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2009 2 2 2. 2.. F(s) G(s) H(s) G(s) F(s) H(s) F(s),G(s) H(s) : V (s) Z(s)I(s) I(s) Y (s)v (s) Z(s): Y (s):

2: ( ( V V 2 I I 2 ) ( ) ( Z Z 2 Z 2 Z 22 ) ( ) ( Y Y 2 Y 2 Y 22 ( ) ( ) Z Z 2 Y Y 2 : : Z 2 Z 22 Y 2 Y 22 Z,Z 22 Z 2,Z 2 ( I I 2 V V 2 ) ) 2..2 :H(s) H(s) P(s) Q(s) b ns n + b n s n + + b 0 a m s m + a m s m + + a 0 a i,b j : H(s) V out(s) V in (s) CRs + 3: (LPF) s s H(s) 2..3 H(s) H(s) P(s) Q(s) b n a m (s s 0)(s s 02 ) (s s 0n ) (s s p )(s s p2 ) (s s pm ) b n H : (scale factor) a m s 0, s 0n (zero) s p, s pn (pole) H(s 0i ) 0 H(s pi ) 2

4: s s, s 2 + (s+i)(s i) s Re Re s n > m s H(s) Hs n m (H: ) H(s) s H(s) (n-m ) n < m H(s) Hs H(s) s m-n m n 2..4 x(t) y(t) X(s) L[x(t)] Y (s) L[y(t)] H(s) Y (s) X(s) y(t) L [Y (s)] L [H(s)X(s)] x(t) δ(t) x(t) δ(t) X(s) L[δ(t)] Y (s) H(s) H(s) y(t) L [H(s)] H(s) K L Ke spit Ke αpit e jωpit s s pi (K : s pi α pi + jω pi ) s pi s s m H(s) K m (s s pi ) m + K m (s s pi ) m + + K (s s pi ) 3

K m L (s s pi ) m K m (m )! tm e spit m 2..5 t m s H(s)X(s) 2.2 2.2. ( V V 2 ) ( ) ( Z Z 2 Z 2 Z 22 I I 2 ), ( I I 2 ) ( ) ( Y Y 2 Y 2 Y 22 V V 2 ) Z,Z 22,Y,Y 22... s 2.2.2 Z 2,Z 2,Y 2,Y 2...n m + 4

2.2.3 H(s) s jω log H(jω) log H(jω) + j arg(h(jω)) 2.3 2.3. H(s) H (s s 0) (s s 0n ) (s s p ) (s s pm ) s jω jω 5: H(jω) H(jω) H d 0d 02 d 0n d p d p2 d pm arg(h(jω)) log H (jω) log H + n m θ 0i i i i θ pi n m log d 0i log d pi i 5

(All pass) 6: (All pass) 2.3.2 H(s) P(s) Q(s) H (s)h 2 (s) H k (s) H i (s) () H(s) b s + b 0 s + a 0 H s + β s + α b,b 0 LP Low-Pass (b 0) H(s) b 0 s + a 0 s jω 7: LP 2 HP High-Pass (b 0 0) H(s) b s s + a 0 s jω 6

8: HP 3 AP All-Pass H(s) s a 0 s + a 0 s jω 9: AP 4 H(s) b s + b 0 s + a 0 s jω 7

0: : (2) H(s) b 2s 2 + b s + b 0 s 2 H s2 + ( ωn Q N )s + ωn 2 + a s + a 0 s 2 + ( ω0 Q 0 )s + ω0 2 H(s) s R L s 2 + s R L + LC 8

2: LP H(s) Hω 2 0 s 2 + ( ω0 Q 0 )s + ω 2 0 3: LP 2 HP Hs 2 H(s) s 2 + ( ω0 Q 0 )s + ω0 2 4: HP 3 BP(Band-Pass) 9

