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Inductance

Inductance is the tendency of an electrical conductor to oppose a change in the electric current flowing through it. The electric current produces a magnetic field around the conductor. The magnetic field strength depends on the magnitude of the electric current, and follows any changes in the magnitude of the current. From Faraday's law of induction, any change in magnetic field through a circuit induces an electromotive force (EMF) (voltage) in the conductors, a process known as electromagnetic induction. This induced voltage created by the changing current has the effect of opposing the change in current. This is stated by Lenz's law, and the voltage is called back EMF.

Inductance is defined as the ratio of the induced voltage to the rate of change of current causing it. It is a proportionality constant that depends on the geometry of circuit conductors (e.g., cross-section area and length) and the magnetic permeability of the conductor and nearby materials. An electronic component designed to add inductance to a circuit is called an inductor. It typically consists of a coil or helix of wire.

The term inductance was coined by Oliver Heaviside in May 1884, as a convenient way to refer to "coefficient of self-induction". It is customary to use the symbol $$L$$ for inductance, in honour of the physicist Heinrich Lenz. In the SI system, the unit of inductance is the henry (H), which is the amount of inductance that causes a voltage of one volt, when the current is changing at a rate of one ampere per second. The unit is named for Joseph Henry, who discovered inductance independently of Faraday.

History
The history of electromagnetic induction, a facet of electromagnetism, began with observations of the ancients: electric charge or static electricity (rubbing silk on amber), electric current (lightning), and magnetic attraction (lodestone). Understanding the unity of these forces of nature, and the scientific theory of electromagnetism was initiated and achieved during the 19th century.

Electromagnetic induction was first described by Michael Faraday in 1831. In Faraday's experiment, he wrapped two wires around opposite sides of an iron ring. He expected that, when current started to flow in one wire, a sort of wave would travel through the ring and cause some electrical effect on the opposite side. Using a galvanometer, he observed a transient current flow in the second coil of wire each time that a battery was connected or disconnected from the first coil. This current was induced by the change in magnetic flux that occurred when the battery was connected and disconnected. Faraday found several other manifestations of electromagnetic induction. For example, he saw transient currents when he quickly slid a bar magnet in and out of a coil of wires, and he generated a steady (DC) current by rotating a copper disk near the bar magnet with a sliding electrical lead ("Faraday's disk").

Source of inductance
A current $$i$$ flowing through a conductor generates a magnetic field around the conductor, which is described by Ampere's circuital law. The total magnetic flux $$\Phi$$ through a circuit is equal to the product of the perpendicular component of the magnetic flux density and the area of the surface spanning the current path. If the current varies, the magnetic flux $$\Phi$$ through the circuit changes. By Faraday's law of induction, any change in flux through a circuit induces an electromotive force (EMF, $\mathcal{E}$) in the circuit, proportional to the rate of change of flux

$$\mathcal{E}(t) = -\frac{ \text{d} }{ \text{d} t }\,\Phi(t) $$

The negative sign in the equation indicates that the induced voltage is in a direction which opposes the change in current that created it; this is called Lenz's law. The potential is therefore called a back EMF. If the current is increasing, the voltage is positive at the end of the conductor through which the current enters and negative at the end through which it leaves, tending to reduce the current. If the current is decreasing, the voltage is positive at the end through which the current leaves the conductor, tending to maintain the current. Self-inductance, usually just called inductance, $$L$$ is the ratio between the induced voltage and the rate of change of the current

$$v(t) = L\,\frac{\text{d}i }{\text{d}t} \qquad \qquad \qquad (1)\;$$

Thus, inductance is a property of a conductor or circuit, due to its magnetic field, which tends to oppose changes in current through the circuit. The unit of inductance in the SI system is the henry (H), named after Joseph Henry, which is the amount of inductance that generates a voltage of one volt when the current is changing at a rate of one ampere per second.

All conductors have some inductance, which may have either desirable or detrimental effects in practical electrical devices. The inductance of a circuit depends on the geometry of the current path, and on the magnetic permeability of nearby materials; ferromagnetic materials with a higher permeability like iron near a conductor tend to increase the magnetic field and inductance. Any alteration to a circuit which increases the flux (total magnetic field) through the circuit produced by a given current increases the inductance, because inductance is also equal to the ratio of magnetic flux to current

$$L = {\Phi(i) \over i}$$

An inductor is an electrical component consisting of a conductor shaped to increase the magnetic flux, to add inductance to a circuit. Typically it consists of a wire wound into a coil or helix. A coiled wire has a higher inductance than a straight wire of the same length, because the magnetic field lines pass through the circuit multiple times, it has multiple flux linkages. The inductance is proportional to the square of the number of turns in the coil, assuming full flux linkage.

The inductance of a coil can be increased by placing a magnetic core of ferromagnetic material in the hole in the center. The magnetic field of the coil magnetizes the material of the core, aligning its magnetic domains, and the magnetic field of the core adds to that of the coil, increasing the flux through the coil. This is called a ferromagnetic core inductor. A magnetic core can increase the inductance of a coil by thousands of times.

If multiple electric circuits are located close to each other, the magnetic field of one can pass through the other; in this case the circuits are said to be inductively coupled. Due to Faraday's law of induction, a change in current in one circuit can cause a change in magnetic flux in another circuit and thus induce a voltage in another circuit. The concept of inductance can be generalized in this case by defining the mutual inductance $$M_{k,\ell}$$ of circuit $$k$$ and circuit $$\ell$$ as the ratio of voltage induced in circuit $$\ell$$ to the rate of change of current in circuit $k$. This is the principle behind a transformer. The property describing the effect of one conductor on itself is more precisely called self-inductance, and the properties describing the effects of one conductor with changing current on nearby conductors is called mutual inductance.

Self-inductance and magnetic energy
If the current through a conductor with inductance is increasing, a voltage $$v(t)$$ is induced across the conductor with a polarity that opposes the current—in addition to any voltage drop caused by the conductor's resistance. The charges flowing through the circuit lose potential energy. The energy from the external circuit required to overcome this "potential hill" is stored in the increased magnetic field around the conductor. Therefore, an inductor stores energy in its magnetic field. At any given time $$t$$ the power $$p(t)$$ flowing into the magnetic field, which is equal to the rate of change of the stored energy $U$, is the product of the current $$i(t)$$ and voltage $$v(t)$$ across the conductor

$$p(t) = \frac{\text{d}U}{\text{d}t} = v(t)\,i(t)$$

From (1) above

$$\begin{align} \frac{\text{d}U}{\text{d}t} &= L(i)\,i\,\frac{\text{d}i}{\text{d}t} \\[3pt] \text{d}U &= L(i)\,i\,\text{d}i\, \end{align}$$

When there is no current, there is no magnetic field and the stored energy is zero. Neglecting resistive losses, the energy $$U$$ (measured in joules, in SI) stored by an inductance with a current $$I$$ through it is equal to the amount of work required to establish the current through the inductance from zero, and therefore the magnetic field. This is given by:

$$U = \int_{0}^{I} L(i)\,i\,\text{d} i\,$$

If the inductance $$L(i)$$ is constant over the current range, the stored energy is

$$\begin{align} U &= L\int_{0}^{I}\,i\,\text{d} i \\[3pt] &= \tfrac{1}{2} L\,I^2 \end{align}$$

Inductance is therefore also proportional to the energy stored in the magnetic field for a given current. This energy is stored as long as the current remains constant. If the current decreases, the magnetic field decreases, inducing a voltage in the conductor in the opposite direction, negative at the end through which current enters and positive at the end through which it leaves. This returns stored magnetic energy to the external circuit.

If ferromagnetic materials are located near the conductor, such as in an inductor with a magnetic core, the constant inductance equation above is only valid for linear regions of the magnetic flux, at currents below the level at which the ferromagnetic material saturates, where the inductance is approximately constant. If the magnetic field in the inductor approaches the level at which the core saturates, the inductance begins to change with current, and the integral equation must be used.

Inductive reactance

When a sinusoidal alternating current (AC) is passing through a linear inductance, the induced back-EMF is also sinusoidal. If the current through the inductance is $$i(t) = I_\text{peak} \sin\left(\omega t\right)$$, from (1) above the voltage across it is $$\begin{align} v(t) &= L \frac{\text{d}i}{\text{d}t} = L\,\frac{\text{d}}{\text{d}t}\left[I_\text{peak} \sin\left(\omega t\right)\right]\\ &= \omega L\,I_\text{peak}\,\cos\left(\omega t\right) = \omega L\,I_\text{peak}\,\sin\left(\omega t + {\pi \over 2}\right) \end{align}$$

where $$I_\text{peak}$$ is the amplitude (peak value) of the sinusoidal current in amperes, $$\omega = 2\pi f$$ is the angular frequency of the alternating current, with $$f$$ being its frequency in hertz, and $$L$$ is the inductance.

Thus the amplitude (peak value) of the voltage across the inductance is

$$V_p = \omega L\,I_p= 2\pi f\,L\,I_p$$

Inductive reactance is the opposition of an inductor to an alternating current. It is defined analogously to electrical resistance in a resistor, as the ratio of the amplitude (peak value) of the alternating voltage to current in the component

$$X_L = \frac{V_p }{ I_p} = 2\pi f\,L$$

Reactance has units of ohms. It can be seen that inductive reactance of an inductor increases proportionally with frequency $f$, so an inductor conducts less current for a given applied AC voltage as the frequency increases. Because the induced voltage is greatest when the current is increasing, the voltage and current waveforms are out of phase; the voltage peaks occur earlier in each cycle than the current peaks. The phase difference between the current and the induced voltage is $$\phi =\tfrac{1}{2} \pi$$ radians or 90 degrees, showing that in an ideal inductor the current lags the voltage by 90°.

Calculating inductance
In the most general case, inductance can be calculated from Maxwell's equations. Many important cases can be solved using simplifications. Where high frequency currents are considered, with skin effect, the surface current densities and magnetic field may be obtained by solving the Laplace equation. Where the conductors are thin wires, self-inductance still depends on the wire radius and the distribution of the current in the wire. This current distribution is approximately constant (on the surface or in the volume of the wire) for a wire radius much smaller than other length scales.

Inductance of a straight single wire
As a practical matter, longer wires have more inductance, and thicker wires have less, analogous to their electrical resistance (although the relationships aren't linear, and are different in kind from the relationships that length and diameter bear to resistance).

Separating the wire from the other parts of the circuit introduces some unavoidable error in any formulas' results. These inductances are often referred to as “partial inductances”, in part to encourage consideration of the other contributions to whole-circuit inductance which are omitted.

