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The phase equaliser based on T topology is the unbalanced equivalent of the lattice filter and has the same phase response. While the circuit diagram may look like a low pass filter it is different in that the two inductor branches are mutually coupled. This results in transformer action between
148:
relationship among various frequencies. Most types of filter reduce the amplitude (i.e. the magnitude) of the signal applied to it for some values of frequency, whereas the all-pass filter allows all frequencies through without changes in level.
2079:{\displaystyle H(z)={\frac {z^{-1}-{\overline {z_{0}}}}{1-z_{0}z^{-1}}}\times {\frac {z^{-1}-z_{0}}{1-{\overline {z_{0}}}z^{-1}}}={\frac {z^{-2}-2\Re (z_{0})z^{-1}+\left|{z_{0}}\right|^{2}}{1-2\Re (z_{0})z^{-1}+\left|z_{0}\right|^{2}z^{-2}}},\ }
1178:
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1352:, is a filter composed of lattice, or X-sections. With single element branches it can produce a phase shift up to 180°, and with resonant branches it can produce phase shifts up to 360°. The filter is an example of a
1544:
1034:
1259:ω=1/RC of the high-pass filter (i.e., when input frequency is 1/(2πRC)), the circuit introduces a 90° phase lead (i.e., output is in quadrature with input; the output appears to be advanced by a quarter
1660:
can be rotated in the complex plane by any angle and retain its all-pass magnitude characteristic. Complex pole-zero pairs in all-pass filters help control the frequency where phase shifts occur.
590:ω=1/RC of the low-pass filter (i.e., when input frequency is 1/(2πRC)), the circuit introduces a 90° shift (i.e., output is in quadrature with input; the output appears to be delayed by a quarter
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They are generally used to compensate for other undesired phase shifts that arise in the system, or for mixing with an unshifted version of the original to implement a notch
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designs. In other applications where inductors are readily available, all-pass filters can be implemented entirely without active components. There are a number of circuit
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or mixed-phase filters to create a stable or minimum-phase filter without changing the magnitude response of the system. For example, by proper choice of
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typically consists of two, four or six of these phase-shifting sections connected in tandem and summed with the original. A low-frequency oscillator (
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To create an all-pass implementation with real coefficients, the complex all-pass filter can be cascaded with an all-pass that substitutes
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filter with an equivalent magnitude response or an unstable filter into a stable filter with an equivalent magnitude response.
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In fact, the phase shift of the all-pass filter is double the phase shift of the high-pass filter at its non-inverting input.
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In fact, the phase shift of the all-pass filter is double the phase shift of the low-pass filter at its non-inverting input.
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to implement a voltage-controlled phase shifter; the voltage on the gate adjusts the phase shift. In electronic music, a
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magnitude for all ω. The filter introduces a different delay at each frequency and reaches input-to-output
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magnitude for all ω. The filter introduces a different delay at each frequency and reaches input-to-output
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165:", where a number of all-pass filters are connected in sequence and the output mixed with the raw signal.
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The bridged T topology is used for delay equalisation, particularly the differential delay between two
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1173:{\displaystyle |H(i\omega )|=1\quad {\text{and}}\quad \angle H(i\omega )=\pi -2\arctan(\omega RC).\,}
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shift as a function of frequency. Generally, the filter is described by the frequency at which the
2314:{\displaystyle y-2\Re (z_{0})y+\left|z_{0}\right|^{2}y=x-2\Re (z_{0})x+\left|z_{0}\right|^{2}x,\,}
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508:{\displaystyle |H(i\omega )|=1\quad {\text{and}}\quad \angle H(i\omega )=-2\arctan(\omega RC).\,}
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367:{\displaystyle H(s)=-{\frac {s-{\frac {1}{RC}}}{s+{\frac {1}{RC}}}}={\frac {1-sRC}{1+sRC}},\,}
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835:{\displaystyle e^{-sT}={\frac {e^{-sT/2}}{e^{sT/2}}}\approx {\frac {1-sT/2}{1+sT/2}},}
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that can be used for this. The following are the most commonly used circuits.
