?= é í÷?μ÷? ?8?à ? A (dB) < (rad) 0 1 π2000 π3000 40 Y{ ?h HzfA 10000 dB1 ≤≤≤ E{ ?h HzfA 1500 dB40 ≥≥ ?B?? ó?￥/ ?Hqs ? ?@? Hq￥a O1 V LC￥Mf ? |??f ?N???1 /í b ?=? ?? a?￥è ^  ?è ^2?ò íq? ? Mf ? |??f ?? ??/í ?¤?￥f ?N???1 LC b ?T?¨"9aL?a H?M￥í÷íqèE aè ?aè?ao?# ?XMa  ?8?? ? ?1 í÷? ?8? b ? ?8? H?¨  ?bv a s e÷aμE FMD ?μ÷íq ?8?? ??1 μ÷? ?8? b ' é?1cí÷? ?|??f ?￥?éD8 ?a/íD 2 ùù5aμ÷ roè ^?b ? ?s  pX?? ?￥Y?+? kX !9E üa ka La_? ? !9? ? ? ?8? ? ?1 p￥Y?+??üVQˉ k7 ?1 !9? ?b D "￥ YV' é￥DF '? ?f ??é￥ ?3g?'8?ZEb ? Bc í÷? ?￥ |??f ? ? 6.1 BB?? ?BB? ? 6.2 í÷? ?|??f ? ? 6.3 í÷? ,aE Ff ?￥?é ? 6.4 LCB g? ?￥ LCB g? ?￥ LC ? 6.5 RCB g? ?￥ LC B g? ?￥ LC ? 6.6 RLB g? ?￥ LC ? 6.6 RLCB g? ?￥ LCeo ?61 BB?? ?BB? ·BB? L=è ^?íqè ?′￥ ? ) Vl? 10 -12 FèE ′ Vr 10 6  10 7 $? ? qS? ? av?V+ Hz ?  $￡ Hzbs?8?￥ ?V??1) ??t vlMμ . ￥ ?aa ?^/?9 ?μ .à9 ?￥nb ×?ê?? ?￥ ?ê P ?1o′1 1¤í 1 ￥′7  ?? ??]B1 èD ?bM?￥è ^?1 BB?è ^ b · "￥ hl9 ?￥?LDμL??TY¨￥8?mV y NYèè ^s?? ?￥′ü V |1 2$ a1Fa2H? · ?BB? BB?￥ I ? ?BB?è ^Rí? L=￥è ^ b · ?BB?è ?  ?D ?y0 e′DBB?′-1 b !BB?a￥? ?′F/S “ N ”V Ub aE F￥BB?D ?BB? !BB?è ?1 k Z 5 ZN ksZsZ )()( = BB? ?BB? )()( sZksZ NZ = ?? ?￥E FBB?D ?BB?Vr T1 . , , CkCkLLkRR ZNZNZN === . , , ZNNZNZ kCCLkLRkR === a ? q￥BB?D ?BB? !BB?è ?1 k < = ss N 1 PE F′?M?μ NNNN CsCk k s sCLsLk k s sL ≡?=≡?= < < < < , ?? ?￥ ? qBB?D ?BB?Vr T1 , , CkCLkLRR NNN << === , , << kCCkLLRR NNN === a] HμE FD ? q￥BB?D ?BB? , , CkkCL k k L k R R ZN Z N Z N < < === 1 , , N Z N Z NZ C kk CL k k LRkR << === è !E F? ? q?üBB?￥è ^ ?m ? U  èa Mf ?¨BB? ? q s N V U1 (*) 2)( )( )( 2 1 2 ++ == NN N N N N ss s sU sU sH + + ? ? )( 1 sU )( 2 sU H1 F 2 1 ?1 ?? ? ? q1 srad /2 ?T1 püBB? ? q?1 10kHz5 ? q ?BB?è ?1 44 104429.410 2 2 ×=×? ? ? ? ? ? = π ω k ¨ s/(4.4429?10 4 )} T (*)?￥ s N ¤ ?BB?a￥M f ? (**) 10479.39104429.4 104429.4 )( )( )( 842 4 1 2 ×+×+ × == ss s sU sU sH N N N H508.22 μ F254.11 μ ?1 ?T1 pè ^?￥è ?′?? 0.10 F5E F ?BB? è ? k Z V9 ? ?/b )10/(1)( 7? ×= ssZ 7 )10254.11/(1)( 6? ××= ssZ N H533.2 m F1.0 μ ?54.112 # ? ? ? ? ? ? ? ? × × === ? ? 6 6 101.0 10254.11 54.112 )( )( sZ sZ k N Z ? q￥BB?D ?B B???YE F′ 7E F￥BB?D ? BB?? PòE FM ?]B ?y7ò íqs¤￥èaè @?Mb ?6-2 í÷? ?|??f ? ?T ?ió?μ ?f ? F(s) ^? ?[ ?T1|?? f ?8?í÷B g? ? ;$ ss s sF 1 2 12 )( 1 += + = ss s sF 1 2 12 )( 2 +?= +? = 1F ?1 )()( 11 sFsZ = 1F ?2 )()( 22 sFsZ = NIC 1 2 =k 1 1 =k ? H Otto Brune? ?? O??μ ?f ? F(s) ^? Lf ? H F(s)? ^ V LC￥í÷? ?￥|??f ?b Ba¨ ? f ?V U￥ Z(s) 2 1 1 * 1 1 * 1 * 1 1 11 1 1 )()( )( )( )( )( )( )( )( I sIsU sI sI sI sU sI sU sZ = = ? ? == ∑ = = b j j j IUIU 2 * 1 * 1 )(sZ N + ? )( 1 sU )( 1 sI + à?? ? ?co? H| ^ VAR1 j j jjj I sC sLRU ) 1 ( ++= 2 1 2 2 1 * 2 2 ) 1 ( )( I sC sLRI I IU sZ b j j jj b j j j j ∑ ∑ = = ++ == ∑ ∑∑ = == = == b j j b j j b j j C IsV LIsTRIsF j jj 2 22 1 )( )( )( 2 0 2 0 2 0 7 )]( 1 )()([ 1 )( 000 2 1 sV s ssTsF I sZ ++= )]( 1 )()([ 1 )( 000 2 1 sV s ssTsF I sZ ++= C L W C UC jV WL I jT PR I jF b j j jj b j j j b j j j 22 0 2 0 2 0 4 1 ) 2 (2)( 4) 2 (2)( 2) 2 (2)( 2 2 2 ω ω ω ω ω == == == ∑ ∑ ∑ = = = F 0 (s)aT 0 (s)aV 0 (s)?1 ? f ?  