Practical formulas
For derivation of the formulas below, see Rosa (1908). The total low frequency inductance (interior plus exterior) of a straight wire is:

$$L_\text{DC} = 200\text{ }\tfrac{\text{nH}}{\text{m}}\, \ell \left[\ln\left(\frac{\,2\,\ell\,}{r}\right) - 0.75 \right]$$

where
 * $$L_\text{DC}$$ is the "low-frequency" or DC inductance in nanohenry (nH or 10−9H),
 * $$\ell$$ is the length of the wire in meters,
 * $$r$$ is the radius of the wire in meters (hence a very small decimal number),
 * the constant $$200\text{ }\tfrac{\text{nH}}{\text{m}}$$ is the permeability of free space, commonly called $$\mu_\text{o}$$, divided by $$2 \pi$$; in the absence of magnetically reactive insulation the value 200 is exact when using the classical definition of μ0 = $L$, and correct to 7 decimal places when using the 2019-redefined SI value of μ0 = $4 H/m$.

The constant 0.75 is just one parameter value among several; different frequency ranges, different shapes, or extremely long wire lengths require a slightly different constant (see below). This result is based on the assumption that the radius $$r$$ is much less than the length $\ell$, which is the common case for wires and rods. Disks or thick cylinders have slightly different formulas.

For sufficiently high frequencies skin effects cause the interior currents to vanish, leaving only the currents on the surface of the conductor; the inductance for alternating current, $$L_\text{AC}$$ is then given by a very similar formula:

$$L_\text{AC} = 200\text{ }\tfrac{\text{nH}}{\text{m}}\, \ell \left[\ln\left(\frac{\,2\,\ell\,}{r}\right) - 1 \right]$$ where the variables $$\ell$$ and $$r$$ are the same as above; note the changed constant term now 1, from 0.75 above.

In an example from everyday experience, just one of the conductors of a lamp cord $1.257 H/m$ long, made of 18 AWG wire, would only have an inductance of about $10 m$ if stretched out straight.

Mutual inductance of two parallel straight wires
There are two cases to consider: Currents in the wires need not be equal, though they often are, as in the case of a complete circuit, where one wire is the source and the other the return.
 * 1) Current travels in the same direction in each wire, and
 * 2) current travels in opposing directions in the wires.

Mutual inductance of two wire loops
This is the generalized case of the paradigmatic two-loop cylindrical coil carrying a uniform low frequency current; the loops are independent closed circuits that can have different lengths, any orientation in space, and carry different currents. Nonetheless, the error terms, which are not included in the integral are only small if the geometries of the loops are mostly smooth and convex: They must not have too many kinks, sharp corners, coils, crossovers, parallel segments, concave cavities, or other topologically "close" deformations. A necessary predicate for the reduction of the 3-dimensional manifold integration formula to a double curve integral is that the current paths be filamentary circuits, i.e. thin wires where the radius of the wire is negligible compared to its length.

The mutual inductance by a filamentary circuit $$m$$ on a filamentary circuit $$n$$ is given by the double integral Neumann formula
 * $$ L_{m,n} = \frac{\mu_0}{4\pi} \oint_{C_m} \oint_{C_n} \frac{\mathrm{d}\mathbf{x}_m\cdot \mathrm{d}\mathbf{x}_n}{\ \left| \mathbf{x}_m - \mathbf{x}_n \right|\ }\ ,$$

where
 * $$C_m$$ and $$C_n$$ are the curves followed by the wires.
 * $$\mu_0$$ is the permeability of free space (4$\pi$× H/m)
 * $$\mathrm{d}\mathbf{x}_m$$ is a small increment of the wire in circuit $19 µH$$C$
 * $$\mathbf{x}_m$$ is the position of $$\mathrm{d}\mathbf{x}_m$$ in space
 * $$\mathrm{d}\mathbf{x}_n$$ is a small increment of the wire in circuit $m$$C$
 * $$\mathbf{x}_n$$ is the position of $$\mathrm{d}\mathbf{x}_n$$ in space.

Derivation
$$ M_{ij} \mathrel\stackrel{\mathrm{def}}{=} \frac{\Phi_{ij}}{I_j} $$

where $$\Phi_{ij} = \int_{S_i} \mathbf{B}_j\cdot\mathrm{d}\mathbf{a} = \int_{S_i} (\nabla\times\mathbf{A_j})\cdot\mathrm{d}\mathbf{a} = \oint_{C_i} \mathbf{A}_j\cdot\mathrm{d}\mathbf{s}_i = \oint_{C_i} \left(\frac{\mu_0 I_j}{4\pi} \oint_{C_j} \frac{\mathrm{d}\mathbf{s}_j}{\left|\mathbf{s}_i-\mathbf{s}_j\right|}\right) \cdot \mathrm{d}\mathbf{s}_i $$
 * $$I_j$$ is the current through the $$j$$th wire, this current creates the magnetic flux $$\Phi_{ij}\ \,$$through the $$i$$th surface
 * $$\Phi_{ij}$$ is the magnetic flux through the ith surface due to the electrical circuit outlined by $C_j$:

where indent=1|1=

$C_i$ is the curve enclosing surface $S_i$; and $S_i$ is any arbitrary orientable area with edge $C_i$

$\mathbf{B}_j$ is the magnetic field vector due to the $j$-th current (of circuit $C_j$).

$\mathbf{A}_j$ is the vector potential due to the $j$-th current.

Stokes' theorem has been used for the 3rd equality step. For the last equality step, we used the retarded potential expression for $$A_j$$ and we ignore the effect of the retarded time (assuming the geometry of the circuits is small enough compared to the wavelength of the current they carry). It is actually an approximation step, and is valid only for local circuits made of thin wires.

Self-inductance of a wire loop
Formally, the self-inductance of a wire loop would be given by the above equation with $$\ m = n\ .$$ However, here $$\ 1/\left|\mathbf{x} - \mathbf{x}'\right|\ $$ becomes infinite, leading to a logarithmically divergent integral. This necessitates taking the finite wire radius $$\ a\ $$ and the distribution of the current in the wire into account. There remains the contribution from the integral over all points and a correction term,

 * $$ L = \frac{\mu_0}{4\pi} \left[\ \ell\ Y + \oint_{C}\oint_{C'} \frac{\mathrm{d}\mathbf{x}\cdot \mathrm{d}\mathbf{x}'}{\ \left|\mathbf{x} - \mathbf{x}'\right|\ }\ \right] + \mathcal{O}_\mathsf{bend} \quad \text{ for } \; \left|\mathbf{s} - \mathbf{s}'\right| > \tfrac{1}{2}a\ $$

where
 * $$\ \mathbf s\ $$ and $$\ \mathbf{s}'\ $$ are distances along the curves $$\ C\ $$ and $$\ C'\ $$ respectively
 * $$\ a\ $$ is the radius of the wire
 * $$\ \ell\ $$ is the length of the wire
 * $$\ Y\ $$ is a constant that depends on the distribution of the current in the wire:
 * $$\ Y = 0\ $$ when the current flows on the surface of the wire (total skin effect),
 * $\ Y = \tfrac{1}{2}\ $ when the current is evenly over the cross-section of the wire.
 * $$\ \mathcal{O}_\mathsf{bend}\ $$ is an error term whose size depends on the curve of the loop:
 * $$\ \mathcal{O}_\mathsf{bend} = \mathcal{O}(\mu_0 a)\ $$ when the loop has sharp corners, and
 * $\ \mathcal{O}_\mathsf{bend} = \mathcal{O}\mathord\left( {\mu_0 a^2}/{\ell} \right)\ $ when it is a smooth curve.
 * Both are small when the wire is long compared to its radius.

Inductance of a solenoid
A solenoid is a long, thin coil; i.e., a coil whose length is much greater than its diameter. Under these conditions, and without any magnetic material used, the magnetic flux density $$B$$ within the coil is practically constant and is given by $$B = \frac{\mu_0\, N\, i}{\ell}$$

where $$\mu_0$$ is the magnetic constant, $$N$$ the number of turns, $$i$$ the current and $$l$$ the length of the coil. Ignoring end effects, the total magnetic flux through the coil is obtained by multiplying the flux density $$B$$ by the cross-section area $A$: $$\Phi = \frac{\mu_0\, N\, i\, A}{\ell},$$

When this is combined with the definition of inductance $L = \frac{N\, \Phi}{i}$, it follows that the inductance of a solenoid is given by: $$L = \frac{\mu_0\, N^2\, A}{\ell}.$$

Therefore, for air-core coils, inductance is a function of coil geometry and number of turns, and is independent of current.

Inductance of a coaxial cable
Let the inner conductor have radius $$r_i$$ and permeability $\mu_i$, let the dielectric between the inner and outer conductor have permeability $\mu_d$, and let the outer conductor have inner radius $r_{o1}$, outer radius $r_{o2}$, and permeability $\mu_0$. However, for a typical coaxial line application, we are interested in passing (non-DC) signals at frequencies for which the resistive skin effect cannot be neglected. In most cases, the inner and outer conductor terms are negligible, in which case one may approximate

$$L' = \frac{\text{d}L}{\text{d}\ell} \approx \frac{\mu_d}{2 \pi} \ln \frac{r_{o1}}{r_i}$$

Inductance of multilayer coils
Most practical air-core inductors are multilayer cylindrical coils with square cross-sections to minimize average distance between turns (circular cross -sections would be better but harder to form).

Magnetic cores
Many inductors include a magnetic core at the center of or partly surrounding the winding. Over a large enough range these exhibit a nonlinear permeability with effects such as magnetic saturation. Saturation makes the resulting inductance a function of the applied current.

The secant or large-signal inductance is used in flux calculations. It is defined as:

$$L_s(i) \mathrel\overset{\underset{\mathrm{def}}{}}{=} \frac{N\ \Phi}{i} = \frac{\Lambda}{i}$$

The differential or small-signal inductance, on the other hand, is used in calculating voltage. It is defined as:

$$L_d(i) \mathrel\overset{\underset{\mathrm{def}}{}}{=} \frac{\text{d}(N \Phi)}{\text{d}i} = \frac{\text{d}\Lambda}{\text{d}i}$$

The circuit voltage for a nonlinear inductor is obtained via the differential inductance as shown by Faraday's Law and the chain rule of calculus.

$$v(t) = \frac{\text{d}\Lambda}{\text{d}t} = \frac{\text{d}\Lambda}{\text{d}i}\frac{\text{d}i}{\text{d}t} = L_d(i)\frac{\text{d}i}{\text{d}t}$$

Similar definitions may be derived for nonlinear mutual inductance.

Mutual inductance
Mutual inductance is defined as the ratio between the EMF induced in one loop or coil by the rate of change of current in another loop or coil. Mutual inductance is given the symbol $n$.

Derivation of mutual inductance
The inductance equations above are a consequence of Maxwell's equations. For the important case of electrical circuits consisting of thin wires, the derivation is straightforward.

