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Description about the working of two port networks
Typology: Lecture notes
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ch19 Two-Port Networks
ch19 Two-Port Networks
3
2 22 1 21 2
2 12 1 11 1
ch19 Two-Port Networks
0 (^22)
22 0 (^21) 21
0 (^12) 12 0 (^11) 11
1
2
1
2
=
=
=
=
I
I
I
I
ch19 Two-Port Networks
5
(^22) 22 (^12) 12
(^21) 21 (^11) 11
ch19 Two-Port Networks
ch19 Two-Port Networks
7
2
1 2 1
ch19 Two-Port Networks
[ ]^
= = = =
Thus
2
2
(^22) 22
(^22)
(^12) 12
(^11)
(^21) 21
1
1
(^11) 11
z
z
z
z
z
(^0) I (^20) I (^20) I 1 0 I 1
-^
-^
ch19 Two-Port Networks
13
1
2
1
2
, ,
=
=
=
=
I V
y
I V
y
I V
y
I V
y
ch19 Two-Port Networks
(^22) 22 (^12) 12
(^21) 21 (^11) 11
ch19 Two-Port Networks
15
S (^5). 0 (^4585)
4 5 (^828)
S 625
. 0 8 5
(^8) ) 5 (^2) || 8 (
S (^5). 0 (^2343)
2 3 (^424)
S (^75). 0 4 3
(^4) ) 3 (^2) || 4 (
0 1 2 21 2 2 1
2 2 0 2 2 22 2
2 2
0 2 12
0 11
1 1
−= − =
= ⇒ = =+ −
= = = ⇒ = =
−= − =
= ⇒ = =+ −
= = = ⇒ = = = = = =
(^11) V V
(^11)
1 V
1 1 2
1 1 1 1 V
1
1 1
I I
I V y I I I
I I I V y I
I V
I I
I V y I I I
I I I V y I
I V
2 2
-^
-^
ch19 Two-Port Networks
-^
ch19 Two-Port Networks
17
-^
ch19 Two-Port Networks
node At
But
node At
2 1 21
2
2 1
1 1 11
1
1
1
1
1 1
1
1
o o
o
o o
o
o o
o o o o o o
o o
o
o o
o V^ V I V y
y
ch19 Two-Port Networks
19
.
reciprocalt isn' network the since case, in this
that Notice
S 25
. 0
(^625). 0 5. 2
(^625). 0
2 8 ) (^5). 2 1 ( 4 (^25). 0
0
2 4 2, nodeAt
S 05
. 0
/
(^5). 2
2 2 4
0
4 2 8 0
0 8 But
4 2 2 0 8 1, nodeAt
19.18(b). Fig. using and get we
Similarly,
(^12) 2 21 2 (^222)
2 1 2 1 2 (^21)
2 2
2
1
2
21 (^12) y y
V V
I V y
V
V V
V I
I I V V
V V I V y
V V V V V V V V V V V I V V V I V
y y
1 ≠
=
⇒
−= −
−→
=
−
−= −= = ⇒
= → −
−= →
−
−= → − =
−
= −
o o
o
o o
o o
o o
o
o o o
o o o
o
o o
o
ch19 Two-Port Networks
-^
ch19 Two-Port Networks
25
-^
ch19 Two-Port Networks
0 2 1 21
1 1
2
0 (^11) 11
1
1 1
(^22)
= V = V
ch19 Two-Port Networks
27
0 2 2 22
2 2
2
0 1 2 12
2 2
1
= I 1 = I 1
ch19 Two-Port Networks
-^
ch19 Two-Port Networks
29
-^
ch19 Two-Port Networks
1 21 2
