Capacitance

Capacitance is the ratio of the change in an electric charge in a system to the corresponding change in its electric potential. There are two closely related notions of capacitance: self capacitance and mutual capacitance. Any object that can be electrically charged exhibits self capacitance. A material with a large self capacitance holds more electric charge at a given voltage than one with low capacitance. The notion of mutual capacitance is particularly important for understanding the operations of the capacitor, one of the three elementary linear electronic components (along with resistors and inductors).

The capacitance is a function only of the geometry of the design (e.g. area of the plates and the distance between them) and the permittivity of the dielectric material between the plates of the capacitor. For many dielectric materials, the permittivity and thus the capacitance, is independent of the potential difference between the conductors and the total charge on them.

The SI unit of capacitance is the farad (symbol: F), named after the English physicist Michael Faraday. A 1 farad capacitor, when charged with 1 coulomb of electrical charge, has a potential difference of 1 volt between its plates.[1] The reciprocal of capacitance is called elastance.

Common symbols C farad μF, nF, pF F = A2 s4 kg−1 m−2 C = charge / voltage M−1 L−2 T4 I2

Self-capacitance

In electrical circuits, the term capacitance is usually a shorthand for the mutual capacitance between two adjacent conductors, such as the two plates of a capacitor. However, for an isolated conductor, there also exists a property called self-capacitance, which is the amount of electric charge that must be added to an isolated conductor to raise its electric potential by one unit (i.e. one volt, in most measurement systems).[2] The reference point for this potential is a theoretical hollow conducting sphere, of infinite radius, with the conductor centered inside this sphere.

Mathematically, the self-capacitance of a conductor is defined by

${\displaystyle C={\frac {q}{V}},}$

where

q is the charge held by the conductor,
${\displaystyle V={1 \over 4\pi \varepsilon _{0}}\int {\sigma \,dS \over r}}$ is the electric potential,
σ is the surface charge density.
dS is an infinitesimal element of area,
r is the length from dS to a fixed point M within the plate
${\displaystyle \varepsilon _{0}}$ is the vacuum permittivity

Using this method, the self-capacitance of a conducting sphere of radius R is:[3]

${\displaystyle C=4\pi \varepsilon _{0}R\,}$

Example values of self-capacitance are:

The inter-winding capacitance of a coil is sometimes called self-capacitance,[5] but this is a different phenomenon. It is actually mutual capacitance between the individual turns of the coil and is a form of stray, or parasitic capacitance. This self-capacitance is an important consideration at high frequencies: It changes the impedance of the coil and gives rise to parallel resonance. In many applications this is an undesirable effect and sets an upper frequency limit for the correct operation of the circuit.

Mutual capacitance

A common form is a parallel-plate capacitor, which consists of two conductive plates insulated from each other, usually sandwiching a dielectric material. In a parallel plate capacitor, capacitance is very nearly proportional to the surface area of the conductor plates and inversely proportional to the separation distance between the plates.

If the charges on the plates are +q and −q, and V gives the voltage between the plates, then the capacitance C is given by

${\displaystyle C={\frac {q}{V}}.}$

which gives the voltage/current relationship

${\displaystyle i(t)=C{\frac {\mathrm {d} v(t)}{\mathrm {d} t}}.}$

The energy stored in a capacitor is found by integrating the work W:

${\displaystyle W_{\text{charging}}={\frac {1}{2}}CV^{2}}$

Capacitance matrix

The discussion above is limited to the case of two conducting plates, although of arbitrary size and shape. The definition ${\displaystyle C=Q/V}$ does not apply when there are more than two charged plates, or when the net charge on the two plates is non-zero. To handle this case, Maxwell introduced his coefficients of potential. If three (nearly ideal) conductors are given charges ${\displaystyle Q_{1},Q_{2},Q_{3}}$, then the voltage at conductor 1 is given by

${\displaystyle V_{1}=P_{11}Q_{1}+P_{12}Q_{2}+P_{13}Q_{3},}$

and similarly for the other voltages. Hermann von Helmholtz and Sir William Thomson showed that the coefficients of potential are symmetric, so that ${\displaystyle P_{12}=P_{21}}$, etc. Thus the system can be described by a collection of coefficients known as the elastance matrix or reciprocal capacitance matrix, which is defined as:

${\displaystyle P_{ij}={\frac {\partial V_{i}}{\partial Q_{j}}}}$

From this, the mutual capacitance ${\displaystyle C_{m}}$ between two objects can be defined[6] by solving for the total charge Q and using ${\displaystyle C_{m}=Q/V}$.

${\displaystyle C_{m}={\frac {1}{(P_{11}+P_{22})-(P_{12}+P_{21})}}}$

Since no actual device holds perfectly equal and opposite charges on each of the two "plates", it is the mutual capacitance that is reported on capacitors.

The collection of coefficients ${\displaystyle C_{ij}={\frac {\partial Q_{i}}{\partial V_{j}}}}$ is known as the capacitance matrix,[7][8] and is the inverse of the elastance matrix.

