Two port-networks
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The document discusses two-port networks and their parameters. It provides examples and solutions to calculate various two-port network parameters like z-parameters, h-parameters, y-parameters, and ABCD parameters. It also discusses conditions for networks to be reciprocal and provides examples to determine if a given network is reciprocal or not based on its parameter matrix. The examples cover calculation of impedance, admittance and other parameters from the given two-port network circuit diagrams.
![Two Port Networks
1. Two Two-port networks are connected in cascade. The combination is to the represented
as a single two ¨C port network, by multiplying the individual
(a) z-parameter matrices
(b) h-parameter matrices
(c) y-parameter matrices
(d) ABCD parameter
[GATE 1991: 2 Marks]
Soln. ABCD parameters relate the voltage and current at one port to voltage and current
at the other port
Option (d)
2. For a 2-port network to be reciprocal,
(a) z11 = z22
(b) y21 = y12
(c) h21 = -h12
(d) AD ¨C BC = 0
[GATE 1992: 2 Marks]
Soln. ? ?? = ? ??
? ? = ?? ??
Option (b) & (c)
3. The condition, that a 2-port network is reciprocal, can be expressed in terms of its ABCD
parameters as¡¡.
[GATE 1994: 1 Mark]
Soln. AD ¨C BC = 1](https://image.slidesharecdn.com/two-port-networks-180207061036/85/Two-port-networks-1-320.jpg)
![4. In the circuit of figure, the equivalent impedance seen across terminals A, B is
4
42
2
Zeq
A
B
j 2
-j 2
a b
(a) (16/3) ?
(b) (8/3) ?
(c) (8/3 + 12j) ?
(d) None of the above
[GATE 1997: 2 Marks]
Soln. The product of the opposite arms are equal, so the bridge is balanced.
The point a and b are at the same potential
? ?? = (?¡¬ ?) + (?¡¬ ?)
=
?
?
+
?
?
=
?
?
Option (b)
5. The short-circuit admittance matrix of a two-port network is
[
0 ?1
2?
1
2? 0
]
The two ¨C port network is
(a) non ¨C reciprocal and passive
(b) non ¨C reciprocal and active
(c) reciprocal and passive
(d) reciprocal and active
[GATE 1998: 1 Marks]](https://image.slidesharecdn.com/two-port-networks-180207061036/85/Two-port-networks-2-320.jpg)
![Soln. ? ?? ¡Ù ? ?? so the network is nonreciprocal. And active networks are
nonreciprocal
Option (b)
6. A 2-port network is shown in the figure. The parameter h21 for this network can be given
by
R
RR
I1 I2
V2V1
++
--
(a) -1/2
(b) +1/2
(c) -3/2
(d) +3/2
[GATE 1999: 1 Mark]
Soln. ? ? = ? ?? ? ? + ? ?? ? ?
? ? = ? ?? ? ? + ? ?? ? ?
? ?? =
? ?
? ?
| ? ?=?
? ? = ?? ? + ?( ? ? + ? ?)
Or ??? ? + ?? ? = ? ?
When ? ? = ?, ??? ? + ?? ? = ?
So,
? ?
? ?
=
??
??
= ?
?
?
Option (a)](https://image.slidesharecdn.com/two-port-networks-180207061036/85/Two-port-networks-3-320.jpg)
![7. The admittance parameter Y12 in the 2-port network in figure is
E1 E2
I1 I2
5 5
20
(a) -0.2 nho
(b) 0.1 mho
(c) -0.05 mho
(d) 0.05 mho
[GATE 2001: 1 Mark]
Soln. ? ?? = ?
?
??
= ??. ?? ????
Option (c)
8. The Z parameters Z11 and Z21 for the 2-port network in the figure are
I1 I2
E2E1
2
4
10E1
(a) ?11 =
?6
11
?, ?21 =
16
11
?
(b) ?11 =
6
11
?, ?21 =
4
11
?
(c) ?11 =
6
11
?, ?21 =
?16
11
?
(d) ?11 =
4
11
?, ?21 =
4
11
?
[GATE 2001: 2 Marks]
Soln. For z ¨C parameters
? ? = ? ?? ? ? + ? ?? ? ?
? ? = ? ?? ? ? + ? ?? ? ?
Writing KVL in LHS loop](https://image.slidesharecdn.com/two-port-networks-180207061036/85/Two-port-networks-4-320.jpg)
![? ? = ?? ? + ?? ? + ?? ? ? ??? ?
Or ??? ? = ?? ? + ?? ? ? ? ? ?(?)
? ?? =
? ?
? ?
| ? ?=? =
?