O ? ìˉ ü ?  ? ^dμ￥??× ?/ü1dμ￥ L ?b N =co? H| ^ VAR1 ∑ ≠ = +++= b jk k kjkj j jjj IMsI sC sLRU 2 ) 1 ( e ?￥ T 0 (s)M1 ∑∑ = ≠ = += b j b jk k jkkjj MsIsILIsM j 22 ][ )()()( 2 0 L WjM 4)( 0 =ω ]" M 0 (s)?0 O M 0 ( j< )g1dμ￥ L ?b =a¨ ? f ?V U￥ Y(s) ][ )( 1 )()( 1 ) 1 ( 1 )( 0 * 0 * 0 2 1 * * * 2 1 2 sV s sTssF U I Cs LsRI U sY j j b j j jj ++= ++= ∑ = I no? H ][ )( 1 )()( 1 )( 0 * 0 * 0 2 1 sV s sMssF U sY ++= ?a? Lf ? (P.R.F.) ˉMf ? F(s)1? Lf ? ? ? ?@ (1) s1 L ? H F(s)ü1 L ? (2) ? Re (s)?0 H Re [F(s)]?0 ·L?í÷ H?M? ?￥|??f ? Z(s)? Y(s) (1 ? Lf ?b ￡ ü ?  ? f ?Vr T? Z(s)? Y(s)A ? ?@Hq (1) !ˉ ? s =6 + j< 5 Re [Z(s)] ][ )( )()( 1 00 22 0 2 1 sMsVsF I σ ωσ σ + + += ^?? Re (s)?0 H Re [Z(s)]?0' Z(s)9 ?@H q (2)# Z(s)1? Lf ?b ] ? V￡ Y(s)1? Lf ? (? “? Lf ?￥? ? ˉ1? Lf ? ”°¤¤2 ? )b ?ó?￥ Z(s) Y(s)1 ?? ? ì ??¨í÷B g LCo3 ? ? ì ^?1? Lf ?b ?63 í÷? ( ,aE ) Ff ?￥?é 1aZ(s)aY(s) s￥ RHP(Right Half Plane) í?b 2aZ(s)aY(s) s￥ RHP í ,?b 3aZ(s)< Y(s)>′à  ?μ?< ,?>o ? ^B ¨￥ O  = ? ^?￥b a !|??f ? = 5s0as [ TKúQ a -μ K?Q a-μ ? ??Vb ?[ s=0)? s=?) ??? ??VB¨b )( )( sD sN 5aZ(s)< Y(s)>′à ￥ L?dμb ' Re [Z( j< )]?0 ? Lf ?￥?NHq (1) s1 L ? H F(s)1 L ? (2) F(s)ˉ ü ?￥ RHP3 (í? ) (3) ′à ?1B¨ O = ?1? (4) Re [F( j< )]?0 ?6-4 LCB g? ?￥ LC Ba LCB g z?f ?￥?é ?? àμèE ? f ? F 0 (s)=0 )( )( )]( 1 )([ )( 1 )( 00 2 1 sD sN sV s ssT sI sZ =+= ][ )( 1 )( * )( 1 )( 0 * 0 2 1 sV s sT sU sY s += ! s z 1Z(s)￥ ,? )()( 00 2 zzz sTsVs ?= s z =j< z ?Z(s)￥ ?? ,? (1B¨ (?Z(s)￥ s z ' Y(s)￥? ) O aC j< à  (? < = 0# < = ?)￥ ,?o ? ^? ,? )b ] ? Z(s)￥ ??? (1B¨ O aC j< à  (? < = 0# < = ?)￥?o ? ^?? )b ? 1 Q T }Q T ( s =0)í ,? H )b L))(()( 2 2 22 1 2 zzN sssKsN << ++= D(s)μ ? ?￥2 ?b? N(s)D D(s)￥  }?A?MQ  ?5 Z( j< )ü? ^B′ ?# L L ))(( ))(( )( )( )( 2 2 22 1 2 2 2 22 1 2 pp zz ss ssKs sD sN sZ << << ++ ++ == L<<<<≤ 2211 0 zpzp <<<< < p1 =0 ^?? D(s)1 Q Ta N(s)1 }Q T￥ f? )  Z(s)￥ ,a??9C′à  N(s)aD(s)￥ZQKoμBQ L+ + + ? ++= ∞ 1 * 1 1 1 0 )( p p p p js k js k s k sksZ ωω y Z(s)?￥ = ?1? L ?μ k p1 = k * p1 , # LL+ + + + ++≡+ + + + ++= ∞∞ 2 2 2 2 2 1 2 10 2 2 2 2 2 1 2 1 0 22 )( ppp p p p s sk s sk s k sk s sk s sk s k sksZ <<<< 2 1 2 2 1 2 11 0 )(2 )( 0 )( p p p s sZ s s kk ss sZ k s ssZk < < ?= + == ∞= = = = ∞ L L + ? + ++= =+ ? + ? +?= ∞ ∞ 222 1 22 11 2 0 22 2 2 22 1 10 )( )( )( )()( ][ << << << < < < < < < < << p p pp k k k d dX jX kkk kjjZ ωω H ,0 )( ∞<> < < < d dX X (< ) < 0 ,a?? 9C′ à b LCB g z?f ?￥?é (1)N(s)aD(s)sY ^ Q T? }Q TQ- (2) N(s)aD(s)￥ZQKo ?μBQ (3) s = 0) ^B? ,? (k 0 =0) ^B?? (k 0 >0) (4) s = ?) ^B? ,? (k ? =0) ^B?? (k ? >0) (5) ,a? (1B¨￥ O?9C′à b (6) ???