Capacitors

The capacitance of the majority of capacitors used in electronic circuits is generally several orders of magnitude smaller than the farad. The most common subunits of capacitance in use today are the microfarad (µF), nanofarad (nF), picofarad (pF), and, in microcircuits, femtofarad (fF). However, specially made supercapacitors can be much larger (as much as hundreds of farads), and parasitic capacitive elements can be less than a femtofarad. In the past, alternate subunits were used in historical electronic books; "mfd" and "mf" for microfarad (µF); "mmfd", "mmf", "µµF" for picofarad (pF); but are rarely used any more.[9][10]

Capacitance can be calculated if the geometry of the conductors and the dielectric properties of the insulator between the conductors are known. A qualitative explanation for this can be given as follows.
Once a positive charge is put unto a conductor, this charge creates an electrical field, repelling any other positive charge to be moved onto the conductor; i.e., increasing the necessary voltage. But if nearby there is another conductor with a negative charge on it, the electrical field of the positive conductor repelling the second positive charge is weakened (the second positive charge also feels the attracting force of the negative charge). So due to the second conductor with a negative charge, it becomes easier to put a positive charge on the already positive charged first conductor, and vice versa; i.e., the necessary voltage is lowered.
As a quantitative example consider the capacitance of a capacitor constructed of two parallel plates both of area A separated by a distance d. If d is sufficiently small with respect to the smallest chord of A, there holds, to a high level of accuracy:

${\displaystyle \ C=\varepsilon _{0}{\frac {A}{d}}}$

where

C is the capacitance, in farads;
A is the area of overlap of the two plates, in square meters;
ε0 is the electric constant (ε0 ≈ 8.854×10−12 F⋅m−1); and
d is the separation between the plates, in meters;

Capacitance is proportional to the area of overlap and inversely proportional to the separation between conducting sheets. The closer the sheets are to each other, the greater the capacitance. The equation is a good approximation if d is small compared to the other dimensions of the plates so that the electric field in the capacitor area is uniform, and the so-called fringing field around the periphery provides only a small contribution to the capacitance.

Combining the equation for capacitance with the above equation for the energy stored in a capacitance, for a flat-plate capacitor the energy stored is:

${\displaystyle W_{\text{stored}}={\frac {1}{2}}CV^{2}={\frac {1}{2}}\varepsilon _{0}{\frac {A}{d}}V^{2}.}$

where W is the energy, in joules; C is the capacitance, in farads; and V is the voltage, in volts.

Stray capacitance

Any two adjacent conductors can function as a capacitor, though the capacitance is small unless the conductors are close together for long distances or over a large area. This (often unwanted) capacitance is called parasitic or "stray capacitance". Stray capacitance can allow signals to leak between otherwise isolated circuits (an effect called crosstalk), and it can be a limiting factor for proper functioning of circuits at high frequency.

Stray capacitance between the input and output in amplifier circuits can be troublesome because it can form a path for feedback, which can cause instability and parasitic oscillation in the amplifier. It is often convenient for analytical purposes to replace this capacitance with a combination of one input-to-ground capacitance and one output-to-ground capacitance; the original configuration — including the input-to-output capacitance — is often referred to as a pi-configuration. Miller's theorem can be used to effect this replacement: it states that, if the gain ratio of two nodes is 1/K, then an impedance of Z connecting the two nodes can be replaced with a Z/(1 − k) impedance between the first node and ground and a KZ/(K − 1) impedance between the second node and ground. Since impedance varies inversely with capacitance, the internode capacitance, C, is replaced by a capacitance of KC from input to ground and a capacitance of (K − 1)C/K from output to ground. When the input-to-output gain is very large, the equivalent input-to-ground impedance is very small while the output-to-ground impedance is essentially equal to the original (input-to-output) impedance.

Capacitance of conductors with simple shapes

Calculating the capacitance of a system amounts to solving the Laplace equation 2φ = 0 with a constant potential φ on the 2-dimensional surface of the conductors embedded in 3-space. This is simplified by symmetries. There is no solution in terms of elementary functions in more complicated cases.

For plane situations analytic functions may be used to map different geometries to each other. See also Schwarz–Christoffel mapping.

Capacitance of simple systems
Type Capacitance Comment
Parallel-plate capacitor ${\displaystyle \varepsilon A/d}$
Coaxial cable ${\displaystyle {\frac {2\pi \varepsilon \ell }{\ln \left(R_{2}/R_{1}\right)}}}$
Pair of parallel wires[11] ${\displaystyle {\frac {\pi \varepsilon \ell }{\operatorname {arcosh} \left({\frac {d}{2a}}\right)}}={\frac {\pi \varepsilon \ell }{\ln \left({\frac {d}{2a}}+{\sqrt {{\frac {d^{2}}{4a^{2}}}-1}}\right)}}}$
Wire parallel to wall[11] ${\displaystyle {\frac {2\pi \varepsilon \ell }{\operatorname {arcosh} \left({\frac {d}{a}}\right)}}={\frac {2\pi \varepsilon \ell }{\ln \left({\frac {d}{a}}+{\sqrt {{\frac {d^{2}}{a^{2}}}-1}}\right)}}}$ a: Wire radius
d: Distance, d > a
: Wire length
Two parallel
coplanar strips[12]
${\displaystyle \varepsilon \ell {\frac {K\left({\sqrt {1-k^{2}}}\right)}{K\left(k\right)}}}$ d: Distance
w1, w2: Strip width
km: d/(2wm+d)

