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electronics The field of electronics is a branch of physics and electrical engineering that deals with the emission, behaviour and effects of electrons using electronic devices. Electronics uses active devices to control electron flow by amplification ...
, impedance matching is the practice of designing or adjusting the
input impedance The input impedance of an electrical network is the measure of the opposition to current ( impedance), both static ( resistance) and dynamic ( reactance), into the load network that is ''external'' to the electrical source. The input admittance (the ...
or
output impedance The output impedance of an electrical network is the measure of the opposition to current flow (impedance), both static ( resistance) and dynamic ( reactance), into the load network being connected that is ''internal'' to the electrical source. The ...
of an electrical device for a desired value. Often, the desired value is selected to maximize
power Power most often refers to: * Power (physics), meaning "rate of doing work" ** Engine power, the power put out by an engine ** Electric power * Power (social and political), the ability to influence people or events ** Abusive power Power may ...
transfer or minimize
signal reflection In telecommunications, signal 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 ...
. For example, impedance matching typically is used to improve power transfer from a radio transmitter via the interconnecting transmission line to the antenna.
Signal In signal processing, a signal is a function that conveys information about a phenomenon. Any quantity that can vary over space or time can be used as a signal to share messages between observers. The '' IEEE Transactions on Signal Processing' ...
s on a transmission line will be transmitted without reflections if the transmission line is terminated with a matching impedance. Techniques of impedance matching include
transformers ''Transformers'' is a media franchise produced by American toy company Hasbro and Japanese toy company Takara Tomy. It primarily follows the Autobots and the Decepticons, two alien robot factions at war that can transform into other forms, su ...
, adjustable networks of lumped resistance,
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 ar ...
and
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 ...
, or properly proportioned transmission lines. Practical impedance-matching devices will generally provide best results over a specified
frequency band A frequency band is an interval in the frequency domain, delimited by a lower frequency and an upper frequency. The term may refer to a radio band or an interval of some other spectrum. The frequency range of a system is the range over which i ...
. The concept of impedance matching is widespread in
electrical engineering Electrical engineering is an engineering discipline concerned with the study, design, and application of equipment, devices, and systems which use electricity, electronics, and electromagnetism. It emerged as an identifiable occupation in the l ...
, but is relevant in other applications in which a form of
energy In physics, energy (from Ancient Greek: ἐνέργεια, ''enérgeia'', “activity”) is the quantitative property that is transferred to a body or to a physical system, recognizable in the performance of work and in the form of h ...
, not necessarily
electrical Electricity is the set of physical phenomena associated with the presence and motion of matter that has a property of electric charge. Electricity is related to magnetism, both being part of the phenomenon of electromagnetism, as described ...
, is transferred between a source and a load, such as in
acoustics Acoustics is a branch of physics that deals with the study of mechanical waves in gases, liquids, and solids including topics such as vibration, sound, ultrasound and infrasound. A scientist who works in the field of acoustics is an acoustic ...
or
optics Optics is the branch of physics that studies the behaviour and properties of light, including its interactions with matter and the construction of instruments that use or detect it. Optics usually describes the behaviour of visible, ultravio ...
.


Theory

Impedance is the opposition by a system to the flow of energy from a source. For constant signals, this impedance can also be constant. For varying signals, it usually changes with frequency. The energy involved can be
electrical Electricity is the set of physical phenomena associated with the presence and motion of matter that has a property of electric charge. Electricity is related to magnetism, both being part of the phenomenon of electromagnetism, as described ...
,
mechanical Mechanical may refer to: Machine * Machine (mechanical), a system of mechanisms that shape the actuator input to achieve a specific application of output forces and movement * Mechanical calculator, a device used to perform the basic operations of ...
, acoustic,
magnetic Magnetism is the class of physical attributes that are mediated by a magnetic field, which refers to the capacity to induce attractive and repulsive phenomena in other entities. Electric currents and the magnetic moments of elementary particles ...
,
optical Optics is the branch of physics that studies the behaviour and properties of light, including its interactions with matter and the construction of instruments that use or detect it. Optics usually describes the behaviour of visible, ultravio ...
, or
thermal A thermal column (or thermal) is a rising mass of buoyant air, a convective current in the atmosphere, that transfers heat energy vertically. Thermals are created by the uneven heating of Earth's surface from solar radiation, and are an example ...
. The concept of electrical impedance is perhaps the most commonly known. Electrical impedance, like electrical resistance, is measured in ohms. In general, impedance (symbol: ''Z'') has a
complex Complex commonly refers to: * Complexity, the behaviour of a system whose components interact in multiple ways so possible interactions are difficult to describe ** Complex system, a system composed of many components which may interact with each ...
value; this means that loads generally have a resistance component (symbol: ''R'') which forms the
real Real may refer to: Currencies * Brazilian real (R$) * Central American Republic real * Mexican real * Portuguese real * Spanish real * Spanish colonial real Music Albums * ''Real'' (L'Arc-en-Ciel album) (2000) * ''Real'' (Bright album) (2010) ...
part and a reactance component (symbol: ''X'') which forms the imaginary part. In simple cases (such as low-frequency or
direct current Direct current (DC) is one-directional flow of electric charge. An electrochemical cell is a prime example of DC power. Direct current may flow through a conductor such as a wire, but can also flow through semiconductors, insulators, or e ...
power transmission) the reactance may be negligible or zero; the impedance can be considered a pure resistance, expressed as a real number. In the following summary we will consider the general case when resistance and reactance are both significant, and the special case in which the reactance is negligible.


