373:
445:
655:
473:
520:
36:
411:
339:
2308:
2288:
429:
357:
602:
464:
420:
348:
1575:
696:
2577:
283:). Campbell published in 1922 but had clearly been using the topology for some time before this. Cauer first picked up on ladders (published 1926) inspired by the work of Foster (1924). There are two forms of basic ladder topologies: unbalanced and balanced. Cauer topology is usually thought of as an unbalanced ladder topology.
543:
rejection or passband-to-stopband transition steepness. Usually the design applies some transform to a simple ladder topology: the resulting topology is ladder-like but no longer obeys the rule that shunt admittances are the dual network of series impedances: it invariably becomes more complex with
588:
The mm'-type topology can be thought of as a double m-type design. Like the m-type it has the same bandform but offers further improved transfer characteristics. It is, however, a rarely used design due to increased component count and complexity as well as its normally requiring basic ladder and
93:
612:
Zobel constant resistance filters use a topology that is somewhat different from other filter types, distinguished by having a constant input resistance at all frequencies and in that they use resistive components in the design of their sections. The higher component and section count of these
236:
Some passive filters, consisting of only one or two filter sections, are given special names including the L-section, T-section and Î -section, which are unbalanced filters, and the C-section, H-section and box-section, which are balanced. All are built upon a very simple "ladder" topology (see
909:
568:
The m-type (m-derived) filter is by far the most commonly used modified image ladder topology. There are two m-type topologies for each of the basic ladder topologies; the series-derived and shunt-derived topologies. These have identical transfer functions to each other but different image
569:
impedances. Where a filter is being designed with more than one passband, the m-type topology will result in a filter where each passband has an analogous frequency-domain response. It is possible to generalise the m-type topology for filters with more than one passband using parameters m
662:
Both the T-section (from ladder topology) and the bridge-T (from Zobel topology) can be transformed into a lattice topology filter section but in both cases this results in high component count and complexity. The most common application of lattice filters (X-sections) is in
2279:, after the order of the second integrator and the inverter has been switched. If a noninverting bandpass filter is required, the order of the second integrator and the inverter can be switched, and the output taken at the output of the inverter's operational amplifier.
1931:
1726:
1553:
The two-integrator-loop topology is derived from rearranging a biquadratic transfer function. The rearrangement will equate one signal with the sum of another signal, its integral, and the integral's integral. In other words, the rearrangement reveals a
1291:
727:
1455:
674:
Although T and bridged-T sections can always be transformed into X-sections the reverse is not always possible because of the possibility of negative values of inductance and capacitance arising in the transform.
2188:
1102:
2090:
1803:
2001:
1795:
2441:
This means Sallen-Key filters, state-variable variable filters, multiple feedback filters and other types are all biquads. There also is a "biquad" topology to help further confuse things.
1599:
986:
613:
designs usually limits their use to equalisation applications. Topologies usually associated with constant resistance filters are the bridged-T and its variants, all described in the
2479:
plethora of single-amplifier second-order active filter circuits … whose numerator and denominator are of second order, i.e., biquadratic; they are therefore referred to as "biquads"
221:
called "sections". There is no formal definition of a section except that it must have at least one series component and one shunt component. Sections are invariably connected in a
493:
Textbooks and design drawings usually show the unbalanced implementations, but in telecoms it is often required to convert the design to the balanced implementation when used with
1349:
2233:
1152:
2375:
General Wave-filters having any Pre-assigned
Transmitting and Attenuating Bands and Propagation Constants Adjustable Without Changing one Mid-point Characteristic Impedance
2296:
2273:
2429:
252:, on the other hand, keep the same basic component values from section to section though the topology may vary and tend to make use of more complex sections.
1160:
2456:
Analog circuit theory and filter design in the digital world : with an introduction to the morphological method for creative solutions and design
904:{\displaystyle H(s)={\frac {V_{o}}{V_{i}}}=-{\frac {1}{As^{2}+Bs+C}}={\frac {K{\omega _{0}}^{2}}{s^{2}+{\frac {\omega _{0}}{Q}}s+{\omega _{0}}^{2}}}}
640:
The bridged-T topology is also used in sections intended to produce a signal delay but in this case no resistive components are used in the design.
2491:
255:
L-sections are never symmetrical but two L-sections back-to-back form a symmetrical topology and many other sections are symmetrical in form.
1512:, such as the MFB or Sallen-Key. However, there is also a specific "biquad" topology. It is also sometimes called the 'ring of 3' circuit.
1359:
2101:
2581:
682:, the difference being merely the drawn representation on the page rather than any real difference in topology, circuitry or function.
992:
298:
of the series impedances if they were duals in the starting network - which is the case with series inductors and shunt capacitors.