11 12
1
12 1 11 1
1
1
2
2 22 1 21 2
2 12 1 11 1
ch19 Two-Port Networks
31
−
6
6
3
22 12 21 22 11
11
2 (^22) TH
11
22 12 21 22 11
11
12 21 22 2
ch19 Two-Port Networks
2 12 22 21
11
2 22 21 1 2 22 (^121)
2 12 1 11
2 12 (^111) 1
2
1
1
1 1
and
or
output, At the
intput at the
19.26(b), Fig. From
h h h
h
h h I V h I h
h I
h
h Ih I
ch19 Two-Port Networks
37
[ ]
⎤ ⎥ ⎥ ⎥ ⎥⎦
⎡ ⎢ ⎢ ⎢ ⎢⎣
++ +
−
=
++ +
=
=
=
⎞⎟⎠
⎛^ ⎜⎝
=
−=
=
−=
=
= ) 1 (
1
1 1
1 1
1 1
Thus,
) 1 (
1
1 1 1
or 1 1
Also,
1 1
or 19.29(b), 1 1 Fig. From
2
2
0 (^22) 22
2 2
0 1 2 12 2
1
s ss s s
s
s
s ss s s s
s s
s
s g
V I g
I V
I I g I
I
1
1
V
V
ch19 Two-Port Networks
-^
ch19 Two-Port Networks
39
2 2 1
2 2
1
[^
]^
2 2
2 2
(^11)
ch19 Two-Port Networks
0 1 2
0 1 2
0 (^12)
0 1 2
2
2
2
2
, ,
=
=
=
=
Ι − =
=
−=
=
V
I
V
I
I
D
I V C
V I
B
V V A
ch19 Two-Port Networks
41
Inverse Transmission Parameters,
t
0 2 1
0 2 1
0 (^21)
0 2 1
1
1
1
1
, ,
=
=
=
=
=
−=
=
V
I
V
I
I d
I V c
V I
b
V V a
ch19 Two-Port Networks
42
-^
ch19 Two-Port Networks
43
1 1 0 1 2
1 1 0 1 2
1 1 1 2 1 1 1
=
=^
2
2
I
I
ch19 Two-Port Networks
Ω 44
=
−=
−=
−=
− ⇒
=
= ⇒
=
=
− −
=
=
(^29). 15 ) (^20) / (^17) (
13
, (^176). 1 (^2017)
Therefore,
1720 0
3 20
13 , 3
, 10 /)
(
and 3
But
0
20
10
19.33(b), Fig. From
1 1
0 1 2
0 1 2
2 1
2 1 1
1 1 1
1 1 1
2
1
I^ I
V V B
I I D
I I
I I I
I V I V
V V I I V
I V V V
2
2
V
V a
a
a
a a
ch19 Two-Port Networks
49
19.6 Relationships Between
Parameters
, 1
,
,
,
1
1
22 22 (^222)
2 (^222) 2 22
1 2 22 2
2
1 2 22
2 22
(^222)
22
(^212)
22
2 (^222) 1
22
(^212)
22
2 22 1 2 22
22 1 2 2
2 1
z h z z
h z z h z h
I V h h
h h I V z
z z
z z
z
z z z z V I
V z z I
z
z z z z V
V z I z z I I z I z V I z I z V
1 1 1 1
11
1
1 11
1
1
1
11 (^12)
1
1
11 1
1 2 2
1
2 1 11 1
=
−=
=
Δ=
⇒
⎤ ⎥⎦ ⎡⎤ ⎢⎥⎣⎦
⎡=⎢⎣ ⎤ ⎥⎦ ⎤ ⎥⎡⎥⎢⎥⎣ ⎥⎦
⎡ ⎢ ⎢ ⎢ ⎢⎣
− −
⎤=⎥⎦ ⎡ ⎢⎣ →
−
= →
−=
→
=
=
z
(^11) ] [ ][
][ ][
− − = ≠ T t
h g
ch19 Two-Port Networks
ch19 Two-Port Networks
51
Thus,
22
21
12
11
22
21
12
11
g
z
g
g
g
g
z
z
z
z
T T
-^
-^
Table From. 37 3 40
is matrix the oft
determinan the4,
2, 1.5, , 10
If
ch19 Two-Port Networks
-^
ch19 Two-Port Networks
53
inverse. no has matrix] [ the0,
