20:
852:
imply wave propagation when sufficient inductance is in the circuit, this square diffusion relationship was thought to provide a fundamental limit to the improvement of long-distance telegraph cables. That old analysis was superseded in the telegraph domain, but remains relevant for long on-chip
769:
711:
577:
835:
The typical digital propagation delay of a resistive wire is about half of R times C; since both R and C are proportional to wire length, the delay scales as the square of wire length. Charge spreads by
309:
401:
499:
170:
209:
211:. The following formulae use it, assuming a constant voltage applied across the capacitor and resistor in series, to determine the voltage across the capacitor against time:
627:
119:, or to discharge the capacitor through the same resistor to approximately 36.8% of its final charge voltage. These values are derived from the mathematical constant
102:
1081:
429:
1029:
798:
transition, may be dominated by resistive-capacitive effects, depending on the distance and other parameters, or may alternatively be dominated by
1039:
57:
1002:
718:
660:
510:
975:
1012:
985:
775:
53:
225:
871:
323:
23:
582:
where resistance in ohms and capacitance in farads yields the time constant in seconds or the cutoff frequency in Hz.
447:
889:
121:
1106:
128:
849:
175:
19:
778:
provides a way of approximating the cutoff frequency by computing a sum of several RC time constants.
588:
960:
939:
866:
832:(typically silicon dioxide) to low-dielectric-constant materials, thus reducing the capacitance.
813:
820:, the RC delay plays an increasingly important role. This delay can be reduced by replacing the
1035:
1008:
981:
893:
884:
78:
906:
898:
862:
810:
432:
1066:
1062:
414:
115:, from an initial charge voltage of zero to approximately 63.2% of the value of an applied
902:
954:
774:
In more complicated circuits consisting of more than one resistor and/or capacitor, the
803:
116:
1111:
1100:
45:
1057:
809:
Resistive-capacitive delay, or RC delay, hinders the further increasing of speed in
795:
215:
Charging toward applied voltage (initially zero voltage across capacitor, constant
828:, thus reducing the resistance; it can also be reduced by changing the interlayer
915:
875:
841:
791:
787:
320:
across capacitor, constant zero voltage across resistor and capacitor together)
65:
911:
879:
829:
817:
799:
61:
920:
845:
837:
108:
1091:
821:
112:
825:
49:
1001:
Jari Nurmi; Hannu
Tenhunen; Jouni Isoaho & Axel Jantsch (2004).
816:. When the feature size becomes smaller and smaller to increase the
764:{\displaystyle t_{r}\approx 2.2\tau \approx {\frac {0.35}{f_{c}}}}
706:{\displaystyle t_{r}\approx 1.4\tau \approx {\frac {0.22}{f_{c}}}}
572:{\displaystyle f_{c}={\frac {1}{2\pi RC}}={\frac {1}{2\pi \tau }}}
69:
18:
41:
786:
The signal delay of a wire or other circuit, measured as
313:
Discharging toward zero from initial voltage (initially
304:{\displaystyle V_{0}:\quad V(t)=V_{0}(1-e^{-t/\tau })}
1069:
721:
663:
591:
513:
450:
417:
326:
228:
178:
131:
81:
56:(RC circuit), is equal to the product of the circuit
1004:
Interconnect-centric Design for
Advanced SoC and NoC
396:{\displaystyle V_{0}:\quad V(t)=V_{0}(e^{-t/\tau })}
1075:
763:
705:
621:
571:
493:
423:
395:
303:
203:
164:
96:
441:, an alternative parameter of the RC circuit, by
585:Short conditional equations using the value for
494:{\displaystyle \tau =RC={\frac {1}{2\pi f_{c}}}}
8:
1068:
753:
744:
726:
720:
695:
686:
668:
662:
602:
596:
590:
551:
527:
518:
512:
482:
466:
449:
416:
380:
373:
360:
331:
325:
288:
281:
262:
233:
227:
192:
177:
153:
144:
130:
80:
794:or the effective propagation delay of a
222:across resistor and capacitor together)
165:{\displaystyle 63.2\%\approx 1{-}e^{-1}}
931:
844:in the mid nineteenth century. Until
107:It is the time required to charge the
7:
204:{\displaystyle 36.8\%\approx e^{-1}}
182:
135:
14:
776:open-circuit time constant method
840:in such a wire, as explained by
1031:An Analog Electronics Companion
340:
242:
1034:. Cambridge University Press.
