Passive, active, and digital filters (3ed., CRC, 2009) - tiera.ru

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Design of Resistively Terminated Networks 9-7The values of the final elements can also be calculated directly byL n ¼ 2R 2 sin p=2n(1 þ a)v c, n odd (9:38a)C n ¼2 sin p=2nR 2 (1 þ a)v c, n even (9:38b)A complete derivation of these formulas was first given by Bossé [1]. Hence we can calculate the elementvalues starting from either the first or the last element. When R 1 ¼ R 2 , formulas Equation 9.36 reduce toL 2m 1 ¼ 2R 1 sin g 4m 3v cC 2m ¼ 2 sin g 4m 1R 1 v c(9:39a)(9:39b)Example 9.1GivenR 1 ¼ 70 V, R 2 ¼ 200 V, v c ¼ 10 5 rad=s, n ¼ 4 (9:40)obtain a Butterworth LC ladder to meet these specifications.Since R 2 > R 1 , we choose the plus sign in Equation 9.32 and obtain r 11 (0) 0, a ¼ 0.833, andg m ¼ 22.5m. Thus, from Equations 9.35 and 9.36 the element values are found to beL 1 ¼2 70 sin 22:5¼ 3:2081 mH (9:41a)(1 0:833) 105 4 sin 22:5 sin 67:5 C 2 ¼L 1 ð1:69391:666 cos 45 ¼ 0:085456 mF (9:41b)Þ1010 4 sin 67:5 sin 112:5 L 3 ¼¼ 2:3587 mH (9:41c)C 2 ð1:69391:666 cos 90 Þ1010 4 sin 112:5 sin 157:5 C 4 ¼¼ 0:020877 mF (9:41d)L 3 ð1:69391:666 cos 135 Þ1010 Alternatively, C 4 can be computed directly from Equation 9.39b asC 4 ¼2 sin 22:5 ¼ 0:020877 mF (9:42)200 (1 þ 0:833) 105 The ladder network together with its termination is presented in Figure 9.3. This network possesses thefourth-order Butterworth transducer power-gain response with a DC gainK 4 ¼ 1 a 8 ¼ 0:7682 (9:43)
V g–V g–9-8 Passive, Active, and Digital Filters3.21 mH2.36 mH70 Ω+0.085 μF 0.021 μF200 ΩFIGURE 9.3Fourth-order Butterworth LC ladder network.Case 2. r 11 (0) < 0. With the choice of the minus sign, the input impedance can be expanded in acontinued fraction as1Z 11 (s) ¼ C 11s þ1L 2 s þ1C 3 s þ.. . þ 1 W(9:44)which can be realized by the LC ladder networks of Figure 9.4, depending on whether W is even or odd,where W is the terminating resistance or conductance. Formulas for the element values are similar toL 2 L 4L n–2L nR 1+C 1 C 3C n–1R 2(a) n evenL 2 L 4 L n–3 L n–1R 1+V g–C 1 C 3 C n–2C nR 2(b) n oddFIGURE 9.4 Butterworth LC ladder networks for r 11 (0) < 0.
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Passive, Active,and DigitalFilters
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The Circuits and Filters HandbookTh
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ContentsPreface ...................
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PrefaceAs circuit complexity contin
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ContributorsPhillip E. AllenSchool
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IPassive FiltersWai-Kai ChenUnivers
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1General Characteristicsof FiltersA
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General Characteristics of Filters
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1-12 Passive, Active, and Digital F
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2-2 Passive, Active, and Digital Fi
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Approximation 2-9K(ω)Large nSmall
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Approximation 2-132π21φ = cos -1
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Approximation 2-15This result is us
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Approximation 2-19Butterworth; put
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Approximation 2-21This however impl
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Approximation 2-23TABLE 2.3 Bessel
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Approximation 2-25R mn (ω)b + εbb
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Approximation 2-27is a measure of t
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Approximation 2-29Recall, now, the
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Approximation 2-31TABLE 2.4 Zeros o
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Approximation 2-33References1. A. M
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4Sensitivityand SelectivityIgor M.