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1291:) ramps the control voltage to produce the characteristic swooshing sound.
1539:{\displaystyle H(z)={\frac {z^{-1}-{\overline {z_{0}}}}{1-z_{0}z^{-1}}}\ }
1384:
1311:
1399:) over a wide bandwidth and is the reason for choosing this topology.
1029:{\displaystyle H(s)={\frac {s-{\frac {1}{RC}}}{s+{\frac {1}{RC}}}},\,}
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the two inductors and an all-pass response even at high frequency.
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An op-amp base all-pass filter incorporating a high-pass filter.
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2542:
Williams, A.B.; Taylor, F.J., Electronic Filter Design
Handbook
221:
An op-amp base all-pass filter incorporating a low-pass filter.
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circuit shown in the adjacent figure implements a single-pole
29:
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broadcasts. This application requires that the filter has a
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crosses 90° (i.e., when the input and output signals go into
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implementation of an all-pass filter with a complex pole at
2574:, analysis steps for a common analog phase-shifter circuit.
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production is in the design of an effects unit known as a "
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circuit shown in adjacent figure implements a single-pole
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at the non-inverting input of the opamp. The filter's
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expansion of the numerator and denominator. By setting
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is complex frequency. This can be approximated using a
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Op Amps for
Everyone, Ron Mancini, Newnes 780750677011
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can be canceled and reflected inside the unit circle.
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Interpretation as a Padé approximation to a pure delay
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at the non-inverting input of the opamp. The filter's
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606:The Laplace transform of a pure delay is given by
533:This implementation uses a low-pass filter at the
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2405:Filters such as the above can be cascaded with
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120:Learn how and when to remove this message
1395:response with frequency (i.e., constant
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1252:(i.e., 180° phase lead) with unity gain.
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2578:filter-solutions.com: All-pass filters
530:at ω=1/RC (i.e., phase shift is 90°).
180: – when there is a quarter
1584:{\displaystyle 1/{\overline {z_{0}}}}
1195:at ω=1/RC (i.e., phase lead is 90°).
919:Implementation using high-pass filter
7:
1275:The resistor can be replaced with a
213:Implementation using low-pass filter
58:adding citations to reliable sources
2382:is the input at discrete time step
1690:{\displaystyle {\overline {z_{0}}}}
1360:is constant over all frequencies).
194:They may also be used to convert a
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1271:Voltage controlled implementation
689:{\displaystyle s\in \mathbb {C} }
144:equally in gain, but changes the
2567:JOS@Stanford on all-pass filters
2517:Maheswari, L.K.; Anand, M.M.S.,
1314:, which are bulky and costly in
1206:to generate the phase shift and
939:all-pass filter that features a
537:to generate the phase shift and
233:all-pass filter that features a
34:
1611:{\displaystyle {\overline {z}}}
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2572:ECE 209 Phase-Shifter Circuit
1298:Passive analog implementation
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1310:is that they do not require
206:Active analog implementation
168:It does this by varying its
2089:which is equivalent to the
1354:constant-resistance network
1198:This implementation uses a
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2685:Digital signal processing
2680:Filter frequency response
2653:
2620:
2614:Signal-processing filters
2450:Bridged T delay equaliser
1379:Bridged T delay equaliser
1051:of each other across the
389:of each other across the
1373:Bridged T-section filter
1047:at 1/RC (i.e., they are
638:{\displaystyle e^{-sT},}
385:at 1/RC (i.e., they are
184:of delay between them).
157:A common application in
138:signal processing filter
27:Signal processing filter
2455:Lattice phase equaliser
1346:lattice phase equaliser
1340:Lattice phase equaliser
1240:At low frequencies and
583:(i.e., no phase shift).
564:At low frequencies and
2630:High-pass filter (HPF)
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1403:Digital implementation
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1308:operational amplifiers
1248:and the circuit is an
1244:, the capacitor is an
1237:(i.e., no phase lead).