Maximum power transfer matching

Complex conjugate matching is used when maximum power transfer is required, namely : Z_\mathsf = Z_\mathsf^* \, where a superscript * indicates the
complex conjugate In mathematics, the complex conjugate of a complex number is the number with an equal real part and an imaginary part equal in magnitude but opposite in sign. That is, (if a and b are real, then) the complex conjugate of a + bi is equal to a - ...
. A conjugate match is different from a reflection-less match when either the source or load has a reactive component. If the source has a reactive component, but the load is purely resistive, then matching can be achieved by adding a reactance of the same magnitude but opposite sign to the load. This simple matching network, consisting of a single element, will usually achieve a perfect match at only a single frequency. This is because the added element will either be a capacitor or an inductor, whose impedance in both cases is frequency dependent, and will not, in general, follow the frequency dependence of the source impedance. For wide
bandwidth Bandwidth commonly refers to: * Bandwidth (signal processing) or ''analog bandwidth'', ''frequency bandwidth'', or ''radio bandwidth'', a measure of the width of a frequency range * Bandwidth (computing), the rate of data transfer, bit rate or thr ...
applications, a more complex network must be designed.


Power transfer

Whenever a source of power ''with a fixed output impedance'' such as an
electric Electricity is the set of physical phenomena associated with the presence and motion of matter that has a property of electric charge. Electricity is related to magnetism, both being part of the phenomenon of electromagnetism, as described ...
signal In signal processing, a signal is a function that conveys information about a phenomenon. Any quantity that can vary over space or time can be used as a signal to share messages between observers. The '' IEEE Transactions on Signal Processing' ...
source, a
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 trans ...
transmitter In electronics and telecommunications, a radio transmitter or just transmitter is an electronic device which produces radio waves with an antenna. The transmitter itself generates a radio frequency alternating current, which is applied to ...
or a mechanical sound (e.g., a
loudspeaker A loudspeaker (commonly referred to as a speaker or speaker driver) is an electroacoustic transducer that converts an electrical audio signal into a corresponding sound. A ''speaker system'', also often simply referred to as a "speaker" or "l ...
) operates into a load, the maximum possible
power Power most often refers to: * Power (physics), meaning "rate of doing work" ** Engine power, the power put out by an engine ** Electric power * Power (social and political), the ability to influence people or events ** Abusive power Power may ...
is delivered to the load when the impedance of the load (
load impedance The input impedance of an electrical network is the measure of the opposition to current ( impedance), both static ( resistance) and dynamic ( reactance), into the load network that is ''external'' to the electrical source. The input admittance (the ...
or
input impedance The input impedance of an electrical network is the measure of the opposition to current ( impedance), both static ( resistance) and dynamic ( reactance), into the load network that is ''external'' to the electrical source. The input admittance (the ...
) is equal to the ''
complex conjugate In mathematics, the complex conjugate of a complex number is the number with an equal real part and an imaginary part equal in magnitude but opposite in sign. That is, (if a and b are real, then) the complex conjugate of a + bi is equal to a - ...
'' of the impedance of the source (that is, its
internal impedance The output impedance of an electrical network is the measure of the opposition to current flow (impedance), both static ( resistance) and dynamic ( reactance), into the load network being connected that is ''internal'' to the electrical source. The ...
or
output impedance The output impedance of an electrical network is the measure of the opposition to current flow (impedance), both static ( resistance) and dynamic ( reactance), into the load network being connected that is ''internal'' to the electrical source. The ...
). For two impedances to be complex conjugates their resistances must be equal, and their reactances must be equal in magnitude but of opposite signs. In low-frequency or DC systems (or 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 In electrical engineering, the maximum power transfer theorem states that, to obtain ''maximum'' external power from a power source with internal resistance, the resistance of the load must equal the resistance of the source as viewed from its ou ...
for a mathematical proof). Impedance matching is not always necessary. For example, if delivering a high voltage (to reduce signal degradation or to reduce power consumption) is more important than maximizing power transfer, then ''
impedance bridging In audio engineering and sound recording, a high impedance bridging, voltage bridging, or simply bridging connection is one in which the load impedance is much larger than the source impedance. The load measures the source's voltage while minima ...
'' or ''voltage bridging'' is often used. In older audio systems (reliant on transformers and passive filter networks, and based on the
telephone A telephone is a telecommunications device that permits two or more users to conduct a conversation when they are too far apart to be easily heard directly. A telephone converts sound, typically and most efficiently the human voice, into e ...
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 these could be amplified or fed to a
four-wire circuit 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. The four-wire circuit gets its ...
. Most modern audio circuits, on the other hand, use active amplification and filtering and can use voltage-bridging connections for greatest accuracy. Strictly speaking, impedance matching only applies when both source and load devices are
linear Linearity is the property of a mathematical relationship (''function'') that can be graphically represented as a straight line. Linearity is closely related to '' proportionality''. Examples in physics include rectilinear motion, the linear re ...
; however, matching may be obtained between nonlinear devices within certain operating ranges.


