396:
1766:
1181:
the phase length of the attached transmission line. That is to take into account not only the phase delay of the reflected wave, but the phase shift that had first been applied to the forward wave, with the reflection coefficient being the quotient of these. The reflection coefficient so measured,
368:
pairs of quantities whose product defines power resolvable into a forward and reverse wave. For instance, with electromagnetic plane waves, one uses the ratio of the electric fields of the reflected to that of the forward wave (or magnetic fields, again with a minus sign); the ratio of each wave's
141:
of a transmission line that's involved, but one can speak of reflection coefficient without any actual transmission line being present. In terms of the forward and reflected waves determined by the voltage and current, the reflection coefficient is defined as the
1770:
129:
of the reflected wave to that of the incident wave. The voltage and current at any point along a transmission line can always be resolved into forward and reflected traveling waves given a specified reference impedance
90:
A wave is partially transmitted and partially reflected when the medium through which it travels suddenly changes. The reflection coefficient determines the ratio of the reflected wave amplitude to the incident wave
359:
847:
at the load. This implies the reflected wave having a 180° phase shift (phase reversal) with the voltages of the two waves being opposite at that point and adding to zero (as a short circuit demands).
995:
1508:
1172:
1520:, the SWR signifies the ratio of the voltage (or current) maxima to minima (or what it would be if the transmission line were long enough to produce them). The above calculation assumes that
272:
1093:
1271:
723:
1205:
1118:
680:
1351:
617:
573:
845:
783:
643:
1627:
1569:
1538:
1315:
1295:
912:
816:
533:
218:
1374:
1607:
1401:
1232:
1029:
884:
753:
513:
486:
455:
428:
198:
171:
1049:
1582:. That SWR remains the same wherever measured along a transmission line (looking towards the load) since the addition of a transmission line length to a load
1629:. While having a one-to-one correspondence with reflection coefficient, SWR is the most commonly used figure of merit in describing the mismatch affecting a
1004:
of the reflection coefficient in a lossless transmission line is constant along the line (as are the powers in the forward and reflected waves). However its
1726:
104:
70:
53:
is a parameter that describes how much of a wave is reflected by an impedance discontinuity in the transmission medium. It is equal to the ratio of the
785:
will remain the same (the powers of the forward and reflected waves stay the same) but with a different phase. In the case of a short circuited load (
65:
to calculate the amount of light that is reflected from a surface with a different index of refraction, such as a glass surface, or in an electrical
87:
1637:
at the transmitter side of a transmission line, but having, as explained, the same value as would be measured at the antenna (load) itself.
287:
281:
associated with the reflected and forward waves, but introducing a minus sign to account for the opposite orientations of the two currents:
1873:
1808:
682:
denotes the proportion of that power that is reflected back to the source, with the power actually delivered toward the load being
1868:
1858:
1781:
1775:
1403:) can directly be read. Before the advent of modern electronic computers, the Smith chart was of particular use as a sort of
920:
1878:
1435:
1707:
Acousticians use reflection coefficients to understand the effect of different materials on their acoustic environments.
1000:
This is the coefficient at the load. The reflection coefficient can also be measured at other points on the line. The
1853:
1126:
230:
855:
The reflection coefficient is determined by the load impedance at the end of the transmission line, as well as the
1746:
1863:
1832:
Application for drawing standing wave diagrams including the reflection coefficient, input impedance, SWR, etc.
1736:
856:
138:
75:
1317:
is given directly by the distance of a point to the center (with the edge of the Smith chart corresponding to
1834:
1751:
385:
1058:
458:
46:
1731:
1646:
1376:
around the chart's center. Using the scales on a Smith chart, the resulting impedance (normalized to
1240:
685:
1422:
1416:
648:
395:
30:
This article is about reflections of waves. For the use of the term with capillary membrames, see
1828:
A flash program that shows how a reflected wave is generated, the reflection coefficient and VSWR
1579:
1320:
645:
implying no reflected power. More generally, the squared-magnitude of the reflection coefficient
582:
576:
538:
365:
114:
73:
is reflected by an impedance discontinuity. The reflection coefficient is closely related to the
821:
758:
622:
1804:
1686:
1660:
1185:
1098:
1052:
1009:
126:
118:
108:
66:
31:
1612:
1554:
1523:
1300:
1280:
889:
788:
518:
203:
1825:
1356:
1585:
1379:
1210:
1014:
862:
731:
491:
464:
433:
406:
176:
149:
1838:
1741:
1034:
728:
Anywhere along an intervening (lossless) transmission line of characteristic impedance
143:
86:
17:
1847:
1721:
1702:
1630:
399:
Simple circuit configuration showing measurement location of reflection coefficient.
