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Two port networks a complete overview, Lecture notes of Electrical and Electronics Engineering

Description about the working of two port networks

Typology: Lecture notes

2018/2019

Uploaded on 02/12/2019

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bg1
Two-Port Networks
Chapter 19
ch19 Two-Port Networks 2
19.1 Introduction
•A two-port network is an electrical network
with two separate ports for input and output.
ch19 Two-Port Networks 3
19.2 Impedance Parameters, z
2221212
2121111
IzIzV
IzIzV
+=
+
=
[]
=
=
2
1
2
1
2221
1211
2
1
I
I
z
I
I
zz
zz
V
V
ch19 Two-Port Networks 4
Impedance Parameters, z
z11 = Open-circuit input impedance
z12 = Open-circuit transfer impedance from port 1 to port 2
z21 = Open-circuit transfer impedance from port 2 to port 1
z22 = Open-circuit output impedance
0
2
2
22
0
1
2
21
0
2
1
12
0
1
1
11
12
12
,
,
==
==
==
==
II
II
I
V
z
I
V
z
I
V
z
I
V
z
pf3
pf4
pf5
pf8
pf9
pfa
pfd
pfe
pff
pf12
pf13

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Two-Port Networks

Chapter 19

ch19 Two-Port Networks

19.1 Introduction

• A

two-port network

is an electrical network

with two separate ports for input and output.

ch19 Two-Port Networks

3

19.2 Impedance Parameters,

z

2 22 1 21 2

2 12 1 11 1

I

z

I

z

V

I

z

I

z

V

[ ]

I I

z

I I

z

z

z

z

V V

ch19 Two-Port Networks

Impedance Parameters,

z

z^11

= Open-circuit input impedance

z^12

= Open-circuit transfer impedance from port 1 to port 2

z^21

= Open-circuit transfer impedance from port 2 to port 1

z^22

= Open-circuit output impedance

0 (^22)

22 0 (^21) 21

0 (^12) 12 0 (^11) 11

1

2

1

2

=

=

=

=

I

I

I

I

V I

z

V I

z

V I

z

V I

z

ch19 Two-Port Networks

5

Fig 19.

(^22) 22 (^12) 12

(^21) 21 (^11) 11

V^ I

z

V I

z

V I

z

V I

z

ch19 Two-Port Networks

Fig 19.4 & Fig 19.

ch19 Two-Port Networks

7

Fig 19.

2

1 2 1

I

I

V

V^

n

n^

ch19 Two-Port Networks

Example 19.

[ ]^

= = = =

Thus

2

2

(^22) 22

(^22)

(^12) 12

(^11)

(^21) 21

1

1

(^11) 11

z

I
I
V I

z

I I
V I

z

I I
V I

z

I
I
V I

z

(^0) I (^20) I (^20) I 1 0 I 1

-^

Determine the

z^ parameters for the circuit in Fig. 19.7.

-^

Solution:

ch19 Two-Port Networks

13

Admittance Parameters,

y

y^11

= Short-circuit input admittance

y^12

= Short-circuit transfer admittance from port 1 to port 2

y^21

= Short-circuit transfer admittance from port 2 to port 1

y^22

= Short-circuit output admittance

1

2

1

2

, ,

=

=

=

=

V
V
V
V

I V

y

I V

y

I V

y

I V

y

ch19 Two-Port Networks

Fig 19.

(^22) 22 (^12) 12

(^21) 21 (^11) 11

V^ I

y

V I

y

V I

y

V I

y

ch19 Two-Port Networks

15

Example 19.

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

-^

Obtain the

y^ parameters for the

network shown in

Fig. 19.14.

-^

Solution:

ch19 Two-Port Networks

-^

Obtain the

y^

parameters for the T network shown in

Fig. 19.16.

Practice Problem 19.

ch19 Two-Port Networks

17

Example 19.

-^

Determine the

y^ parameters for the

T^

network shown

in Fig. 19.17.

ch19 Two-Port Networks

Example 19.

S

node At

S

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

V V V I I I V
V V
I V

y

V V V I V V V V V
V V V V V I
V
V
I
V
V

ch19 Two-Port Networks

19

Example 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

Practice Problem 19.