k2: k1k2
K: Elliptic integral
l: Length

Concentric spheres ${\displaystyle {\frac {4\pi \varepsilon }{{\frac {1}{R_{1}}}-{\frac {1}{R_{2}}}}}}$
Two spheres,
${\displaystyle 2\pi \varepsilon a\sum _{n=1}^{\infty }{\frac {\sinh \left(\ln \left(D+{\sqrt {D^{2}-1}}\right)\right)}{\sinh \left(n\ln \left(D+{\sqrt {D^{2}-1}}\right)\right)}}}$
${\displaystyle =2\pi \varepsilon a\left\{1+{\frac {1}{2D}}+{\frac {1}{4D^{2}}}+{\frac {1}{8D^{3}}}+{\frac {1}{8D^{4}}}+{\frac {3}{32D^{5}}}+O\left({\frac {1}{D^{6}}}\right)\right\}}$
${\displaystyle =2\pi \varepsilon a\left\{\ln 2+\gamma -{\frac {1}{2}}\ln \left(2D-2\right)+O\left(2D-2\right)\right\}}$
d: Distance, d > 2a
D = d/2a, D > 1
γ: Euler's constant
Sphere in front of wall[13] ${\displaystyle 4\pi \varepsilon a\sum _{n=1}^{\infty }{\frac {\sinh \left(\ln \left(D+{\sqrt {D^{2}-1}}\right)\right)}{\sinh \left(n\ln \left(D+{\sqrt {D^{2}-1}}\right)\right)}}}$ a: Radius
d: Distance, d > a
D = d/a
Sphere ${\displaystyle 4\pi \varepsilon a}$ a: Radius
Circular disc[15] ${\displaystyle 8\varepsilon a}$ a: Radius
Prolate (thin) spheroid[16] ${\displaystyle {\frac {\varepsilon a}{\ln \left(2a/b\right)}}}$ rotating about a (> b)
Thin straight wire,
finite length[17][18][19]
${\displaystyle {\frac {2\pi \varepsilon \ell }{\Lambda }}\left\{1+{\frac {1}{\Lambda }}\left(1-\ln 2\right)+{\frac {1}{\Lambda ^{2}}}\left[1+\left(1-\ln 2\right)^{2}-{\frac {\pi ^{2}}{12}}\right]+O\left({\frac {1}{\Lambda ^{3}}}\right)\right\}}$ a: Wire radius
: Length
Λ: ln(ℓ/a)

Energy storage

The energy (measured in joules) stored in a capacitor is equal to the work required to push the charges into the capacitor, i.e. to charge it. Consider a capacitor of capacitance C, holding a charge +q on one plate and −q on the other. Moving a small element of charge dq from one plate to the other against the potential difference V = q/C requires the work dW:

${\displaystyle \mathrm {d} W={\frac {q}{C}}\,\mathrm {d} q}$

where W is the work measured in joules, q is the charge measured in coulombs and C is the capacitance, measured in farads.

The energy stored in a capacitor is found by integrating this equation. Starting with an uncharged capacitance (q = 0) and moving charge from one plate to the other until the plates have charge +Q and −Q requires the work W:

${\displaystyle W_{\text{charging}}=\int _{0}^{Q}{\frac {q}{C}}\,\mathrm {d} q={\frac {1}{2}}{\frac {Q^{2}}{C}}={\frac {1}{2}}QV={\frac {1}{2}}CV^{2}=W_{\text{stored}}.}$

Nanoscale systems

The capacitance of nanoscale dielectric capacitors such as quantum dots may differ from conventional formulations of larger capacitors. In particular, the electrostatic potential difference experienced by electrons in conventional capacitors is spatially well-defined and fixed by the shape and size of metallic electrodes in addition to the statistically large number of electrons present in conventional capacitors. In nanoscale capacitors, however, the electrostatic potentials experienced by electrons are determined by the number and locations of all electrons that contribute to the electronic properties of the device. In such devices, the number of electrons may be very small, however, the resulting spatial distribution of equipotential surfaces within the device are exceedingly complex.

Single-electron devices

The capacitance of a connected, or "closed", single-electron device is twice the capacitance of an unconnected, or "open", single-electron device.[20] This fact may be traced more fundamentally to the energy stored in the single-electron device whose "direct polarization" interaction energy may be equally divided into the interaction of the electron with the polarized charge on the device itself due to the presence of the electron and the amount of potential energy required to form the polarized charge on the device (the interaction of charges in the device's dielectric material with the potential due to the electron).[21]

Few-electron devices

The derivation of a "quantum capacitance" of a few-electron device involves the thermodynamic chemical potential of an N-particle system given by

${\displaystyle \mu (N)=U(N)-U(N-1)}$

whose energy terms may be obtained as solutions of the Schrödinger equation. The definition of capacitance,

${\displaystyle {1 \over C}\equiv {\Delta \,V \over \Delta \,Q}}$,

with the potential difference

${\displaystyle \Delta \,V={\Delta \,\mu \, \over e}={\mu (N+\Delta \,N)-\mu (N) \over e}}$

may be applied to the device with the addition or removal of individual electrons,

${\displaystyle \Delta \,N=1}$ and ${\displaystyle \Delta \,Q=e}$.

Then

${\displaystyle C_{Q}(N)={e^{2} \over \mu (N+1)-\mu (N)}={e^{2} \over E(N)}}$

is the "quantum capacitance" of the device.[22]

This expression of "quantum capacitance" may be written as

${\displaystyle C_{Q}(N)={e^{2} \over U(N)}}$

which differs from the conventional expression described in the introduction where ${\displaystyle W_{\text{stored}}=U}$, the stored electrostatic potential energy,

${\displaystyle C={Q^{2} \over 2U}}$

by a factor of 1/2 with ${\displaystyle Q=Ne}$.

