2?t bt?vD
2005-11-25
1
? tc
Mèa1
￥8?
2?t bt?vD
2005-11-25
2
? 7.1 Mf
?￥?é
? 7.2 .
{
,?
? 7.3 .
{
,? S=0 a ?￥ RC0??
?
LC
? 7.4μ
Là
.
{
,?￥ RC0??
?
LC
? 7.5 RC0??
?￥i ó
? 7.6 èaMf
?￥ LC0??
?
LC
? 7.7 ?H{ LC0??
?￥Mèa1
? 7.8
?H{ LC0??
?
s a ?￥ 0??
?
LC
2?t bt?vD
2005-11-25
3
?7 1 Mf
?￥?é
B a¨ ?
f
?V
U￥
? gˉ?
q
)(
)(
)(
)(
)(
)(
)(
22
21
11
21
1
2
sY
sY
sZ
sZ
sU
sU
sH
?
===
1
1'
2
2'
I
1
I
2
U
1
U
2
N
0
2
=I
|??f
?
?
Lf
?
|??f
?
?
Lf
?
?
?
?
?
?
?
?
?
?
?
?
?
=
?
?
?
?
?
?
)2(
)(
)2(
)(
2
1
2221
1211
2
1
I
sI
ZZ
ZZ
U
sU
ZIU=
2?t bt?vD
2005-11-25
4
∑
=
=+=
b
j
j
j
T
***
IUIUIU
3
2
2
1
1
*
IU
*
TT
IZI=
?
?
?
?
?
?
?
?
?
?
?
?
?
?
)(
)(
)(
)(
2
*
1
*
2
1
sI
sI
sU
sU
T
∑
=
=
b
j
j
j
U
3
*
IIZI
*
TT
)(
1
)()(
000
3
*
sV
s
ssMsFU
b
j
j
j
++==
∑
=
IIZI
*
TT
=
g =
?
?μ|
^
é? p?
ZZ
T
=
=
2112
zz
2?t bt?vD
2005-11-25
5
)()(][2)()(
2
*
222
2
121
1
*
111
*
*
Re sIsIZIIZsIsIZ
T
++=IZI
! I
1
= a
1
+ jb
1
, I
2
= a
2
+ jb
2
B???=Q?￥ ??l1 ?? ? B??
L=
Q?￥ ? V[?l1 ?
L ? b
)(
1
)()(
000
3
*
sV
s
ssMsFU
b
j
j
j
++==
∑
=
*
TT
IZII
dμ
dμ
dμ?
Lf
?
RLC=
g￥ Z?
? ?
^B??
L ?
2?t bt?vD
2005-11-25
6
() ()
2
2
2
222212121
2
1
2
111
212121
2
222
2
111
2
121
2
222
2
111
1
212
2
121
2
222
2
111
000
)(2
)(2||||
]I[2||||
II||||
)(
1
)()()(
*
**
**
Re
baZbbaaZbaZ
bbaaZIZIZ
IZIZIZ
ZIZIIZIZ
sV
s
ssMsFsF
TT
+++++=
+++=
++=
+++=
=++== IZIIU
)(2
||||)(
2121
2
222
2
111
21
bbaa
IZIZsF
Z
+
??
=
2?t bt?vD
2005-11-25
7
= a Z
21
(s)￥
=
?HqD
L?Hq
! F(s)D Z
11
aZ
22
aZ
21
j< à
?￥
=
?sY
1k ak
11
ak
22
ak
21
5?
?@
0)2()2(
)(2)()(
2
2222121
2
111
2
2222121
2
111
212121
2
2
2
222
2
1
2
111
≥+++++=
+++++=
bkbbkbkakaakak
bbaakbakbakk
)(2
||||)(
2121
2
222
2
111
21
bbaa
IZIZsF
Z
+
??
=
ME F Z
21
(s) ·? ü
?9í ?′à
￥
?
^B¨￥ b
Z
21
(s) ′à
￥ ?￥
=
??
?@B?Hq b
2?t bt?vD
2005-11-25
8
0 ,0)]([
,0)]([
2
2122112222
1111
Re
Re
≥?≥=
≥=
rrrjZr
jZr
<
<
0 ,0 ,0
2
2122112211
≥?≥≥ kkkkk
a ab1 ?i
L
?
H
T (3
?@
?[
?? ?| = (
?dμV
ü Z?
? j< à
?￥
=
?μ1￥=
Q?
^???￥'
^ ??? ￥ b
?
?
?
?
?
?
2221
2111
kk
kk
=
?Hq
L?s
L?Hq
2?t bt?vD
2005-11-25
9
? a Z
21
(s) Y
21
(s)￥?é
^ s￥
L"
?μ ?f
? s￥ RHP3
′à
?1B¨ ? F(s)1?
Lf
? z
21
￥ ?
9
^ F(s)￥ ?
′à
?￥
=
?
?@
=
?Hq
′à
￥
L?
?@
L?Hq
?
ì￥
,?
àμK? b
?
=
?Hq Vn ? k
21
?0 1k
11
ak
22
?0' j< à
) ? Z
21
μB? ?5 Z
11
aZ
22
B?9μ ?)
￥ ? b?Q- Z
11
aZ
22
ü Vμ1-￥
2μ ? b
2?t bt?vD
2005-11-25
10
?7-2 .
{
,? (transmission zero )
B a.
{
,?￥+?
Mf
?￥
,??1 .
{
,? t ?il
^??
? ?
q￥
{1
, b
0??
?￥.