Impedance-matching devices

Adjusting the source impedance or the load impedance, in general, is called "impedance matching". There are three ways to improve an impedance mismatch, all of which are called "impedance matching": * Devices intended to present an apparent load to the source of ''Z''load = ''Z''source* (complex conjugate matching). Given a source with a fixed voltage and fixed source impedance, the
maximum power theorem In electrical engineering, the maximum power transfer theorem states that, to obtain ''maximum'' external power from a power source with internal resistance, the resistance of the load must equal the resistance of the source as viewed from its ou ...
says this is the only way to extract the maximum power from the source. * Devices intended to present an apparent load of ''Z''load = ''Z''line (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 audio engineering and sound recording, a high impedance bridging, voltage bridging, or simply bridging connection is one in which the load impedance is much larger than the source impedance. The load measures the source's voltage while minima ...
connection also minimizes
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 sig ...
and
electromagnetic interference Electromagnetic interference (EMI), also called radio-frequency interference (RFI) when in the radio frequency spectrum, is a disturbance generated by an external source that affects an electrical circuit by electromagnetic induction, electros ...
; it is also used in modern audio amplifiers and signal-processing devices. There are a variety of devices used between a source of energy and a load that perform "impedance matching". To match electrical impedances, engineers use combinations of
transformer A transformer is a passive component that transfers electrical energy from one electrical circuit to another circuit, or multiple circuits. A varying current in any coil of the transformer produces a varying magnetic flux in the transformer's ...
s,
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 ...
s,
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 ...
s,
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 a c ...
s and
transmission lines In electrical engineering, a transmission line is a specialized cable or other structure designed to conduct electromagnetic waves in a contained manner. The term applies when the conductors are long enough that the wave nature of the transmis ...
. These passive (and active) impedance-matching devices are optimized for different applications and include
balun A balun (from "balanced to unbalanced", originally, but now dated from "balancing unit") is an electrical device that allows balanced and unbalanced lines to be interfaced without disturbing the impedance arrangement of either line. A balun ...
s,
antenna tuner An antenna tuner (and any of the names in the list below) is a device that is inserted between a radio transmitter and its antenna; when placed close by the antenna and properly adjusted (tuned) it optimizes power transfer by matching the im ...
s (sometimes called ATUs or roller-coasters, because of their appearance), acoustic horns, matching networks, and terminators.


