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36:
1076:
There are often other contributions to power loss for electromagnetic waves that are not included in this expression, such as due to the wall currents of the conductors of a transmission line or waveguide. Also, a similar analysis could be applied to the magnetic permeability where
1516:
469:
986:
1292:(ESR), as shown in the figure below. The ESR represents losses in the capacitor. In a low-loss capacitor the ESR is very small (the conduction is high leading to a low resistivity), and in a lossy capacitor the ESR can be large. Note that the ESR is
642:
218:. Dielectrics are often used in all of these environments to mechanically support electrical conductors and keep them at a fixed separation, or to provide a barrier between different gas pressures yet still transmit electromagnetic power.
1382:
A real capacitor has a lumped element model of a lossless ideal capacitor in series with an equivalent series resistance (ESR). The loss tangent is defined by the angle between the capacitor's impedance vector and the negative reactive
1263:
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1300:. The ESR is a derived quantity representing the loss due to both the dielectric's conduction electrons and the bound dipole relaxation phenomena mentioned above. In a dielectric, one of the conduction electrons or the
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components of the propagating waves that satisfy the boundary conditions of the specific environment's geometry. In such electromagnetic analyses, the parameters
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typically dominates loss in a particular dielectric and manufacturing method. For the case of the conduction electrons being the dominant loss, then
1403:
of the angle between the capacitor's impedance vector and the negative reactive axis, as shown in the adjacent diagram. The loss tangent is then
1310:
1209:
812:
For dielectrics with small loss, square root can be approximated using only zeroth and first order terms of binomial expansion. Also,
505:
1698:
1667:
119:
1511:{\displaystyle \tan \delta ={\frac {\mathrm {ESR} }{|X_{c}|}}=\omega C\cdot \mathrm {ESR} ={\frac {\sigma }{\varepsilon '\omega }}}
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charge and dipole relaxation phenomena, which gives rise to energy loss that is indistinguishable from the loss due to the
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464:{\displaystyle \nabla \times \mathbf {H} =j\omega \varepsilon '\mathbf {E} +(\omega \varepsilon ''+\sigma )\mathbf {E} }
981:{\displaystyle E=E_{o}e^{-jk\left(1-j{\frac {\tan \delta }{2}}\right)z}=E_{o}e^{-k{\frac {\tan \delta }{2}}z}e^{-jkz},}
79:
46:
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Since power is electric field intensity squared, it turns out that the power decays with propagation distance
219:
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power oscillating in the capacitor. For this reason, a capacitor's loss tangent is sometimes stated as its
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is a discrete electrical circuit component typically made of a dielectric placed between conductors. One
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is then defined as the ratio (or angle in a complex plane) of the lossy reaction to the electric field
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637:{\displaystyle \tan \delta ={\frac {\omega \varepsilon ''+\sigma }{\omega \varepsilon '}}.}
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of a capacitor includes a lossless ideal capacitor in series with a resistor termed the
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790:{\displaystyle k=\omega {\sqrt {\mu \varepsilon '}}={\tfrac {2\pi }{\lambda }},}
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1361:{\displaystyle \mathrm {ESR} ={\frac {\sigma }{\varepsilon '\omega ^{2}C}}}
494:
represents the familiar lossless permittivity given by the product of the
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1258:{\displaystyle \tan \delta _{e}={\frac {\varepsilon ''}{\varepsilon '}},}
1296:
simply the resistance that would be measured across a capacitor by an
171:
1387:
When representing the electrical circuit parameters as vectors in a
27:
Amount of electromagnetic energy dissipated by a dielectric material
1690:
Microwave
Electronics: Measurement and Materials Characterization
647:
Solution for the electric field of the electromagnetic wave is
549:{\displaystyle \varepsilon '=\varepsilon _{0}\varepsilon '_{r}.}
1268:
upon introduction of an effective dielectric conductivity (see
255:
through which the waves propagate. The permittivity can have
29:
152:(e.g. heat). It can be parameterized in terms of either the
373:{\displaystyle \mathbf {E} =\mathbf {E} _{o}e^{j\omega t},}
311:{\displaystyle \varepsilon =\varepsilon '-j\varepsilon ''.}
1607:{\displaystyle \tan \delta =\mathrm {DF} ={\frac {1}{Q}}.}
198:, the electromagnetic energy is typically viewed as waves
1189:{\displaystyle \tan \delta _{m}={\frac {\mu ''}{\mu '}}.}
720:{\displaystyle E=E_{o}e^{-jk{\sqrt {1-j\tan \delta }}z},}
478:
is the imaginary component of permittivity attributed to
768:
182:(lossy) component of an electromagnetic field and its
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If we assume that we have a wave function such that
387:equation for the magnetic field can be written as:
60:. Unsourced material may be challenged and removed.