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Sensitivity and Selectivity 4-34.3
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Sensitivity and Selectivity 4-5Beca
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Sensitivity and Selectivity 4-7Simi
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Sensitivity and Selectivity 4-9comp
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Sensitivity and Selectivity 4-11In
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Sensitivity and Selectivity 4-13and
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Sensitivity and Selectivity 4-154.8
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Sensitivity and Selectivity 4-17cha
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Sensitivity and Selectivity 4-19Tak
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Sensitivity and Selectivity 4-21I p
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Sensitivity and Selectivity 4-23Att
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Sensitivity and Selectivity 4-25 In
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Sensitivity and Selectivity 4-27the
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Sensitivity and Selectivity 4-29is
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Sensitivity and Selectivity 4-311.
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5Passive Immittancesand Positive-Re
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Passive Immittances and Positive-Re
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Page 136 and 137: 6Passive CascadeSynthesisWai-Kai Ch
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Page 152 and 153: 7Synthesis of LCM andRC One-Port Ne
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Page 194 and 195: 10Design of BroadbandMatching Netwo
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Page 224 and 225: IIActive FiltersWai-Kai ChenUnivers
Page 226 and 227: 11Low-Gain Active FiltersPhillip E.
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Low-Gain Active Filters 11-11For th
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Low-Gain Active Filters 11-13The se
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Low-Gain Active Filters 11-15Y 1H22
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Low-Gain Active Filters 11-17R 2+R
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Low-Gain Active Filters 11-19To con
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Low-Gain Active Filters 11-21+10k 1
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Low-Gain Active Filters 11-23TABLE
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Low-Gain Active Filters 11-25The ph
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Low-Gain Active Filters 11-27TABLE
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Low-Gain Active Filters 11-29I n1E
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Low-Gain Active Filters 11-3150 nVS
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12Single-AmplifierMultiple-Feedback
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Single-Amplifier Multiple-Feedback
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13-10 Passive, Active, and Digital
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14The CurrentGeneralizedImmittance
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The Current Generalized Immittance
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15High-Order FiltersRolf SchaumannP
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High-Order Filters 15-3V inV o2V oi
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High-Order Filters 15-5Choosing the
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High-Order Filters 15-7where we def
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High-Order Filters 15-9where we int
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High-Order Filters 15-11where s is
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High-Order Filters 15-1315.4.1 Sign
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High-Order Filters 15-15Ri2R 4V oR
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High-Order Filters 15-17Notice that
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High-Order Filters 15-19v i g i(α
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High-Order Filters 15-21TABLE 15.1
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High-Order Filters 15-23R a1 ¼ ^C
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High-Order Filters 15-25I 1 1V 1 sk
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High-Order Filters 15-27664154015.2
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16Continuous-TimeIntegrated Filters
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Continuous-Time Integrated Filters
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17Switched-CapacitorFiltersJose Sil
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Switched-Capacitor Filters 17-3C SC
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Switched-Capacitor Filters 17-5For
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Switched-Capacitor Filters 17-7φ 2
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Switched-Capacitor Filters 17-9A 3
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Switched-Capacitor Filters 17-11whe
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Switched-Capacitor Filters 17-1317.
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Switched-Capacitor Filters 17-15C i
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Switched-Capacitor Filters 17-1717.
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Switched-Capacitor Filters 17-19The
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Switched-Capacitor Filters 17-21Dur
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Switched-Capacitor Filters 17-23sig
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Switched-Capacitor Filters 17-25C 1
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Switched-Capacitor Filters 17-27φC
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Switched-Capacitor Filters 17-29for
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Switched-Capacitor Filters 17-31If
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Switched-Capacitor Filters 17-33FIG
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Switched-Capacitor Filters 17-35CH1
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IIIDigital FiltersRashid AnsariUniv
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18FIR FiltersM. H. ErNanyang Techno
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FIR Filters 18-3Consequently,tan (v
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FIR Filters 18-5TABLE 18.1Frequency
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FIR Filters 18-7H d (e jω )1To und
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FIR Filters 18-90-10-20Amplitude re
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FIR Filters 18-110-5-10Amplitude re
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FIR Filters 18-130-20Amplitude resp
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FIR Filters 18-15TABLE 18.2Spectral
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FIR Filters 18-17If it were possibl
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FIR Filters 18-19The alternation th
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FIR Filters 18-21respectively, and
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FIR Filters 18-23Rejection of super
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FIR Filters 18-25The selective step
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FIR Filters 18-27TABLE 18.4 Impulse
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FIR Filters 18-29selective step-by-
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FIR Filters 18-31Odd filter lengthM
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FIR Filters 18-33and1a 1 ¼ ~c 02 ~
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FIR Filters 18-35a useful property
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FIR Filters 18-37with the number of
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FIR Filters 18-39F(z L )z −LN F /
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FIR Filters 18-411F(Lω)G 1 (ω)0 0
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FIR Filters 18-43TABLE 18.11Algorit
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FIR Filters 18-451N ove ¼ N optL
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FIR Filters 18-47TABLE 18.13 Implem
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FIR Filters 18-494. If r ¼ R, then
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FIR Filters 18-51In this case, the
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FIR Filters 18-53Estimated orders11
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FIR Filters 18-550Amplitude (db)−
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FIR Filters 18-57In the above, the
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FIR Filters 18-59TABLE 18.15Data fo
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FIR Filters 18-614. Y. C. Lim and Y
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20Finite WordlengthEffectsBruce W.
