256:
2248:
1896:
1548:
In the cases above, gain will be a dimensionless quantity, as it is the ratio of like units (decibels are not used as units, but rather as a method of indicating a logarithmic relationship). In the bipolar transistor example, it is the ratio of the output current to the input current, both measured
767:
1166:
606:
451:
1256:
911:
2003:
1336:
991:
1718:
1741:
666:
1058:
2252:
527:
372:
1177:
832:
250:
1907:
1264:
919:
1891:{\displaystyle {\text{gain}}={\frac {V_{\text{out}}^{2}/50}{V_{\text{in}}^{2}/50}}={\frac {V_{\text{out}}^{2}}{V_{\text{in}}^{2}}}={\frac {10^{2}}{1^{2}}}=100~{\text{W/W}}.}
1633:
824:
508:
1644:
1606:
1543:
1408:
1381:
797:
481:
1516:
1489:
1462:
1435:
658:
1050:
334:
293:
2221:
762:{\displaystyle {\text{gain-db}}=10\log {\frac {\frac {V_{\text{out}}^{2}}{R_{\text{out}}}}{\frac {V_{\text{in}}^{2}}{R_{\text{in}}}}}~\mathrm {dB} .}
1161:{\displaystyle {\text{gain-db}}=10\log {\left({\frac {I_{\text{out}}^{2}R_{\text{out}}}{I_{\text{in}}^{2}R_{\text{in}}}}\right)}~{\text{dB}}.}
127:
where the input and output have different units; in such cases the gain units must be specified, as in "5 microvolts per photon" for the
2013:
A gain of factor 1 (equivalent to 0 dB) where both input and output are at the same voltage level and impedance is also known as
1723:
The units V/V are optional but make it clear that this figure is a voltage gain and not a power gain. Using the expression for power,
80:(dB) units ("dB gain"). A gain greater than one (greater than zero dB), that is, amplification, is the defining property of an
1558:
2257:
345:
with a voltage gain of 3 with an arbitrary input signal. At any instant the output voltage is three times the input voltage.
2197:
2187:
601:{\displaystyle {\text{gain-np}}={\frac {1}{2}}\ln \left({\frac {P_{\text{out}}}{P_{\text{in}}}}\right)~{\text{Np}}.}
2130:
2040:
2263:
54:
2300:
2231:
2170:
2140:
446:{\displaystyle {\text{gain-db}}=10\log _{10}\left({\frac {P_{\text{out}}}{P_{\text{in}}}}\right)~{\text{dB}},}
2290:
2090:
1251:{\displaystyle {\text{gain-db}}=10\log \left({\frac {I_{\text{out}}}{I_{\text{in}}}}\right)^{2}~{\text{dB}},}
906:{\displaystyle {\text{gain-db}}=10\log \left({\frac {V_{\text{out}}}{V_{\text{in}}}}\right)^{2}~{\text{dB}},}
123:
amplifiers it usually refers to power gain. Furthermore, the term gain is also applied in systems such as
1998:{\displaystyle {\text{gain-db}}=G_{\text{dB}}=10\log G_{\text{W/W}}=10\log 100=10\times 2=20~{\text{dB}}.}
2295:
2160:
1331:{\displaystyle {\text{gain-db}}=20\log \left({\frac {I_{\text{out}}}{I_{\text{in}}}}\right)~{\text{dB}}.}
986:{\displaystyle {\text{gain-db}}=20\log \left({\frac {V_{\text{out}}}{V_{\text{in}}}}\right)~{\text{dB}}.}
217:
1016:
In the same way, when power gain is calculated using current instead of power, making the substitution
1713:{\displaystyle {\text{gain}}={\frac {V_{\text{out}}}{V_{\text{in}}}}={\frac {10}{1}}=10~{\text{V/V}}.}
1171:
In many cases, the input and output impedances are equal, so the above equation can be simplified to:
2285:
1611:
802:
486:
194:
of the applied signal. Unless otherwise stated, the term refers to the gain for frequencies in the
2105:
2065:
1584:
1521:
1386:
1359:
775:
459:
1494:
1467:
1440:
1413:
1581:
Q. An amplifier has an input impedance of 50 ohms and drives a load of 50 ohms. When its input (
2045:
622:
1019:
303:
262:
116:
70:
2070:
1901:
Again, the units W/W are optional. Power gain is more usually expressed in decibels, thus:
1346:
1005:
617:
8:
2030:
211:
1353:
136:
38:
2227:
2193:
2166:
2136:
514:
2267:
1562:
104:
81:
203:
120:
85:
2085:
2075:
1566:
46:
2279:
73:
to the amplitude or power at the input port. It is often expressed using the
2100:
2055:
2035:
1573:), because the gain is a ratio of the output current to the input voltage.
