78:
4425:
4878:
49:
4330:
1945:
3909:
5114:
1642:
1603:
is large, this zero is important only at frequencies too high to matter in this discussion, so the numerator can be approximated as unity.) However, although the amplifier does have a two-pole behavior, the two time-constants are more complicated than the above expression suggests because the Miller
2163:
3390:
94:
in the amplifier of Figure 1 has two results: first it causes the lowest frequency pole of the amplifier to move still lower in frequency and second, it causes the higher pole to move higher in frequency. The amplifier of Figure 1 has a low frequency pole due to the added input resistance
593:
4325:{\displaystyle {\begin{aligned}\tau _{2}&={\frac {(C_{C}C_{L}+C_{L}C_{i}+C_{i}C_{C})(R_{A}\|R_{i})(R_{O}\|R_{L})}{(C_{M}+C_{i})(R_{A}\|R_{i})+(C_{L}+C_{C})(R_{o}\|R_{L})}}\\&\approx {\frac {C_{C}C_{L}+C_{L}C_{i}+C_{i}C_{C}}{C_{M}}}(R_{O}\|R_{L})\ ,\\\end{aligned}}}
3830:
4870:
416:
4911:
708:
Turning to the second objective, showing the higher pole moves still higher in frequency, it is necessary to look at the output side of the circuit, which contributes a second factor to the overall gain, and additional frequency dependence. The voltage
5536:
35:
lowest in frequency (usually an input pole) to lower frequencies, pole splitting causes the pole next in frequency (usually an output pole) to move to a higher frequency. This pole movement increases the stability of the amplifier and improves its
1940:{\displaystyle {\begin{aligned}C_{M}&=C_{C}\left(1-{\frac {v_{\ell }}{v_{i}}}\right)\\&=C_{C}\left(1-A_{v}{\frac {R_{L}}{R_{L}+R_{o}}}{\frac {1+j\omega C_{C}R_{o}/A_{v}}{1+j\omega (C_{L}+C_{C})(R_{o}\|R_{L})}}\right)\ .\\\end{aligned}}}
1587:
1113:
5413:
4672:
2898:
1215:
1337:
85:
to replace the compensation capacitor with a Miller capacitor at the input and a frequency-dependent current source at the output. (edit: This figure is faulty, as the + and - signs should be switched. There needs to be negative
1967:
963:
3522:
2770:
1437:
3128:
2667:
2542:
442:
4486:, the Bode gain plot breaks slope to fall at 20 dB/decade. The aim is to maintain the 20 dB/decade slope all the way down to zero dB, and taking the ratio of the desired drop in gain (in dB) of 20 log
5550:. Figure 4 shows an example using this equation. At low values of gain this example amplifier satisfies the pole-ratio condition without compensation (that is, in Figure 4 the compensation capacitor
4701:
is not this large, the second break in the Bode plot that occurs at the second pole interrupts the plot before the gain drops to 0 dB with consequent lower stability and degraded step response.
703:
3709:
4734:
3914:
3133:
1647:
447:
2456:
253:
5109:{\displaystyle {\frac {\tau _{1}}{\tau _{2}}}\approx {\frac {(\tau _{1}+\tau _{2})^{2}}{\tau _{1}\tau _{2}}}\approx A_{v}{\frac {R_{i}}{R_{i}+R_{A}}}\cdot {\frac {R_{L}}{R_{L}+R_{o}}}\ ,}
4465:) requires the amplifier gain to drop at 20 dB/decade from the corner frequency down to 0 dB gain, or even lower. With this design the amplifier is stable and has near-optimal
5897:
As an aside, the higher the high-frequency pole is made in frequency, the more likely it becomes for a real amplifier that other poles (not considered in this analysis) play a part.
801:
5417:
3872:
2209:
1604:
capacitance contains a buried frequency dependence that has no importance at low frequencies, but has considerable effect at high frequencies. That is, assuming the output
2387:
3644:
1441:
967:
5854:
5618:
The above is a small-signal analysis. However, when large signals are used, the need to charge and discharge the compensation capacitor adversely affects the amplifier
5129:
4369:
3899:
3692:
3608:
3581:
3554:
3101:
3074:
3047:
3020:
2993:
2959:
2932:
833:
625:
3113:
At low frequencies near the lowest pole of this amplifier, ordinarily the linear term in ω is more important than the quadratic term, so the low frequency behavior of
863:
737:
243:
213:
2306:
4557:
5820:
The sum of the time constants is the coefficient of the term linear in jω and the product of the time constants is the coefficient of the quadratic term in (jω).
2784:
1596:
This gain formula appears to show a simple two-pole response with two time constants. (It also exhibits a zero in the numerator but, assuming the amplifier gain
1128:
1229:
2158:{\displaystyle {\frac {v_{\ell }}{v_{a}}}=A_{v}{\frac {R_{i}}{R_{i}+R_{A}}}{\frac {R_{L}}{R_{L}+R_{o}}}{\frac {1+j\omega C_{C}R_{o}/A_{v}}{D_{\omega }}}\ ,}
5888:, but the difference is minor assuming the load capacitance is not so large that it controls the low frequency response instead of the Miller capacitance.
873:
5557:
is small at low gain), but as gain increases, a compensation capacitance rapidly becomes necessary (that is, in Figure 4 the compensation capacitor
3416:
3385:{\displaystyle {\begin{aligned}\ D_{\omega }&=1+j\omega \\&=1+j\omega (\tau _{1}+\tau _{2})\approx 1+j\omega \tau _{1}\ ,\ \\\end{aligned}}}
2682:
1341:
2546:
2460:
588:{\displaystyle {\begin{aligned}f_{1}&={\frac {1}{2\pi (C_{M}+C_{i})(R_{A}\|R_{i})}}\\&={\frac {1}{2\pi \tau _{1}}}\ ,\\\end{aligned}}}
5715:
1626:), corresponds to a frequency well above the low frequency pole, the accurate form of the Miller capacitance must be used, rather than the
6025:
design for a two-pole amplifier. However, real amplifiers have more than two poles, and a factor greater than two often is necessary.
5752:
5989:
5948:
5918:
5796:
5762:
2968:. They correspond to the time constants of the two poles of the amplifier. One or the other time constant is the longest; suppose
5979:
1120:
This expression is combined with the gain factor found earlier for the input side of the circuit to obtain the overall gain as
3825:{\displaystyle \tau _{2}={\frac {\tau _{1}\tau _{2}}{\tau _{1}}}\approx {\frac {\tau _{1}\tau _{2}}{\tau _{1}+\tau _{2}}}\ .}
627:
for the time constant of the lowest pole. This frequency is lower than the initial low frequency of the amplifier, which for
4865:{\displaystyle {\frac {\tau _{1}}{\tau _{2}}}\approx A_{v}{\frac {R_{i}}{R_{i}+R_{A}}}\cdot {\frac {R_{L}}{R_{L}+R_{o}}}\ ,}
637:
181:, the circuit of Figure 1 is transformed to that of Figure 2, which is electrically equivalent to Figure 1. Application of
5705:
5564:
increases rapidly with gain) because the necessary pole ratio increases with gain. For still larger gain, the necessary
2391:
1959:
is negative.) Upon substitution of this result into the gain expression and collecting terms, the gain is rewritten as:
411:{\displaystyle {\frac {v_{i}}{v_{a}}}={\frac {R_{i}}{R_{i}+R_{A}}}{\frac {1}{1+j\omega (C_{M}+C_{i})(R_{A}\|R_{i})}}\ ,}
808:
Using this relation and applying
Kirchhoff's current law to the output side of the circuit determines the load voltage
5811:
Although this example appears very specific, the associated mathematical analysis is very much used in circuit design.
6047:
173:
The first objective, to show the lowest pole moves down in frequency, is established using the same approach as the
77:
6071:
182:
6038:
3694:
is valid, the second time constant, the position of the high frequency pole, is found from the quadratic term in
6066:
73:. (edit: This figure is faulty, as the + and - signs should be switched. There needs to be negative feedback.)