In a system of $$K$$ wire loops, each with one or several wire turns, the flux linkage of loop $m$, $\lambda_m$, is given by $$\displaystyle \lambda_m = N_m \Phi_m = \sum\limits_{n=1}^K L_{m,n}\ i_n\,.$$

Here $$N_m$$ denotes the number of turns in loop $m$; $$\Phi_m$$ is the magnetic flux through loop $m$; and $$L_{m,n}$$ are some constants described below. This equation follows from Ampere's law: magnetic fields and fluxes are linear functions of the currents. By Faraday's law of induction, we have

$$\displaystyle v_m = \frac{\text{d}\lambda_m}{\text{d}t} = N_m \frac{\text{d}\Phi_m}{\text{d}t} = \sum\limits_{n=1}^K L_{m,n}\frac{\text{d}i_n}{\text{d}t},$$

where $$v_m$$ denotes the voltage induced in circuit $m$. This agrees with the definition of inductance above if the coefficients $$L_{m,n}$$ are identified with the coefficients of inductance. Because the total currents $$N_n\ i_n$$ contribute to $$\Phi_m$$ it also follows that $$L_{m,n}$$ is proportional to the product of turns $N_m\ N_n$.

Mutual inductance and magnetic field energy
Multiplying the equation for vm above with imdt and summing over m gives the energy transferred to the system in the time interval dt, $$ \sum \limits_m^K i_m v_m \text{d}t = \sum\limits_{m,n=1}^K i_m L_{m,n} \text{d}i_n \mathrel\overset{!}{=} \sum\limits_{n=1}^K \frac{\partial W \left(i\right)}{\partial i_n} \text{d}i_n. $$

This must agree with the change of the magnetic field energy, W, caused by the currents. The integrability condition

$$\displaystyle\frac{\partial^2 W}{\partial i_m \partial i_n} = \frac{\partial^2 W}{\partial i_n \partial i_m}$$

requires Lm,n = Ln,m. The inductance matrix, Lm,n, thus is symmetric. The integral of the energy transfer is the magnetic field energy as a function of the currents, $$\displaystyle W\left(i\right) = \frac{1}{2} \sum \limits_{m,n=1}^K i_m L_{m,n} i_n.$$

This equation also is a direct consequence of the linearity of Maxwell's equations. It is helpful to associate changing electric currents with a build-up or decrease of magnetic field energy. The corresponding energy transfer requires or generates a voltage. A mechanical analogy in the K = 1 case with magnetic field energy (1/2)Li2 is a body with mass M, velocity u and kinetic energy (1/2)Mu2. The rate of change of velocity (current) multiplied with mass (inductance) requires or generates a force (an electrical voltage).

Mutual inductance occurs when the change in current in one inductor induces a voltage in another nearby inductor. It is important as the mechanism by which transformers work, but it can also cause unwanted coupling between conductors in a circuit.

The mutual inductance, $M_{ij}$, is also a measure of the coupling between two inductors. The mutual inductance by circuit $$i$$ on circuit $$j$$ is given by the double integral Neumann formula, see calculation techniques

The mutual inductance also has the relationship: $$M_{21} = N_1\ N_2\ P_{21} \!$$ where

1=

$M_{21}$ is the mutual inductance, and the subscript specifies the relationship of the voltage induced in coil 2 due to the current in coil 1.

$N_1$ is the number of turns in coil 1,

$N_2$ is the number of turns in coil 2,

$P_{21}$ is the permeance of the space occupied by the flux.
 * indent=1

Once the mutual inductance $$M$$ is determined, it can be used to predict the behavior of a circuit: $$ v_1 = L_1\ \frac{\text{d}i_1}{\text{d}t} - M\ \frac{\text{d}i_2}{\text{d}t} $$ where

1=

$v_1$ is the voltage across the inductor of interest;

$L_1$ is the inductance of the inductor of interest;

$\text{d}i_1\,/\,\text{d}t$ is the derivative, with respect to time, of the current through the inductor of interest, labeled 1;

$\text{d}i_2\,/\,\text{d}t$ is the derivative, with respect to time, of the current through the inductor, labeled 2, that is coupled to the first inductor; and

$M$ is the mutual inductance.
 * indent=1

The minus sign arises because of the sense the current $$i_2$$ has been defined in the diagram. With both currents defined going into the dots the sign of $$M$$ will be positive (the equation would read with a plus sign instead).

Coupling coefficient
The coupling coefficient is the ratio of the open-circuit actual voltage ratio to the ratio that would be obtained if all the flux coupled from one magnetic circuit to the other. The coupling coefficient is related to mutual inductance and self inductances in the following way. From the two simultaneous equations expressed in the two-port matrix the open-circuit voltage ratio is found to be:

$${V_2 \over V_1}_\text{open circuit} = {M \over L_1}$$ where

indent=1|1=

$M^{2} = M_1 M_2$

while the ratio if all the flux is coupled is the ratio of the turns, hence the ratio of the square root of the inductances

$${V_2 \over V_1}_\text{max coupling} = \sqrt{ L_2 \over L_1\ }$$

thus,

$$M = k \sqrt{L_1\ L_2\ } $$ where

indent=1|1=

$k$ is the coupling coefficient,

$L_1$ is the inductance of the first coil, and

$L_2$ is the inductance of the second coil.

The coupling coefficient is a convenient way to specify the relationship between a certain orientation of inductors with arbitrary inductance. Most authors define the range as $ 0 \le k < 1$, but some define it as $ -1 < k < 1\,$. Allowing negative values of $$k$$ captures phase inversions of the coil connections and the direction of the windings.

Matrix representation
Mutually coupled inductors can be described by any of the two-port network parameter matrix representations. The most direct are the z parameters, which are given by

$$ [\mathbf z] = s \begin{bmatrix} L_1 \ M \\ M \ L_2 \end{bmatrix} .$$

The y parameters are given by

$$ [\mathbf y] = \frac{1}{s} \begin{bmatrix} L_1 \ M \\ M \ L_2 \end{bmatrix}^{-1} .$$ Where $$s$$ is the complex frequency variable, $$L_1$$ and $$L_2$$ are the inductances of the primary and secondary coil, respectively, and $$M$$ is the mutual inductance between the coils.

Multiple Coupled Inductors
Mutual inductance may be applied to multiple inductors simultaneously. The matrix representations for multiple mutually coupled inductors are given by $$ \begin{align} &[\mathbf z] = s \begin{bmatrix} L_1 & M_{12} & M_{13} & \dots & M_{1N} \\ M_{12} & L_2 & M_{23} & \dots & M_{2N} \\ M_{13} & M_{23} & L_3 & \dots & M_{3N} \\ \vdots & \vdots &\vdots & \ddots \\ M_{1N} & M_{2N} & M_{3N} & \dots & L_N \\ \end{bmatrix} \\

\end{align} $$

T-circuit
Mutually coupled inductors can equivalently be represented by a T-circuit of inductors as shown. If the coupling is strong and the inductors are of unequal values then the series inductor on the step-down side may take on a negative value.

This can be analyzed as a two port network. With the output terminated with some arbitrary impedance $Z$, the voltage gain $A_v$, is given by,

$$ A_\mathrm{v} = \frac{s M Z}{\, s^2 L_1 L_2 - s^2 M^2 + s L_1 Z \,} = \frac{k}{\, s \left(1 - k^2\right) \frac{ \sqrt{L_1 L_2} }{Z} + \sqrt{\frac{L_1}{L_2}} \,} $$

where $$k$$ is the coupling constant and $$s$$ is the complex frequency variable, as above. For tightly coupled inductors where $$k = 1$$ this reduces to

$$ A_\mathrm v = \sqrt {L_2 \over L_1} $$

which is independent of the load impedance. If the inductors are wound on the same core and with the same geometry, then this expression is equal to the turns ratio of the two inductors because inductance is proportional to the square of turns ratio.

The input impedance of the network is given by,

$$Z_\text{in} = \frac {s^2 L_1 L_2 - s^2 M^2 + s L_1 Z}{sL_2 + Z} = \frac{L_1}{L_2}\, Z\, \left( \frac{ 1 }{ 1 + \frac{Z}{\, s L_2 \,} } \right) \left( 1  + \frac{1 - k^2}{ \frac{Z}{\, s L_2 \,} } \right) $$

For $$k = 1$$ this reduces to

$$ Z_\text{in} = \frac{s L_1 Z}{sL_2 + Z} = \frac{L_1}{L_2}\, Z\, \left( \frac{ 1 }{ 1 + \frac{Z}{\, s L_2 \,} } \right)$$

Thus, current gain $$A_i$$ is independent of load unless the further condition

$$|sL_2| \gg |Z|$$

is met, in which case,

$$ Z_\text{in} \approx {L_1 \over L_2} Z $$

and

$$ A_\text{i} \approx \sqrt {L_1 \over L_2} = {1 \over A_\text{v}} $$

π-circuit
Alternatively, two coupled inductors can be modelled using a π equivalent circuit with optional ideal transformers at each port. While the circuit is more complicated than a T-circuit, it can be generalized to circuits consisting of more than two coupled inductors. Equivalent circuit elements $L_\text{s}$, $$L_\text{p}$$ have physical meaning, modelling respectively magnetic reluctances of coupling paths and magnetic reluctances of leakage paths. For example, electric currents flowing through these elements correspond to coupling and leakage magnetic fluxes. Ideal transformers normalize all self-inductances to 1 Henry to simplify mathematical formulas.

Equivalent circuit element values can be calculated from coupling coefficients with $$\begin{align} L_{S_{ij}} &= \frac{\det(\mathbf{K})}{-\mathbf{C}_{ij}} \\[3pt] L_{P_i} &= \frac{\det(\mathbf{K})}{\sum_{j=1}^N\mathbf{C}_{ij}} \end{align}$$

where coupling coefficient matrix and its cofactors are defined as
 * $$\mathbf{K} =

\begin{bmatrix} 1 & k_{12} & \cdots & k_{1N} \\ k_{12} &     1 & \cdots & k_{2N} \\ \vdots & \vdots & \ddots & \vdots \\ k_{1N} & k_{2N} & \cdots &     1 \end{bmatrix}\quad $$ and $$\quad \mathbf{C}_{ij} = (-1)^{i+j}\,\mathbf{M}_{ij}.$$

For two coupled inductors, these formulas simplify to
 * $$L_{S_{12}} = \frac{-k_{12}^2 + 1}{k_{12}}\quad$$ and $$\quad L_{P_1} = L_{P_2} \!=\! k_{12} + 1,$$

and for three coupled inductors (for brevity shown only for $$L_\text{s12}$$ and $$L_\text{p1}$$)

L_{S_{12}} = \frac{2\,k_{12}\,k_{13}\,k_{23} - k_{12}^2 - k_{13}^2 - k_{23}^2 + 1} {k_{13}\,k_{23} - k_{12}} \quad$$ and $$\quad L_{P_1} = \frac{2\,k_{12}\,k_{13}\,k_{23} - k_{12}^2 - k_{13}^2 - k_{23}^2 + 1} {k_{12}\,k_{23} + k_{13}\,k_{23} - k_{23}^2 - k_{12}-k_{13} + 1}. $$

Resonant transformer
When a capacitor is connected across one winding of a transformer, making the winding a tuned circuit (resonant circuit) it is called a single-tuned transformer. When a capacitor is connected across each winding, it is called a double tuned transformer. These resonant transformers can store oscillating electrical energy similar to a resonant circuit and thus function as a bandpass filter, allowing frequencies near their resonant frequency to pass from the primary to secondary winding, but blocking other frequencies. The amount of mutual inductance between the two windings, together with the Q factor of the circuit, determine the shape of the frequency response curve. The advantage of the double tuned transformer is that it can have a wider bandwidth than a simple tuned circuit. The coupling of double-tuned circuits is described as loose-, critical-, or over-coupled depending on the value of the coupling coefficient $k$. When two tuned circuits are loosely coupled through mutual inductance, the bandwidth is narrow. As the amount of mutual inductance increases, the bandwidth continues to grow. When the mutual inductance is increased beyond the critical coupling, the peak in the frequency response curve splits into two peaks, and as the coupling is increased the two peaks move further apart. This is known as overcoupling.