￥ = ?1?￥ L ?b )())(( )())(( )( )1( 2 2 22 4 22 2 2 2 12 22 3 22 1 2 1 n n ssss sssA sZ <<< <<< +++ +++ = ? L L k <<<< <<<<L 321 ! è Ff ? Z(s) [ Y(s) ]???[/ 1?? T )())(( )())(( )( )2( 2 2 22 4 22 2 2 2 12 22 3 22 1 2 2 n n ssss sssA sZ <<< <<< +++ +++ = + L L )())(( )())(( )( )3( 2 12 22 3 22 1 2 2 2 22 4 22 2 2 3 ? +++ +++ = n n sss ssssA sZ <<< <<< L L )())(( )())(( )( )4( 2 12 22 3 22 1 2 2 2 22 4 22 2 2 3 + +++ +++ = n n sss ssssA sZ <<< <<< L L =a LCB g z?f ?￥8? 1a?ss TZ 7E  ? Z(s)?ss TZ 7 ——Foster I? i i pi i pp sL sC sL sC sC sL s sk s sk s sk s k sksZ 1 1 1 11 )( 1 1 0 222 2 2 2 2 1 2 10 + ++ + ++= + ++ + + + ++= ∞ ∞ L L <<< L , , 1 )( )( 0 )( 11 22 1 2 2 1 2 1 0 0 pi i i i i p p k L k C s sZ s s k ss sZ kL s ssZ k C << < == ?= + = ∞= == = == ∞∞ Z(s)￥ò[MF 1 ó Z(s)s ￥ò[MF i ó L 1 L 2 L ? C 0 C 1 C 2 Foster I?è ^ ?? Z(s)￥ N(s)1 D(s)úB¨ H?μ L ? íq? ce?)￥? H??μ C 0 íq?51sY ¤ - ? ?íq￥9 ??? N(s)aD(s)?KúQ a ?b  ? Y(s)?ss TZ 7 ——Foster II? i i i i sC sL sC sL sL sC s sk s sk s sk s k sksY 1 1 1 11 )( 1 1 0 222 2 2 2 2 1 2 10 + ++ + ++= + ++ + + + ++= ∞ ∞ L L <<< L , , 1 )( )( 0 )( 11 2 2 1 2 2 1 2 1 0 0 i i i i i k C k L s sY s s k ss sY kC s ssY k L < < < == ?= + = ∞= == = == ∞∞ Y(s)￥ò[MF i ó Y(s)s ￥ò[MF 1 ó C' ? L ' 0 L ' 1 L ' 2 C' 1 C' 2 Foster II?è ^ ?? Y(s)￥ N(s)1 D(s)úB¨ H?μ C ? íq? Y(s)ce?)￥? H??μ L 0 íq?5s Y 7 ^- ? ?íq￥9 ? ˉ?? N(s)aD(s)?K úQ a ?b k¨ Foster I?? II?è ^8?|??E Ff ? 34 )86( )( 24 24 ++ ++ = ss sss sZ s s s s s s s s s s ss sss sZ 6 1 1 2 1 2 3 1 3 2 1 3 2 1 1 2 3 )3)(1( )4)(2( )( 2222 22 + + + += + + + += ++ ++ = è 1 3 Foster I?è ^ 1.5H (16)H 1H (23)F 2F L ? C 1 L 1 s s s ss s s s s s sss ss sY 32 3 1 3 8 1 8 1 1 4 1 3 8 1 4 8 3 2 4 1 8 3 )4)(2( )3)(1( )( 2222 22 + + + += + + + += ++ ++ = Foster II?è ^ 8 3   1 8  32 H F 4H H F L 0 L 1 C 1 è Ff ?￥ Foster ? ?+ LC F(s)Z 7 T?￥[ è ^ LC F(s)1E Ff ? F(s)1? ,f ? sK ∞ ∞∞ = KL s K 0 22 pi i s sK ω+ i i K C 1 = 2 pi i i K L ω = 0 0 1 K C = ∞∞ = KC 0 0 1 K L = i i K L 1 = 2 pi i i K C ω = l2 ?è Ff ? ^|??E F Z LC (s) H   LC? ??| V?? 2 μ1E F?í1 ó ?¤??2?1 Foster I?b ? Z LC (s) s=0)μ ,?5 K 0 =0y7 LC? ?? ? C 0 ?í ? Z LC (s) s=?)μ ,?5 K ? =0y7 LC? ?? ? L 0 ?í ?è Ff ? ^|??? , Y LC (s) H   LC? ??| V?? 3 μ1? ,?íi ó ?¤??2?1 Foster II?b ? Y LC (s) s=0)μ ,? LC? ?? ? L 0 ?í ? Y LC (s) s=?)μ ,? LC? ?? ? C 0 ?íb 2a ?s TZ 7E  ?M<E Fa? , s=?)￥? ——Cauer I? ? s=?) ^ Z(s) Y(s)￥? ?M<?"￥B?? è Ff ?L??B¨°à8??? L+ + + += + += +=+= sk sk sk sk sZ sk sk sY sksZsksZ 4 3 2 1 2 2 1 1 111 1 1 1 )( 1 1 )( 1 )()( ? a ?é" p¤ Z(s) s=?)￥???1D￥è? Y(s) s=?) ￥???iD￥è ?b L 3 L 1 L n Cauer I?è ^ C 2 C 4 ?íq￥9 ??? N(s)aD(s)Kú￥¨Q ? N(s)¨Q l? D(s)51V Y(s) 7 S ?é" (N H  T?￥ k 1 = 0 è ^ViD￥è ? 7 S )b ?K 1B1Dè?5 V üa ?￥E F1 0'? aF iD￥ ^Lb ?