H(s) H( ω0 Q 0 )s s 2 + ( ω0 Q 0 )s + ω 2 0 5: BP 4 H(s) H(s2 + ω 2 N ) s 2 + ( ω0 Q 0 )s + ω 2 0 6: 5 AP ( ) H(s) H(s2 ( ω0 Q 0 )s + ω 2 0) s 2 + ( ω0 Q 0 )s + ω 2 0 0

7: AP 2.4 2.4. 8: 9: (All-pass) Z a Z b R 0

H(s) R 0 Z a (s) R 0 + Z a (s) Z a,z b All-Pass Z in R 0 R 0 ) Z a Z a (s) Z a (s) Z a ( s) H(s) s p R 0 + Z a (s p ) 0 R 0 Z a ( s p ) 0 R 0 Z a (s) s s p s p s p s p 2.4.2 H(s) (s s 0) (s s 0n )(s s 0)(s s 02) (s s p ) (s s pm ) s 0 s 0n : s 0,s 02 : (s + s 0)(s + s 02) H(s) (s s 0) (s s 0n )(s + s 0)(s + s 02) (s s p ) (s s pm ) (s s 0)(s s 02) (s + s 0 )(s + s 02 ) H(s) 20: H( ) H(s) /H(s) 2

2: 2.4.3 H(s) H(s) 2.5 R,L,C 2.5. e(t) i(t) t e(t )i(t )dt 0 2.5.2 Hurwitz Z(s) )s 2)Re(s) > 0 ReZ(s) > 0 Z(s) Z(/s),/Z(s) Z(s) ReZ(jω) 0 s jω s Z(s) (Re(s) > 0) ReZ(s) > 0 s Z(s) 0 Z(s) Z(s) s 3

Z(s) ()s (2)Re(s) > 0 Z(s) (3) Re(jω) 0 (4) 2.6 L,C 2.6. 2.6.2 Z(s) P(s) Q(s) P(s) Q(s) Z(s) Z(s) H (s 2 s 2. 0) (s 2 s 2 0n) s (s 2 s 2 p ) (s2 s 2 p(n ) ) 2. H s (s 2 s 2 0) (s 2 s 2 0n) (s 2 s 2 p ) (s2 s 2 pn) 4. 3. Hs (s2 s 2 0) (s 2 s 2 0n) (s 2 s 2 p ) (s2 s 2 pn) H s s p,,s pn, s p,, s pn s 0,,s 0n, s 0,, s 0n (s 2 s 2 0) (s 2 s 2 0(n ) ) (s 2 s 2 p ) (s2 s 2 pn). 2. 3. 4. s 0 0 0 s 0 0 0 0 0 0 2.6.3 2 s,0 3 Z(s) Z(jω) jx(ω) () dx(ω) dω > 0 X(ω) 4

(2)X(ω) 22: 0 23: 0 24: 0 25: 0 26: 27: 28: 0 0 29: 0 0 5

2.6.4 Z(s) Z(s) s5 +6s 3 +8s (s 2 +)(s 2 +3) )Foster s 4 +4s 2 +3 s(s2 +2)(s 2 +4) Z(s) sl sc s /s Z(s) s5 + 6s 3 3 + 8s s 4 + 4s 2 + 3 s + 2 s s 2 + + 2 s s 2 + 3 s + 2 3 s + 3 2 s + 2s + 6 s 30: Foster 2)Foster Y (s) /Z(s) /sl,sc s Y (s) Z(s) s4 + 4s 2 + 3 s 5 + 6s 3 + 8s 8 3 s + 4 s 3 s 2 + 2 + 8 s s 2 + 4 8 3 s + 4s + 8 s + 8 3 s + 3 32 s 3: Foster 3)Cauer Z(s) Z(s) L s + C s + L 2s+ 6