Stongly-coupled self-resonant coils can be used for wireless power transfer between devices in the mid range distances (up to two metres). Strong coupling is required for a high percentage of power transferred, which results in peak splitting of the frequency response.

Ideal transformers
When $k = 1$, the inductor is referred to as being closely coupled. If in addition, the self-inductances go to infinity, the inductor becomes an ideal transformer. In this case the voltages, currents, and number of turns can be related in the following way:

$$V_\text{s} = \frac{N_\text{s}}{N_\text{p}} V_\text{p} $$ where

1=

$V_\text{s}$ is the voltage across the secondary inductor,

$V_\text{p}$ is the voltage across the primary inductor (the one connected to a power source),

$N_\text{s}$ is the number of turns in the secondary inductor, and

$N_\text{p}$ is the number of turns in the primary inductor.
 * indent=1

Conversely the current:

$$I_\text{s} = \frac{N_\text{p}}{N_\text{s}} I_\text{p} $$ where

1=

$I_\text{s}$ is the current through the secondary inductor,

$I_\text{p}$ is the current through the primary inductor (the one connected to a power source),

$N_\text{s}$ is the number of turns in the secondary inductor, and

$N_\text{p}$ is the number of turns in the primary inductor.
 * indent=1

The power through one inductor is the same as the power through the other. These equations neglect any forcing by current sources or voltage sources.

Self-inductance of thin wire shapes
The table below lists formulas for the self-inductance of various simple shapes made of thin cylindrical conductors (wires). In general these are only accurate if the wire radius $$a$$ is much smaller than the dimensions of the shape, and if no ferromagnetic materials are nearby (no magnetic core).

$$Y$$ is an approximately constant value between 0 and 1 that depends on the distribution of the current in the wire: $Y = 0$ when the current flows only on the surface of the wire (complete skin effect), $Y = 1$ when the current is evenly spread over the cross-section of the wire (direct current). For round wires, Rosa (1908) gives a formula equivalent to:

$$Y \approx \frac{1}{\, 1 + a\ \sqrt{\tfrac{1}{8}\mu\sigma\omega \,} \,}$$

where

indent=1|1=

$\omega = 2\pi f$ is the angular frequency, in radians per second;

$\mu = \mu_0\,\mu_\text{r}$ is the net magnetic permeability of the wire;

$\sigma$ is the wire's specific conductivity; and

$a$ is the wire radius.

$$\mathcal{O}(x)$$ is represents small term(s) that have been dropped from the formula, to make it simpler. Read the term $${}+ \mathcal{O}(x)$$ as "plus small corrections that vary on the order of $x$" (see big O notation).

General references

 * Küpfmüller K., Einführung in die theoretische Elektrotechnik, Springer-Verlag, 1959.
 * Heaviside O., Electrical Papers. Vol.1. – L.; N.Y.: Macmillan, 1892, p. 429-560.
 * Fritz Langford-Smith, editor (1953). Radiotron Designer's Handbook, 4th Edition, Amalgamated Wireless Valve Company Pty., Ltd. Chapter 10, "Calculation of Inductance" (pp. 429–448), includes a wealth of formulas and nomographs for coils, solenoids, and mutual inductance.
 * F. W. Sears and M. W. Zemansky 1964 University Physics: Third Edition (Complete Volume), Addison-Wesley Publishing Company, Inc. Reading MA, LCCC 63-15265 (no ISBN).
 * Küpfmüller K., Einführung in die theoretische Elektrotechnik, Springer-Verlag, 1959.
 * Heaviside O., Electrical Papers. Vol.1. – L.; N.Y.: Macmillan, 1892, p. 429-560.
 * Fritz Langford-Smith, editor (1953). Radiotron Designer's Handbook, 4th Edition, Amalgamated Wireless Valve Company Pty., Ltd. Chapter 10, "Calculation of Inductance" (pp. 429–448), includes a wealth of formulas and nomographs for coils, solenoids, and mutual inductance.
 * F. W. Sears and M. W. Zemansky 1964 University Physics: Third Edition (Complete Volume), Addison-Wesley Publishing Company, Inc. Reading MA, LCCC 63-15265 (no ISBN).

title: Inductance


text:
Stereophonics

Stereophonics are a Welsh rock band formed in 1992 in the village of Cwmaman in the Cynon Valley, Wales. The band consists of Kelly Jones (lead vocals, lead guitar, keyboards), Richard Jones (no relation to Kelly; bass guitar, harmonica, backing vocals), Adam Zindani (rhythm guitar, backing vocals), Jamie Morrison (drums, percussion) and touring member Tony Kirkham (keyboards). The group previously included the late Stuart Cable (1992–2003) and then Javier Weyler (2004–2012) on drums. Stereophonics have released twelve studio albums, including eight UK number one albums. A successful compilation album, Decade in the Sun, was released in November 2008 and charted at number two on the UK Album Chart.

Described as "classic UK rock delivered with whiskey vocals", the band have been summarised as possessing a sound akin to the genres of alternative rock and "British traditional rock". Stereophonics' debut album, Word Gets Around, was released in August 1997 and charted at number six in the UK, aided by the singles "Local Boy in the Photograph", "More Life in a Tramps Vest" and "A Thousand Trees". The band reached mainstream success with the release of Performance and Cocktails (and its promotional singles "The Bartender and the Thief", "Just Looking" and "Pick a Part That's New") in 1999 and have achieved a total of ten top-ten singles as well as one number one: "Dakota" (2005). Having sold around 10 million copies worldwide by 2016, Stereophonics are one of the most successful Welsh rock acts. Upon their release of Pull the Pin, they achieved five consecutive UK number one albums.

The band have also been praised for their live performances, which have landed them headlining slots at many of the UK and Ireland's most high-profile music festivals, including Reading and Leeds in 2000, Glastonbury in 2002, V Festival in 2002, the Isle of Wight in 2004 and 2009, Oxegen in 2010, Tramlines Festival and TRNSMT in 2018, and Latitude in 2019. The band is part of the Cardiff music scene.

Formation and early years (1986–1991)
Kelly Jones and Stuart Cable lived on the same street in the Welsh village of Cwmaman. Jones heard Cable played drums so asked if he wanted to jam together. After some time practising in Jones' dad's garage, Nicholas Geake joined in on guitar. Later, Jones invited Paul Rosser and Chris Davies to play on bass guitar and keyboards, respectively. Cable recalls he was the one who suggested that Jones be the singer, as his dad was a singer back in the sixties who supported Roy Orbison. In 1986 the band recorded a demo under the name "Zephyr". When Jones went on holiday the band played a gig without him, which resulted in Jones leaving the band and Jones and Cable going their separate ways. Jones, Rosser and Davies formed their own R&B band called "Silent Runner" while Cable joined a glam-rock band named "King Catwalk" on drums.

A few years later, Cable got sacked from the band. A few weeks after, Cable waved to Jones from a bus, and Jones, who was standing at a bus stop, waved back. It was the first contact they had since Zephyr had broken up. Two weeks later, Jones and Cable started speaking again. They agreed to give the band another go, but Cable only wanted to play their own songs. Jones agreed. The duo invited Mark Everett to play for them on bass guitar and Jones then started writing his own songs.

Everett went on holiday for two weeks but Jones and Cable wanted to continue rehearsing, so Jones invited long-time friend Richard Jones to fill in for Everett. Stunned by Richard's appearance and bass playing, Cable convinced Kelly to keep him instead of Everett. The band decided they needed another member to play lead guitar. Simon Collier was the first guitarist brought in, but didn't stay in the band; he did, however, become Kelly's guitar technician. The band tried hiring two other guitarists, another Richard Jones and Glenn Hyde. Neither stayed for long. Hyde did however play harmonica on "Rooftop" for the band's 2001 album Just Enough Education to Perform. After Hyde left, the band stuck as a three-piece act.

Name change and V2 Records (1992–1996)
Kelly, Richard and Cable began writing and performing music in working men's clubs together in 1992 as a band known as "Tragic Love Company", a name inspired by their favourite bands (the Tragically Hip, Mother Love Bone and Bad Company). After Tragic Love Company supported Smalltown Heroes in the Borderline Club, London, they met Marshall Bird and Steve Bush who were interested in producing for the band. The band agreed and recorded a demo for "A Thousand Trees".

Wayne Coleman organised a series of concerts throughout South Wales after receiving a demo from the band. Wayne liked it a lot but hated the band name and told them they wouldn't be performing unless they changed it. After Cable read the manufacturer name of a gramophone, "Falcon Stereophonic", he told Kelly and the band agreed to change their name to "the Stereophonics". In March 1996, the band played a gig at their local Coliseum Theatre, Aberdare with Catatonia along with local bands Krazy Keyboards (later to become Dylan Thorn), and the Pocket Devils. When the band finished their slot, John Brand approached them and he became their manager. Brand managed to get over 35 record companies in the UK interested in signing the Stereophonics. In May 1996, they signed with V2, the first artists to be signed to newly formed record label. Upon signing, they dropped "the" from their name and simply became "Stereophonics".

Debut album and ascent to fame (1997–2000)
In August 1997, the band released their first studio album, Word Gets Around, which reached number six in the UK charts, from which five singles were released. The debut single, released 25 November 1996, was "Looks Like Chaplin". Afterwards, the band embarked on a successful world tour.

In February 1998, the band received a BRIT Award for Best New Group. In the same week, the band re-released the single "Local Boy in the Photograph", which in turn reached number fourteen in the UK Singles Chart. The band's debut album, Word Gets Around, also went gold in the UK.

In November 1998, "The Bartender and the Thief" (the first single from the album Performance and Cocktails) was released, eventually reaching number three on the UK charts. "Just Looking" was released next and reached number four in March 1999. In that same month, the album was released, entering at number one and going platinum within three weeks. Later that year, the band played in front of 50,000 people at Morfa Stadium in Swansea. The concert was filmed and released on DVD the following year. They also collaborated with Tom Jones on a cover of the Randy Newman song "Mama Told Me Not To Come", for the Tom Jones album Reload.