622:{\displaystyle 10^{6}/(2\pi )}
616:
607:
390:
366:
350:
344:
298:
268:
252:
246:
16:Time constant of an RC circuit
1:
639:in Hz = 159155 / τ in ÎĽs
653:Other useful equations are:
1058:RC Time Constant Calculator
1128:
890:Filter (signal processing)
54:resistor–capacitor circuit
1063:Conversion time constant
806:effects in other realms.
977:From Obscurity to Enigma
642:τ in ÎĽs = 159155 /
97:{\displaystyle \tau =RC}
1028:Scott Hamilton (2007).
940:"Capacitor Discharging"
715:rise time (10% to 90%)
657:rise time (20% to 80%)
1077:
765:
707:
623:
573:
495:
425:
397:
305:
205:
166:
98:
27:
1083:to cutoff frequency f
1078:
1076:{\displaystyle \tau }
766:
708:
624:
574:
496:
426:
424:{\displaystyle \tau }
398:
306:
206:
167:
99:
22:
1067:
953:Andrew Gray (1908).
719:
661:
589:
511:
448:
415:
324:
226:
176:
129:
79:
974:Ido Yavetz (1995).
850:Maxwell's equations
824:conducting wire by
814:integrated circuits
1073:
867:frequency response
761:
703:
619:
569:
504:or, equivalently,
491:
431:is related to the
421:
411:The time constant
393:
301:
201:
162:
94:
64:) and the circuit
28:
1041:978-0-521-68780-5
894:transfer function
885:Exponential decay
759:
701:
567:
546:
489:
1119:
1092:RC time constant
1082:
1080:
1079:
1074:
1046:
1045:
1025:
1019:
1018:
998:
992:
991:
971:
965:
964:
959:. Dent. p.
950:
944:
943:
936:
907:band-pass filter
899:High-pass filter
863:Cutoff frequency
848:discovered that
770:
768:
767:
762:
760:
758:
757:
745:
731:
730:
712:
710:
709:
704:
702:
700:
699:
687:
673:
672:
628:
626:
625:
620:
606:
601:
600:
578:
576:
575:
570:
568:
566:
552:
547:
545:
528:
523:
522:
500:
498:
497:
492:
490:
488:
487:
486:
467:
433:cutoff frequency
430:
428:
427:
422:
407:Cutoff frequency
402:
400:
399:
394:
389:
388:
384:
365:
364:
336:
335:
310:
308:
307:
302:
297:
296:
292:
267:
266:
238:
237:
210:
208:
207:
202:
200:
199:
171:
169:
168:
163:
161:
160:
148:
103:
101:
100:
95:
38:
32:RC time constant
1127:
1126:
1122:
1121:
1120:
1118:
1117:
1116:
1107:Analog circuits
1097:
1096:
1086:
1065:
1064:
1054:
1049:
1042:
1027:
1026:
1022:
1015:
1000:
999:
995:
988:
973:
972:
968:
952:
951:
947:
938:
937:
933:
929:
903:low-pass filter
859:
853:interconnects.
811:microelectronic
784:
749:
722:
717:
716:
691:
664:
659:
658:
648:
638:
592:
587:
586:
556:
532:
514:
509:
508:
478:
471:
446:
445:
440:
413:
412:
409:
369:
356:
327:
322:
321:
319:
318:
277:
258:
229:
224:
223:
221:
220:
188:
174:
173:
149:
127:
126:
77:
76:
36:
17:
12:
11:
5:
1125:
1123:
1115:
1114:
1109:
1099:
1098:
1095:
1094:
1089:
1084:
1072:
1060:
1053:
1052:External links
1050:
1048:
1047:
1040:
1020:
1013:
993:
986:
980:. Birkhäuser.