ó?|??f ? V¨ LCB g LC￥ 1Hq9 V V U1 N(s)D D(s)￥  }?MQ O?|??f ? ?Z 7 1?W? ?[￥ ? " ?￥ ?s T b L 1111 )( 432 1 +++ += sksksk sksZ  ?M<E Fa? , s=0)￥? ——Cauer II? ? s=0) ^ Z(s) Y(s)￥? ?M<?"￥B?? è Ff ?L??B¨°à8??? L L 1111 1 1 1 )( 432 1 4 3 2 1 +++ +≡ + + + += s k s k s ks k s ks ks ks k sZ 6 a ?é" p¤ Z(s) s=0)￥???1D￥è ? Y(s) s=0)￥ ???iD￥è?b C 1 C 3 L 2 L 4 Cauer II?è ^ a ü íq￥9 ??? N(s)aD(s)Kú￥¨Qb ? Z(0)?? 51V Y(s) 7 S ?é" (N H  T?￥ k 1 = 0è ^V iD￥è? 7 S )b LCB g￥8???B O  ? 1?8?? V?- é?b è 2 k¨ Cauer I?? II?è ^8?|??E Ff ? 34 )86( )( 24 24 ++ ++ = ss sss sZ 3 |s0as ? a ? ¤ 34 86 )( 24 35 ++ ++ = ss sss sZ (s0¨QúV Z 7 S ) 0 3 1 3 2 3 2 3 3 2 3 42 3 4 52 3 2 3 2 5 2 1 3452 34 8634 () () () () () 2 2 3 32 24 243 35 3524 s ss s sss ss ssss ss sssss sss ssssss + + ++ + +++ ++ ++++ Cauer I?è ^ H1 H 3 4 H 3 1 F 2 1 F 2 3 34 )86( )( 24 24 ++ ++ = ss sss sZ |s0as  6 a ? ¤ 42 53 43 68 )( ss sss sZ ++ ++ = (Z(0)??V Y 7 S ) 0 44 3 44 3 44 3 7 22 21 968 7 22 44 3 88 49 4 7 88 49 8 5 4 7 7 22 7 20 8 7 32 68 8 5 4 7 8 3 4 9 3 8 3 4368 4 45 3 534 42 4253 3 5342 42 4253 () () () () () s s ss s s sss ss s ssss ss s sssss ss s sssss + + ++ + +++ ++ ++++ Cauer II?è ^ F 32 7 F 908 21 H 8 3 H 49 88 H 3 44 è 3 k¨ Cauer I? LC|??? ,f ? 910 6420 )( 24 35 ++ ++ = ss sss sY 3 s0as Xü? a ? Z 71 ?s T s s s s ssY 9 35 1 70 9 1 9 20 1 10 1 1 )( + + + += 0 35s 9 35 9)35s 4.5 70 9 93s)4.5s 2010 9 20 5510)94.5s 5.5 10 1 910)5510 910 (6420)910 2 2 3 32 24 243 35 3524 s s s ss sss ss sssss sss ssssss ? ? ? ? ? ? + + ? ? ? ++ + ? ? ? +++ ++ ++++ H 10 1 H 70 9 F1 F 9 20 F 9 35 s s s s ssY 9 35 1 70 9 1 9 20 1 10 1 1 )( + + + += à?M"b?BQ￥  s1s @D? ,? úM ? Y(s)?)￥B?? ?BQ￥  ^1DE F? úM ?￥ ^?BQ :?f ?￥? ??)￥? ?"QˉM"b s 10 1 k¨ Cauer I? LC|??? ,f ? 910 2 )( 24 3 ++ + = ss ss sY è 4 3 Y(s)?μB ,?7í?#| Y(s) |? ? ? ¤ Z(s)A?μ?5 Z(s)Z 7 |? ? b# 5[ Y(s)￥s 1$" TZM" s s s s sZ sY 72 7 1 7 64 1 8 1 1 1 )( 1 )( + + + == 0 8 7 72 7 8 7 9) 8 7 64 98) 8 7 8 9 8 1 2)98 2 (910)2 2 2 3 32 24 243 s ss s sss ss ssss ss sssss ? ? ? ? ? ? + + ? ? ? ++ + +++ H1 H 7 64 F 8 1 F 72 7 s s s s sZ sY 72 7 1 7 64 1 8 1 1 1 )( 1 )( + + + == k¨ Cauer II? LC|??? ,f ? ss ss sZ 2 910 )( 3 24 + ++ = è 5 3 | Z(s)?1N(s aD(s) (? 6 a ??￥? T 3 42 2 109 )( ss ss sZ + ++ = s s s s sZ 571.1 1 1 116.0 1 1 75.2 1 1 222.0 1 )( + + += .75H2 .222F0 .571H1 .116F0 l2 I:ú? ^V Z(s)? Y(s)f ???91M ? s=?)￥ ?b ?MB? Z LC (s)￥??è ^?CB?1 Dè? ?MB? Y LC (s)￥??è ^?CB ?s @Dè ?bKa¤?￥ I:ú?è ^ ^1D (1 è?as @D (1è ?￥0?? ?b I:?? ^V Z(s)? Y(s)f ???91M ? s=0)￥ ?b ?MB? Z LC (s)￥??è ^?CB?1 Dè ? ?MB? Y LC (s)￥??è ^?CB ?s @Dè?bKa¤?￥ I:??è ^ ^1D (1 è ?as @D (1è?￥0?? ?b ?6-5 RCB g? ?￥ LC Ba RCB g|??f ?￥?é RCf ? E Ff ?a? ,f ? ?μ￥ ,???? C s ü ?￥μ Là byN RCf ?￥s0[ T ?s [ TB? μ ?/? T LL))()(()( 321 σσσ +++= ssssP 1dμ L ?aaLL 321 σσσ RCE Ff ??