{
,?D DE FWμdè°4￥ ó" b
?0??
? 1DE F1íKv
H?
?ü
àμ
{
D ?
a0?1D￥ ?ü
^.
{
,? N??0?
?
? iDE F1
,
H ? ,1íKv
?
?9
àμ
{
?[0?iD? ,￥ ?9
^.
{
,? b
1
z
2
Y
3
z
5
z
1
U
+
?
4
Y
2?t bt?vD
2005-11-25
11
C
L
L
L
C
C
L
C
0=s
∞=s
LC
js
1
±=
2?t bt?vD
2005-11-25
12
í÷0??
? .
{
,?
^?1DE F￥ ??iD
E F￥
,?? y1?t1D?iDE Ff
?'
&
^?
Lf
?
?[
, ??? ?C ·? ü
? b
yN0??
?￥Mf
?A ?
^KlMMf
? b
?
a0??
?o ?
LCKlMMf
? b
àμ·? ü
?.
{
,?￥Mf
??1KlMMf
?
?T0??
?
^è F=
g?
?'ò?1D?iD
?
^è Fíq5 .
{
,?A? ′à
b
0?￥B?Do??B¨.
{
,? ?T+?1D?
iD￥.
{
,??M]5 V??ר.
{
,? b
2?t bt?vD
2005-11-25
13
1
U
+
?
C
L
0?1DE F￥ ??iDE F￥
,?o
^??.
{
,?￥A1Hq7?
^ sHq 9ü
^
aμ.
{
,?
HA?μ ?1DE F1íKv? ?iDE
F1
, ?
^1DE F￥ ??iDE F￥
,?i?
B???.
{
,? b
s=0)μ ¨.
{
,? s= ?)μB¨.
{
,? b
2005-11-25
)(
)(
)(
)(
)(
)(
)( 0
22
21
11
21
1
2
2
sY
sY
sZ
sZ
sU
sU
sHI
?
====
Hμ
?H(s) ￥.
{
,?
^? Z
21
(s)￥
2μ
,?? Z
11
(s)￥
2
μ ???￥ ?
^? Y
21
(s)￥
2μ
,?? Y
22
(s)￥
2μ ???￥ b
7 Z
21
(s) aY
21
(s)￥
,? V[ê? s ü
?￥ ??1Z
1H(s) ￥.
{
,?g ?N b
??
LC H(s) ￥.
{
,? ;$
2?t bt?vD
2005-11-25
15
= a.
{
,?￥0??
?
LC
￥.
{
,?
￥ ?
￥ ?
?|$ ?
^
E??|YV
iD
1D
)(
)(
)(
sH
Y
Z
?
1 aZ
1D
￥ ? V
LC[/.
{
,?
0=s
L
C
C
L
C
L
R
R
∞=s
RC
s
1
?=
LC
js
1
=
L
R
s ?=
2?t bt?vD
2005-11-25
16
2 aY
iD
￥ ? V
LC[/.
{
,?
RC0??
? V
LC s = 0 a ?#μ
Là
￥.
{
,?
LC0??
? V
LC s = 0 a ?#′à
￥.
{
,? b
3 aB?￥ˉ
?.
{
,? VYVi ó?ZE
LC
0=s
∞=s
RC
s
1
?=
LC
js
1
=
L
R
s ?=
L
L
L
C
C
C
R
R
2?t bt?vD
2005-11-25
17
? a è#)
?
U
2
U
1
1) μ ?? s = ?￥.
{
,?
cbsass
H
sH
+++
=
23
0
)(
2)
U
1
U
2
C
2
R
2
?￥.
{
,?1 s = 0 a–1 (R
2
C
2
)
bass
CR
ssH
sH
++
+
=
2
22
0
)(
1
)(
2?t bt?vD
2005-11-25
18
3)
U
1
U
2
L
2
C
2
C
1
L
1
C
3 L
4
R
5
4)
U
2
U
1
s = 0?
^.
{
,?y1g1 ￥
,? b
iD
Y
.
{
,?μ 0 ?
11
CL
j
22
CL
j
2?t bt?vD
2005-11-25
19
d0?í÷?
? Y- ?MD0??
?
é7 Vs .
{
,? b
U
2
U
1
′à
μB.
{
,?
2?t bt?vD
2005-11-25
20
?7 3 .
{
,? s = 0 a ?￥ RC0??
?
LC
RC0?è
^￥èaMf
?￥ ??.
{
,?
(1μ
L
? ?
^B¨￥ b
(*)
)()())((
)(
0
21
0
sD
sH
sss
sH
sH
p
n
p
=
+++
=
666 L
D(s) μμ
L?
H(s) s = 0)μ p?.
{
,? s = ?)μ (n-p)?
.
{
,? b
? p" 0
H ??.
{
,?ê? s = ?)? n" p
H
??.
{
,?ê? s = 0) b
2?t bt?vD
2005-11-25
21
B a?
LC
)(
)(
)(
)(
)(
11
21
1
2
sZ
sZ
sU
sU
sH ==
RC
0??
?
)()(
)()(
)(
)(
)(
)(
)(
1111
2121
11
21
1
2
sDsN
sDsN
sZ
sZ
sU
sU
sH
=
==
! Z
11
àμ “
2μ ” ?5μ D
11
(s)=D
21
(s)
)(
)(
)(
11
21
sN
sN
sH =
p
sHsNsDsN
02111
)( )()( ==
(*)
)()())((
)(
0
21
0
sD
sH
sss
sH
sH
p
n
p
=
+++
=
666 L
2?t bt?vD
2005-11-25
22
1
LC
T (*)￥èaMf
? H(s) V[¨
LC?
a￥|??E Ff
? z
11
=N
11
(s)/D
11
(s) ?é? b 8
aü
^
!Es?B? RC|??E Ff
? z
11
?￥
s0 N
11
(s)?? H(s)￥s D(s)7]
H? ?