207:
128:
58:
20:
2050:
997:
132:
27:
2095:
2015:
359:
57:
from the input to the output port by adding energy converted from some
616:
The power gain can be calculated using voltage instead of power using
190:
The gain of an electronic device or circuit generally varies with the
2080:
2060:
342:
198:, the intended operating frequency range of the equipment. The term
191:
115:). In the field of audio and general purpose amplifiers, especially
74:
50:
42:
1345:
in decibels and is equivalent to the power gain if and only if the
195:
95:
alone is ambiguous, and can refer to the ratio of output to input
35:
16:
Ability of a circuit to increase the power or amplitude of a signal
1004:
in decibels and is equivalent to a power gain if and only if the
363:
255:
96:
77:
1550:
124:
66:
1553:. In the case of other devices, the gain will have a value in
518:
62:
1410:, is normally given as a dimensionless number, the ratio of
2226:(3 ed.). University of Washington Press. p. 18.
169:(the small-signal current gain, the slope of the graph of
139:
normally refers to forward current transfer ratio, either
1570:
1554:
826:
are equal, so the above equation can be simplified to:
2189:
Fundamentals of RF and
Microwave Transistor Amplifiers
1910:
1744:
1647:
1614:
1587:
1524:
1497:
1470:
1443:
1416:
1389:
1362:
1267:
1180:
1061:
1022:
922:
835:
805:
778:
669:
625:
530:
489:
462:
375:
306:
265:
220:
252:(mean radiation intensity from a lossless antenna).
1635:) is 10 volts. What is its voltage and power gain?
119:, the term usually refers to voltage gain, but in
1997:
1890:
1712:
1627:
1600:
1537:
1510:
1483:
1456:
1429:
1402:
1375:
1330:
1250:
1160:
1044:
985:
905:
818:
791:
761:
652:
600:
502:
475:
445:
328:
287:
244:
349:
61:to the signal. It is usually defined as the mean
2277:
1341:This simplified formula is used to calculate a
517:instead of a decimal logarithm, resulting in
2219:
513:A similar calculation can be done using a
254:
2215:
2213:
2211:
2209:
162:at some operating point), or sometimes
2278:
2162:Dictionary of Pure and Applied Physics
2154:
2152:
2124:
2122:
1559:operational transconductance amplifier
2220:White, Glenn; Louie, Gary J (2005).
2206:
2185:
2158:
2128:
2192:. John Wiley and Sons. p. 34.
2179:
2149:
2135:(7 ed.). Newnes. p. 314.
2119:
772:In many cases, the input impedance
483:is the power applied to the input,
245:{\displaystyle P_{\text{in}}/4\pi }
88:will have a gain of less than one.
13:
752:
749:
14:
2312:
1557:units. Such is the case with the
69:amplitude or power at the output
34:is a measure of the ability of a
2251: This article incorporates
2246:
2132:Modern Dictionary of Electronics
2041:Aperture-to-medium coupling loss
2264:General Services Administration
1561:, which has an open-loop gain (
1349:at input and output are equal.
1011:
1008:at input and output are equal.
611:
1628:{\displaystyle V_{\text{out}}}
819:{\displaystyle R_{\text{out}}}
510:is the power from the output.
503:{\displaystyle P_{\text{out}}}
350:Logarithmic units and decibels
323:
317:
282:
276:
214:from a directional antenna to
1:
2112:
2008:
1601:{\displaystyle V_{\text{in}}}
1538:{\displaystyle h_{\text{fe}}}
1403:{\displaystyle h_{\text{fe}}}
1376:{\displaystyle h_{\text{FE}}}
996:This simplified formula, the
792:{\displaystyle R_{\text{in}}}
476:{\displaystyle P_{\text{in}}}
366:(dB), is defined as follows:
354:
146:("beta", the static ratio of
1511:{\displaystyle I_{\text{b}}}
1484:{\displaystyle I_{\text{c}}}
1457:{\displaystyle I_{\text{b}}}
1430:{\displaystyle I_{\text{c}}}
7:
2023:
1638:A. Voltage gain is simply:
202:has a different meaning in
10:
2317:
2165:. CRC Press. p. 157.
1576:
18:
1608:) is 1 volt, its output (
1000:, is used to calculate a
653:{\displaystyle P=V^{2}/R}
2129:Graf, Rudolf F. (1999).