1785:
1353:). Its evolution along a transmission line is likewise described by a rotation of
1791:
1674:
1673:
can refer to either the amplitude reflection coefficient described here, or the
1274:
80:
35:
1677:, depending on context. Typically, the reflectance is represented by a capital
1716:
1681:, while the amplitude reflection coefficient is represented by a lower-case
1651:
Reflection coefficient is used in feeder testing for reliability of medium.
1634:
389:
54:
1571:, the SWR intentionally ignores the specific value of the load impedance
1404:
364:
The reflection coefficient may also be established using other field or
1273:, corresponding to passive loads) may be displayed graphically using a
42:
354:{\displaystyle \Gamma =-{\frac {I^{-}}{I^{+}}}={\frac {V^{-}}{V^{+}}}}
1690:
1666:
430:
possibly followed by a transmission line of characteristic impedance
62:
58:
403:
In the accompanying figure, a signal source with internal impedance
57:
of the reflected wave to the incident wave, with each expressed as
394:
221:
122:
85:
1831:
1177:
Note that the phase of the reflection coefficient is changed by
95:
Different specialties have different applications for the term.
1513:
Along a lossless transmission line of characteristic impedance
1207:, corresponds to an impedance which is generally dissimilar to
83:
of a system is also sometimes called a reflection coefficient.
1578:
responsible for it, but only the magnitude of the resulting
1803:. Upper Saddle River, New Jersey: Pearson Education, Inc.
1031:
from the load. If the coefficient is measured at a point
392:
one uses the acoustic pressure and velocity respectively.
990:{\displaystyle \Gamma ={Z_{L}-Z_{0} \over Z_{L}+Z_{0}}.}
886:
terminating a line with a characteristic impedance of
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1588:
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1438:
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1323:
1303:
1283:
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1213:
1188:
1129:
1101:
1061:
1037:
1017:
923:
892:
865:
824:
791:
761:
734:
688:
651:
625:
585:
541:
521:
494:
467:
436:
409:
290:
233:
206:
179:
152:
1503:{\displaystyle SWR={1+|\Gamma | \over 1-|\Gamma |}.}
1547:as the reference impedance. Since it uses only the
1621:
1601:
1563:
1532:
1502:
1395:
1368:
1345:
1309:
1289:
1265:
1237:The complex reflection coefficient (in the region
1234:present at the far side of the transmission line.
1226:
1199:
1166:
1112:
1087:
1043:
1023:
989:
906:
878:
839:
810:
777:
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717:
674:
637:
611:
567:
527:
507:
480:
449:
422:
353:
266:
212:
192:
165:
137:. The reference impedance used is typically the
32:Starling equation § Reflection coefficient
1167:{\displaystyle \Gamma '=\Gamma e^{-i\,2\phi }}
1008:will be shifted by an amount dependent on the
755:, the magnitude of the reflection coefficient
267:{\displaystyle \Gamma ={\frac {V^{-}}{V^{+}}}}
8:
146:ratio of the voltage of the reflected wave (
1826:Flash tutorial for understanding reflection
1727:Reflections of signals on conducting lines
488:. For a real (resistive) source impedance
121:theory, the reflection coefficient is the
105:Reflections of signals on conducting lines
1614:
1609:only changes the phase, not magnitude of
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584:
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246:
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232:
205:
184:
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157:
151:
1685:. These related concepts are covered by
200:). This is typically represented with a
914:will have a reflection coefficient of
1277:. The Smith chart is a polar plot of
1088:{\displaystyle \phi =2\pi L/\lambda }
7:
1633:or antenna system. It is most often
277:It can as well be defined using the
1616:
1558:
1527:
1486:
1465:
1425:(SWR) is determined solely by the
1329:
1304:
1284:
1249:
1190:
1141:
1131:
1103:
924:
825:
767:
700:
657:
626:
522:
291:
234:
207:
25:
1669:and electromagnetics in general,
859:of the line. A load impedance of
1769: This article incorporates
1764:
173:) to that of the incident wave (
1815:Figure 8-2 and Eqn. 8-1 Pg. 279
1782:General Services Administration
1703:Acoustic wave § Reflection
1429:of the reflection coefficient:
1266:{\displaystyle |\Gamma |\leq 1}
718:{\displaystyle 1-|\Gamma |^{2}}
1490:
1482:
1469:
1461:
1333:
1325:
1253:
1245:
771:
763:
705:
696:
662:
653:
535:using the reference impedance
61:. For example, it is used in
1:
1801:Signal Integrity - Simplified
1297:, therefore the magnitude of
1051:meters from the load, so the
675:{\displaystyle |\Gamma |^{2}}
69:to calculate how much of the
34:. For intensity ratios, see
27:Measure of wave reflectivity
1346:{\displaystyle |\Gamma |=1}
612:{\displaystyle Z_{L}=Z_{0}}
568:{\displaystyle Z_{0}=Z_{S}}
388:in a vacuum). Similarly in
1895:
1700:
1658:
1644:
1540:has been calculated using
1414:
851:Relation to load impedance
840:{\displaystyle \Gamma =-1}
577:maximum power is delivered
102:
29:
1095:radians, the coefficient
778:{\displaystyle |\Gamma |}
638:{\displaystyle \Gamma =0}
224:) and can be written as:
1874:Telecommunication theory
1737:Transmission coefficient
1200:{\displaystyle \Gamma '}
1113:{\displaystyle \Gamma '}
857:characteristic impedance
139:characteristic impedance
76:transmission coefficient
1752:Reflection phase change
1622:{\displaystyle \Gamma }
1564:{\displaystyle \Gamma }
1533:{\displaystyle \Gamma }
1310:{\displaystyle \Gamma }
1290:{\displaystyle \Gamma }
1120:at that point will be
907:{\displaystyle Z_{0}\,}
811:{\displaystyle Z_{L}=0}
528:{\displaystyle \Gamma }
386:impedance of free space
213:{\displaystyle \Gamma }
1869:Seismology measurement
1859:Electronic engineering
1799:Bogatin, Eric (2004).