P
?¤
è
^4ó? H(s)
?3￥.
{
,? b
ê4B?|??E Ff
?
P
?￥
,??? H(s)￥
?
?￥ ?;?ê?μ
Là
??D
,??
9C ]
H V
7 z
11
s [
T D
11
(s)￥Q
?1 n
?a
LC z
11
￥V??
!Eá
3
T (* )
?1 p￥.
{
,?9M??Y$ z
21
￥
LC b
(*)
)()())((
)(
0
21
0
sD
sH
sss
sH
sH
p
n
p
=
+++
=
666 L
2?t bt?vD
2005-11-25
23
ê Z
11
(s)￥s0 =H(s)￥s
? RC|??f
?￥1 pê Z
11
(s)￥s
Z
11
￥
, a ??9C μ
Là
OK Líe?
(èêe? )￥
^ Z
11
￥ ? b
? H(s).
{
,?
^ s = 0?
^ s = ?YV Cauer I a
Cauer II
??9 ?8? Z
11
(s) b
ZE
? ó? H(s)￥s ?s0￥ p? n-W￥1" V
[s p=0 ap=n? 0<p<n ? I
n b
2?t bt?vD
2005-11-25
24
L
! p=0
)()())((
)(
0
21
0
sD
H
sss
H
sH
n
=
+++
=
666 L
?¨ Cauer I ?
LC 8?
RC|??E F Z
11
(s)5
?
μ i óD1è ? ?"
?μ.
{
,? (|ê? s = ?)
yN¨???
T ?
LC
?ê4￥ Z
11
(s)ü ?1?
?
@eó?Mf
? H(s).
{
,?￥1 p b
¨ RC0?è
^
LCèaMf
?
45
2
)(
2
++
=
ss
sH
è 1
2?t bt?vD
2005-11-25
25
3
)4)(1(
2
45
2
)(
2
++
=
++
=
ssss
sH
Z
11
V[μ ??]￥ê4?
?￥s0??
^
H(s)￥s
6???
P
?
?@ RC|??f
?￥
L
CHq b
)3(
)4)(1(
11
+
++
=
ss
ss
Z
Vó?￥ H(s) V[ p¤
)3(
2
21
+
=
ss
Z
H(s)￥ 2?.
{
,? ( s = ?)1¨ Cauer I ?8?
? Z
11
(s)
2?t bt?vD
2005-11-25
26
s
s
ss
ss
Z
4
2
1
2
1
1
1
3
45
2
2
11
+
+
+=
+
++
=
1$
2$
1
U F
4
1
+
+
?
?
2
U
F
2
1
11
Z
??=
g0?è
^￥.
{
,? (ê? s= ?)yN
?@ H(s)￥1 p b
45
4
)(
2
++
=
ss
sH
2?t bt?vD
2005-11-25
27
?@ó? H(s)￥1 p b?s0MμB?1 èy0 b¨
í÷è
^ ?
LCèaMf
?
HB???C??
f ? b ?1¤
?1 p￥9mè
?531? |
a?
￥n
@ ? V[¨ ?XMa èabvè
^?? b
H(s)￥.
{
,? (ê? s = ?)5?¨ Cauer I ?8?
L
! p=n
)()())((
)(
0
21
0
sD
sH
sss
sH
sH
n
n
n
=
+++
=
666 L
?μ.
{
,? (|ê? s = )
?? f ?/ V[¨
Cauer II ?
LC
?ê4￥ Z
11
(s)N
H 1 óD1è ?
i óD1èE y7 ?1?á
3
?31￥.
{
,? b
2?t bt?vD
2005-11-25
28
¨ RC0?è
^
LCèaMf
?
45
)(
2
2
0
++
=
ss
sH
sH
è 2
)3(
)4)(1(
11
+
++
=
ss
ss
Z
H(s)￥
?μ.
{
,? (|ê? s = )
¨ Cauer II ?
L
C
?ê4￥ Z
11
(s)
2
11
6
121
1
11
9
1
3
4
3
45
2
2
11
+
+
+=
+
++
=
s
sss
ss
Z
3
2?t bt?vD
2005-11-25
29
1
U
F
4
3
+
+
??
2
U
?
9
11
11
Z
F
121
6
?
2
11
45
)(
2
2
++
=
ss
s
sH
H(s)￥ nD p-W1 0<p<n
H￥ f ? b s = )? s = ?
) (μ.
{
,? büê?￥|??E Ff
? Z
11
￥B?
s s = ) a
6B?s s = ?)¨ ?s
TZ 7[á
3
?31￥.
{
,? bYè V[¨ Cauer￥B??
T
?¤
?31￥?s.
{
,? ?¨ Cauer￥
6B
??
T ??? b
2?t bt?vD
2005-11-25
30
¨ RC0?è
^
LCèaMf
?
45
)(
2
0
++
=
ss
sH
sH
è 3
ó?￥ H(s) s = )? s = ?)sYμB?.
{
,?
)3(
)4)(1(
11
+
++
=
ss
ss
Z
5¨ Cauer I ?
LC s = ?)￥.
{
,?