2106:Transmitter power output
2066:Effective radiated power
1352:The "current gain" of a
1045:{\displaystyle P=I^{2}R}
329:{\displaystyle v_{o}(t)}
288:{\displaystyle v_{i}(t)}
19:Not to be confused with
2259:Federal Standard 1037C
2253:public domain material
2046:Automatic gain control
1999:
1892:
1714:
1629:
1602:
1539:
1512:
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1431:
1404:
1377:
1332:
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1162:
1046:
987:
907:
820:
793:
763:
654:
602:
504:
477:
447:
346:
330:
289:
246:
117:operational amplifiers
2301:Electrical parameters
2000:
1893:
1735:, the power gain is:
1715:
1630:
1603:
1540:
1513:
1486:
1459:
1432:
1405:
1378:
1333:
1253:
1163:
1047:
988:
908:
821:
799:and output impedance
794:
764:
655:
603:
521:instead of decibels:
505:
478:
448:
331:
290:
258:
247:
111:) or electric power (
2291:Electronics concepts
2223:The Audio Dictionary
2186:Bahl, Inder (2009).
2159:Basu, Dipak (2000).
2071:Gain before feedback
1908:
1742:
1645:
1612:
1585:
1522:
1495:
1468:
1441:
1414:
1387:
1360:
1265:
1178:
1059:
1020:
920:
833:
803:
776:
667:
623:
528:
487:
460:
373:
304:
263:
218:
84:or circuit, while a
2031:Active laser medium
1841:
1826:
1795:
1770:
1128:
1101:
731:
704:
341:of an ideal linear
300:and output voltage
259:Graph of the input
212:radiation intensity
2296:Transfer functions
1995:
1888:
1827:
1812:
1781:
1756:
1710:
1625:
1598:
1535:
1508:
1481:
1454:
1427:
1400:
1373:
1354:bipolar transistor
1328:
1248:
1158:
1114:
1087:
1052:, the formula is:
1042:
983:
903:
816:
789:
759:
717:
690:
660:; the formula is:
650:
598:
500:
473:
443:
347:
326:
285:
242:
137:bipolar transistor
135:. The "gain" of a
45:) to increase the
1990:
1986:
1948:
1926:
1914:
1883:
1879:
1869:
1842:
1834:
1819:
1805:
1788:
1763:
1748:
1705:
1701:
1691:
1678:
1675:
1665:
1651:
1622:
1595:
1532:
1505:
1478:
1464:(or slope of the
1451:
1424:
1397:
1370:
1323:
1319:
1311:
1308:
1298:
1271:
1243:
1239:
1225:
1222:
1212:
1184:
1153:
1149:
1140:
1136:
1121:
1109:
1094:
1065:
978:
974:
966:
963:
953:
926:
898:
894:
880:
877:
867:
839:
813:
786:
747:
743:
742:
739:
724:
715:
712:
697:
673:
618:Joule's first law
593:
589:
581:
578:
568:
547:
534:
515:natural logarithm
497:
470:
438:
434:
426:
423:
413:
379:
228:
2308:
2286:Antennas (radio)
2272:
2271:
2266:. Archived from
2250:
2249:
2238:
2237:
2217:
2204:
2203:
2183:
2177:
2176:
2156:
2147:
2146:
2126:
2004:
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1984:
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1563:transconductance
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1111:
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82:active component
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1199:
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121:radio frequency
86:passive circuit
24:
17:
12:
11:
5:
2314:
2304:
2303:
2298:
2293:
2288:
2274:
2273:
2270:on 2022-01-22.