5531:{\displaystyle {\color {White}\cdot }=A_{v}{\frac {R_{i}}{R_{i}+R_{A}}}\cdot {\frac {R_{L}}{R_{L}+R_{o}}}\ ,}
4704:
Figure 3 shows that to obtain the correct gain dependence on frequency, the second pole is at least a factor
163:). The upward movement of the high-frequency pole occurs because the Miller-amplified compensation capacitor
32:
747:
5638:
20:
3840:
2185:
24:
1582:{\displaystyle \cdot {\frac {1+j\omega C_{C}R_{o}/A_{v}}{1+j\omega (C_{L}+C_{C})(R_{o}\|R_{L})}}\ .}
1108:{\displaystyle \cdot {\frac {1+j\omega C_{C}R_{o}/A_{v}}{1+j\omega (C_{L}+C_{C})(R_{o}\|R_{L})}}\ .}
1631:
1627:
178:
128:
82:
31:
is introduced between the input and output sides of the amplifier with the intention of moving the
5408:{\displaystyle {\frac {^{2}}{(C_{C}C_{L}+C_{L}C_{i}+C_{i}C_{C})(R_{A}\|R_{i})(R_{O}\|R_{L})}}\,\!}
2310:
6022:
5725:
5687:
3620:
5832:
4424:
4347:
3877:
3670:
3586:
3559:
3532:
3079:
3052:
3025:
2998:
2971:
2937:
2910:
811:
603:
5985:
5944:
5938:
5914:
5792:
5758:
5711:
838:
712:
218:
188:
5691:
4712:
4667:{\displaystyle =20{\frac {\mathrm {log_{10}} (A_{v})}{\mathrm {log_{10}} (f_{2}/f_{1})}}\ ,}
3529:
which is simply the previous Miller capacitance evaluated at low frequencies. On this basis
5913:(Fifth ed.). New York: Oxford University Press. pp. 849 and Example 8.6, p. 853.
4469:
even as a unity gain voltage buffer. A more aggressive technique is two-pole compensation.
2893:{\displaystyle =1+j\omega ({\tau }_{1}+{\tau }_{2}))+(j\omega )^{2}\tau _{1}\tau _{2}\ ,\ }
2213:
1210:{\displaystyle {\frac {v_{\ell }}{v_{a}}}={\frac {v_{\ell }}{v_{i}}}{\frac {v_{i}}{v_{a}}}}
5737:
4896:
4877:
2674:
Every quadratic has two factors, and this expression looks simpler if it is rewritten as
131:. The amplifier is given a high frequency output pole by addition of the load resistance
3667:
At high frequencies the quadratic term becomes important. Assuming the above result for
1332:{\displaystyle =A_{v}{\frac {R_{i}}{R_{i}+R_{A}}}\cdot {\frac {R_{L}}{R_{L}+R_{o}}}\,\!}
5663:
5622:; in particular, the response to an input ramp signal is limited by the need to charge
3837:
Substituting in this expression the quadratic coefficient corresponding to the product
48:
6060:
5754:
Intuitive analog circuit design: a problem-solving approach using design case studies
5658:
5648:
5643:
5607:
4466:
3405:
174:
37:
958:{\displaystyle {\frac {v_{\ell }}{v_{i}}}=A_{v}{\frac {R_{L}}{R_{L}+R_{o}}}\,\!}
3517:{\displaystyle C_{M}=C_{C}\left(1-A_{v}{\frac {R_{L}}{R_{L}+R_{o}}}\right)\ ,}
81:
Figure 2: Operational amplifier with compensation capacitor transformed using
6051:
6042:
5683:
5653:
5619:
4429:
2995:
is the longest time constant, corresponding to the lowest pole, and suppose
2765:{\displaystyle \ D_{\omega }=(1+j\omega {\tau }_{1})(1+j\omega {\tau }_{2})}
1432:{\displaystyle \cdot {\frac {1}{1+j\omega (C_{M}+C_{i})(R_{A}\|R_{i})}}\,\!}
28:
5943:. Boston, MA: Kluwer Academic. pp. §6.2, pp.205–206 and Figure 6.2.1.
4392:); that is, the higher pole has moved still higher in frequency because of
5606:
on the right side of this equation. See Sansen or
Huijsing and article on
5543:
which provides a quadratic equation to determine an appropriate value for
4711:
higher in frequency than the first pole. The gain is reduced a bit by the
2662:{\displaystyle \ +(j\omega )^{2}C_{C}C_{L}(R_{A}\|R_{i})(R_{O}\|R_{L})\ .}
2537:{\displaystyle \cdot \left(1-A_{v}{\frac {R_{L}}{R_{L}+R_{O}}}\right)\,\!}
5964:
5908:
5782:
424:
2961:
are combinations of the capacitances and resistances in the formula for
59:
between input and output; notice the amplifier has both input impedance
4496:
to the required change in frequency (on a log frequency scale) of ( log
739:
is determined by the gain of the ideal op amp inside the amplifier as
90:
This example shows that introduction of the capacitor referred to as C
6004:
That is, the frequency is plotted in powers of ten, as 1, 10, 10
4903:
Using the approximations for the time constants developed above,
4715:
at the input and output of the amplifier, so with corrections to
215:
to the ideal op amp as a function of the applied signal voltage
5571:
drops with increasing gain because the Miller amplification of
4432:
for a two pole amplifier design. Gain drops from first pole at
4409:
moved the low pole lower and the high pole higher, so the term
170:
alters the frequency dependence of the output voltage divider.
5592:
To provide more safety margin for design uncertainties, often
4479:
to obtain the design is shown in Figure 3. At the lowest pole
5707:
Trade-offs in analog circuit design: the designer's companion
4457:? For general purpose use, traditional design (often called
177:
article. Following the procedure described in the article on
3901:, an estimate for the position of the second pole is found:
52:
Figure 1: Operational amplifier with compensation capacitor
5686:
is selected to be the fastest possible consistent with low
185:
to the input side of Figure 2 determines the input voltage
5704:
C. Toumazu, Moschytz GS & Gilbert B (Editors) (2007).
5710:. New York/Berlin/Dordrecht: Springer. pp. 272–275.
5835:
5420:
5132:
4914:
4737:
4560:
4350:
3912:
3880:
3843:
3712:
3673:
3623:
3589:
3562:
3535:
3419:
3131:
3082:
3055:
3028:
3001:
2974:
2940:
2913:
2787:
2685:
2549:
2463:
2394:
2313:
2216:
2188:
1970:
1645:
1444:
1344:
1232:
1131:
970:
876:
841:
814:
750:
715:
698:{\displaystyle {\frac {1}{2\pi C_{i}(R_{A}\|R_{i})}}}
640:
606:
445:
256:
221:
191:
5787:. New York; Berlin: Springer. pp. §097, p. 266
5848:
5530:
5407:
5108:
4864:
4666:
4363:
4324:
3893:
3866:
3824:
3686:
3638:
3602:
3575:
3548:
3516:
3384:
3095:
3068:
3041:
3014:
2987:
2953:
2926:
2892:
2764:
2661:
2536:
2451:{\displaystyle \ +j\omega C_{C}(R_{A}\|R_{i})\,\!}
2450:
2381:
2300:
2203:
2157:
1939:
1581:
1431:
1331:
1209:
1107:
957:
857:
827:
795:
731:
697:
619:
587:
410:
237:
207:
5404:
4881:Figure 4: Miller capacitance at low frequencies
4722:for the voltage dividers at input and output the
2533:
2447:
2378:
2297:
2200:
1428:
1328:
954:
127:). This pole is moved down in frequency by the
8:
5384:
5355:
5242:
5181:
4446:where the slope increases to 40 dB / decade.
4296:
4172:
4111:
4051:
4022:
3274:
3213:
2637:
2608:
2430:
2358:
2277:
1903:
1554:
1408:
1080:
676:
521:
383:
5932:
5930:
5757:. Amsterdam: Elsevier Newnes. p. 200.