1777:Federal Standard 1037C
1771:public domain material
1671:reflection coefficient
1623:
1603:
1565:
1534:
1504:
1397:
1370:
1369:{\displaystyle 2\phi }
1347:
1311:
1291:
1267:
1228:
1201:
1168:
1114:
1089:
1045:
1025:
991:
908:
880:
841:
812:
779:
749:
719:
676:
639:
613:
569:
529:
509:
482:
457:is represented by its
451:
424:
400:
377:is again an impedance
373:to its magnetic field
355:
268:
214:
194:
167:
92:
51:reflection coefficient
47:electrical engineering
18:Reflection Coefficient
1879:Dimensionless numbers
1790: (in support of
1747:Hagen–Rubens relation
1732:Scattering parameters
1655:Optics and microwaves
1647:Reflection seismology
1624:
1604:
1602:{\displaystyle Z_{L}}
1566:
1535:
1505:
1398:
1396:{\displaystyle Z_{0}}
1371:
1348:
1312:
1292:
1268:
1229:
1227:{\displaystyle Z_{L}}
1202:
1169:
1115:
1090:
1046:
1026:
1024:{\displaystyle \phi }
992:
909:
881:
879:{\displaystyle Z_{L}}
842:
813:
780:
750:
748:{\displaystyle Z_{0}}
720:
677:
640:
614:
570:
530:
510:
508:{\displaystyle Z_{S}}
483:
481:{\displaystyle Z_{L}}
452:
450:{\displaystyle Z_{S}}
425:
423:{\displaystyle Z_{S}}
398:
356:
269:
215:
195:
193:{\displaystyle V^{+}}
168:
166:{\displaystyle V^{-}}
89:
1613:
1586:
1555:
1524:
1436:
1417:Standing wave ratio
1411:Standing wave ratio
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1357:
1321:
1301:
1281:
1241:
1211:
1186:
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1099:
1059:
1035:
1015:
921:
890:
863:
822:
789:
759:
732:
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623:
583:
539:
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492:
465:
434:
407:
288:
231:
204:
177:
150:
71:electromagnetic wave
1423:standing wave ratio
1053:electrical distance
1010:electrical distance
461:, driving the load
459:Thévenin equivalent
1854:Geometrical optics
1837:2020-11-25 at the
1619:
1599:
1580:impedance mismatch
1561:
1530:
1500:
1407:for this purpose.
1393:
1366:
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1307:
1287:
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1224:
1197:
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1110:
1085:
1041:
1021:
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876:
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808:
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715:
672:
635:
609:
575:then the source's
565:
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351:
264:
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190:
163:
115:telecommunications
99:Transmission lines
93:
1687:Fresnel equations
1661:Fresnel equations
1495:
1055:from the load is
1044:{\displaystyle L}
982:
349:
322:
262:
127:complex amplitude
119:transmission line
109:Signal reflection
67:transmission line
16:(Redirected from
1886:
1814:
1795:
1789:
1784:. Archived from
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1767:
1691:classical optics
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1820:External links
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1788:on 2022-01-22.