However, within the framework of purely classical electrostatic interactions, the appearance of the factor of 1/2 is the result of integration in the conventional formulation,

${\displaystyle W_{\text{charging}}=U=\int _{0}^{Q}{\frac {q}{C}}\,\mathrm {d} q}$

which is appropriate since ${\displaystyle \mathrm {d} q=0}$ for systems involving either many electrons or metallic electrodes, but in few-electron systems, ${\displaystyle \mathrm {d} q\to \Delta \,Q=e}$. The integral generally becomes a summation. One may trivially combine the expressions of capacitance and electrostatic interaction energy,

${\displaystyle Q=CV}$ and ${\displaystyle U=QV}$,

respectively, to obtain,

${\displaystyle C=Q{1 \over V}=Q{Q \over U}={Q^{2} \over U}}$

which is similar to the quantum capacitance. A more rigorous derivation is reported in the literature.[23] In particular, to circumvent the mathematical challenges of the spatially complex equipotential surfaces within the device, an average electrostatic potential experiences by each electron is utilized in the derivation.

The reason for apparent mathematical differences is understood more fundamentally as the potential energy, ${\displaystyle U(N)}$, of an isolated device (self-capacitance) is twice that stored in a "connected" device in the lower limit N=1. As N grows large, ${\displaystyle U(N)\to U}$.[21] Thus, the general expression of capacitance is

${\displaystyle C(N)={(Ne)^{2} \over U(N)}}$.

In nanoscale devices such as quantum dots, the "capacitor" is often an isolated, or partially isolated, component within the device. The primary differences between nanoscale capacitors and macroscopic (conventional) capacitors are the number of excess electrons (charge carriers, or electrons, that contribute to the device's electronic behavior) and the shape and size of metallic electrodes. In nanoscale devices, nanowires consisting of metal atoms typically do not exhibit the same conductive properties as their macroscopic, or bulk material, counterparts.

Capacitance in electronic and semiconductor devices

In electronic and semiconductor devices, transient or frequency-dependent current between terminals contains both conduction and displacement components. Conduction current is related to moving charge carriers (electrons, holes, ions, etc.), while displacement current is caused by time-varying electric field. Carrier transport is affected by electric field and by a number of physical phenomena - such as carrier drift and diffusion, trapping, injection, contact-related effects, impact ionization, etc. As a result, device admittance is frequency-dependent, and a simple electrostatic formula for capacitance ${\displaystyle C=q/V,}$ is not applicable. A more general definition of capacitance, encompassing electrostatic formula, is:[24]

${\displaystyle C={\frac {\operatorname {Im} (Y(\omega ))}{\omega }},}$

where ${\displaystyle Y(\omega )}$ is the device admittance, and ${\displaystyle \omega }$ is the angular frequency.

In general case, capacitance is a function of frequency. At high frequencies, capacitance approached a constant value, equal to "geometric" capacitance, determined by the terminals' geometry and dielectric content in the device. A paper by Steven Laux[24] presents a review of numerical techniques for capacitance calculation. In particular, capacitance can be calculated by a Fourier transform of a transient current in response to a step-like voltage excitation:

${\displaystyle C(\omega )=1/(\Delta V)\int _{0}^{\infty }[i(t)-i(\infty )]cos(\omega t)dt.}$

Negative capacitance in semiconductor devices

Usually, capacitance in semiconductor devices is positive. However, in some devices and under certain conditions (temperature, applied voltages, frequency, etc.), capacitance can become negative. Non-monotonic behavior of the transient current in response to a step-like excitation has been proposed as the mechanism of negative capacitance.[25] Negative capacitance has been demonstrated and explored in many different types of semiconductor devices.[26]