4371:is reduced in size from its original value
19:is a phenomenon exploited in some forms of
3646:is much larger than its original value of
5940:Operational amplifiers: theory and design
5840:
5834:
5513:
5500:
5489:
5483:
5471:
5458:
5447:
5441:
5435:
5421:
5419:
5403:
5391:
5378:
5362:
5349:
5333:
5323:
5310:
5300:
5287:
5277:
5262:
5249:
5236:
5220:
5207:
5188:
5175:
5159:
5146:
5133:
5131:
5091:
5078:
5067:
5061:
5049:
5036:
5025:
5019:
5013:
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4987:
4975:
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4952:
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4913:
4847:
4834:
4823:
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4738:
4736:
4646:
4637:
4631:
4617:
4606:
4595:
4581:
4570:
4567:
4559:
4439:at 20 dB / decade down to second pole at
4355:
4349:
4303:
4290:
4275:
4264:
4254:
4241:
4231:
4218:
4208:
4201:
4179:
4166:
4150:
4137:
4118:
4105:
4089:
4076:
4058:
4045:
4029:
4016:
4000:
3990:
3977:
3967:
3954:
3944:
3934:
3921:
3913:
3911:
3885:
3879:
3858:
3848:
3842:
3807:
3794:
3782:
3772:
3765:
3754:
3743:
3733:
3726:
3717:
3711:
3678:
3672:
3630:
3625:
3622:
3594:
3588:
3567:
3561:
3540:
3534:
3494:
3481:
3470:
3464:
3458:
3437:
3424:
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3363:
3335:
3322:
3281:
3268:
3252:
3239:
3220:
3207:
3191:
3178:
3143:
3132:
3130:
3087:
3081:
3060:
3054:
3033:
3027:
3006:
3000:
2979:
2973:
2945:
2939:
2918:
2912:
2875:
2865:
2855:
2827:
2822:
2812:
2807:
2786:
2753:
2748:
2723:
2718:
2693:
2684:
2644:
2631:
2615:
2602:
2589:
2579:
2569:
2548:
2532:
2518:
2505:
2494:
2488:
2482:
2462:
2446:
2437:
2424:
2411:
2393:
2377:
2365:
2352:
2339:
2312:
2296:
2284:
2271:
2255:
2242:
2215:
2199:
2193:
2187:
2141:
2130:
2121:
2115:
2105:
2086:
2077:
2064:
2053:
2047:
2038:
2025:
2014:
2008:
2002:
1987:
1977:
1971:
1969:
1910:
1897:
1881:
1868:
1841:
1832:
1826:
1816:
1797:
1788:
1775:
1764:
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1731:
1704:
1694:
1688:
1671:
1654:
1646:
1644:
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1548:
1532:
1519:
1492:
1483:
1477:
1467:
1448:
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1427:
1415:
1402:
1386:
1373:
1348:
1343:
1327:
1318:
1305:
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1240:
1231:
1199:
1189:
1183:
1175:
1165:
1159:
1148:
1138:
1132:
1130:
1087:
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993:
974:
969:
953:
944:
931:
920:
914:
908:
893:
883:
877:
875:
849:
840:
819:
813:
781:
771:
758:
749:
723:
714:
683:
670:
657:
641:
639:
611:
605:
566:
550:
528:
515:
499:
486:
467:
454:
446:
444:
390:
377:
361:
348:
323:
314:
301:
290:
284:
273:
263:
257:
255:
229:
220:
199:
190:
5776:
5774:
4876:
4423:
76:
47:
5675:
5733:
5723:
5981:Audio power amplifier design handbook
5578:, which increases with gain (see the
5422:
4895:(bottom) as a function of gain using
1634:, the Miller capacitance is given by
865:at the input to the ideal op amp as:
796:{\displaystyle \ v_{o}=A_{v}v_{i}\ .}
7:
5984:. Oxford: Newnes. pp. 191–193.
4679:which is 20 dB/decade provided
4402:In short, introduction of capacitor
3104:
1952:(For a positive Miller capacitance,
5599:is increased to two or three times
4534:) the slope of the segment between
2177:given by a quadratic in ω, namely:
5907:A.S. Sedra and K.C. Smith (2004).
4614:
4610:
4607:
4578:
4574:
4571:
3867:{\displaystyle \tau _{1}\tau _{2}}
14:
4888:(top) and compensation capacitor
4726:for good step response becomes:
4450:What value is a good choice for
40:at the cost of decreased speed.
6017:A factor of two results in the
5582:), allows a smaller value for
4554:Slope per decade of frequency
3049:. (Good step response requires
2204:{\displaystyle D_{\omega }\,\!}
5397:
5371:
5368:
5342:
5339:
5270:
5259:
5255:
5229:
5226:
5200:
5194:
5168:
5165:
5139:
5136:
4972:
4945:
4652:
4624:
4601:
4588:
4309:
4283:
4185:
4159:
4156:
4130:
4124:
4098:
4095:
4069:
4064:
4038:
4035:
4009:
4006:
3937:
3341:
3315:
3290:
3287:
3261:
3258:
3232:
3226:
3200:
3197:
3171:
3168:
2852:
2842:
2836:
2833:
2803:
2759:
2732:
2729:
2702:
2650:
2624:
2621:
2595:
2566:
2556:
2443:
2417:
2374:
2371:
2345:
2320:
2293:
2290:
2264:
2261:
2235:
2220:
1916:
1890:
1887:
1861:
1630:. According to the article on
1567:
1541:
1538:
1512:
1421:
1395:
1392:
1366:
1093:
1067:
1064:
1038:
689:
663:
534:
508:
505:
479:
396:
370:
367:
341:
1:
835:as a function of the voltage
3874:along with the estimate for
3617:is large, the time constant
2382:{\displaystyle \cdot \ \,\!}
427:with frequency beginning at
5937:Huijsing, Johan H. (2001).
5781:Willy M. C. Sansen (2006).
5579:
4899:. Capacitance units are pF.
3639:{\displaystyle {\tau }_{1}}
6088:
4413:seems a good description.
600:which introduces notation
5881:) as found initially for
5856:differs a little from (
5849:{\displaystyle \tau _{1}}
5751:Marc T. Thompson (2006).
4364:{\displaystyle \tau _{2}}
3894:{\displaystyle \tau _{1}}
3687:{\displaystyle \tau _{1}}
3603:{\displaystyle \tau _{2}}
3576:{\displaystyle \tau _{1}}
3549:{\displaystyle \tau _{1}}
3096:{\displaystyle \tau _{2}}
3069:{\displaystyle \tau _{1}}
3042:{\displaystyle \tau _{2}}
3015:{\displaystyle \tau _{1}}
2988:{\displaystyle \tau _{1}}
2954:{\displaystyle \tau _{2}}
2927:{\displaystyle \tau _{1}}
828:{\displaystyle v_{\ell }}
620:{\displaystyle \tau _{1}}
145:, with the time constant
109:, with the time constant
44:Example of pole splitting
5910:Microelectronic circuits
5784:Analog design essentials
4463:single-pole compensation
3556:is determined, provided
6050:in the Control Systems
3404:is redefined using the
858:{\displaystyle \ v_{i}}
732:{\displaystyle \ v_{o}}
238:{\displaystyle \ v_{a}}
208:{\displaystyle \ v_{i}}
183:Kirchhoff's current law
6041:in the Circuit Theory
5978:Self, Douglas (2006).
5850:
5639:Frequency compensation
5532:
5409:
5110:
4900:
4866:
4668:
4506: − log
4447:
4365:
4326:
3895:
3868:
3826:
3688:
3640:
3604:
3577:
3550:
3518:
3386:
3097:
3070:
3043:
3016:
2989:
2955:
2928:
2894:
2766:
2663:
2538:
2452:
2383:
2302:
2205:
2159:
1941:
1583:
1433:
1333:
1211:
1109:
959:
859:
829:
797:
733:
699:
621:
589:
412:
239:
209:
87:
74:
21:frequency compensation
5966:Two-pole compensation
5851:
5533:
5410:
5111:
4880:
4867:
4669:
4427:
4366:
4327:
3896:
3869:
3827:
3689:
3641:
3605:
3578:
3551:
3519:
3387:
3098:
3071:
3044:
3017:
2990:
2956:
2929:
2895:
2767:
2664:
2539:
2453:
2384:
2303:
2301:{\displaystyle =\,\!}
2206:
2160:
1942:
1584:
1434:
1334:
1212:
1110:
960:
860:
830:
798:
734:
700:
622:
590:
413:
240:
210:
80:
66:and output impedance
51:
5833:
5670:References and notes
5418:
5130:
4912:
4735:
4724:pole-ratio condition
4558:
4472:The way to position
4428:Figure 3: Idealized
4348:
3910:
3878:
3841:
3710:
3671:
3621:
3587:
3560:
3533:
3417:
3406:Miller approximation
3129:
3080:
3053:
3026:
2999:
2972:
2938:
2911:
2785:
2683:
2547:
2461:
2392:
2311:
2214:
2186:
1968:
1643:
1628:Miller approximation
1442:
1342:
1230:
1129:
968:
874:
839:
812:
748:
713:
638:
604:
443:
254:
219:
189:
25:electronic amplifier
5829:The expression for
4344:is large, it seems
5846:
5736:has generic name (
5528:
5426:
5405:
5106:
4901:
4862:
4664:
4448:
4361:
4322:
4320:
3891:
3864:
3822:
3684:
3636:
3600:
3573:
3546:
3514:
3382:
3380:
3093:
3066:
3039:
3012:
2985:
2951:
2924:
2890:
2762:
2659:
2534:
2448:
2379:
2298:
2201:
2155:
1937:
1935:
1579:
1429:
1329:
1207:
1105:
955:
855:
825:
793:
729:
695:
617:
585:
583:
408:
235:
205:
88:
75:
6072:Electronic design
5717:978-1-4020-7037-2
5524:
5520:
5478:
5401:
5102:
5098:
5056:
5004:
4937:
4858:
4854:
4812:
4760:
4660:
4656:
4314:
4281:
4189:
3818:
3814:
3760:
3510:
3501:
3377:
3371:
3138:
2889:
2883:
2688:
2655:
2552:
2525:
2397:
2319:
2151:
2147:
2084:
2045:
1993:
1929:
1920:
1795:
1710:
1575:
1571:
1425:
1325:
1283:
1205:
1181:
1154:
1101:
1097:
951:
899:
844:
789:
753:
718:
693:
577:
573:
538:
423:which exhibits a
404:
400:
321:
279:
224:
194:
6079:
6026:
6015:
6009:
6002:
5996:
5995:
5975:
5969:
5963:Feucht, Dennis:
5961:
5955:
5954:
5934:
5925:
5924:
5904:
5898:
5895:
5889:
5855:
5853:
5852:
5847:
5845:
5844:
5827:
5821:
5818:
5812:
5809:
5803:
5802:
5778:
5769:
5768:
5748:
5742:
5741:
5735:
5731:
5729:
5721:
5701:
5695:
5680:
5537:
5535:
5534:
5529:
5522:
5521:
5519:
5518:
5517:
5505:
5504:
5494:
5493:
5484:
5479:
5477:
5476:
5475:
5463:
5462:
5452:
5451:
5442:
5440:
5439:
5427:
5414:
5412:
5411:
5406:
5402:
5400:
5396:
5395:
5383:
5382:
5367:
5366:
5354:
5353:
5338:
5337:
5328:
5327:
5315:
5314:
5305:
5304:
5292:
5291:
5282:
5281:
5268:
5267:
5266:
5254:
5253:
5241:
5240:
5225:
5224:
5212:
5211:
5193:
5192:
5180:
5179:
5164:
5163:
5151:
5150:
5134:
5115:
5113:
5112:
5107:
5100:
5099:
5097:
5096:
5095:
5083:
5082:
5072:
5071:
5062:
5057:
5055:
5054:
5053:
5041:
5040:
5030:
5029:
5020:
5018:
5017:
5005:
5003:
5002:
5001:
4992:
4991:
4981:
4980:
4979:
4970:
4969:
4957:
4956:
4943:
4938:
4936:
4935:
4926:
4925:
4916:
4871:
4869:
4868:
4863:
4856:
4855:
4853:
4852:
4851:
4839:
4838:
4828:
4827:
4818:
4813:
4811:
4810:
4809:
4797:
4796:
4786:
4785:
4776:
4774:
4773:
4761:
4759:
4758:
4749:
4748:
4739:
4713:voltage dividers
4673:
4671:
4670:
4665:
4658:
4657:
4655:
4651:
4650:
4641:
4636:
4635:
4623:
4622:
4621:
4604:
4600:
4599:
4587:
4586:
4585:
4568:
4370:
4368:
4367:
4362:
4360:
4359:
4331:
4329:
4328:
4323:
4321:
4312:
4308:
4307:
4295:
4294:
4282:
4280:
4279:
4270:
4269:
4268:
4259:
4258:
4246:
4245:
4236:
4235:
4223:
4222:
4213:
4212:
4202:
4194:
4190:
4188:
4184:
4183:
4171:
4170:
4155:
4154:
4142:
4141:
4123:
4122:
4110:
4109:
4094:
4093:
4081:
4080:
4067:
4063:
4062:
4050:
4049:
4034:
4033:
4021:
4020:
4005:
4004:
3995:
3994:
3982:
3981:
3972:
3971:
3959:
3958:
3949:
3948:
3935:
3926:
3925:
3900:
3898:
3897:
3892:
3890:
3889:
3873:
3871:
3870:
3865:
3863:
3862:
3853:
3852:
3831:
3829:
3828:
3823:
3816:
3815:
3813:
3812:
3811:
3799:
3798:
3788:
3787:
3786:
3777:
3776:
3766:
3761:
3759:
3758:
3749:
3748:
3747:
3738:
3737:
3727:
3722:
3721:
3693:
3691:
3690:
3685:
3683:
3682:
3645:
3643:
3642:
3637:
3635:
3634:
3629:
3609:
3607:
3606:
3601:
3599:
3598:
3582:
3580:
3579:
3574:
3572:
3571:
3555:
3553:
3552:
3547:
3545:
3544:
3523:
3521:
3520:
3515:
3508:
3507:
3503:
3502:
3500:
3499:
3498:
3486:
3485:
3475:
3474:
3465:
3463:
3462:
3442:
3441:
3429:
3428:
3391:
3389:
3388:
3383:
3381:
3375:
3369:
3368:
3367:
3340:
3339:
3327:
3326:
3296:
3286:
3285:
3273:
3272:
3257:
3256:
3244:
3243:
3225:
3224:
3212:
3211:
3196:
3195:
3183:
3182:
3148:
3147:
3136:
3102:
3100:
3099:
3094:
3092:
3091:
3075:
3073:
3072:
3067:
3065:
3064:
3048:
3046:
3045:
3040:
3038:
3037:
3021:
3019:
3018:
3013:
3011:
3010:
2994:
2992:
2991:
2986:
2984:
2983:
2960:
2958:
2957:
2952:
2950:
2949:
2933:
2931:
2930:
2925:
2923:
2922:
2899:
2897:
2896:
2891:
2887:
2881:
2880:
2879:
2870:
2869:
2860:
2859:
2832:
2831:
2826:
2817:
2816:
2811:
2771:
2769:
2768:
2763:
2758:
2757:
2752:
2728:
2727:
2722:
2698:
2697:
2686:
2668:
2666:
2665:
2660:
2653:
2649:
2648:
2636:
2635:
2620:
2619:
2607:
2606:
2594:
2593:
2584:
2583:
2574:
2573:
2550:
2543:
2541:
2540:
2535:
2531:
2527:
2526:
2524:
2523:
2522:
2510:
2509:
2499:
2498:
2489:
2487:
2486:
2457:
2455:
2454:
2449:
2442:
2441:
2429:
2428:
2416:
2415:
2395:
2388:
2386:
2385:
2380:
2370:
2369:
2357:
2356:
2344:
2343:
2317:
2307:
2305:
2304:
2299:
2289:
2288:
2276:
2275:
2260:
2259:
2247:
2246:
2210:
2208:
2207:
2202:
2198:
2197:
2164:
2162:
2161:
2156:
2149:
2148:
2146:
2145:
2136:
2135:
2134:
2125:
2120:
2119:
2110:
2109:
2087:
2085:
2083:
2082:
2081:
2069:
2068:
2058:
2057:
2048:
2046:
2044:
2043:
2042:
2030:
2029:
2019:
2018:
2009:
2007:
2006:
1994:
1992:
1991:
1982:
1981:
1972:
1946:
1944:
1943:
1938:
1936:
1927:
1926:
1922:
1921:
1919:
1915:
1914:
1902:
1901:
1886:
1885:
1873:
1872:
1847:
1846:
1845:
1836:
1831:
1830:
1821:
1820:
1798:
1796:
1794:
1793:
1792:
1780:
1779:
1769:
1768:
1759:
1757:
1756:
1736:
1735:
1720:
1716:
1712:
1711:
1709:
1708:
1699:
1698:
1689:
1676:
1675:
1659:
1658:
1588:
1586:
1585:
1580:
1573:
1572:
1570:
1566:
1565:
1553:
1552:
1537:
1536:
1524:
1523:
1498:
1497:
1496:
1487:
1482:
1481:
1472:
1471:
1449:
1438:
1436:
1435:
1430:
1426:
1424:
1420:
1419:
1407:
1406:
1391:
1390:
1378:
1377:
1349:
1338:
1336:
1335:
1330:
1326:
1324:
1323:
1322:
1310:
1309:
1299:
1298:
1289:
1284:
1282:
1281:
1280:
1268:
1267:
1257:
1256:
1247:
1245:
1244:
1216:
1214:
1213:
1208:
1206:
1204:
1203:
1194:
1193:
1184:
1182:
1180:
1179:
1170:
1169:
1160:
1155:
1153:
1152:
1143:
1142:
1133:
1114:
1112:
1111:
1106:
1099:
1098:
1096:
1092:
1091:
1079:
1078:
1063:
1062:
1050:
1049:
1024:
1023:
1022:
1013:
1008:
1007:
998:
997:
975:
964:
962:
961:
956:
952:
950:
949:
948:
936:
935:
925:
924:
915:
913:
912:
900:
898:
897:
888:
887:
878:
864:
862:
861:
856:
854:
853:
842:
834:
832:
831:
826:
824:
823:
802:
800:
799:
794:
787:
786:
785:
776:
775:
763:
762:
751:
738:
736:
735:
730:
728:
727:
716:
704:
702:
701:
696:
694:
692:
688:
687:
675:
674:
662:
661:
642:
626:
624:
623:
618:
616:
615:
594:
592:
591:
586:
584:
575:
574:
572:
571:
570:
551:
543:
539:
537:
533:
532:
520:
519:
504:
503:
491:
490:
468:
459:
458:
417:
415:
414:
409:
402:
401:
399:
395:
394:
382:
381:
366:
365:
353:
352:
324:
322:
320:
319:
318:
306:
305:
295:
294:
285:
280:
278:
277:
268:
267:
258:
244:
242:
241:
236:
234:
233:
222:
214:
212:
211:
206:
204:
203:
192:
179:Miller's theorem
175:Miller's theorem
138:and capacitance
102:and capacitance
83:Miller's theorem
6087:
6086:
6082:
6081:
6080:
6078:
6077:
6076:
6067:Analog circuits
6057:
6056:
6035:
6030:
6029:
6016:
6012:
6003:
5999:
5992:
5977:
5976:
5972:
5962:
5958:
5951:
5936:
5935:
5928:
5921:
5906:
5905:
5901:
5896:
5892:
5886:
5879:
5872:
5865:
5861:
5836:
5831:
5830:
5828:
5824:
5819:
5815:
5810:
5806:
5799:
5780:
5779:
5772:
5765:
5750:
5749:
5745:
5732:
5722:
5718:
5703:
5702:
5698:
5681:
5677:
5672:
5635:
5627:
5616:
5604:
5597:
5587:
5580:Miller equation
5576:
5569:
5562:
5555:
5548:
5509:
5496:
5495:
5485:
5467:
5454:
5453:
5443:
5431:
5416:
5415:
5387:
5374:
5358:
5345:
5329:
5319:
5306:
5296:
5283:
5273:
5269:
5258:
5245:
5232:
5216:
5203:
5184:
5171:
5155:
5142:
5135:
5128:
5127:
5087:
5074:
5073:
5063:
5045:
5032:
5031:
5021:
5009:
4993:
4983:
4982:
4971:
4961:
4948:
4944:
4927:
4917:
4910:
4909:
4893:
4886:
4843:
4830:
4829:
4819:
4801:
4788:
4787:
4777:
4765:
4750:
4740:
4733:
4732:
4720:
4709:
4699:
4692:
4688:
4684:
4642:
4627:
4613:
4605:
4591:
4577:
4569:
4556:
4555:
4547:
4540:
4533:
4526:
4519:
4515:
4509:
4505:
4499:
4494:
4489:
4485:
4478:
4455:
4444:
4437:
4422:
4420:
4407:
4397:
4390:
4383:
4376:
4351:
4346:
4345:
4342:
4319:
4318:
4299:
4286:
4271:
4260:
4250:
4237:
4227:
4214:
4204:
4203:
4192:
4191:
4175:
4162:
4146:
4133:
4114:
4101:
4085:
4072:
4068:
4054:
4041:
4025:
4012:
3996:
3986:
3973:
3963:
3950:
3940:
3936:
3927:
3917:
3908:
3907:
3881:
3876:
3875:
3854:
3844:
3839:
3838:
3803:
3790:
3789:
3778:
3768:
3767:
3750:
3739:
3729:
3728:
3713:
3708:
3707:
3699:
3674:
3669:
3668:
3662:
3658:
3651:
3624:
3619:
3618:
3615:
3590:
3585:
3584:
3563:
3558:
3557:
3536:
3531:
3530:
3490:
3477:
3476:
3466:
3454:
3447:
3443:
3433:
3420:
3415:
3414:
3402:
3379:
3378:
3359:
3331:
3318:
3294:
3293:
3277:
3264:
3248:
3235:
3216:
3203:
3187:
3174:
3149:
3139:
3127:
3126:
3118:
3108:
3083:
3078:
3077:
3056:
3051:
3050:
3029:
3024:
3023:
3002:
2997:
2996:
2975:
2970:
2969:
2966:
2941:
2936:
2935:
2914:
2909:
2908:
2871:
2861:
2851:
2821:
2806:
2783:
2782:
2747:
2717:
2689:
2681:
2680:
2640:
2627:
2611:
2598:
2585:
2575:
2565:
2545:
2544:
2514:
2501:
2500:
2490:
2478:
2471:
2467:
2459:
2458:
2433:
2420:
2407:
2390:
2389:
2361:
2348:
2335:
2309:
2308:
2280:
2267:
2251:
2238:
2212:
2211:
2189:
2184:
2183:
2175:
2137:
2126:
2111:
2101:
2088:
2073:
2060:
2059:
2049:
2034:
2021:
2020:
2010:
1998:
1983:
1973:
1966:
1965:
1957:
1934:
1933:
1906:
1893:
1877:
1864:
1848:
1837:
1822:
1812:
1799:
1784:
1771:
1770:
1760:
1748:
1741:
1737:
1727:
1718:
1717:
1700:
1690:
1681:
1677:
1667:
1660:
1650:
1641:
1640:
1624:
1620:
1613:
1601:
1557:
1544:
1528:
1515:
1499:
1488:
1473:
1463:
1450:
1440:
1439:
1411:
1398:
1382:
1369:
1353:
1340:
1339:
1314:
1301:
1300:
1290:
1272:
1259:
1258:
1248:
1236:
1228:
1227:
1195:
1185:
1171:
1161:
1144:
1134:
1127:
1126:
1083:
1070:
1054:
1041:
1025:
1014:
999:
989:
976:
966:
965:
940:
927:
926:
916:
904:
889:
879:
872:
871:
845:
837:
836:
815:
810:
809:
777:
767:
754:
746:
745:
719:
711:
710:
679:
666:
653:
646:
636:
635:
632:
607:
602:
601:
582:
581:
562:
555:
541:
540:
524:
511:
495:
482:
472:
460:
450:
441:
440:
432:
386:
373:
357:
344:
328:
310:
297:
296:
286:
269:
259:
252:
251:
225:
217:
216:
195:
187:
186:
168:
161:
157:
150:
143:
136:
125:
121:
114:
107:
100:
93:
71:
64:
57:
46:
12:
11:
5:
6085:
6083:
6075:
6074:
6069:
6059:
6058:
6055:
6054:
6045:
6034:
6033:External links
6031:
6028:
6027:
6019:maximally flat
6010:
5997:
5990:
5970:
5956:
5949:
5926:
5919:
5899:
5890:
5884:
5877:
5870:
5863:
5859:
5843:
5839:
5822:
5813:
5804:
5797:
5770:
5763:
5743:
5716:
5696:
5674:
5673:
5671:
5668:
5667:
5666:
5664:CMOS amplifier
5661:
5656:
5651:
5646:
5641:
5634:
5631:
5625:
5615:
5612:
5602:
5595:
5585:
5574:
5567:
5560:
5553:
5546:
5541:
5540:
5539:
5538:
5527:
5516:
5512:
5508:
5503:
5499:
5492:
5488:
5482:
5474:
5470:
5466:
5461:
5457:
5450:
5446:
5438:
5434:
5430:
5425:
5399:
5394:
5390:
5386:
5381:
5377:
5373:
5370:
5365:
5361:
5357:
5352:
5348:
5344:
5341:
5336:
5332:
5326:
5322:
5318:
5313:
5309:
5303:
5299:
5295:
5290:
5286:
5280:
5276:
5272:
5265:
5261:
5257:
5252:
5248:
5244:
5239:
5235:
5231:
5228:
5223:
5219:
5215:
5210:
5206:
5202:
5199:
5196:
5191:
5187:
5183:
5178:
5174:
5170:
5167:
5162:
5158:
5154:
5149:
5145:
5141:
5138:
5119:
5118:
5117:
5116:
5105:
5094:
5090:
5086:
5081:
5077:
5070:
5066:
5060:
5052:
5048:
5044:
5039:
5035:
5028:
5024:
5016:
5012:
5008:
5000:
4996:
4990:
4986:
4978:
4974:
4968:
4964:
4960:
4955:
4951:
4947:
4941:
4934:
4930:
4924:
4920:
4891:
4884:
4875:
4874:
4873:
4872:
4861:
4850:
4846:
4842:
4837:
4833:
4826:
4822:
4816:
4808:
4804:
4800:
4795:
4791:
4784:
4780:
4772:
4768:
4764:
4757:
4753:
4747:
4743:
4718:
4707:
4697:
4690:
4686:
4682:
4677:
4676:
4675:
4674:
4663:
4654:
4649:
4645:
4640:
4634:
4630:
4626:
4620:
4616:
4612:
4609:
4603:
4598:
4594:
4590:
4584:
4580:
4576:
4573:
4566:
4563:
4545:
4538:
4531:
4524:
4517:
4513:
4507:
4503:
4497:
4492:
4487:
4483:
4476:
4453:
4442:
4435:
4421:
4418:
4417:Selection of C
4415:
4411:pole splitting
4405:
4395:
4388:
4381:
4374:
4358:
4354:
4340:
4335:
4334:
4333:
4332:
4317:
4311:
4306:
4302:
4298:
4293:
4289:
4285:
4278:
4274:
4267:
4263:
4257:
4253:
4249:
4244:
4240:
4234:
4230:
4226:
4221:
4217:
4211:
4207:
4200:
4197:
4195:
4193:
4187:
4182:
4178:
4174:
4169:
4165:
4161:
4158:
4153:
4149:
4145:
4140:
4136:
4132:
4129:
4126:
4121:
4117:
4113:
4108:
4104:
4100:
4097:
4092:
4088:
4084:
4079:
4075:
4071:
4066:
4061:
4057:
4053:
4048:
4044:
4040:
4037:
4032:
4028:
4024:
4019:
4015:
4011:
4008:
4003:
3999:
3993:
3989:
3985:
3980:
3976:
3970:
3966:
3962:
3957:
3953:
3947:
3943:
3939:
3933:
3930:
3928:
3924:
3920:
3916:
3915:
3888:
3884:
3861:
3857:
3851:
3847:
3835:
3834:
3833:
3832:
3821:
3810:
3806:
3802:
3797:
3793:
3785:
3781:
3775:
3771:
3764:
3757:
3753:
3746:
3742:
3736:
3732:
3725:
3720:
3716:
3697:
3681:
3677:
3660:
3656:
3649:
3633:
3628:
3613:
3597:
3593:
3570:
3566:
3543:
3539:
3527:
3526:
3525:
3524:
3513:
3506:
3497:
3493:
3489:
3484:
3480:
3473:
3469:
3461:
3457:
3453:
3450:
3446:
3440:
3436:
3432:
3427:
3423:
3400:
3395:
3394:
3393:
3392:
3374:
3366:
3362:
3358:
3355:
3352:
3349:
3346:
3343:
3338:
3334:
3330:
3325:
3321:
3317:
3314:
3311:
3308:
3305:
3302:
3299:
3297:
3295:
3292:
3289:
3284:
3280:
3276:
3271:
3267:
3263:
3260:
3255:
3251:
3247:
3242:
3238:
3234:
3231:
3228:
3223:
3219:
3215:
3210:
3206:
3202:
3199:
3194:
3190:
3186:
3181:
3177:
3173:
3170:
3167:
3164:
3161:
3158:
3155:
3152:
3150:
3146:
3142:
3135:
3134:
3116:
3106:
3105:Selection of C
3090:
3086:
3063:
3059:
3036:
3032:
3009:
3005:
2982:
2978:
2964:
2948:
2944:
2921:
2917:
2905:
2904:
2903:
2902:
2901:
2900:
2886:
2878:
2874:
2868:
2864:
2858:
2854:
2850:
2847:
2844:
2841:
2838:
2835:
2830:
2825:
2820:
2815:
2810:
2805:
2802:
2799:
2796:
2793:
2790:
2775:
2774:
2773:
2772:
2761:
2756:
2751:
2746:
2743:
2740:
2737:
2734:
2731:
2726:
2721:
2716:
2713:
2710:
2707:
2704:
2701:
2696:
2692:
2672:
2671:
2670:
2669:
2658:
2652:
2647:
2643:
2639:
2634:
2630:
2626:
2623:
2618:
2614:
2610:
2605:
2601:
2597:
2592:
2588:
2582:
2578:
2572:
2568:
2564:
2561:
2558:
2555:
2530:
2521:
2517:
2513:
2508:
2504:
2497:
2493:
2485:
2481:
2477:
2474:
2470:
2466:
2445:
2440:
2436:
2432:
2427:
2423:
2419:
2414:
2410:
2406:
2403:
2400:
2376:
2373:
2368:
2364:
2360:
2355:
2351:
2347:
2342:
2338:
2334:
2331:
2328:
2325:
2322:
2316:
2295:
2292:
2287:
2283:
2279:
2274:
2270:
2266:
2263:
2258:
2254:
2250:
2245:
2241:
2237:
2234:
2231:
2228:
2225:
2222:
2219:
2196:
2192:
2173:
2168:
2167:
2166:
2165:
2154:
2144:
2140:
2133:
2129:
2124:
2118:
2114:
2108:
2104:
2100:
2097:
2094:
2091:
2080:
2076:
2072:
2067:
2063:
2056:
2052:
2041:
2037:
2033:
2028:
2024:
2017:
2013:
2005:
2001:
1997:
1990:
1986:
1980:
1976:
1955:
1950:
1949:
1948:
1947:
1932:
1925:
1918:
1913:
1909:
1905:
1900:
1896:
1892:
1889:
1884:
1880:
1876:
1871:
1867:
1863:
1860:
1857:
1854:
1851:
1844:
1840:
1835:
1829:
1825:
1819:
1815:
1811:
1808:
1805:
1802:
1791:
1787:
1783:
1778:
1774:
1767:
1763:
1755:
1751:
1747:
1744:
1740:
1734:
1730:
1726:
1723:
1721:
1719:
1715:
1707:
1703:
1697:
1693:
1687:
1684:
1680:
1674:
1670:
1666:
1663:
1661:
1657:
1653:
1649:
1648:
1622:
1618:
1611:
1599:
1594:
1593:
1592:
1591:
1590:
1589:
1578:
1569:
1564:
1560:
1556:
1551:
1547:
1543:
1540:
1535:
1531:
1527:
1522:
1518:
1514:
1511:
1508:
1505:
1502:
1495:
1491:
1486:
1480:
1476:
1470:
1466:
1462:
1459:
1456:
1453:
1447:
1423:
1418:
1414:
1410:
1405:
1401:
1397:
1394:
1389:
1385:
1381:
1376:
1372:
1368:
1365:
1362:
1359:
1356:
1352:
1347:
1321:
1317:
1313:
1308:
1304:
1297:
1293:
1287:
1279:
1275:
1271:
1266:
1262:
1255:
1251:
1243:
1239:
1235:
1220:
1219:
1218:
1217:
1202:
1198:
1192:
1188:
1178:
1174:
1168:
1164:
1158:
1151:
1147:
1141:
1137:
1118:
1117:
1116:
1115:
1104:
1095:
1090:
1086:
1082:
1077:
1073:
1069:
1066:
1061:
1057:
1053:
1048:
1044:
1040:
1037:
1034:
1031:
1028:
1021:
1017:
1012:
1006:
1002:
996:
992:
988:
985:
982:
979:
973:
947:
943:
939:
934:
930:
923:
919:
911:
907:
903:
896:
892:
886:
882:
852:
848:
822:
818:
806:
805:
804:
803:
792:
784:
780:
774:
770:
766:
761:
757:
726:
722:
691:
686:
682:
678:
673:
669:
665:
660:
656:
652:
649:
645:
630:
614:
610:
598:
597:
596:
595:
580:
569:
565:
561:
558:
554:
549:
546:
544:
542:
536:
531:
527:
523:
518:
514:
510:
507:
502:
498:
494:
489:
485:
481:
478:
475:
471:
466:
463:
461:
457:
453:
449:
448:
430:
421:
420:
419:
418:
407:
398:
393:
389:
385:
380:
376:
372:
369:
364:
360:
356:
351:
347:
343:
340:
337:
334:
331:
327:
317:
313:
309:
304:
300:
293:
289:
283:
276:
272:
266:
262:
232:
228:
202:
198:
166:
159:
155:
148:
141:
134:
123:
119:
112:
105:
98:
91:
69:
62:
55:
45:
42:
17:Pole splitting
13:
10:
9:
6:
4:
3:
2:
6084:
6073:
6070:
6068:
6065:
6064:
6062:
6053:
6049:
6046:
6044:
6040:
6037:
6036:
6032:
6024:
6020:
6014:
6011:
6007:
6001:
5998:
5993:
5991:0-7506-8072-5
5987:
5983:
5982:
5974:
5971:
5968:
5967:
5960:
5957:
5952:
5950:0-7923-7284-0
5946:
5942:
5941:
5933:
5931:
5927:
5922:
5920:0-19-514251-9
5916:
5912:
5911:
5903:
5900:
5894:
5891:
5887:
5880:
5873:
5866:
5841:
5837:
5826:
5823:
5817:
5814:
5808:
5805:
5800:
5798:0-387-25746-2
5794:
5790:
5786:
5785:
5777:
5775:
5771:
5766:
5764:0-7506-7786-4
5760:
5756:
5755:
5747:
5744:
5739:
5734:|author=
5727:
5719:
5713:
5709:
5708:
5700:
5697:
5693:
5689:
5685:
5682:That is, the
5679:
5676:
5669:
5665:
5662:
5660:
5659:Step response
5657:
5655:
5652:
5650:
5649:Common source
5647:
5645:
5644:Miller effect
5642:
5640:
5637:
5636:
5632:
5630:
5628:
5621:
5613:
5611:
5609:
5608:step response
5605:
5598:
5590:
5588:
5581:
5577:
5570:
5563:
5556:
5549:
5525:
5514:
5510:
5506:
5501:
5497:
5490:
5486:
5480:
5472:
5468:
5464:
5459:
5455:
5448:
5444:
5436:
5432:
5428:
5423:
5392:
5388:
5379:
5375:
5363:
5359:
5350:
5346:
5334:
5330:
5324:
5320:
5316:
5311:
5307:
5301:
5297:
5293:
5288:
5284:
5278:
5274:
5263:
5250:
5246:
5237:
5233:
5221:
5217:
5213:
5208:
5204:
5197:
5189:
5185:
5176:
5172:
5160:
5156:
5152:
5147:
5143:
5126:
5125:
5124:
5123:
5122:
5103:
5092:
5088:
5084:
5079:
5075:
5068:
5064:
5058:
5050:
5046:
5042:
5037:
5033:
5026:
5022:
5014:
5010:
5006:
4998:
4994:
4988:
4984:
4976:
4966:
4962:
4958:
4953:
4949:
4939:
4932:
4928:
4922:
4918:
4908:
4907:
4906:
4905:
4904:
4898:
4894:
4887:
4879:
4859:
4848:
4844:
4840:
4835:
4831:
4824:
4820:
4814:
4806:
4802:
4798:
4793:
4789:
4782:
4778:
4770:
4766:
4762:
4755:
4751:
4745:
4741:
4731:
4730:
4729:
4728:
4727:
4725:
4721:
4714:
4710:
4702:
4700:
4693:
4661:
4647:
4643:
4638:
4632:
4628:
4618:
4596:
4592:
4582:
4564:
4561:
4553:
4552:
4551:
4550:
4549:
4544:
4537:
4530:
4523:
4512:
4502:
4495:
4482:
4475:
4470:
4468:
4467:step response
4464:
4460:
4459:dominant-pole
4456:
4445:
4438:
4431:
4426:
4416:
4414:
4412:
4408:
4400:
4398:
4391:
4384:
4377:
4356:
4352:
4343:
4315:
4304:
4300:
4291:
4287:
4276:
4272:
4265:
4261:
4255:
4251:
4247:
4242:
4238:
4232:
4228:
4224:
4219:
4215:
4209:
4205:
4198:
4196:
4180:
4176:
4167:
4163:
4151:
4147:
4143:
4138:
4134:
4127:
4119:
4115:
4106:
4102:
4090:
4086:
4082:
4077:
4073:
4059:
4055:
4046:
4042:
4030:
4026:
4017:
4013:
4001:
3997:
3991:
3987:
3983:
3978:
3974:
3968:
3964:
3960:
3955:
3951:
3945:
3941:
3931:
3929:
3922:
3918:
3906:
3905:
3904:
3903:
3902:
3886:
3882:
3859:
3855:
3849:
3845:
3819:
3808:
3804:
3800:
3795:
3791:
3783:
3779:
3773:
3769:
3762:
3755:
3751:
3744:
3740:
3734:
3730:
3723:
3718:
3714:
3706:
3705:
3704:
3703:
3702:
3700:
3679:
3675:
3665:
3663:
3652:
3631:
3626:
3616:
3595:
3591:
3568:
3564:
3541:
3537:
3511:
3504:
3495:
3491:
3487:
3482:
3478:
3471:
3467:
3459:
3455:
3451:
3448:
3444:
3438:
3434:
3430:
3425:
3421:
3413:
3412:
3411:
3410:
3409:
3407:
3403:
3372:
3364:
3360:
3356:
3353:
3350:
3347:
3344:
3336:
3332:
3328:
3323:
3319:
3312:
3309:
3306:
3303:
3300:
3298:
3282:
3278:
3269:
3265:
3253:
3249:
3245:
3240:
3236:
3229:
3221:
3217:
3208:
3204:
3192:
3188:
3184:
3179:
3175:
3165:
3162:
3159:
3156:
3153:
3151:
3144:
3140:
3125:
3124:
3123:
3122:
3121:
3119:
3111:
3109:
3088:
3084:
3061:
3057:
3034:
3030:
3007:
3003:
2980:
2976:
2967:
2946:
2942:
2919:
2915:
2884:
2876:
2872:
2866:
2862:
2856:
2848:
2845:
2839:
2828:
2823:
2818:
2813:
2808:
2800:
2797:
2794:
2791:
2788:
2781:
2780:
2779:
2778:
2777:
2776:
2754:
2749:
2744:
2741:
2738:
2735:
2724:
2719:
2714:
2711:
2708:
2705:
2699:
2694:
2690:
2679:
2678:
2677:
2676:
2675:
2656:
2645:
2641:
2632:
2628:
2616:
2612:
2603:
2599:
2590:
2586:
2580:
2576:
2570:
2562:
2559:
2553:
2528:
2519:
2515:
2511:
2506:
2502:
2495:
2491:
2483:
2479:
2475:
2472:
2468:
2464:
2438:
2434:
2425:
2421:
2412:
2408:
2404:
2401:
2398:
2366:
2362:
2353:
2349:
2340:
2336:
2332:
2329:
2326:
2323:
2314:
2285:
2281:
2272:
2268:
2256:
2252:
2248:
2243:
2239:
2232:
2229:
2226:
2223:
2217:
2194:
2190:
2182:
2181:
2180:
2179:
2178:
2176:
2152:
2142:
2138:
2131:
2127:
2122:
2116:
2112:
2106:
2102:
2098:
2095:
2092:
2089:
2078:
2074:
2070:
2065:
2061:
2054:
2050:
2039:
2035:
2031:
2026:
2022:
2015:
2011:
2003:
1999:
1995:
1988:
1984:
1978:
1974:
1964:
1963:
1962:
1961:
1960:
1958:
1930:
1923:
1911:
1907:
1898:
1894:
1882:
1878:
1874:
1869:
1865:
1858:
1855:
1852:
1849:
1842:
1838:
1833:
1827:
1823:
1817:
1813:
1809:
1806:
1803:
1800:
1789:
1785:
1781:
1776:
1772:
1765:
1761:
1753:
1749:
1745:
1742:
1738:
1732:
1728:
1724:
1722:
1713:
1705:
1701:
1695:
1691:
1685:
1682:
1678:
1672:
1668:
1664:
1662:
1655:
1651:
1639:
1638:
1637:
1636:
1635:
1633:
1632:Miller effect
1629:
1625:
1614:
1607:
1602:
1576:
1562:
1558:
1549:
1545:
1533:
1529:
1525:
1520:
1516:
1509:
1506:
1503:
1500:
1493:
1489:
1484:
1478:
1474:
1468:
1464:
1460:
1457:
1454:
1451:
1445:
1416:
1412:
1403:
1399:
1387:
1383:
1379:
1374:
1370:
1363:
1360:
1357:
1354:
1350:
1345:
1319:
1315:
1311:
1306:
1302:
1295:
1291:
1285:
1277:
1273:
1269:
1264:
1260:
1253:
1249:
1241:
1237:
1233:
1226:
1225:
1224:
1223:
1222:
1221:
1200:
1196:
1190:
1186:
1176:
1172:
1166:
1162:
1156:
1149:
1145:
1139:
1135:
1125:
1124:
1123:
1122:
1121:
1102:
1088:
1084:
1075:
1071:
1059:
1055:
1051:
1046:
1042:
1035:
1032:
1029:
1026:
1019:
1015:
1010:
1004:
1000:
994:
990:
986:
983:
980:
977:
971:
945:
941:
937:
932:
928:
921:
917:
909:
905:
901:
894:
890:
884:
880:
870:
869:
868:
867:
866:
850:
846:
820:
816:
790:
782:
778:
772:
768:
764:
759:
755:
744:
743:
742:
741:
740:
724:
720:
706:
684:
680:
671:
667:
658:
654:
650:
647:
643:
633:
612:
608:
578:
567:
563:
559:
556:
552:
547:
545:
529:
525:
516:
512:
500:
496:
492:
487:
483:
476:
473:
469:
464:
462:
455:
451:
439:
438:
437:
436:
435:
433:
426:
405:
391:
387:
378:
374:
362:
358:
354:
349:
345:
338:
335:
332:
329:
325:
315:
311:
307:
302:
298:
291:
287:
281:
274:
270:
264:
260:
250:
249:
248:
247:
246:
230:
226:
200:
196:
184:
180:
176:
171:
169:
162:
151:
144:
137:
130:
129:Miller effect
126:
115:
108:
101:
84:
79:
72:
65:
58:
50:
43:
41:
39:
38:step response
34:
30:
26:
22:
18:
6018:
6013:
6005:
6000:
5980:
5973:
5965:
5959:
5939:
5909:
5902:
5893:
5882:
5875:
5868:
5857:
5825:
5816:
5807:
5788:
5783:
5753:
5746:
5706:
5699:
5678:
5623:
5617:
5600:
5593:
5591:
5583:
5572:
5565:
5558:
5551:
5544:
5542:
5120:
4902:
4889:
4882:
4723:
4716:
4705:
4703:
4695:
4680:
4678:
4542:
4535:
4528:
4521:
4510:
4500:
4490:
4480:
4473:
4471:
4462:
4458:
4451:
4449:
4440:
4433:
4410:
4403:
4401:
4393:
4386:
4379:
4372:
4338:
4337:and because
4336:
3836:
3695:
3666:
3654:
3647:
3611:
3528:
3398:
3396:
3114:
3112:
2962:
2906:
2673:
2171:
2169:
1953:
1951:
1616:
1609:
1605:
1597:
1595:
1119:
807:
707:
628:
599:
428:
422:
172:
164:
153:
146:
139:
132:
117:
110:
103:
96:
89:
67:
60:
53:
16:
15:
6023:Butterworth
23:used in an
6061:Categories
6048:Bode Plots
6039:Bode Plots
3610:. Because
3397:where now
1608:product,
634:= 0 F is
245:, namely,
86:feedback.)
