ch_4_soln
DESCRIPTION
Quiz solution for network analysisTRANSCRIPT
-
4.8
Z1V 2V2I1I
2
1
1 111 12
21 222 2
2 1 11 1
(1) 10 11
1
(2) 20 22
2
2 21 1 22 2
1 11 1 12 2
port-2 open 0
with ( ) (as defines)
likewise: ( )
with port-2 shorted 0
oc I
oc I
V IZ ZZ ZV I
I V Z IVZ ZIVZ ZI
V Z I Z IV Z I Z I
=
=
= = == =
= = = = +
= +
2
21 111 1 12
22
(1)1 12 210 11
1 22(1)
12 21 11 22
(1) (1) (2)
2 2 (1) (1) (12 21
( )
( )
( )
( )
for reciprocal network ( )
v sc
sc
oc sc oc
oc sc oc
Z IZ I ZZ
V Z ZZ ZI ZZ Z Z Z Z
Z Z Z2)Z Z Z Z Z
=
= +
= == =
= =
-
4.9
Z1V 2V2I1I
( )(1)
11
(2)22
(1)0 1
11 (1)0 1
(2)0 2
22 (2)0 2
20 0.44 0.08
20(2-open) 500.44(1-open) 50
0.0850 50 1 9050 50
50 5050 50
in
in
in
in
in
in
jz
j
Z Z jjjZ Z j
Z Z VjS jZ Z j VZ Z VjS jZ Z j V
+
+
= = = =
= = = = = = = =+ + = = = =+ +
-
4.11
2a1a 2'a
1
'a
AS BS
'2b1
'b2b1b
2
' ' '1 1 1 111 12 11 12 1 2
'' '2 221 22 21 22 1 22 2
1 111 12' '
21 22 2
2 21 1 22 2
; ;
from A-matrix:
B-mat
A A B B
A A B B
A A
b a b aS S S S a bb aS S S S b ab a
b aS Sb S S a
b S a S a
= = = = =
= +1 2 2
2
2
21 1
' ' ' '1 2 11 12 11 2 12
'2 21 1 22 11 2 12
'22 11 2 21 1 22 12
' '21 2 21 1 2
' ' '2 2
rix:
( )
(1 ) equation 1
is defines as: (when 0)
but from B-matrix (when 0
B B B B
A A B B
A B A A B
B
b a S a S a S b S a
b S a S S b S a
S S b S a S S a
S b S a ab S a a
= = + = + = + + = +
= == =
'1 2
21 21 211 1
' 2 212
1 22 11
21 2121
22 11
)
from equeation 1: if 01
1
B B
A
A B
B A
A B
a bS S Sa a
b Saa S S
S SSS S
= =
= = =
-
4.16
2
11 11
42
0.1 90 0.8 45 0.3 45 00.8 45 0 0 0.4 45
( )0.3 45 0 0 0.6 45
0 0.4 45 0.6 45 0
) Check | | 1, no lossy
b) Check , yes
c) S 0.1; Return Loss=-20log|S | 20d) S 0.4 45; Insertion
ijj
ij ji
S
a S
S Sj d
= =
== + ==
B
2 4 3 3
3 3 1
1 1 3
1 1
1 1
1 1
1
1
Loss=-20log|0.4 | 7.9645
) 0; 0.3 45
0.1 90 0.3 45 0.1 90 0.09 90 0.1 0.09
0.01
0.01
dBphasee a a a ba b a
b a aa a
ja jab jab ja
==
= = = = = = + = + = == =
-
4.19
( ) 10.3 0.07 0.6
0.6 0.3 0.7
1 (1 )
0.7 0.7 0.6 0.99 45 0.6(1 )
0.6 0.7 0.7 0.6 0.99 45
0.045 1.045 0.8960.896 0.045 1.045
j jS
j j
Z S S
j j jS
j j jj j
j j
+ = = +
= = + + =