Two Port Networks
1. Two Two-port networks are connected in cascade. The combination is to the represented as a single two – port network, by multiplying the individual (a) z-parameter matrices (c) y-parameter matrices (b) h-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 (c) h21 = -h12 (b) y21 = y12 (d) AD – BC = 0 [GATE 1992: 2 Marks]
Soln. 풚ퟐퟏ = 풚ퟏퟐ
풉ퟐ = −풉ퟏퟐ
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 – BC = 1
4. In the circuit of figure, the equivalent impedance seen across terminals A, B is
A
2 4 j 2
Zeq a b -j 2
2 4 B
(a) (16/3) Ω (c) (8/3 + 12j) Ω (b) (8/3) Ω (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
풁풆풒 = (ퟐ‖ퟒ) + (ퟐ‖ퟒ)
ퟒ ퟒ ퟖ = + = ퟑ ퟑ ퟑ Option (b)
5. The short-circuit admittance matrix of a two-port network is 0 −1⁄ [ 2] 1 ⁄2 0 The two – port network is (a) non – reciprocal and passive (c) reciprocal and passive (b) non – reciprocal and active (d) reciprocal and active [GATE 1998: 1 Marks]
Soln. 풚ퟏퟐ ≠ 풚ퟐퟏ 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
I1 I2 + + R R
V1 R V2
- - (a) -1/2 (c) -3/2 (b) +1/2 (d) +3/2 [GATE 1999: 1 Mark]
Soln. 푽ퟏ = 풉ퟏퟏ푰ퟏ + 풉ퟏퟐ푽ퟐ
푰ퟐ = 풉ퟐퟏ푰ퟏ + 풉ퟐퟐ푽ퟐ
푰ퟏ 풉ퟐퟏ = |푽ퟐ=ퟎ 푰ퟐ
푽ퟐ = 푹푰ퟐ + 푹(푰ퟏ + 푰ퟐ)
Or ퟐ푹푰ퟐ + 푹푰ퟏ = 푽ퟐ
When 푽ퟐ = ퟎ, ퟐ푹푰ퟐ + 푹푰ퟏ = ퟎ 푰 −푹 ퟏ So, ퟐ = = − 푰ퟏ ퟐ푹 ퟐ Option (a)
7. The admittance parameter Y12 in the 2-port network in figure is
I1 20 I2
E1 5 5 E2
(a) -0.2 nho (c) -0.05 mho (b) 0.1 mho (d) 0.05 mho [GATE 2001: 1 Mark]
ퟏ Soln. 풚 = − = −ퟎ. ퟎퟓ 풎풉풐풔 ퟏퟐ ퟐퟎ
Option (c)
8. The Z parameters Z11 and Z21 for the 2-port network in the figure are
I1 2 I2 4
E1 E2
10E1
−6 16 6 −16 (a) 푍 = Ω, 푍 = Ω (c) 푍 = Ω, 푍 = Ω 11 11 21 11 11 11 21 11 6 4 4 4 (b) 푍 = Ω, 푍 = Ω (d) 푍 = Ω, 푍 = Ω 11 11 21 11 11 11 21 11 [GATE 2001: 2 Marks]
Soln. For z – parameters
푬ퟏ = 풁ퟏퟏ푰ퟏ + 풁ퟏퟐ푰ퟐ
푬ퟐ = 풁ퟐퟏ푰ퟏ + 풁ퟐퟐ푰ퟐ
Writing KVL in LHS loop
푬ퟏ = ퟐ푰ퟏ + ퟒ푰ퟏ + ퟒ푰ퟐ − ퟏퟎ푬ퟏ
Or ퟏퟏ푬ퟏ = ퟔ푰ퟏ + ퟒ푰ퟐ − − − −(푰)
푬ퟏ ퟔ 풁ퟏퟏ = |푰ퟐ=ퟎ = Ω 푰ퟏ ퟏퟏ
푬ퟏ ퟒ 풁ퟏퟐ = |푰ퟏ=ퟎ = Ω 푰ퟐ ퟏퟏ
Writing KVL in RHS Loop
푬ퟐ = ퟒ(푰ퟏ + 푰ퟐ) − ퟏퟎ푬ퟏ − − − − − (푰푰) ퟔ푰 +ퟒ푰 Substituting 푬 = ퟏ ퟐ 풊풏 풆풒풖풂풕풊풐풏 − −(푰푰푰) ퟏ ퟏퟏ
ퟏퟎ(ퟔ푰 +ퟒ푰 ) 푬 = ퟒ(푰 + 푰 ) − ퟏ ퟐ ퟐ ퟏ ퟐ ퟏퟏ
푬ퟐ −ퟏퟔ 풁ퟐퟏ = |푰ퟐ=ퟎ = Ω 푰ퟏ ퟏퟏ
Option (c)
9. The impedance parameters Z11 and Z12 of the two-port network in the figure are
2 2 2 1 2
1 1
1 2
(a) 푍11 = 2.75Ω 푎푛푑 푍12 = 0.25 Ω (c) 푍11 = 3 Ω 푎푛푑 푍12 = 0.25Ω (b) 푍11 = 3 Ω 푎푛푑 푍12 = 0.5Ω (d) 푍11 = 2.25Ω 푎푛푑 푍12 = 0.5 Ω [GATE 2003: 2 Marks]