Transformers

Transformer A transformer is a passive component that transfers electrical energy from one electrical circuit to another circuit, or multiple circuits. A varying current in any coil of the transformer produces a varying magnetic flux in the transformer's ...
s are sometimes used to match the impedances of circuits. A transformer converts
alternating current Alternating current (AC) is an electric current which periodically reverses direction and changes its magnitude continuously with time in contrast to direct current (DC) which flows only in one direction. Alternating current is the form in whic ...
at one
voltage Voltage, also known as electric pressure, electric tension, or (electric) potential difference, is the difference in electric potential between two points. In a static electric field, it corresponds to the work needed per unit of charge to ...
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). One example of this method involves a television
balun A balun (from "balanced to unbalanced", originally, but now dated from "balancing unit") is an electrical device that allows balanced and unbalanced lines to be interfaced without disturbing the impedance arrangement of either line. A balun ...
transformer. This transformer allows interfacing a balanced line (300-ohm
twin-lead Twin-lead cable is a two-conductor flat cable used as a balanced transmission line to carry radio frequency (RF) signals. It is constructed of two stranded or solid copper or copper-clad steel wires, held a precise distance apart by a plastic ...
) and an unbalanced line (75-ohm coaxial cable such as
RG-6 RG-6/U is a common type of coaxial cable used in a wide variety of residential and commercial applications. An RG-6/U coaxial cable has a characteristic impedance of 75 ohms. The term, ''RG-6'', is generic and is applied to a wide variety o ...
). To match the impedances, both cables must be connected to a matching transformer with a turns ratio of 2:1. In this example, the 300-ohm line is connected to the transformer side with more turns; the 75-ohm cable is connected to the transformer side with fewer turns. The formula for calculating the transformer turns ratio for this example is: : \text = \sqrt


Resistive network

Resistive impedance matches are easiest to design and can be achieved with a simple L pad consisting of two resistors. Power loss is an unavoidable consequence of using resistive networks, and they are only (usually) used to transfer
line level Line level is the specified strength of an audio signal used to transmit analog audio between components such as CD and DVD players, television sets, audio amplifiers, and mixing consoles. Line level sits between other levels of audio signal ...
signals.


Stepped transmission line

Most lumped-element devices can match a specific range of load impedances. For example, in order to match an inductive load into a real impedance, a capacitor needs to be used. If the load impedance becomes capacitive, the matching element must be replaced by an inductor. In many cases, there is a need to use the same circuit to match a broad range of load impedance and thus simplify the circuit design. This issue was addressed by the stepped transmission line, where multiple, serially placed, quarter-wave dielectric slugs are used to vary a transmission line's characteristic impedance. By controlling the position of each element, a broad range of load impedances can be matched without having to reconnect the circuit.


Filters

Filters Filter, filtering or filters may refer to: Science and technology Computing * Filter (higher-order function), in functional programming * Filter (software), a computer program to process a data stream * Filter (video), a software component th ...
are frequently used to achieve impedance matching in telecommunications and radio engineering. In general, it is not theoretically possible to achieve perfect impedance matching at all
frequencies 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 ...
with a network of discrete components. Impedance matching networks are designed with a definite bandwidth, take the form of a filter, and use filter theory in their design. Applications requiring only a narrow bandwidth, such as radio tuners and transmitters, might use a simple tuned
filter Filter, filtering or filters may refer to: Science and technology Computing * Filter (higher-order function), in functional programming * Filter (software), a computer program to process a data stream * Filter (video), a software component that ...
such as a
stub Stub or Stubb may refer to: Shortened objects and entities * Stub (stock), the portion of a corporation left over after most but not all of it has been bought out or spun out * Stub, a tree cut and allowed to regrow from the trunk; see Pollard ...
. This would provide a perfect match at one specific frequency only. Wide bandwidth matching requires filters with multiple sections.


L-section

A simple electrical impedance-matching network requires one capacitor and one inductor. In the figure to the right, R1 > R2, however, either R1 or R2 may be the source and the other the load. One of X1 or X2 must be an inductor and the other must be a capacitor. 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 to low impedance. The analysis is as follows. Consider a real source impedance of R_1 and real load impedance of R_2. If a reactance X_1 is in parallel with the source impedance, the combined impedance can be written as: : \frac If the imaginary part of the above impedance is canceled by the series reactance, the real part is : R_2 = \frac Solving for X_1 : \left\vert X_1 \right\vert = \frac . : \left\vert X_2 \right\vert = Q R_2 . :where Q = \sqrt . Note, X_1, the reactance in parallel, has a negative reactance because it is typically a capacitor. This gives the L-network the additional feature of harmonic suppression since it is a low pass filter too. The inverse connection (impedance step-up) is simply the reverse—for example, 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 In electrical engineering, a transmission line is a specialized cable or other structure designed to conduct electromagnetic waves in a contained manner. The term applies when the conductors are long enough that the wave nature of the transm ...
matching networks can be modeled as infinitely many L-sections wired in cascade. Optimal matching circuits can be designed for a particular system using
Smith chart The Smith chart, invented by Phillip H. Smith (1905–1987) and independently by Mizuhashi Tosaku, is a graphical calculator or nomogram designed for electrical and electronics engineers specializing in radio frequency (RF) engineering to assist ...
s.