References

1. ^ "Definition of 'farad'". Collins.
2. ^ William D. Greason (1992). Electrostatic discharge in electronics. Research Studies Press. p. 48. ISBN 978-0-86380-136-5. Retrieved 4 December 2011.
3. ^ Lecture notes; University of New South Wales
4. ^ Tipler, Paul; Mosca, Gene (2004). Physics for Scientists and Engineers (5th ed.). Macmillan. p. 752. ISBN 978-0-7167-0810-0.
5. ^ Massarini, A.; Kazimierczuk, M.K. (1997). "Self-capacitance of inductors". IEEE Transactions on Power Electronics. 12 (4): 671–676. Bibcode:1997ITPE...12..671M. doi:10.1109/63.602562: example of the use of the term 'self-capacitance'.
6. ^ Jackson, John David (1999). Classical Electrodynamic (3rd ed.). John Wiley & Sons. p. 43. ISBN 978-0-471-30932-1.
7. ^ Maxwell, James (1873). "3". A treatise on electricity and magnetism. 1. Clarendon Press. p. 88ff.
8. ^ "Capacitance : Charge as a Function of Voltage". Av8n.com. Retrieved 20 September 2010.
9. ^ "Capacitor MF-MMFD Conversion Chart". Just Radios.
10. ^ Fundamentals of Electronics. Volume 1b — Basic Electricity — Alternating Current. Bureau of Naval Personnel. 1965. p. 197.
11. ^ a b Jackson, J. D. (1975). Classical Electrodynamics. Wiley. p. 80.
12. ^ Binns; Lawrenson (1973). Analysis and computation of electric and magnetic field problems. Pergamon Press. ISBN 978-0-08-016638-4.
13. ^ a b Maxwell, J. C. (1873). A Treatise on Electricity and Magnetism. Dover. p. 266ff. ISBN 978-0-486-60637-8.
14. ^ Rawlins, A. D. (1985). "Note on the Capacitance of Two Closely Separated Spheres". IMA Journal of Applied Mathematics. 34 (1): 119–120. doi:10.1093/imamat/34.1.119.
15. ^ Jackson, J. D. (1975). Classical Electrodynamics. Wiley. p. 128, problem 3.3.
16. ^ Berg, Howard C. (1993). Random walks in biology (Expanded ed.). Princeton, N.J.: Princeton University Press. ISBN 978-0691000640. OCLC 27810154.
17. ^ Maxwell, J. C. (1878). "On the electrical capacity of a long narrow cylinder and of a disk of sensible thickness". Proc. London Math. Soc. IX: 94–101. doi:10.1112/plms/s1-9.1.94.
18. ^ Vainshtein, L. A. (1962). "Static boundary problems for a hollow cylinder of finite length. III Approximate formulas". Zh. Tekh. Fiz. 32: 1165–1173.
19. ^ Jackson, J. D. (2000). "Charge density on thin straight wire, revisited". Am. J. Phys. 68 (9): 789–799. Bibcode:2000AmJPh..68..789J. doi:10.1119/1.1302908.
20. ^ Raphael Tsu (2011). Superlattice to Nanoelectronics. Elsevier. pp. 312–315. ISBN 978-0-08-096813-1.
21. ^ a b T. LaFave Jr. (2011). "Discrete charge dielectric model of electrostatic energy". J. Electrostatics. 69 (6): 414–418. arXiv:1203.3798. doi:10.1016/j.elstat.2011.06.006.
22. ^ G. J. Iafrate; K. Hess; J. B. Krieger; M. Macucci (1995). "Capacitive nature of atomic-sized structures". Phys. Rev. B. 52 (15): 10737–10739. Bibcode:1995PhRvB..5210737I. doi:10.1103/physrevb.52.10737.
23. ^ T. LaFave Jr; R. Tsu (March–April 2008). "Capacitance: A property of nanoscale materials based on spatial symmetry of discrete electrons" (PDF). Microelectronics Journal. 39 (3–4): 617–623. doi:10.1016/j.mejo.2007.07.105. Archived from the original (PDF) on 22 February 2014. Retrieved 12 February 2014.
24. ^ a b Laux, S.E. (Oct 1985). "Techniques for small-signal analysis of semiconductor devices". IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems. 4 (4): 472–481. doi:10.1109/TCAD.1985.1270145.
25. ^ Jonscher, A.K. (1986). "The physical origin of negative capacitance". J. Chem. Soc. Faraday Trans. II. 82: 75–81. doi:10.1039/F29868200075.
26. ^ Ershov, M.; Liu, H.C.; Li, L.; Buchanan, M.; Wasilewski, Z.R.; Jonscher, A.K. (Oct 1998). "Negative capacitance effect in semiconductor devices". IEEE Trans. Electron Devices. 45 (10): 2196–2206. arXiv:cond-mat/9806145. Bibcode:1998ITED...45.2196E. doi:10.1109/16.725254.

• Tipler, Paul (1998). Physics for Scientists and Engineers: Vol. 2: Electricity and Magnetism, Light (4th ed.). W. H. Freeman. ISBN 1-57259-492-6
• Serway, Raymond; Jewett, John (2003). Physics for Scientists and Engineers (6th ed.). Brooks Cole. ISBN 0-534-40842-7
• Saslow, Wayne M.(2002). Electricity, Magnetism, and Light. Thomson Learning. ISBN 0-12-619455-6. See Chapter 8, and especially pp. 255–259 for coefficients of potential.
Capacitance Electronic Disc

The Capacitance Electronic Disc (CED) is an analog video disc playback system developed by RCA, in which video and audio could be played back on a TV set using a special needle and high-density groove system similar to phonograph records.

First conceived in 1964, the CED system was widely seen as a technological success which was able to increase the density of a long-playing record by two orders of magnitude. Despite this achievement, the CED system fell victim to poor planning, conflicts within RCA, and technical difficulties that slowed development and stalled production of the system for 17 years—until 1981, by which time it had already been made obsolete by laser videodisc (DiscoVision, later called LaserVision and LaserDisc) as well as Betamax and VHS video cassette formats. Sales for the system were nowhere near projected estimates. In 1984—before it was absorbed by General Electric—RCA discontinued player production, continuing software production until 1986, losing an estimated \$600 million in the process. RCA had initially intended to release the SKT425 CED player with their high end Dimensia system in 1984, but cancelled CED player production just prior to the Dimensia system's release.The format was commonly known as "videodisc", leading to much confusion with the contemporaneous LaserDisc format. LaserDiscs are read optically with a laser beam, whereas CED discs are read physically with a stylus (similar to a conventional gramophone record). The two systems are mutually incompatible.

RCA used the brand "SelectaVision" for the CED system, a name also used for some early RCA brand VCRs, and other experimental projects at RCA.

