1001:
5405:
2617:
1689:
3902:
3910:
419:
5392:
25:
3896:
2071:
5195:
1875:
426:
The simplest RC circuit consists of a resistor and a charged capacitor connected to one another in a single loop, without an external voltage source. Once the circuit is closed, the capacitor begins to discharge its stored energy through the resistor. The voltage across the capacitor, which is
4505:
3671:
2450:
5684:
4082:
2988:
5554:
5346:
1174:
1336:
3580:), the capacitor voltage is in phase with the signal voltage while the resistor voltage leads it by 90°. As frequency increases, the capacitor voltage comes to have a 90° lag relative to the signal and the resistor voltage comes to be in-phase with the signal.
3567:
3459:
3351:
2780:
2606:
5805:) must be on the negative real axis and alternate between poles and zeroes with an equal number of each. Further, the critical frequency nearest the origin must be a pole, assuming the rational function represents an impedance rather than an admittance.
4136:
as time passes, while the voltage across the resistor tends towards 0, as shown in the figures. This is in keeping with the intuitive point that the capacitor will be charging from the supply voltage as time passes, and will eventually be fully charged.
1886:
5069:
1702:
2283:
3179:. If, though, the output is taken across the resistor, high frequencies are passed and low frequencies are attenuated (since the capacitor blocks the signal as its frequency approaches 0). In this configuration, the circuit behaves as a
1472:
5775:
1607:
2173:
4939:
3019:
expressions. Analysis of them will show which frequencies the circuits (or filters) pass and reject. This analysis rests on a consideration of what happens to these gains as the frequency becomes very large and very small.
3891:{\displaystyle {\begin{aligned}V_{\mathrm {in} }(s)&=V\cdot {\frac {1}{s}}\\V_{C}(s)&=V\cdot {\frac {1}{1+sRC}}\cdot {\frac {1}{s}}\\V_{R}(s)&=V\cdot {\frac {sRC}{1+sRC}}\cdot {\frac {1}{s}}\,.\end{aligned}}}
4358:
4668:
4574:
This means that the capacitor has insufficient time to charge up and so its voltage is very small. Thus the input voltage approximately equals the voltage across the resistor. To see this, consider the expression for
2298:
990:
5565:
3930:
3168:
3093:
2823:
4847:
5446:
5206:
4765:
1025:
498:
5570:
5451:
5211:
5074:
4363:
3935:
3676:
2303:
3252:
590:
1185:
5058:
5006:
4714:
4569:
3477:
3375:
3264:
2645:
2466:
2066:{\displaystyle G_{R}={\big |}H_{R}(j\omega ){\big |}=\left|{\frac {V_{R}(j\omega )}{V_{\mathrm {in} }(j\omega )}}\right|={\frac {\omega RC}{\sqrt {1+\left(\omega RC\right)^{2}}}}\,,}
1667:
827:
771:
3173:
This shows that, if the output is taken across the capacitor, high frequencies are attenuated (shorted to ground) and low frequencies are passed. Thus, the circuit behaves as a
394:, with the acronyms indicating which components are used. These circuits, among them, exhibit a large number of important types of behaviour that are fundamental to much of
5190:{\displaystyle {\begin{aligned}I&\approx {\frac {V_{\mathrm {in} }}{\frac {1}{j\omega C}}}\\V_{\mathrm {in} }&\approx {\frac {I}{j\omega C}}=V_{C}\,.\end{aligned}}}
431:. The current through the resistor must be equal in magnitude (but opposite in sign) to the time derivative of the accumulated charge on the capacitor. This results in the
1870:{\displaystyle G_{C}={\big |}H_{C}(j\omega ){\big |}=\left|{\frac {V_{C}(j\omega )}{V_{\mathrm {in} }(j\omega )}}\right|={\frac {1}{\sqrt {1+\left(\omega RC\right)^{2}}}}}
677:
914:
2184:
291:
5559:
This shows that the capacitor current is 90° out of phase with the resistor (and source) current. Alternatively, the governing differential equations may be used:
4593:
1356:
5695:
340:
and these will produce different responses. A first order RC circuit is composed of one resistor and one capacitor and is the simplest type of RC circuit.
1483:
4318:. When the voltage source is replaced with a short circuit, with the capacitor fully charged, the voltage across the capacitor drops exponentially with
2082:
4858:
4500:{\displaystyle {\begin{aligned}{\frac {V_{\mathrm {in} }-V_{C}}{R}}&=C{\frac {dV_{C}}{dt}}\\V_{R}&=V_{\mathrm {in} }-V_{C}\,.\end{aligned}}}
2445:{\displaystyle {\begin{aligned}V_{C}&=G_{C}V_{\mathrm {in} }e^{j\phi _{C}}\\V_{R}&=G_{R}V_{\mathrm {in} }e^{j\phi _{R}}\,.\end{aligned}}}
5384:
4601:
5011:
This means that the capacitor has time to charge up until its voltage is almost equal to the source's voltage. Considering the expression for
284:
5378:
922:
890:
Sinusoidal steady state is a special case in which the input voltage consists of a pure sinusoid (with no exponential decay). As a result,
428:
4091:; for discharging, the equations are vice versa. These equations can be rewritten in terms of charge and current using the relationships
5679:{\displaystyle {\begin{aligned}I_{R}&={\frac {V_{\mathrm {in} }}{R}}\\I_{C}&=C{\frac {dV_{\mathrm {in} }}{dt}}\,.\end{aligned}}}
4077:{\displaystyle {\begin{aligned}V_{C}(t)&=V\left(1-e^{-{\frac {t}{RC}}}\right)\\V_{R}(t)&=Ve^{-{\frac {t}{RC}}}\,.\end{aligned}}}
4154:
being the time it takes the voltage across the component to either rise (across the capacitor) or fall (across the resistor) to within
2983:{\displaystyle h_{R}(t)=\delta (t)-{\frac {1}{RC}}e^{-{\frac {t}{RC}}}u(t)=\delta (t)-{\frac {1}{\tau }}e^{-{\frac {t}{\tau }}}u(t)\,,}
343:
RC circuits can be used to filter a signal by blocking certain frequencies and passing others. The two most common RC filters are the
3111:
3036:
2632:
of the corresponding transfer function. It represents the response of the circuit to an input voltage consisting of an impulse or
277:
5549:{\displaystyle {\begin{aligned}I_{R}&={\frac {V_{\mathrm {in} }}{R}}\\I_{C}&=j\omega CV_{\mathrm {in} }\,.\end{aligned}}}
5341:{\displaystyle {\begin{aligned}V_{R}&=IR=C{\frac {dV_{C}}{dt}}R\\V_{R}&\approx RC{\frac {dV_{in}}{dt}}\,,\end{aligned}}}
4783:
1169:{\displaystyle V_{C}(s)={\frac {\frac {1}{Cs}}{R+{\frac {1}{Cs}}}}V_{\mathrm {in} }(s)={\frac {1}{1+RCs}}V_{\mathrm {in} }(s)}
5408:
4725:
407:
3359:
Clearly, the phases also depend on frequency, although this effect is less interesting generally than the gain variations.
1004:
440:
403:
5415:
The parallel RC circuit is generally of less interest than the series circuit. This is largely because the output voltage
5949:
89:
3202:
1331:{\displaystyle V_{R}(s)={\frac {R}{R+{\frac {1}{Cs}}}}V_{\mathrm {in} }(s)={\frac {RCs}{1+RCs}}V_{\mathrm {in} }(s)\,.}
524:
61:
4087:
These equations are for calculating the voltage across the capacitor and resistor respectively while the capacitor is
3562:{\displaystyle \phi _{C}\to -90^{\circ }=-{\frac {\pi }{2}}{\mbox{ radians}}\quad {\mbox{and}}\quad \phi _{R}\to 0\,.}
5913:
108:
3454:{\displaystyle \phi _{C}\to 0\quad {\mbox{and}}\quad \phi _{R}\to 90^{\circ }={\frac {\pi }{2}}{\mbox{ radians}}\,.}
5021:
4969:
4679:
4532:
3346:{\displaystyle \omega _{\mathrm {c} }={\frac {1}{RC}}\quad {\mbox{or}}\quad f_{\mathrm {c} }={\frac {1}{2\pi RC}}}
68:
2775:{\displaystyle h_{C}(t)={\frac {1}{RC}}e^{-{\frac {t}{RC}}}u(t)={\frac {1}{\tau }}e^{-{\frac {t}{\tau }}}u(t)\,,}
2601:{\displaystyle I(s)={\frac {V_{\mathrm {in} }(s)}{R+{\frac {1}{Cs}}}}={\frac {Cs}{1+RCs}}V_{\mathrm {in} }(s)\,.}
5928:
46:
3189:
4514:
and the second follows easily; the solutions are exactly the same as those obtained via
Laplace transforms.