Power factor correction

Power factor correction In electrical engineering, the power factor of an AC power system is defined as the ratio of the ''real power'' absorbed by the load to the '' apparent power'' flowing in the circuit. Real power is the average of the instantaneous product of v ...
devices are intended to cancel 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 minimizes power wasted in the resistance of those power lines. For example, a
maximum power point tracker Maximum power point tracking (MPPT) or sometimes just power point tracking (PPT), is a technique used with variable power sources to maximize energy extraction as conditions vary. The technique is most commonly used with photovoltaic (PV) solar s ...
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. That connection is an
impedance bridging In audio engineering and sound recording, a high impedance bridging, voltage bridging, or simply bridging connection is one in which the load impedance is much larger than the source impedance. The load measures the source's voltage while minima ...
connection; it emulates a high-voltage, low-resistance source to maximize efficiency. On the
power grid An electrical grid is an interconnected network for electricity delivery from producers to consumers. Electrical grids vary in size and can cover whole countries or continents. It consists of:Kaplan, S. M. (2009). Smart Grid. Electrical Power ...
the overall load is usually inductive. Consequently, power factor correction is most commonly achieved with banks of
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 a c ...
s. It is only necessary for correction to be achieved at one single frequency, the frequency of the supply. Complex networks are only required when a band of frequencies must be matched and this is the reason why simple capacitors are all that is usually required for power factor correction.


Transmission lines

In RF connections, impedance matching is desirable, because otherwise reflections may be created at the end of the mismatched transmission line. The reflection may cause frequency-dependent loss. In electrical systems involving
transmission line In electrical engineering, a transmission line is a specialized cable or other structure designed to conduct electromagnetic waves in a contained manner. The term applies when the conductors are long enough that the wave nature of the transm ...
s (such as radio and
fiber optics An optical fiber, or optical fibre in Commonwealth English, is a flexible, transparent fiber made by drawing glass (silica) or plastic to a diameter slightly thicker than that of a human hair. Optical fibers are used most often as a means ...
)—where the length of the line is long 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 may be matched to the transmission line's
characteristic impedance The characteristic impedance or surge impedance (usually written Z0) of a uniform transmission line is the ratio of the amplitudes of voltage and current of a single wave propagating along the line; that is, a wave travelling in one direction i ...
(Z_c) to prevent reflections of the signal at the ends of the line. 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). The general form of the voltage
reflection coefficient In physics and electrical engineering the reflection coefficient is a parameter that describes how much of a wave is reflected by an impedance discontinuity in the transmission medium. It is equal to the ratio of the amplitude of the reflected wa ...
for a wave moving from medium 1 to medium 2 is given by : \Gamma_ = while the voltage reflection coefficient for a wave moving from medium 2 to medium 1 is : \Gamma_ = : \Gamma_ = -\Gamma_ \, so the reflection coefficient is the same (except for sign), no matter from which direction the wave approaches the boundary. There is also a current reflection coefficient, which is the negative of the voltage reflection coefficient. If the wave encounters an open at the load end, positive voltage and negative current pulses are transmitted back toward the source (negative current means the current is going the opposite direction). Thus, at each boundary there are four reflection coefficients (voltage and current on one side, and voltage and current on the other side). All four are the same, except that two are positive and two are negative. The voltage reflection coefficient and current reflection coefficient on the same side have opposite signs. Voltage reflection coefficients on opposite sides of the boundary have opposite signs. Because they are all the same except for sign it is traditional to interpret the reflection coefficient as the voltage reflection coefficient (unless otherwise indicated). Either end (or both ends) of a transmission line can be a source or a load (or both), so there is no inherent preference for which side of the boundary is medium 1 and which side is medium 2. With a single transmission line it is customary to define the voltage reflection coefficient for a wave incident on the boundary from the transmission line side, regardless of whether a source or load is connected on the other side.