L s C s Z(s) L Z(s) s5 + 6s 3 + 8s s 4 + 4s 2 + 3 s(s4 + 4s 2 + 3) + 2s 3 + 5s s 4 + 4s 2 s + 2s3 + 5s + 3 s 4 + 4s 2 + 3 s + s + 2 s + 4 3 s+ 3 2 s+ s 3 s 4 +4s 2 +3 2s 3 +5s 32: Causer 33: Causer 4)Cauer 2 Z(s) Z(s) C s + L + s C 2 s + 2 Z(s) + 6s2 + 6s 4 2s + 8s 3 ( + 4s2 ) + 2s 2 + 6s 4 2s( + 4s 2 ) 2s + s + s +3s Z(s) s5 + 6s 3 + 8s s 4 + 4s 2 + 3 3+4s 2 +s 4 8s+6s 3 +s 5 2s + 2s+8s 3 2s 2 +6s 4 + 8 3 s 7 32 s+ 88 49 s + 2 968 s + 443 s 34: Causer 2 7

35: Causer 2 36: Causer 2 2 2.6.5 Z(s) Z(s) Z(s) ( Z (s) Z 2 (s) ) Z 2 (s) Z 22 (s) Z Re[Z (s)x 2 + 2Z 2 (s)x x 2 + Z 22 (s)x 2 2] > 0 (Re[s] > 0 ) Z 2 Z 2 x,x 2 Q Z (s)x 2 + 2Z 2 (s)x x 2 + Z 22 (s)x 2 2 Q Q Z Z Q (Re(s) > 0 Q > 0 Z (Y ) s a + bj x,x 2,a,b 4 Z Z Z,Z 22 ( ) Z 2 (Foster ) Z (s) h(0) s + k Z 22 (s) h(0) 22 s + k Z 2 (s) h(0) 2 s + k 2sh (k) s 2 + ωk 2 + h ( ) s 2sh (k) 22 s 2 + ωk 2 + h ( ) 22 s 2sh (k) 2 s 2 + ωk 2 + h ( ) 2 s 8

h 0 s h (0) 0 h(0) 22 0 h(0) h(0) 22 (h(0) 2 )2 0 h (k) 0 h(k) 22 0 h(k) h(k) 22 (h(k) 2 )2 0 h ( ) 0 h ( ) 22 0 h ( ) h( ) 22 (h ( ) 2 )2 0 Z,2 2 Z 2 k a,b (a,b) ( s 2 +a s 3 +4s b s 3 +4s ( ( a 4 )s s 2 +4 + ( a 4 ) s ( b 4 )s s 2 +4 + ( b 4 ) s b s 3 +4s s 2 +2 s 3 +4s ) ( b 4 )s s 2 +4 + ( b 4 ) s ( 2 )s s 2 +4 + ( 2 ) s a 4 0, 2 0, ( a 4 ) 2 (b 4 )2 0 ) a 4 0, 2 0, a 4 2 (b 4 )2 0 a 2 b2, 8 b 2 a, 0 a 4 2 37: a-b 9

2.7 RL RC 2.7. RL RC RL Z (s) ψ(s) (R C ) Z LC(s) Z RL (s) ψ(s) Z LC (s) s ψ(s2 ) Z RL (s) s3 + 6s 2 + 8s s 2 + 4s + 3 Z LC(s) s s6 + s 4 + 8s 2 s 4 + 4s 2 + 3 Foster RC R L Z RC (s) φ(s) Z LC (s) sφ(s 2 ) 3 ( ) 38: g6 3. ω 0 20

LPF LPF,HPF,BPF,BEF Butterworth( ) : Tchebyscheff( ) : LPF ( )F(jω) F(jω) 2 + ϕ 2 (ω) (0 < ω < ), ( < ω) 0 ( log 0 ) ω ϕ 0,ω ϕ ϕ LPF 3.. Butterworth ϕ(ω) ω n F(jω) 2 + ω 2n n Butterworth F(j0) 2 F(j ) 2 0 F(j) 2 2 s jω F(jω) 2 F(jω)F(jω) F(jω)F( jω) F(s)F( s) + ( ) n s 2n + ( ) n s 2n 0 s 2n ( ) n+ ( ) n (e πj ) n e (n )πj e ((n )π+2kπ)j k : s e (n )π+2kπ 2n j 2n 2