-^

Determine the

y^

parameters for the

T^

network shown

in Fig. 19.19.

ch19 Two-Port Networks

25

Example 19.

-^

Find the hybrid parameters for the two-port networkof Fig. 19.22.

ch19 Two-Port Networks

Example 19.

19.23(a),Fig. 2 (

From

0 2 1 21

1 1

2

0 (^11) 11

1

1 1

(^22)

= V = V

I I

h

I

I

I

V I

h

I

I

V

ch19 Two-Port Networks

27

Example 19.

91 S 9

Also,

19.23(b),

Fig.

From

0 2 2 22

2 2

2

0 1 2 12

2 2

1

= I 1 = I 1

I V

h

I

I

V

V V

h

V

V

V

ch19 Two-Port Networks

Practice Problem 19.

-^

Find the hybrid parameters for the two-port networkof Fig. 19.24.

ch19 Two-Port Networks

29

Example 19.

-^

Determine the Thevenin equivalent at the output portof the circuit in Fig. 19.25.

ch19 Two-Port Networks

Example 19.6^22

1 21 2

11 12

1

12 1 11 1

1

1

2

2 22 1 21 2

2 12 1 11 1

getwe 40

,I

and, 1

But

h

I

h

I

h

h

I

h

I

h

I

V

V

V

h

I

h

I

V

h

I

h

V

ch19 Two-Port Networks

31

Example 19.

× × + + × ×

Therefore,

6

6

3

22 12 21 22 11

11

2 (^22) TH

11

22 12 21 22 11

11

12 21 22 2

h

h

h

h

h

h

I

V I

Z

h

h h h h h h

h

h

h

I

ch19 Two-Port Networks

Example 19.

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

V

h h h

h

V

h h I V h I h

V

h I

h

V

h Ih I

I
I
V
V
I
⎡^ ⎢⎣

ch19 Two-Port Networks

37

Example 19.

[ ]

⎤ ⎥ ⎥ ⎥ ⎥⎦

⎡ ⎢ ⎢ ⎢ ⎢⎣

++ +

=

++ +

=

=

=

⎞⎟⎠

⎛^ ⎜⎝

=

−=

=

−=

=

= ) 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

Practice Problem 19.

-^

Find the

g^

parameters as functions of s for the circuit

in Fig. 19.30.

ch19 Two-Port Networks

39

19.5 Transmission Parameters,

T

2 2 1

2 2

1

DI

CV

I

BI

AV

V

[^

]^

2 2

2 2

(^11)

V^ I

T

V I

D

C

B

A

V I

ch19 Two-Port Networks

Transmission Parameters,

T

A^

= Open-circuit voltage ratio

B^

= Negative short-circuit transfer impedance

C^

= Open-circuit transfer admittance

D^

= Negative short-circuit current ratio

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

a^ = Open-circuit voltage gain b^ = Negative short-circuit transfer impedance c^ = Open-circuit transfer admittance d^ = Negative short-circuit current gain

0 2 1

0 2 1

0 (^21)

0 2 1

1

1

1

1

, ,

=

=

=

=

Ι−

=

−=

=

V

I

V

I

I d

I V c

V I

b

V V a

−^

bc

ad

BC

AD

ch19 Two-Port Networks

42

Example 19.

-^

Find the transmission parameters for the two-port networkin Fig. 19.

ch19 Two-Port Networks

43

Example 19.

S

Thus

and

19.33(a),

Fig.

From

1 1 0 1 2

1 1 0 1 2

1 1 1 2 1 1 1

=

=^

I I

I V

C

I I

V V

A

I I I V I I V

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

Example 19.

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

Example 19.

S
][
][

Thus,

22

21

12

11

22

21

12

11

g

z

B A

g

A

g

A

g

C A

g

D C

z

C

z

C

z

A C

z

T T

-^

Find [

z ] and [

g ] of a two-port network if

-^

Solution:

⎡^ ⎢⎣

=^

S 2

]

[ T

Table From. 37 3 40

is matrix the oft

determinan the4,

2, 1.5, , 10

If

BC
AD
D
C
B
A T

ch19 Two-Port Networks

Example 19.