Throughout 1998 and 1999, the band toured in Europe, Australia and the US. On 12 June 1998, Stereophonics played to over 10,000 spectators in the grounds of Cardiff Castle in Wales. Footage of the concert was released on VHS and DVD, titled Live at Cardiff Castle.

Mainstream success (2001–2004)
The band released their third album, Just Enough Education to Perform, in April 2001. The album included the track "Mr. Writer", which includes lyrics that criticise a critic who the band believe gave them a negative review. The album also contained one of the band's most famous tracks, "Have a Nice Day", which reached number five in the UK charts. To promote the new album, Just Enough Education to Perform, the Stereophonics played a two-day festival, which was called A Day at the Races. This event was held in Donington Park on the first day and at Cardiff's Millennium Stadium on the second. The concerts were supported by Ash, Black Crowes and the Crocketts, with Proud Mary playing Donington only. Over 200,000 separate tickets were sold for the weekend festival. The performance was released on a DVD in 2002.

2003 saw the release of their fourth album, titled You Gotta Go There to Come Back. The album contained one of the band's most popular songs, "Maybe Tomorrow". In September 2003, drummer Stuart Cable was sacked. According to reports, it was because of his lack of commitment to the band. Cable, at the time, presented a TV show called "Cable TV" and felt that the band would never improve. Because of this, he missed several rehearsals and live concerts. He was eventually replaced by Javier Weyler. Steve Gorman, from the Black Crowes, stood in for Cable during the band's live performances until Weyler was appointed. When asked about Cable leaving the band in a 2010 interview with Rip It Up magazine, Kelly Jones acknowledged the difficulty of the situation.

Towards the end of the year, Stereophonics did a sold-out tour of the UK, ending with a Christmas show at the Millennium Stadium, Cardiff, supported by Feeder, Ocean Colour Scene and Adam Masterson. The show was closed with a live version of "Merry Xmas Everybody", originally recorded by Slade. The group took a break after their 2003–2004 world tour, which included a set at the Manchester Move Festival in July 2004.

Drummer change and Stuart Cable's death (2005–2010)
Their fifth studio album, Language. Sex. Violence. Other? was released in March 2005. It marked their first recording with new drummer Javier Weyler. The band achieved their first number one hit in the UK singles charts with the album's first single, "Dakota". The second single from the album was "Superman". However, that song did not repeat the success of "Dakota", peaking at number thirteen. After "Superman" came "Devil", featuring a controversial video and reaching number eleven in the charts. The album was nominated for a Pop Factory award at the end of the year, losing out to Feeder's Pushing the Senses.

On 2 July 2005, the group appeared at the Live 8 concert in Hyde Park, London, playing to their biggest audience yet. The band were also scheduled to support Oasis for a number of dates across Europe, in early 2006, but pulled out due to family commitments. 2006 also saw the release of Stereophonics' first live album, Live from Dakota. The album is a two-disc compilation, featuring twenty tracks spanning all five of the band's albums and capturing the best of their 2005 world tour. Rather than being a recording of a single show, the tour was recorded every night and the band picked out the best version of each song individually. The album also features a track titled "Jayne", later released as part of Kelly Jones' solo album, Only the Names Have Been Changed.

Pull the Pin was released in the UK on 15 October 2007, along with a download-only taster; "Bank Holiday Monday". The track was also available for free to people who pre-ordered tickets for the band's concerts in 2007. The album was written and recorded by November 2006 but held back for release until late 2007. "It Means Nothing" was the first single of the album, released in September before the LP was released a week later on 15 October. The album contains twelve songs and reached number one in the UK's official album chart. The next single, "My Friends", reached number thirty-two in the UK charts, their poorest chart performance since "More Life in a Tramps Vest" from their debut album.

On 20 May 2007, at Radio 1's Big Weekend in Preston, the band were joined on stage by Casino frontman Adam Zindani. Zindani continued to tour with the band for the remainder of the Pull the Pin tour, playing lead guitar and backing vocals. He has been credited for writing and performing on two of the band's new tracks, "You're My Star" and "My Own Worst Enemy". On "You're My Star", he sings backing vocals and plays lead guitar, whereas on "My Own Worst Enemy" he only plays lead guitar. In November 2008, Stereophonics released their first greatest hits compilation, Decade in the Sun.

On 8 December 2009, the Vancouver Organizing Committee for the 2010 Olympic and Paralympic Winter Games announced the line up for performers for the nightly Victory Ceremonies. These ceremonies included 30 minutes of entertainment from the evening's host province/territory, 30 minutes of medal presentations, and a one-hour performance by a musical talent. Stereophonics performed their song "I Got Your Number" at this event on 20 February – Yukon Night. The band's seventh album, titled Keep Calm and Carry On, was released on 16 November 2009. They decided on this name after seeing a poster in the White Horse pub in Richmond where they spent a lot of time whilst recording the album. The album's debut single was "Innocent". The second single from the album, "Could You Be the One?", was released on 15 February 2010. The band embarked on a seven-date tour to support the new album in March 2010 playing at Aberdeen, Newcastle, Glasgow, Nottingham, Birmingham, Manchester, Sheffield and London. with support from Glasgow band Hip Parade.

On 5 June 2010, Stereophonics played the first-ever gig at the Cardiff City Stadium with support from unsigned South Wales band 4th Street Traffic, followed by Kids in Glass Houses and Doves. The concert, known as "Summer in the City", was played to a sold-out audience of 30,000. Two days later, original drummer Stuart Cable was found dead in his home in Aberdare having choked on his own vomit after binge drinking. After the Keep Calm and Carry On Tour concluded, and their contract with Universal at an end, Kelly Jones wanted to change the way the band worked and so decided to take a break from writing and recording an album every two years.

Graffiti on the Train, Keep the Village Alive and Scream Above the Sounds (2011–2018)
On 3 March 2011, Stereophonics announced on their Facebook page that they were working on new music in the studio. In July 2012 it was announced that Weyler and the band had parted company. The announcement was made on the band's Facebook page, though no reason was given for his departure. It was announced on 24 September 2012 that Jamie Morrison, former drummer for Noisettes, had replaced Weyler in the band. On 8 October 2012, Stereophonics released the video to a track titled "Violins and Tambourines" from the upcoming album. On 4 November, the first single from the new album, "In a Moment", was released as a free download from the band's website. On the same day, NME.com reported that the album would be titled Graffiti on the Train. The album was released on 4 March 2013. Second single preceding the album, "Indian Summer" was released in January 2013; by 10 March it had peaked at number 30 in the UK, making it their group's first UK top-40 single since 2007. A third single, the album's title track, was released on 13 May.

In late September 2014, it was announced via their Twitter page that a new album has been mixed and that it should be released in 2015. On 21 March 2015, Stereophonics performed in Bristol and in London's Royal Albert Hall and debuted 3 new songs "C'est La Vie", "I Wanna Get Lost With You" and "Song for the Summer" which are to be on their 9th album Keep the Village Alive with the release date of 11 September. "C'est la Vie" was released as the first single of the album. In September 2015 the band appeared on BBC Two's Later... with Jools Holland. During the Keep the Summer Alive Tour, Kelly Jones announced he would like to release the band's tenth studio album "before next summer" to commemorate the 20th anniversary of Word Gets Around, rather than release a compilation album.

On 27 July 2017 the band announced Scream Above the Sounds as the title for the album and will be released on 27 October 2017. It became available to pre-order on the same day. The album was released under the new distribution label "Parlophone", as the band parted ways with the old label V2. The band released "All In One Night" on the same day as the lead single from it. On 4 September 2017 "Caught By The Wind" was released as the second single from the album followed by "Before Anyone Knew Our Name" as the third single on 20 October 2017.They released the album's fourth and final single, "What's All the Fuss About?" on 4 December 2017. They embarked on the Scream Above The Sounds tour in 2018.

Kind. and Oochya! (2019–present)
In January 2019, Stereophonics announced two shows as part of Forest Live, the summer concert series promoted by the Forestry Commission: 13 June at Westonbirt Arboretum, near Tetbury, Gloucestershire and 23 June at Thetford Forest, near Brandon, Suffolk. Kind. became their seventh number-one album later that year.

Originally intending to release another greatest hits album, the band announced their twelfth album, Oochya! on 6 September 2021. It became their eighth number-one album, putting them level with Oasis, R.E.M. and Taylor Swift for the most UK number-one albums ever.

On 18 June 2022, the second of the band's two concerts at the Principality Stadium in Cardiff, was broadcast live on BBC One Wales and BBC Two, with special guest Sir Tom Jones.

Other projects
On 9 October 2007, a retrospective DVD was released in the United States, Rewind: The First 10 Years. The DVD is a double disc with a runtime of nearly four hours. Much of this footage was recorded around the time that the You Gotta Go There to Come Back album was being recorded. This is because a similar band history DVD was listed for release shortly after that album but was never released, due to the departure of Stuart Cable. This explains Jones' hairstyle (circa 2003/2004) in the interview footage and the appearance of Stuart and the rest of the band freely talking about their togetherness and solidarity as the original three members. The original footage was updated by adding further footage to the end, bringing it up to date with the band's fifth album. Stuart does not appear on any of the extra footage. Availability coincides with the US re-release of the Language.Sex.Violence.Other? DVD, and the worldwide digital debut of their latest studio album, Pull the Pin.

In 2007, Jones released a solo album, titled Only the Names Have Been Changed, while recording the band's sixth studio album, Pull the Pin. The album contains ten tracks (all named after women) and features minimal instrumentation. The album also includes the song "Jayne", a previously unreleased Stereophonics track featured on the live album Live from Dakota and the Rewind DVD.

Stereophonics also performed the original opening theme tune for the TV series Long Way Round. The song's lyrics were slightly altered for the follow-up series, Long Way Down and Long Way Up.

Members
Current members
 * Kelly Jones – lead vocals, guitar, keyboards, piano (1992–present)
 * Richard Jones – bass guitar, harmonica, backing vocals (1992–present)
 * Adam Zindani – guitar, backing vocals (2007–present)
 * Jamie Morrison – drums, percussion (2012–present)

Current touring musicians
 * Tony Kirkham – keyboards, piano, harmonica, acoustic guitar, backing vocals (1999–present)
 * Gavin Fitzjohn - saxophone, guitar (2018–present)

Former members
 * Stuart Cable – drums, percussion (1992–2003; died 2010)
 * Javier Weyler – drums, percussion, backing vocals (2004–2012)

Former touring musicians
 * Scott James – guitar, backing vocals (2001–2004)
 * Aileen McLaughlin – backing vocals (2002–2003)
 * Anna Ross – backing vocals (2002–2003)
 * Steve Gorman – drums, percussion (2003–2004)
 * Sam Yapp – drums, percussion (2012)

Discography

 * Word Gets Around (1997)
 * Performance and Cocktails (1999)
 * Just Enough Education to Perform (2001)
 * You Gotta Go There to Come Back (2003)
 * Language. Sex. Violence. Other? (2005)
 * Pull the Pin (2007)
 * Keep Calm and Carry On (2009)
 * Graffiti on the Train (2013)
 * Keep the Village Alive (2015)
 * Scream Above the Sounds (2017)
 * Kind (2019)
 * Oochya! (2022)

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/

title: Stereophonics


text:
Talk:Monocistronic

Monocistronic is a term used in biochemistry to describe the capacity of eukaryotes to code one gene per one mRNA, as opposed to prokaryotes which can code many genes, sometimes all, on one mRNA, polycistronic.

title: Talk:Monocistronic


text:
User:Qaz/Sandbox

Possible work/To Do
Aime Argand

Discover (magazine)

Congener

title: User:Qaz/Sandbox


text:
Talk:Syllabary

Untitled
This page mentions (and has a broken link to) the "ethiopic language". I assume it is referring to Amharic - since it is the predominant official language in Ethipia - though it may also be referring to Ge'ez.
 * You are on the right track. Although "Ethiopic" is an umbrella term including Amharic, Ge'ez and Trigri.