Capacitance probe

Capacitance sensors (or Dielectric sensors) use capacitance to measure the dielectric permittivity of a surrounding medium.

The configuration is like the neutron probe where an access tube made of PVC is installed in the soil; probes can also be modular (comb-like) and connected to a logger. The sensing head consists of an oscillator circuit, the frequency is determined by an annular electrode, fringe-effect capacitor, and the dielectric constant of the soil.

Each capacitor sensor consists of two metal rings mounted on the circuit board at some distance from the top of the access tube. These rings are a pair of electrodes, which form the plates of the capacitor with the soil acting as the dielectric in between. The plates are connected to an oscillator, consisting of an inductor and a capacitor. The oscillating electrical field is generated between the two rings and extends into the soil medium through the wall of the access tube. The capacitor and the oscillator form a circuit, and changes in dielectric constant of surrounding media are detected by changes in the operating frequency. The capacitance sensors are designed to oscillate in excess of 100 MHz inside the access tube in free air. The output of the sensor is the frequency response of the soil’s capacitance due to its soil moisture level.

Capacitive sensing

In electrical engineering, capacitive sensing (sometimes capacitance sensing) is a technology, based on capacitive coupling, that can detect and measure anything that is conductive or has a dielectric different from air.

Many types of sensors use capacitive sensing, including sensors to detect and measure proximity, position and displacement, force, humidity, fluid level, and acceleration. Human interface devices based on capacitive sensing, such as trackpads, can replace the computer mouse. Digital audio players, mobile phones, and tablet computers use capacitive sensing touchscreens as input devices. Capacitive sensors can also replace mechanical buttons.

Capacitor

A capacitor is a passive two-terminal electronic component that stores electrical energy in an electric field. The effect of a capacitor is known as capacitance. While some capacitance exists between any two electrical conductors in proximity in a circuit, a capacitor is a component designed to add capacitance to a circuit. The capacitor was originally known as a condenser or condensator. The original name is still widely used in many languages, but not commonly in English.

The physical form and construction of practical capacitors vary widely and many capacitor types are in common use. Most capacitors contain at least two electrical conductors often in the form of metallic plates or surfaces separated by a dielectric medium. A conductor may be a foil, thin film, sintered bead of metal, or an electrolyte. The nonconducting dielectric acts to increase the capacitor's charge capacity. Materials commonly used as dielectrics include glass, ceramic, plastic film, paper, mica, and oxide layers. Capacitors are widely used as parts of electrical circuits in many common electrical devices. Unlike a resistor, an ideal capacitor does not dissipate energy.

When two conductors experience a potential difference, for example, when a capacitor is attached across a battery, an electric field develops across the dielectric, causing a net positive charge to collect on one plate and net negative charge to collect on the other plate. No current actually flows through the dielectric. However, there is a flow of charge through the source circuit. If the condition is maintained sufficiently long, the current through the source circuit ceases. If a time-varying voltage is applied across the leads of the capacitor, the source experiences an ongoing current due to the charging and discharging cycles of the capacitor.

Capacitance is defined as the ratio of the electric charge on each conductor to the potential difference between them. The unit of capacitance in the International System of Units (SI) is the farad (F), defined as one coulomb per volt (1 C/V). Capacitance values of typical capacitors for use in general electronics range from about 1 picofarad (pF) (10−12 F) to about 1 millifarad (mF) (10−3 F).

The capacitance of a capacitor is proportional to the surface area of the plates (conductors) and inversely related to the gap between them. In practice, the dielectric between the plates passes a small amount of leakage current. It has an electric field strength limit, known as the breakdown voltage. The conductors and leads introduce an undesired inductance and resistance.

Capacitors are widely used in electronic circuits for blocking direct current while allowing alternating current to pass. In analog filter networks, they smooth the output of power supplies. In resonant circuits they tune radios to particular frequencies. In electric power transmission systems, they stabilize voltage and power flow. The property of energy storage in capacitors was exploited as dynamic memory in early digital computers.

Capacitor types

Capacitors are manufactured in many forms, styles, lengths, girths, and from many materials. They all contain at least two electrical conductors (called "plates") separated by an insulating layer (called the dielectric). Capacitors are widely used as parts of electrical circuits in many common electrical devices.

Capacitors, together with resistors, and inductors, belong to the group of "passive components" used in electronic equipment. Although, in absolute figures, the most common capacitors are integrated capacitors (e.g. in DRAMs or flash memory structures), this article is concentrated on the various styles of capacitors as discrete components.

Small capacitors are used in electronic devices to couple signals between stages of amplifiers, as components of electric filters and tuned circuits, or as parts of power supply systems to smooth rectified current. Larger capacitors are used for energy storage in such applications as strobe lights, as parts of some types of electric motors, or for power factor correction in AC power distribution systems. Standard capacitors have a fixed value of capacitance, but adjustable capacitors are frequently used in tuned circuits. Different types are used depending on required capacitance, working voltage, current handling capacity, and other properties.

Ceramic capacitor

A ceramic capacitor is a fixed-value capacitor in which ceramic material acts as the dielectric. It is constructed of two or more alternating layers of ceramic and a metal layer acting as the electrodes. The composition of the ceramic material defines the electrical behavior and therefore applications. Ceramic capacitors are divided into two application classes:

Class 1 ceramic capacitors offer high stability and low losses for resonant circuit applications.