R
Z
s
s
s
ss
ss
Z
1
2
1
1
1
2
4
1
2
1
1
1
3
45
2
2
11
+
+=
+
+
+=
+
++
=
3
2?t bt?vD
2005-11-25
31
s
s
Z
R
42 +
=
?
HXüμB?i óè ? ?á
3B?.
{
,?
:?
￥|??E Ff
? Z
R
¨ Cauer II ?Z 7
LC
1$
1
U
+
?
F
2
1
11
Z
R
Z
2
42442
+=
+
=
+
=
ss
s
s
s
Z
R
2?t bt?vD
2005-11-25
32
1$
2$
1
U
F
4
1
+
+
?
?
2
U
F
2
1
11
Z
R
Z
45
2
)(
2
++
=
ss
s
sH
2?t bt?vD
2005-11-25
33
3
5¨ Cauer II ?
LC s = )￥.
{
,?
R
Zs
ss
ss
s
ss
ss
ss
ss
Z
+=
+
+
+=
+
++
=
+
++
=
3
4
3
3
11
3
4
3
54
3
45
2
2
2
2
2
2
11
1
U
+
?
11
Z
R
Z
F
4
3
2
2
3
3
11
ss
ss
Z
R
+
+
=
2?t bt?vD
2005-11-25
34
N Z
R
s = ?)1μK′
¨ Cauer I ?
LC Z
R
9
2
1
2
3
1
1
3
3
11
3
3
11
2
2
2
2
+
+=
+
+
=
+
+
=
s
ss
ss
ss
ss
Z
R
1
U
F
4
3
+
+
??
2
U
?
9
2
11
Z
?1
F
2
3
R
Z
45
3
2
)(
2
++
=
ss
s
sH
2?t bt?vD
2005-11-25
35
= a?
LC
)(
)(
)(
)(
)(
22
21
1
2
sY
sY
sU
sU
sH
?
==
V·àP ??è
^
kYV Y
22
(s)×3 è 1 b
è 5
3
1 ,2 ,0 ,
45
)(
2
0
=
++
= p
ss
sH
sH
p
K Líe?￥
^ Y
22
￥
,?
6
2
9
1
3
1
1
2
45
2
)4)(1(
)(
2
22
+
+
+=
+
++
=
+
++
=
s
s
s
ss
s
ss
sY
0 =p
2?t bt?vD
2005-11-25
36
Y
22
?
6
1
?
3
1
F
2
9
F1
6
2
9
1
3
1
1
2
45
2
)4)(1(
)(
2
22
+
+
+=
+
++
=
+
++
=
s
s
s
ss
s
ss
sY
4
4
1)0(
0
0
=
==
H
H
H
2?t bt?vD
2005-11-25
37
39
1
3
2
1
2
2
45
2
)4)(1(
)(
2
22
ss
s
ss
s
ss
sY
+
+
+=
+
++
=
+
++
=
2 =p
0
1)( HH ==∞
Y
22
F3
F
2
3
?
9
1
?
2
1
2?t bt?vD
2005-11-25
38
2
9
6
1
3
1
1
2
45
2
)4)(1(
)(
2
22
s
s
s
ss
s
ss
sY
+
+
+=
+
++
=
+
++
=
1 =p
3
1010
3
)1(
0
0
=
==
H
H
H
Y
22
F1
F
2
9
?
6
1
?
3
1
2?t bt?vD
2005-11-25
39
????Y H(s)
2
)45(2
)(
2
22
+
++
=
s
ss
sY
?μ
Là
￥.
{
,? ??¨ RC0??
?
LC ;$
2?t bt?vD
2005-11-25
40
?7 4 μ
Là
.
{
,?￥ RC0??
?
LC
k8?-i p H
0
)4)(2(
)5)(1(
)(
0
1
2
++
++
==
ss
ssH
U
U
sH
ê
)3(
)4)(2(
)(
11
+
++
=
ss
ss
sZ
?Z
11
(-1)= -1.5<0
7 Z
11
(-5)= 0.3>0
V5
LC s = - 5￥.
{
,?
è
3
2?t bt?vD
2005-11-25
41
s
s
s
sY
s
s
ss
s
sZ
sY
s
s
s
s
s
ss
ss
sY
ss
ss
sZsZ
sZsZ
50
133
50
133
1
)1(133
50
)(
50
)1(133
350
1197
133
50
7
16
11
)(
)(
4
19
20
19
1
7
16
133
50
5
19
20
)
7
16
)(5(
)3(
7
10
)(
3
81.57.0
3.0)()(
)(3.0)(
3
2
2
1
2
2
111
111
+
=
+
=
+
+=
+?+
=
+
+
=
+
+
+
=
++
+
=
+
++
=?=
+=
'
7
2?t bt?vD
2005-11-25
42
#è
^1
Z
11
Y
1
Z
2
Y
3
0.3$
350
1197
F
133
50
$
19
20
$
19
F
50
133
F
H( ?)=H
0
=1
NE?
?@[/
?
!.
{
,?1 z
i
5?êB?
P Z
11
(z
i
) ? ￥.
{
,
? 7
S
2)Z
11
(z
i
) ?Z
11
( ?)?5 Z
1
Y
1
?
?@ z?f
?￥?é
?s????
,??
6ê Z
11
￥ ? b
2?t bt?vD
2005-11-25
43
μ RC
? g?
?
)5)(3(
)1(
)(
0
1
2
++
+
==
ss
sH
U
U
sH
¤μèE (1 1$ BB?′
k8?- b
U
1
R
1
1$
R
2
1$
RC
U
2
è
2?t bt?vD
2005-11-25
44
RC?