??
?
? ?? =
? ?
? ?
| ? ?=? =
?
??
?
Writing KVL in RHS Loop
? ? = ?( ? ? + ? ?) ? ??? ? ? ? ? ? ? (??)
Substituting ? ? =
?? ?+?? ?
??
?? ???????? ? ?(???)
? ? = ?( ? ? + ? ?) ?
??(?? ?+?? ?)
??
? ?? =
? ?
? ?
| ? ?=? =
???
??
?
Option (c)
9. The impedance parameters Z11 and Z12 of the two-port network in the figure are
1
1 1
2
2 2 2
1 2
(a) ?11 = 2.75? ??? ?12 = 0.25 ?
(b) ?11 = 3 ? ??? ?12 = 0.5?
(c) ?11 = 3 ? ??? ?12 = 0.25?
(d) ?11 = 2.25? ??? ?12 = 0.5 ?
[GATE 2003: 2 Marks]](https://image.slidesharecdn.com/two-port-networks-180207061036/85/Two-port-networks-5-320.jpg)
![Soln. Using ? ? ? conversion, the circuit reduces to
Z1
2 0.5
0.25
0.5 2
Z2
Z3
? ?? = ? ? + ? ?
= ?. ? + ?. ??
= ?. ???
? ?? = ? ? = ?. ???
Option (a)
10. The h parameter of the circuit shown in the figure are
+
20
10
+
- -
I1 I2
V1 V2
(a) [
0.1 0.1
?0.1 0.3
]
(b) [
10 ?1
1 0.05
]
(c) [
30 20
20 30
]
(d) [
10 1
?1 0.05
]
[GATE 2005: 2 Marks]](https://image.slidesharecdn.com/two-port-networks-180207061036/85/Two-port-networks-6-320.jpg)
![re
I1
r0
I2
¦ÂI1
(a) ?? ??? ??0
(b) 0 ??? ? ??0
(c) 0 ??? ??0
(d) ?? ??? ???0
[GATE 2006: 1 Mark]
Soln.
re
I1
r0
I2
¦ÂI1V1 V2
? ? = ? ?? ? ? + ? ?? ? ?
? ? = ? ?? ? ? + ? ?? ? ?
? ?? =
? ?
? ?
| ? ?=?
When ? ? = ?, ? ? = ?, ?? ? ?? = ?
? ?? =
? ?
? ?
| ? ?=?
When ? ? = ?, ? ? = ??? ? ? ?
? ?? = ??? ?
Option (b)](https://image.slidesharecdn.com/two-port-networks-180207061036/85/Two-port-networks-8-320.jpg)
![12. For the two-port network shown, the short-circuit admittance parameter matrix is
1
0.5 0.5
2
0.5
1
ya
yb
yc
(a) [
4 ?2
?2 4
] ?
(b) [
1 ?0.5
?0.5 4
] ?
(c) [
1 ?0.5
0.5 1
] ?
(d) [
4 2
2 4
] ?
[GATE 2010: 1 Mark]
Soln. The short circuit admittance parameters of a two port ¦Ð network:
? ?? = ? ? + ? ? =
?
?.?
+
?
?.?
= ??
? ?? = ? ?? = ?? ? = ?
?
?.?
= ???
? ?? = ? ? + ? ? =
?
?.?
+
?
?.?
= ??
Option (a)
13. If the scattering matrix [S] of a two port network is
[?] = [0.2¡Ï00
0.9¡Ï00
0.9¡Ï00
0.1¡Ï00]
Then the network is
(a) Lossless and reciprocal
(b) Lossless but not reciprocal
(c) Not lossless but reciprocal
(d) Neither lossless not reciprocal
[GATE 2010: 1 Mark]
Soln. For the reciprocal network | ? ??| = | ? ??|
For a loss less network | ? ??| ?
+ | ? ??| ?
= ?
( ?. ?) ?
+ ( ?. ?) ?
¡Ù ?](https://image.slidesharecdn.com/two-port-networks-180207061036/85/Two-port-networks-9-320.jpg)
![The network is lossy and reciprocal.
Option (c)
14. In the circuit shown below, the network N is described by the following Y matrix:
? = [
0.1? ?0.01?
0.01? 0.1?
] The voltage gain
?2
?1
is
(a) 1/90
(b) -1/90
(c) -1/99
(d) -1/11
[GATE 2011: 2 Marks]
Soln.
I1 I225
100
-
V1
-
V2
++
N
100V
? ? = ? ?? ? ? + ? ?? ? ?
= ?. ?? ? ? + ?. ? ? ? ? ? ? ? ? ? ? (?)