Class 2 ceramic capacitors offer high volumetric efficiency for buffer, by-pass, and coupling applications.Ceramic capacitors, especially multilayer ceramic capacitors (MLCCs), are the most produced and used capacitors in electronic equipment that incorporate approximately one trillion (1012) pieces per year.Ceramic capacitors of special shapes and styles are used as capacitors for RFI/EMI suppression, as feed-through capacitors and in larger dimensions as power capacitors for transmitters.

Compliance (physiology)

Compliance is the ability of a hollow organ (vessel) to distend and increase volume with increasing transmural pressure or the tendency of a hollow organ to resist recoil toward its original dimensions on application of a distending or compressing force. It is the reciprocal of "elastance", hence elastance is a measure of the tendency of a hollow organ to recoil toward its original dimensions upon removal of a distending or compressing force.

Electroscope

An electroscope is a scientific instrument used to detect the presence and magnitude of electric charge on a body. It was the first electrical measuring instrument. The first electroscope, a pivoted needle called the versorium, was invented by British physician William Gilbert around 1600. The pith-ball electroscope and the gold-leaf electroscope are two classical types of electroscope that are still used in physics education to demonstrate the principles of electrostatics. A type of electroscope is also used in the quartz fiber radiation dosimeter. Electroscopes were used by the Austrian scientist Victor Hess in the discovery of cosmic rays.

Electroscopes detect electric charge by the motion of a test object due to the Coulomb electrostatic force. Since the electric potential or voltage of an object with respect to ground equals its charge divided by its capacitance to ground, an electroscope can be regarded as a crude voltmeter. However, the accumulation of enough charge to detect with an electroscope requires hundreds or thousands of volts, so electroscopes are only used with high-voltage sources such as static electricity and electrostatic machines. Electroscopes generally give only a rough, qualitative indication of the magnitude of the charge. An instrument that measures charge quantitatively is called an electrometer.

The farad (symbol: F) is the SI derived unit of electrical capacitance, the ability of a body to store an electrical charge. It is named after the English physicist Michael Faraday.

Frequency domain sensor

Frequency domain (FD) sensor is an instrument developed for measuring soil moisture content. The instrument has an oscillating circuit, the sensing part of the sensor is embedded in the soil, and the operating frequency will depend on the value of soil's dielectric constant.

There are two types of sensors:

Capacitance probe, or fringe capacitance sensor. Capacitance probes use capacitance to measure the dielectric permittivity of the soil. The volume of water in the total volume of soil most heavily influences the dielectric permittivity of the soil because the dielectric constant of water (80) is much greater than the other constituents of the soil (mineral soil: 4, organic matter: 4, air: 1). Thus, when the amount of water changes in the soil, the probe will measure a change in capacitance (from the change in dielectric permittivity) that can be directly correlated with a change in water content. Circuitry inside some commercial probes change the capacitance measurement into a proportional millivolt output. Other configuration are like the neutron probe where an access tube made of PVC is installed in the soil. The probe consists of sensing head at fixed depth. The sensing head consists of an oscillator circuit, the frequency is determined by an annular electrode, fringe-effect capacitor, and the dielectric constant of the soil.

Electrical impedance sensor, which consists of soil probes and using electrical impedance measurement. The most common configuration is based on the standing wave principle (Gaskin & Miller, 1996). The device comprises a 100 MHz sinusoidal oscillator, a fixed impedance coaxial transmission line, and probe wires which is buried in the soil. The oscillator signal is propagated along the transmission line into the soil probe, and if the probe's impedance differs from that of the transmission line, a proportion of the incident signal is reflected back along the line towards the signal source.Compared to time domain reflectometer (TDR), FD sensors are cheaper to build and have a faster response time. However, because of the complex electrical field around the probe, the sensor needs to be calibrated for different soil types. Some commercial sensors have been able to remove the soil type sensitivity by using a high frequency.

Lumped element model

The lumped element model (also called lumped parameter model, or lumped component model) simplifies the description of the behaviour of spatially distributed physical systems into a topology consisting of discrete entities that approximate the behaviour of the distributed system under certain assumptions. It is useful in electrical systems (including electronics), mechanical multibody systems, heat transfer, acoustics, etc.

Mathematically speaking, the simplification reduces the state space of the system to a finite dimension, and the partial differential equations (PDEs) of the continuous (infinite-dimensional) time and space model of the physical system into ordinary differential equations (ODEs) with a finite number of parameters.

Parasitic capacitance

Parasitic capacitance, or stray capacitance is an unavoidable and usually unwanted capacitance that exists between the parts of an electronic component or circuit simply because of their proximity to each other. When two electrical conductors at different voltages are close together, the electric field between them causes electric charge to be stored on them; this effect is parasitic capacitance. All actual circuit elements such as inductors, diodes, and transistors have internal capacitance, which can cause their behavior to depart from that of 'ideal' circuit elements. Additionally, there is always non-zero capacitance between any two conductors; this can be significant at higher frequencies with closely spaced conductors, such as wires or printed circuit board traces.

The parasitic capacitance between the turns of an inductor or other wound component is often described as self-capacitance. However, the term self-capacitance more correctly refers to a different phenomenon; the capacitance of a conductive object without reference to another object.

RC circuit

A resistor–capacitor circuit (RC circuit), or RC filter or RC network, is an electric circuit composed of resistors and capacitors driven by a voltage or current source. A first order RC circuit is composed of one resistor and one capacitor and is the simplest type of RC circuit.