μ[/? T )())(( )())(( )(Z 21 21 pnpp zmzz RC sss sss Ks σσσ σσσ +++ +++ = L L )())(( )())(( )(Z 21 21 pnpp zmzz RC sss sss Ks σσσ σσσ +++ +++ = L L zmpnzpzp σσσσσσ <<<<≤LL 2211 0 m=n  m=n-1 μ Là K Líe?￥ ^ Z RC (s)￥? ? 9 Vê?e?) e?Kù￥ ^ Z RC (s) ￥ , ? ?9 Vê? s = ?)b RCB g|??E Ff ? Z RC (s)￥?é (1)Z RC (s)￥ ,a? (ê? s ü ?￥μ Là  O? ^ ?¨￥ (2)Z RC (6 ) ^6￥?ì ??hf ? bZ RC (s)￥ ,a? μ Là ?9 ?  (3)Z RC (s)e? V ?μ??? V ?μ ,?b Z RC (s)  s=?) V ?μ ,??? V ?μ?b? Z RC (0)? Z RC (?) (1μK′ HAμ Z RC (0)>Z RC (?) (4)Z RC (s)= N(s)/D(s) N(s)D D(s)￥¨ ?M? D (s) ? N (s)úB¨ (5)Z RC (s) ?μ?)￥ = ?1 ? L ?b RC? ,f ??μ[/? T )())(( )())(( )(Y 21 21 pnpp zmzz RC sss sss Ks σσσ σσσ +++ +++ = L L pnzmpzpz σσσσσσ <<<<≤LL 2211 0 m=n  m=n+1 μ Là K Líe?￥ ^ Y RC (s)￥ ,?  ?9 Vê?e?) e?Kù￥ ^ Y RC (s) ￥? ?9 Vê? s = ?)b RCB g|??? ,f ? Y RC (s)￥?é (1)Y RC (s)￥ ,a? (ê? s ü ?￥μ Là  O? ^ ?¨￥ (5)Y RC (s) ?μμK′?)￥ = ?1μ L ?b (2)Y RC (6 ) ^6￥ ?ì??9f ? bY RC (s)￥ ,a? μ Là ?9 ?  (3)Y RC (s)e? V ?μ ,??? V ?μ?b Y RC (s)  s=?) V ?μ??? V ?μ ,?b? Y RC (0)? Y RC (?) (1μK′ HAμ Y RC (?)>Y RC (0) (4)Y RC (s)= N(s)/D(s) N(s)D D(s)￥¨ ?M? D (s) ? N (s)?B¨ [ 1? Z RC (s)? Y RC (s)￥?é V¨ ?_B?μ ? f ? ^?1 RCf ?[# ^E Ff ?? ,f ?b[L ??¨ I 1? ? ? LCb )())(( )())(( )( )1( 242 12211 n n ssss sssA sZ σσσ σσσ +++ +++ = ? L L k σσσσ <<<<L 321 ! E Ff ? Z(s) ???[/ 1?? T )())(( )())(( )( )2( 242 12212 n n ssss sssA sZ σσσ σσσ +++ +++ = + L L )())(( )())(( )( )3( 1231 2423 ? +++ +++ = n n sss sssA sZ σσσ σσσ L L )())(( )())(( )( )3( 1231 2423 + +++ +++ = n n sss sssA sZ σσσ σσσ L L =a RCB g|??f ?￥8? 1a?ss TZ 7E 1)? Z(s)?ss TZ 7 ——Foster I? L LL , , 1 )()( 0 )( 11 )( 1 11 )( 1 11 0 0 1 1 01 10 i i i i i k R k C s sZsk s ssZ k C s sZkR R sC sC R s k s k ksZ 66 6 6 == ?= += = == ∞= == + + ++=+ + ++= ∞∞ ∞∞ |òμ1￥E F?í1 ó ?¤M¤? Foster I? R 1 R 2 R ? C 0 C 1 C 2 Foster I?è ^ ?? Z RC (s)￥ N(s)D D(s)]¨ H?μ R ? íq?c e?)￥? H??μ C 0 íq?51sY ¤-  íq￥9 ??? N(s)aD(s)[ ?-? –1b ? Z RC (s)e?í?5 k 0 0y7 LCè ^? ? C 0 íqb ? Z RC (s)í kù)μ ,?5 k ? 0y7 LC è ^? ? R ? íqb 2)? [Y(s)s]?ss TZ 7 —— Foster II ? L LL L , , 1 )( 0 )( 11 )( 1 11 )( )( ' ' ' ' ' ' 1 ' 1 ' 1 ' 0 ' 0 '' ' 1 ' 1 ' 0 ' ' 1 ' 1 ' 0 ' ' 1 ' 1 ' 0 ' i i i i i k C k R s sY s s k s sY k R ss sY kC sC R R sC s sk ksksY s k s k k s sY 6 6 6 6 6 == ?= + = = == ∞= == + + ++=+ + ++= + + ++= ∞∞ ∞∞ ∞ |òμ1￥E F?íi ó ?¤M¤? Foster II? R ' 1 R ' 2 C' ? R ' 0 C' 1 C' 2 Foster II?è ^ ?? Y(s)￥ N(s)1 D(s)úB¨ H?μ C ? íq? Y(s) ?ce?)￥ ,? H??μ R 0 íq?5sY 7 ^ - íq￥9 ??? N(s)aD(s)[ ?-? –1b ? Y RC (s)e?μB ,?5 k 0 0y7 LCè ^? ? R 0 íqb ? Y RC (s)í kù) àμ?5 k ? 0y 7 LCè ^? ? C ? íqb RCE F ? ,f ?￥? ?+ LC F(s)Z 7 T?￥[ è ^ LC F(s)1E Ff ? F(s)1? ,f ? ∞ K s K 0 pi i s K σ+ 0 0 1 K C = ∞∞ = KC ∞∞ = KR i i K C 1 = pi i i K L σ = 0 0 1 K R = i i K R 1 = pi i i K C σ = è 1 ?f ? F(s) ^?1 RCf ?b ?1 RCf ? k¨ Foster I?? II?