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1715:"Considerations for a High Performance Capacitor"
1658:Ramo, S.; Whinnery, J.R.; Van Duzer, T. (1994).
1662:(3rd ed.). New York: John Wiley and Sons.
573:in the curl equation to the lossless reaction:
1660:Fields and Waves in Communication Electronics
808:is the wavelength in the dielectric material.
8:
1537:, the loss tangent is also the ratio of the
1052:{\displaystyle P=P_{o}e^{-kz\tan \delta },}
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802:is the angular frequency of the wave, and
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120:Learn how and when to remove this message
1687:; Varadan, Vijay K. (19 November 2004).
1377:
486:charge conduction that is quantified by
1623:
178:whose real and imaginary parts are the
1683:Chen, L. F.; Ong, C. K.; Neo, C. P.;
7:
1131:with the subsequent definition of a
58:adding citations to reliable sources
1121:{\displaystyle \mu =\mu '-j\mu '',}
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1270:relative permittivity#Lossy medium
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263:components (the latter excluding
190:Electromagnetic field perspective
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251:represent the properties of the
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502:real/absolute permittivity, or
45:needs additional citations for
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267:effects, see below) such that
1:
1541:power loss in the ESR to the
1375:is the lossless capacitance.
1290:equivalent series resistance
1276:Discrete circuit perspective
1551:, or the reciprocal of its
1526:current flows through both
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1203:can be similarly defined:
186:(lossless) counterpart.
1757:Electrical engineering
1738:, frequency dependence
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150:electromagnetic energy
134:electrical engineering
1632:"Maxwell's Equations"
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1201:electric loss tangent
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1133:magnetic loss tangent
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498:permittivity and the
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170:. Both refer to the
159:or the corresponding
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1286:lumped element model
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1072:is the initial power
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54:improve this article
1736:Loss in dielectrics
1639:www.ece.rutgers.edu
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222:are solved for the
220:Maxwell’s equations
214:line, or through a
142:dielectric material
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490:. The component
208:transmission line
194:For time-varying
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69:"Dielectric loss"
16:(Redirected from
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1752:Electromagnetism
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1717:. Archived from
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1730:External links
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1721:on 2008-11-19.
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1693:. eq. (1.13).
1685:Varadan, V. V.
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1669:0-471-58551-3
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65:Find sources:
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43:This article
41:
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32:
31:
19:
1719:the original
1709:
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1678:
1659:
1653:
1642:. Retrieved
1638:
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1397:loss tangent
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565:loss tangent
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559:Loss tangent
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246:conductivity
239:permeability
232:permittivity
193:
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161:loss tangent
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144:'s inherent
137:
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110:October 2014
107:
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52:Please help
47:verification
44:
18:Loss tangent
200:propagating
146:dissipation
1746:Categories
1644:2023-11-06
1618:References
823:for small
496:free space
212:microstrip
204:free space
154:loss angle
80:newspapers
1575:δ
1572:
1539:resistive
1503:ω
1496:ε
1491:σ
1472:⋅
1466:ω
1420:δ
1417:
1344:ω
1336:ε
1331:σ
1282:capacitor
1244:ε
1236:ε
1221:δ
1217:
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285:ε
278:ε
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216:waveguide
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