?o1
!E
P?B?íq1vl1 R
1
￥
1DèEKaB?íq1vl1 R
2
￥èE' V
# |
)(1
)4)(2(
)5)(3(
)(
111
sZ
ss
ss
sZ +=
++
++
=
)(
1
)4)(2(
72
1)()(
1
111
sYss
s
sZsZ =
++
+
=?=
H(s)￥.
{
,?1 s = -1# s = ?7a??
^ Y
1
(s)￥
? V??
aé"B?
LC-'
)(
272
85.2
272
86
)(
2
2
1
sY
s
s
ss
s
ss
sY +=
+
+
+=
+
++
=
3
2?t bt?vD
2005-11-25
45
1
LC s = -1￥.
{
,?MD ?/
1
3
17
50
3
50
3
1
3
20
50
3
50
3
1
)1(3.0
5)1(2
)1(3.0
72
)(
)(
1
10
11
72
)1(3.0
1.1)(
3.0
1.1
87
5.22
72
)1()72(
72
85.2
)(
3
3
2
2
++
+
=+
+
=
+
++
=
+
+
=
+=
+
+
+=
?
?
?
=
=
?
?
?
?
=+
=+
?
+
+++
=
+
+
=
ss
s
s
s
s
sZ
sZs
s
sY
b
a
ba
ba
s
sbsa
s
s
sY
2?t bt?vD
2005-11-25
46
Z
11
Y
1
Z
2
Y
3
11
50
1$
50
$
17
$
F
1$
10
$
F
H
0
= 0.3
2?t bt?vD
2005-11-25
47
?7 5 RC0??
?￥i ó
1)RC0??
?
^ ?
?
? i ó9
^μr￥9￥
^? , ???òi ó?
?
^? , ?-? b
!E
Pòi ó?
?￥ Z
11
Y
22
4NM?'êM]
￥ Z
11
Y
22
?8??]￥.
{
,? b
? 2) 8?
H??á?]￥ H
0
1N+??
?i ó
??¨F ? ü (￥ “i ó ”Z
T b
2?t bt?vD
2005-11-25
48
? ???
?i óe5 H(s)￥s0sY1
H
01
s
2
aH
02
s aH
03
s (1 D(s)i óa￥s
01H
0
(s
2
+ as + b)5
. 1 ,
, ,
,
)(
)(
)(
)(
002
002001
2
0
0302
2
01
=++=
==
++
=
++
=
'&%'
&%
'&%
O
¤
bHH
aHHHH
sD
bassH
sD
HsHsH
sH
N V3 V7¤ò0?
?F ?i ó
￥ò"
? b'¨ % e[? 1??
??￥
?μ￥? , ¨ &
e[? 2??
??￥
?μ￥? , ¨ ' e[? 3??
??￥
?μ￥? , b
0
, , H#'&%
2?t bt?vD
2005-11-25
49
p RC?
? b
45
)8(
)(
2
2
0
++
+
=
ss
sH
sH
ê
2
45
)(
2
22
+
++
=
s
ss
sY
? ? 7-2? p = 2? 0
H￥è
^sY1
6
121
F
F
11
$
11
$
H
01
=1
3
è
2?t bt?vD
2005-11-25
50
1$
2$
F
F
H
02
=4
?
^
33
32
,
33
1
,
33
4
. 1 ,8 ,4
,
)(
)8(
)(
)(
0
00
2
002
2
===?
=+==
+
=
+
=
&%
&%&%
&%
H
HH
sD
sH
sD
Hs
sH
O¤
4
#
L=i ó￥
0?
?sY1
2
1331
2
44
9
F F
363
$
363
$
1632
3333
33 33
16
$
$
F
F
2?t bt?vD
2005-11-25
51
?7 6 èaMf
?￥ LC0??
?
LC
B a bè F?
? H(s)￥?é
! Z
11
Y
22
(í
2μ ?5 Z
21
D Z
11
￥s M]
)(
)(
)(
)(
)(
)(
)(
11
21
11
21
1
2
sN
sN
sZ
sZ
sU
sU
sH ===
H(s)￥ ?1 Z
11
(s)￥
,?
( ′à
O1B¨
Z
11
(s)s0s }?MQ' Z
11
(s)1s￥ f
? O
Re[Z
11
( j< )]=0( ?í R )
2?t bt?vD
2005-11-25
52
?
L?Hq? Re[Z
21
( j< )]=0
Z
21
(s)1B f
? ( }f
?￥?
L?
d
, ),# H(s)1B }f
? (= )
LC?
? Z
11
?c s=0)￥
,? (LC? g?é )9?c
s= ?)￥
,? (?51 H(s)￥?¨ ? 1 Z
21
s= ?)A?
^ ? 1 Z
21
s ¨
?úV7 s= ?)A1
,?D
Z
11
?)￥
,?h ) 1H(s) ?c s= ?)￥ ? b
bè F?
? H(s)￥?é
1) ? ′à
O1?¨
2) 1 }f
?
3) s=0 as= ?)? V ?
^ ?
2?t bt?vD
2005-11-25
53
= a b H(s)￥ LC0??
?8?
1.
{
,? s=0 as= ?)
np
sss
sH
sH
n
p
≤
+++
= ,
)())((
)(
222
2
22
1
2
2
0
<<< L
(1) p=0H(s)￥s01è
? ??.
{
,? (ê?
s= ?)¨ Cauer ú?
