908:
916:
125:
137:
1057:
152:
will have a roll-off of 20 dB/decade. This is approximately equal (to within normal engineering required accuracy) to 6 dB/octave and is the more usual description given for this roll-off. This can be shown to be so by considering the voltage
374:
726:
1133:
machines. Here the filters mostly make do with a basic 6 dB/8ve roll-off, however, some instruments provide a switchable 35 Hz filter at the high frequency end with a faster roll-off to help filter out noise generated by muscle activity.
91:
point of the frequency curve. Roll-off enables the cut-off performance of such a filter network to be reduced to a single number. Note that roll-off can occur with decreasing frequency as well as increasing frequency, depending on the
600:
897:
514:
1076:
construction is used to realise the filter. In a ladder filter each section of the filter has an effect on its immediate neighbours and a lesser effect on more remote sections so the response is not a simple
1044:
239:
1129:: here the need is not so much for a high roll-off but that the roll-offs of the high frequency and low-frequency sections are symmetrical and complementary. An interesting need for high roll-off arises in
439:
810:
981:
1105:
the roll-off near the cut-off frequency is much faster and elsewhere the response is anything but monotonic. Nevertheless, all filter classes eventually converge to a roll-off of 6
68:
of the network, but can, in principle, be applied to any relevant function of frequency, and any technology, not just electronics. It is usual to measure roll-off as a function of
264:
611:
1109: dB/8ve theoretically at some arbitrarily high frequency, but in many applications this will occur in a frequency band of no interest to the application and
529:
116:; the same principles may be applied to high-pass filters by interchanging phrases such as "above cut-off frequency" and "below cut-off frequency".
821:
87:
The concept of roll-off stems from the fact that in many networks roll-off tends towards a constant gradient at frequencies well away from the
112:
will roll-off with decreasing frequency. For brevity, this article describes only low-pass filters. This is to be taken in the spirit of
450:
992:
167:
1072:
The calculation of transfer function becomes somewhat more complicated when the sections are not all identical, or when the popular
385:
145:
737:
49:
1311:
1285:
1270:
1255:
1204:
1174:
1122:
1121:
Filters with a high roll-off were first developed to prevent crosstalk between adjacent channels on telephone
941:
935:
identical first-order sections in cascade, the voltage transfer function of the complete network is given by;
369:{\displaystyle |A|^{2}={\frac {1}{1+\left({\omega \over \omega _{c}}\right)^{2}}}={\frac {1}{1+\omega ^{2}}}}
1306:
721:{\displaystyle \Delta L=20\log \left({\omega _{2} \over \omega _{1}}\right)\ \mathrm {dB/interval_{2,1}} }
924:
1301:
93:
53:
244:
1065:
1061:
17:
1110:
1060:
LC low-pass ladder circuit. Each element (that is L or C) adds an order to the filter and a
923:
A higher order network can be constructed by cascading first-order sections together. If a
27:
Steepness of a transfer function with frequency, particularly in electrical network analysis
81:
8:
31:
1086:
1082:
77:
595:{\displaystyle L\approx 10\log \left(\omega ^{2}\right)=20\log \omega \ \mathrm {dB} }
1281:
1266:
1251:
1200:
1170:
154:
88:
69:
41:
30:
This article is about roll-off in electrical network analysis. For the dumpster, see
1098:
113:
109:
101:
1126:
1102:
1073:
919:
Roll-off graph of higher-order low-pass filters showing various rates of roll-off
907:
140:
Roll-off of a first-order low-pass filter at 6 dB/octave (20 dB/decade)
129:
97:
1081:
even when all the sections are identical. For some filter classes, such as the
931:
is used) there is no interaction between the stages. In that circumstance, for
80:(dB/decade), where a decade is a tenfold increase in frequency, or decibels per
1050:
65:
1295:
928:
915:
892:{\displaystyle \Delta L=20\log 2\approx 20\times 0.3=6\ \mathrm {dB/8ve} }
124:
149:
1143:
1090:
136:
45:
1056:
1053:
by repeatedly applying the same filtering algorithm to the signal.