è ^ LC F(s) 34 16122 )( 2 2 ++ ++ = ss ss sF 3 f ? F(s)Ty Ts3¤ ( )( ) ()()31 42 2)( ++ ++ = ss ss sF F(s)￥?? ,?sY1 4 ,2 ,3 ,1 2121 ?=??=??=??=? zzpp σσσσ ?a ,? (1μ L ?i O? ^?¨￥bs0s  (1=Q Tb 2211 0 zpzp σσσσ <<<< μ Là ?a ,??9CK Líe?￥ ^ ?  Kù ?e?￥ ,? bF(0)? F(?) ( 1μK′ ( ) 1p σ? ( ) 2z σ? 33.5 3 8 2)0( =×=F 2)( =∞F F(s) ^ RCE Ff ? )()0( ∞> FF 34 16122 )()( 2 2 ++ ++ == ss ss sFsZ RC 3 1 1 3 2)( + + + += ss sZ RC ?2 ?3 ? 3 1 F 3 1 F1 Foster I?è ^ 4 4 3 2 4 1 2 1 16122 34 )( 1 )( 2 2 + ? + + ? += ++ ++ == ssss ss sF sY RC Y RC (s)￥? 2a4) = ? (1μ′íE¨í ÷íq LCb 4 16 3 2 8 1 16 3 21216 43 )( 2 2 + + + += ++ ++ = s s s s ss ss sY RC Foster II?è ^ ? 3 16 ?8 ? 3 16 F 16 1 F 64 3 )( 16 3 )4)(2( 8 7 16 5 16 3 21216 8 5 4 7 16 3 21216 43 )( 1 2 2 2 2 sY ss s s ss ss ss ss sY RC += ? ? ? ? ? ? ? ? ? ? ++ + += ++ + += ++ ++ = ? ? ? ? ? ? ? ? ? ? ++ + = )4)(2( 8 7 16 5 )( 1 ss s ssY 4 16 3 2 8 1 16 3 )( + + + += s s s s sY RC 4 16 3 2 8 1 )( 1 + + + = sss sY l2 Foster I? ? Z RC (s)e?í?5 K 0 =0y7 L C? ?? ? C 0 ?íb ? Z RC (s)í kù)μ ,? 5 K ? =0y7 LC? ?? ? R ? ?íb Foster II? ? Y RC (s)e?μB ,?5 K 0 =0y 7 LC? ?? ? R 0 ?íb ? Y RC (s)í kù) à ?5 K ? =0y7 LC? ?? ? C ? ?íb 2a ?s TZ 7E  ?M<E Fa? , s=?)￥? ——Cauer I? Z 7 VYV? a ?é" p¤ ? Z(?)=0,5? ? Y(s) 7 Sé"  íq￥9 ??? N(s)aD(s)[ ?- ? –1b · Z(s) s=?)￥???1D￥èE Y(s) s=?)￥???iD￥è ?b R 1 R 3 C 2 C 4 Cauer I?è ^ è 2 Cauer I?è ^ LC F(s) ( ) ()()31 2 )( ++ + = ss ss sF 3 ? F(s)￥?? ,?￥s? V[ ? F(s) ^ RC? ,f ?' F(s) " Y RC (s) Y RC (s)￥s 0as Q ?M] ?T°¤é? ?s TZ 7 ?¤?? ?í÷ LC￥2TbyNA?5 |? ?' Z RC (s)=1/ F(s)é? ?s TZ 7 )( 2 34 )( 1 2 2 sZ ss ss sF RC = + ++ = 0 2 1 6 1 2 1 3) 2s 4 (32 ) 2 1 2 3 s 2 1 23)2s 2s 1 (34 )2 2 2 2 22 s ss ss s sss s ssss ? ? ? + + ? ? ? ++ + +++ s s sZ sF RC 6 1 1 4 1 2 1 1 1 1 )( 1 )( + + + == Cauer I?è ^ ?1 ?4 F 6 1  ?M<E Fa? , s=0)￥? ——Cauer II? Z 7 VYV 6 a ?é" p¤ , ? Z(0)<?,5?? Y(s) 7 Sé"b · Z(s) s=0)￥???1D￥è ? Y(s) s=0) ￥???iD￥èE C 1 C 3 R 2 R 4 Cauer II?è ^ è 3 Cauer II?è ^ LC[/ RCE Ff ? )5)(3( )4)(2( )( ++ ++ = sss ss sZ RC 3 32 2 23 2 815 68 158 86 )( sss ss sss ss sZ RC ++ ++ = ++ ++ = F875.1 .286F2 4.25F3 ?1156.0 ?00737.0 Cauer II?è ^ s s s sZ RC 0292.0 1 7.135 14375.0 1 654.8 15333.0 )( + + + += F875.1 .286F2 4.25F3 ?1156.0 ?00737.0 Cauer II?è ^ s0 s  s 5333.0 654.8 32 815 sss ++ 2 68 ss++ 2 2 4667.0733.1 5333.0267.48 ss ss + ++ 32 2 3.961 039.415 ss ss + + 7.135 s 4375.0 0 0292.0 2 s 2 2 0292.0 4375.0733.1 s ss+ 3 2 s 3.961s s 0292.0 l2 Cauer I? ? Z RC (?)=05 K ? =0N H??5? Y RC (s)=1/ Z RC (s)é?Z 77?B?íq| ^i óè ?b?? Z RC (0)1μK′#KaBH| ^11 óè Eb ?T Z RC (0)" ?5Ka￥? ?| ^i óè ?b ?¤0?è ^ ^[èE11Dè ?1iDb¨é" Eé? H? s￥? a ?é?b Cauer II? ? Z RC (0)<  5?B?1 óè ?