Since
is matrix] [ the oft
determinan The
Hence,( . /
But
Also,
as and of in terms
expressed be can which
ams, op the of inals
input term
enter the can current no Since
21 12 22 11
3 22 (^231) 1 21
2 3 1 (^231) 1 2
1
2 1 1 (^23) 2
(^11)
2 1 (^23) 2
12
11 2 1 1
2 1
1
yy y yy
y y
y
y
y V V I
y o y
o
ch19 Two-Port Networks
-^
ch19 Two-Port Networks
55
19.7 Interconnection of Networks
] [ ] [ ][
b a^
z z z^
=
-^
b a b a
b a b a
22 22 2 2
2 2
22 2
2
22 22
2 2
2 2 2
2 2
z z z z
z z z z z z
z z
I z z I z z
I z z I z z
Iz Iz
V
Iz Iz V
Iz Iz V
Iz Iz V
1 1
1 1 11 11
1
1 11
2 b a 1 1b 1a
b a
2 b 1 a 1 1 11b 11a
1b 1a 1
2b 2a 2 1b 1a 1
2b 22 1b 21 2b
2b 12 1b 11 1b
2a 22 1a 21 2a
2a 12 1a 11 1a
ch19 Two-Port Networks
b a^
22b 22a 21b 21a
12b 12a 11b 11a 22 21
12 11
2 22b 22a 1 21b 21a
2b 2a 2
2 12b 12a 1 11b 11a
1b 1a 1
2b 2a 2 1b 1a 1
2b 22 1b 21 2b
2b 12 1b 11 1b
2a 22 1a 21 2a
2a 12 1a 11 1a
y y y y
y y y y y y
y y
y (y )V y (y
y (y )V y (y
y V y I
y V y I
y V y I
y V y I
ch19 Two-Port Networks
61
-^
ch19 Two-Port Networks
22
11 21
12
22
11 21
12
b a b
b
a a
b
a
a
a a
a
ch19 Two-Port Networks
63
-^
ch19 Two-Port Networks
and
and
3 2
2
2
3 2 1 3
1 2 b
b
b
b
a b
a
a
a
a
-^
Find the transmission parameters for the circuit in Fig. 19.46.
-^
Solution:
ch19 Two-Port Networks
65
. 1
that Notice
42 S (^5). 5
206 27
4 9 6 1 (^5). 0 9 1 1
4 44 6 5 (^5). 0 44 1 5
4 (^5). 0
6 1 9 1
44 5 ] [] [ ] [
19.46, Fig.in
network total for the, Thud
= Δ= Δ= Δ
⎤ ⎥⎦
⎡^ ⎢⎣
Ω
=
⎤ ⎥⎦
⎡ ⎢⎣
× + × × + × × + × × + × = ⎤ ⎥⎦
⎡⎤ ⎢⎥⎣⎦
⎡=⎢⎣ ⋅ =
T T b T a
b a T T T
ch19 Two-Port Networks
-^
Find the transmission parameters for the circuit in Fig. 19.48.
ch19 Two-Port Networks
67
19.9 Applications 19.9.1 Transistor Circuits
0 (^22) out
1 1 in
(^2121)
=
V^ s
v i
ch19 Two-Port Networks
22
21
12
o
f
r
ch19 Two-Port Networks
73
2 22 1 21 2
2 12 1 11 1
L^ L
21 22
ch19 Two-Port Networks
74
22
21
o
e o
e
o e
L
o e o
e
o e
L
o
o e
o e
e
e o
e o
o e o
e
e
e o
o
e o
e o
ch19 Two-Port Networks
75
-^
-^
L L
L L
(^23) 22
3 21 21 22
21 22
3 2 3
2
3
2
3
ch19 Two-Port Networks
76
2
3
2
3
3 2 22
B
A
B
A
1 2 1
2
2
C
B B