75:
1627:
793:
731:
432:
202:
42:
5858:
57:
399:
219:
172:
167:
135:
5944:
3632:
3192:. The point at which the filter attenuates the signal to half its unfiltered power is termed its
2797:
2278:{\displaystyle \phi _{R}=\angle H_{R}(j\omega )=\tan ^{-1}\left({\frac {1}{\omega RC}}\right)\,.}
1673:
1618:
649:
213:
35:
2616:
5798:
1688:
893:
225:
185:
5373:
4349:
3005:
2633:
1677:
372:
8:
5433:— as a result, this circuit does not act as a filter on the input signal unless fed by a
5368:
can also be achieved by placing resistors and capacitors as appropriate on the input and
2289:
82:
5853:
4578:
4511:
1467:{\displaystyle H_{C}(s)={\frac {V_{C}(s)}{V_{\mathrm {in} }(s)}}={\frac {1}{1+RCs}}\,.}
1000:
878:
395:
230:
142:
1477:
Similarly, the transfer function from the input to the voltage across the resistor is
5924:
5909:
5790:
5786:
5770:{\displaystyle {\frac {V_{\mathrm {out} }}{I_{\mathrm {in} }}}={\frac {R}{1+sRC}}\,.}
5404:
3921:
3604:
2629:
1347:
874:
857:
777:
703:
515:
192:
124:
1602:{\displaystyle H_{R}(s)={\frac {V_{R}(s)}{V_{\rm {in}}(s)}}={\frac {RCs}{1+RCs}}\,.}
5833:
5809:
5802:
4141:
3917:
3193:
3181:
3016:
2625:
640:
356:
352:
344:
321:
197:
147:
3356:
which is the frequency that the filter will attenuate to half its original power.
2460:
The current in the circuit is the same everywhere since the circuit is in series:
2168:{\displaystyle \phi _{C}=\angle H_{C}(j\omega )=\tan ^{-1}\left(-\omega RC\right)}
5813:
5689:
When fed by a current source, the transfer function of a parallel RC circuit is:
4934:{\displaystyle V_{C}\approx {\frac {1}{RC}}\int _{0}^{t}V_{\mathrm {in} }\,dt\,,}
4088:
3175:
1012:
348:
162:
152:
2288:
These expressions together may be substituted into the usual expression for the
5821:
5434:
5352:
3603:
The most straightforward way to derive the time domain behaviour is to use the
3573:
840:
784:
375:
337:
333:
4307:
toward its final value. So the capacitor will be charged to about 63.2% after
3901:
5938:
5863:
3909:
2811:
1672:
In addition, the transfer function for the voltage across the resistor has a
207:
157:
5797:. For synthesis to be possible in passive elements, the function must be a
4771:
4342:
4126:
4663:{\displaystyle I={\frac {V_{\mathrm {in} }}{R+{\frac {1}{j\omega C}}}}\,,}
5848:
391:
263:
418:
5843:
5838:
5817:
5365:
4945:
4297:, the voltage will have moved about 63.2% of the way from its level at
3595:
871:
387:
383:
360:
258:
253:
4341:, in the circuit behaves as the voltage across the resistor does, via
985:{\displaystyle Z_{C}={\frac {1}{j\omega C}}=-{\frac {j}{\omega C}}\,.}
5391:
329:
24:
5369:
5361:
379:
325:
5801:. To synthesise as an RC circuit, all the critical frequencies (
4326:
towards 0. The capacitor will be discharged to about 36.8% after
1016:
3163:{\displaystyle G_{C}\to 1\quad {\mbox{and}}\quad G_{R}\to 0\,.}
3088:{\displaystyle G_{C}\to 0\quad {\mbox{and}}\quad G_{R}\to 1\,.}
722:
3188:
The range of frequencies that the filter passes is called its
1692:
Amplitude and phase transfer functions for a series RC circuit
1350:
from the input voltage to the voltage across the capacitor is
3577:
861:
3196:. This requires that the gain of the circuit be reduced to
2817:
Similarly, the impulse response for the resistor voltage is
4673:
but note that the frequency condition described means that
5808:
The synthesis can be achieved with a modification of the
4842:{\displaystyle V_{C}={\frac {1}{C}}\int _{0}^{t}I\,dt\,,}
1696:
The magnitude of the gains across the two components are
714:
378:
components: the resistor (R), the capacitor (C), and the
4760:{\displaystyle I\approx {\frac {V_{\mathrm {in} }}{R}}}
4330:, and essentially fully discharged (0.7%) after about
3532:
3524:
3441:
3397:
3300:
3133:
3058:
5698:
5568:
5449:
5209:
5072:
5024:
4972:
4861:
4786:
4728:
4682:
4604:
4581:
4535:
4361:
4132:
Thus, the voltage across the capacitor tends towards
3933:
3674:
3480:
3378:
3267:
3205:
3114:
3039:
2826:
2648:
2469:
2301:
2187:
2085:
1889:
1705:
1630:
1486:
1359:
1188:
1028:
925:
896:
796:
734:
652:
527:
493:{\displaystyle C{\frac {dV}{dt}}+{\frac {V}{R}}=0\,,}
443:
16:
Electric circuit composed of resistors and capacitors
4311:, and essentially fully charged (99.3%) after about
4140:
These equations show that a series RC circuit has a
49:. Unsourced material may be challenged and removed.
5769:
5678:
5548:
5340:
5189:
5052:
5000:
4933:
4841:
4759:
4708:
4662:
4587:
4563:
4499:
4076:
3890:
3561:
3453:
3345:
3247:{\displaystyle G_{C}=G_{R}={\frac {1}{\sqrt {2}}}}
3246:
3162:
3087:
3010:
2982:
2774:
2639:The impulse response for the capacitor voltage is
2600:
2444:
2277:
2167:
2065:
1869:
1661:
1601:
1466:
1330:
1168:
984:
908:
821:
765:
671:
584:
492:
382:(L). These may be combined in the RC circuit, the
4348:These results may also be derived by solving the
585:{\displaystyle V(t)=V_{0}e^{-{\frac {t}{RC}}}\,,}
402:. This article considers the RC circuit, in both
363:, though crude ones can be made with RC filters.
5936:
5923:(3rd edition), Cambridge University Press, 2015
5053:{\displaystyle R\ll {\frac {1}{\omega C}}\,,}
5001:{\displaystyle \omega \ll {\frac {1}{RC}}\,.}
4709:{\displaystyle \omega C\gg {\frac {1}{R}}\,,}
4564:{\displaystyle \omega \gg {\frac {1}{RC}}\,.}
3583:
1934:
1905:
1750:
1721:
614:The time required for the voltage to fall to
285:
4522:Consider the output across the capacitor at
4959:Consider the output across the resistor at
2620:The impulse response of a series RC circuit
885:
292:
278:
5824:of resistors and capacitors will result.
5763:
5668:
5538:
5330:
5179:
5046:
4994:
4927:
4920:
4835:
4828:
4702:
4656:
4557:
4510:The first equation is solved by using an
4489:
4066:
3880:
3621:given above. This effectively transforms
3555:
3447:
3156:
3081:
2976:
2768:
2594:
2434:
2271:
2059:
1655:
1595:
1460:
1324:
978:
815:
665:
578:
486:
398:. In particular, they are able to act as
109:Learn how and when to remove this message
5403:
5390:
3908:
3900:
2615:
1687:
1179:and the voltage across the resistor is:
999:
417:
410:forms, as shown in the diagrams below.
5937:
1617:Both transfer functions have a single
427:time-dependent, can be found by using
371:There are three basic, linear passive
5820:. In the case of Cauer synthesis, a
1662:{\displaystyle s=-{\frac {1}{RC}}\,.}
1341:
822:{\displaystyle s=\sigma +j\omega \,,}
766:{\displaystyle Z_{C}={\frac {1}{sC}}}
507:is the capacitance of the capacitor.
5385:operational amplifier differentiator
3590:This section relies on knowledge of
697:
47:adding citations to reliable sources
18:
5399:
2611:
413:
13:
5891:Bakshi & Bakshi, pp. 3-30–3-37
5728:
5725:
5713:
5710:
5707:
5651:
5648:
5601:
5598:
5532:
5529:
5482:
5479:
5135:
5132:
5098:
5095:
4914:
4911:
4746:
4743:
4622:
4619:
4470:
4467:
4378:
4375:
3688:
3685:
3313:
3274:
3258:Solving the above equation yields
2579:
2576:
2497:
2494:
2408:
2405:
2342:
2339:
2201:
2099:
1982:
1979:
1798:
1795:
1612:
1542:
1539:
1415:
1412:
1309:
1306:
1250:
1247:
1151:
1148:
1100:
1097:
717:) of a capacitor with capacitance
14:
5961:
4954:
1683:
995:
604:is the capacitor voltage at time
5919:Horowitz, Paul; Hill, Winfield,
5379:operational amplifier integrator
3905:Capacitor voltage step-response.
2628:for each voltage is the inverse
23:
5908:, Technical Publications, 2009
5898:
3913:Resistor voltage step-response.