5838:τ
5726:cite book
5688:overshoot
5684:rise time
5654:Bode plot
5620:slew rate
5614:Slew rate
5481:⋅
5424:⋅
5385:‖
5356:‖
5243:‖
5182:‖
5059:⋅
5007:≈
4995:τ
4985:τ
4963:τ
4950:τ
4940:≈
4929:τ
4919:τ
4815:⋅
4763:≈
4752:τ
4742:τ
4430:Bode plot
4353:τ
4297:‖
4199:≈
4173:‖
4112:‖
4052:‖
4023:‖
3919:τ
3883:τ
3856:τ
3846:τ
3805:τ
3792:τ
3780:τ
3770:τ
3763:≈
3752:τ
3741:τ
3731:τ
3715:τ
3676:τ
3627:τ
3592:τ
3583:>>
3565:τ
3538:τ
3452:−
3361:τ
3357:ω
3345:≈
3333:τ
3320:τ
3313:ω
3275:‖
3214:‖
3166:ω
3145:ω
3085:τ
3076:>>
3058:τ
3031:τ
3022:>>
3004:τ
2977:τ
2943:τ
2916:τ
2873:τ
2863:τ
2849:ω
2824:τ
2809:τ
2801:ω
2750:τ
2745:ω
2720:τ
2715:ω
2695:ω
2638:‖
2609:‖
2563:ω
2476:−
2465:⋅
2431:‖
2405:ω
2359:‖
2333:ω
2315:⋅
2278:‖
2233:ω
2195:ω
2143:ω
2099:ω
1979:ℓ
1904:‖
1859:ω
1810:ω
1746:−
1696:ℓ
1686:−
1555:‖
1510:ω
1461:ω
1446:⋅
1409:‖
1364:ω
1346:⋅
1286:⋅
1167:ℓ
1140:ℓ
1081:‖
1036:ω
987:ω
972:⋅
885:ℓ
821:ℓ
677:‖
651:π
609:τ
564:τ
560:π
522:‖
477:π
384:‖
339:ω
29:capacitor
27:. When a
6052:Wikibook
6043:Wikibook
5633:See also
3110:below.)
425:roll-off
5692:ringing
4516:) = log
5988:
5947:
5917:
5795:
5789:et seq
5761:
5714:
5523:
5101:
4857:
4659:
4313:
3817:
3509:
3376:
3370:
3137:
3103:. See
2907:where
2888:
2882:
2687:
2654:
2551:
2396:
2318:
2150:
1928:
1574:
1100:
843:
788:
752:
717:
576:
434:where
403:
223:
193:
4897:Excel
4694:. If
2170:with
5986:ISBN
5945:ISBN
5915:ISBN
5867:) (
5793:ISBN
5759:ISBN
5738:help
5712:ISBN
5690:and
4548:is:
4541:and
3659:|| R
3120:is:
2934:and
1621:|| R
158:|| R
122:|| R
33:pole
6021:or
6006:etc
5874:||
5121:or
4685:= A
4461:or
4385:||
3701:as
3664:).
3408:as
1606:R-C
6063::
5929:^
5862:+C
5791:.
5773:^
5730::
5728:}}
5724:{{
5629:.
5610:.
5589:.
4619:10
4583:10
4565:20
4527:/
4520:(
4518:10
4508:10
4498:10
4488:10
4399:.
4378:(
3653:(
1615:(
705:.
116:(
6008:.
5994:.
5953:.
5923:.
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5869:R
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5801:.
5767:.
5740:)
5720:.
5694:.
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5393:L
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5364:i
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5340:)
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5325:i
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5317:+
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5264:2
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3932:=
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3698:ω
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3431:=
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3259:)
3254:C
3250:C
3246:+
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3233:(
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3201:(
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3193:i
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3169:[
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3160:+
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3141:D
3117:ω
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2221:[
2218:=
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2174:ω
2172:D
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2123:/
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2040:A
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2032:+
2027:i
2023:R
2016:i
2012:R
2004:v
2000:A
1996:=
1989:a
1985:v
1975:v
1956:v
1954:A
1931:.
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1917:)
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1818:C
1814:C
1807:j
1804:+
1801:1
1790:o
1786:R
1782:+
1777:L
1773:R
1766:L
1762:R
1754:v
1750:A
1743:1
1739:(
1733:C
1729:C
1725:=
1714:)
1706:i
1702:v
1692:v
1683:1
1679:(
1673:C
1669:C
1665:=
1656:M
1652:C
1623:L
1619:o
1617:R
1612:L
1610:C
1600:v
1598:A
1577:.
1568:)
1563:L
1559:R
1550:o
1546:R
1542:(
1539:)
1534:C
1530:C
1526:+
1521:L
1517:C
1513:(
1507:j
1504:+
1501:1
1494:v
1490:A
1485:/
1479:o
1475:R
1469:C
1465:C
1458:j
1455:+
1452:1
1422:)
1417:i
1413:R
1404:A
1400:R
1396:(
1393:)
1388:i
1384:C
1380:+
1375:M
1371:C
1367:(
1361:j
1358:+
1355:1
1351:1
1320:o
1316:R
1312:+
1307:L
1303:R
1296:L
1292:R
1278:A
1274:R
1270:+
1265:i
1261:R
1254:i
1250:R
1242:v
1238:A
1234:=
1201:a
1197:v
1191:i
1187:v
1177:i
1173:v
1163:v
1157:=
1150:a
1146:v
1136:v
1103:.
1094:)
1089:L
1085:R
1076:o
1072:R
1068:(
1065:)
1060:C
1056:C
1052:+
1047:L
1043:C
1039:(
1033:j
1030:+
1027:1
1020:v
1016:A
1011:/
1005:o
1001:R
995:C
991:C
984:j
981:+
978:1
946:o
942:R
938:+
933:L
929:R
922:L
918:R
910:v
906:A
902:=
895:i
891:v
881:v
851:i
847:v
817:v
791:.
783:i
779:v
773:v
769:A
765:=
760:o
756:v
725:o
721:v
690:)
685:i
681:R
672:A
668:R
664:(
659:i
655:C
648:2
644:1
631:C
629:C
613:1
579:,
568:1
557:2
553:1
548:=
535:)
530:i
526:R
517:A
513:R
509:(
506:)
501:i
497:C
493:+
488:M
484:C
480:(
474:2
470:1
465:=
456:1
452:f
431:1
429:f
406:,
397:)
392:i
388:R
379:A
375:R
371:(
368:)
363:i
359:C
355:+
350:M
346:C
342:(
336:j
333:+
330:1
326:1
316:A
312:R
308:+
303:i
299:R
292:i
288:R
282:=
275:a
271:v
265:i
261:v
231:a
227:v
201:i
197:v
167:C
165:C
160:L
156:o
154:R
152:(
149:L
147:C
142:L
140:C
135:L
133:R
124:i
120:A
118:R
113:i
111:C
106:i
104:C
99:i
97:R
92:C
70:o
68:R
63:i
61:R
56:C
54:C
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