2240:
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2199:978-0470462317
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2141:
2117:
2116:
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2111:
2109:
2108:
2103:
2098:
2093:
2088:
2086:Open-loop gain
2083:
2078:
2076:Insertion gain
2073:
2068:
2063:
2058:
2053:
2048:
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2033:
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1278:
1275:
1259:
1258:
1247:
1234:
1229:
1218:
1208:
1202:
1197:
1194:
1191:
1188:
1169:
1168:
1157:
1144:
1132:
1126:
1117:
1105:
1099:
1090:
1083:
1078:
1075:
1072:
1069:
1041:
1036:
1032:
1028:
1025:
1013:
1010:
994:
993:
982:
970:
959:
949:
943:
939:
936:
933:
930:
914:
913:
902:
889:
884:
873:
863:
857:
852:
849:
846:
843:
809:
782:
770:
769:
758:
754:
751:
735:
729:
720:
708:
702:
693:
686:
683:
680:
677:
649:
645:
639:
635:
631:
628:
613:
610:
609:
608:
597:
585:
574:
564:
558:
554:
551:
546:
543:
538:
493:
466:
454:
453:
442:
430:
419:
409:
403:
399:
394:
390:
386:
383:
356:
353:
351:
348:
325:
322:
319:
314:
310:
284:
281:
278:
273:
269:
241:
238:
234:
224:
182:
173:
166:
159:
150:
143:
15:
9:
6:
4:
3:
2:
2313:
2302:
2299:
2297:
2294:
2292:
2289:
2287:
2284:
2283:
2281:
2269:
2265:
2261:
2260:
2254:
2244:
2243:
2235:
2229:
2225:
2224:
2216:
2214:
2212:
2210:
2201:
2195:
2191:
2190:
2182:
2174:
2168:
2164:
2163:
2155:
2153:
2144:
2138:
2134:
2133:
2125:
2123:
2118:
2107:
2104:
2102:
2099:
2097:
2094:
2092:
2089:
2087:
2084:
2082:
2079:
2077:
2074:
2072:
2069:
2067:
2064:
2062:
2059:
2057:
2054:
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2049:
2047:
2044:
2042:
2039:
2037:
2034:
2032:
2029:
2028:
2021:
2019:
2017:
1992:
1981:
1978:
1975:
1972:
1969:
1966:
1963:
1960:
1957:
1954:
1951:
1942:
1938:
1935:
1932:
1929:
1920:
1916:
1904:
1903:
1902:
1885:
1874:
1871:
1864:
1860:
1854:
1850:
1844:
1837:
1828:
1822:
1813:
1807:
1801:
1797:
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1782:
1776:
1772:
1766:
1757:
1750:
1738:
1737:
1736:
1734:
1730:
1726:
1707:
1696:
1693:
1688:
1685:
1680:
1669:
1659:
1653:
1641:
1640:
1639:
1636:
1616:
1589:
1574:
1572:
1568:
1564:
1560:
1556:
1552:
1546:
1526:
1499:
1472:
1445:
1418:
1391:
1364:
1355:
1350:
1348:
1344:
1325:
1313:
1302:
1292:
1286:
1282:
1279:
1276:
1273:
1261:
1260:
1245:
1232:
1227:
1216:
1206:
1200:
1195:
1192:
1189:
1186:
1174:
1173:
1172:
1155:
1142:
1130:
1124:
1115:
1103:
1097:
1088:
1081:
1076:
1073:
1070:
1067:
1055:
1054:
1053:
1039:
1034:
1030:
1026:
1023:
1009:
1007:
1003:
999:
980:
968:
957:
947:
941:
937:
934:
931:
928:
916:
915:
900:
887:
882:
871:
861:
855:
850:
847:
844:
841:
829:
828:
827:
807:
780:
756:
733:
727:
718:
706:
700:
691:
684:
681:
678:
675:
663:
662:
661:
647:
643:
637:
633:
629:
626:
619:
595:
583:
572:
562:
556:
552:
549:
544:
541:
536:
524:
523:
522:
520:
516:
511:
491:
464:
440:
428:
417:
407:
401:
397:
392:
388:
384:
381:
369:
368:
367:
365:
361:
344:
340:
320:
312:
308:
299:
279:
271:
267:
257:
253:
239:
236:
232:
222:
213:
209:
205:
201:
197:
193:
188:
187:at a point).
