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1205:
139:
is the property of a substance to permit the passage of light, with some or none of the incident light being absorbed in the process. If some light is absorbed by the substance, then the transmitted light will be a combination of the wavelengths of the light that was transmitted and not absorbed. For
1557:{\displaystyle T={\frac {\displaystyle \exp \left(-2\int _{x_{1}}^{x_{2}}dx{\sqrt {{\frac {2m}{\hbar ^{2}}}\left(V(x)-E\right)}}\,\right)}{\displaystyle \left(1+{\frac {1}{4}}\exp \left(-2\int _{x_{1}}^{x_{2}}dx{\sqrt {{\frac {2m}{\hbar ^{2}}}\left(V(x)-E\right)}}\,\right)\right)^{2}}}\ ,}
1791:
458:
722:
are used to describe the behavior of waves incident on a barrier. The transmission coefficient represents the probability flux of the transmitted wave relative to that of the incident wave. This coefficient is often used to describe the probability of a particle
864:
1009:
694:, will meet specified performance criteria is also sometimes called the "transmission coefficient" of that portion of the system. The value of the transmission coefficient is inversely related to the quality of the line, circuit, channel or trunk.
578:
672:
140:
example, a blue light filter appears blue because it absorbs red and green wavelengths. If white light is shone through the filter, the light transmitted also appears blue because of the absorption of the red and green wavelengths.
159:
of the wave. Either is calculated by taking the ratio of the value after the surface or element to the value before. The transmission coefficient for total power is generally the same as the coefficient for intensity.
1647:
271:
will be reflected back to the source. Because the voltage on a transmission line is always the sum of the forward and reflected waves at that point, if the incident wave amplitude is 1, and the reflected wave is
353:
745:
992:
913:
1200:{\displaystyle R={\frac {{\vec {J}}_{\mathrm {refl} }\cdot \left(-{\hat {n}}\right)}{{\vec {J}}_{\mathrm {inc} }\cdot {\hat {n}}}}={\frac {|J_{\mathrm {refl} }|}{|J_{\mathrm {inc} }|}}}
1632:
496:
249:
220:
1840:
1606:
347:
is uniquely determined from first principles by noting that the incident power on the discontinuity must equal the sum of the power in the reflected and transmitted waves:
1608:
are the two classical turning points for the potential barrier. In the classical limit of all other physical parameters much larger than Planck's constant, abbreviated as
322:
942:
482:
345:
290:
269:
1242:
594:
30:
An electromagnetic (or any other) wave experiences partial transmittance and partial reflectance when the medium through which it travels suddenly changes.
1856:
173:
1244:, which in one dimension reduces to the fact that the sum of the transmitted and reflected currents is equal in magnitude to the incident current.
20:
54:
is considered. A transmission coefficient describes the amplitude, intensity, or total power of a transmitted wave relative to an incident wave.
1786:{\displaystyle T\approx 16{\frac {E}{U_{0}}}\left(1-{\frac {E}{U_{0}}}\right)\exp \left(-2L{\sqrt {{\frac {2m}{\hbar ^{2}}}(U_{0}-E)}}\right)}
27:
1964:
1927:
1879:
1249:
453:{\displaystyle {1 \over Z_{\mathrm {A} }}={{\Gamma ^{2} \over Z_{\mathrm {A} }}+{(1+\Gamma )^{2} \over Z_{\mathrm {B} }}}}
62:
Different fields of application have different definitions for the term. All the meanings are very similar in concept: In
93:
Although conceptually the same, the details in each field differ, and in some cases the terms are not an exact analogy.
859:{\displaystyle T={\frac {{\vec {J}}_{\mathrm {trans} }\cdot {\hat {n}}}{{\vec {J}}_{\mathrm {inc} }\cdot {\hat {n}}}},}
1954:
51:
186:
is the ratio of the amplitude of the complex transmitted wave to that of the incident wave at a discontinuity in the
1949:
947:
109:, there appears a certain "transmission coefficient" for overcoming a potential barrier. It is (often) taken to be
874:
683:
1959:
687:
151:) passes through a surface or an optical element. Transmission coefficients can be calculated for either the
106:
1634:, the transmission coefficient goes to zero. This classical limit would have failed in the situation of a
1903:
1851:
718:
486:
169:
43:
1611:
573:{\displaystyle {\Gamma ={{Z_{\mathrm {B} }-Z_{\mathrm {A} }} \over {Z_{\mathrm {B} }+Z_{\mathrm {A} }}}}}
78:
it is the amplitude of a wave transmitted through a medium or conductor to that of the incident wave; in
1882:. Institute for Telecommunication Sciences, National Telecommunications and Information Administration.
