impedance, like electrical resistance, is measured in ohms. In general, impedance has a complex value, which means that loads generally have a resistance to the source that is in phase with the source signal and reactance that is out of phase to the source. The total impedance (symbol: Z) is the vector sum of the resistance (symbol: R; a real number) and the reactance (symbol: X; an imaginary number). Electrical impedance, or simply impedance, is a measure of opposition to a sinusoidal alternating electric current. ... The ohm (symbol: Ω) is the SI unit of electric resistance. ... A complex number can be visually represented as a pair of numbers forming a vector on a diagram called an Argand diagram In mathematics, the complex numbers are the extension of the real numbers obtained by adjoining an imaginary unit, denoted i, which satisfies:[1] Every complex number can be... Electrical resistance is a measure of the degree to which an electrical component opposes the passage of current. ... This article is about a portion of a periodic process. ... It has been suggested that Electric reactance be merged into this article or section. ... This article is about vectors that have a particular relation to the spatial coordinates. ... In mathematics, the real numbers may be described informally as numbers that can be given by an infinite decimal representation, such as 2. ...

In simple cases, such as low-frequency or direct-current power transmission, the reactance is negligible 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. Although related to the more mathematical concepts of infinitesimal , the idea of something being negligible is particularly useful in practical disciplines like physics, chemistry, mechanical and electronic engineering, computer programming and in everyday decision-making. ...

Reflectionless or broadband matching

Impedance matching to minimize reflections and maximise 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, Z_load = Z_line = Z_source, where Z_line is the characteristic impedance 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'. The characteristic impedance of a uniform transmission line is the ratio of the amplitudes of a single pair of voltage and current waves propagating along the line in the absence of reflections. ...

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 load at a single frequency. In this case, If an electric circuit has a well-defined output terminal, the circuit connected to this terminal (or its input impedance) is the load. ...

Z_load = Z_source*

(where * indicates the complex conjugate). In mathematics, the complex conjugate of a complex number is given by changing the sign of the imaginary part. ...

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

Main article: Maximum power theorem

Whenever a source of power, such as an electric signal source, a radio transmitter, or even mechanical sound (e.g., a loudspeaker) operates into a load, the maximum possible power is delivered to the load when the impedance of the load (load impedance) is equal to the complex conjugate 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 electrical engineering, the maximum power (transfer) theorem states that, to obtain maximum power from a source with a fixed internal resistance, the resistance of the load must be made the same as that of the source. ... The article on electrical energy is located elsewhere. ... In telecommunication, signalling (or signaling) has the following meanings: The use of signals for controlling communications. ... Antenna tower of Crystal Palace transmitter, London A transmitter is an electronic device which, usually with the aid of an antenna, propagates an electromagnetic signal such as radio, television, or other telecommunications. ... An inexpensive low fidelity 3. ... If an electric circuit has a well-defined output terminal, the circuit connected to this terminal (or its input impedance) is the load. ... In physics, power (symbol: P) is the rate at which work is performed or energy is transmitted, or the amount of energy required or expended for a given unit of time. ... The input impedance or load impedance of a circuit or electronic device is the impedance actually experienced by a signal which is connected to it. ... In mathematics, the complex conjugate of a complex number is given by changing the sign of the imaginary part. ... The output impedance, source impedance, or internal impedance of an electronic device is the opposition exhibited by its output terminals to the flow of an alternating current (AC) of a particular frequency as a result of resistance, induction and capacitance. ...

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 theorem for a proof. In electrical engineering, the maximum power (transfer) theorem states that, to obtain maximum power from a source with a fixed internal resistance, the resistance of the load must be made the same as that of the source. ...

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 if 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 bridging 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. For the amplifier configuration, see bridged amplifier. ...

In older audio systems, reliant on transformers and passive filter networks, and based on the telephone 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 transformers used at central exchange equipment to separate outgoing from incoming speech so that these could be amplified or fed to a four-wire circuit. Most modern audio circuits, on the other hand, use active amplification and filtering, and they can use voltage bridging connections for best accuracy. For other uses, see Telephone (disambiguation). ... A hybrid coil (or bridge transformer) is a single transformer that effectively has three windings, and which is designed to be configured as a circuit having four branches, (i. ... In 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. ...

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 transformers, resistors, inductors and capacitors. For other uses, see Transformer (disambiguation). ... Resistor symbols (American) Resistor symbols (Europe, IEC) Axial-lead resistors on tape. ... An inductor is a passive electrical device employed in electrical circuits for its property of inductance. ... See Capacitor (component) for a discussion of specific types. ...