185:
181:
176:
172:
165:
158:
153:
149:
142:
138:
134:
130:
126:
122:
118:
114:
110:
106:
102:
98:
94:
89:
87:
83:
79:
76:
72:
68:
64:
60:
56:
52:
48:
44:
40:
37:
33:
29:
22:
2268:the original
2258:
2222:
2188:
2181:
2161:
2131:
2101:Process gain
2056:Complex gain
2036:Antenna gain
2014:
2012:
1900:
1732:
1728:
1724:
1722:
1637:
1580:
1547:
1351:
1343:current gain
1342:
1340:
1170:
1015:
1012:Current gain
1002:voltage gain
1001:
995:
771:
615:
612:Voltage gain
512:
455:
358:
336:
295:
208:antenna gain
199:
189:
183:
179:
174:
170:
163:
156:
151:
147:
140:
129:responsivity
112:
109:current gain
108:
101:voltage gain
100:
92:
90:
59:power supply
31:
25:
21:Antenna gain
2051:Attenuation
1518:graph, for
998:20 log rule
155:divided by
133:photosensor
75:logarithmic
28:electronics
2280:Categories
2233:0295984988
2172:1420050222
2142:0080511988
2113:References
2096:Power gain
2009:Unity gain
1347:impedances
1006:impedances
360:Power gain
355:Power gain
113:power gain
41:(often an
2081:Loop gain
2061:DC offset
1973:×
1961:
1939:
1283:
1196:
1077:
938:
851:
685:
553:
398:
343:amplifier
240:π
192:frequency
91:The term
51:amplitude
43:amplifier
2091:Net gain
2024:See also
1491:-versus-
364:decibels
206:design;
196:passband
178:against
36:two-port
1913:gain-db
1577:Example
1567:siemens
1551:amperes
1270:gain-db
1183:gain-db
1064:gain-db
925:gain-db
838:gain-db
672:gain-db
533:gain-np
378:gain-db
204:antenna
125:sensors
105:current
97:voltage
78:decibel
65:of the
39:circuit
2230:
2196:
2169:
2139:
1985:
1878:
1700:
1318:
1238:
1148:
973:
893:
746:
588:
519:nepers
456:where
433:
297:(blue)
67:signal
55:signal
2255:from
2016:unity
1565:) in
362:, in
338:(red)
131:of a
63:ratio
53:of a
47:power
2228:ISBN
2194:ISBN
2167:ISBN
2137:ISBN
2018:gain
1747:gain
1650:gain
1571:mhos
200:gain
93:gain
71:port
32:gain
1964:100
1958:log
1947:W/W
1936:log
1882:W/W
1875:100
1818:out
1762:out
1704:V/V
1664:out
1621:out
1549:in
1545:).
1437:to
1383:or
1356:,
1297:out
1280:log
1211:out
1193:log
1108:out
1093:out
1074:log
952:out
935:log
866:out
848:log
812:out
711:out
696:out
682:log
567:out
496:out
412:out
389:log
103:),
49:or
26:In
2282::
2262:.
2208:^
2151:^
2121:^
2020:.
1989:dB
1982:20
1970:10
1955:10
1933:10
1925:dB
1851:10
1833:in
1802:50
1787:in
1777:50
1727:=
1697:10
1686:10
1674:in
1594:in
1555:SI
1531:fe
1396:fe
1369:FE
1322:dB
1307:in
1277:20
1242:dB
1221:in
1190:10
1152:dB
1135:in
1120:in
1071:10
977:dB
962:in
932:20
897:dB
876:in
845:10
785:in
738:in
723:in
679:10
592:Np
577:in
550:ln
469:in
437:dB
422:in
393:10
385:10
227:in
167:fe
144:FE
30:,
2236:.
2202:.
2175:.
2145:.
1993:.
1979:=
1976:2
1967:=
1952:=
1943:G
1930:=
1921:G
1917:=
1886:.
1872:=
1865:2
1861:1
1855:2
1845:=
1838:2
1829:V
1823:2
1814:V
1808:=
1798:/
1792:2
1783:V
1773:/
1767:2
1758:V
1751:=
1733:R
1731:/
1729:V
1725:P
1708:.
1694:=
1689:1
1681:=
1670:V
1660:V
1654:=
1617:V
1590:V
1569:(
1527:h
1504:b
1500:I
1477:c
1473:I
1450:b
1446:I
1423:c
1419:I
1392:h
1365:h
1326:.
1314:)
1303:I
1293:I
1287:(
1274:=
1246:,
1233:2
1228:)
1217:I
1207:I
1201:(
1187:=
1156:.
1143:)
1131:R
1125:2
1116:I
1104:R
1098:2
1089:I
1082:(
1068:=
1040:R
1035:2
1031:I
1027:=
1024:P
981:.
969:)
958:V
948:V
942:(
929:=
901:,
888:2
883:)
872:V
862:V
856:(
842:=
808:R
781:R
757:.
753:B
750:d
734:R
728:2
719:V
707:R
701:2
692:V
676:=
648:R
644:/
638:2
634:V
630:=
627:P
596:.
584:)
573:P
563:P
557:(
545:2
542:1
537:=
492:P
465:P
441:,
429:)
418:P
408:P
402:(
382:=
324:)
321:t
318:(
313:o
309:v
283:)
280:t
277:(
272:i
268:v
237:4
233:/
223:P
184:b
180:I
175:c
171:I
164:h
160:b
157:I
152:c
148:I
141:h
107:(
99:(
23:.
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