267:
2259:
1907:
1559:
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
778:
1177:
617:
462:
1267:
922:
2014:
1347:
1002:
1729:
1752:
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677:
1069:
538:
383:
1188:
843:
261:
1918:
1275:
930:
1902:{\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}}.}
1644:
835:
519:
1655:
1617:
1554:
1419:
1392:
808:
492:
1527:
1500:
1473:
1446:
669:
1061:
345:
304:
2232:
773:{\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} .}
1569:
1172:{\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}}.}
138:
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
2208:
2024:
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
1734:
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,
2051:
91:(dB) units ("dB gain"). A gain greater than one (greater than zero dB), that is, amplification, is the defining property of an
2274:
65:
2268:
356:
with a voltage gain of 3 with an arbitrary input signal. At any instant the output voltage is three times the input voltage.
2311:
2242:
2181:
2151:
2301:
2101:
2306:
2198:
612:{\displaystyle {\text{gain-np}}={\frac {1}{2}}\ln \left({\frac {P_{\text{out}}}{P_{\text{in}}}}\right)~{\text{Np}}.}
2141:
2296:
2116:
2076:
457:{\displaystyle {\text{gain-db}}=10\log _{10}\left({\frac {P_{\text{out}}}{P_{\text{in}}}}\right)~{\text{dB}},}
1262:{\displaystyle {\text{gain-db}}=10\log \left({\frac {I_{\text{out}}}{I_{\text{in}}}}\right)^{2}~{\text{dB}},}
917:{\displaystyle {\text{gain-db}}=10\log \left({\frac {V_{\text{out}}}{V_{\text{in}}}}\right)^{2}~{\text{dB}},}
134:
amplifiers it usually refers to power gain. Furthermore, the term gain is also applied in systems such as
2056:
2009:{\displaystyle {\text{gain-db}}=G_{\text{dB}}=10\log G_{\text{W/W}}=10\log 100=10\times 2=20~{\text{dB}}.}
2171:
1342:{\displaystyle {\text{gain-db}}=20\log \left({\frac {I_{\text{out}}}{I_{\text{in}}}}\right)~{\text{dB}}.}
997:{\displaystyle {\text{gain-db}}=20\log \left({\frac {V_{\text{out}}}{V_{\text{in}}}}\right)~{\text{dB}}.}
228:
127:
81:
1027:
In the same way, when power gain is calculated using current instead of power, making the substitution
1724:{\displaystyle {\text{gain}}={\frac {V_{\text{out}}}{V_{\text{in}}}}={\frac {10}{1}}=10~{\text{V/V}}.}
1182:
In many cases, the input and output impedances are equal, so the above equation can be simplified to:
2081:
1357:
1016:
628:
1622:
813:
497:
205:
of the applied signal. Unless otherwise stated, the term refers to the gain for frequencies in the
2041:
1595:
1532:
1397:
1370:
786:
470:
222:
1505:
1478:
1451:
1424:
1364:
147:
49:
1592:
Q. An amplifier has an input impedance of 50 ohms and drives a load of 50 ohms. When its input (
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2177:
2147:
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92:
1912:
Again, the units W/W are optional. Power gain is more usually expressed in decibels, thus:
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131:
96:
2096:
2086:
1577:
57:
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2111:
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2046:
218:
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31:
2061:
1008:
143:
38:
2106:
2026:
370:
84:
to the amplitude or power at the input port. It is often expressed using the
2091:
2071:
353:
266:
202:
85:
61:
53:
17:
1584:), because the gain is a ratio of the output current to the input voltage.
206:
46:
374:
107:
88:
68:
from the input to the output port by adding energy converted from some
627:
The power gain can be calculated using voltage instead of power using
201:
The gain of an electronic device or circuit generally varies with the
1561:
209:, the intended operating frequency range of the equipment. The term
135:
126:). In the field of audio and general purpose amplifiers, especially
77:
1356:
in decibels and is equivalent to the power gain if and only if the
106:
alone is ambiguous, and can refer to the ratio of output to input
27:
Ability of a circuit to increase the power or amplitude of a signal
529:
265:
73:
1015:
in decibels and is equivalent to a power gain if and only if the
1581:
1564:. In the case of other devices, the gain will have a value in
1421:, is normally given as a dimensionless number, the ratio of
1565:
2237:(3 ed.). University of Washington Press. p. 18.
180:(the small-signal current gain, the slope of the graph of
150:
normally refers to forward current transfer ratio, either
837:
are equal, so the above equation can be simplified to:
2200:
Fundamentals of RF and
Microwave Transistor Amplifiers
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1755:
1658:
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473:
386:
317:
276:
231:
263:(mean radiation intensity from a lossless antenna).
1646:) is 10 volts. What is its voltage and power gain?