RC circuits can be used to filter a signal by blocking certain frequencies and passing others. The two most common RC filters are the high-pass filters and low-pass filters; band-pass filters and band-stop filters usually require RLC filters, though crude ones can be made with RC filters.

RKM code

The RKM code, also referred to as "letter and digit code for resistance and capacitance values and tolerances" or "R notation", is a notation to specify resistor and capacitor values defined in the international standard IEC 60062 (formerly IEC 62) since 1952. It is also adopted by various other standards including DIN 40825 (1973), BS 1852 (1974), IS 8186 (1976) and EN 60062 (1993). The significantly updated IEC 60062:2016 comprises the most recent release of the standard.

Supercapacitor

A supercapacitor (SC) (also called a supercap, ultracapacitor or Goldcap) is a high-capacity capacitor with capacitance values much higher than other capacitors (but lower voltage limits) that bridge the gap between electrolytic capacitors and rechargeable batteries. They typically store 10 to 100 times more energy per unit volume or mass than electrolytic capacitors, can accept and deliver charge much faster than batteries, and tolerate many more charge and discharge cycles than rechargeable batteries.

Supercapacitors are used in applications requiring many rapid charge/discharge cycles rather than long term compact energy storage: within cars, buses, trains, cranes and elevators, where they are used for regenerative braking, short-term energy storage or burst-mode power delivery. Smaller units are used as memory backup for static random-access memory (SRAM).

Unlike ordinary capacitors, supercapacitors do not use the conventional solid dielectric, but rather, they use electrostatic double-layer capacitance and electrochemical pseudocapacitance, both of which contribute to the total capacitance of the capacitor, with a few differences:

Electrostatic double-layer capacitors (EDLCs) use carbon electrodes or derivatives with much higher electrostatic double-layer capacitance than electrochemical pseudocapacitance, achieving separation of charge in a Helmholtz double layer at the interface between the surface of a conductive electrode and an electrolyte. The separation of charge is of the order of a few ångströms (0.3–0.8 nm), much smaller than in a conventional capacitor.

Electrochemical pseudocapacitors use metal oxide or conducting polymer electrodes with a high amount of electrochemical pseudocapacitance additional to the double-layer capacitance. Pseudocapacitance is achieved by Faradaic electron charge-transfer with redox reactions, intercalation or electrosorption.

Hybrid capacitors, such as the lithium-ion capacitor, use electrodes with differing characteristics: one exhibiting mostly electrostatic capacitance and the other mostly electrochemical capacitance.The electrolyte forms an ionic conductive connection between the two electrodes which distinguishes them from conventional electrolytic capacitors where a dielectric layer always exists, and the so-called electrolyte (e.g., MnO2 or conducting polymer) is in fact part of the second electrode (the cathode, or more correctly the positive electrode). Supercapacitors are polarized by design with asymmetric electrodes, or, for symmetric electrodes, by a potential applied during manufacture.

Touch switch

A touch switch is a type of switch that only has to be touched by an object to operate. It is used in many lamps and wall switches that have a metal exterior as well as on public computer terminals. A touchscreen includes an array of touch switches on a display.

A touch switch is the simplest kind of tactile sensor.

Touchscreen

A touchscreen, or touch screen, is an input device and normally layered on the top of an electronic visual display of an information processing system. A user can give input or control the information processing system through simple or multi-touch gestures by touching the screen with a special stylus or one or more fingers. Some touchscreens use ordinary or specially coated gloves to work while others may only work using a special stylus or pen. The user can use the touchscreen to react to what is displayed and, if the software allows, to control how it is displayed; for example, zooming to increase the text size.

The touchscreen enables the user to interact directly with what is displayed, rather than using a mouse, touchpad, or other such devices (other than a stylus, which is optional for most modern touchscreens).

Touchscreens are common in devices such as Nintendo game consoles, personal computers, electronic voting machines, and point-of-sale (POS) systems. They can also be attached to computers or, as terminals, to networks. They play a prominent role in the design of digital appliances such as personal digital assistants (PDAs) and some e-readers.

The popularity of smartphones, tablets, and many types of information appliances is driving the demand and acceptance of common touchscreens for portable and functional electronics. Touchscreens are found in the medical field, heavy industry, automated teller machines (ATMs), and kiosks such as museum displays or room automation, where keyboard and mouse systems do not allow a suitably intuitive, rapid, or accurate interaction by the user with the display's content.

Historically, the touchscreen sensor and its accompanying controller-based firmware have been made available by a wide array of after-market system integrators, and not by display, chip, or motherboard manufacturers. Display manufacturers and chip manufacturers have acknowledged the trend toward acceptance of touchscreens as a user interface component and have begun to integrate touchscreens into the fundamental design of their products.

Variable capacitor

A variable capacitor is a capacitor whose capacitance may be intentionally and repeatedly changed mechanically or electronically. Variable capacitors are often used in L/C circuits to set the resonance frequency, e.g. to tune a radio (therefore it is sometimes called a tuning capacitor or tuning condenser), or as a variable reactance, e.g. for impedance matching in antenna tuners.

Varicap

In electronics, a varicap diode, varactor diode, variable capacitance diode, variable reactance diode or tuning diode is a type of diode designed to exploit the voltage-dependent capacitance of a reverse-biased p–n junction.

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