39: F(s) F( s) s F(s) 2n F(s) F(s) 2 +( ) n s 2n n F (s)f ( s) s 2 ( s)( + s) F (s) + s 3..2 Tchebyscheff ϕ(ω) εv n (ω) n Tchebyscheff V n (ω):n cos(ncos ω) ω V n (ω) cosh(ncosh ω) ω V n (ω) 2ωV n (ω) V n 2 (ω) (V 0 (ω), V (ω) ω) V n (ω) ω n F(jω) 2 F(jω)F( jω) ω + ε 2 V 2 n (ω) ω V n (ω), V n () + ε 2 + ε 2 V 2 n (ω) 22

40: g6 3..3 H(jω) H(jω) e jθ(ω) τ(ω) dθ(ω) dω τ(ω) θ(ω) ω 3.2 LC 4: F(jω) V 2 V 0 23

0, 0 R R 2 R 0 R 2 3.2. ( ) V I ( A C ) ( B D V 2 I 2 ) 42: ( ) ( ) ( ) ( ) V A B A 2 B 2 V 3 I C D C 2 D 2 I 3 ( ) ( ) A A 2 + B C 2 A B 2 + B D 2 V 3 43: C A 2 + D C 2 C B 2 + D D 2 I 3 V 3 V H(s) V 3 V A A 2 + B C 2 44: I I 2 I, V V 2 IZ ( ) ( ) ( ) V Z V 2 0 I I 2 24

45: V V 2 V, I I 2 (I I 2 )Z V ( ) ( )( ) V 0 V 2 I Z I 2 LPF ( ) ( ) ( ) ( ) V R 0 V 2 I 0 sc I 2 ( )( ) + scr R V 2 sc H(s) 46: LPF + scr I 2 ( ) ( ) ( ) ( )( ) V sl 0 sl 2 V 2 I 0 sc 0 I 2 ( )( ) s 2 CL + s 3 CL L 2 + s(l + L 2 ) V 2 sc s 2 CL 2 + I 2 ( ) ( ) V 2 I 2 47: Z in, Z out ( ) ( ) ( V A B C D I V AV 2 + BI 2 V 2 I 2 ) 48: I CV 2 + DI 2 25

Z in V I AV 2 + BI 2 CV 2 + DI 2 AR 2 + B CR 2 + D ( V 2 I 2 R 2 ) Z in Z in Z in s Cauer Z out Z out DR + B CR + A 3.2.2 R R 49: R ( ) ( ) ( ) R A B A + CR B + DR 0 C D C D F(s), T(s) F(s) T(s) V 0 V 2 A + CR N (s I20 2 ) + sn 2 (s 2 ) I 2 0 A C A N (s 2 ),CR sn 2 (s 2 ) Z in AR 2 + B CR 2 + D A + B R 2 C + D R 2 R 2 A C N (s 2 ) sn 2 (s 2 ) R :3 R T(s) s 3 + 2s 2 + 2s + 26

3 ( 6 ) R N (s 2 ) 2s 2 + sn 2 (s 2 ) s(s 2 + 2) Z in R Z in 2s2 + s 3 + 2s 2 s + 4 3 s+ 3 2 s 50: 3 R R 2 3.2.3 0 R 0 R 5: 0 R ( ) ( ) ( ) A B 0 A + B R 2 B C D R 2 C + D R 2 D 27

F(s), T(s) F(s) T(s) V 0 V 2 A + B N (s I20 2 ) + sn 2 (s 2 ) R 2 I 2 0 A B A N (s 2 ), B R 2 sn 2 (s 2 ) Z out DR + B CR + A R 0 B A sn 2(s 2 ) N (s 2 ) R 2 3 :3 R 2 Z out s3 + 2s 2s 2 + 2 s + 4 3 s + 3 2 s 52: 3 0 R Z out R 0 3.2.4 R R 2 3.3 LPF ( ) ω 0 ω c R R LPF LPF,HPF,BPF,BEF 3.3. LPF LPF (cut off Freq) ω c R 28