The article says "It would be rather cumbersome to write the English word extra in CV syllables." To me, "CV" means "curriculum vitae". Obviously it means something else here. Whoever wrote that should explain. Michael Hardy 23:27 Jan 13, 2003 (UTC)

 * consonant-vowel would fit. Matthew Woodcraft

I had already surmised that, but it would have been inappropriate to inform the author of the page of my surmise. His or her way of writing it is uncouth. Michael Hardy 23:43 Jan 13, 2003 (UTC)

The paragraph...
 * The Indian languages and the Ethiopian languages have alphabets (called abugidas by some scholars) that look like syllabaries to western eyes, but are not. They both use separate consonant and vowel signs. Most often, the vowel sign is added to the consonant sign which may give the impression of a syllabic unit.

...stands in direct contrast to the fairly learned looking. I suppose that the term syllabery is used sometimes to refer to such languages. The paragraph in the article is wrong to some extent - actually, the consonants such these languages carry a vowel, in that writing the so-called consonant 'k' actually results in the complete syllable 'ka', which is changed to another complete syllable 'ke', 'ko', etc. by the addition of a vowel suffix. --prat 05:38, 2004 Feb 23 (UTC)

 * Hrrm, writing systems cleans this up .. syllabaries "have one distinct symbol per possible syllable, and the signs for each syllable have no systematic graphic similarity". The above source labels languages with systematic graphic similarity between syllables as syllabaries, and is therefore incorrect. --prat 05:42, 2004 Feb 23 (UTC)

English Language
Actually, it seems that one would need a syllable for 'ba' and a syllable for 'g' to write 'bag'. In the long run it would be very simple to write a syllabary for English if one follows this pattern. In other words, ban, bad, bag, bat, barrio, bastard, Bantu, barrister would use one first syllabary element and ball, bought, balk, born, boring, borscht, Boston, boron, Baltimore, baud, Baltic would use another. Bat, bought, fought and Crete would use one ending element and fog, bag, grog, frog, gig, big, log, brag, tug and brig would use another. It is very simple; I don't know if these examples are American English as opposed to British English; perhaps the syllabaries would differ. I suppose regional differences would show up easily in a syllabary system. Why isn't a syllabary constucted already? --McDogm 00:55, 20 Jun 2005 (UTC)
 * It's possible, but I don't think it's "simple", and it would require the reader to learn more characters than currently for reading a text, without giving any other true advantage. (Basically, Japanese has twice as many phonetic characters than English, but only half as many sounds.) If you're suggesting English ortography should be more phonetic, it could easily be done with an alphabet, as proven by the International Phonetic Alphabet. 惑乱 分からん 17:12, 23 April 2006 (UTC)
 * Also, what you're proposing doesn't really seem as a true syllabary, but more of a syllabic-like alphabet, similar to hangul. 惑乱 分からん 14:24, 25 April 2006 (UTC)

English Reading and the Teaching of Reading
I have not been able to find a suitable place to ask this question, or make this suggestion, but the lists of syllables in the entry above tempted me to write it here. I am a former English teacher, now a psychologist, and have some familiarity with linguistics, and a lot of familiarity with learning theory. What I am interested is not a syllabary, per se, but it would teach in terms of syllables. It seems to me that the teaching of reading would be facilitated by lists of English syllables and minimal pairs of syllables. A child or new reader could learn all the words or syllables ending in, for example, "ab". They would be bab, cab, dab, fab, gab, hab, jab, and so on. Some of these are words, and some are contained in other words, but I am inclined to think that learning the simple ones first, (the three letter ones,) would give a student a sense of the logic of spelling, and command of a great many simple words. Of course, there are a lot of four letter words in English, and familiarity with all of the phonetically simple ones would be a very strong base for being a proficient reader and speller. I am not aware of any system which would use such a sequence to teach reading and spelling. More advanced lists might be such things as all the "ite" words and syllables -- bite, kite, mite, site, ... and "ight" words or syllables -- fight, light, night, right, tight, wight (now obsolete), wright, or "ought" words or syllables -- bought, fought, thought. Some of these lists would be short, but that would make them easy to learn. Consider the syllable "cience" and the words efficience, proficience, science, ... Not many words in the same list as "yacht" -- there are many oddities in English, but it helps to classify them, as oddities. I would appreciate being redirected to sites where such an idea is developed or considered. Janice Vian jvian@eidnet.org  Janice Vian, Ph.D. (talk) 02:06, 30 June 2011 (UTC)
 * Since you seem to be interested in methods of teaching how to write, the syllable article, i.e. phonology, probably isn’t the best place to start, but I guess you’re looking for something like reverse dictionary, maybe combined with features of a phonetic dictionary. — Christoph Päper 06:39, 1 July 2011 (UTC)
 * I am more interested in teaching how to read, and the use of lists, such as I have suggested above, seem to me to allow for a playful and enjoyable way to learn the phonetics of English, and to rapidly give the learner a command of a huge number of words. Since the lists are intended to be essentially an exhaustive inventory of English syllables, the spelling of multi-syllabic words ought to seem logical and straightforward.  At the same time, the many exceptions and oddities of spelling, for which English is famous, are easily identified as exceptions to the general phonetic patterns, which should tend to lessen the confusion they create.  I would like to know if there is any program for teaching literacy which makes use of these ideas. Janice Vian, Ph.D. (talk) 16:09, 7 July 2011 (UTC) I have just revisited this page, and I am still interested in a phonetic, syllable-based method of teaching reading.  Janice Vian, Ph.D. (talk) 22:31, 21 November 2017 (UTC)

Syllabaries most often begin as simplified logograms?
On this article the image on top says that Syllabaries most often begin as simplified logograms. What makes anyone say that? As far as I can tell only Japanese hiragana, katakana and Nü Shu have been invented in this way. Meanwhile all of the other Syllabaries I have found so far were either invented by a single man, missionary, or developed independently. I really don’t see how most of the Syllabaries on earth begin as simplified logograms when only 3 of the 15 Syllabaries I have seen so far have began that way. Are there some other Syllabaries that began this way that Idont know about?--66.176.63.70 20:16, 9 November 2007 (UTC)

Derivation Of Katakana Characters Pictures
Hi,

From the original:

http://upload.wikimedia.org/wikipedia/commons/1/11/Katakana_origine.png

to

http://upload.wikimedia.org/wikipedia/commons/0/0c/Katakana_origine.svg

I noticed a few mistakes:

The last (bottom) stroke in the top radical in the kana for "sa" in the svg is highlighted red. That is incorrect

"te" also has a problem: the length of the descending left stroke between the horizontal strokes are highlighted red. This is also incorrect. Can you amend the svg, upload, replace, delete the links to the files in the corresponding articles (wikipedia and anywhere else), and copypasta? Thanks.174.3.103.39 (talk) 05:12, 9 June 2009 (UTC)

Specifity of intro section
User:Kwamikagami lately added this text to the introduction:"In a syllabary, there is no systematic similarity between the symbols which represent syllables with the same consonant or vowel. That is, the symbol for ka does not resemble in any predictable way the symbol for ki, nor the symbol for a." The reference cited is Daniels / Bright. These scholars, who are quite influential but not beyond critique, limit syllabaries to this definition indeed, but other authors disagree (and subsequently don’t use nor need names like abugida). Therefore this text should not appear in the introductory section. When I get the time (and back to my desk) I will move that part and add more references, unless someone does so earlier. — Christoph Päper 15:38, 17 October 2011 (UTC)
 * But that would have nothing to do with abugidas. If you don't use a specific term like abugida, those are just alphabets, not syllabaries. 21:31, 17 October 2011 (UTC)
 * That’s just a side note. Nevertheless, scholars who group scripts or writing systems by types of read-write entities instead of their original phonologic level of analysis do consider as syllabaries everything that Daniels / Bright label abugidas. — Christoph Päper 12:38, 18 October 2011 (UTC)

Comparison to Latin alphabet section
The second reference on this page (for the fact English has well over 10,000 possible syllable) links to a quora answer which itself has a broken article. At the very least, this should be replaced with a better source.

But is this section even worth saving? Almost half of the section is just listing different English monosyllabic words beginning with the letter B. — Preceding unsigned comment added by 188.113.158.182 (talk) 12:53, 4 November 2016 (UTC)

Sources and References
Seems like a lack of sources and references. One of the sources is a Quora entry. Dubious. MythicalAlien (talk) 01:58, 23 December 2016 (UTC)

Why does this website resemble this Wiki page? https://www.premierdentalclinic.co.uk/site/7ae57f-what-is-syllabary — Preceding unsigned comment added by JesseA123 (talk • contribs) 03:09, 26 October 2020 (UTC)

Disadvantages of an alphabet
The last paragraph is very culturally ignorant and in no way can Quora serve as a source, everyone could make up an answer just for it to be included on Wikipedia. Listing a bunch of words is not comparing, it just ridiculously implies the inefficiency of a syllabary in general and the alphabet's superiority. Someone should add something similiar to the article on alphabets. How about mentioning that alphabetic scripts use space very inefficiently? Long words span horizontally, screwing up table layouts. It often wastes more paper since sounds cannot be stacked and are expressed through several letters. --92.75.195.124 (talk) 02:46, 15 March 2017 (UTC)

title: Talk:Syllabary


text:
Jack Hodgins

Jack Hodgins (born October 3, 1938 in Comox Valley, British Columbia) is a Canadian novelist and short story writer. Critically acclaimed, among his best received works is Broken Ground (1998), a historical novel set after the First World War, for which he received the Ethel Wilson Fiction Prize and many other accolades.

Biography
Jack Hodgins grew up in Merville, a small town in the Comox Valley of British Columbia. He left home for Vancouver, where he attended the University of British Columbia, and was encouraged by Earle Birney, graduating with a bachelor's degree in Education. Hodgins spent the next 18 years of his career teaching English in Nanaimo, back on Vancouver Island.

