Two Port Network: Calculate Characteristic Impedance (Z0)

[agata78]

Homework Statement

Calculate the characteristic impedance ( Z0) of the two port network shown below:

Could you help me with this question please.

Homework Equations

The Attempt at a Solution

 

[gneill]

agata78, the Relevant Equations and Attempt at a Solution sections are not optional. If you want help, you'll have to show your attempt first so we'll know how to help you. We can't do your homework for you!

 

[agata78]

Calculate the characteristic impedance (Z0) of the two port network shown below:

In this example :
R1 = 40 ohm
R2 = 40 ohm
R3 = 20 ohm

V1 = I1 (R1+R2)

Then, Z11 = V1/I1 = R1+R3 = 40+20 = 60 ohm

V2 = V1 (R3 / R1+R3) = I1 (R3+ R1) (R3 / (R1+R3)) = I1 R3

Then, Z21 = V2 / I1 = R3 = 20 ohm

Am I correct so far?

 

[gneill]

Calculate the characteristic impedance (Z0) of the two port network shown below:

In this example :
R1 = 40 ohm
R2 = 40 ohm
R3 = 20 ohm

V1 = I1 (R1+R2)

Then, Z11 = V1/I1 = R1+R3 = 40+20 = 60 ohm

V2 = V1 (R3 / R1+R3) = I1 (R3+ R1) (R3 / (R1+R3)) = I1 R3

Then, Z21 = V2 / I1 = R3 = 20 ohm

Am I correct so far?

Sure. Note that you can drive a port with a current source rather than a voltage source. This might make some of your work easier, not having to fiddle about with voltage dividers and determining the input current separately.

For example, for Z21 if you drive I1 into the first port then the output voltage on the second port is clearly V2 = I1*20Ω, yielding V2/I1 = 20Ω.

 

[agata78]

I found the way to calculate T network, where Zor is a characteristic impedance

Zoc= R1 + R2 = 40 + 20 = 60Ω

Zso = (R1 * R2 ) /( R1 + R2 ) + R1

Zso= (40 + 20) / (40+ 20 ) + 40

Zso= 800/ 60 + 40 = 13.333+ 40 = 53.333Ω


Zor= √ Zoc Zsc = √60 + 53.333= √ 113.333 = 10.645 Ω

I hope I am on right path this time

 

[cpscdave]

This may or may not help you or not...
But the key moment when I was learning 2 port neworks is that Z and Y (I think don't have access to my notes atm) are bassically you just doing Mesh and Nodal Analysis

 

[agata78]

I am still confused. Is the workings out in my previous posting correct or incorrect?

I don't want to start going down the wrong track.

 

[The Electrician]

I found the way to calculate T network, where Zor is a characteristic impedance

Zoc= R1 + R2 = 40 + 20 = 60Ω

Zso = (R1 * R2 ) /( R1 + R2 ) + R1

Zso= (40 + 20) / (40+ 20 ) + 40

Zso= 800/ 60 + 40 = 13.333+ 40 = 53.333Ω


Zor= √ Zoc Zsc = √60 + 53.333= √ 113.333 = 10.645 Ω

I hope I am on right path this time

The part in red is incorrect. You have Zor = sqrt(Zoc) + Zsc

It should be Zor = sqrt(Zoc * Zsc) = sqrt(60 * 53.333) = sqrt(3200) = 56.57

 

[agata78]

Zoc = R1 + R2 = 40 + 20 = 60Ω

Zso = (R1 * R2 ) /( R1 + R2 ) + R1

Zso = (40 + 20) / (40+ 20 ) + 40

Zso = 800/ 60 + 40 = 13.333+ 40 = 53.333ΩZor = √ Zoc Zsc = √60 x 53.333 = √ 3200 = 56.568

Characteristic Impedance = 56.57 Ω

Thanks for your help! Can you please let me know that this is the correct answer for the Characteristic Impedance or is there further calculations?

 

[The Electrician]

This is correct.