LPF x jx j ω ω c LPF ω ω ω c jxa i j ω ω c a i j a i ω c ω ω c jxb i jωb i j bi ω c ω x ω P64 R R R R R a i a ir ω c b i b i ω c R L C LPF LPF 3.3.2 LPF HPF x < x > ω c jx j ω ω c x ω c ω jxa i j ω c ω a i j( ω ca i )ω R j( ω ca i )ω j( ω ca ir )ω C ω ca ir j ω jxb i ω c b i j R ω c b i ω L R ω cb i 29

3.3.3 LPF BPF x < ω < ω < ω 2 HPF LPF ω ω x k ω 0 k 0 2 ω ω ω 0 x 0 ω 0 ω ω 2 k k 2 k ω0 ω 2 ω ω b ω b ω 2 ω p64 jx j ω 0 ω b ( ω ω 0 ω 0 ω ) p65 3.3.4 LPF BEF BEF BPF jx j ω0 ω b ( ω ω 0 ω0 ω ) 53: LPF 4 5 30

5. x Z,Y : 54: 5.2 55: { V (x) V (x + x) + Z xi(x) I(x + x) I(x) Y xv (x + x) { V (x+ x) V (x) x ZI(x) I(x+ x) I(x) x 0 () x Y V (x + x) { dv (x) dx ZI(x) di(x) dx Y V (x + x) Z,Y x { V (x) Ae γx + Be γx I(x) Z 0 (Ae γx Be γx ) γ Y Z : Z 0 Z γ : 3

(2) γ α + βj Ae γx e αx x Be γx 56: Z 0 57: 0 B 0 V Ae γx I Z 0 Ae γx x V I Z 0 Z 0 Z 0 Z,Y Z jωl Y jωc γ Y Z jω LC jβ L Z 0 C λ 2π β 2π ω LC 32

5.3 x V ( l) V,I( l) I,V (0) V 2,I(0) I 2 () { A + B V 2 A B Z 0 I 2 A V 2 + Z 0 I 2, B V 2 Z 0 I 2 2 2 58: () x l V V 2 cosh γl + Z 0 I 2 sinhγl I V 2 Z 0 sinhγl + I 2 cosh γl (3) 59: Z 2 Z V 2 I 2 Z 2 Z V I Z 0 V 2 cos γl + Z 0 I 2 sinhγl V 2 sin γl + Z 0 I 2 cosh γl Z 0 Z 2 + Z 0 tanh γl Z 0 + Z 2 tanh γl Z Z 2 0) Z s Z Z20 Z 0 tanh γl 33

Z 2 ) Z f Z Z2 Z 0 tanh γl Z 0 coth γl Z s Z f Z 2 0 Z 0 Z s Z f, tanhγl Z 0 Z 0 (Z s ) ( ) (Z f Z s Z f { Z s jz 0 tan βl Z f jz 0 cot βl l λ 4 β 2π λ βl π 2 Z s Z f 0 l λ 4 λ 4 l Z s Z f 0 < l < λ 4 L C λ 4 < l < λ 2 C L 5.4 Z L (2) { V Ae γx + Be γx Z 0 I Ae γx Be γx 60: x 0 V,I V Z L I A + B, Z L Z 0 A + B A B Z 0 I A B B A Z L Z 0 Z L + Z 0 s 34

s A B Z L Z 0 s 0 B 0 Z L 0 s Z L s Ae γx : Be γx : s(x) Beγx Ae γx B A e2γx : ( ) s(0)e 2γx s(0)e 2αx e 2jβx γ α + jβ s 5.5 6 s age 7 3 TEX : 7/3( ) : : 7:40 : 3000 m( )m 35

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