3538:
3530:
3403:
3395:
3306:
3298:
3139:
3131:
3064:
3056:
3011:Frequency-domain considerations
366:
34:needs additional citations for
5885:
5876:
5424:is equal to the input voltage
4028:
4022:
3954:
3948:
3819:
3813:
3746:
3740:
3700:
3694:
3549:
3491:
3414:
3389:
3150:
3125:
3075:
3050:
2973:
2967:
2928:
2922:
2913:
2907:
2858:
2852:
2843:
2837:
2765:
2759:
2720:
2714:
2665:
2659:
2591:
2585:
2509:
2503:
2479:
2473:
2223:
2214:
2121:
2112:
1997:
1988:
1968:
1959:
1929:
1920:
1813:
1804:
1784:
1775:
1745:
1736:
1554:
1548:
1528:
1522:
1503:
1497:
1427:
1421:
1401:
1395:
1376:
1370:
1321:
1315:
1262:
1256:
1205:
1199:
1163:
1157:
1112:
1106:
1045:
1039:
537:
531:
1:
5869:
4517:
4174:of its final value. That is,
168:Optimum "L" (Legendre) filter
5904:Bakshi, U.A.; Bakshi, A.V.,
5882:Horowitz & Hill, p. 1.13
5785:It is sometimes required to
5780:
3596:natural logarithmic constant
1011:By viewing the circuit as a
433:linear differential equation
7:
5827:
5789:an RC circuit from a given
3920:expansions and the inverse
672:{\displaystyle \tau =RC\,.}
10:
5966:
5950:Electronic filter topology
5859:List of electronics topics
3584:Time-domain considerations
2455:
916:and the impedance becomes
510:Solving this equation for
306:resistor–capacitor circuit
5440:With complex impedances:
4337:. Note that the current,
2292:representing the output:
2076:and the phase angles are
1019:across the capacitor is:
909:{\displaystyle \sigma =0}
332:. It may be driven by a
220:Bridged T delay equaliser
136:Network synthesis filters
4352:describing the circuit:
4245:The rate of change is a
686:is measured in seconds,
3607:of the expressions for
2798:Heaviside step function
886:Sinusoidal steady state
514:yields the formula for
429:Kirchhoff's current law
186:Image impedance filters
153:Elliptic (Cauer) filter
5921:The Art of Electronics
5799:positive-real function
5771:
5680:
5550:
5412:
5396:
5374:operational amplifiers
5342:
5191:
5054:
5002:
4935:
4843:
4761:
4710:
4664:
4589:
4565:
4501:
4350:differential equations
4273:. Thus, in going from
4078:
3914:
3906:
3892:
3563:
3455:
3347:
3248:
3164:
3089:
2984:
2776:
2621:
2602:
2446:
2279:
2169:
2067:
1871:
1693:
1663:
1603:
1468:
1332:
1170:
1008:
986:
910:
823:
767:
673:
586:
494:
423:
226:Composite image filter
5906:Circuit Analysis - II
5772:
5681:
5551:
5407:
5395:PWM RC Series Circuit
5394:
5343:
5192:
5055:
5003:
4936:
4844:
4762:
4711:
4665:
4590:
4566:
4502:
4178:is the time it takes
4079:
3912:
3904:
3893:
3564:
3456:
3348:
3249:
3165:
3090:
2985:
2777:
2619:
2603:
2447:
2280:
2170:
2068:
1872:
1691:
1664:
1604:
1469:
1333:
1171:
1003:
987:
911:
824:
768:
674:
587:
495:
421:
203:General image filters
173:Linkwitz–Riley filter
5696:
5566:
5447:
5207:
5070:
5022:
4970:
4949:across the capacitor
4859:
4784:
4726:
4680:
4602:
4579:
4533:
4359:
3931:
3672:
3478:
3376:
3265:
3203:
3112:
3037:
3006:Dirac delta function
2824:
2646:
2634:Dirac delta function
2467:
2299:
2185:
2083:
1887:
1703:
1628:
1484:
1357:
1186:
1026:
923:
894:
794:
732:
650:
525:
441:
43:improve this article
5816:used to synthesise
5356:across the resistor
4904:
4824:
210:(constant R) filter
5854:Electrical network
5767:
5676:
5674:
5546:
5544:
5413:
5397:
5338:
5336:
5187:
5185:
5050:
4998:
4931:
4890:
4839:
4810:
4757:
4706:
4660:
4585:
4561:
4512:integrating factor
4497:
4495:
4144:, usually denoted
4074:
4072:
3915:
3907:
3888:
3886:
3605:Laplace transforms
3559:
3536:
3528:
3451:
3445:
3401:
3343:
3304:
3244:
3160:
3137:
3085:
3062:
2980:
2772:
2622:
2598:
2442:
2440:
2275:
2165:
2063:
1867:
1694:
1659:
1599:
1464:
1342:Transfer functions
1328:
1166:
1009:
982:
906:
879:radians per second
819:
783:is, in general, a
763:
669:
582:
490:
424:
396:analog electronics
143:Butterworth filter
127:electronic filters
5791:rational function
5761:
5734:
5666:
5610:
5491:
5328:
5268:
5164:
5120:
5119:
5044:
4992:
4888:
4808:
4755:
4700:
4654:
4651:
4588:{\displaystyle I}
4555:
4438:
4401:
4062:
3999:
3922:Laplace transform
3918:Partial fractions
3878:
3865:
3797:
3784:
3724:
3535:
3527:
3521:
3444:
3438:
3400:
3341:
3303:
3296:
3242:
3241:
3136:
3061:
2960:
2942:
2900:
2877:
2752:
2734:
2707:
2684:
2630:Laplace transform
2568:
2536:
2533:
2265:
2057:
2056:
2001:
1865:
1864:
1817:
1653:
1593:
1558:
1458:
1431:
1348:transfer function
1298:
1239:
1236:
1140:
1089:
1086:
1065:
976:
955:
875:angular frequency
858:exponential decay
778:complex frequency
761:
704:complex impedance
698:Complex impedance
682:In this formula,
643:and is given by,
574:
516:exponential decay
478:
465:
357:band-stop filters
353:band-pass filters
345:high-pass filters
302:
301:
193:Constant k filter
119:
118:
111:
93:
5957:
5892:
5889:
5883:
5880:
5834:RC time constant
5810:Foster synthesis
5803:poles and zeroes
5776:
5774:
5773:
5768:
5762:
5760:
5740:
5735:
5733:
5732:
5731:
5718:
5717:
5716:
5700:
5685:
5683:
5682:
5677:
5675:
5667:
5665:
5657:
5656:
5655:
5654:
5637:
5625:
5624:
5611:
5606:
5605:
5604:
5591:
5582:
5581:
5555:
5553:
5552:
5547:
5545:
5537:
5536:
5535:
5506:
5505:
5492:
5487:
5486:
5485:
5472:
5463:
5462:
5432:
5423:
5400:Parallel circuit
5347:
5345:
5344:
5339:
5337:
5329:
5327:
5319:
5318:
5317:
5301:
5286:
5285:
5269:
5267:
5259:
5258:
5257:
5244:
5223:
5222:
5196:
5194:
5193:
5188:
5186:
5178:
5177:
5165:
5163:
5149:
5140:
5139:
5138:
5121:
5118:
5104:
5103:
5102:
5101:
5088:
5059:
5057:
5056:
5051:
5045:
5043:
5032:
5014:
5007:
5005:
5004:
4999:
4993:
4991:
4980:
4963:frequency i.e.,
4940:
4938:
4937:
4932:
4919:
4918:
4917:
4903:
4898:
4889:
4887:
4876:
4871:
4870:
4848:
4846:
4845:
4840:
4823:
4818:
4809:
4801:
4796:
4795:
4766:
4764:
4763:
4758:
4756:
4751:
4750:
4749:
4736:
4715:
4713:
4712:
4707:
4701:
4693:
4669:
4667:
4666:
4661:
4655:
4653:
4652:
4650:
4636:
4627:
4626:
4625:
4612:
4594:
4592:
4591:
4586:
4570:
4568:
4567:
4562:
4556:
4554:
4543:
4526:frequency, i.e.