These passive and active impedance matching devices are optimized for different applications, and are called baluns, antenna tuners (sometimes called ATUs or roller coasters because of their appearance), acoustic horns, matching networks, and terminators. A balun, pronounced // (bal-un), is a passive electronic device that converts between balanced and unbalanced electrical signals, such as between coaxial cable and ladder line. ... A modern ATU for ham operators. ... A typical roller coaster The roller coaster is a popular amusement ride developed for amusement parks and modern theme parks. ... Electrical termination of a signal ceases its energy flow through the electrical circuit. ...

Transformers are sometimes used to match the impedances of circuits with different impedances. A transformer converts alternating current at one voltage 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. City lights viewed in a motion blurred exposure. ... International safety symbol Caution, risk of electric shock (ISO 3864), colloquially known as high voltage symbol. ...

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 filters, such as stubs, to match impedances at specific frequencies. These can distribute different frequencies to different places in the circuit. Television signal splitter consisting of a hi-pass filter (left) and a low-pass filter (right). ...

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 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 connection also minimizes distortion, so it is also used in modern audio amplifiers.

In addition, there is the closely related idea of In electrical engineering, the maximum power (transfer) theorem states that, to obtain maximum power from a source with a fixed internal resistance, the resistance of the load must be made the same as that of the source. ... For the amplifier configuration, see bridged amplifier. ...

• 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 tracker 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 bridging connection -- it emulates a high-voltage, low-resistance source, to maximize efficiency. Power factor correction (PFC) is a technique of counteracting the undesirable effects of electric loads that create a power factor (p. ... Solar cell I-V curves where a line intersects the knee of the curves where the maximum power point is located A maximum power point tracker (or MPPT) is a high efficiency DC to DC converter which functions as an optimal electrical load for a photovoltaic (PV) cell, most commonly... For the amplifier configuration, see bridged amplifier. ...

"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 narrowband matching network. It has been suggested that Electric reactance be merged into this article or section. ... Narrowband (narrow bandwidth) refers to a signal which occupies only a small amount of space on the radio spectrum -- the opposite of broadband or wideband. ...

The analysis is as follows. Consider a real source impedance of R₁ and real load impedance of R₂. If a reactance X₁ 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 X₁

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 Q of the inductor. Multiple "L" sections can be wired in cascade to achieve higher impedance ratios or greater bandwidth. Transmission line 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 chart. This article or section does not cite any references or sources. ... A 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. ... An impedance Smith chart (with no data plotted) The Smith Chart, invented by Phillip H. Smith (1905-1987),[1][2] is a graphical aid or nomogram designed for electrical and electronics engineers specialising in radio frequency (RF) 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 wave, which leads to further power waste. In these systems, impedance matching is essential. Vibration and standing waves in a string, The fundamental and the first 6 overtones A standing wave, also known as a stationary wave, is a wave that remains in a constant position. ...

In electrical systems involving transmission lines, 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 impedance, Z₀ 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 antenna (37 ohms with an ideal ground plane but can be matched to 50 ohms by using a modified ground plane or a matching network). A 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. ... Fiber Optic strands An optical fiber in American English or fibre in British English is a transparent thin fiber for transmitting light. ... The characteristic impedance of a uniform transmission line 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 ohm (symbol: Ω) is the SI unit of electric resistance. ... A Yagi-Uda beam antenna Short Wave Curtain Antenna (Moosbrunn, Austria) A building rooftop supporting numerous dish and sectored mobile telecommunications antennas (Doncaster, Victoria, Australia) An antenna is a transducer designed to transmit or receive radio waves which are a class of electromagnetic waves. ...

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 Z₁) will be equal to the waves on the load side (with impedance Z₂). The derivatives will also be equal. Using that equality, we solve for all wave functions, getting a reflection coefficient: The reflection coefficient is used in physics and electrical engineering when wave propagation in a medium containing discontinuities is considered. ...

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 Z₁ and Z₂ so that they are equal (Γ = 0).

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 heat). This means that if the voltage is changing rapidly, the current must also change rapidly. For other uses, see Heat (disambiguation) In physics, heat, symbolized by Q, is energy transferred from one body or system to another due to a difference in temperature. ...