In 1968, his first piece of literary work was accepted by a publication, and the exposure allowed him the chance to expand his work in print. With the publication of his first book of short stories, "Spit Delaney's Island" (1976), and his first novel "The Invention of the World" (1977), Jack Hodgins was well on his way to becoming a recognized name in Canadian literature, before taking a position at the University of Victoria in the Creative Writing Department.

He began receiving short-term teaching positions at universities throughout Canada, including Simon Fraser University and the University of Ottawa. (http://www.nwpassages.com/bios/hodgins.asp). His passion to educate led him around the world- he lectured in countries such as Japan, Finland, Norway, Germany, Spain, and Australia. In 1983, he accepted a position as a professor of Creative Writing at the University of Victoria. He and his family settled themselves in Victoria and stayed through until the time of his retirement from teaching, in 2002.

Hodgins continues his life in Victoria today and occasionally gives lectures on writing and speaks at a workshop in Mallorca, Spain annually. Hodgins has received much recognition for his work including the Eaton's BC Book Award for "Spit Delaney's Island," the Lieutenant Governor's Award for Literary Excellence in 2006, and the Terasen Lifetime Achievement Award. In 2001, a play based on several short stories from his book "The Barclay Family Theatre" was made into an opera by composer Christopher Donnison and premiered on stage in Victoria, BC. His life has been commemorated in a National Film Board Film entitled Jack Hodgins' Island.

Literature and the Environment
In an email interview with students from the University of Victoria, Hodgins elaborates on place affecting his writing, and uses "Macken Charm" as his example.
 * Hodgins' close relationship with the environment stems from his personal experiences within the temperate rainforests and seasides of British Columbia. Places like Comox Valley, Nanaimo, and Victoria, as well as his travels abroad, have influenced his writing and the contents of his books. His characters in "Innocent Cities" are based on actual residents of the city of Victoria in the late 1900s, as well as people he met on his travels to Australia. "The Invention of the World" is based on the legendary cult leader Brother Twelve and his followers from outside Nanaimo, BC. "The Macken Charm", set in 1956, illustrates the Comox Valley with characters inspired by influential people in his life. He based the many settings in "Spit Delaney's Island" around places he has lived or previously travelled.

"In The Macken Charm the family gathers (after a family funeral) at the site of a burnt hotel owned by the family. This place exists still. My own memories go back to playing as a child in that hotel when it was no longer in use. I knew that my parents began their married life in that hotel—the old uncle who owned it asked them to move in and look after it and them. My mother learned to cook on a stove big enough for a hotel dining room full of guests! All of this is in the novel, pretty well just as it happens, though the characters are fictitious replacements for the originals. The beach, the trees, the roads, the cars of 1956, the store, the funeral parlour, the bridge over the river in Courtenay, the glacier—they're all there. The story is fiction but the place is real."

Awards and honours

 * 2009 Member of the Order of Canada
 * 2006 Lieutenant Governor's Award for Literary Excellence
 * 2006 Terasen Lifetime Achievement Award "for an outstanding literary career in British Columbia"
 * 2004 Honorary D.Litt, University of Victoria
 * 2004 Distance: shortlisted for the inaugural City of Victoria Book Award
 * 2004 Distance: longlisted for the IMPAC/Dublin Award
 * 2000 Broken Ground: the Torgi Talking Book of the Year
 * 2000 Broken Ground: longlisted for the IMPAC/Dublin Award
 * 2000 Broken Ground: the Ethel Wilson Prize for fiction in British Columbia
 * 1999 Broken Ground: The Drummer General Award (Different Drummer Bookstore)
 * 1999 Broken Ground: jury choice as Best Novel of the Year in Quill and Quire
 * 1999 Broken Ground: in Globe and Mail Top Ten
 * 1999 Elected to the Royal Society of Canada
 * 1998 Honorary D.Litt., Malaspina University-College
 * 1996 "Finding Merville": (Comox Valley Record) first place in Neville Shanks Memorial Award for Historical Writing
 * 1995 Honorary D.Litt., University of British Columbia
 * 1988 The Honorary Patron: short listed for the Stephen Leacock Award for Humour
 * 1988 The Honorary Patron: the Commonwealth Literature Prize (Canada-Caribbean region)
 * 1986 The Canada-Australia Prize
 * 1979 The Resurrection of Joseph Bourne: The Governor General's Literary Award for Fiction
 * 1978 The Invention of the World: shortlisted for the Books in Canada First Novel Award
 * 1978 The Invention of the World: Gibson's First Novel Award
 * 1977 Spit Delaney's Island: short listed for the Governor General's Award
 * 1977 Spit Delaney's Island: the Eaton's B.C. Book Award
 * 1973 "After the Season": the President's Medal, University of Western Ontario

Novels

 * The Invention of the World – 1977
 * The Resurrection of Joseph Bourne – 1979 (winner of the Governor General's Award for English Language Fiction)
 * The Honorary Patron – 1987
 * Innocent Cities – 1990
 * The Macken Charm – 1995
 * Broken Ground – 1998 (winner of the 1999 Ethel Wilson Fiction Prize)
 * Distance – 2004
 * The Master of Happy Endings - 2010 (finalist for the Ethel Wilson Fiction Prize)

Short stories

 * Spit Delaney's Island –1976 (winner of the Eaton's BC Book Award)
 * "By The River"
 * The Barclay Family Theatre – 1981
 * Damage Done by the Storm – 2005

Children's literature

 * Left Behind in Squabble Bay – 1989

Non-fiction

 * Over Forty in Broken Hill – 1992
 * A Passion for Narrative: A Guide for Writing Fiction – 1994

Periodicals
Short stories and articles have been published in several magazines in Canada, France, Australia, and the US, including:

 * Northwest Review
 * Antigonish Review
 * Wascana Review
 * Descant (Texas)
 * Capilano Review
 * Prism International
 * Paris Intercontinental
 * Saturday Night
 * Vancouver
 * Westerly
 * Story
 * Toronto Life
 * North American Review
 * Event
 * Canadian Fiction Magazine
 * Sound Heritage
 * Alphabet
 * Viva
 * Journal of Canadian Fiction
 * The Canadian Forum
 * Forum (Houston)
 * Island No.2
 * Meanjin
 * The Literary Half-yearly
 * Overland

Anthologies
Teaching Short Fiction, edited with Bruce Nesbitt: (ComCept Publishing)

Voice and Vision, edited with W.H. New: (McClelland and Stewart)

The Frontier Experience: (Macmillan of Canada, 1975)

The West Coast Experience: (Macmillan of Canada, 1976)

BEGINNINGS: samplings from a long apprenticeship: novels which were imagined, written, re-written, rejected, abandoned, and supplanted: (Grand Union Press, 1983)

title: Jack Hodgins


text:
Application server

An application server is a server that hosts applications or software that delivers a business application through a communication protocol. For a typical web application, the application server sits behind the web servers.

An application server framework is a service layer model. It includes software components available to a software developer through an application programming interface. An application server may have features such as clustering, fail-over, and load-balancing. The goal is for developers to focus on the business logic.

Java application servers
Jakarta EE (formerly Java EE or J2EE) defines the core set of API and features of Java application servers.

The Jakarta EE infrastructure is partitioned into logical containers.
 * EJB container: Enterprise Beans are used to manage transactions. According to the Java BluePrints, the business logic of an application resides in Enterprise Beans—a modular server component providing many features, including declarative transaction management, and improving application scalability.
 * Web container: the web modules include Jakarta Servlets and Jakarta Server Pages (JSP).
 * JCA container (Jakarta Connectors)
 * JMS provider (Jakarta Messaging)

Commercial Java application servers have been dominated by WebLogic Application Server by Oracle, WebSphere Application Server from IBM and the open source JBoss Enterprise Application Platform (JBoss EAP) by Red Hat. Another example of web server which can be used as an application server for the Java EE ecosystem is Apache Tomcat.

Microsoft
Microsoft's .NET positions their middle-tier applications and services infrastructure in the Windows Server operating system and the .NET Framework technologies in the role of an application server. The Windows Application Server role includes Internet Information Services (IIS) to provide web server support, the .NET Framework to provide application support, ASP.NET to provide server side scripting, COM+ for application component communication, Message Queuing for multithreaded processing, and the Windows Communication Foundation (WCF) for application communication.

PHP application servers
PHP application servers run and manage PHP applications.

 * Zend Server, built by Zend, provides application server functionality for the PHP-based applications.
 * RoadRunner, built by Spiral Scout is a high-performance PHP application server, load-balancer, and process manager written in Go.

Third-party

 * Mono (a cross platform open-source implementation of .NET supporting nearly all its features, with the exception of Windows OS-specific features), sponsored by Microsoft and released under the MIT License

Mobile application servers
Mobile application servers provide data delivery to mobile devices.

Mobile features
Core capabilities of mobile application services include
 * Data routing– data is packaged in smaller (REST) objects with some business logic to minimize demands on bandwidth and battery
 * Orchestration– transactions and data integration across multiple sources
 * Authentication service– secure connectivity to back-end systems is managed by the mobile middleware
 * Off-line support– allows users to access and use data even though the device is not connected
 * Security– data encryption, device control, SSL, call logging

Mobile challenges
Although most standards-based infrastructure (including SOAs) are designed to connect to any independent of any vendor, product or technology, most enterprises have trouble connecting back-end systems to mobile applications, because mobile devices add the following technological challenges:
 * Limited resources – mobile devices have limited power and bandwidth
 * Intermittent connectivity – cellular service and wifi coverage is often not continuous
 * Difficult to secure  – mobility and BYOD practices make it hard to secure mobile devices

Deployment models
An application server can be deployed:
 * On premises
 * Cloud
 * Private cloud
 * Platform as a service (PaaS)

title: Application server


text:
Crazy Taxi (video game)

Crazy Taxi (クレイジータクシー) is a racing video game developed and published by Sega. It is the first game in the Crazy Taxi series. The game was first released in arcades in 1999 and then was ported to the Dreamcast in 2000. Gameplay is based on picking up taxi customers and driving to their destination as quickly as possible. Reception to Crazy Taxi has been mostly positive. It was ported to other platforms numerous times, including the PlayStation 2 and GameCube by Acclaim in 2001, and then Windows in 2002.

The game has also been rereleased for the PlayStation Network, Xbox Live Arcade, iOS and Android, and is also featured on the Dreamcast Collection. It became one of the few Sega All Stars on the Dreamcast and also earned Greatest Hits and Player's Choice status on PlayStation 2 and GameCube respectively. Sega followed up on the success of Crazy Taxi with numerous sequels, the first being Crazy Taxi 2 for the Dreamcast, which included several gameplay changes.

Gameplay
The main objective of the game is to pick up customers and take them to their chosen destination as quickly as possible. Along the way, money can be earned by performing stunts, such as near misses with other vehicles. The player is directed to a destination by a large green arrow at the top of the screen. The arrow does not adjust based on obstacles but rather points in the general direction of the destination. Once the player arrives near the destination, they must stop within a specified zone. When the destination is reached, the customer's fare is added to the player's total money earned. Ratings are then awarded depending on how long the player took to complete the journey. If the customer's timer runs out before the player reaches the destination, the customer will jump from the taxi without paying the driver.