? ? = ?? ? ? ? = ????? ?
? ? =
?? ?
???
Substituting the value of I2 in equation (i)
?? ?
???
= ?. ??? ? + ?. ?? ?
Or
? ?
? ?
=
??
??
Option (d)](https://image.slidesharecdn.com/two-port-networks-180207061036/85/Two-port-networks-10-320.jpg)
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Two port-networks
- 1. Two Port Networks 1. Two Two-port networks are connected in cascade. The combination is to the represented as a single two ¨C port network, by multiplying the individual (a) z-parameter matrices (b) h-parameter matrices (c) y-parameter matrices (d) ABCD parameter [GATE 1991: 2 Marks] Soln. ABCD parameters relate the voltage and current at one port to voltage and current at the other port Option (d) 2. For a 2-port network to be reciprocal, (a) z11 = z22 (b) y21 = y12 (c) h21 = -h12 (d) AD ¨C BC = 0 [GATE 1992: 2 Marks] Soln. ? ?? = ? ?? ? ? = ?? ?? Option (b) & (c) 3. The condition, that a 2-port network is reciprocal, can be expressed in terms of its ABCD parameters as¡¡. [GATE 1994: 1 Mark] Soln. AD ¨C BC = 1
- 2. 4. In the circuit of figure, the equivalent impedance seen across terminals A, B is 4 42 2 Zeq A B j 2 -j 2 a b (a) (16/3) ? (b) (8/3) ? (c) (8/3 + 12j) ? (d) None of the above [GATE 1997: 2 Marks] Soln. The product of the opposite arms are equal, so the bridge is balanced. The point a and b are at the same potential ? ?? = (?¡¬ ?) + (?¡¬ ?) = ? ? + ? ? = ? ? Option (b) 5. The short-circuit admittance matrix of a two-port network is [ 0 ?1 2? 1 2? 0 ] The two ¨C port network is (a) non ¨C reciprocal and passive (b) non ¨C reciprocal and active (c) reciprocal and passive (d) reciprocal and active [GATE 1998: 1 Marks]
- 3. Soln. ? ?? ¡Ù ? ?? so the network is nonreciprocal. And active networks are nonreciprocal Option (b) 6. A 2-port network is shown in the figure. The parameter h21 for this network can be given by R RR I1 I2 V2V1 ++ -- (a) -1/2 (b) +1/2 (c) -3/2 (d) +3/2 [GATE 1999: 1 Mark] Soln. ? ? = ? ?? ? ? + ? ?? ? ? ? ? = ? ?? ? ? + ? ?? ? ? ? ?? = ? ? ? ? | ? ?=? ? ? = ?? ? + ?( ? ? + ? ?) Or ??? ? + ?? ? = ? ? When ? ? = ?, ??? ? + ?? ? = ? So, ? ? ? ? = ?? ?? = ? ? ? Option (a)
- 4. 7. The admittance parameter Y12 in the 2-port network in figure is E1 E2 I1 I2 5 5 20 (a) -0.2 nho (b) 0.1 mho (c) -0.05 mho (d) 0.05 mho [GATE 2001: 1 Mark] Soln. ? ?? = ? ? ?? = ??. ?? ???? Option (c) 8. The Z parameters Z11 and Z21 for the 2-port network in the figure are I1 I2 E2E1 2 4 10E1 (a) ?11 = ?6 11 ?, ?21 = 16 11 ? (b) ?11 = 6 11 ?, ?21 = 4 11 ? (c) ?11 = 6 11 ?, ?21 = ?16 11 ? (d) ?11 = 4 11 ?, ?21 = 4 11 ? [GATE 2001: 2 Marks] Soln. For z ¨C parameters ? ? = ? ?? ? ? + ? ?? ? ? ? ? = ? ?? ? ? + ? ?? ? ? Writing KVL in LHS loop