LC Z
11
(s)
?¤0?è
^￥ 1
óD1è?i óD1è ?
?
ì|á
3
?31￥.
{
,? b
(2) p=n ??.
{
,? (ê? s=0)¨ Cauer ??
L
C Z
11
(s) b
(3) 0<p<n.
{
,? (ê? s=0? s= ?)?
P¨
Cauer ú a ?? ?
LC b
2?t bt?vD
2005-11-25
54
)16)(1(
)(
22
0
++
=
ss
H
sH
¨ LC0??
?
LC/
èaMf
?i p H
0
b
è 1
3
ss
ss
ss
ss
Z
9
1617
)9(
)16)(1(
3
24
2
22
11
+
++
=
+
++
=
)9(
2
0
21
+
=
ss
H
Z
??.
{
,? (ê? s= ?) V[¨ Cauer ú? ?
LC
Z
11
(s) b
2?t bt?vD
2005-11-25
55
s
s
s
s
ss
ss
Z
16
7
1
7
8
1
8
1
1
9
1617
3
24
11
+
+
+=
+
++
=
H1
H
7
8
F
8
1
F
16
7
11
Z
)16)(1(
16
1617
16
)(
2224
++
=
++
=
ssss
sH
2?t bt?vD
2005-11-25
56
)16)(1(
)(
22
2
0
++
=
ss
sH
sH
¨ LC0??
?
LC/
èaMf
?i p H
0
b
è 2
3
ss
ss
ss
ss
Z
9
1617
)9(
)16)(1(
3
24
2
22
11
+
++
=
+
++
=
ó?Mf
?μ
? s=0)￥.
{
,?
6?
?ê
? s= ?)5
P¨ Cauer ú
LC Z
11
?" V[á
3
s= ?).
{
,? b
R
ys
s
s
s
s
s
ss
ss
Z
+
+=
+
+
+=
+
++
=
8
1
1
168
7
8
1
1
9
1617
2
3
24
11
2?t bt?vD
2005-11-25
57
168
7
2
+
=
s
s
y
R
¨ Cauer ??
T
LC y
R
b
s
ss
s
y
z
R
R
8
7
1
7
16
7
1681
2
+=
+
==
H1
H
7
8
F
8
1
F
16
7
11
Z
R
z
1617
8
)(
24
2
++
=
ss
s
sH
2?t bt?vD
2005-11-25
58
2 ,1 ,0 ,
)3)(1(
)(
22
2
0
=
++
= p
ss
sH
sH
p
p LC?
?i p H
0
b
è 3
)2(
)3)(1(
)(
2
22
22
+
++
=
ss
ss
sY
1)p = 0
H¨ Cauer I8?
3
s
s
s
s
ss
ss
sY
6
4
1
2
1
2
34
)(
3
24
22
+
+
+=
+
++
=
H
0
=3
Y
22
4F
1F
H
6
1
H
2
1
2?t bt?vD
2005-11-25
59
2)p = 1
H5 Cauer Ia Cauer II8?
s
s
s
s
ss
ss
sY
4
6
1
2
1
2
34
)(
3
24
22
+
+
+=
+
++
=
H
0
=2
Y
22
F4
F1
H
2
1
H
6
1
2?t bt?vD
2005-11-25
60
H
0
=1
2 .
{
,? ′à
,?M?E
3)p = 2
H¨ Cauer II8?
s
s
s
s
ss
ss
sY
5
2
25
1
5
4
1
2
3
2
43
)(
3
42
22
+
+
+=
+
++
=
Y
22
F5 F
5
4
H
25
2
H
3
2
2?t bt?vD
2005-11-25
61
Vê
0)2( ,
)2(
)3)(1(
)(
2
22
11
=
+
++
= jH
ss
ss
sZ ? ú
s
s
s
s
Z
Z
s
s
s
s
s
s
Y
ss
ss
sZZ
jj
j
jZ
8
21
16
35
35
16
4
1
4
7
8
2.1
35
16
4
7
8
)2(8
)2.1)(4(5
8
3
)2(
8
3
4
3
)4(2
)1)(3(
)2(
2
2
2
222
1
2
22
111
11
+=
+
=
+
+
=
+
+
+
=
+
++
=?=
×==
?×
??
=
3
)3)(1(
)4(
)(
22
2
0
++
+
=
ss
sH
sH
p LC?
?i p H
0
è 4
2?t bt?vD
2005-11-25
62
H
0
=3 4
RC
? g Vs ￥èEàμ LCü??
??
) ? ;$
Z
2
Z
11
Y
1
H
8
3
H
16
35
H
8
7
F
21
8
F
7
2
2?t bt?vD
2005-11-25
63
?7 7 ?H{ LC0??
?￥Mèa1
B a·
μ R
2
=1$ (BB? )
)(
)(
)(
)( ,
1
)(
2222
21
22
22
21
22
22
22
22
22
21
1
2
222
2221212
sD
sN
ND
N
sH
D
N
Y
D
N
Y
Y
Y
U
U
sH
IRU
UYUYI
Y
?
+
?
=∴
==
+
?
==∴
?=
+=
í
2μ ?
!7
U
1
I
1
I
2
LC
R
2
1$
U
2
2?t bt?vD
2005-11-25
64
T?
N
21
1 f
? }f
? ? :
1 f
?
2)D
22
D N
21
}?MQ O
e
ì￥? ( j< à
?9
C b
)())((
)())((
)(
2
2
22
4
22
2
2
2
12
22
3
22
1
2
2222
n
n
sssks
sss
NDsD
<<<
<<<
++++
+++=
+=
+
L
L
#
T? k1?