229:
topology, consisting of additional copies of the same section or of completely different sections. The rules of series and parallel
185:(such as transistors, op amps, and other integrated circuits) that require power. Further, topologies may be implemented either in
2013:
290:
form the topology would consist of series inductors and shunt capacitors. Other bandforms would have an equally simple topology
112:
circuits without taking note of the values of the components used but only the manner in which those components are connected.
2464:
1926:{\displaystyle H(s)={\frac {G_{\mathrm {bpf} }{\frac {\omega _{0}}{Q}}s}{s^{2}+{\frac {\omega _{0}}{Q}}s+{\omega _{0}}^{2}}}}
1461:
For finding suitable component values to achieve the desired filter properties, a similar approach can be followed as in the
226:
2597:
214:
2421:
1940:
1734:
1721:{\displaystyle H(s)={\frac {G_{\mathrm {lpf} }{\omega _{0}}^{2}}{s^{2}+{\frac {\omega _{0}}{Q}}s+{\omega _{0}}^{2}}}}
79:
57:
50:
535:
as the ladder on which they are based but their transfer functions are modified to improve some parameter such as
1462:
921:
170:
1562:
The SAB topology is sensitive to component choice and can be more difficult to adjust. Hence, usually the term
178:
558:
182:
17:
714:. A diagram of the circuit topology for a second order low pass filter is shown in the figure on the right.
527:
Image filter design commonly uses modifications of the basic ladder topology. These topologies, invented by
248:
usually repeat the simplest form of L-section topology though component values may change in each section.
291:
233:
would combine two sections consisting only of series components or shunt components into a single section.
2321:
The Sallen-Key design is a non-inverting second-order filter with the option of high Q and passband gain.
2549:
Zobel, O J, "Distortion correction in electrical networks with constant resistance recurrent networks",
501:
286:
A ladder network consists of cascaded asymmetrical L-sections (unbalanced) or C-sections (balanced). In
1302:
2275:. If a noninverting low-pass filter is required, the output can be taken at the output of the second
2197:
1108:
245:
1558:
structure. By using different states as outputs, any kind of second-order filter can be implemented.
2373:
There is no universally-recognised name for this kind of filter: Zobel (1923, p.11) used the title
44:
2538:
Cauer, W, "Die
Verwirklichung der Wechselstromwiderstande vorgeschriebener Frequenzabhängigkeit",
589:
m-type sections in the same filter for impedance matching reasons. It is normally only found in a
2241:
1539:
1535:
668:
585:-type filters which have bandforms that can differ in different parts of the frequency spectrum.
249:
163:
154:. Once the transfer function for a filter is chosen, the particular topology to implement such a
2335:
590:
276:
237:
below). The chart at the bottom of the page shows these various topologies in terms of general
105:
61:
2345:
2276:
1555:
1475:
654:
372:
230:
2299:, that uses an actively compensated Miller integrator, which improves filter performance.
8:
2316:
444:
294:
from the lowpass topology. The transformed network will have shunt admittances that are
2485:
1495:
1352:
717:
The transfer function of the multiple feedback topology circuit, like all second-order
553:
536:
519:
222:
159:
472:
2470:
2460:
2007:
1491:
1286:{\displaystyle Q={\frac {\sqrt {R_{3}R_{4}C_{2}C_{5}}}{(R_{4}+R_{3}+|K|R_{3})C_{5}}}}
711:
707:
280:
238:
119:
109:
2330:
2236:
1587:
548:
218:
198:
194:
155:
147:
143:
135:
131:
96:
An elementary filter topology introduces a capacitor into the feedback path of an
1583:
664:
649:
305:
287:
272:
186:
151:
139:
2516:
Zobel, O J, "Theory and Design of
Uniform and Composite Electric Wave Filters",
2095:
1532:
295:
2474:
410:
338:
100:
to achieve an unbalanced active implementation of a low-pass transfer function
2591:
2340:
2307:
1516:
1487:
718:
614:
268:
190:
174:
127:
115:
2454:
2287:
428:
202:
356:
1582:
For example, the basic configuration in Figure 1 can be used as either a
1543:
1504:
601:
463:
419:
347:
181:: resistors, capacitors, and inductors. Active topologies also include
1547:
1450:{\displaystyle \omega _{0}=2\pi f_{0}=1/{\sqrt {R_{3}R_{4}C_{2}C_{5}}}}
528:
2183:{\displaystyle Q={\sqrt {\frac {{R_{3}}^{2}C_{1}}{R_{2}R_{4}C_{2}}}}}
1294:
606:
605:
Typical bridged-T Zobel network equaliser used to correct high end
540:
532:
494:
158:
can be selected so that, for example, one might choose to design a
123:
92:
1566:
refers to the two-integrator-loop state variable filter topology.