Players can select three-, five-, or ten-minute settings, or the Arcade Rules used in the original coin-op version of the game. In the three time-limited settings, play continues for the designated period of time, after which the cab automatically stops and no more points can be scored. Under Arcade Rules, the player starts with an initial time limit of one minute, which can be extended through time bonuses earned for quick deliveries. Console versions of the game also feature a mode known as Crazy Box, a set of minigames that feature challenges, such as picking up and dropping off a number of customers within a time limit, bowling using the taxi as a ball, and popping giant balloons in a field.

The arcade version of the game includes one stage, and an additional "Original" stage was added for the console versions. Both stages are based in sunny coastal Californian locales, with steep hills and other strong similarities to San Francisco. The player has a choice of four drivers (Axel, B.D. Joe, Gena, and Gus) and their cabs, each of which has slightly different attributes.

Development and marketing
The arcade edition of the game was developed by Hitmaker as a variation from then-current arcade titles. The Crazy Taxi cabinet ran on Sega Naomi hardware. It was originally released in arcades as a sit-down machine. An upright version was later released. Over the next few years, the game would be ported to the Dreamcast, GameCube, PlayStation 2, and Windows; the latter port was published by Empire Interactive and developed by their internal studio Strangelite. Crazy Taxi was later ported to PlayStation Network and Xbox Live Arcade. These ports originally were to force a 4:3 aspect ratio, with widescreen monitors showing blue bars on either side of the screen, resulting in featuring full widescreen support for these ports. The game is a port of the Dreamcast version, including both the original arcade and the Dreamcast-exclusive level. The PlayStation Network port was released on November 16, 2010, while the Xbox Live Arcade version was released the following week. The game was also announced for the Zeebo console, though no port was ever released.

Crazy Taxi was brought to the App Store on iOS devices in October 2012. The game includes the arcade map and the map that was introduced for consoles. It also includes all Crazy Box challenges. As in the console versions, if all challenges are completed, a pedicab is unlocked to play the main game with. The taxi can be controlled though either the touch screen or by tilting the device making use of its accelerometer. Critics were impressed with this port because the maps remained unchanged and the controls were intuitive.

Sega applied for and was awarded U.S. Patent 6,200,138 – "Game display method, moving direction indicating method, game apparatus and drive simulating apparatus" – in 2001. The mechanics in the "138 patent" describe an arcade cabinet similar to Sega's previous arcade game Harley-Davidson & L.A. Riders (1997) but also describe the arrow navigation system and pedestrian avoidance aspects that were used in Crazy Taxi.

Crazy Taxi producer Kenji Kanno noted that the time extension on gameplay was a breakaway of the current "100 yen for three minutes" that persisted at the time for arcade games, and it rewarded players with longer playing times by performing well in the game. In addition to providing a game that could be played in short sessions, Kanno wanted a game to explore the "daily life and routine" of a taxi driver. In the development of the Dreamcast version of the original arcade game, the developers included a larger map in addition to the arcade one, as to create a feeling of "being lost" and allowing home console players to have fun "learning the town". Mini-games were developed for this version as to "let the player play longer if he improved skill" by offering challenges that were both fun and educational. Over one hundred different ideas for mini-games were developed by the team, but then pared down for the Crazy Box mini-game challenges for the game.

Crazy Taxi is also notable for its soundtrack featuring the bands Bad Religion and The Offspring, who provided all of the tracks for the arcade, Dreamcast, PlayStation 2 and GameCube ports. The PC featured an entirely new soundtrack, omitting the original bands in favor of music from Pivit, Too Rude and Total Chaos. The PlayStation 3 and Xbox 360 versions of Crazy Taxi also exclude the original bands, providing an original soundtrack for the ports. Custom soundtracks can also be used on the PlayStation 3 and Xbox 360 via their system firmware. The iOS and Android versions feature the original soundtrack.

In addition to generic destinations, such as the city's police station, rail terminal and lookout point, passengers may also request to be taken to Pizza Hut, Tower Records, the FILA sportswear store, the Levi's store or KFC. Crazy Taxi also featured vans on the roads with the WOW! logo on the side. Each of these chains are modeled as a location in the game. This is considered one of the most prominent examples of product placement in video gaming history. These establishments have been replaced with generic businesses in later versions, due to licensing difficulties.

Reception
In Japan, Game Machine listed Crazy Taxi on their April 1, 1999 issue as being the second most-successful arcade game of the month. It went on to be the biggest hit from Sega's Hitmaker studio.

Sales for the game were generally high, with the Dreamcast version being the second highest selling Dreamcast game in the United States in 2000, selling nearly 750,000 units. American sales later reached 2.2 million units across the Dreamcast and PlayStation 2, including 1.11 million for the Dreamcast and 1.07 million for the PS2. In the UK, the Dreamcast version was reported to have sold out. The PlayStation 2 version received a "Platinum" sales award from the Entertainment and Leisure Software Publishers Association (ELSPA), indicating sales of at least 300,000 copies in the United Kingdom. In Japan, the Dreamcast, PS2 and GameCube versions sold 155,714 units. Xbox Live Arcade sales for 2011 were high, with the game selling nearly 100,000 units.

The Dreamcast version of Crazy Taxi was critically acclaimed, averaging 90% at video game aggregate site GameRankings based on 37 reviews. Subsequent ports of the game have also received generally positive reviews, but had a trend of declining average scores. The PlayStation 2 port averaged 79% at GameRankings and 80/100 at Metacritic respectively. The next port for the GameCube scored lower, with aggregate scores of 70% and 69/100. The PC port was the poorest rated of the ports, scoring an average of 56% at GameRankings.

Critics generally praised the overall gameplay. Brandon Justice of IGN said: "I can't stress enough how addictive this game is". Of the Dreamcast port, Game Revolution felt that "a great arcade game became a good home game". They further noted the game's high difficulty and added that while the game was difficult, it was not frustrating. Michael Goncalves of PALGN added that the game was either a "love or hate" title, adding "if you love it, you will cherish the game and play it to your hearts content". Goncalves also pointed out that the game featured occasional pop up and clipping. Reviews were split across the releases in regards to the game's soundtrack. PALGN cited Bad Religion and The Offspring as a high point of the game, while Game Revolution felt that the tracks were repetitive. GameSpot reviewer Jeff Gerstmann felt that the soundtrack was subjective to personal preference, stating "you'll either want to crank the volume up or turn the music all the way down". In a review for the PC version's altered soundtrack, fellow GameSpot reviewer Andrew Park felt that the new music was fitting for the game. However, they criticized the PC version for frame rate issues and recommended the Dreamcast version instead.

James Bottorff of The Cincinnati Enquirer gave the Dreamcast version three-and-a-half stars out of four and wrote that "the only bug on Crazy Taxi's window is the lack of longevity. The game can grow tiresome after multiple plays. However, the amount of fun packed into its short life span makes it a worthwhile addition to your library of games". Maxim gave the same version a score of six out of ten: "We don’t like how the pesky pedestrians always manage to dodge your cab, but the graphics of the San Francisco-like city are amazingly detailed". In Japan, Famitsu gave the Dreamcast version a score of 34 out of 40, and the PS2 version 30 out of 40. GameFan gave the Dreamcast version a score of 96%, while Edge gave both the Dreamcast and PS2 versions a score of seven out of 10.

Hilary Goldstein in IGN called the Xbox Live Arcade release "a mad dash of fun", adding "there's almost no depth to Crazy Taxi, but that's just fine". Goldstein praised the fact that the port stayed true to the original source, but felt that the lack of the original soundtrack "kills half the reason to pick Crazy Taxi up again". Criticism also pointed to the lack of visual updates such as higher resolution models and textures. GamePro's Dave Rudden also lauded the fact that the port played faithfully to the original. Rudden echoed Goldstein's comments in regards to poor visuals, saying it had "ugly character models and boxy traffic cars".

Robert Workman from GameZone praised the game for sticking to its Sega roots: "Crazy Taxi isn't just a nostalgic trip, but also a wondrous stress reliever and an all-around entertaining game". Russ Pitts of The Escapist gave it four stars out of five: "In spite of dated graphics and other technical whizbangery, Crazy Taxi will remind you why you love driving games – and who started that fire. It's a game that's fun to play in short bursts that will become longer and longer the more of them you devote to it". In contrast, Daniel Feit of Wired gave it a score of six stars out of ten: "Gameplay is pure repetition; fun in short bursts but little lasting attraction".

Jeff Lundrigan and Daniel Erickson reviewed the Dreamcast and PlayStation 2 versions for Next Generation, respectively, and each gave their games four stars out of five: "A strangely addictive experience overall, Crazy Taxi is perfect for the gaming obsessive, but also makes a great party game". Erickson described it as "a near-perfect port of a fantastic game".

The Dreamcast version was a runner-up GameSpot's annual "Best Driving Game" award among console games, losing to Test Drive Le Mans.

During the 3rd Annual Interactive Achievement Awards, Crazy Taxi won "Console Action Game of the Year"; it also received nominations for "Console Game of the Year" and "Outstanding Achievement in Game Play Engineering".

Legacy
Crazy Taxi's success prompted Sega to produce multiple sequels. In 2001, Crazy Taxi 2 was released, followed by Crazy Taxi 3: High Roller in 2002. THQ would publish the Graphic State developed Crazy Taxi: Catch a Ride in 2003, the only title for the Game Boy Advance. Crazy Taxi: Fare Wars, a compilation of Crazy Taxi and Crazy Taxi 2, was released in 2007 for the PlayStation Portable. A mobile-exclusive entry to the series, titled Crazy Taxi: City Rush, was released on the iOS and Google Play app stores in 2014.

Crazy Taxi and its sequels have also prompted several games which clone its core gameplay. The Simpsons: Road Rage was the first of these titles, released in 2001. In 2003, Sega filed a lawsuit against Fox Interactive, Electronic Arts, and Radical Entertainment. Sega claimed that the game was a patent infringement of Crazy Taxi. The case, Sega of America, Inc. v. Fox Interactive, et al., was settled in private for an undisclosed amount. The poorly received Emergency Mayhem for the Wii utilizes the same core gameplay of the Crazy Taxi series but adds additional elements in regards to driving emergency response vehicles.

Team6 Game Studios would later release a similar game called Taxi Chaos, which could be considered as a spiritual successor to Crazy Taxi. The game was released on February 23, 2021, for the PlayStation 4, Nintendo Switch, and Xbox One. The game takes place in a fictionalized version of New York City and has the same format as the original Crazy Taxi games.

Film adaptation
In 2001, Richard Donner was attached to a live-action version of Crazy Taxi but eventually left the project. Talk of a screen adaptation of Crazy Taxi was renewed in 2014, as Sega optioned the film and TV rights to its library.

title: Crazy Taxi (video game)