|?i b? Z RC (?)1μK′ HK?￥BH| ^| ^i ó èE7? Z RC (?)" 0 H5NèE|?ib ?¤ 0?è ^ ^[è ?11DèE1iDb¨é"Eé ? H? s￥ 6 a ?é?b ?66 RLB g? ?￥ LC Ba RLB g z?f ?￥?é   ,a? ( ^B¨￥ O?9Cμ Là   Y(s)?￥ = ?1? Z(s)?￥ = ?1μ (s = ?) "? )7 [Z(s)s] ?￥ = ?1?  K Líe?￥ ^ Y(s)￥? [Z(s)￥ ,? ] ?9 Vê ?e?) e?Kù￥ ^ Y(s)￥ ,? [Z(s)￥? ] ?9 Vê? s = ?)b Foster I? L 1 L 2 L ? R 0 R 1 R 2 =a RLB g z?f ?￥8? Z 71 Foster I?aFoster II?aCauer I?aCauer II ?íq￥9 ??? N(s)aD(s)[ ?-? –1b R ' 1 R ' 2 R' ? L ' 0 L' 1 L' 2 Foster II? L 1 L 3 R 2 R 4 Cauer I? R 1 R 3 L 2 L 4 Cauer II? ?67 RLCB g? ?￥ LCeo  LC H1?i￡ Z(s) Y(s)?$ LC￥?s ˉA? 1? Lf ?b Ba t? Lf ?￥ V¨ RLC0?B g LC 8? z?f ? è 2644 23522 )()1( 23 234 +++ ++++ = sss ssss sY 1 2432 )()2( 2 23 ++ +++ = ss sss sZ 3 (1) ?¨ ?é"¤ 1 1 1 2 1 2 1 1 2 1 2 1322 1 2 )( 2 23 2 + + + += ++ + + += +++ ++ += s s s s ss s s s sss sss sY #  LCè ^1 F 2 1 F1 ?1 H1H2 (2) ]"μ 1 1 1 12 1 1 12)( 2 + + ++= ++ + ++= s s s ss s ssZ #  LCè ^1 2H 1$ 1H 1$ 1F =a Brune LC U è ?l 1 ′à  (c s=0# s=?)í ,a?￥f ??1 lè Ff ?b +? N(s)aD(s)KúQ a ?M] O N(s)aD(s) (c è ?[b ?l 2 lè Ff ? Z m (s) ? ? q/  L? |l ′5 ???èEa￥f ??1l L?f ?b' 5? p < 1 0)]([ }{ 1 =< < jZ d d m  p R 1 = Re [Z m ( j< 1 )] 5 Z 1 (s)=Z m (s)–R 1 '1l L?f ?b +? Re [Z 1 ( j< 1 )]=0 . ] H1l L??′?￥f ??1lf ?b è 3  k8?-b 1201124 48 )( 23 2 +++ ++ = sss ss sZ 3 (1) M< Z(s)?￥è Ff ? —1lè Ff ? Z m (s) 'M< ′à# s=0as=?)￥ ,a?b ?  V5¨iD￥ C 1 M ? Z(s)￥? ,? ' Y(s) s=?)￥? 0)( = ∞→s sZ )(3 48 188 3 48 1201124 )( 2 2 2 23 1 sYs ss ss s ss sss sY m += ++ ++ + ++ +++ = ?? aé " C 1 =3F ?? Y m (s) j< à Xí ,a?# Z m (s)=1 [Y m (s)]1lè Ff ?b (2) p ￥l′ 1lf ? Z 1 (s) = Z m (s)  R 1  )]([ <jZ m 3F )]([ 11 <jZR m 3F= 222 22 222 222 64)81( ) 4 1 (64 64)81( 8)81)(84( )]([ << < << <<< < +? ? = +? +?? =jZ m 3F  < 1 =05)μBl′ 0)]50([ 1 == 3F jZR Z 1 (s) = Z m (s)R 1 = Z m (s)1l L?f ?'1lf ? (3) M ? )( 1111 <<< jZXjLj == 1Z 2 (s) = Z 1 (s)  sL 1 =1Y 2 (s)  HLjjZ 1 50 50)50( 11 ?= ? =→?= <   188 42168 )()()( 2 23 1112 ++ +++ = +=?= ss sss ssZsLsZsZ ' )168)(25.0( 188 )( 2 2 2 ++ ++ = ss ss sY (4) M ? Y 2 (s)  s = j< 1 )￥? —1Y 3 (s) 5.0 2 )()2( 5.0 25.0 )( 25.0 42 1 2 1 2 1 2 5.0 25.0 5.0 2 25.0 )( 22 2 2 2 1 2 2 2 1 2 = ?= += = ?= + = + + + = + + + = + + + = s sYsK s sY s s K s s s s s s s K s sK sY (4) :/￥ Z 3 (s)=2s+4X V°¤ LC b?51í ?? (2)?×ˉ  ?V? ?1 Brune?ì b (5) ?￥è ^1 R 1 L 1 L 3 R 3 0$ 1H 2H 4$ C 1 3F L 2 2H C 2 2F QV ?¨o?h ?E V LC m?￥μè? ( | M = 2H L 1 ' = L 1 +M =1H L 2 ' = L 3 +M = 4H k = 2 1?4 =1 ?@1 p ) R 1 L 1 ' 2H L 2 ' R 3 0$ * 1H 4H * 4$ C 1 3F C 2 2F ? Bc (í÷? ?￥|??f ? )1? BaBB?? ?BB? ] HμE FD ? q￥BB?D ?BB? . , , CkkCL k k L k R R ZN Z N Z N < < === . 1 , , N Z N Z NZ C kk CL k k LRkR << === =aí÷? ?|??f ? ¨ ? f ?V U￥ Z(s)? Y(s)  ][ )( 1 )()( 1 )( )]( 1 )()([ 1 )( 000 2 1 000 2 1 sV s ssTsF U sY sV s ssTsF I sZ ++= ++= I no? Hμ ? ?