Unit - 5
Two-port network and Filters
Q1) Find overall Y-parameter?
A1) V1 – I1R – V2 = 0
V1 – V2 = I1R
I1 = V1 - V2
V2 = I2R + V1
I2 = - V1 + V2
Y11 =
Y12 = Y21 =
Y22 =
Q2) Find overall Y-parameter?
A2) Y-parameter does not exist as V1 = V2
Q3) Find overall Y-parameter?
A3) I1 = V1Ya + (V1 – V2)Yc
I1 = (Ya + Yc)V1 - YcV2
I2 = V2Yb + (V2 – V1)Yc
I1 = (Yb + Yc)V2 - YcV1
Y11 = Yb + Yc
Y12 = Y21 = - Yc
Y22 = Yb + Yc
Q4) Find overall Y-parameter?
A4)
Q5) Find overall Y-parameter?
A5)
-I1 + – 2V2 + + 2V1 = 0
I1= V1 + V1 - 3V2 + 2V1
I1= 4V1 - 3V2V
V2 + 2V2- 2V1 = 2(I2 + 2V1)
- 2V1 + 3V2 = 2(I2 + 2V1)
3V2 - 2V1 – 4V1 = 2I2
I2 = -3V1 + V2
Y11 = 4
Y12 = -3
Y21 = -3
Y22 =
Q6) Find Z-parameter
A6) I1 = -I2
Current dependent so Z-parameter doesn’t exist
Q7) Find Z-parameter
A7) V1 =R (I1 + I2)
V2 = R (I1 + I2)
Z11 = Z12 = Z21 = Z22 = R
Q8) Find Z-parameter
A8) V1 = I1Za + I1Zc + I2Zc
= (Za + Zc)I1 + ZcI2
V2 = I2Zb + I2Zc + I1Zc
= (Zb + Zc)I1 + ZcI1
Z11 = (Za + Zc)
Z12 = Zc = Z21
Z22 = (Zb + Zc)
Q9) Find Z-parameter
A9) V1 = Za(I1 - I)
(I - I1)Za+ IZc+ Zb(I + I2) = 0
I(Za + Zb + Zc) – I1Za + I2Zb = 0
I =
V1 = ZaI1 - Za
= I1 + I2
V2 = Zb(I2 + I)
= ZbI2 + Zb
= I2 + I2
Z11 =
Z12 = Z21 =
Z22 =
Can be solved by Y-A conversion
Q10) Find Z-parameter
A10)
Z11 = I2=0
V1 - (Za + Zb) = 0
= Z11 =
Z21 = I2=0
V2 - Zb +Za = 0
=
Z12 =
Z22 =
Q11) Find Z21?
A11) Z21 = I2=0
I1/2 =
= I1
V2 = I1/2
= × I1
= I1
Z21 = I2 = 0 = I1 Ω
Q12) Find overall z-parameter?
A12) + + 2V1 = 0
2Vx – 2V1 + Vx – V2 + 2V1 = 0
3Vx = V2
Vx =
I1 = V1 +
= 3V1 – 2Vx
= 3V1 – 2
V1 =
+ 2V2 = I2
3V2 - = I2
V2 = I2
V2 = I2
V1 =
=
Z11 =
Z12 =
Z21 = 0
Z22 =
Q13) Find Transmission parameters?
A13)
-3V1 – I1 + + = 0
+ = I1
V1 – V2 = I1
V1 = V2 + I1
V1= V2- I1----------------(1)
I2 = 3V1 + V2 + V2 – V1
I2 = 2V1 + 2V2
2V1 = I2 - 2V2
2V1 = - 2V2 + I2
V1 = -V2 + I2 ----------------(2)
A = -1
B =
From (1) & (2)
-V2 + I2 = I1 - V2
V2 - V2 + I2 = I1
I1 = V2 + V2 - I2
I1 = V2 - I2
C =
D =
Q14) Find all h-parameter?
A14) + = I1
V1 - = I1
V1 = + I1
V1 = + I1
- + 3I1 = I2
3I1 + V2 = I2
From (1)
I2 = 3I1 + V2 – [ I1 + V2]
I2 = I1 + V2
h11 =
h12 =
h21 =
h22 =
Q15) A LPF circuit consisting of a resistor of 40KΩ in series with capacitor 47nF across a 10V sinusoidal supply. Calculate VO at frequency 1Kz?
A15)
R = 40KΩ
C = 47nF
Vi = 10V
F = 1000 Hz
For LPF,
Capacitive Reactance is XC
The output voltage is given as
VO = Vi
XC = =
XC = 3.386KΩ
VO =
=10 x
= 10 x
VO = 0.843 V
(b) RL LPF
FC = R / 2nt
VO = Vi
Q16) An RL LPF consists of a 5.6mH coil a 3.3 KΩ resistor. The output voltage is taken across the resistor. Calculate the critical frequency?
A16) Given:
L = 5.6 x 10-3 H
R = 3.3 x 103Ω
For RL LPF
F ==
F = 93.78 KHz
Q17) A sinusoidal voltage with a peak to the peak value of 10 V is applied to an RC LPF. If reactance at the input is zero, find output voltage?
A17)
VO =
XC =
F = XC = 0, F ->∞
Hence, VO = 0V.
Q18) An RC – LPF consists of a 120 Ω resistor and 0.02 µF capacitor. The output is taken through the capacitor. Calculate the critical frequency?
A18) For RC LPF FC is given as
FC==
FC = 66.31 KHz