December 2015
Intermediate to advanced
737 pages
23h 39m
English
Content preview from Network Analysis and Synthesis, 1st Edition by Pearson
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Network Functions − s-Domain Analysis of Circuits 437
K
PZPZ
PPPP
j
1
1112
1213
2
2
4041
43 3
=
--
--
=
-- --
---
()()
()()
()[()]
()(
---+43 3j )
K
jj
j
1
22
2
43
1313
212
13
22
19
24
=
-×-
-+ --
=
×
-+
=
×
+
=
()()
() ()
.
For the pole P
2
at s = -3 + j3
KK
PZPZ
PPPP
jj
j
2
2122
2123
2
330331
33
=
--
--
=
-+ ---+
-+
()()
()()
()
()
( ++--++
=-+
4333 3
1
5
18
)(
)
()
jj
j
For the pole P
3
at s = - 3 - j3
KK
j
32
1
5
18==
--Conjugate of
()
Thus, substituting the values of K
1
, K
2
and K
3
,
Vs
K
sP
K
sP
K
sP
()=
-
+
-
+
-
1
1
2
2
3
3
Taking the inverse Laplace transform, we get the following form:
or
Vt LVsL
s
j
sj
j
sj
() ()
.
()
.( ).
()
==
-
+
-+
+-
+
--
++
--11
24
4
02 18
33
02
18
33
=+-+ +--
--
+-
-
Vt ej
ej
e
tj
tj
() ..() .( )
()
()
24 02 18 02 18
43
33
3 tt
tt jt jt jt j
Vt ee
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