966:
945:
930:
928:
925:
924:
923:
918:
909:
896:
887:
882:
869:
858:
855:
804:speed of light
783:
780:
772:
771:
756:
752:
748:
743:
740:
737:
734:
729:
725:
713:
698:
694:
690:
685:
682:
679:
676:
671:
667:
651:
650:
646:
640:
636:
618:
615:
612:
609:
605:
599:
595:
580:
579:
565:
562:
559:
555:
550:
544:
541:
538:
535:
531:
526:
521:
517:
502:
501:
485:
481:
477:
474:
470:
465:
462:
459:
456:
453:
438:
420:
408:
405:
404:
403:
392:
387:
383:
379:
376:
372:
368:
363:
359:
355:
352:
349:
346:
343:
339:
334:
330:
316:
314:
311:
300:
295:
291:
287:
284:
280:
276:
273:
270:
265:
261:
257:
254:
251:
248:
245:
241:
236:
232:
218:
216:
198:
195:
191:
187:
184:
181:
159:
156:
152:
147:
143:
140:
137:
134:
111:, through the
105:
104:
93:
90:
87:
84:
15:
13:
10:
9:
6:
4:
3:
2:
1124:
1113:
1110:
1108:
1105:
1104:
1102:
1093:
1090:
1088:
1070:
1061:
1059:
1056:
1055:
1051:
1043:
1037:
1033:
1032:
1024:
1021:
1016:
1014:1-4020-7835-8
1010:
1006:
1005:
997:
994:
989:
987:3-7643-5180-2
983:
979:
978:
970:
967:
962:
958:
957:
949:
946:
941:
935:
932:
926:
922:
919:
917:
913:
910:
908:
904:
900:
897:
895:
891:
888:
886:
883:
881:
877:
873:
870:
868:
864:
861:
860:
856:
854:
851:
847:
843:
839:
833:
831:
827:
823:
819:
815:
812:
807:
805:
801:
797:
793:
789:
781:
779:
777:
754:
750:
746:
741:
738:
735:
732:
727:
723:
714:
696:
692:
688:
683:
680:
677:
674:
669:
665:
656:
655:
654:
645:
641:
635:
632:
631:
630:
613:
610:
603:
597:
593:
583:
563:
560:
557:
553:
548:
542:
539:
536:
533:
529:
524:
519:
515:
507:
506:
505:
483:
479:
475:
472:
468:
463:
460:
457:
454:
451:
444:
443:
442:
437:
434:
418:
406:
385:
381:
377:
374:
370:
361:
357:
353:
347:
341:
337:
332:
328:
312:
293:
289:
285:
282:
278:
274:
271:
263:
259:
255:
249:
243:
239:
234:
230:
214:
213:
212:
196:
193:
189:
185:
179:
157:
154:
150:
145:
141:
138:
132:
124:
123:
118:
114:
110:
91:
88:
85:
82:
75:
74:
73:
71:
67:
63:
59:
55:
51:
47:
46:time constant
43:
39:
33:
25:
21:
1030:
1023:
1007:. Springer.
1003:
996:
976:
969:
955:
948:
934:
834:
808:
802:, wave, and
785:
773:
652:
643:
633:
584:
581:
503:
435:
410:
120:
106:
35:
31:
29:
956:Lord Kelvin
916:RLC circuit
876:preemphasis
842:Lord Kelvin
818:clock speed
792:phase delay
788:group delay
66:capacitance
40:(lowercase
1101:Categories
927:References
912:RL circuit
880:deemphasis
830:dielectric
117:DC voltage
58:resistance
34:, denoted
26:RC circuit
1071:τ
921:Rise time
846:Heaviside
838:diffusion
800:inductive
742:≈
739:τ
733:≈
684:≈
681:τ
675:≈
614:π
564:τ
561:π
537:π
476:π
452:τ
419:τ
386:τ
375:−
294:τ
283:−
275:−
194:−
186:≈
183:%
155:−
146:−
139:≈
136:%
109:capacitor
83:τ
1087:and back
872:Emphasis
857:See also
822:aluminum
125:, where
113:resistor
796:digital
52:) of a
50:seconds
44:), the
1038:
1011:
984:
914:, and
826:copper
70:farads
24:Series
782:Delay
649:in Hz
1112:Time
1036:ISBN
1009:ISBN
982:ISBN
892:and
865:and
747:0.35
689:0.22
180:36.8
172:and
133:63.2
72:):
68:(in
62:ohms
60:(in
48:(in
30:The
961:265
790:or
736:2.2
678:1.4
42:tau
1103::
905:,
901:,
878:,
874:,
629::
594:10
1085:c
1044:.
1017:.
990:.
963:.
942:.
755:c
751:f
728:r
724:t
697:c
693:f
670:r
666:t
647:c
644:f
637:c
634:f
617:)
611:2
608:(
604:/
598:6
558:2
554:1
549:=
543:C
540:R
534:2
530:1
525:=
520:c
516:f
484:c
480:f
473:2
469:1
464:=
461:C
458:R
455:=
439:c
436:f
391:)
382:/
378:t
371:e
367:(
362:0
358:V
354:=
351:)
348:t
345:(
342:V
338::
333:0
329:V
317:0
315:V
299:)
290:/
286:t
279:e
272:1
269:(
264:0
260:V
256:=
253:)
250:t
247:(
244:V
240::
235:0
231:V
219:0
217:V
197:1
190:e
158:1
151:e
142:1
122:e
92:C
89:R
86:=
37:Ď„
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