1641:
If the transmission coefficient is much less than 1, it can be approximated with the following formula:
679:
225:
196:
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79:
667:{\displaystyle {{1+\Gamma }={{2Z_{\mathrm {B} }} \over {Z_{\mathrm {B} }+Z_{\mathrm {A} }}}}}
467:
330:
275:
254:
1635:
47:
19:
This article is about the concept in physics and chemistry. For the concept in biology, see
1215:
114:
915:
is the probability current in the wave incident upon the barrier with normal unit vector
82:
it is used to describe the behavior of waves incident on a barrier, in a way similar to
994:
is the probability current in the wave moving away from the barrier on the other side.
193:
Consider a wave travelling through a transmission line with a step in impedance from
26:
1943:
1267:
Using the WKB approximation, one can obtain a tunnelling coefficient that looks like
126:
1887:
730:
The transmission coefficient is defined in terms of the incident and transmitted
251:. When the wave transitions through the impedance step, a portion of the wave
110:
152:
102:
63:
292:, then the amplitude of the forward wave must be sum of the two waves or
691:
39:
132:
83:
71:
148:
25:
70:
refers to a chemical reaction overcoming a potential barrier; in
1886:. United States Department of Commerce. 1996. Archived from
143:
The transmission coefficient is a measure of how much of an
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113:for monomolecular reactions. It appears in the
987:{\displaystyle {\vec {J}}_{\mathrm {trans} }}
8:
1920:Introduction to Quantum Mechanics (2nd ed.)
1913:
1911:
908:{\displaystyle {\vec {J}}_{\mathrm {inc} }}
1857:Reflections of signals on conducting lines
174:Reflections of signals on conducting lines
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1842:is the length of the barrier potential.
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1212:Law of total probability requires that
21:Transmission coefficient (epidemiology)
7:
678:The probability that a portion of a
1627:{\displaystyle \hbar \rightarrow 0}
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16:A concept in physics and chemistry
14:
244:{\displaystyle Z_{\mathrm {B} }}
215:{\displaystyle Z_{\mathrm {A} }}
1900:See also the wikipedia article
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1:
1835:{\displaystyle L=x_{2}-x_{1}}
1601:{\displaystyle x_{1},\,x_{2}}
1250:rectangular potential barrier
1247:For sample calculations, see
1918:Griffiths, David J. (2004).
997:The reflection coefficient
732:probability current density
317:{\displaystyle (1+\Gamma )}
1981:
1965:Fiber-optic communications
1260:
937:{\displaystyle {\hat {n}}}
701:
464:Solving the quadratic for
167:
124:
18:
1880:"Federal Standard 1037C"
1001:is defined analogously:
714:transmission coefficient
586:transmission coefficient
184:transmission coefficient
68:transmission coefficient
36:transmission coefficient
477:{\displaystyle \Gamma }
340:{\displaystyle \Gamma }
285:{\displaystyle \Gamma }
264:{\displaystyle \Gamma }
107:transition state theory
50:in a medium containing
1904:Federal Standard 1037C
1852:Reflection coefficient
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44:electrical engineering
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1237:{\displaystyle T+R=1}
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708:In non-relativistic
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145:electromagnetic wave
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727:through a barrier.
105:, in particular in
1955:Geometrical optics
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704:Quantum tunnelling
682:, such as a line,
664:
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484:leads both to the
474:
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212:
164:Telecommunications
88:telecommunications
76:telecommunications
32:
1950:Quantum mechanics
1922:. Prentice Hall.
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1257:WKB approximation
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698:Quantum mechanics
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188:transmission line
180:telecommunication
80:quantum mechanics
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48:wave propagation
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1960:Physical optics
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115:Eyring equation
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52:discontinuities
24:
17:
12:
11:
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1261:Main article:
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336:
327:The value for
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165:
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125:Main article:
122:
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59:
56:
15:
13:
10:
9:
6:
4:
3:
2:
1977:
1966:
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1931:
1929:0-13-111892-7
1925:
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1908:
1905:
1901:
1890:on 2009-03-02
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