1574:
2576:
2564:, US patent 1 792 523, filed 12 March 1927, issued 17 Feb 1931.
1097:{\displaystyle B=R_{3}C_{5}+R_{1}C_{5}+R_{1}R_{3}C_{5}/R_{4}\,}
706:
is an electronic filter topology which is used to implement an
695:
97:
2509:
Campbell, G A, "Physical Theory of the
Electric Wave-Filter",
2295:
Figure 2 shows a variant of the Tow-Thomas topology, known as
581:
etc., which are not equal to each other resulting in general m
2085:{\displaystyle \omega _{0}=1/{\sqrt {R_{2}R_{4}C_{1}C_{2}}}}
1590:
filter depending on where the output signal is taken from.
1508:. Any second-order filter topology can be referred to as a
1797:. The second-order bandpass transfer function is given by
27:
Electronic filter circuits defined by component connection
1593:
The second-order low-pass transfer function is given by
2291:
Figure 2. The
Akerberg-Mossberg biquad filter topology.
1578:
Figure 1. The common Tow-Thomas biquad filter topology.
1550:
in order to generate the proper filter characteristics.
1474:
For the digital implementation of a biquad filter, see
134:. Common types of linear filter transfer function are;
177:
types. Passive topologies are composed exclusively of
2311:
Figure 1: The generic Sallen–Key filter topology
2244:
2200:
2104:
2016:
1943:
1806:
1737:
1602:
1362:
1305:
1163:
1111:
995:
924:
730:
678:Lattice topology is identical to the more familiar
2267:
2227:
2182:
2084:
1995:
1925:
1789:
1720:
1449:
1343:
1285:
1146:
1096:
980:
903:
658:Lattice topology X-section phase correction filter
544:higher component count. Such topologies include;
118:characterises filter circuits primarily by their
2589:
1465:section of the alternative Sallen–Key topology.
1996:{\displaystyle G_{\mathrm {bpf} }=-R_{3}/R_{1}}
1790:{\displaystyle G_{\mathrm {lpf} }=-R_{2}/R_{1}}
2513:, November 1922, vol. 1, no. 2, pp. 1–32.
690:
514:
300:
2377:. Since Zobel refers to the parameters as m
2282:
1531:The SAB topology uses feedback to generate
2490:: CS1 maint: location missing publisher (
981:{\displaystyle A=(R_{1}R_{3}C_{2}C_{5})\,}
205:may require arrays of identical circuits.
2422:"A Beginner's Guide to Filter Topologies"
2393:seems reasonable terminology to use here.
1468:
1340:
1143:
1093:
977:
636:Balanced short-circuit C-section topology
80:Learn how and when to remove this message
2452:
2306:
2286:
1573:
1542:. In particular, the feedback moves the
694:
653:
633:Balanced open-circuit C-section topology
600:
518:
303:
91:
43:This article includes a list of general
596:
14:
2590:
2302:
492:
169:Filter topologies may be divided into
331:
328:
325:
208:
2527:Foster, R M, "A reactance theorem",
2235:, and Q is sometimes expressed as a
1569:
685:
383:
313:
258:
29:
699:Multiple feedback topology circuit.
643:
24:
1956:
1953:
1950:
1837:
1834:
1831:
1750:
1747:
1744:
1633:
1630:
1627:
471:
462:
443:
427:
418:
409:
371:
355:
346:
337:
49:it lacks sufficient corresponding
25:
2609:
2569:
2194:The bandwidth is approximated by
2575:
1344:{\displaystyle K=-R_{4}/R_{1}\,}
630:Short-circuit L-section topology
34:
2432:from the original on 2019-10-28
2228:{\displaystyle B=\omega _{0}/Q}
1147:{\displaystyle C=R_{1}/R_{4}\,}
627:Open-circuit L-section topology
2446:
2414:
2405:
2396:
2367:
2358:
1816:
1810:
1612:
1606:
1267:
1253:
1245:
1215:
974:
931:
740:
734:
263:Ladder topology, often called
13:
1:
2551:Bell System Technical Journal
2529:Bell System Technical Journal
2518:Bell System Technical Journal
2511:Bell System Technical Journal
2502:
1521:single-amplifier biquad (SAB)
1515:Biquad filters are typically
389:
317:
275:), was in fact first used by
217:. Most are built from simple
2453:Moschytz, George S. (2019).