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Finite Wordlength Effects 20-3the q
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Finite Wordlength Effects 20-5From
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Finite Wordlength Effects 20-7In ge
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Finite Wordlength Effects 20-9To ob
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Finite Wordlength Effects 20-11Howe
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Finite Wordlength Effects 20-13wher
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Finite Wordlength Effects 20-15 y(4
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Finite Wordlength Effects 20-17j1.0
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Finite Wordlength Effects 20-1921.
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23Two-DimensionalIIR FiltersA. G. C
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Two-Dimensional IIR Filters 23-323.
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Two-Dimensional IIR Filters 23-5a 1
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Two-Dimensional IIR Filters 23-7x(n
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Two-Dimensional IIR Filters 23-9+π
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Two-Dimensional IIR Filters 23-11TA
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Two-Dimensional IIR Filters 23-13wh
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Two-Dimensional IIR Filters 23-15ω
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Two-Dimensional IIR Filters 23-17x
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Two-Dimensional IIR Filters 23-19St
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Two-Dimensional IIR Filters 23-21In
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Two-Dimensional IIR Filters 23-23an
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Two-Dimensional IIR Filters 23-25-1
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Two-Dimensional IIR Filters 23-2711
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Two-Dimensional IIR Filters 23-29is
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Two-Dimensional IIR Filters 23-33Co
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Two-Dimensional IIR Filters 23-35In
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Two-Dimensional IIR Filters 23-37f
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Two-Dimensional IIR Filters 23-39If
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Two-Dimensional IIR Filters 23-41TA
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Two-Dimensional IIR Filters 23-43f
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Two-Dimensional IIR Filters 23-45St
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241-D MultirateFilter BanksNick G.
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1-D Multirate Filter Banks 24-324.2
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1-D Multirate Filter Banks 24-5Subs
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1-D Multirate Filter Banks 24-7y 00
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1-D Multirate Filter Banks 24-9Haar
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1-D Multirate Filter Banks 24-11H k
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1-D Multirate Filter Banks 24-13Now
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1-D Multirate Filter Banks 24-1510h
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1-D Multirate Filter Banks 24-17Equ
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1-D Multirate Filter Banks 24-191Da
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1-D Multirate Filter Banks 24-211An
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1-D Multirate Filter Banks 24-231Ne
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1-D Multirate Filter Banks 24-25dur
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1-D Multirate Filter Banks 24-27Rec
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1-D Multirate Filter Banks 24-29pre
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1-D Multirate Filter Banks 24-31The
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1-D Multirate Filter Banks 24-332An
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1-D Multirate Filter Banks 24-352.
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1-D Multirate Filter Banks 24-39by
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1-D Multirate Filter Banks 24-41x0
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1-D Multirate Filter Banks 24-43pri
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1-D Multirate Filter Banks 24-45The
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1-D Multirate Filter Banks 24-47Two
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1-D Multirate Filter Banks 24-49" #
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1-D Multirate Filter Banks 24-51Tre
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ω 1πω 1π25-8 Passive, Active, a
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26Nonlinear FilteringUsing Statisti
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Nonlinear Filtering Using Statistic
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27Nonlinear Filtering forImage Deno
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Nonlinear Filtering for Image Denoi
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IN-2Indeximpulse invariance method,
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IN-4Indexprescribed specification,2
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IN-6Indexfilter rank ordering, 2-32
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IN-8Indexpassband and stopband ripp
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IN-10Indexstate-space filter realiz
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IN-12Indexnonessential singularitye
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IN-14Indexreal-valued weights andop
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IN-16Indexbaseband communication,26
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IN-18Indexarbitrary specificationCh
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IN-20IndexVoltage-controlled curren
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