L
? b?
^ D(s)1?
L"
? O? ?[￥ [
T O V[￡
ü D(s)=0￥? ??
? LHP(? ?′à )
?? [
T?1?ì￥ :?G (Hurwitz) [
T b
2?t bt?vD
2005-11-25
65
ó? H(s)= N(s) D(s) O R
2
=1$ ￥8??? ?/
Y
L
z?f
? ( ? Y
22
) V LC
LC￥ 1Hq
^ s
0s -?1?ì￥
f [
T b
&?
? a D(s)1?ì￥
f [
T O N(s)1Q
?l?
D(s)￥ Q }Q [
T
&a
| D(s)￥ }?D ?s 7 D(s)= D
e
(s) + D
o
(s)
&?
? N(s)= N
e
(s)5 |
o
e
D
D
Y =
22
? N(s)= N
o
(s)5 |
e
o
D
D
Y =
22
&?
Y$ H(s)￥.
{
,? ?8?
? Y
22
b
2?t bt?vD
2005-11-25
66
k¨μèE1 $ ￥ LC?
?
LC-i p H
0
1 f
?
#ê
15156
)(
)(
)(
23
0
1
2
+++
==
sss
sH
sU
sU
sH
NssDsD
oe
,15 ,156
32
+=+=
156
15
2
3
22
+
+
==
s
ss
D
D
Y
e
o
7 H(s) s=0)μB.
{
,? (Cauer II1 C),
s= ?)μ
.
{
,? (Cauer Ii C1 L)#5
Cauer IIa Cauer I
3
è
2?t bt?vD
2005-11-25
67
s
ss
s
ss
s
ss
s
sY 3
5
11
5
15
11
15
615
)(
1
2
33
2
22
+
+=
+
+=
+
+
=
Y
22
U
2
U
1
H
1F
F 1$
H
0
=15
2?t bt?vD
2005-11-25
68
= aP
¤ R
1
=1$ (BB? )
N
H
oe
DD
N
ND
N
Z
Z
U
U
sH
IZU
IZIU
+
=
+
=
+
==∴
=
+?=
1111
21
11
21
1
2
1212
11111
1
)(
1
U
1
I
1
R
1
I
2
= 0
LC
1$
U
2
? N(s)= N
e
(s)5 |
o
e
D
D
Z =
11
? N(s)= N
o
(s)5 |
e
o
D
D
Z =
11
2?t bt?vD
2005-11-25
69
122
)(
)(
)(
23
2
0
1
2
+++
==
sss
sH
sU
sU
sH
k¨P
¤èE1 1$ ￥ LC?
?
LC-i p H
0
.
1 }f
? ,
NssDsD
oe
,2 ,12
32
+=+=
7 H(s) s= ?)μB.
{
,? (Cauer Ii C
s=0)
μ
.
{
,? Cauer I1 Ci L) V5 Cauer Ia
Cauer II
#ê
ss
s
D
D
Z
o
e
2
12
3
2
11
+
+
==
3
4
3
2
11
5.1
21
1
2
12
2
)(
1
22
3
11
s
s
s
s
s
s
s
ss
sZ
+
+=
+
+=
+
+
=
3
è
2?t bt?vD
2005-11-25
70
Z
11
U
2
U
1
1$
F
F
H
H
0
=2
)
? ?
?¤μ?
^ 1$
H 1 ?BB? b
2?t bt?vD
2005-11-25
71
?/
Tê 5 (s)
)()(
4
1)()(
2
1
sHsH
R
R
ss ??=?55
|
)(1
)(1
)(
1
s
s
RsZ
i
5
5
m
±
=
T? Z
i
(s)11PH 1$ èE·§_· A￥ ?
èE b
￡ Z
i
(0)?Dó?￥ R
2
^??? b
?7 8
?H{ LC0??
?
2?t bt?vD
2005-11-25
72
? tc Mèa1￥8?
1?
B a Z
21
(s) Y
21
(s)￥?é
^ s￥
L"
?μ ?f
? s RHP3
′à
?1B¨ ( ?F(s)1?
Lf
? z
21
￥ ?
9
^ F(s)￥ ? )
′à
?￥
=
?
?@
=
?Hq
0 ,0 ,0
2
2122112211
≥?≥≥ kkkkk
′à
￥
L?
?@
L?Hq
2?t bt?vD
2005-11-25
73
?
ì￥
,?
àμK? b
?
=
?Hq Vn ? k
21
?0 1k
11
ak
22
?0' j< à
) ? Z
21
μB? ?5 Z
11
aZ
22
B?9μ ?)
￥ ? b?Q- Z
11
aZ
22
ü Vμ1-￥
2μ ? b
:?
?μ ?
?￥2
? b
= a.
{
,?
0 ,0)]([
,0)]([
2
2122112222
1111
Re
Re
≥?≥=
≥=
rrrjZr
jZr
<
<
)(
)(
)(
)(
)(
)(
)( 0
22
21
11
21
1
2
2
sY
sY
sZ
sZ
sU
sU
sHI
?
====
Hμ
2?t bt?vD
2005-11-25
74
H(s) ￥.
{
,?
^? Z
21
(s)￥
2μ
,?? Z
11
(s)￥
2μ
???￥ ?
^?? Y
21
(s)￥
2μ
,?? Y
22
(s)￥
2μ
???￥ b
? a.
{
,? s = 0 a ?￥ RC0??
?