Single-source transmission line driving a load


Load-end conditions

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 is only one boundary, at the load.) Let : V_i \, and I_i \, be the voltage and current that is incident on the boundary from the source side. : V_t \, and I_t \, be the voltage and current that is transmitted to the load. : V_r \, and I_r \, be the voltage and current that is reflected back toward the source. On the line side of the boundary V_i = Z_c I_i \, and V_r = -Z_c I_r \, and on the load side V_t = Z_L I_t \, where V_i \, , V_r \, , V_t \, , I_i \, , I_r \, , and I_t \, are
phasor In physics and engineering, a phasor (a portmanteau of phase vector) is a complex number representing a sinusoidal function whose amplitude (''A''), angular frequency (''ω''), and initial phase (''θ'') are time-invariant. It is related to ...
s. At a boundary, voltage and current must be continuous, therefore : V_t = V_i + V_r \, : I_t = I_i + I_r \, All these conditions are satisfied by : V_r = \Gamma_ V_i \, : I_r = - \Gamma_ I_i \, : V_t = (1 + \Gamma_ ) V_i \, : I_t = ( 1 - \Gamma_ ) I_i \, where \Gamma_ \, the
reflection coefficient In physics and electrical engineering the reflection coefficient is a parameter that describes how much of a wave is reflected by an impedance discontinuity in the transmission medium. It is equal to the ratio of the amplitude of the reflected wa ...
going from the transmission line to the load. : \Gamma_ = = \Gamma_L \,


Source-end conditions

At the source end of the transmission line, there may be waves incident both from the source and from the line; a reflection coefficient for each direction may be computed with : - \Gamma_ = \Gamma_ = = \Gamma_S \, , where ''Zs'' is the source impedance. The source of waves incident from the line are the reflections from the load end. If the source impedance matches the line, reflections from the load end will be absorbed at the source end. If the transmission line is not matched at both ends reflections from the load will be re-reflected at the source and re-re-reflected at the load end ''ad infinitum'', losing energy on each transit of the transmission line. This can cause a resonance condition and strongly frequency-dependent behavior. In a narrow-band system this can be desirable for matching, but is generally undesirable in a wide-band system.


=Source-end impedance

= : Z_ = Z_c \frac \, where T \ , is the one-way transfer function (from either end to the other) when the transmission line is exactly matched at source and load. T \, accounts for everything that happens to the signal in transit (including delay, attenuation and dispersion). If there is a perfect match at the load, \Gamma_L = 0 \, and Z_ = Z_c \,


=Transfer function

= : V_L = V_S \frac \, where V_S \, is the open circuit (or unloaded) output voltage from the source. Note that if there is a perfect match at both ends : \Gamma_L = 0 \, and \Gamma_S = 0 \, and then : V_L = V_S \frac \, .


Electrical examples


Telephone systems

Telephone A telephone is a telecommunications device that permits two or more users to conduct a conversation when they are too far apart to be easily heard directly. A telephone converts sound, typically and most efficiently the human voice, into e ...
systems also use matched impedances to minimise echo on long-distance lines. This is related to transmission-line theory. Matching also enables the telephone ''
hybrid coil A hybrid coil (or bridge transformer, or sometimes hybrid) is a transformer that has three windings, and which is designed to be configured as a circuit having four ports that are conjugate in pairs. A signal arriving at one port is divided eq ...
'' (2- to 4-wire conversion) to operate correctly. As the signals are sent and received on the same
two-wire circuit In telecommunication, 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. The subscriber local loop from the telco ce ...
to the central office (or exchange), cancellation is necessary at the telephone earpiece so excessive
sidetone Sidetone is audible feedback to someone speaking or otherwise producing sound as an indication of active transmission. Sidetone is introduced by some communications circuits and anti-sidetone circuitry is used to control its level. Sidetone is exp ...
is not heard. All devices used in telephone signal paths are generally dependent on matched cable, source and load impedances. In the local loop, the impedance chosen is 600 ohms (nominal). Terminating networks are installed at the exchange 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 about 600 ohms over the
voice frequency A voice frequency (VF) or voice band is the range of audio frequencies used for the transmission of speech. Frequency band In telephony, the usable voice frequency band ranges from approximately 300 to 3400  Hz. It is for this reason that ...
band.