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1872:
1870:
1867:
1865:
1862:
1860:
1857:
1855:
1852:
1851:
1849:
1840:
1836:
1833:
1830:
1827:
1824:
1823:
1819:
1812:
1810:0-13-066946-6
1806:
1802:
1797:
1793:
1787:
1783:
1779:
1778:
1772:
1762:
1761:
1757:
1753:
1750:
1748:
1745:
1743:
1740:
1738:
1735:
1733:
1730:
1728:
1725:
1723:
1722:Mismatch loss
1720:
1718:
1715:
1714:
1710:
1708:
1704:
1696:
1694:
1692:
1688:
1684:
1680:
1676:
1672:
1668:
1662:
1654:
1652:
1648:
1640:
1638:
1636:
1632:
1631:radio antenna
1594:
1590:
1581:
1577:
1550:
1543:
1516:
1497:
1478:
1475:
1457:
1454:
1448:
1445:
1442:
1439:
1432:
1431:
1430:
1428:
1424:
1418:
1410:
1408:
1406:
1388:
1384:
1363:
1360:
1340:
1337:
1276:
1260:
1257:
1235:
1219:
1215:
1193:
1180:
1159:
1156:
1152:
1149:
1145:
1138:
1134:
1123:
1122:
1121:
1106:
1082:
1078:
1074:
1071:
1068:
1065:
1062:
1054:
1038:
1018:
1011:
1007:
1003:
984:
976:
972:
968:
963:
959:
951:
947:
943:
938:
934:
927:
917:
916:
915:
898:
894:
871:
867:
858:
850:
848:
834:
831:
828:
818:), one finds
805:
802:
797:
793:
740:
736:
726:
710:
692:
689:
667:
632:
629:
604:
600:
596:
591:
587:
578:
560:
556:
552:
547:
543:
500:
496:
473:
469:
460:
442:
438:
415:
411:
397:
393:
391:
387:
380:
376:
372:
367:
344:
340:
334:
330:
324:
317:
313:
307:
303:
297:
294:
284:
283:
282:
280:
257:
253:
247:
243:
237:
227:
226:
225:
223:
185:
181:
158:
154:
145:
140:
136:
128:
124:
120:
116:
110:
106:
98:
96:
88:
84:
82:
78:
77:
72:
68:
64:
60:
56:
52:
48:
44:
37:
33:
19:
1800:
1786:the original
1776:
1706:
1682:
1678:
1670:
1664:
1650:
1572:
1548:
1541:
1514:
1512:
1426:
1420:
1236:
1178:
1176:
1005:
1001:
999:
854:
727:
402:
378:
374:
370:
363:
278:
276:
131:
112:
94:
74:
50:
40:
1792:MIL-STD-188
1675:reflectance
1275:Smith chart
81:reflectance
36:Reflectance
1848:Categories
1758:References
1641:Seismology
579:to a load
103:See also:
91:amplitude.
1717:Microwave
1697:Acoustics
1617:Γ
1559:Γ
1549:magnitude
1528:Γ
1487:Γ
1479:−
1466:Γ
1427:magnitude
1364:ϕ
1330:Γ
1305:Γ
1285:Γ
1258:≤
1250:Γ
1191:Γ
1160:ϕ
1150:−
1142:Γ
1132:Γ
1104:Γ
1083:λ
1072:π
1063:ϕ
1019:ϕ
1002:magnitude
944:−
925:Γ
832:−
826:Γ
768:Γ
701:Γ
693:−
658:Γ
627:Γ
523:Γ
390:acoustics
335:−
308:−
298:−
292:Γ
248:−
235:Γ
220:(capital
208:Γ
159:−
55:amplitude
1835:Archived
1711:See also
1635:measured
1194:′
1135:′
1107:′
279:currents
366:circuit
144:complex
125:of the
59:phasors
43:physics
1807:
1667:optics
79:. The
63:optics
1773:from
1179:twice
1006:phase
222:gamma
123:ratio
1805:ISBN
1421:The
117:and
107:and
49:the
45:and
1689:in
1665:In
1551:of
113:In
41:In
1850::
1794:).
1780:.
1693:.
725:.
1813:.
1683:r
1679:R
1595:L
1591:Z
1575:L
1573:Z
1545:0
1542:Z
1518:0
1515:Z
1498:.
1491:|
1483:|
1476:1
1470:|
1462:|
1458:+
1455:1
1449:=
1446:R
1443:W
1440:S
1389:0
1385:Z
1361:2
1341:1
1338:=
1334:|
1326:|
1261:1
1254:|
1246:|
1220:L
1216:Z
1157:2
1153:i
1146:e
1139:=
1079:/
1075:L
1069:2
1066:=
1039:L
985:.
977:0
973:Z
969:+
964:L
960:Z
952:0
948:Z
939:L
935:Z
928:=
899:0
895:Z
872:L
868:Z
835:1
829:=
806:0
803:=
798:L
794:Z
772:|
764:|
741:0
737:Z
711:2
706:|
697:|
690:1
668:2
663:|
654:|
633:0
630:=
605:0
601:Z
597:=
592:L
588:Z
561:S
557:Z
553:=
548:0
544:Z
501:S
497:Z
474:L
470:Z
443:S
439:Z
416:S
412:Z
382:0
379:Z
375:H
371:E
345:+
341:V
331:V
325:=
318:+
314:I
304:I
295:=
258:+
254:V
244:V
238:=
186:+
182:V
155:V
134:0
132:Z
38:.
20:)
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