130:, the term usually refers to voltage gain, but in
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72:to the signal. It is usually defined as the mean
1352:This simplified formula is used to calculate a
528:instead of a decimal logarithm, resulting in
8:
524:A similar calculation can be done using a
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1956:
1934:
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281:
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242:
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2226:
2224:
2222:
2220:
2129:
173:at some operating point), or sometimes
2173:Dictionary of Pure and Applied Physics
2165:
2163:
2135:
2133:
1570:operational transconductance amplifier
7:
2231:White, Glenn; Louie, Gary J (2005).
2203:. John Wiley and Sons. p. 34.
2146:(7 ed.). Newnes. p. 314.
783:In many cases, the input impedance
494:is the power applied to the input,
256:{\displaystyle P_{\text{in}}/4\pi }
99:will have a gain of less than one.
763:
760:
25:
1568:units. Such is the case with the
80:amplitude or power at the output
45:is a measure of the ability of a
2262: This article incorporates
2257:
2143:Modern Dictionary of Electronics
2052:Aperture-to-medium coupling loss
2275:General Services Administration
1572:, which has an open-loop gain (
1360:at input and output are equal.
1019:at input and output are equal.
1639:{\displaystyle V_{\text{out}}}
830:{\displaystyle R_{\text{out}}}
521:is the power from the output.
514:{\displaystyle P_{\text{out}}}
361:Logarithmic units and decibels
334:
328:
293:
287:
225:from a directional antenna to
1:
1612:{\displaystyle V_{\text{in}}}
1549:{\displaystyle h_{\text{fe}}}
1414:{\displaystyle h_{\text{fe}}}
1387:{\displaystyle h_{\text{FE}}}
1007:This simplified formula, the
803:{\displaystyle R_{\text{in}}}
487:{\displaystyle P_{\text{in}}}
377:(dB), is defined as follows:
157:("beta", the static ratio of
1522:{\displaystyle I_{\text{b}}}
1495:{\displaystyle I_{\text{c}}}
1468:{\displaystyle I_{\text{b}}}
1441:{\displaystyle I_{\text{c}}}
1649:A. Voltage gain is simply:
213:has a different meaning in
2328:
2176:. CRC Press. p. 157.
29:
1619:) is 1 volt, its output (
1011:, is used to calculate a
664:{\displaystyle P=V^{2}/R}
2140:Graf, Rudolf F. (1999).
2117:Transmitter power output
2077:Effective radiated power
1363:The "current gain" of a
1056:{\displaystyle P=I^{2}R}
340:{\displaystyle v_{o}(t)}
299:{\displaystyle v_{i}(t)}
30:Not to be confused with
2270:Federal Standard 1037C
2264:public domain material
2057:Automatic gain control
2010:
1903:
1725:
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458:
357:
341:
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257:
128:operational amplifiers
2312:Electrical parameters
2011:
1904:
1746:, the power gain is:
1726:
1641:
1614:
1551:
1524:
1497:
1470:
1443:
1416:
1389:
1344:
1264:
1174:
1058:
999:
919:
832:
810:and output impedance
805:
775:
666:
614:
532:instead of decibels:
516:
489:
459:
342:
301:
269:
258:
122:) or electric power (
2302:Electronics concepts
2234:The Audio Dictionary
2197:Bahl, Inder (2009).
2170:Basu, Dipak (2000).
2082:Gain before feedback
1919:
1753:
1656:
1623:
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1506:
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1452:
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1371:
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787:
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384:
315:
274:
229:
95:or circuit, while a
2042:Active laser medium
1852:
1837:
1806:
1781:
1139:
1112:
742:
715:
352:of an ideal linear
311:and output voltage
270:Graph of the input
223:radiation intensity
2307:Transfer functions
2006:
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1721:
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1465:
1438:
1411:
1384:
1365:bipolar transistor
1339:
1259:
1169:
1125:
1098:
1063:, the formula is:
1053:
994:
914:
827:
800:
770:
728:
701:
671:; the formula is:
661:
609:
511:
484:
454:
358:
337:
296:
253:
148:bipolar transistor
146:. The "gain" of a
56:) to increase the
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1689:
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1606:
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1516:
1489:
1475:(or slope of the
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1435:
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1334:
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1322:
1319:
1309:
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1254:
1250:
1236:
1233:
1223:
1195:
1164:
1160:
1151:
1147:
1132:
1120:
1105:
1076:
989:
985:
977:
974:
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905:
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824:
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723:
708:
684:
629:Joule's first law
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579:
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526:natural logarithm
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481:
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445:
437:
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390:
239:
16:(Redirected from
2319:
2297:Antennas (radio)
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2282:
2277:. Archived from
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132:radio frequency
97:passive circuit
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2281:on 2022-01-22.
