undefined | unit 5 two port network and network functions

Unit - 5

Two Port Network and Network Functions

Q1) For the network shown below 1) show that with port 2) open the driving point input impedance 1π) b) find the voltage, ratio transfer function 1/2 for the two-port network.

A1) From above network we take L.T

Fig 1 Laplace Transform for above circuit

Reducing we get,

Z1= (25+25*1 / 25+1) *1

25+25*1 / 25+1*1

Z1=4S2+45/452+65+1

Z2=(1/4S/1/4+1/5+1/5) *2=1/45/1/4+1/3+1/5+2

=2(5+5+4) / 5+5+4+25(5+4) = 2(25+4)/252+10S+4

Z2=25+4/252+10+4

Applying KVL, in the circuit

V1=I1Z1+I, Z2 -----------1

V2= I1Z2 ...............2

.: V1=I1Z1+V

V1 / I1= (Z1+Z2) (from----1)

Dividing equation 2 by 1

G12=Z 2 / Z1+Z2

calculating z11 we have,

Z11=Z1+Z2

Z11 = 4S2+4S / 4S2+6S+1 * 2S+4/S2+SS+2

=(4S2+4S) (S2+SS+2) +(2S+4) (4S2+6S+1) / (4S2+6S+1) (S2+SS+2)

Z11=4S4+20S3+8S2+4S3+20S2+8S+8S3+12S2+25+16S2+4 /(4S2+6S+1) (S2+SS+2)

= (4S4+32S3+5652+345+4 / (4S2+6S+1) (S2+SS+2)

G12= Z2 / Z1+Z2

= (2S+4) / (S2+SS+2) / (4S+32S3+56S2+34S+4) / (4S2+6S+1) (S2+SS+)

G12= (2S+4) (4S2+6S+1) / 4S4+32S3+56S2+34S+4

Q2) For the network shown, find driving point input impedance. plot the pole zero pattern for each as well

Fig 2 (1) Circuit Diagram Fig 2(2) Circuit Diagram

A2): From Fig 2(1) taking L.T we have

Fig 3 Laplace for Fig 2(1) with roots

Z11= 1+ 1 /S/3+1/25+1/1/4S

=1+ 1/ 5/3+1/6S

=1+ 18S/6S2+3

Z11=6S2+3+18S/ 6S2+3 =2S2+6S+2/2S2+1

Zeros of equations are taking lt. of circuit b)

Fig 4 Laplace for Fig 2(2)

Z11= 1*4/5

=1+4/5+2.8/3/2+8/5+1

=4/5+4 + 16/ 25+8+1

= 4/5+4+8/5+4+1

=s+12+4/ (5+4)

Z11= S+16/(S+4)

For zeros of system

s+16=0

s=-16

for poles of system

s+4=0

s=-4

Q3) Find Z-parameter

A3) I1 = -I2

Current dependent so Z-parameter doesn’t exist

Q4) Find z-parameter

A4) V1 =R (I1 + I2)

V2 = R (I1 + I2)

Z11 = Z12 = Z21 = Z22 = R

Q5) Find z-parameter?

A5) 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)

Q6) Find z-parameter?

A6) 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 =

Q7) Find z parameter using conversion?

A7)

Z11 = I2=0

V1 - (Za + Zb) = 0

= Z11 =

Z21 = I2=0

V2 - Zb +Za = 0

Z12 =

Z22 =

Q8) Find Z21?

A8) Z21 = I2=0

I1/2 =

= I1

V2 = I1/2

= × I1

= I1

Z21 = I2 = 0 = I1 Ω

Q9) Find overall Y-parameter?

A9) V1 – I1R – V2 = 0

V1 – V2 = I1R

I1 = V1 - V2

V2 = I2R + V1

I2 = - V1 + V2

Y11 =

Y12 = Y21 =

Y22 =

The over all Y parameter is given as

Q10) Find overall Y-parameter

A10) Y-parameter does not exist as V1 = V2

Q11) Find overall Y-parameter?

A11) 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

Q12) Find overall Y-parameter?

A12)

The overall y parameter is given by

Q13) Find all the 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 the Transmission parameters?

A14) V1 = RI1 + V2 ----------------(1)

I2R = V2 – V1

I2 = V2 - V1

I2R = V2 – V1

V1 = I2R - V2 --------------------(2)

A = 1

B = R

From (2) in (1)

V2 - I2R = V2 + RI1

I2 = -I1

C = 0

D = 1

Q15) Find all the Transmission parameters?

A15) V1 = R (I1 + I2)

V2 = R (I1 + I2)

V1 = V2 + 0I2

A = 1

B = 0

V2 = RI1 + RI2

RI1= V2 - RI2

I1 = V2 – I2

C = , D = 1

Q16) Find all h-parameter?

A16)

+ = I1

V1 - = I1

V1 = + I1

- + 3I1 = I2

3I1 + V2 = I2

From (1)

I2 = 3I1 + V2 – [ I1 + V2]

I2 = I1 + V2

h11 =

h12 =

h21 =

h22 =

Q17) Find out overall transmission parameter?

A17)

Q18) Find overall Y-parameter?

A18)

Q19) Explain the series parallel connection of two port network. Derive the equations of h-parameter for the network?

A19)

I1 = I1a = I1b

V1 = V1a +V1b

If two 2-ports are connected in series parallel then overall h-parameter is sum of individual h-parameter

Q20) When the two-port network are connected in series which parameter is calculated. Derive and explain?

A20)

V1 = V1a +V1b

I1 = I1a = I1b

V2 = V2a +V2b

I2 = I2a = I2b

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