1371:
141:
304:
608:
368:
478:
1095:
423:
677:
644:
771:
741:
711:
501:
446:
391:
333:
1408:
773:
for the case of short-circuited source resistance. As with the extra-element result, differences are in the perspective leading to the formula.
1243:
1085:
1056:
1162:
962:
858:
1123:
1437:
1401:
61:
1442:
1427:
921:
796:
167:= loop transmission with an open circuit across the terminal pair. The loop transmission also is referred to as the
19:
is a general procedure for calculating the change in an impedance due to feedback in a circuit. It was published by
1447:
1432:
1029:
184:
1394:
1299:
1268:
869:
1037:
Blackman is not cited by
Middlebrook, but see Eq. 1.4, p. 3 in this discussion of the extra element theorem:
782:
1224:
ISCAS '98. Proceedings of the 1998 IEEE International
Symposium on Circuits and Systems (Cat. No.98CH36187)
513:
811:
28:
1180:
44:
40:
32:
1073:
1221:
Borivoje Nikolić; Slavoljub
Marjanović (May 1998). "A general method of feedback amplifier analysis".
338:
1339:
1222:
1195:
1107:
983:
451:
20:
816:
1249:
829:
847:
Ultra Low Power
Bioelectronics: Fundamentals, Biomedical Applications, and Bio-Inspired Systems
396:
1239:
1158:
1081:
1052:
958:
952:
854:
842:
649:
616:
36:
24:
1378:
1146:
746:
716:
686:
1347:
1327:
1231:
1203:
1115:
1040:
1003:
991:
911:
821:
483:
428:
373:
315:
1343:
1199:
1111:
987:
915:
171:. Blackman's formula can be compared with Middlebrook's result for the input impedance
868:
Amaldo D'Amico; Christian
Falconi; Gianluca Giustolisi; Gaetano Palumbo (April 2007).
1421:
160:= loop transmission with a small-signal short across the selected terminal pair, and
1253:
833:
797:"Extending Blackman's formula to feedback networks with multiple dependent sources"
168:
1370:
825:
1235:
924:
no longer is available from
Alcatel-Lucent, but an online version is found at
1119:
927:
978:
J. Choma, Jr. (April 1990). "Signal flow analysis of feedback networks".
507:
Blackman's formula also can be compared with Choma's signal-flow result:
1207:
1351:
995:
843:"§10.7 Driving-point transistor impedances with Blackman's formula"
51:
between two selected terminals of a negative feedback amplifier as
1045:
Fast
Analytical Techniques for Electrical and Electronic Circuits
1181:"A comparison of two approaches to feedback circuit analysis"
877:
IEEE Transactions on
Circuits and Systems – II Express Briefs
47:. Blackman's approach leads to the formula for the impedance
804:
IEEE Transactions on
Circuits and Systems II: Express Briefs
870:"Resistance of feedback amplifiers: A novel representation"
1324:
Blackman is not cited by Choma, but see Eq. 38, p. 460 in
1382:
902:
RB Blackman (1943). "Effect of feedback on impedance".
136:{\displaystyle Z=Z_{D}{\frac {1+T_{SC}}{1+T_{OC}}}\ ,}
1153:. Springer Science & Business Media. pp. 74
1030:"Null double injection and the extra element theorem"
749:
719:
689:
652:
619:
516:
486:
454:
431:
399:
376:
341:
318:
187:
64:
1096:"A Simplified Method of Feedback Amplifier Analysis"
178:of a circuit based upon the extra-element theorem:
765:
735:
705:
671:
638:
602:
495:
472:
440:
417:
385:
362:
327:
298:
135:
679:under the condition that a selected parameter
1402:
1023:
1021:
8:
1041:"Introduction: The joys of network analysis"
299:{\displaystyle Z_{in}=Z_{in}^{\infty }\left}
1328:"Signal flow analysis of feedback networks"
1292:
1290:
1145:Gaetano Palumbo; Salvatore Pennisi (2002).
1004:"Signal flow analysis of feedback networks"
849:. Cambridge University Press. pp. 258
480:is the impedance seen by the extra element
425:is the impedance seen by the extra element
1409:
1395:
1332:IEEE Transactions on Circuits and Systems
1047:. Cambridge University Press. pp. 2
980:IEEE Transactions on Circuits and Systems
815:
754:
748:
724:
718:
694:
688:
657:
651:
624:
618:
581:
563:
550:
537:
521:
515:
485:
464:
459:
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404:
398:
375:
354:
346:
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317:
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275:
270:
250:
244:
239:
226:
216:
208:
192:
186:
115:
94:
81:
75:
63:
153:= impedance with the feedback disabled,
1298:Dennis L. Feucht (September 15, 2013).