￥? Tb ? Lf ? (P.R.F.) (1)s1 L ? H F(s)ü1 L ? (2)? Re (s)?0 H Re [F(s)]?0 . L?í÷ H?M? ?￥|??f ? Z(s)? Y(s) (1 ? Lf ?b ?aí÷? Ff ?￥?é 1Z(s)aY(s) s￥ RHP í?b 2Z(s)aY(s) s￥ RHP í ,?b 3Z(s)< Y(s)>′à  ?μ?< ,?>o ? ^B¨￥ O  = ? ^?￥b 4s0as [ TKúQ a-μ (K?Q a -μ )? ??V 1b 5Z(s)< Y(s)>′à ￥ L?dμb ' Re [Z( j< )]?0 1aLCB g? ?￥ LC 1.LCB g z?f ?￥?é (1)N(s)aD(s)sY ^ Q T? }Q TQ- (2) N(s)aD(s)￥ZQKo ?μBQ (3) s = 0) ^B? ,? (k 0 =0) ^B?? (k 0 >0) (4) s = ?) ^B? ,? (k ? =0) ^B?? (k ? >0) (5) ,a? (1B¨￥ O?9C′à  (6) ???￥ = ?1?￥ L ?b 2.LCB g z?f ?￥8? ? Z(s)?ss TZ 7 ——Foster I? ? Y(s)?ss TZ 7 ——Foster II? ? a ?é"Z 7 ——Cauer I? 6 a ?é"Z 7 ——Cauer II? íq￥9 ??? N(s)aD(s)Kú￥¨Qb ?a RCB g? ?￥ LC 1. RCB g z?f ?￥?é   ,a? ( ^B¨￥ O?9Cμ Là   ; T ?￥ = ?1? : T ?￥ = ?1μ T ?)"? 7< : T T>?￥ = ?1?  K Líe?￥ ^ ; T ￥?< : T ￥ ,?> ?9 V ê?e?) e?Kù￥ ^ ; T ￥ ,?< : T ￥? > ?9 Vê? T?) 2.RCB g z?f ?￥8? ]" VZ 71 Foster I?aFoster II?aCauer I?a Cauer II?íq￥9 ??? N(s)aD(s)[ ?-? –1 b Ba RLB g? ?￥ LC 1.RLB g z?f ?￥?é D RCB g }V {b 2.RLB g z?f ?￥8? ]" VZ 71 Foster I?aFoster II?aCauer I?a Cauer II?íq￥9 ??? N(s)aD(s)[ ?-? –1 b ta RLCB g? ?￥ LCeo  t? Lf ?￥ V°¤¨ RLC0?B g LC 2.Brune LCeo i) M< Z(s)?￥è Ff ? —1lè Ff ? Z m (s) ii) p ￥l′ 1lf ? Z 1 (s) = Z m (s)  R 1  )]([ <jZ m 3F )]([ 11 <jZR m 3F= iii) M ? —1Z 2 (s) = Z 1 (s)  sL 1 =1Y 2 (s)  )( 1111 <<< jZXjLj == iv) M ? Y 2 (s)  s = j< 1 )￥? —1Y 3 (s)  v) Y 3 (s)? ?°¤ LC Hí? - ?? ii)?b ? Bc í÷? ?￥|??f ? 5 )5)(3)(1( )4)(2( )( 222 22 +++ ++ = sss sss sZ 6-1 k¨ Foster I aII?è ^ LCb 6-2 k¨ Cauer I aII?è ^ LC 5E Fb 6-3 X? B g? ? < = 104 a3?104 rad/s H ? 31 ó~? < = 2?104 a4?104 rad/s H? 3 i ó~? O? Z( j5000) = – j148$b (1) ù Z(0) =$ Z(?) =$ (2) kê ? qBB?" ? k< i pBB?? ? (3) p ?BB?? ?b )3)(1( )4)(2( )( ++ ++ = ss sss sY 6-4 k¨ Foster I aII?è ^ LCb p 5￥ Cauer I aII?è ^b6-5 )( 1 )( , )4)(2( )3)(1( )( 12 22 22 1 sZ s sZ sss ss sZ = ++ ++ = 6-6 k LC Z 2 (s) b )()( 12 sZssZ = 6-7 ? 5  LC Z 2 (s) )()( , )3)(1( )4)(2( )( 2 121 ssZsZ ss ss sZ = ++ ++ = 6-8 k LC Z 2 (s) b X? Z(–1000) = Z(–3000) = Z(–5000) = 0  Z(– 2000) = Z(–4000) = ?Z(?) = 10  k LC? ? ?b 6-9 sss sss sZ ++ +++ = 23 23 2 245 )( 6-10 ￡ ü ?1? Lf ?i¨ RLCB g? ? LCb 6-11 sss sss sZ ++ +++ = 23 23 1343 )( ￡ ü ?1? Lf ?i¨ RLCB g? ? LCb ?6.1 m U roè ^ ^?BB? ? q 1 rad /s [# R 1 =2$a R 2 =1$ !9￥ ? C=0.6538F L=15132HbC L= ? qà1 24 MHz R 1 =150$ aR 2 =75$ p ?3￥ CaL′b L i S R 1 C R 2 ?6.2 k ??/  z?f ? ??¨ LCB g ? LCb )25)(9( )16)(1( 22 22 ++ ++ ss sss (a) 97 65 24 24 ++ ++ ss ss (b) 23 5.1 24 3 ++ + ss ss (c) ss ss 4 910 3 24 + ++ (d) ?6.3 k ??/  z?f ? ??¨ RCB g ? LCb 133 127 )( 23 2 +++ ++ = sss ss sZ (a) 127 23 )( 2 2 ++ ++ = ss ss sZ (b) 75.34 6116 )( 2 23 ++ +++ = ss sss sY (c) BB? LC? g RC? g RLC? g Ex. ?6.1a6.3? 6.2a6.1a6.2? 6.3a6.4a6.5 6.10 a6.11 .