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2210:978-0470462317
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2097:Open-loop gain
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2087:Insertion gain
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1245:
1240:
1229:
1219:
1213:
1208:
1205:
1202:
1199:
1180:
1179:
1168:
1155:
1143:
1137:
1128:
1116:
1110:
1101:
1094:
1089:
1086:
1083:
1080:
1052:
1047:
1043:
1039:
1036:
1024:
1021:
1005:
1004:
993:
981:
970:
960:
954:
950:
947:
944:
941:
925:
924:
913:
900:
895:
884:
874:
868:
863:
860:
857:
854:
820:
793:
781:
780:
769:
765:
762:
746:
740:
731:
719:
713:
704:
697:
694:
691:
688:
660:
656:
650:
646:
642:
639:
624:
621:
620:
619:
608:
596:
585:
575:
569:
565:
562:
557:
554:
549:
504:
477:
465:
464:
453:
441:
430:
420:
414:
410:
405:
401:
397:
394:
367:
364:
362:
359:
336:
333:
330:
325:
321:
295:
292:
289:
284:
280:
252:
249:
245:
235:
193:
184:
177:
170:
161:
154:
26:
24:
14:
13:
10:
9:
6:
4:
3:
2:
2324:
2313:
2310:
2308:
2305:
2303:
2300:
2298:
2295:
2294:
2292:
2280:
2276:
2272:
2271:
2265:
2255:
2254:
2246:
2240:
2236:
2235:
2227:
2225:
2223:
2221:
2217:
2212:
2206:
2202:
2201:
2193:
2190:
2185:
2179:
2175:
2174:
2166:
2164:
2160:
2155:
2149:
2145:
2144:
2136:
2134:
2130:
2123:
2118:
2115:
2113:
2110:
2108:
2105:
2103:
2100:
2098:
2095:
2093:
2090:
2088:
2085:
2083:
2080:
2078:
2075:
2073:
2070:
2068:
2065:
2063:
2060:
2058:
2055:
2053:
2050:
2048:
2045:
2043:
2040:
2039:
2034:
2032:
2030:
2028:
2019:
2003:
1992:
1989:
1986:
1983:
1980:
1977:
1974:
1971:
1968:
1965:
1962:
1953:
1949:
1946:
1943:
1940:
1931:
1927:
1915:
1914:
1913:
1896:
1885:
1882:
1875:
1871:
1865:
1861:
1855:
1848:
1839:
1833:
1824:
1818:
1812:
1808:
1802:
1793:
1787:
1783:
1777:
1768:
1761:
1749:
1748:
1747:
1745:
1741:
1737:
1718:
1707:
1704:
1699:
1696:
1691:
1680:
1670:
1664:
1652:
1651:
1650:
1647:
1627:
1600:
1587:
1585:
1583:
1579:
1575:
1571:
1567:
1563:
1557:
1537:
1510:
1483:
1456:
1429:
1402:
1375:
1366:
1361:
1359:
1355:
1336:
1324:
1313:
1303:
1297:
1293:
1290:
1287:
1284:
1272:
1271:
1256:
1243:
1238:
1227:
1217:
1211:
1206:
1203:
1200:
1197:
1185:
1184:
1183:
1166:
1153:
1141:
1135:
1126:
1114:
1108:
1099:
1092:
1087:
1084:
1081:
1078:
1066:
1065:
1064:
1050:
1045:
1041:
1037:
1034:
1022:
1020:
1018:
1014:
1010:
991:
979:
968:
958:
952:
948:
945:
942:
939:
927:
926:
911:
898:
893:
882:
872:
866:
861:
858:
855:
852:
840:
839:
838:
818:
791:
767:
744:
738:
729:
717:
711:
702:
695:
692:
689:
686:
674:
673:
672:
658:
654:
648:
644:
640:
637:
630:
622:
606:
594:
583:
573:
567:
563:
560:
555:
552:
547:
535:
534:
533:
531:
527:
522:
502:
475:
451:
439:
428:
418:
412:
408:
403:
399:
395:
392:
380:
379:
378:
376:
372:
365:
360:
355:
351:
331:
323:
319:
310:
290:
282:
278:
268:
264:
250:
247:
243:
233:
224:
220:
216:
212:
208:
204:
199:
198:at a point).