Loudspeaker amplifiers

Audio amplifier An audio power amplifier (or power amp) is an electronic amplifier that amplifies low-power electronic audio signals, such as the signal from a radio receiver or an electric guitar pickup, to a level that is high enough for driving loudspe ...
s typically do not match impedances, but provide an output impedance that is lower than the load impedance (such as < 0.1 ohm in typical
semiconductor A semiconductor is a material which has an electrical conductivity value falling between that of a conductor, such as copper, and an insulator, such as glass. Its resistivity falls as its temperature rises; metals behave in the opposite way. ...
amplifiers), for improved speaker
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 inc ...
. For
vacuum tube A vacuum tube, electron tube, valve (British usage), or tube (North America), is a device that controls electric current flow in a high vacuum between electrodes to which an electric voltage, potential difference has been applied. The type kn ...
amplifiers, impedance-changing transformers are often used to get a low output impedance, and to better match the amplifier's performance to the load impedance. Some tube amplifiers have output transformer taps to adapt the amplifier output to typical loudspeaker impedances. The output
transformer A transformer is a passive component that transfers electrical energy from one electrical circuit to another circuit, or multiple circuits. A varying current in any coil of the transformer produces a varying magnetic flux in the transformer's ...
in
vacuum-tube A vacuum tube, electron tube, valve (British usage), or tube (North America), is a device that controls electric current flow in a high vacuum between electrodes to which an electric potential difference has been applied. The type known as a ...
-based amplifiers has two basic functions: *Separation of the AC component (which contains the audio signals) from the DC component (supplied by the
power supply A power supply is an electrical device that supplies electric power to an electrical load. The main purpose of a power supply is to convert electric current from a source to the correct voltage, current, and frequency to power the load. As ...
) in the anode circuit of a vacuum-tube-based power stage. A loudspeaker should not be subjected to DC current. *Reducing the output impedance of power
pentode A pentode is an electronic device having five electrodes. The term most commonly applies to a three-grid amplifying vacuum tube or thermionic valve that was invented by Gilles Holst and Bernhard D.H. Tellegen in 1926. The pentode (called a ''tripl ...
s (such as the
EL34 The EL34 is a thermionic vacuum tube of the power pentode type. The EL34 was introduced in 1955 by Mullard, who were owned by Philips. The EL34 has an octal base (indicated by the '3' in the part number) and is found mainly in the final output st ...
) in a
common-cathode An amplifier, electronic amplifier or (informally) amp is an electronic device that can increase the magnitude of a signal (a time-varying voltage or current). It may increase the power significantly, or its main effect may be to boost the ...
configuration. The impedance of the loudspeaker on the secondary coil of the transformer will be transformed to a higher impedance on the primary coil in the circuit of the power pentodes by the square of the turns ratio, which forms the ''impedance scaling factor''. The output stage in
common-drain In electronics, a common-drain amplifier, also known as a source follower, is one of three basic single-stage field-effect transistor (FET) amplifier topologies, typically used as a voltage buffer. In this circuit (NMOS) the gate terminal of the t ...
or
common-collector In electronics, a common collector amplifier (also known as an emitter follower) is one of three basic single-stage bipolar junction transistor (BJT) amplifier topologies, typically used as a voltage buffer. In this circuit the base terminal ...
semiconductor-based end stages with
MOSFET The metal–oxide–semiconductor field-effect transistor (MOSFET, MOS-FET, or MOS FET) is a type of field-effect transistor (FET), most commonly fabricated by the controlled oxidation of silicon. It has an insulated gate, the voltage of which d ...
s or power transistors has a very low output impedance. If they are properly balanced, there is no need for a transformer or a large
electrolytic capacitor An electrolytic capacitor is a polarized capacitor whose anode or positive plate is made of a metal that forms an insulating oxide layer through anodization. This oxide layer acts as the dielectric of the capacitor. A solid, liquid, or gel e ...
to separate AC from DC current.


Non-electrical examples


Acoustics

Similar to electrical transmission lines, an impedance matching problem exists when transferring sound energy from one medium to another. If the
acoustic impedance Acoustic impedance and specific acoustic impedance are measures of the opposition that a system presents to the acoustic flow resulting from an acoustic pressure applied to the system. The SI unit of acoustic impedance is the pascal-second per cu ...
of the two media are very different most sound energy will be reflected (or absorbed), rather than transferred across the border. The gel used in
medical ultrasonography Medical ultrasound includes diagnostic techniques (mainly imaging techniques) using ultrasound, as well as therapeutic applications of ultrasound. In diagnosis, it is used to create an image of internal body structures such as tendons, muscle ...
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. The bones in the
middle ear The middle ear is the portion of the ear medial to the eardrum, and distal to the oval window of the cochlea (of the inner ear). The mammalian middle ear contains three ossicles, which transfer the vibrations of the eardrum into waves in the ...
provide impedance matching between the eardrum (which is acted upon by vibrations in air) and the fluid-filled inner ear. Horns in loudspeaker systems are used like transformers in electrical circuits to match the impedance of the transducer to the impedance of the air. This principle is used in both
horn loudspeaker A horn loudspeaker is a loudspeaker or loudspeaker element which uses an acoustic horn to increase the overall efficiency of the driving element(s). A common form ''(right)'' consists of a compression driver which produces sound waves with a sma ...
s and musical instruments. Because most driver impedances are poorly matched to the impedance of free air at low frequencies, loudspeaker enclosures are designed to both match impedance and minimize destructive phase cancellations between output from the front and rear of a speaker cone. The loudness of sound produced in air from a
loudspeaker A loudspeaker (commonly referred to as a speaker or speaker driver) is an electroacoustic transducer that converts an electrical audio signal into a corresponding sound. A ''speaker system'', also often simply referred to as a "speaker" or "l ...
is directly related to the ratio of the diameter of the speaker to the wavelength of the sound being produced: larger speakers can produce lower frequencies at a higher level than smaller speakers. Elliptical speakers are a complex case, acting like large speakers lengthwise and small speakers crosswise. Acoustic impedance matching (or the lack of it) affects the operation of a
megaphone A megaphone, speaking-trumpet, bullhorn, blowhorn, or loudhailer is usually a portable or hand-held, cone-shaped acoustic horn used to amplify a person's voice or other sounds and direct it in a given direction. The sound is introduced int ...
, an
echo In audio signal processing and acoustics, an echo is a reflection of sound that arrives at the listener with a delay after the direct sound. The delay is directly proportional to the distance of the reflecting surface from the source and the lis ...
and
soundproofing Soundproofing is any means of impeding sound propagation. There are several basic approaches to reducing sound: increasing the distance between source and receiver, decoupling, using noise barriers to reflect or absorb the energy of the sound wa ...
.