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879:{\displaystyle RC=T/2}
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568:, the capacitor is an
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2625:Low-pass filter (LPF)
2525:, PHI Learning, 2009
2490:Lattice delay network
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2429:{\displaystyle z_{0}}
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1717:{\displaystyle z_{0}}
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2544:, McGraw-Hill, 1995
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908:{\displaystyle H(s)}
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54:improve this article
2091:difference equation
1250:inverting amplifier
1204:non-inverting input
1061:magnitude and phase
559:inverting amplifier
535:non-inverting input
399:magnitude and phase
153:Common applications
2519:Analog Electronics
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2656:Electronic filter
2465:Hilbert transform
2395:{\displaystyle k}
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661:{\displaystyle T}
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69:"All-pass filter"
16:(Redirected from
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2229:
2226:
2223:
2220:
2217:
2214:
2211:
2208:
2205:
2202:
2199:
2196:
2193:
2190:
2187:
2182:
2177:
2172:
2168:
2164:
2159:
2156:
2153:
2150:
2147:
2144:
2141:
2138:
2133:
2129:
2125:
2122:
2119:
2116:
2113:
2110:
2107:
2104:
2087:
2086:
2072:
2064:
2061:
2057:
2051:
2046:
2041:
2037:
2033:
2028:
2023:
2020:
2016:
2012:
2007:
2003:
1999:
1996:
1993:
1990:
1987:
1980:
1975:
1969:
1965:
1960:
1955:
1950:
1947:
1943:
1939:
1934:
1930:
1926:
1923:
1920:
1917:
1912:
1909:
1905:
1898:
1890:
1887:
1883:
1877:
1872:
1868:
1862:
1859:
1852:
1848:
1844:
1839:
1836:
1832:
1825:
1817:
1814:
1810:
1804:
1800:
1796:
1793:
1786:
1781:
1777:
1771:
1766:
1763:
1759:
1752:
1749:
1746:
1743:
1740:
1711:
1707:
1684:
1679:
1675:
1647:
1643:
1605:
1602:
1578:
1573:
1569:
1562:
1558:
1547:
1546:
1527:
1524:
1520:
1514:
1510:
1506:
1503:
1496:
1491:
1487:
1481:
1476:
1473:
1469:
1462:
1459:
1456:
1453:
1450:
1425:
1421:
1404:
1401:
1377:Main article:
1374:
1371:
1365:
1362:
1338:Main article:
1327:
1326:Lattice filter
1324:
1299:
1296:
1272:
1269:
1265:
1264:
1253:
1238:
1235:voltage buffer
1181:
1180:
1168:
1165:
1162:
1159:
1156:
1153:
1150:
1147:
1144:
1141:
1138:
1135:
1132:
1129:
1126:
1123:
1120:
1117:
1107:
1104:
1100:
1096:
1093:
1090:
1087:
1084:
1080:
1039:which has one
1037:
1036:
1024:
1015:
1012:
1008:
1003:
1000:
992:
989:
985:
980:
977:
971:
968:
965:
962:
959:
920:
917:
904:
901:
898:
895:
875:
871:
867:
864:
861:
858:
843:
842:
831:
825:
821:
817:
814:
811:
808:
803:
799:
795:
792:
789:
786:
780:
773:
769:
765:
762:
758:
752:
748:
744:
741:
738:
734:
728:
723:
720:
717:
713:
700:, as follows:
684:
680:
677:
657:
646:
645:
634:
629:
626:
623:
619:
603:
600:
596:
595:
584:
581:voltage buffer
562:
557:, creating an
516:
515:
503:
500:
497:
494:
491:
488:
485:
482:
479:
476:
473:
470:
467:
464:
461:
458:
455:
445:
442:
438:
434:
431:
428:
425:
422:
418:
377:which has one
375:
374:
362:
356:
353:
350:
347:
344:
339:
336:
333:
330:
327:
321:
312:
309:
305:
300:
297:
289:
286:
282:
277:
274:
268:
265:
262:
259:
256:
253:
214:
211:
207:
204:
198:filter into a
154:
151:
128:
127:
42:
40:
33:
26:
24:
14:
13:
10:
9:
6:
4:
3:
2:
2697:
2686:
2683:
2681:
2678:
2676:
2673:
2672:
2670:
2657:
2652:
2646:
2643:
2641:
2638:
2636:
2633:
2631:
2628:
2626:
2623:
2622:
2619:
2615:
2608:
2603:
2601:
2596:
2594:
2589:
2588:
2585:
2579:
2576:
2573:
2570:
2568:
2565:
2564:
2560:
2553:
2551:
2547:
2539:
2536:
2532:
2531:9788120327221
2528:
2524:
2520:
2514:
2511:
2505:
2502:
2495:
2491:
2488:
2486:
2483:
2481:
2478:
2476:
2473:
2471:
2468:
2466:
2463:
2461:
2460:Minimum phase
2458:
2456:
2453:
2451:
2448:
2447:
2443:
2441:
2439:
2421:
2417:
2408:
2403:
2389:
2366:
2360:
2337:
2331:
2307:
2301:
2295:
2290:
2285:
2280:
2276:
2272:
2267:
2261:
2258:
2255:
2249:
2241:
2237:
2227:
2224:
2218:
2215:
2212:
2206:
2203:
2197:
2194:
2191:
2185:
2180:
2175:
2170:
2166:
2162:
2157:
2151:
2148:
2145:
2139:
2131:
2127:
2117:
2114:
2108:
2102:
2095:
2094:
2093:
2092:
2070:
2062:
2059:
2055:
2049:
2044:
2039:
2035:
2031:
2026:
2021:
2018:
2014:
2005:
2001:
1991:
1988:
1985:
1978:
1973:
1967:
1963:
1958:
1953:
1948:
1945:
1941:
1932:
1928:
1918:
1915:
1910:
1907:
1903:
1896:
1888:
1885:
1881:
1870:
1866:
1860:
1857:
1850:
1846:
1842:
1837:
1834:
1830:
1823:
1815:
1812:
1808:
1802:
1798:
1794:
1791:
1779:
1775:
1769:
1764:
1761:
1757:
1750:
1744:
1738:
1731:
1730:
1729:
1727:
1709:
1705:
1677:
1673:
1661:
1645:
1641:
1632:
1629:
1625:
1621:
1600:
1571:
1567:
1560:
1556:
1525:
1522:
1518:
1512:
1508:
1504:
1501:
1489:
1485:
1479:
1474:
1471:
1467:
1460:
1454:
1448:
1441:
1440:
1439:
1423:
1419:
1410:
1402:
1400:
1398:
1394:
1390:
1386:
1380:
1372:
1370:
1363:
1361:
1359:
1355:
1351:
1347:
1341:
1332:
1325:
1323:
1321:
1317:
1313:
1309:
1305:
1297:
1295:
1292:
1290:
1286:
1282:
1278:
1270:
1268:
1262:
1258:
1254:
1251:
1247:
1243:
1239:
1236:
1233:
1229:
1225:
1224:short circuit
1221:
1217:
1213:
1212:
1211:
1209:
1205:
1201:
1196:
1194:
1190:
1186:
1166:
1160:
1157:
1154:
1148:
1145:
1142:
1139:
1136:
1133:
1127:
1124:
1118:
1105:
1102:
1091:
1088:
1082:
1070:
1069:
1068:
1066:
1062:
1058:
1057:complex plane
1054:
1050:
1046:
1042:
1022:
1013:
1010:
1006:
1001:
998:
990:
987:
983:
978:
975:
969:
963:
957:
950:
949:
948:
947:is given by:
946:
942:
938:
934:
925:
918:
916:
899:
893:
873:
869:
865:
862:
859:
856:
848:
847:Taylor series
829:
823:
819:
815:
812:
809:
806:
801:
797:
793:
790:
787:
784:
778:
771:
767:
763:
760:
756:
750:
746:
742:
739:
736:
732:
726:
721:
718:
715:
711:
703:
702:
701:
699:
678:
675:
655:
632:
627:
624:
621:
617:
609:
608:
607:
601:
599:
593:
589:
585:
582:
579:
575:
572:, creating a
571:
567:
563:
560:
556:
555:short circuit
552:
548:
544:
543:
542:
540:
536:
531:
529:
525:
521:
501:
495:
492:
489:
483:
480:
477:
474:
471:
465:
462:
456:
443:
440:
429:
426:
420:
408:
407:
406:
404:
400:
396:
395:complex plane
392:
388:
384:
380:
360:
354:
351:
348:
345:
342:
337:
334:
331:
328:
325:
319:
310:
307:
303:
298:
295:
287:
284:
280:
275:
272:
266:
263:
257:
251:
244:
243:
242:
241:is given by:
240:
236:
232:
228:
219:
212:
210:
205:
203:
201:
200:minimum phase
197:
192:
190:
185:
183:
179:
175:
171:
166:
164:
160:
152:
150:
147:
143:
139:
135:
124:
121:
113:
102:
99:
95:
92:
88:
85:
81:
78:
74:
71: –
70:
66:
65:Find sources:
59:
55:
49:
48:
43:This article
41:
37:
32:
31:
19:
2634:
2543:
2538:
2518:
2513:
2504:
2404:
2323:
2088:
1662:
1623:
1618:denotes the
1548:
1406:
1393:linear phase
1382:
1367:
1349:
1345:
1343:
1301:
1293:
1280:
1274:
1266:
1246:open circuit
1197:
1192:
1182:
1055:axis of the
1048:
1038:
930:
915:from above.
844:
647:
605:
597:
570:open circuit
532:
527:
517:
393:axis of the
386:
376:
224:
209:
193:
186:
167:
156:
133:
131:
116:
107:
97:
90:
83:
76:
64:
52:Please help
47:verification
44:
2523:pp. 213-214
2438:unit circle
1726:Z-transform
1631:unit circle
1624:reflections
1409:Z-transform
1397:group delay
1356:(i.e., its
1216:frequencies
1049:reflections
886:we recover
547:frequencies
387:reflections
196:mixed phase
189:comb filter
174:phase shift
142:frequencies
2669:Categories
2552:, p. 10.7.
2550:0070704414
2496:References
1320:topologies
1281:ohmic mode
1193:quadrature
528:quadrature
182:wavelength
178:quadrature
110:March 2009
80:newspapers
2259:−
2231:ℜ
2225:−
2216:−
2195:−
2149:−
2121:ℜ
2115:−
2060:−
2019:−
1995:ℜ
1989:−
1946:−
1922:ℜ
1916:−
1908:−
1886:−
1876:¯
1861:−
1843:−
1835:−
1824:×
1813:−
1795:−
1785:¯
1770:−
1762:−
1683:¯
1604:¯
1577:¯
1523:−
1505:−
1495:¯
1480:−
1472:−
1385:landlines
1312:inductors
1220:capacitor
1155:ω
1149:
1140:−
1137:π
1128:ω
1116:∠
1092:ω
1053:imaginary
979:−
788:−
779:≈
737:−
716:−
679:∈
622:−
551:capacitor
490:ω
484:
475:−
466:ω
454:∠
430:ω
391:imaginary
329:−
276:−
267:−
2444:See also
2407:unstable
1591:, where
1214:At high
545:At high
1628:complex
1279:in its
1255:At the
1202:at the
1059:). The
586:At the
397:). The
94:scholar
2548:
2529:
2324:where
2074:
1534:
1350:filter
1285:phaser
1261:period
1218:, the
1146:arctan
1067:ω are
937:active
648:where
592:period
549:, the
481:arctan
405:ω are
231:active
163:phaser
96:
89:
82:
75:
67:
1348:, or
1306:like
1228:unity
1222:is a
1185:unity
574:unity
553:is a
520:unity
170:phase
146:phase
136:is a
101:JSTOR
87:books
2546:ISBN
2527:ISBN
1697:for
1344:The
1232:gain
1189:gain
1045:zero
1041:pole
931:The
578:gain
524:gain
383:zero
379:pole
225:The
73:news
1438:is
1289:LFO
1277:FET
1111:and
449:and
132:An
56:by
2671::
2521:,
2402:.