126:. Transfer functions may be
7:
2324:
2268:{\displaystyle \zeta =1/2Q}
710:by adding two poles to the
624:Balanced bridged-T topology
499:
215:long in development and use
10:
2614:
2598:Electronic filter topology
2582:Electronic filter topology
2314:
2297:Akerberg-Mossberg topology
704:Multiple feedback topology
691:Multiple feedback topology
647:
515:Modified ladder topologies
457:X Section (mid-Î -Derived)
454:X Section (mid-T-Derived)
213:Passive filters have been
197:. Implementations such as
2546:, pp. 355–388, 1926.
2540:Archiv fĂĽr Elektrotechnik
2535:, pp. 259–267, 1924.
1494:that is the ratio of two
523:series m-derived topology
489:
485:
470:
461:
456:
453:
442:
437:
426:
417:
408:
403:
400:
397:
392:
370:
365:
354:
345:
336:
320:
164:Sallen–Key topology
2351:
2283:Akerberg-Mossberg filter
1519:and implemented with a
1457:is the corner frequency
244:Filters designed using
64:more precise citations.
2562:Phase-shifting network
2336:Topology (electronics)
2312:
2292:
2269:
2229:
2184:
2086:
1997:
1927:
1791:
1722:
1579:
1469:Biquad filter topology
1451:
1345:
1287:
1148:
1098:
982:
905:
700:
659:
609:
524:
476:
467:
448:
432:
423:
414:
376:
360:
351:
342:
250:Image designed filters
193:form when employed in
101:
2459:. Cham, Switzerland.
2346:State variable filter
2310:
2290:
2277:operational amplifier
2270:
2230:
2185:
2087:
2003:. In both cases, the
1998:
1928:
1792:
1723:
1577:
1556:state variable filter
1538:and possibly complex
1476:Digital biquad filter
1452:
1346:
1288:
1149:
1099:
983:
906:
698:
657:
604:
522:
475:
466:
447:
431:
422:
413:
375:
359:
350:
341:
95:
2584:at Wikimedia Commons
2557:(1928), p. 438.
2385:etc., the shorthand
2242:
2198:
2102:
2014:
1941:
1804:
1735:
1731:where low-pass gain
1600:
1360:
1303:
1161:
1109:
993:
922:
728:
597:Bridged-T topologies
148:band-reject or notch
2317:Sallen-Key topology
2303:Sallen–Key topology
1937:with bandpass gain
1525:two-integrator-loop
1496:quadratic functions
2313:
2293:
2265:
2225:
2180:
2082:
1993:
1923:
1787:
1718:
1580:
1490:that implements a
1447:
1351:is the DC voltage
1341:
1283:
1144:
1094:
978:
901:
701:
669:phase equalisation
660:
621:Bridged-T topology
610:
537:impedance matching
525:
477:
468:
449:
433:
424:
415:
377:
361:
352:
343:
239:constant k filters
209:Passive topologies
179:passive components
160:Butterworth filter
122:rather than their
104:Electronic filter
102:
2580:Media related to
2466:978-3-030-00096-7
2178:
2177:
2080:
2008:Natural frequency
1921:
1893:
1858:
1716:
1688:
1570:Tow-Thomas filter
1492:transfer function
1445:
1281:
1213:
915:In an MF filter,
899:
871:
811:
768:
712:transfer function
708:electronic filter
686:Active topologies
512:
511:
508:
507:
504:
481:
480:
381:
380:
281:constant k filter
279:(inventor of the
271:(inventor of the
259:Ladder topologies
246:network synthesis
219:two-port networks
199:electronic mixers
195:balanced circuits
183:active components
120:transfer function
110:electronic filter
90:
89:
82:
16:(Redirected from
2605:
2579:
2496:
2495:
2489:
2481:
2450:
2444:
2443:
2438:
2437:
2426:Maxim Integrated
2418:
2412:
2409:
2403:
2400:
2394:
2371:
2365:
2362:
2331:Prototype filter
2274:
2272:
2271:
2266:
2258:
2237:damping constant
2234:
2232:
2231:
2226:
2221:
2216:
2215:
2189:
2187:
2186:
2181:
2179:
2176:
2175:
2174:
2165:
2164:
2155:
2154:
2144:
2143:
2142:
2133:
2132:
2127:
2126:
2125:
2113:
2112:
2091:
2089:
2088:
2083:
2081:
2079:
2078:
2069:
2068:
2059:
2058:
2049:
2048:
2039:
2037:
2026:
2025:
2002:
2000:
1999:
1994:
1992:
1991:
1982:
1977:
1976:
1961:
1960:
1959:
1932:
1930:
1929:
1924:
1922:
1920:
1919:
1918:
1913:
1912:
1911:
1894:
1889:
1888:
1879:
1874:
1873:
1863:
1859:
1854:
1853:
1844:
1842:
1841:
1840:
1823:
1796:
1794:
1793:
1788:
1786:
1785:
1776:
1771:
1770:
1755:
1754:
1753:
1727:
1725:
1724:
1719:
1717:
1715:
1714:
1713:
1708:
1707:
1706:
1689:
1684:
1683:
1674:
1669:
1668:
1658:
1657:
1656:
1651:
1650:
1649:
1638:
1637:
1636:
1619:
1456:
1454:
1453:
1448:
1446:
1444:
1443:
1434:
1433:
1424:
1423:
1414:
1413:
1404:
1402:
1391:
1390:
1372:
1371:
1350:
1348:
1347:
1342:
1339:
1338:
1329:
1324:
1323:
1292:
1290:
1289:
1284:
1282:
1280:
1279:
1278:
1266:
1265:
1256:
1248:
1240:
1239:
1227:
1226:
1212:
1211:
1202:
1201:
1192:
1191:
1182:
1181:
1172:
1171:
1153:
1151:
1150:
1145:
1142:
1141:
1132:
1127:
1126:
1103:
1101:
1100:
1095:
1092:
1091:
1082:
1077:
1076:
1067:
1066:
1057:
1056:
1044:
1043:
1034:
1033:
1021:
1020:
1011:
1010:
987:
985:
984:
979:
973:
972:
963:
962:
953:
952:
943:
942:
910:
908:
907:
902:
900:
898:
897:
896:
891:
890:
889:
872:
867:
866:
857:
852:
851:
841:
840:
839:
834:
833:
832:
817:
812:
810:
794:
793:
777:
769:
767:
766:
757:
756:
747:
665:all-pass filters
644:Lattice topology
591:composite filter
549:m-derived filter
531:, have the same
500:
487:
486:
390:
318:
301:
189:form or else in
156:prototype filter
85:
78:
74:
71:
65:
60:this article by
51:inline citations
38:
37:
30:
21:
2613:
2612:
2608:
2607:
2606:
2604:
2603:
2602:
2588:
2587:
2572:
2567:
2505:
2500:
2499:
2483:
2482:
2467:
2451:
2447:
2435:
2433:
2420:
2419:
2415:
2410:
2406:
2401:
2397:
2390:
2384:
2380:
2372:
2368:
2363:
2359:
2354:
2327:
2319:
2305:
2285:
2254:
2243:
2240:
2239:
2217:
2211:
2207:
2199:
2196:
2195:
2170:
2166:
2160:
2156:
2150:
2146:
2145:
2138:
2134:
2128:
2121:
2117:
2116:
2115:
2114:
2111:
2103:
2100:
2099:
2074:
2070:
2064:
2060:
2054:
2050:
2044:
2040:
2038:
2033:
2021:
2017:
2015:
2012:
2011:
1987:
1983:
1978:
1972:
1968:
1949:
1948:
1944:
1942:
1939:
1938:
1914:
1907:
1903:
1902:
1901:
1884:
1880:
1878:
1869:
1865:
1864:
1849:
1845:
1843:
1830:
1829:
1825:
1824:
1822:
1805:
1802:
1801:
1781:
1777:
1772:
1766:
1762:
1743:
1742:
1738:
1736:
1733:
1732:
1709:
1702:
1698:
1697:
1696:
1679:
1675:
1673:
1664:
1660:
1659:
1652:
1645:
1641:
1640:
1639:
1626:
1625:
1621:
1620:
1618:
1601:
1598:
1597:
1572:
1471:
1439:
1435:
1429:
1425:
1419:
1415:
1409:
1405:
1403:
1398:
1386:
1382:
1367:
1363:
1361:
1358:
1357:
1334:
1330:
1325:
1319:
1315:
1304:
1301:
1300:
1274:
1270:
1261:
1257:
1252:
1244:
1235:
1231:
1222:
1218:
1214:
1207:
1203:
1197:
1193:
1187:
1183:
1177:
1173:
1170:
1162:
1159:
1158:
1137:
1133:
1128:
1122:
1118:
1110:
1107:
1106:
1087:
1083:
1078:
1072:
1068:
1062:
1058:
1052:
1048:
1039:
1035:
1029:
1025:
1016:
1012:
1006:
1002:
994:
991:
990:
968:
964:
958:
954:
948:
944:
938:
934:
923:
920:
919:
892:
885:
881:
880:
879:
862:
858:
856:
847:
843:
842:
835:
828:
824:
823:
822:
818:
816:
789:
785:
781:
776:
762:
758:
752:
748:
746:
729:
726:
725:
693:
688:
680:bridge topology
652:
650:Lattice network
646:
599:
584:
580:
576:
572:
562:
554:mm'-type filter
517:
438:Ladder network
398:C Half-section
366:Ladder network
332:Π Section
326:L Half section
309:
308:filter sections
277:George Campbell
273:elliptic filter
261:
211:
86:
75:
69:
66:
56:Please help to
55:
39:
35:
28:
23:
22:
15:
12:
11:
5:
2611:
2601:
2600:
2586:
2585:
2571:
2570:External links
2568:
2566:
2565:
2558:
2547:
2536:
2525:
2514:
2506:
2504:
2501:
2498:
2497:
2465:
2445:
2413:
2404:
2395:
2388:
2382:
2378:
2366:
2356:
2355:
2353:
2350:
2349:
2348:
2343:
2338:
2333:
2326:
2323:
2315:Main article:
2304:
2301:
2284:
2281:
2264:
2261:
2257:
2253:
2250:
2247:
2224:
2220:
2214:
2210:
2206:
2203:
2192:
2191:
2173:
2169:
2163:
2159:
2153:
2149:
2141:
2137:
2131:
2124:
2120:
2110:
2107:
2096:Quality factor
2093:
2077:
2073:
2067:
2063:
2057:
2053:
2047:
2043:
2036:
2032:
2029:
2024:
2020:
1990:
1986:
1981:
1975:
1971:
1967:
1964:
1958:
1955:
1952:
1947:
1935:
1934:
1917:
1910:
1906:
1900:
1897:
1892:
1887:
1883:
1877:
1872:
1868:
1862:
1857:
1852:
1848:
1839:
1836:
1833:
1828:
1821:
1818:
1815:
1812:
1809:
1784:
1780:
1775:
1769:
1765:
1761:
1758:
1752:
1749:
1746:
1741:
1729:
1728:
1712:
1705:
1701:
1695:
1692:
1687:
1682:
1678:
1672:
1667:
1663:
1655:
1648:
1644:
1635:
1632:
1629:
1624:
1617:
1614:
1611:
1608:
1605:
1571:
1568:
1560:
1559:
1551:
1470:
1467:
1463:Design choices
1459:
1458:
1442:
1438:
1432:
1428:
1422:
1418:
1412:
1408:
1401:
1397:
1394:
1389:
1385:
1381:
1378:
1375:
1370:
1366:
1355:
1337:
1333:
1328:
1322:
1318:
1314:
1311:
1308:
1298:
1277:
1273:
1269:
1264:
1260:
1255:
1251:
1247:
1243:
1238:
1234:
1230:
1225:
1221:
1217:
1210:
1206:
1200:
1196:
1190:
1186:
1180:
1176:
1169:
1166:
1155:
1154:
1140:
1136:
1131:
1125:
1121:
1117:
1114:
1104:
1090:
1086:
1081:
1075:
1071:
1065:
1061:
1055:
1051:
1047:
1042:
1038:
1032:
1028:
1024:
1019:
1015:
1009:
1005:
1001:
998:
988:
976:
971:
967:
961:
957:
951:
947:
941:
937:
933:
930:
927:
913:
912:
895:
888:
884:
878:
875:
870:
865:
861:
855:
850:
846:
838:
831:
827:
821:
815:
809:
806:
803:
800:
797:
792:
788:
784:
780:
775:
772:
765:
761:
755:
751:
745:
742:
739:
736:
733:
719:linear filters
692:
689:
687:
684:
648:Main article:
645:
642:
638:
637:
634:
631:
628:
625:
622:
598:
595:
582:
578:
574:
570:
566:
565:
560:
556:
551:
516:
513:
510:
509:
506:
505:
498:
491:
483:
482:
479:
478:
469:
459:
458:
455:
451:
450:
440:
439:
435:
434:
425:
416:
406:
405:
402:
399:
395:
394:
386:
385:
382:
379:
378:
368:
367:
363:
362:
353:
344:
334:
333:
330:
327:
323:
322:
315:
311:
310:
304:
265:Cauer topology
260:
257:
210:
207:
88:
87:
42:
40:
33:
26:
9:
6:
4:
3:
2:
2610:
2599:
2596:
2595:
2593:
2583:
2578:
2574:
2573:
2563:
2559:
2556:
2552:
2548:
2545:
2541:
2537:
2534:
2530:
2526:
2523:
2519:
2515:
2512:
2508:
2507:
2493:
2487:
2480:
2476:
2472:
2468:
2462:
2458:
2457:
2449:
2442:
2431:
2427:
2423:
2417:
2408:
2399:
2392:
2376:
2370:
2361:
2357:
2347:
2344:
2342:
2341:Linear filter
2339:
2337:
2334:
2332:
2329:
2328:
2322:
2318:
2309:
2300:
2298:
2289:
2280:
2278:
2262:
2259:
2255:
2251:
2248:
2245:
2238:
2222:
2218:
2212:
2208:
2204:
2201:
2171:
2167:
2161:
2157:
2151:
2147:
2139:
2135:
2129:
2122:
2118:
2108:
2105:
2097:
2094:
2075:
2071:
2065:
2061:
2055:
2051:
2045:
2041:
2034:
2030:
2027:
2022:
2018:
2009:
2006:
2005:
2004:
1988:
1984:
1979:
1973:
1969:
1965:
1962:
1945:
1915:
1908:
1904:
1898:
1895:
1890:
1885:
1881:
1875:
1870:
1866:
1860:
1855:
1850:
1846:
1826:
1819:
1813:
1807:
1800:
1799:
1798:
1782:
1778:
1773:
1767:
1763:
1759:
1756:
1739:
1710:
1703:
1699:
1693:
1690:
1685:
1680:
1676:
1670:
1665:
1661:
1653:
1646:
1642:
1622:
1615:
1609:
1603:
1596:
1595:
1594:
1591:
1589:
1585:
1576:
1567:
1565:
1557:
1552:
1549:
1545:
1541:
1537:
1534:
1530:
1529:
1528:
1526:
1522:
1518:
1513:
1511:
1507:
1506:
1502:is short for
1501:
1497:
1493:
1489:
1488:linear filter
1486:is a type of
1485:
1484:biquad filter
1480:
1479:
1477:
1466:
1464:
1440:
1436:
1430:
1426:
1420:
1416:
1410:
1406:
1399:
1395:
1392:
1387:
1383:
1379:
1376:
1373:
1368:
1364:
1356:
1354:
1335:
1331:
1326:
1320:
1316:
1312:
1309:
1306:
1299:
1296:
1275:
1271:
1262:
1258:
1249:
1241:
1236:
1232:
1228:
1223:
1219:
1208:
1204:
1198:
1194:
1188:
1184:
1178:
1174:
1167:
1164:
1157:
1156:
1138:
1134:
1129:
1123:
1119:
1115:
1112:
1105:
1088:
1084:
1079:
1073:
1069:
1063:
1059:
1053:
1049:
1045:
1040:
1036:
1030:
1026:
1022:
1017:
1013:
1007:
1003:
999:
996:
989:
969:
965:
959:
955:
949:
945:
939:
935:
928:
925:
918:
917:
916:
893:
886:
882:
876:
873:
868:
863:
859:
853:
848:
844:
836:
829:
825:
819:
813:
807:
804:
801:
798:
795:
790:
786:
782:
778:
773:
770:
763:
759:
753:
749:
743:
737:
731:
724:
723:
722:
720:
715:
713:
709:
705:
697:
683:
681:
676:
672:
670:
666:
656:
651:
641:
635:
632:
629:
626:
623:
620:
619:
618:
616:
615:Zobel network
608:
603:
594:
592:
586:
564:
557:
555:
552:
550:
547:
546:
545:
542:
538:
534:
530:
521:
503:
496:
488:
484:
474:
465:
460:
452:
446:
441:
436:
430:
421:
412:
407:
396:
391:
388:
387:
374:
369:
364:
358:
349:
340:
335:
324:
319:
316:
312:
307:
302:
299:
297:
296:dual networks
293:
289:
284:
282:
278:
274:
270:
269:Wilhelm Cauer
266:
256:
253:
251:
247:
242:
240:
234:
232:
228:
227:"daisy-chain"
224:
220:
216:
206:
204:
200:
196:
192:
188:
184:
180:
176:
172:
167:
165:
161:
157:
153:
149:
145:
141:
137:
133:
129:
125:
121:
117:
116:Filter design
113:
111:
107:
99:
94:
84:
81:
73:
70:November 2014
63:
59:
53:
52:
46:
41:
32:
31:
19:
18:Ladder filter
2561:
2560:Zobel, O J,
2554:
2550:
2543:
2539:
2532:
2528:
2521:
2517:
2510:
2478:
2455:
2448:
2440:
2434:. Retrieved
2425:
2416:
2407:
2398:
2386:
2374:
2369:
2360:
2320:
2294:
2193:
1936:
1730:
1592:
1581:
1563:
1561:
1546:poles of an
1524:
1520:
1514:
1509:
1503:
1499:
1483:
1481:
1473:
1472:
1460:
914:
716:
703:
702:
679:
677:
673:
661:
639:
611:
587:
567:
563:-type filter
526:
404:Box Section
285:
264:
262:
254:
243:
235:
212:
203:stereo sound
168:
114:
103:
76:
67:
48:
2411:Zobel, 1931
2402:Zobel, 1928
2364:Zobel, 1923
1527:topology.