LC
ê Z
11
(s) Y
22
(s)￥s0 =H(s)￥s
￥.
{
,?
￥ ?
￥ ?
?|$ ?
^
E??|YV
iD
1D
)(
)(
)(
sH
Y
Z
?
? RC z?f
?￥1 pê Z
11
(s) Y
22
(s)￥s
' Z
11
aY
22
￥
, a ??9C μ
Là
OK L
íe? (èêe? )￥
^ Z
11
￥ ? a Y
22
￥
,? b
2?t bt?vD
2005-11-25
75
3)? H(s).
{
,?
^ s = 0?
^ s = ?YV Cauer I a
Cauer II
??9 ?8? Z
11
(s) Y
22
(s) b Y
22
(s)1
?i1?·àP ??è
^ b
1 aμ
Là
.
{
,?￥ RC0??
?
LC
!.
{
,?1 z
i
5?êB?
P Z
11
(z
i
) ? ￥.
{
,? 7
S
?
?@[/
?
2)Z
11
(zi) ?Z
11
( ?)?5 Z
1
Y
1
?
?@ z?f
?￥?
é
?s????
,??
6ê Z
11
￥ ? b
c
2?t bt?vD
2005-11-25
76
? a RC0??
?￥i ó
1)RC0??
?
^ ?
?
? i ó9
^μr￥9￥
^? , ???òi ó?
?
^? , ?-? b
!E
Pòi ó?
?￥ Z
11
Y
22
4NM?'êM]
￥ Z
11
Y
22
?8??]￥.
{
,? b
? 2) 8?
H??á?]￥ H
0
1N+??
?i ó
??¨F ? ü (￥ “i ó ”Z
T b
? ???
?i óe5 H(s)￥s0sY1
H
01
s
2
aH
02
s aH
03
s (1 D(s)i óa￥
s01 H
0
(s
2
+ as + b)5
2?t bt?vD
2005-11-25
77
. 1 ,
, ,
,
)(
)(
)(
)(
002
002001
2
0
0302
2
01
=++=
==
++
=
++
=
'&%'
&%
'&%
O
¤
bHH
aHHHH
sD
bassH
sD
HsHsH
sH
N V3 V7¤ò0?
?F ?i ó￥
ò"
? b'¨ % e[? ??
??￥
?μ￥? , ¨ & e
[? ??
??￥
?μ￥? , ¨ ' e[? ??
??￥
?
μ￥? , b
0
, , H#'&%
2?t bt?vD
2005-11-25
78
bè F?
? ) T
￥?é
? ′à
O1?¨
1 }f
?
T a T ?)? V ?
^ ?
bH(s)￥ LC0??
?8?
? H(s).
{
,?
^ s = 0?
^ s = ?YV Cauer I a
Cauer II
??9 ?8? Z
11
(s) Y
22
(s) b Y
22
(s)1
?i1?·àP ??è
^ b
.
{
,? ′à
H V?¨ ?
?? ? 7-4￥
,?
M?E b
B aèaMf
?￥ LC0??
?
LC
2?t bt?vD
2005-11-25
79
t a?H{ LC0??
?￥Mèa1
ó? H(s)= N(s)/D(s) O R
2
=1$ ￥8??? ?/
&?
? a D(s)1?ì￥
f [
T O N(s)1Q
?l?
D(s)￥ Q }Q [
T
&a
| D(s)￥ }?D ?s 7 D(s)= D
e
(s) + D
o
(s)
&?
? N(s)= N
e
(s)5 |
o
e
D
D
Y =
22
? N(s)= N
o
(s)5 |
e
o
D
D
Y =
22
&?
Y$ H(s)￥.
{
,? ?8?
? Y
22
.
2?t bt?vD
2005-11-25
80
ó? H(s)= N(s) D(s) O R
1
=1$ ￥8???DD -
? 1
M] b
t a
?H{ LC0??
?
?12
?1
?/
Tê 5 (s)
)()(
4
1)()(
2
1
sHsH
R
R
ss ??=?55
|
)(1
)(1
)(
1
s
s
RsZ
i
5
5
m
±
=
T? Z
i
(s)11PH 1$ èE·§_· A￥ ?
èE b
￡ Z
i
(0)?Dó?￥ R
2
^??? b
2?t bt?vD
2005-11-25
81
? tc T<
)4)(2(
)(
2
0
++
=
ss
sH
sH
7-1
p RC?
?i p H
0
￥′ b
7-2
)5)(3)(1(
)(
0
+++
=
sss
H
sH
p RC?
?i p H
0
￥′ b
?2 , ?1 ,
)5)(3)(1(
)(
21
0
==
+++
= RR
sss
sH
sH
7-3
p RC?
?i p H
0
￥′ b
)5)(1(
)4)(2(
)(
0
++
++
=
ss
ssH
sH
7-4
p RC?
?i p H
0
￥′ b
2?t bt?vD
2005-11-25
82
7-5
158
)1(
)(
2
2
0
++
++
=
ss
ssH
sH
p RC?
? b
7-6
)5)(3)(1(
)(
222
4
0
+++
=
sss
sH
sH
p LC?
? b
7-7
324
)(
234
0
++++
=
ssss
sH
sH
μèE R
2
= 1$
k p LC?
? b
324
)(
234
0
++++
=
ssss
sH
sH7-8
R
1
= 1$
k p LC?
?
2?t bt?vD
2005-11-25
83
122
)(
23
3
0
+++
=
sss
sH
sH
7-9
μèE R
1
= R
2
= 1$
k p LC?
? b