1407:A
1242:DC
1210:.
566:DC
541:.
191:.
2606:e
2599:t
2592:v
2533:.
2422:0
2418:z
2390:k
2370:]
2367:k
2364:[
2361:x
2341:]
2338:k
2335:[
2332:y
2308:,
2305:]
2302:k
2299:[
2296:x
2291:2
2286:|
2281:0
2277:z
2273:|
2268:+
2265:]
2262:1
2256:k
2253:[
2250:x
2247:)
2242:0
2238:z
2234:(
2228:2
2222:]
2219:2
2213:k
2210:[
2207:x
2204:=
2201:]
2198:2
2192:k
2189:[
2186:y
2181:2
2176:|
2171:0
2167:z
2163:|
2158:+
2155:]
2152:1
2146:k
2143:[
2140:y
2137:)
2132:0
2128:z
2124:(
2118:2
2112:]
2109:k
2106:[
2103:y
2071:,
2063:2
2056:z
2050:2
2045:|
2040:0
2036:z
2032:|
2027:+
2022:1
2015:z
2011:)
2006:0
2002:z
1998:(
1992:2
1986:1
1979:2
1974:|
1968:0
1964:z
1959:|
1954:+
1949:1
1942:z
1938:)
1933:0
1929:z
1925:(
1919:2
1911:2
1904:z
1897:=
1889:1
1882:z
1871:0
1867:z
1858:1
1851:0
1847:z
1838:1
1831:z
1816:1
1809:z
1803:0
1799:z
1792:1
1780:0
1776:z
1765:1
1758:z
1751:=
1748:)
1745:z
1742:(
1739:H
1710:0
1706:z
1678:0
1674:z
1646:0
1642:z
1601:z
1572:0
1568:z
1561:/
1557:1
1526:1
1519:z
1513:0
1509:z
1502:1
1490:0
1486:z
1475:1
1468:z
1461:=
1458:)
1455:z
1452:(
1449:H
1424:0
1420:z
1230:-
1187:-
1167:.
1164:)
1161:C
1158:R
1152:(
1143:2
1134:=
1131:)
1125:i
1122:(
1119:H
1106:1
1103:=
1099:|
1095:)
1089:i
1086:(
1083:H
1079:|
1023:,
1014:C
1011:R
1007:1
1002:+
999:s
991:C
988:R
984:1
976:s
970:=
967:)
964:s
961:(
958:H
903:)
900:s
897:(
894:H
874:2
870:/
866:T
863:=
860:C
857:R
830:,
824:2
820:/
816:T
813:s
810:+
807:1
802:2
798:/
794:T
791:s
785:1
772:2
768:/
764:T
761:s
757:e
751:2
747:/
743:T
740:s
733:e
727:=
722:T
719:s
712:e
683:C
676:s
656:T
633:,
628:T
625:s
618:e
576:-
522:-
502:.
499:)
496:C
493:R
487:(
478:2
472:=
469:)
463:i
460:(
457:H
444:1
441:=
437:|
433:)
427:i
424:(
421:H
417:|
361:,
355:C
352:R
349:s
346:+
343:1
338:C
335:R
332:s
326:1
320:=
311:C
308:R
304:1
299:+
296:s
288:C
285:R
281:1
273:s
264:=
261:)
258:s
255:(
252:H
123:)
117:(
112:)
108:(
98:·
91:·
84:·
77:·
50:.
20:)
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