196:
192:
187:
183:
176:
169:
164:
160:
153:
149:
145:
141:
137:
133:
129:
125:
121:
117:
113:
109:
105:
100:
98:
94:
90:
87:
83:
79:
75:
71:
67:
63:
59:
55:
51:
48:
44:
40:
33:
19:
2279:the original
2269:
2233:
2199:
2192:
2172:
2142:
2112:Process gain
2067:Complex gain
2047:Antenna gain
2025:
2023:
1911:
1743:
1739:
1735:
1733:
1648:
1591:
1558:
1362:
1354:current gain
1353:
1351:
1181:
1026:
1023:Current gain
1013:voltage gain
1012:
1006:
782:
626:
623:Voltage gain
523:
466:
369:
347:
306:
219:antenna gain
210:
200:
194:
190:
185:
181:
174:
167:
162:
158:
151:
140:responsivity
123:
120:current gain
119:
112:voltage gain
111:
103:
101:
70:power supply
42:
36:
32:Antenna gain
18:Current gain
2062:Attenuation
1529:graph, for
1009:20 log rule
166:divided by
144:photosensor
86:logarithmic
39:electronics
2291:Categories
2244:0295984988
2183:1420050222
2153:0080511988
2124:References
2107:Power gain
2020:Unity gain
1358:impedances
1017:impedances
371:Power gain
366:Power gain
124:power gain
52:(often an
2092:Loop gain
2072:DC offset
1984:×
1972:
1950:
1294:
1207:
1088:
949:
862:
696:
564:
409:
354:amplifier
251:π
203:frequency
102:The term
62:amplitude
54:amplifier
2102:Net gain
2035:See also
1502:-versus-
375:decibels
217:design;
207:passband
189:against
47:two-port
1924:gain-db
1588:Example
1578:siemens
1562:amperes
1281:gain-db
1194:gain-db
1075:gain-db
936:gain-db
849:gain-db
683:gain-db
544:gain-np
389:gain-db
215:antenna
136:sensors
116:current
108:voltage
89:decibel
76:of the
50:circuit
2241:
2207:
2180:
2150:
1996:
1889:
1711:
1329:
1249:
1159:
984:
904:
757:
599:
530:nepers
467:where
444:
308:(blue)
78:signal
66:signal
2266:from
2027:unity
1576:) in
373:, in
349:(red)
142:of a
74:ratio
64:of a
58:power
2239:ISBN
2205:ISBN
2178:ISBN
2148:ISBN
2029:gain
1758:gain
1661:gain
1582:mhos
211:gain
104:gain
82:port
43:gain
1975:100
1969:log
1958:W/W
1947:log
1893:W/W
1886:100
1829:out
1773:out
1715:V/V
1675:out
1632:out
1560:in
1556:).
1448:to
1394:or
1367:,
1308:out
1291:log
1222:out
1204:log
1119:out
1104:out
1085:log
963:out
946:log
877:out
859:log
823:out
722:out
707:out
693:log
578:out
507:out
423:out
400:log
114:),
60:or
37:In
2293::
2273:.
2219:^
2162:^
2132:^
2031:.
2000:dB
1993:20
1981:10
1966:10
1944:10
1936:dB
1862:10
1844:in
1813:50
1798:in
1788:50
1738:=
1708:10
1697:10
1685:in
1605:in
1566:SI
1542:fe
1407:fe
1380:FE
1333:dB
1318:in
1288:20
1253:dB
1232:in
1201:10
1163:dB
1146:in
1131:in
1082:10
988:dB
973:in
943:20
908:dB
887:in
856:10
796:in
749:in
734:in
690:10
603:Np
588:in
561:ln
480:in
448:dB
433:in
404:10
396:10
238:in
178:fe
155:FE
41:,
2247:.
2213:.
2186:.
2156:.
2004:.
1990:=
1987:2
1978:=
1963:=
1954:G
1941:=
1932:G
1928:=
1897:.
1883:=
1876:2
1872:1
1866:2
1856:=
1849:2
1840:V
1834:2
1825:V
1819:=
1809:/
1803:2
1794:V
1784:/
1778:2
1769:V
1762:=
1744:R
1742:/
1740:V
1736:P
1719:.
1705:=
1700:1
1692:=
1681:V
1671:V
1665:=
1628:V
1601:V
1580:(
1538:h
1515:b
1511:I
1488:c
1484:I
1461:b
1457:I
1434:c
1430:I
1403:h
1376:h
1337:.
1325:)
1314:I
1304:I
1298:(
1285:=
1257:,
1244:2
1239:)
1228:I
1218:I
1212:(
1198:=
1167:.
1154:)
1142:R
1136:2
1127:I
1115:R
1109:2
1100:I
1093:(
1079:=
1051:R
1046:2
1042:I
1038:=
1035:P
992:.
980:)
969:V
959:V
953:(
940:=
912:,
899:2
894:)
883:V
873:V
867:(
853:=
819:R
792:R
768:.
764:B
761:d
745:R
739:2
730:V
718:R
712:2
703:V
687:=
659:R
655:/
649:2
645:V
641:=
638:P
607:.
595:)
584:P
574:P
568:(
556:2
553:1
548:=
503:P
476:P
452:,
440:)
429:P
419:P
413:(
393:=
335:)
332:t
329:(
324:o
320:v
294:)
291:t
288:(
283:i
279:v
248:4
244:/
234:P
195:b
191:I
186:c
182:I
175:h
171:b
168:I
163:c
159:I
152:h
118:(
110:(
34:.
20:)
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