4506:
4504:
4503:
4498:
4496:
4488:
4487:
4475:
4474:
4473:
4453:
4452:
4439:
4437:
4429:
4428:
4427:
4414:
4402:
4397:
4396:
4395:
4383:
4382:
4381:
4367:
4340:
4336:
4329:
4325:
4321:
4317:
4310:
4306:
4296:
4282:
4272:
4268:
4267:
4265:
4264:
4259:
4256:
4241:
4239:
4237:
4236:
4231:
4228:
4216:
4209:
4207:
4205:
4204:
4199:
4196:
4184:
4177:
4173:
4172:
4170:
4169:
4164:
4161:
4153:
4135:
4124:
4114:
4112:
4110:
4109:
4106:
4103:
4083:
4081:
4080:
4075:
4073:
4065:
4064:
4063:
4061:
4050:
4021:
4020:
4007:
4003:
4002:
4001:
4000:
3998:
3987:
3947:
3946:
3897:
3895:
3894:
3889:
3887:
3879:
3871:
3866:
3864:
3847:
3836:
3812:
3811:
3798:
3790:
3785:
3783:
3763:
3739:
3738:
3725:
3717:
3693:
3692:
3691:
3664:
3651:
3644:
3630:
3620:
3613:
3593:
3568:
3566:
3565:
3560:
3548:
3547:
3537:
3533:
3529:
3525:
3522:
3514:
3506:
3505:
3490:
3489:
3470:
3460:
3458:
3457:
3452:
3446:
3442:
3439:
3431:
3426:
3425:
3413:
3412:
3402:
3398:
3388:
3387:
3368:
3352:
3350:
3349:
3344:
3342:
3340:
3323:
3318:
3317:
3316:
3305:
3301:
3297:
3295:
3284:
3279:
3278:
3277:
3253:
3251:
3250:
3245:
3243:
3237:
3233:
3228:
3227:
3215:
3214:
3194:cutoff frequency
3182:high-pass filter
3169:
3167:
3166:
3161:
3149:
3148:
3138:
3134:
3124:
3123:
3104:
3094:
3092:
3091:
3086:
3074:
3073:
3063:
3059:
3049:
3048:
3029:
3017:frequency domain
3003:
2989:
2987:
2986:
2981:
2963:
2962:
2961:
2953:
2943:
2935:
2903:
2902:
2901:
2899:
2888:
2878:
2876:
2865:
2836:
2835:
2809:
2795:
2781:
2779:
2778:
2773:
2755:
2754:
2753:
2745:
2735:
2727:
2710:
2709:
2708:
2706:
2695:
2685:
2683:
2672:
2658:
2657:
2626:impulse response
2612:Impulse response
2607:
2605:
2604:
2599:
2584:
2583:
2582:
2569:
2567:
2550:
2542:
2537:
2535:
2534:
2532:
2521:
2512:
2502:
2501:
2500:
2486:
2451:
2449:
2448:
2443:
2441:
2433:
2432:
2431:
2430:
2413:
2412:
2411:
2398:
2397:
2381:
2380:
2367:
2366:
2365:
2364:
2347:
2346:
2345:
2332:
2331:
2315:
2314:
2284:
2282:
2281:
2276:
2270:
2266:
2264:
2250:
2241:
2240:
2213:
2212:
2197:
2196:
2174:
2172:
2171:
2166:
2164:
2160:
2139:
2138:
2111:
2110:
2095:
2094:
2072:
2070:
2069:
2064:
2058:
2055:
2054:
2049:
2045:
2023:
2022:
2011:
2006:
2002:
2000:
1987:
1986:
1985:
1971:
1958:
1957:
1947:
1938:
1937:
1919:
1918:
1909:
1908:
1899:
1898:
1876:
1874:
1873:
1868:
1866:
1863:
1862:
1857:
1853:
1831:
1827:
1822:
1818:
1816:
1803:
1802:
1801:
1787:
1774:
1773:
1763:
1754:
1753:
1735:
1734:
1725:
1724:
1715:
1714:
1668:
1666:
1665:
1660:
1654:
1652:
1641:
1608:
1606:
1605:
1600:
1594:
1592:
1575:
1564:
1559:
1557:
1547:
1546:
1545:
1531:
1521:
1520:
1510:
1496:
1495:
1473:
1471:
1470:
1465:
1459:
1457:
1437:
1432:
1430:
1420:
1419:
1418:
1404:
1394:
1393:
1383:
1369:
1368:
1337:
1335:
1334:
1329:
1314:
1313:
1312:
1299:
1297:
1280:
1269:
1255:
1254:
1253:
1240:
1238:
1237:
1235:
1224:
1212:
1198:
1197:
1175:
1173:
1172:
1167:
1156:
1155:
1154:
1141:
1139:
1119:
1105:
1104:
1103:
1090:
1088:
1087:
1085:
1074:
1064:
1053:
1052:
1038:
1037:
991:
989:
988:
983:
977:
975:
964:
956:
954:
940:
935:
934:
915:
913:
912:
907:
869:
864:per second), and
855:
849:
838:
828:
826:
825:
820:
782:
772:
770:
769:
764:
762:
760:
749:
744:
743:
720:
712:
693:
689:
685:
678:
676:
675:
670:
641:RC time constant
638:
637:
635:
634:
629:
626:
610:
603:
591:
589:
588:
583:
577:
576:
575:
573:
562:
552:
551:
513:
506:
499:
497:
496:
491:
479:
471:
466:
464:
456:
448:
414:Natural response
359:usually require
349:low-pass filters
322:electric circuit
294:
287:
280:
198:m-derived filter
148:Chebyshev filter
121:
120:
114:
107:
103:
100:
94:
92:
51:
27:
19:
5965:
5964:
5960:
5959:
5958:
5956:
5955:
5954:
5945:Analog circuits
5935:
5934:
5901:
5896:
5895:
5890:
5886:
5881:
5877:
5872:
5830:
5814:Cauer synthesis
5783:
5744:
5739:
5724:
5723:
5719:
5706:
5705:
5701:
5699:
5697:
5694:
5693:
5673:
5672:
5658:
5647:
5646:
5642:
5638:
5636:
5626:
5620:
5616:
5613:
5612:
5597:
5596:
5592:
5590:
5583:
5577:
5573:
5569:
5567:
5564:
5563:
5543:
5542:
5528:
5527:
5523:
5507:
5501:
5497:
5494:
5493:
5478:
5477:
5473:
5471:
5464:
5458:
5454:
5450:
5448:
5445:
5444:
5431:
5425:
5422:
5416:
5402:
5366:differentiation
5335:
5334:
5320:
5310:
5306:
5302:
5300:
5287:
5281:
5277:
5274:
5273:
5260:
5253:
5249:
5245:
5243:
5224:
5218:
5214:
5210:
5208:
5205:
5204:
5184:
5183:
5173:
5169:
5153:
5148:
5141:
5131:
5130:
5126:
5123:
5122:
5108:
5094:
5093:
5089:
5087:
5080:
5073:
5071:
5068:
5067:
5036:
5031:
5023:
5020:
5019:
5012:
4984:
4979:
4971:
4968:
4967:
4957:
4910:
4909:
4905:
4899:
4894:
4880:
4875:
4866:
4862:
4860:
4857:
4856:
4819:
4814:
4800:
4791:
4787:
4785:
4782:
4781:
4742:
4741:
4737:
4735:
4727:
4724:
4723:
4692:
4681:
4678:
4677:
4640:
4635:
4628:
4618:
4617:
4613:
4611:
4603:
4600:
4599:
4580:
4577:
4576:
4547:
4542:
4534:
4531:
4530:
4520:
4494:
4493:
4483:
4479:
4466:
4465:
4461:
4454:
4448:
4444:
4441:
4440:
4430:
4423:
4419:
4415:
4413:
4403:
4391:
4387:
4374:
4373:
4369:
4368:
4366:
4362:
4360:
4357:
4356:
4338:
4331:
4327:
4323:
4319:
4312:
4308:
4298:
4284:
4274:
4270:
4260:
4257:
4254:
4253:
4251:
4249:
4232:
4229:
4226:
4225:
4223:
4218:
4215:
4211:
4200:
4197:
4194:
4193:
4191:
4186:
4183:
4179:
4175:
4165:
4162:
4159:
4158:
4156:
4155:
4145:
4133:
4116:
4107:
4104:
4101:
4100:
4098:
4092:
4071:
4070:
4054:
4049:
4045:
4041:
4031:
4016:
4012:
4009:
4008:
3991:
3986:
3982:
3978:
3971:
3967:
3957:
3942:
3938:
3934:
3932:
3929:
3928:
3885:
3884:
3870:
3848:
3837:
3835:
3822:
3807:
3803:
3800:
3799:
3789:
3767:
3762:
3749:
3734:
3730:
3727:
3726:
3716:
3703:
3684:
3683:
3679:
3675:
3673:
3670:
3669:
3659:
3653:
3646:
3642:
3636:
3622:
3619:
3615:
3612:
3608:
3591:
3586:
3543:
3539:
3531:
3523:
3513:
3501:
3497:
3485:
3481:
3479:
3476:
3475:
3465:
3440:
3430:
3421:
3417:
3408:
3404:
3396:
3383:
3379:
3377:
3374:
3373:
3363:
3327:
3322:
3312:
3311:
3307:
3299:
3288:
3283:
3273:
3272:
3268:
3266:
3263:
3262:
3232:
3223:
3219:
3210:
3206:
3204:
3201:
3200:
3176:low-pass filter
3144:
3140:
3132:
3119:
3115:
3113:
3110:
3109:
3099:
3069:
3065:
3057:
3044:
3040:
3038:
3035:
3034:
3024:
3013:
2994:
2952:
2948:
2944:
2934:
2892:
2887:
2883:
2879:
2869:
2864:
2831:
2827:
2825:
2822:
2821:
2801:
2786:
2744:
2740:
2736:
2726:
2699:
2694:
2690:
2686:
2676:
2671:
2653:
2649:
2647:
2644:
2643:
2614:
2575:
2574:
2570:
2551:
2543:
2541:
2525:
2520:
2513:
2493:
2492:
2488:
2487:
2485:
2468:
2465:
2464:
2458:
2439:
2438:
2426:
2422:
2418:
2414:
2404:
2403:
2399:
2393:
2389:
2382:
2376:
2372:
2369:
2368:
2360:
2356:
2352:
2348:
2338:
2337:
2333:
2327:
2323:
2316:
2310:
2306:
2302:
2300:
2297:
2296:
2254:
2249:
2245:
2233:
2229:
2208:
2204:
2192:
2188:
2186:
2183:
2182:
2147:
2143:
2131:
2127:
2106:
2102:
2090:
2086:
2084:
2081:
2080:
2050:
2035:
2031:
2030:
2012:
2010:
1978:
1977:
1973:
1972:
1953:
1949:
1948:
1946:
1942:
1933:
1932:
1914:
1910:
1904:
1903:
1894:
1890:
1888:
1885:
1884:
1858:
1843:
1839:
1838:
1826:
1794:
1793:
1789:
1788:
1769:
1765:
1764:
1762:
1758:
1749:
1748:
1730:
1726:
1720:
1719:
1710:
1706:
1704:
1701:
1700:
1686:
1676:located at the
1645:
1640:
1629:
1626:
1625:
1615:
1613:Poles and zeros
1576:
1565:
1563:
1538:
1537:
1533:
1532:
1516:
1512:
1511:
1509:
1491:
1487:
1485:
1482:
1481:
1441:
1436:
1411:
1410:
1406:
1405:
1389:
1385:
1384:
1382:
1364:
1360:
1358:
1355:
1354:
1344:
1305:
1304:
1300:
1281:
1270:
1268:
1246:
1245:
1241:
1228:
1223:
1216:
1211:
1193:
1189:
1187:
1184:
1183:
1147:
1146:
1142:
1123:
1118:
1096:
1095:
1091:
1078:
1073:
1066:
1057:
1051:
1033:
1029:
1027:
1024:
1023:
1013:voltage divider
998:
968:
963:
944:
939:
930:
926:
924:
921:
920:
895:
892:
891:
888:
867:
853:
844:
839:represents the
836:
795:
792:
791:
780:
753:
748:
739:
735:
733:
730:
729:
718:
711:
707:
700:
691:
687:
683:
651:
648:
647:
630:
627:
625:
619:
618:
616:
615:
605:
602:
596:
566:
561:
557:
553:
547:
543:
526:
523:
522:
511:
504:
470:
457:
449:
447:
442:
439:
438:
416:
400:passive filters
369:
298:
269:
268:
244:
236:
235:
231:mm'-type filter
188:
178:
177:
163:Gaussian filter
138:
126:
115:
104:
98:
95:
52:
50:
40:
28:
17:
12:
11:
5:
5963:
5953:
5952:
5947:
5933:
5932:
5917:
5900:
5897:
5894:
5893:
5884:
5874:
5873:
5871:
5868:
5867:
5866:
5861:
5856:
5851:
5846:
5841:
5836:
5829:
5826:
5822:ladder network
5782:
5779:
5778:
5777:
5766:
5759:
5756:
5753:
5750:
5747:
5743:
5738:
5730:
5727:
5722:
5715:
5712:
5709:
5704:
5687:
5686:
5671:
5664:
5661:
5653:
5650:
5645:
5641:
5635:
5632:
5629:
5627:
5623:
5619:
5615:
5614:
5609:
5603:
5600:
5595:
5589:
5586:
5584:
5580:
5576:
5572:
5571:
5557:
5556:
5541:
5534:
5531:
5526:
5522:
5519:
5516:
5513:
5510:
5508:
5504:
5500:
5496:
5495:
5490:
5484:
5481:
5476:
5470:
5467:
5465:
5461:
5457:
5453:
5452:
5435:current source
5429:
5420:
5401:
5398:
5353:differentiator
5349:
5348:
5333:
5326:
5323:
5316:
5313:
5309:
5305:
5299:
5296:
5293:
5290:
5288:
5284:
5280:
5276:
5275:
5272:
5266:
5263:
5256:
5252:
5248:
5242:
5239:
5236:
5233:
5230:
5227:
5225:
5221:
5217:
5213:
5212:
5198:
5197:
5182:
5176:
5172:
5168:
5162:
5159:
5156:
5152:
5147:
5144:
5142:
5137:
5134:
5129:
5125:
5124:
5117:
5114:
5111:
5107:
5100:
5097:
5092:
5086:
5083:
5081:
5079:
5076:
5075:
5061:
5060:
5049:
5042:
5039:
5035:
5030:
5027:
5009:
5008:
4997:
4990:
4987:
4983:
4978:
4975:
4956:
4955:Differentiator
4953:
4942:
4941:
4930:
4926:
4923:
4916:
4913:
4908:
4902:
4897:
4893:
4886:
4883:
4879:
4874:
4869:
4865:
4850:
4849:
4838:
4834:
4831:
4827:
4822:
4817:
4813:
4807:
4804:
4799:
4794:
4790:
4770:which is just
4768:
4767:
4754:
4748:
4745:
4740:
4734:
4731:
4717:
4716:
4705:
4699:
4696:
4691:
4688:
4685:
4671:
4670:
4659:
4649:
4646:
4643:
4639:
4634:
4631:
4624:
4621:
4616:
4610:
4607:
4584:
4572:
4571:
4560:
4553:
4550:
4546:
4541:
4538:
4519:
4516:
4508:
4507:
4492:
4486:
4482:
4478:
4472:
4469:
4464:
4460:
4457:
4455:
4451:
4447:
4443:
4442:
4436:
4433:
4426:
4422:
4418:
4412:
4409:
4406:
4404:
4400:
4394:
4390:
4386:
4380:
4377:
4372:
4365:
4364:
4213:
4181:
4085:
4084:
4069:
4060:
4057:
4053:
4048:
4044:
4040:
4037:
4034:
4032:
4030:
4027:
4024:
4019:
4015:
4011:
4010:
4006:
3997:
3994:
3990:
3985:
3981:
3977:
3974:
3970:
3966:
3963:
3960:
3958:
3956:
3953:
3950:
3945:
3941:
3937:
3936:
3899:
3898:
3883:
3877:
3874:
3869:
3863:
3860:
3857:
3854:
3851:
3846:
3843:
3840:
3834:
3831:
3828:
3825:
3823:
3821:
3818:
3815:
3810:
3806:
3802:
3801:
3796:
3793:
3788:
3782:
3779:
3776:
3773:
3770:
3766:
3761:
3758:
3755:
3752:
3750:
3748:
3745:
3742:
3737:
3733:
3729:
3728:
3723:
3720:
3715:
3712:
3709:
3706:
3704:
3702:
3699:
3696:
3690:
3687:
3682:
3678:
3677:
3657:
3640:
3617:
3610:
3601:
3600:
3585:
3582:
3570:
3569:
3558:
3554:
3551:
3546:
3542:
3520:
3517:
3512:
3509:
3504:
3500:
3496:
3493:
3488:
3484:
3462:
3461:
3450:
3437:
3434:
3429:
3424:
3420:
3416:
3411:
3407:
3394:
3391:
3386:
3382:
3354:
3353:
3339:
3336:
3333:
3330:
3326:
3321:
3315:
3310:
3294:
3291:
3287:
3282:
3276:
3271:
3256:
3255:
3240:
3236:
3231:
3226:
3222:
3218:
3213:
3209:
3171:
3170:
3159:
3155:
3152:
3147:
3143:
3130:
3127:
3122:
3118:
3096:
3095:
3084:
3080:
3077:
3072:
3068:
3055:
3052:
3047:
3043:
3012:
3009:
2991:
2990:
2979:
2975:
2972:
2969:
2966:
2959:
2956:
2951:
2947:
2941:
2938:
2933:
2930:
2927:
2924:
2921:
2918:
2915:
2912:
2909:
2906:
2898:
2895:
2891:
2886:
2882:
2875:
2872:
2868:
2863:
2860:
2857:
2854:
2851:
2848:
2845:
2842:
2839:
2834:
2830:
2783:
2782:
2771:
2767:
2764:
2761:
2758:
2751:
2748:
2743:
2739:
2733:
2730:
2725:
2722:
2719:
2716:
2713:
2705:
2702:
2698:
2693:
2689:
2682:
2679:
2675:
2670:
2667:
2664:
2661:
2656:
2652:
2613:
2610:
2609:
2608:
2597:
2593:
2590:
2587:
2581:
2578:
2573:
2566:
2563:
2560:
2557:
2554:
2549:
2546:
2540:
2531:
2528:
2524:
2519:
2516:
2511:
2508:
2505:
2499:
2496:
2491:
2484:
2481:
2478:
2475:
2472:
2457:
2454:
2453:
2452:
2437:
2429:
2425:
2421:
2417:
2410:
2407:
2402:
2396:
2392:
2388:
2385:
2383:
2379:
2375:
2371:
2370:
2363:
2359:
2355:
2351:
2344:
2341:
2336:
2330:
2326:
2322:
2319:
2317:
2313:
2309:
2305:
2304:
2286:
2285:
2274:
2269:
2263:
2260:
2257:
2253:
2248:
2244:
2239:
2236:
2232:
2228:
2225:
2222:
2219:
2216:
2211:
2207:
2203:
2200:
2195:
2191:
2176:
2175:
2163:
2159:
2156:
2153:
2150:
2146:
2142:
2137:
2134:
2130:
2126:
2123:
2120:
2117:
2114:
2109:
2105:
2101:
2098:
2093:
2089:
2074:
2073:
2062:
2053:
2048:
2044:
2041:
2038:
2034:
2029:
2026:
2021:
2018:
2015:
2009:
2005:
1999:
1996:
1993:
1990:
1984:
1981:
1976:
1970:
1967:
1964:
1961:
1956:
1952:
1945:
1941:
1936:
1931:
1928:
1925:
1922:
1917:
1913:
1907:
1902:
1897:
1893:
1878:
1877:
1861:
1856:
1852:
1849:
1846:
1842:
1837:
1834:
1830:
1825:
1821:
1815:
1812:
1809:
1806:
1800:
1797:
1792:
1786:
1783:
1780:
1777:
1772:
1768:
1761:
1757:
1752:
1747:
1744:
1741:
1738:
1733:
1729:
1723:
1718:
1713:
1709:
1685:
1684:Gain and phase
1682:
1670:
1669:
1658:
1651:
1648:
1644:
1639:
1636:
1633:
1614:
1611:
1610:
1609:
1598:
1591:
1588:
1585:
1582:
1579:
1574:
1571:
1568:
1562:
1556:
1553:
1550:
1544:
1541:
1536:
1530:
1527:
1524:
1519:
1515:
1508:
1505:
1502:
1499:
1494:
1490:
1475:
1474:
1463:
1456:
1453:
1450:
1447:
1444:
1440:
1435:
1429:
1426:
1423:
1417:
1414:
1409:
1403:
1400:
1397:
1392:
1388:
1381:
1378:
1375:
1372:
1367:
1363:
1343:
1340:
1339:
1338:
1327:
1323:
1320:
1317:
1311:
1308:
1303:
1296:
1293:
1290:
1287:
1284:
1279:
1276:
1273:
1267:
1264:
1261:
1258:
1252:
1249:
1244:
1234:
1231:
1227:
1222:
1219:
1215:
1210:
1207:
1204:
1201:
1196:
1192:
1177:
1176:
1165:
1162:
1159:
1153:
1150:
1145:
1138:
1135:
1132:
1129:
1126:
1122:
1117:
1114:
1111:
1108:
1102:
1099:
1094:
1084:
1081:
1077:
1072:
1069:
1063:
1060:
1056:
1050:
1047:
1044:
1041:
1036:
1032:
997:
996:Series circuit
994:
993:
992:
981:
974:
971:
967:
962:
959:
953:
950:
947:
943:
938:
933:
929:
905:
902:
899:
887:
884:
883:
882:
865:
851:
841:imaginary unit
830:
829:
818:
814:
811:
808:
805:
802:
799:
785:complex number
774:
773:
759:
756:
752:
747:
742:
738:
709:
699:
696:
680:
679:
668:
664:
661:
658:
655:
639:is called the
623:
600:
593:
592:
581:
572:
569:
565:
560:
556:
550:
546:
542:
539:
536:
533:
530:
501:
500:
489:
485:
482:
477:
474:
469:
463:
460:
455:
452:
446:
415:
412:
376:analog circuit
368:
365:
338:current source
300:
299:
297:
296:
289:
282:
274:
271:
270:
267:
266:
261:
256:
251:
245:
243:Simple filters
242:
241:
238:
237:
234:
233:
228:
223:
217:
214:Lattice filter
211:
205:
200:
195:
189:
184:
183:
180:
179:
176:
175:
170:
165:
160:
155:
150:
145:
139:
134:
133:
130:
129:
117:
116:
31:
29:
22:
15:
9:
6:
4:
3:
2:
5962:
5951:
5948:
5946:
5943:
5942:
5940:
5930:
5926:
5922:
5918:
5915:
5914:9788184315974
5911:
5907:
5903:
5902:
5888:
5879:
5875:
5865:
5864:Step response
5862:
5860:
5857:
5855:
5852:
5850:
5847:
5845:
5842:
5840:
5837:
5835:
5832:
5831:
5825:
5823:
5819:
5815:
5811:
5806:
5804:
5800:
5796:
5792:
5788:
5764:
5757:
5754:
5751:
5748:
5745:
5741:
5736:
5720:
5702:
5692:
5691:
5690:
5669:
5662:
5659:
5643:
5639:
5633:
5630:
5628:
5621:
5617:
5607:
5593:
5587:
5585:
5578:
5574:
5562:
5561:
5560:
5539:
5524:
5520:
5517:
5514:
5511:
5509:
5502:
5498:
5488:
5474:
5468:
5466:
5459:
5455:
5443:
5442:
5441:
5438:
5436:
5428:
5419:
5410:
5406:
5393:
5389:
5387:
5386:
5381:
5380:
5375:
5371:
5367:
5363:
5359:
5357:
5354:
5331:
5324:
5321:
5314:
5311:
5307:
5303:
5297:
5294:
5291:
5289:
5282:
5278:
5270:
5264:
5261:
5254:
5250:
5246:
5240:
5237:
5234:
5231:
5228:
5226:
5219:
5215:
5203:
5202:
5201:
5180:
5174:
5170:
5166:
5160:
5157:
5154:
5150:
5145:
5143:
5127:
5115:
5112:
5109:
5105:
5090:
5084:
5082:
5077:
5066:
5065:
5064:
5047:
5040:
5037:
5033:
5028:
5025:
5018:
5017:
5016:
4995:
4988:
4985:
4981:
4976:
4973:
4966:
4965:
4964:
4962:
4952:
4950:
4947:
4928:
4924:
4921:
4906:
4900:
4895:
4891:
4884:
4881:
4877:
4872:
4867:
4863:
4855:
4854:
4853:
4836:
4832:
4829:
4825:
4820:
4815:
4811:
4805:
4802:
4797:
4792:
4788:
4780:
4779:
4778:
4775:
4773:
4752:
4738:
4732:
4729:
4722:
4721:
4720:
4703:
4697:
4694:
4689:
4686:
4683:
4676:
4675:
4674:
4657:
4647:
4644:
4641:
4637:
4632:
4629:
4614:
4608:
4605:
4598:
4597:
4596:
4595:given above:
4582:
4558:
4551:
4548:
4544:
4539:
4536:
4529:
4528:
4527:
4525:
4515:
4513:
4490:
4484:
4480:
4476:
4462:
4458:
4456:
4449:
4445:
4434:
4431:
4424:
4420:
4416:
4410:
4407:
4405:
4398:
4392:
4388:
4384:
4370:
4355:
4354:
4353:
4351:
4346:
4344:
4335:
4316:
4305:
4301:
4295:
4291:
4287:
4281:
4277:
4263:
4248:
4243:
4235:
4221:
4203:
4189:
4168:
4152:
4148:
4143:
4142:time constant
4138:
4130:
4128:
4123:
4119:
4113:
4095:
4090:
4067:
4058:
4055:
4051:
4046:
4042:
4038:
4035:
4033:
4025:
4017:
4013:
4004:
3995:
3992:
3988:
3983:
3979:
3975:
3972:
3968:
3964:
3961:
3959:
3951:
3943:
3939:
3927:
3926:
3925:
3923:
3919:
3911:
3903:
3881:
3875:
3872:
3867:
3861:
3858:
3855:
3852:
3849:
3844:
3841:
3838:
3832:
3829:
3826:
3824:
3816:
3808:
3804:
3794:
3791:
3786:
3780:
3777:
3774:
3771:
3768:
3764:
3759:
3756:
3753:
3751:
3743:
3735:
3731:
3721:
3718:
3713:
3710:
3707:
3705:
3697:
3680:
3668:
3667:
3666:
3665:afterwards):
3663:
3656:
3649:
3639:
3634:
3631:. Assuming a
3629:
3625:
3606:
3598:
3597:
3588:
3587:
3581:
3579:
3575:
3556:
3552:
3544:
3540:
3526: radians
3518:
3515:
3510:
3507:
3502:
3498:
3494:
3486:
3482:
3474:
3473:
3472:
3468:
3448:
3443: radians
3435:
3432:
3427:
3422:
3418:
3409:
3405:
3392:
3384:
3380:
3372:
3371:
3370:
3366:
3360:
3357:
3337:
3334:
3331:
3328:
3324:
3319:
3308:
3292:
3289:
3285:
3280:
3269:
3261:
3260:
3259:
3238:
3234:
3229:
3224:
3220:
3216:
3211:
3207:
3199:
3198:
3197:
3195:
3191:
3186:
3184:
3183:
3178:
3177:
3157:
3153:
3145:
3141:
3128:
3120:
3116:
3108:
3107:
3106:
3102:
3082:
3078:
3070:
3066:
3053:
3045:
3041:
3033:
3032:
3031:
3027:
3021:
3018:
3008:
3007:
3001:
2997:
2977:
2970:
2964:
2957:
2954:
2949:
2945:
2939:
2936:
2931:
2925:
2919:
2916:
2910:
2904:
2896:
2893:
2889:
2884:
2880:
2873:
2870:
2866:
2861:
2855:
2849:
2846:
2840:
2832:
2828:
2820:
2819:
2818:
2815:
2813:
2812:time constant
2808:
2804:
2799:
2793:
2789:
2769:
2762:
2756:
2749:
2746:
2741:
2737:
2731:
2728:
2723:
2717:
2711:
2703:
2700:
2696:
2691:
2687:
2680:
2677:
2673:
2668:
2662:
2654:
2650:
2642:
2641:
2640:
2637:
2635:
2631:
2627:
2618:
2595:
2588:
2571:
2564:
2561:
2558:
2555:
2552:
2547:
2544:
2538:
2529:
2526:
2522:
2517:
2514:
2506:
2489:
2482:
2476:
2470:
2463:
2462:
2461:
2435:
2427:
2423:
2419:
2415:
2400:
2394:
2390:
2386:
2384:
2377:
2373:
2361:
2357:
2353:
2349:
2334:
2328:
2324:
2320:
2318:
2311:
2307:
2295:
2294:
2293:
2291:
2272:
2267:
2261:
2258:
2255:
2251:
2246:
2242:
2237:
2234:
2230:
2226:
2220:
2217:
2209:
2205:
2198:
2193:
2189:
2181:
2180:
2179:
2161:
2157:
2154:
2151:
2148:
2144:
2140:
2135:
2132:
2128:
2124:
2118:
2115:
2107:
2103:
2096:
2091:
2087:
2079:
2078:
2077:
2060:
2051:
2046:
2042:
2039:
2036:
2032:
2027:
2024:
2019:
2016:
2013:
2007:
2003:
1994:
1991:
1974:
1965:
1962:
1954:
1950:
1943:
1939:
1926:
1923:
1915:
1911:
1900:
1895:
1891:
1883:
1882:
1881:
1859:
1854:
1850:
1847:
1844:
1840:
1835:
1832:
1828:
1823:
1819:
1810:
1807:
1790:
1781:
1778:
1770:
1766:
1759:
1755:
1742:
1739:
1731:
1727:
1716:
1711:
1707:
1699:
1698:
1697:
1690:
1681:
1679:
1675:
1656:
1649:
1646:
1642:
1637:
1634:
1631:
1624:
1623:
1622:
1620:
1596:
1589:
1586:
1583:
1580:
1577:
1572:
1569:
1566:
1560:
1551:
1534:
1525:
1517:
1513:
1506:
1500:
1492:
1488:
1480:
1479:
1478:
1461:
1454:
1451:
1448:
1445:
1442:
1438:
1433:
1424:
1407:
1398:
1390:
1386:
1379:
1373:
1365:
1361:
1353:
1352:
1351:
1349:
1325:
1318:
1301:
1294:
1291:
1288:
1285:
1282:
1277:
1274:
1271:
1265:
1259:
1242:
1232:
1229:
1225:
1220:
1217:
1213:
1208:
1202:
1194:
1190:
1182:
1181:
1180:
1160:
1143:
1136:
1133:
1130:
1127:
1124:
1120:
1115:
1109:
1092:
1082:
1079:
1075:
1070:
1067:
1061:
1058:
1054:
1048:
1042:
1034:
1030:
1022:
1021:
1020:
1018:
1014:
1006:
1002:
979:
972:
969:
965:
960:
957:
951:
948:
945:
941:
936:
931:
927:
919:
918:
917:
903:
900:
897:
880:
876:
873:
866:
863:
860:constant (in
859:
852:
847:
842:
835:
834:
833:
816:
812:
809:
806:
803:
800:
797:
790:
789:
788:
786:
779:
757:
754:
750:
745:
740:
736:
728:
727:
726:
724:
716:
705:
695:
666:
662:
659:
656:
653:
646:
645:
644:
642:
633:
622:
612:
608:
599:
579:
570:
567:
563:
558:
554:
548:
544:
540:
534:
528:
521:
520:
519:
517:
508:
487:
483:
480:
475:
472:
467:
461:
458:
453:
450:
444:
437:
436:
435:
434:
430:
420:
411:
409:
405:
401:
397:
393:
389:
385:
381:
377:
374:
364:
362:
358:
354:
350:
346:
341:
339:
335:
331:
327:
323:
319:
315:
311:
307:
295:
290:
288:
283:
281:
276:
275:
273:
272:
265:
262:
260:
257:
255:
252:
250:
247:
246:
240:
239:
232:
229:
227:
224:
221:
218:
215:
212:
209:
208:Zobel network
206:
204:
201:
199:
196:
194:
191:
190:
187:
182:
181:
174:
171:
169:
166:
164:
161:
159:
158:Bessel filter
156:
154:
151:
149:
146:
144:
141:
140:
137:
132:
131:
128:
125:Linear analog
123:
122:
113:
110:
102:
91:
88:
84:
81:
77:
74:
70:
67:
63:
60: –
59:
55:
54:Find sources:
48:
44:
38:
37:
32:This article
30:
26:
21:
20:
5920:
5905:
5899:Bibliography
5887:
5878:
5807:
5794:
5784:
5688:
5558:
5439:
5426:
5417:
5414:
5383:
5377:
5360:
5355:
5350:
5199:
5062:
5015:again, when
5010:
4960:
4958:
4948:
4944:which is an
4943:
4851:
4776:
4769:
4718:
4672:
4573:
4523:
4521:
4509:
4347:
4333:
4314:
4303:
4299:
4293:
4289:
4285:
4279:
4275:
4261:
4246:
4244:
4233:
4219:
4201:
4187:
4166:
4150:
4146:
4139:
4131:
4121:
4117:
4097:
4093:
4086:
3916:
3661:
3654:
3647:
3637:
3627:
3623:
3602:
3589:
3571:
3466:
3463:
3364:
3361:
3358:
3355:
3257:
3187:
3180:
3174:
3172:
3100:
3097:
3025:
3022:
3014:
2999:
2995:
2992:
2816:
2806:
2802:
2791:
2787:
2784:
2638:
2623:
2459:
2287:
2177:
2075:
1879:
1695:
1671:
1616:
1476:
1345:
1178:
1010:
889:
845:
831:
775:
701:
690:in ohms and
681:
631:
620:
613:
606:
597:
594:
509:
502:
425:
370:
367:Introduction
342:
324:composed of
317:
313:
309:
305:
303:
248:
105:
96:
86:
79:
72:
65:
58:"RC circuit"
53:
41:Please help
36:verification
33:
5849:RLC circuit
5818:LC circuits
5362:Integration
5351:which is a
1621:located at
694:in farads.
392:RLC circuit
361:RLC filters
5939:Categories
5929:0521809266
5870:References
5844:LC circuit
5839:RL circuit
5787:synthesise
5411:RC circuit
4946:integrator
4518:Integrator
4247:fractional
3633:step input
3015:These are
1007:RC circuit
872:sinusoidal
422:RC circuit
390:, and the
388:LC circuit
384:RL circuit
330:capacitors
318:RC network
310:RC circuit
264:RLC filter
222:(all-pass)
216:(all-pass)
99:March 2018
69:newspapers
5781:Synthesis
5518:ω
5292:≈
5158:ω
5146:≈
5113:ω
5085:≈
5038:ω
5029:≪
4977:≪
4974:ω
4892:∫
4873:≈
4812:∫
4772:Ohm's Law
4733:≈
4690:≫
4684:ω
4645:ω
4540:≫
4537:ω
4477:−
4385:−
4343:Ohm's Law
4217:to reach
4185:to reach
4127:Ohm's law
4047:−
3984:−
3976:−
3868:⋅
3833:⋅
3787:⋅
3760:⋅
3714:⋅
3652:and then
3550:→
3541:ϕ
3516:π
3511:−
3503:∘
3495:−
3492:→
3483:ϕ
3433:π
3423:∘
3415:→
3406:ϕ
3390:→
3381:ϕ
3332:π
3270:ω
3190:bandwidth
3151:→
3126:→
3076:→
3051:→
2958:τ
2950:−
2940:τ
2932:−
2920:δ
2885:−
2862:−
2850:δ
2750:τ
2742:−
2732:τ
2692:−
2424:ϕ
2358:ϕ
2256:ω
2243:
2235:−
2221:ω
2202:∠
2190:ϕ
2152:ω
2149:−
2141:
2133:−
2119:ω
2100:∠
2088:ϕ
2037:ω
2014:ω
1995:ω
1966:ω
1927:ω
1845:ω
1811:ω
1782:ω
1743:ω
1638:−
970:ω
961:−
949:ω
898:σ
813:ω
804:σ
654:τ
559:−
326:resistors
314:RC filter
259:LC filter
254:RL filter
249:RC filter
5828:See also
5409:Parallel
5372:loop of
5370:feedback
4089:charging
3576:(0
408:parallel
380:inductor
320:, is an
4266:
4252:
4238:
4224:
4206:
4192:
4171:
4157:
4111:
4099:
3924:yield:
3645:before
3635:(i.e.
3004:is the
2810:is the
2796:is the
2456:Current
1017:voltage
870:is the
856:is the
636:
617:
334:voltage
83:scholar
5927:
5912:
3594:, the
3572:So at
2993:where
2785:where
2290:phasor
1678:origin
1015:, the
1005:Series
862:nepers
832:where
725:) is
723:farads
595:where
503:where
404:series
386:, the
373:lumped
312:), or
85:
78:
71:
64:
56:
5376:(see
5200:Now,
4777:Now,
4322:from
4190:(1 −
4125:(see
90:JSTOR
76:books
5925:ISBN
5910:ISBN
5382:and
5364:and
4524:high
4292:+ 1)
4269:per
4250:1 −
4210:and
4115:and
3614:and
2800:and
2624:The
2178:and
1880:and
1674:zero
1619:pole
1346:The
877:(in
848:= −1
776:The
721:(in
715:ohms
713:(in
702:The
406:and
355:and
347:and
328:and
62:news
5812:or
5793:in
5421:out
5388:).
5063:so
4961:low
4852:so
4719:so
4288:= (
4283:to
4129:).
3650:= 0
3643:= 0
3534:and
3469:→ ∞
3464:As
3399:and
3367:→ 0
3362:As
3135:and
3103:→ 0
3098:As
3060:and
3028:→ ∞
3023:As
2231:tan
2129:tan
609:= 0
518::
336:or
316:or
45:by
5941::
5437:.
5430:in
5358:.
4951:.
4774:.
4345:.
4304:Nτ
4302:=
4280:Nτ
4278:=
4242:.
4151:RC
4149:=
4122:IR
4120:=
4096:=
3660:=
3658:in
3641:in
3626:→
3624:jω
3578:Hz
3574:DC
3499:90
3471::
3419:90
3369::
3302:or
3185:.
3105::
3030::
2814:.
2807:RC
2805:=
2636:.
1680:.
881:).
843::
787:,
706:,
611:.
351:;
304:A
5931:.
5916:.
5795:s
5765:.