- 5. ? ? = ?? ? + ?? ? + ?? ? ? ??? ? Or ??? ? = ?? ? + ?? ? ? ? ? ?(?) ? ?? = ? ? ? ? | ? ?=? = ? ?? ? ? ?? = ? ? ? ? | ? ?=? = ? ?? ? Writing KVL in RHS Loop ? ? = ?( ? ? + ? ?) ? ??? ? ? ? ? ? ? (??) Substituting ? ? = ?? ?+?? ? ?? ?? ???????? ? ?(???) ? ? = ?( ? ? + ? ?) ? ??(?? ?+?? ?) ?? ? ?? = ? ? ? ? | ? ?=? = ??? ?? ? Option (c) 9. The impedance parameters Z11 and Z12 of the two-port network in the figure are 1 1 1 2 2 2 2 1 2 (a) ?11 = 2.75? ??? ?12 = 0.25 ? (b) ?11 = 3 ? ??? ?12 = 0.5? (c) ?11 = 3 ? ??? ?12 = 0.25? (d) ?11 = 2.25? ??? ?12 = 0.5 ? [GATE 2003: 2 Marks]
- 6. Soln. Using ? ? ? conversion, the circuit reduces to Z1 2 0.5 0.25 0.5 2 Z2 Z3 ? ?? = ? ? + ? ? = ?. ? + ?. ?? = ?. ??? ? ?? = ? ? = ?. ??? Option (a) 10. The h parameter of the circuit shown in the figure are + 20 10 + - - I1 I2 V1 V2 (a) [ 0.1 0.1 ?0.1 0.3 ] (b) [ 10 ?1 1 0.05 ] (c) [ 30 20 20 30 ] (d) [ 10 1 ?1 0.05 ] [GATE 2005: 2 Marks]
- 7. Soln. ? ? = ? ?? ? ? + ? ?? ? ? ? ? = ? ?? ? ? + ? ?? ? ? Writing KVL in LHS and RHS Loop ? ? = ??? ? + ??( ? ? + ? ?) ? ? ? ? ? ?(?) ? ? = ??( ? ? + ? ?) ? ? ? ? ? ?(??) Or ? ? = ??? ? + ? ? ? ?? = ? ? ? ? | ? ?=? = ?? ? ?? = ? ? ? ? | ? ?=? = ?? ? ?? = ? ? ? ? | ? ?=? = ? ? ?? = ? ? ? ? | ? ?=? = ? ?? = ?. ??? Option (d) 11. In the two network shown in the figure below Z12 and Z21 are, respectively
- 8. re I1 r0 I2 ¦ÂI1 (a) ?? ??? ??0 (b) 0 ??? ? ??0 (c) 0 ??? ??0 (d) ?? ??? ???0 [GATE 2006: 1 Mark] Soln. re I1 r0 I2 ¦ÂI1V1 V2 ? ? = ? ?? ? ? + ? ?? ? ? ? ? = ? ?? ? ? + ? ?? ? ? ? ?? = ? ? ? ? | ? ?=? When ? ? = ?, ? ? = ?, ?? ? ?? = ? ? ?? = ? ? ? ? | ? ?=? When ? ? = ?, ? ? = ??? ? ? ? ? ?? = ??? ? Option (b)
- 9. 12. For the two-port network shown, the short-circuit admittance parameter matrix is 1 0.5 0.5 2 0.5 1 ya yb yc (a) [ 4 ?2 ?2 4 ] ? (b) [ 1 ?0.5 ?0.5 4 ] ? (c) [ 1 ?0.5 0.5 1 ] ? (d) [ 4 2 2 4 ] ? [GATE 2010: 1 Mark] Soln. The short circuit admittance parameters of a two port ¦Ð network: ? ?? = ? ? + ? ? = ? ?.? + ? ?.? = ?? ? ?? = ? ?? = ?? ? = ? ? ?.? = ??? ? ?? = ? ? + ? ? = ? ?.? + ? ?.? = ?? Option (a) 13. If the scattering matrix [S] of a two port network is [?] = [0.2¡Ï00 0.9¡Ï00 0.9¡Ï00 0.1¡Ï00] Then the network is (a) Lossless and reciprocal (b) Lossless but not reciprocal (c) Not lossless but reciprocal (d) Neither lossless not reciprocal [GATE 2010: 1 Mark] Soln. For the reciprocal network | ? ??| = | ? ??| For a loss less network | ? ??| ? + | ? ??| ? = ? ( ?. ?) ? + ( ?. ?) ? ¡Ù ?
- 10. The network is lossy and reciprocal. Option (c) 14. In the circuit shown below, the network N is described by the following Y matrix: ? = [ 0.1? ?0.01? 0.01? 0.1? ] The voltage gain ?2 ?1 is (a) 1/90 (b) -1/90 (c) -1/99 (d) -1/11 [GATE 2011: 2 Marks] Soln. I1 I225 100 - V1 - V2 ++ N 100V ? ? = ? ?? ? ? + ? ?? ? ? = ?. ?? ? ? + ?. ? ? ? ? ? ? ? ? ? ? (?) ? ? = ?? ? ? ? = ????? ? ? ? = ?? ? ??? Substituting the value of I2 in equation (i) ?? ? ??? = ?. ??? ? + ?. ?? ? Or ? ? ? ? = ?? ?? Option (d)