Normalized filter design

Normalized filter design - _..¢____.__...

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Unformatted text preview: _..¢____.__ ———-—____.__.____ W ——-———_____._.__.._____ 5‘2 SFGC/AL Pam flemc/?:Am/u5 Bur/’awo/LW *7 MAx/MALW Flu/x7“ 'Céeéyséeq/ «9 Emu: (ltPPce’ Low‘PASS [HE—‘3 EWV/Ofl 1g Wmdmuf scAuefl To (H6)me 07ml flay/13 WWW “’"‘|———————-——______ IL JL M (F OLS‘) 1Ll= (0 Mail} = 3'38 N U] C Insertion 1033, 018 b—A O 02 0. 0. 0.8 1 1.2 1.4 Normalized frequency, £2 1.8 1.6 Figure 5-16 Butterworth low-pass filter design. "10>lo?<l“lr‘l~]2)= IOIOngF} |O loggl-I— CZZJLZN} ,UORMALJ MEI) 3C FILTER (9R DER —— —- =1 J). 3Q l I l I 2” + Figure 5-17 Two equivalent realizations of the generic multisection low-pass filter with normalized elements. 3 T- lM—Crnd gamefa‘hnr rCS(5+'CLV\C.Q_ (0.) CoNdUchmu. (to) gm : llUduchmca 14>," Series (tack/char Capacr/me 7%.” SAW’WL CQ/ad/SR FM- Ma (J ...J A/ g/wl T LOAD RPS/SMMCE if 0/157” ELL-.‘WHUT '15 A SHUNT CAP/1cme LOAD Cououcmpuc’ /F OAS?“ eléMrw/T/S A Same? WWW Table 5-2 Coefficients for maximally flat low-pass filter (N = 1 to 10) g2 £3 8 10 85 87 88 -------- -------- ---- 0.7654 1.8478 0.7654 --- - 811 1 0.6180 1.6180 2.0000 1.6180 0.6180 10000 0.5176 1.4142 1.9318 1.9318 14142 0.5176 1.0000 - 0 450 1.2470 1.8019 2.0000 1.8019 1.2470 0.4450 1.0000 03902 1.1111 1.6629 1.9615 1.9615 1.6629 1.1111 0.3902 1.0000 - 03473 1.0000 1.5321 1.8794 2.0000 1.8794 1.5321 1.0000 0.3473 1.0000 0.3129 0.9080 1.4142 1.7820 1.9754 1.9754 1.7820 1.4142 0.9080 0.3129 1.0000 7160c; NO/lMAkRng FOR 30: I . t MW___W-WHHW___F—a_—_Mm ...... _,__.,~_____.._.,,______._.. Attenuation, dB 1.1 1.2 1.3 1.51.7 2 3 4 6 8 11 Normalized frequency, 9 Figure 5-18 Attenuation behavior of maximally flat low-pass filter versus normalized frequency. Fm (1+ .rf‘" W W fl >2] LI: 1) 8V ZONdyc/ECQJC r777._..«___.__...._#_mmwwwm.__.w___—r_~~m~mv l Table 5-3 Coefficients for linear phase low-pass filter (N = 1 to 10). 2.0000 1.5774 1.0000 1.0598 0.1104 1.0000 - 0.9303 0.4577 0.3312 0.2090 0.0718 1.0000 IE - - 0.8377 0.2364 0.1480 0.0505 1.0000 - 0.7677 0.2378 0.1778 0.1104 0.0375 10000 - - 07125 0.3446 0.2735 0.2297 0.1867 0.1387 0.0855 0.0289 1.0000 0.6678 0.3203 0.2547 0.2184 0.1859 0.1506 0.1111 0.0682 0.0230 10000 06305 0.3002 0.2384 0.2066 0.1808 0.1539 0.1240 0.0911 00557 0.0187 1.0000 _ 7* + REZALL (13(01): +01% ‘ M #71556: Ref/7761)] 672007) 09.07 15 : claw) 3 “‘W (15.41) 3 A1 11(14—A1JLM : 01. d7“) ZN 3 “11“ =40+A<2~HM J 7, .__._____.—_—_~___—W_w__u_mm—_r——~ 1 . . A -1 ~1~0.8~—O.6—O.4—0.2 0 0.2 0.4 0.6 0.8 1 Normalized frequency, (2 Figure 5-19 Chebyshev polynomials T162) through T4(Q) in the normalized frequency range ~ISQSI. To : l ALL PotYMO/M/ALS OSCILLNE Tfi/O— wow A 4"! INTERVAL " 2533' ‘ ‘ " ll: "' 4' T3: “an + ML" [WE-ll: Wm H712) TZl-‘l"8f2_1+8fl_4 = l V I +a‘7zoz) //’: 6L=l THEM AT __Q_:1 z: | u M? e W W“ :. ‘707 «368 m l- ‘ L - o dB V7 Loss factor .2 0.4 0.6 0.8 1 1.2 1.4 Normalized frequency, (2 1.6 1.8 2 Insertion loss, dB 3-dB ripples 0.2 0.4 0.6 0.8 l 1.2 1.4 1.8 2 Normalized frequency, £2 1.6 Figure 5-20 Frequency dependence of the bee factor and insertion loss of the Chebyshev low-pass filter, ____ .