5758:C
5755:R
5752:s
5749:+
5746:1
5742:R
5737:=
5729:n
5726:i
5721:I
5714:t
5711:u
5708:o
5703:V
5670:.
5663:t
5660:d
5652:n
5649:i
5644:V
5640:d
5634:C
5631:=
5622:C
5618:I
5608:R
5602:n
5599:i
5594:V
5588:=
5579:R
5575:I
5540:.
5533:n
5530:i
5525:V
5521:C
5515:j
5512:=
5503:C
5499:I
5489:R
5483:n
5480:i
5475:V
5469:=
5460:R
5456:I
5427:V
5418:V
5332:,
5325:t
5322:d
5315:n
5312:i
5308:V
5304:d
5298:C
5295:R
5283:R
5279:V
5271:R
5265:t
5262:d
5255:C
5251:V
5247:d
5241:C
5238:=
5235:R
5232:I
5229:=
5220:R
5216:V
5181:.
5175:C
5171:V
5167:=
5161:C
5155:j
5151:I
5136:n
5133:i
5128:V
5116:C
5110:j
5106:1
5099:n
5096:i
5091:V
5078:I
5048:,
5041:C
5034:1
5026:R
5013:I
4996:.
4989:C
4986:R
4982:1
4929:,
4925:t
4922:d
4915:n
4912:i
4907:V
4901:t
4896:0
4885:C
4882:R
4878:1
4868:C
4864:V
4837:,
4833:t
4830:d
4826:I
4821:t
4816:0
4806:C
4803:1
4798:=
4793:C
4789:V
4753:R
4747:n
4744:i
4739:V
4730:I
4704:,
4698:R
4695:1
4687:C
4658:,
4648:C
4642:j
4638:1
4633:+
4630:R
4623:n
4620:i
4615:V
4609:=
4606:I
4583:I
4559:.
4552:C
4549:R
4545:1
4491:.
4485:C
4481:V
4471:n
4468:i
4463:V
4459:=
4450:R
4446:V
4435:t
4432:d
4425:C
4421:V
4417:d
4411:C
4408:=
4399:R
4393:C
4389:V
4379:n
4376:i
4371:V
4339:I
4334:τ
4332:5
4328:τ
4324:V
4320:t
4315:τ
4313:5
4309:τ
4300:t
4294:τ
4290:N
4286:t
4276:t
4271:τ
4262:e
4258:/
4255:1
4240:)
4234:e
4230:/
4227:1
4222:(
4220:V
4214:R
4212:V
4208:)
4202:e
4198:/
4195:1
4188:V
4182:C
4180:V
4176:τ
4167:e
4163:/
4160:1
4147:τ
4134:V
4118:V
4108:V
4105:/
4102:Q
4094:C
4068:.
4059:C
4056:R
4052:t
4043:e
4039:V
4036:=
4029:)
4026:t
4023:(
4018:R
4014:V
4005:)
3996:C
3993:R
3989:t
3980:e
3973:1
3969:(
3965:V
3962:=
3955:)
3952:t
3949:(
3944:C
3940:V
3882:.
3876:s
3873:1
3862:C
3859:R
3856:s
3853:+
3850:1
3845:C
3842:R
3839:s
3830:V
3827:=
3820:)
3817:s
3814:(
3809:R
3805:V
3795:s
3792:1
3781:C
3778:R
3775:s
3772:+
3769:1
3765:1
3757:V
3754:=
3747:)
3744:s
3741:(
3736:C
3732:V
3722:s
3719:1
3711:V
3708:=
3701:)
3698:s
3695:(
3689:n
3686:i
3681:V
3662:V
3655:V
3648:t
3638:V
3628:s
3618:R
3616:V
3611:C
3609:V
3599:.
3592:e
3557:.
3553:0
3545:R
3519:2
3508:=
3487:C
3467:ω
3449:.
3436:2
3428:=
3410:R
3393:0
3385:C
3365:ω
3338:C
3335:R
3329:2
3325:1
3320:=
3314:c
3309:f
3293:C
3290:R
3286:1
3281:=
3275:c
3254:.
3239:2
3235:1
3230:=
3225:R
3221:G
3217:=
3212:C
3208:G
3158:.
3154:0
3146:R
3142:G
3129:1
3121:C
3117:G
3101:ω
3083:.
3079:1
3071:R
3067:G
3054:0
3046:C
3042:G
3026:ω
3002:)
3000:t
2998:(
2996:δ
2978:,
2974:)
2971:t
2968:(
2965:u
2955:t
2946:e
2937:1
2929:)
2926:t
2923:(
2917:=
2914:)
2911:t
2908:(
2905:u
2897:C
2894:R
2890:t
2881:e
2874:C
2871:R
2867:1
2859:)
2856:t
2853:(
2847:=
2844:)
2841:t
2838:(
2833:R
2829:h
2803:τ
2794:)
2792:t
2790:(
2788:u
2770:,
2766:)
2763:t
2760:(
2757:u
2747:t
2738:e
2729:1
2724:=
2721:)
2718:t
2715:(
2712:u
2704:C
2701:R
2697:t
2688:e
2681:C
2678:R
2674:1
2669:=
2666:)
2663:t
2660:(
2655:C
2651:h
2596:.
2592:)
2589:s
2586:(
2580:n
2577:i
2572:V
2565:s
2562:C
2559:R
2556:+
2553:1
2548:s
2545:C
2539:=
2530:s
2527:C
2523:1
2518:+
2515:R
2510:)
2507:s
2504:(
2498:n
2495:i
2490:V
2483:=
2480:)
2477:s
2474:(
2471:I
2436:.
2428:R
2420:j
2416:e
2409:n
2406:i
2401:V
2395:R
2391:G
2387:=
2378:R
2374:V
2362:C
2354:j
2350:e
2343:n
2340:i
2335:V
2329:C
2325:G
2321:=
2312:C
2308:V
2273:.
2268:)
2262:C
2259:R
2252:1
2247:(
2238:1
2227:=
2224:)
2218:j
2215:(
2210:R
2206:H
2199:=
2194:R
2162:)
2158:C
2155:R
2145:(
2136:1
2125:=
2122:)
2116:j
2113:(
2108:C
2104:H
2097:=
2092:C
2061:,
2052:2
2047:)
2043:C
2040:R
2033:(
2028:+
2025:1
2020:C
2017:R
2008:=
2004:|
1998:)
1992:j
1989:(
1983:n
1980:i
1975:V
1969:)
1963:j
1960:(
1955:R
1951:V
1944:|
1940:=
1935:|
1930:)
1924:j
1921:(
1916:R
1912:H
1906:|
1901:=
1896:R
1892:G
1860:2
1855:)
1851:C
1848:R
1841:(
1836:+
1833:1
1829:1
1824:=
1820:|
1814:)
1808:j
1805:(
1799:n
1796:i
1791:V
1785:)
1779:j
1776:(
1771:C
1767:V
1760:|
1756:=
1751:|
1746:)
1740:j
1737:(
1732:C
1728:H
1722:|
1717:=
1712:C
1708:G
1657:.
1650:C
1647:R
1643:1
1635:=
1632:s
1597:.
1590:s
1587:C
1584:R
1581:+
1578:1
1573:s
1570:C
1567:R
1561:=
1555:)
1552:s
1549:(
1543:n
1540:i
1535:V
1529:)
1526:s
1523:(
1518:R
1514:V
1507:=
1504:)
1501:s
1498:(
1493:R
1489:H
1462:.
1455:s
1452:C
1449:R
1446:+
1443:1
1439:1
1434:=
1428:)
1425:s
1422:(
1416:n
1413:i
1408:V
1402:)
1399:s
1396:(
1391:C
1387:V
1380:=
1377:)
1374:s
1371:(
1366:C
1362:H
1326:.
1322:)
1319:s
1316:(
1310:n
1307:i
1302:V
1295:s
1292:C
1289:R
1286:+
1283:1
1278:s
1275:C
1272:R
1266:=
1263:)
1260:s
1257:(
1251:n
1248:i
1243:V
1233:s
1230:C
1226:1
1221:+
1218:R
1214:R
1209:=
1206:)
1203:s
1200:(
1195:R
1191:V
1164:)
1161:s
1158:(
1152:n
1149:i
1144:V
1137:s
1134:C
1131:R
1128:+
1125:1
1121:1
1116:=
1113:)
1110:s
1107:(
1101:n
1098:i
1093:V
1083:s
1080:C
1076:1
1071:+
1068:R
1062:s
1059:C
1055:1
1049:=
1046:)
1043:s
1040:(
1035:C
1031:V
980:.
973:C
966:j
958:=
952:C
946:j
942:1
937:=
932:C
928:Z
904:0
901:=
868:ω
854:σ
850:,
846:j
837:j
817:,
810:j
807:+
801:=
798:s
781:s
758:C
755:s
751:1
746:=
741:C
737:Z
719:C
710:C
708:Z
692:C
688:R
684:τ
667:.
663:C
660:R
657:=
632:e
628:/
624:0
621:V
607:t
601:0
598:V
580:,
571:C
568:R
564:t
555:e
549:0
545:V
541:=
538:)
535:t
532:(
529:V
512:V
505:C
488:,
484:0
481:=
476:R
473:V
468:+
462:t
459:d
454:V
451:d
445:C
308:(
293:e
286:t
279:v
112:)
106:(
101:)
97:(
87:·
80:·
73:·
66:·
39:.
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