1505:biquadratic
1498:. The name
321:Unbalanced
292:transformed
62:introducing
2503:References
2475:1100066185
2436:2021-07-30
1548:RC circuit
529:Otto Zobel
401:H Section
329:T Section
187:unbalanced
162:using the
45:references
2486:cite book
2387:general m
2246:ζ
2209:ω
2019:ω
1966:−
1905:ω
1882:ω
1847:ω
1760:−
1700:ω
1677:ω
1643:ω
1380:π
1365:ω
1313:−
883:ω
860:ω
826:ω
774:−
667:used for
617:article;
559:General m
533:passbands
393:Balanced
231:impedance
223:"cascade"
136:high-pass
132:nonlinear
2592:Category
2430:Archived
2325:See also
1588:bandpass
1584:low-pass
1295:Q factor
607:roll-off
541:stopband
495:balanced
288:low pass
191:balanced
152:all-pass
144:bandpass
140:low-pass
124:topology
108:defines
106:topology
2524:(1923).
1533:complex
1293:is the
497:lines.
384:
314:
171:passive
58:improve
2555:Vol. 7
2533:Vol. 3
2522:Vol. 2
2473:
2463:
1564:biquad
1517:active
1510:biquad
1500:biquad
721:, is:
267:after
175:active
128:linear
98:op-amp
47:, but
2391:-type
2352:Notes
1540:zeros
1536:poles
490:N.B.
306:Image
2492:link
2471:OCLC
2461:ISBN
2098:is
2010:is
1544:real
1353:gain
502:edit
201:and
173:and
150:and
2381:, m
1586:or
1523:or
577:, m
573:, m
225:or
130:or
2594::
2553:,
2544:17
2542:,
2531:,
2520:,
2488:}}
2484:{{
2477:.
2469:.
2439:.
2428:.
2424:.
1482:A
671:.
593:.
539:,
241:.
166:.
146:,
142:,
138:,
2494:)
2389:n
2383:2
2379:1
2263:Q
2260:2
2256:/
2252:1
2249:=
2223:Q
2219:/
2213:0
2205:=
2202:B
2190:.
2172:2
2168:C
2162:4
2158:R
2152:2
2148:R
2140:1
2136:C
2130:2
2123:3
2119:R
2109:=
2106:Q
2092:.
2076:2
2072:C
2066:1
2062:C
2056:4
2052:R
2046:2
2042:R
2035:/
2031:1
2028:=
2023:0
1989:1
1985:R
1980:/
1974:3
1970:R
1963:=
1957:f
1954:p
1951:b
1946:G
1933:.
1916:2
1909:0
1899:+
1896:s
1891:Q
1886:0
1876:+
1871:2
1867:s
1861:s
1856:Q
1851:0
1838:f
1835:p
1832:b
1827:G
1820:=
1817:)
1814:s
1811:(
1808:H
1783:1
1779:R
1774:/
1768:2
1764:R
1757:=
1751:f
1748:p
1745:l
1740:G
1711:2
1704:0
1694:+
1691:s
1686:Q
1681:0
1671:+
1666:2
1662:s
1654:2
1647:0
1634:f
1631:p
1628:l
1623:G
1616:=
1613:)
1610:s
1607:(
1604:H
1478:.
1441:5
1437:C
1431:2
1427:C
1421:4
1417:R
1411:3
1407:R
1400:/
1396:1
1393:=
1388:0
1384:f
1377:2
1374:=
1369:0
1336:1
1332:R
1327:/
1321:4
1317:R
1310:=
1307:K
1297:.
1276:5
1272:C
1268:)
1263:3
1259:R
1254:|
1250:K
1246:|
1242:+
1237:3
1233:R
1229:+
1224:4
1220:R
1216:(
1209:5
1205:C
1199:2
1195:C
1189:4
1185:R
1179:3
1175:R
1168:=
1165:Q
1139:4
1135:R
1130:/
1124:1
1120:R
1116:=
1113:C
1089:4
1085:R
1080:/
1074:5
1070:C
1064:3
1060:R
1054:1
1050:R
1046:+
1041:5
1037:C
1031:1
1027:R
1023:+
1018:5
1014:C
1008:3
1004:R
1000:=
997:B
975:)
970:5
966:C
960:2
956:C
950:3
946:R
940:1
936:R
932:(
929:=
926:A
911:.
894:2
887:0
877:+
874:s
869:Q
864:0
854:+
849:2
845:s
837:2
830:0
820:K
814:=
808:C
805:+
802:s
799:B
796:+
791:2
787:s
783:A
779:1
771:=
764:i
760:V
754:o
750:V
744:=
741:)
738:s
735:(
732:H
583:n
579:3
575:2
571:1
561:n
83:)
77:(
72:)
68:(
54:.
20:)
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
