Ch17Ex Solution Dorf Circuitos Elétricos

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Chapter 17- Two-Port and Three Port Networks 
Exercises 
 
Ex. 17.2-1 
 
 
1
100(25) 10 
250
a c
a b c
R R
R
R R R
= = =+ + Ω 
2
125(25) 12.5 
250
b c
a b c
R R
R
R R R
= = =+ + Ω 
3
100(125) 50 
250
a b
a b c
R R
R
R R R
= = =+ + Ω 
 
Ex. 17.3-1 
 
 
 
12 21
1 S
21
Y Y− = − = 
( )
( )
11 12 11
22 21 22
1 1 31 S2142 42 42 14
1 11 10.5 S2110.5 7
Y Y Y
Y Y Y
+ = ⇒ = − − = =
+ = ⇒ = − − =
1
 
 
1 1 14 21 
1 1 21 7
⎡ ⎤−⎢ ⎥= ⎢ ⎥−⎢ ⎥⎣ ⎦
Y S 
 
2
1
1
 011
1 
2
22 0
2
42 (21 10.5) 18 42 31.5
10.5(63) 9 73.5
I
I
VZ I
VZ I
=
=
+= = =+
= = = Ω
Ω
 
 
2 1 2
10.5 42(10.5)Since , then 6
73.5 73.5 2
I I V I I== = 
1
1
 012 21
2
 6 I
VZ Z I == = = Ω 
 
18 6
= 
6 9
⎡ ⎤ Ω⎢ ⎥⎣ ⎦Z 
 
 
 
 
 
 
1 
 
 
Ex. 17.4-1 
 
 
1
11
1
2
21
1
1 S
6
1 0.167 S
6
IY V
IY V
= =
= = − = −
 
 
 
1
12
2
2
22
2
0.0567 S
0.944 S
IY V
IY V
= =
= =
 
 
 
Ex. 17.5-1 
 
2 2 1 6 , (9 1) 10 , 1I i V i i V i= = + = = 
 
2
22
2
1
12
2
6 0.6 S
10
 0.1
10
I ih
V i
V ih
V i
= = =
= = =
 
 
 
 
 
 
1
1
1
1
2
 1 
10 
9 9
44 5 
9 9
V i
VI i i
VI i i
=
= + =
= − =
 
Therefore 
( )
( )
( )
1
11
1
2
21
1
 0.9 
10
9
44
9 4.4
10
9
V ih
I i
iIh
I i
= = =
= = =
Ω
 
 
 
2 
Ex. 17.6-1 
1
2 1 2 1 12 64 1 115 5 5 5and 30
1 2 75 50 30 1 2 3 4 10 5 10 15
Y −
−⎡ ⎤ ⎡ ⎤ ⎡ ⎤⎢ ⎥ ⎢ ⎥= Δ = − = ⇒ = = = ⎢ ⎥⎢ ⎥ ⎢ ⎥− ⎣ ⎦⎣ ⎦ ⎣ ⎦
Y Z Y 
 
 
Ex. 17.6-2 
( ) ( )
( ) ( )
2 / 5 1 
1/10 1/10 4 10
1/ 30 2 /15 1/ 3 4 / 3 
1/10 1/10
⎡ ⎤− −⎢ ⎥− − ⎡ ⎤⎢ ⎥= = ⎢ ⎥⎢ ⎥ ⎣ ⎦− −⎢ ⎥− −⎣ ⎦
T 
 
Ex. 17.7-1 
The transmission parameters of the two-port networks are: 
 
a b c
1 12 1 0 1 3
 = , = and = 
0 1 1/6 1 0 1
⎡ ⎤ ⎡ ⎤ ⎡⎢ ⎥ ⎢ ⎥ ⎢⎣ ⎦ ⎣ ⎦ ⎣T T T
⎤⎥⎦
⎤⎥⎦
 
 
The transmission parameters of the cascade circuit are: 
 
1 12 1 0 3 12 1 3 3 21
0 1 1/ 6 1 1/ 6 1 0 1 1/ 6 3 / 2a b c c
⎡ ⎤ ⎡ ⎤ ⎡ ⎤ ⎡ ⎤ ⎡= = =⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢⎣ ⎦ ⎣ ⎦ ⎣ ⎦ ⎣ ⎦ ⎣T T T T 
 
 
3 
	Chapter 17- Two-Port and Three Port Networks 
	Exercises 
	Ex. 17.2-1
	Ex. 17.3-1
	Ex. 17.4-1
	Ex. 17.5-1
	Ex. 17.6-1 
	Ex. 17.6-2 
	Ex. 17.7-1