Optics

A similar effect occurs when
light Light or visible light is electromagnetic radiation that can be perceived by the human eye. Visible light is usually defined as having wavelengths in the range of 400–700 nanometres (nm), corresponding to frequencies of 750–420 t ...
(or any electromagnetic wave) hits the interface between two media with different
refractive indices In optics, the refractive index (or refraction index) of an optical medium is a dimensionless number that gives the indication of the light bending ability of that medium. The refractive index determines how much the path of light is bent, or ...
. For non-magnetic materials, the refractive index is inversely proportional to the material's characteristic impedance. An ''optical'' or ''wave impedance'' (that depends on the propagation direction) can be calculated for each medium, and may be used in the transmission-line reflection equation : r = to calculate reflection and transmission coefficients for the interface. For non-magnetic dielectrics, this equation is equivalent to the
Fresnel equations The Fresnel equations (or Fresnel coefficients) describe the reflection and transmission of light (or electromagnetic radiation in general) when incident on an interface between different optical media. They were deduced by Augustin-Jean Fresne ...
. Unwanted reflections can be reduced by the use of an anti-reflection
optical coating An optical coating is one or more thin layers of material deposited on an optical component such as a lens, prism or mirror, which alters the way in which the optic reflects and transmits light. These coatings have become a key technology in t ...
.


Mechanics

If a body of mass ''m'' collides elastically with a second body, maximum energy transfer to the second body will occur when the second body has the same mass ''m''. In a head-on collision of equal masses, the energy of the first body will be completely transferred to the second body (as in
Newton's cradle The Newton's cradle is a device that demonstrates the conservation of momentum and the conservation of energy with swinging spheres. When one sphere at the end is lifted and released, it strikes the stationary spheres, transmitting a force thro ...
for example). In this case, the masses act as "mechanical impedances", which must be matched. If m_1 and m_2 are the masses of the moving and stationary bodies, and ''P'' is the momentum of the system (which remains constant throughout the collision), the energy of the second body after the collision will be ''E''2: : E_2=\frac which is analogous to the power-transfer equation. These principles are useful in the application of highly energetic materials (explosives). If an explosive charge is placed on 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 (such as the opposite side of the target), tension waves reflect back and create
spall Spall are fragments of a material that are broken off a larger solid body. It can be produced by a variety of mechanisms, including as a result of projectile impact, corrosion, weathering, cavitation, or excessive rolling pressure (as in a ball ...
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.


See also

*
Ringing (signal) In electronics, signal processing, and video, ringing is oscillation of a signal, particularly in the step response (the response to a sudden change in input). Often ringing is undesirable, but not always, as in the case of resonant inductive cou ...
*
Standing wave ratio In radio engineering and telecommunications, standing wave ratio (SWR) is a measure of impedance matching of loads to the characteristic impedance of a transmission line or waveguide. Impedance mismatches result in standing waves along the transm ...
*
Line isolation transformer A line isolation transformer for telephone use is a special type of impedance matching transformer that is used to couple telephone land lines to subscriber equipment to prevent dangerous common mode voltages from appearing on the line. It has a ...


Notes


References

* * * * * * * {{refend


External links


Impedance Matching
Impedance Matching with the Smith Chart Electronic design Electronics concepts Filter theory es:Adaptación de impedancias