509:{\displaystyle L=10\log \left({1+\omega ^{2}}\right)\ \mathrm {dB} }
1250:, pages 23–25, Society for Industrial and Applied Mathematics 1998
1167:
Advanced AC circuits and electronics: principles & applications
105:
61:
57:
1039:{\displaystyle \Delta L_{\text{T}}=n\,\Delta L=6n{\text{ dB/8ve}}}
234:{\displaystyle A={\frac {V_{o}}{V_{i}}}={\frac {1}{1+i\omega RC}}}
73:
434:{\displaystyle 10\log \left({\frac {1}{1+\omega ^{2}}}\right)}
84:(dB/8ve), where an octave is a twofold increase in frequency.
1248:
Classical control using H methods: an introduction to design
1125:
systems. Roll-off is also significant on audio loudspeaker
805:{\displaystyle \Delta L=20\log 10=20\ \mathrm {dB/decade} }
1278:
Fundamentals of EEG Technology: Basic concepts and methods
72:
frequency; consequently, the units of roll-off are either
1130:
1280:, pages 101–102, Lippincott Williams & Wilkins 1983
1276:
Fay S. Tyner, John
Russell Knott, W. Brem Mayer (ed.),
1113:
may well start to dominate long before this happens.
995:
944:
824:
740:
614:
532:
453:
388:
267:
170:
1216:Lundheim, L, "On Shannon and "Shannon's Formula",
1038:
975:
891:
804:
720:
594:
508:
433:
368:
258: = 1 and forming the power ratio gives,
233:
911:Multiple order RC filter buffered between stages.
1293:
1199:, pages 129–130, McGraw-Hill Professional 2007
100:will roll-off with increasing frequency, but a
96:of the filter being considered: for instance a
986:consequently, the total roll-off is given by,
927:is placed between each section (or some other
1263:Event-related potentials: a methods handbook
1197:Electronic filter simulation & design
1097: dB/8ve, but in others, such as the
1015:
52:, and most especially in connection with
1055:
1049:A similar effect can be achieved in the
976:{\displaystyle A_{\mathrm {T} }=A^{n}\ }
914:
906:
902:
135:
123:
1265:, pages 89–92, 107–109, MIT Press 2004
1169:, pages 150-152, Cengage Learning 2003
1161:
1159:
119:
64:. It is most typically applied to the
14:
1294:
1195:Giovanni Bianchi, Roberto Sorrentino,
1089:increasing with frequency and quickly
1156:
1246:J. William Helton, Orlando Merino,
24:
1016:
996:
951:
885:
882:
871:
868:
825:
798:
795:
792:
789:
786:
783:
775:
772:
741:
702:
698:
695:
692:
689:
686:
683:
680:
672:
669:
615:
588:
585:
502:
499:
25:
1323:
1116:
1227:
1210:
1189:
1180:
1085:, the insertion loss is still
278:
269:
13:
1:
1240:
1093:converges to a roll-off of 6
56:in the transition between a
7:
1137:
925:unity gain buffer amplifier
50:electrical network analysis
10:
1328:
519:At frequencies well above
379:In decibels this becomes,
29:
1312:Filter frequency response
1224:, no. 1, 2002, pp. 24–25.
1233:Mayer et al, pp 104–105.
1149:
523:=1, this simplifies to,
444:or expressed as a loss,
1066:driving point impedance
1069:
1040:
977:
920:
912:
893:
806:
731:For a decade this is;
722:
605:Roll-off is given by,
596:
510:
435:
370:
235:
141:
133:
128:First-order RC filter
40:is the steepness of a
1059:
1041:
978:
918:
910:
903:Higher order networks
894:
807:
723:
597:
511:
436:
371:
236:
161:, of the RC network:
139:
127:
993:
942:
822:
738:
612:
530:
451:
386:
265:
168:
120:First-order roll-off
1307:Tone, EQ and filter
815:and for an octave,
32:Roll-off (dumpster)
1165:J. Michael Jacob,
1083:Butterworth filter
1070:
1036:
973:
921:
913:
889:
802:
718:
592:
506:
431:
366:
231:
148:network such as a
142:
134:
48:, particularly in
1302:Electronic design
1127:crossover filters
1111:parasitic effects
1034:
1006:
972:
866:
770:
667:
659:
583:
497:
425:
364:
336:
323:
245:Frequency scaling
229:
199:
155:transfer function
114:prototype filters
42:transfer function
16:(Redirected from
1319:
1234:
1231:
1225:
1214:
1208:
1193:
1187:
1186:Todd, pp 107–108
1184:
1178:
1163:
1045:
1043:
1042:
1037:
1035:
1032:
1008:
1007:
1004:
982:
980:
979:
974:
970:
969:
968:
956:
955:
954:
898:
896:
895:
890:
888:
878:
864:
811:
809:
808:
803:
801:
782:
768:
727:
725:
724:
719:
717:
716:
715:
679:
665:
664:
660:
658:
657:
648:
647:
638:
601:
599:
598:
593:
591:
581:
565:
561:
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515:
513:
512:
507:
505:
495:
494:
490:
489:
488:
440:
438:
437:
432:
430:
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422:
403:
375:
373:
372:
367:
365:
363:
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361:
342:
337:
335:
334:
333:
328:
324:
322:
321:
309:
292:
287:
286:
281:
272:
240:
238:
237:
232:
230:
228:
205:
200:
198:
197:
188:
187:
178:
110:band-pass filter
102:high-pass filter
21:
1327:
1326:
1322:
1321:
1320:
1318:
1317:
1316:
1292:
1291:
1261:Todd C. Handy,
1243:
1238:
1237:
1232:
1228:
1215:
1211:
1194:
1190:
1185:
1181:
1164:
1157:
1152:
1140:
1119:
1103:elliptic filter
1074:ladder topology
1031:
1003:
999:
994:
991:
990:
964:
960:
950:
949:
945:
943:
940:
939:
929:active topology
905:
874:
867:
823:
820:
819:
778:
771:
739:
736:
735:
705:
701:
675:
668:
653:
649:
643:
639:
637:
633:
613:
610:
609:
584:
556:
552:
548:
531:
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527:
498:
484:
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473:
469:
452:
449:
448:
418:
414:
407:
402:
398:
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384:
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357:
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329:
317:
313:
308:
304:
303:
296:
291:
282:
277:
276:
268:
266:
263:
262:
254: = 1/
253:
209:
204:
193:
189:
183:
179:
177:
169:
166:
165:
130:low-pass filter
122:
98:low-pass filter
54:filter circuits
35:
28:
23:
22:
15:
12:
11:
5:
1325:
1315:
1314:
1309:
1304:
1290:
1289:
1274:
1259:
1242:
1239:
1236:
1235:
1226:
1209:
1188:
1179:
1154:
1153:
1151:
1148:
1147:
1146:
1139:
1136:
1118:
1115:
1091:asymptotically
1051:digital domain
1047:
1046:
1030:
1027:
1024:
1021:
1018:
1014:
1011:
1002:
998:
984:
983:
967:
963:
959:
953:
948:
904:
901:
900:
899:
887:
884:
881:
877:
873:
870:
863:
860:
857:
854:
851:
848:
845:
842:
839:
836:
833:
830:
827:
813:
812:
800:
797:
794:
791:
788:
785:
781:
777:
774:
767:
764:
761:
758:
755:
752:
749:
746:
743:
729:
728:
714:
711:
708:
704:
700:
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691:
688:
685:
682:
678:
674:
671:
663:
656:
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629:
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623:
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602:
590:
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580:
577:
574:
571:
568:
564:
559:
555:
551:
547:
544:
541:
538:
535:
517:
516:
504:
501:
493:
487:
483:
479:
476:
472:
468:
465:
462:
459:
456:
442:
441:
429:
421:
417:
413:
410:
406:
401:
397:
394:
391:
377:
376:
360:
356:
352:
349:
345:
340:
332:
327:
320:
316:
312:
307:
302:
299:
295:
290:
285:
280:
275:
271:
251:
242:
241:
227:
224:
221:
218:
215:
212:
208:
203:
196:
192:
186:
182:
176:
173:
121:
118:
66:insertion loss
26:
9:
6:
4:
3:
2:
1324:
1313:
1310:
1308:
1305:
1303:
1300:
1299:
1297:
1287:
1286:0-89004-385-X
1283:
1279:
1275:
1272:
1271:0-262-08333-7
1268:
1264:
1260:
1257:
1256:0-89871-424-9
1253:
1249:
1245:
1244:
1230:
1223:
1219:
1213:
1206:
1205:0-07-149467-7
1202:
1198:
1192:
1183:
1176:
1175:0-7668-2330-X
1172:
1168:
1162:
1160:
1155:
1145:
1142:
1141:
1135:
1132:
1128:
1124:
1114:
1112:
1108:
1104:
1100:
1096:
1092:
1088:
1087:monotonically
1084:
1080:
1075:
1067:
1063:
1058:
1054:
1052:
1028:
1025:
1022:
1019:
1012:
1009:
1000:
989:
988:
987:
965:
961:
957:
946:
938:
937:
936:
934:
930:
926:
917:
909:
879:
875:
861:
858:
855:
852:
849:
846:
843:
840:
837:
834:
831:
828:
818:
817:
816:
779:
765:
762:
759:
756:
753:
750:
747:
744:
734:
733:
732:
712:
709:
706:
676:
661:
654:
650:
644:
640:
634:
630:
627:
624:
621:
618:
608:
607:
606:
578:
575:
572:
569:
566:
562:
557:
553:
549:
545:
542:
539:
536:
533:
526:
525:
524:
522:
491:
485:
481:
477:
474:
470:
466:
463:
460:
457:
454:
447:
446:
445:
427:
419:
415:
411:
408:
404:
399:
395:
392:
389:
382:
381:
380:
358:
354:
350:
347:
343:
338:
330:
325:
318:
314:
310:
305:
300:
297:
293:
288:
283:
273:
261:
260:
259:
257:
250:
246:
225:
222:
219:
216:
213:
210:
206:
201:
194:
190:
184:
180:
174:
171:
164:
163:
162:
160:
156:
151:
147:
138:
131:
126:
117:
115:
111:
107:
104:or the lower
103:
99:
95:
90:
85:
83:
79:
75:
71:
67:
63:
59:
55:
51:
47:
43:
39:
33:
19:
1277:
1262:
1247:
1229:
1221:
1218:Telektronikk
1217:
1212:
1196:
1191:
1182:
1166:
1120:
1117:Applications
1106:
1094:
1078:
1071:
1048:
1033: dB/8ve
985:
932:
922:
814:
730:
604:
520:
518:
443:
378:
255:
248:
243:
158:
143:
86:
37:
36:
146:first-order
70:logarithmic
1296:Categories
1241:References
150:RC circuit
1144:Bode plot
1099:Chebyshev
1017:Δ
997:Δ
853:×
847:≈
841:
826:Δ
757:
742:Δ
651:ω
641:ω
631:
616:Δ
579:ω
576:
554:ω
546:
537:≈
482:ω
467:
416:ω
396:
355:ω
315:ω
311:ω
220:ω
144:A simple
46:frequency
1138:See also
247:this to
132:circuit.
106:stopband
94:bandform
74:decibels
62:stopband
58:passband
38:Roll-off
1222:vol. 98
1064:to the
89:cut-off
18:Rolloff
1284:
1269:
1254:
1203:
1173:
971:
865:
769:
666:
582:
496:
82:octave
78:decade
60:and a
1150:Notes
108:of a
44:with
1282:ISBN
1267:ISBN
1252:ISBN
1201:ISBN
1171:ISBN
1062:pole
76:per
1131:EEG
1123:FDM
1101:or
856:0.3
838:log
754:log
628:log
573:log
543:log
464:log
393:log
1298::
1220:,
1158:^
850:20
835:20
766:20
760:10
751:20
625:20
570:20
540:10
461:10
390:10
256:RC
157:,
1288:.
1273:.
1258:.
1207:.
1177:.
1107:n
1095:n
1079:A
1068:.
1029:n
1026:6
1023:=
1020:L
1013:n
1010:=
1005:T
1001:L
966:n
962:A
958:=
952:T
947:A
933:n
886:e
883:v
880:8
876:/
872:B
869:d
862:6
859:=
844:2
832:=
829:L
799:e
796:d
793:a
790:c
787:e
784:d
780:/
776:B
773:d
763:=
748:=
745:L
713:1
710:,
707:2
703:l
699:a
696:v
693:r
690:e
687:t
684:n
681:i
677:/
673:B
670:d
662:)
655:1
645:2
635:(
622:=
619:L
589:B
586:d
567:=
563:)
558:2
550:(
534:L
521:ω
503:B
500:d
492:)
486:2
478:+
475:1
471:(
458:=
455:L
428:)
420:2
412:+
409:1
405:1
400:(
359:2
351:+
348:1
344:1
339:=
331:2
326:)
319:c
306:(
301:+
298:1
294:1
289:=
284:2
279:|
274:A
270:|
252:c
249:ω
226:C
223:R
217:i
214:+
211:1
207:1
202:=
195:i
191:V
185:o
181:V
175:=
172:A
159:A
34:.
20:)
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