1267:Dennis L. Feucht (September 15, 2013).
894:
503:with the input open (or made infinite).
448:with the input shorted (or made zero);
335:is the impedance of the extra element;
1377:This engineering-related article is a
1151:Feedback Amplifiers: Theory and Design
713:is evaluated with zero excitation and
603:{\displaystyle Z_{SS}=Z_{S0}\left\ ,}
7:
1367:
1365:
1300:"Blackman's Impedance Theorem (BZT)"
1304:Middlebrook's Extra Element theorem
1273:Middlebrook's Extra Element theorem
1143:For a derivation and examples, see
1381:. You can help Knowledge (XXG) by
1177:For example, see Eq. 8, p. 255 in
916:10.1002/j.1538-7305.1943.tb00443.x
465:
355:
276:
217:
14:
1230:. Vol. 3. pp. 415–418.
954:Handbook of Analog Circuit Design
904:The Bell System Technical Journal
795:Eugene Paperno (September 2012).
1369:
363:{\displaystyle Z_{in}^{\infty }}
957:. Academic Press. p. 147.
929:Effect of feedback on impedance
473:{\displaystyle Z_{e}^{\infty }}
1188:IEEE Transactions on Education
1100:IEEE Transactions on Education
1074:"§2.3 Asymptotic gain formula"
31:, and was made popular in the
1:
1080:. Macmillan USA. p. 16.
1078:Feedback amplifier principles
683:is set to zero, return ratio
1179:Paul J Hurst (August 1992).
393:removed (or made infinite);
370:is the input impedance with
1147:"§3.5 The Blackman Theorem"
1094:Solomon Rosenstark (1974).
1072:Solomon Rosenstark (1986).
1464:
1364:
826:10.1109/TCSII.2012.2213355
23:in 1943, was connected to
1236:10.1109/ISCAS.1998.704038
1039:Vatché Vorpérian (2002).
1000:On-line version found at
951:Dennis L. Feucht (2014).
841:Rahul Sarpeshkar (2010).
418:{\displaystyle Z_{e}^{0}}
672:{\displaystyle Z_{SS}\ }
639:{\displaystyle Z_{S0}\ }
1120:10.1109/TE.1974.4320925
982:. CAS-37 (4): 455–463.
766:{\displaystyle T_{Z}\ }
736:{\displaystyle T_{I}\ }
706:{\displaystyle T_{Z}\ }
1326:J. Choma, Jr. (1990).
1296:Comparison is made by
1269:"Impedance EET (ZEET)"
767:
737:
707:
673:
640:
604:
497:
474:
442:
419:
387:
364:
329:
300:
137:
1438:Electronic amplifiers
768:
738:
708:
674:
641:
605:
498:
475:
443:
420:
388:
365:
330:
301:
138:
41:asymptotic gain model
33:extra element theorem
1035:. RDMiddlebrook.com.
926:RB Blackman (1943).
783:Mason's gain formula
747:
717:
687:
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617:
514:
484:
452:
429:
397:
374:
339:
316:
185:
62:
25:signal-flow analysis
21:Ralph Beebe Blackman
1443:Control engineering
1428:Electronic feedback
1344:1990ITCS...37..455C
1200:1992ITEdu..35..253H
1112:1974ITEdu..17..192R
988:1990ITCS...37..455C
496:{\displaystyle Z\ }
469:
441:{\displaystyle Z\ }
414:
386:{\displaystyle Z\ }
359:
328:{\displaystyle Z\ }
280:
249:
221:
763:
733:
703:
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53:Blackman's formula
45:Solomon Rosenstark
17:Blackman's theorem
1448:Engineering stubs
1433:Signal processing
1390:
1389:
1245:978-0-7803-4455-6
1208:10.1109/13.144656
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37:R. D. Middlebrook
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1352:10.1109/31.52748
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1122:. Archived from
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1062:
1036:
1034:
1028:RD Middlebrook.
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1016:
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1011:
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996:10.1109/31.52748
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646:is the value of
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82:
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1325:
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900:
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867:
861:
840:
817:10.1.1.695.4656
810:(10): 658–662.
799:
794:
791:
789:Further reading
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1338:(4): 455–463.
1317:
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1213:
1194:(3): 253–261.
1170:
1163:
1136:
1106:(4): 192–198.
1087:978-0029478103
1086:
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1058:978-0521624718
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910:(3): 269–277.
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1306:. EDN Network
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1376:
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889:References
29:John Choma
812:CiteSeerX
466:∞
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1312:2014
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