__._.__.—... __.—.~—__—_~mw_w—w——_HM__—_m_ Attemation, dB 1.1 1.2 1.4 1.72 3 5 811 Normalized frequency, (2 0 ‘ ' 1.01 1.02 1.04 Figure 5-21 Attenuation response for 3 dB Chebyshev design. Attenuation, dB 1.2 1.4 1.7 2 3 5 Normalized frequency, 9 Figure 5-22 Attenuation response for 0.5 dB Chebyshev design. Table 5-4 (a) Chebyshev filter coefficients; 3 dB filter design (N = 1 to 10) g2 1.0000 - 0.5339 3.3487 0.7117 1.0000 0.7483 0.5920 0.7618 0.7618 - 0.7685 0.7929 0.6033 0.7771 Table 5-4 (h) Chebyshev filter coefficients; 0.5 dB filter design (N = 1 to 10) gl nun 1.5963 10967 1.5963 1.0000 - ---- --- 1.7504 1.2690 26678 1.3673 27939 1.3673 2.6678 1.2690 1.7504 1.0000 1.7543 1.2721 2.6754 1.3725 2.7392 1.3806 2.7231 1.3485 2.5239 0.8842 1.9841 .A b6 62, .4 .9- 053493 a amusmu‘r PMer 7777137“ mews as 70 Coumw 7W Hawk-r 0F PASSBAAJD RIPPLES. 3. IL (5 max M’rmd 71(31):] 5c:— 0413 MW TAU-VD IL” )0 [030 +0?) 11—46 V10 /’° ~I Attenuation, dB r—A N U: C p—A O -2 —1.5 1.5 2 Normalized fiequency, S2 Figure 5-24 Fourth-order low-pass Chebyshev filter with 3 dB ripples in the passband. Figure 5-25 30 25 g 20 8” g 15 § E 10 .LA 0 0.2 0.4 0.6 0.8 1 1.2 Frequency, GHz 1.4 1.6 1.8 2 Conversion of standard low-pass filter prototype into low—pass realization. Cut-off frequency is f0 = 1 GHz. Attenuation, (18 Figure 5-26 30 N U] N O p—A (I! H O 0 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 Frequency, GHz Conversion of standard low-pass filter prototype into high-pass realization. Cut-off frequency is fo = 1 GHz. 313’ a = Z :l =1 " We: 2 93 34 I Lg hail—J C (1155 0.8518 0193—2 [.00 L a / 257,4 [- . _. key, SLw L,_ a o.lqzzH C" o‘fizg 3‘3'19—1 on“? 3-3437 L00 L,= 3.3%87 H R A L1=3.3"l8'7 (a _\ Cg. =2 0.7“? F: RL ‘ | A1— ' v — 754! L” (11 :. \é‘ ‘ QQ‘f‘flL 0'3- Va 7 3 0‘s (1 VA: Emmet.) V G Zancawam Zak/ac" Vz 7‘ (Rb VA QL+ ELZ “r—w—m‘fim____. Attenuation, dB c» 00 S B A Normalized frequency, (2 Figure 5-23 Comparison of the frequency response of the Buttenrvorth, linear phase, and 3—dB Chebyshev third-order filters. 1P 5mm Tuesmow FmM PASSBMD TD SmPeANo l5 Reameeb ) AND RMPLES CAN Be Tau-fiéATED‘ \ L/WLR Prime #255 A Seoul TYLAwsmoN 307‘ 15 QwFuL FDF rvs (Anew PQAS€ nu MODULD‘DBN «LN/sz 1 Q,\Q.C01‘r5- ._._.__.__.._._._..-...____.__p—— _____.._._____,_.____.____..._ _,,._. ‘,W___.-M_____—__———————.—.—__.__—.___F____—— |.__.________ r ...
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Normalized filter design - _..¢____.__...

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