Soln. Using ∆ − 풀 conversion, the circuit reduces to
2 0.5 0.5 2
Z1 Z2
Z3 0.25
풁ퟏퟏ = 풁ퟏ + 풁ퟑ = ퟐ. ퟓ + ퟎ. ퟐퟓ = ퟐ. ퟕퟓΩ
풁ퟏퟐ = 풁ퟑ = ퟎ. ퟐퟓΩ
Option (a)
10. The h parameter of the circuit shown in the figure are
I1 I 10 2 + +
V1 20 V2
- -
0.1 0.1 30 20 (a) [ ] (c) [ ] −0.1 0.3 20 30 10 −1 10 1 (b) [ ] (d) [ ] 1 0.05 −1 0.05 [GATE 2005: 2 Marks]
Soln. 푽ퟏ = 풉ퟏퟏ푰ퟏ + 풉ퟏퟐ푽ퟐ
푰ퟐ = 풉ퟐퟏ푰ퟏ + 풉ퟐퟐ푽ퟐ Writing KVL in LHS and RHS Loop
푽ퟏ = ퟏퟎ푰ퟏ + ퟐퟎ(푰ퟏ + 푰ퟐ) − − − − − −(풊)
푽ퟐ = ퟐퟎ(푰ퟐ + 푰ퟏ) − − − − − −(풊풊)
Or 푽ퟏ = ퟏퟎ푰ퟏ + 푽ퟐ
푽ퟏ 풉ퟏퟏ = |푽ퟐ=ퟎ = ퟏퟎ 푰ퟏ
푰ퟐ 풉ퟐퟏ = |푽ퟐ=ퟎ = −ퟏ 푰ퟏ
푽ퟏ 풉ퟏퟐ = |푰ퟏ=ퟎ = ퟏ 푽ퟐ
푰ퟐ ퟏ
풉ퟐퟐ = |푰ퟏ=ퟎ = = ퟎ. ퟎퟓΩ 푽ퟐ ퟐퟎ
Option (d)
11. In the two network shown in the figure below Z12 and Z21 are, respectively
I1 I2
re βI1 r0
(a) 푟푒 푎푛푑 훽푟0 (c) 0 푎푛푑 훽푟0 (b) 0 푎푛푑 − 훽푟0 (d) 푟푒 푎푛푑 −훽푟0 [GATE 2006: 1 Mark]
Soln.
I1 I2
V1 re βI1 r0 V2
푽ퟏ = 풁ퟏퟏ푰ퟏ + 풁ퟏퟐ푰ퟐ
푽ퟐ = 풁ퟐퟏ푰ퟏ + 풁ퟐퟐ푰ퟐ
푽ퟏ 풁ퟏퟐ = |푰ퟏ=ퟎ 푰ퟐ
When 푰ퟏ = ퟎ, 푽ퟏ = ퟎ, 풔풐 풁ퟏퟐ = ퟎ
푽ퟐ 풁ퟐퟏ = |푽ퟐ=ퟎ 푰ퟏ
When 푰ퟐ = ퟎ, 푽ퟐ = −휷푰ퟏ풓ퟎ
풁ퟐퟏ = −휷풓ퟎ
Option (b)
12. For the two-port network shown, the short-circuit admittance parameter matrix is
0.5 1 2 yb
0.5 ya yc 0.5
1
4 −2 1 −0.5 (a) [ ] 푆 (c) [ ] 푆 −2 4 0.5 1 1 −0.5 4 2 (b) [ ] 푆 (d) [ ] 푆 −0.5 4 2 4 [GATE 2010: 1 Mark]
Soln. The short circuit admittance parameters of a two port π network:
ퟏ ퟏ 풚 = 풚 + 풚 = + = ퟒΩ ퟏퟏ 풂 풃 ퟎ.ퟓ ퟎ.ퟓ ퟏ 풚 = 풚 = −풚 = − = −ퟐΩ ퟏퟐ ퟐퟏ 풃 ퟎ.ퟓ ퟏ ퟏ 풚 = 풚 + 풚 = + = ퟒΩ ퟐퟐ 풃 풄 ퟎ.ퟓ ퟎ.ퟓ
Option (a)
13. If the scattering matrix [S] of a two port network is 0 0 [푆] = [0.2∠0 0.9∠0 ] 0.9∠00 0.1∠00 Then the network is (a) Lossless and reciprocal (c) Not lossless but reciprocal (b) Lossless but not reciprocal (d) Neither lossless not reciprocal [GATE 2010: 1 Mark]
Soln. For the reciprocal network |푺ퟏퟐ| = |푺ퟐퟏ|
ퟐ ퟐ For a loss less network |푺ퟏퟏ| + |푺ퟏퟐ| = ퟏ
(ퟎ. ퟐ)ퟐ + (ퟎ. ퟗ)ퟐ ≠ ퟏ
The network is lossy and reciprocal.
Option (c)
14. In the circuit shown below, the network N is described by the following Y matrix:
0.1푆 −0.01푆 푉2 푌 = [ ] The voltage gain is 0.01푆 0.1푆 푉1
(a) 1/90 (c) -1/99 (b) -1/90 (d) -1/11 [GATE 2011: 2 Marks]
Soln.
25 I1 I2 + + N 100 100V V -1 V-2
푰ퟐ = 풚ퟐퟏ푽ퟏ + 풚ퟐퟐ푽ퟐ
= ퟎ. ퟎퟏ 푽ퟏ + ퟎ. ퟏ 푽ퟐ − − − − − − − (풊)
푽ퟐ = −푰ퟐ푹푳 = −ퟏퟎퟎ푰ퟐ −푽 푰 = ퟐ ퟐ ퟏퟎퟎ
Substituting the value of I2 in equation (i)
−푽ퟐ = ퟎ. ퟎퟏ푽 + ퟎ. ퟏ푽 ퟏퟎퟎ ퟏ ퟐ
푽ퟐ −ퟏ Or = 푽ퟏ ퟏퟏ
Option (d)