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, Z_L, than the line, the voltage will be V_L = Z_LI 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, Γ (from the formula above):

Examples

Telephone systems

Telephone 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 coil (2 to 4 wire conversion) to operate correctly. As the signals are sent and received on the same two-wire circuit to the central office (or exchange), cancellation is necessary at the telephone earpiece so that excessive sidetone 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 frequency band. For other uses, see Telephone (disambiguation). ... A hybrid coil (or bridge transformer) is a single transformer that effectively has three windings, and which is designed to be configured as a circuit having four branches, (i. ... A 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 telephony, sidetone is the effect of sound that is picked up the the telephones mouthpiece and reproduced by the earpiece of the same handset. ... A voice frequency (VF) or voice band is one of the frequencies, within part of the audio range, that is used for the transmission of speech. ...

Loudspeaker amplifiers

Modern solid state audio amplifiers do not use matched impedances, contrary to myth. The driver amplifier has a low output impedance, such as < 0.1 ohm, and the loudspeaker 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 bridging, and it provides better damping of the loudspeaker cone to minimize distortion. Mission Cyrus 1 Hi Fi integrated audio amplifier An audio amplifier is an electronic amplifier that amplifies low-power audio signals (signals composed primarily of frequencies between 20 hertz to 20,000 hertz, the human range of hearing) to a level suitable for driving loudspeakers and is the final stage... An inexpensive low fidelity 3. ... For the amplifier configuration, see bridged amplifier. ... In audio system terminology the damping factor gives the ratio of the rated impedance of the loudspeaker to the source impedance. ...

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 impedance matching examples

Acoustics

Similar to electrical transmission lines, the impedance matching problem exists when transferring sound energy from one medium to another. If the acoustic impedance 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 acoustic impedance Z (or sound impedance) is a frequency f dependent parameter and is very useful, for example, for describing the behaviour of musical wind instruments. ...

The gel used in medical ultrasonography 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. Sonography redirects here. ...

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 loudspeaker 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. An inexpensive low fidelity 3. ... Elliptical may refer to: Ellipse: a shape and mathematical construct Elliptical trainer: an exercise machine This is a disambiguation page — a navigational aid which lists other pages that might otherwise share the same title. ...

Acoustic impedance matching (or the lack of it) affects the operation of a megaphone, an echo, and soundproofing. A megaphone, with a three-inch lighter to scale. ... In audio signal processing and acoustics, an echo (plural echoes) is a reflection of sound, arriving at the listener some time after the direct sound. ... Soundproofing is any means of to reducing the intensity of sound with respect to a specified source and receptor. ...

Optics

A similar effect occurs when light (or any electromagnetic wave) transfers between two media with different refractive indices. 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 equations. Unwanted reflections can be reduced by the use of an anti-reflection optical coating. For other uses, see Light (disambiguation). ... The refractive index (or index of refraction) of a medium is a measure for how much the speed of light (or other waves such as sound waves) is reduced inside the medium. ... The Fresnel equations, deduced by Augustin-Jean Fresnel, describe the behaviour of light when moving between media of differing refractive indices. ... An optical coating is a thin layer of material placed on an optical component such as a lens or mirror which alters the way in which the optic reflects and transmits light. ...

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 m₁ and m₂ 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 spalling. 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. Very high speed photography of a small projectile impacting a thin aluminium plate at 7000 m/s. ...

See also

• Maximum power theorem
• Power (physics)
• Electronics
• Impedance bridging

In electrical engineering, the maximum power (transfer) theorem states that, to obtain maximum power from a source with a fixed internal resistance, the resistance of the load must be made the same as that of the source. ... In physics, power (symbol: P) is the rate at which work is performed or energy is transmitted, or the amount of energy required or expended for a given unit of time. ... Surface mount electronic components Electronics is the study of the flow of charge through various materials and devices such as semiconductors, resistors, inductors, capacitors, nano-structures and vacuum tubes. ... For the amplifier configuration, see bridged amplifier. ...

References

• Young, EC, The Penguin Dictionary of Electronics, Penguin, ISBN 0-14-051187-3 (see 'maximum power theorem', 'impedance matching')

External links

• Unity Gain and Impedance Matching
• Impedance matching for microphones: Is it necessary? No.
• Calculation: Damping of impedance matching - connecting Zout and Zin
• Impedance matching: A primer
• Tutorial on RF impedance matching using the Smith Chart
• A description of impedance matching
• Conjugate matching versus reflectionless matching - pdf
• Impedance Matching Networks