Exercises for Frequency Response. ECE 102, Fall 2012, F. Najmabadi

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1 Eecses Fequency espnse EE 0, Fall 0, F. Najabad

2 Eecse : Fnd the d-band an and the lwe cut- equency the aple belw. µ n (W/ 4 A/, t 0.5, λ 0, 0 µf, and µf Bth capacts ae lw- capacts. F. Najabad, EE0, Fall 0 (/0

3 Bas: GS-K: I I I 6 GS µ O 0.5 n O O I O O O O W O 0.5 A O I O A/ and λi d-band Gan: G Ap.: ( 5 k 0 k F. Najabad, EE0, Fall 0 (/0

4 we cut- equency: c 0 µf (see ccut c p 8 k 8 k Ω.8 z c µf (see ccut c 0 k 5 k 5 k p z p p p z F. Najabad, EE0, Fall 0 (4/0

5 Eecse : A Inn, nd the d-band an, and Z the ccut belw I 00 µa. B Fnd such that 00 z. µ n 400 µa/, µ p 00 µa/, An.8, Ap., (W/ n (W/ p 0, s 0 F, and d db sb 5 F. In any ccut, a hh-equency ple has t be ntduced n de t achee an and phase an necessay stablty ( n ths pble. Ths s called the dnant ple cpensatn. F. Najabad, EE0, Fall 0 (5/0

6 Bas: W I 0.5µ n O O 0.5 I I O An.79 A/ 9 k d-band Gan: A A.79 0 and ( 6 I 0 Ap O 0.5 k (9 k 0.5 k 8.68 h- apacts: d, d, n s d d ( A 5( F ( / A 5( / F d, d, F d db db F F. Najabad, EE0, Fall 0 (6/0

7 n : : 0 τ 0 (N Ple τ 4.85 k b τ τ b Gz z d 57 Gz Pat B: (Ple at 00 z F 4 F d, b d db db 0.6 F. Najabad, EE0, Fall 0 (7/0

8 Eecse : A dy the ccut belw t nclude a dnant ple at 00 z ( 00 Ω, k, k, / 00 Ω, λ 0, and ne ntenal capactances the OS. B pute the dnant ple n the ccut yu dened s educed by a hal. pute the dnant ple n the ccut yu dened s educed by a hal. Thee ae tw ways t ntduce a dnant ple n a S aple: A capact between utput & und A capact between nput & utput F. Najabad, EE0, Fall 0 (8/0

9 . nant ple a a capact between utput & und esstance seen between tenals s: ( 0 / ( ( Pat A (Fnd 00 z F k, ( k 0.667k pf Pat B (Fnd 00 Ω : s ndependent s n chane n the dnant ple Pat (Fnd k : F k, ( k 0.5k z F. Najabad, EE0, Fall 0 (9/0

10 F. Najabad, EE0, Fall 0 (0/0. nant ple a a capact between nput & utput lle s Thee 0 λ d A ( / ( / ( ( (,, A A / ( ( /(,, π

11 . nant ple a a capact between nput & utput (cntnued /( [( ( / ] Pat A (Fnd 00 z F ( k, k ( /, pf 0.667k and Ω 6.67 Pat B (Fnd 00 Ω : F ( k, k ( /,54 50 z 0.667k and Ω 6.67 Pat (Fnd k : F. Najabad, EE0, Fall 0 (/0 F ( k, k ( /,800 8 z 0.5k and Ω 5.0

12 Eecse 4: Fnd the ccut belw wthut usn lle s Thee. We cannt use undaental s lle capact. esstance acss tenals d shuld be und usn OS SS. F. Najabad, EE0, Fall 0 (/0

13 s : db : τ s τ ( ( db F. Najabad, EE0, Fall 0 (/0

14 F. Najabad, EE0, Fall 0 (4/0. d (cannt use eleentay s ( ( / ] ( ( [ ( ( d s s A I I I I I d d τ ( ( ] ( [ /( ( ( ( ( d db d s d d db s A b A b b π τ τ τ lle s apacts

15 Eecse 5: Fnd the d-band an, lwe and uppe cut- equency ths tw-stae aple (dentcal tanssts wth s 50 F, d 80 F, / 00 Ω, λ 0, and ne db. Eanatn the ccut shws that bth 00 and 500 nf capacts esult n lw-equency ples. h-equency espnse s set by the ntenal capactances tanssts. F nal ccut 0k and 00k bas essts Q appea n paallel wth each the. F. Najabad, EE0, Fall 0 (5/0

16 d-band an (/ 00 Ω, λ 0 The lw-equency capacts shuld be sht The hh-equency capacts pen. Ths s a tw-stae aple (bth S cnuatn: A ( k 9.0 A (k 0,, (0 k 00 k 9.09 k 9.0 ( F. Najabad, EE0, Fall 0 (6/0

17 w-equency espnse: 500 nf capact: 00 nf capact: p (/ Ω 4.77 kz (k p, 0. 0 k 9.09 k 0.k z p p p kz F. Najabad, EE0, Fall 0 (7/0

18 h-equency espnse: ue t ntenal capactances tanssts. w-equency capacts ae sht. sb bth NOS ae shted ut. Ine db (pe pble nstuctn. eplace d usn lle s Thee. n s d, d, d, s F. Najabad, EE0, Fall 0 (8/0 d,

19 A s 9.0, A 0 s 50 F d d 80 F d, d, d, d, d d d d ( A 80( F ( / A 80( F ( A ( / A 80( F 80( /0 88 F n d, d, d, s d, 88 F ,050 F s ,9 F F. Najabad, EE0, Fall 0 (9/0

20 n,050 F,9 F d, 88 F n,050 F 00 Ω τ.0 0 n 0 k 9.09 k 0.90 k τ,9 F d, k τ 88 F d, F. Najabad, EE0, Fall 0 (0/0 9 b τ τ τ.06 0 b 7.z

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