-^

Obtain the

y^ parameters of the op amp circuit in Fig. 19.37.

Show that the circuit has no

z^ parameters.

ch19 Two-Port Networks

53

Example 19.

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

V V I V I V
V
I
I
I
V

y

y V V I

V
V
I

y o y

o

R
R RR
R
R
R RR
R
R
R
R
R
R
R
R
R

ch19 Two-Port Networks

Practice Problem 19.

-^

Obtain the

z^ parameters of the op amp circuit in Fig. 19.38.

Show that the circuit has no

y^

parameters.

ch19 Two-Port Networks

55

19.7 Interconnection of Networks

] [ ] [ ][

b a^

z z z^

=

-^

The series connection

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

V
V
V

I z z I z z

V
V
V
I I I I I I

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

Fig 19.

]

[

]

[

][

b a^

y

y

y^

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

)V

y (y )V y (y

I
I
I
)V

y (y )V y (y

I
I
I
V
V
V,
V
V
V
V

y V y I

V

y V y I

V

y V y I

V

y V y I

ch19 Two-Port Networks

61

Example 19.

-^

Find the

y^ parameters of the two-port in Fig. 19.44.

ch19 Two-Port Networks

Example 19.

S

4 4 2 6 ] [ ] [ ] [

S

]

[

or

and

S

]

[

or

22

11 21

12

22

11 21

12

j

j

j

j

j

j

j

j

j

j

j

j

j

j

j

b a b

b

a a

b

a

a

a a

a

y

y

y y

y

y

y

y

y

y

y

y

y

ch19 Two-Port Networks

63

Practice Problem 19.

-^

Find the

y^ parameters of the two-port in Fig. 19.45.

ch19 Two-Port Networks

Example 19.

⎡^ ⎢⎣
Ω = × + = = + =
⎡^ ⎢⎣
Ω = × + = = + =
S
]
[
S, 1

and

S 1
]
[
S, 1

and

3 2

2

2

3 2 1 3

1 2 b

b

b

b

a b

a

a

a

a

R R
R
R
R
R
R
R
R R
T
D
C
B
T A
D
C
B
A
D
C
B
A

-^

Find the transmission parameters for the circuit in Fig. 19.46.

-^

Solution:

ch19 Two-Port Networks

65

Example 19.

. 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

Practice Problem 19.

-^

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

s

I

s

V

Z

s

I

s

V

Z

s

I

s

I

A

s

V

s

V

A

ch19 Two-Port Networks

Transistor Circuits

admittance

Output

gain

current

collector-

Basic

ratio

feedback

voltage

Reverse

imdepance

input

Basic

,^

22

21

12

= ie re fe oe

o

f

r

i h h h h

h h h h h h h h

ch19 Two-Port Networks

73

Fig 19.

2 22 1 21 2

2 12 1 11 1

V

V

I

V

V

I

y

y

y

y

L^ L

s^

Y

y

Y

y

H^

21 22

ch19 Two-Port Networks

74

Ladder Network Synthesis

and

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

s

s

s s

s

N

D D

N

D D

y Y

N

N D

N

N D

y Y

N

D

D

D

N

N

D

D

D N H N D D

N

N

D

D

N

H

D

D

N

N

N D

H

ch19 Two-Port Networks

75

Example 19.

-^

Design the

LC

ladder network terminated with a 1-

reistor that has the normalized transfer function.

-^

Solution:

s

s s

y

s

s

y

y y

s

Y

R

y y

s

s s

s

s

s

s

s

s

s

s

s

s

L L

L L

when

(^23) 22

3 21 21 22

21 22

3 2 3

2

3

2

3

H

Y Y

D H

ch19 Two-Port Networks

76

Example 19.

H, 5.

2

3

2

3

3 2 22

s

s

Z

L

s

s

s

Z

Z

sL

s

s

s

y

Z

B

A

B

A

H 5

andF

which

from

1 2 1

2

2

L

sL

s

Y

C

Y

sC

s

s

s

s

Z

Y C

C

B B