Transmission line and measuring Zo

[TheRedDevil18]

Homework Statement

Figure 2:

Homework Equations

The Attempt at a Solution

3.2) I made an equation for the input voltage and input current
Vi = Vs*(Zi)/(Zi+Rs+Rm)

Ii = Vs/(Zi+Rs+Rm)

I am a bit confused about what voltages V1 and V2 are measuring, and what do they mean by using the phase ?, I don't know the phase

3.3) After some research I found this equation for a twisted pair cable

Though I'm not sure what to use for Er. On the site it says
εR=(c/v)^2

but I don't know the velocity of the signal

http://www.sigcon.com/Pubs/edn/TwistedImpedance.htm

 

[tech99]

Homework Statement

View attachment 104936
Figure 2:
View attachment 104937

Homework Equations

The Attempt at a Solution

3.2) I made an equation for the input voltage and input current
Vi = Vs*(Zi)/(Zi+Rs+Rm)

Ii = Vs/(Zi+Rs+Rm)

I am a bit confused about what voltages V1 and V2 are measuring, and what do they mean by using the phase ?, I don't know the phase

3.3) After some research I found this equation for a twisted pair cable

Though I'm not sure what to use for Er. On the site it says
εR=(c/v)^2

but I don't know the velocity of the signal

http://www.sigcon.com/Pubs/edn/TwistedImpedance.htm

No none else answering yet, this is my best shot:-
1) One of the methods of finding Zo is from Zo = SQRT (Zoc * Zsc)
To find Zsc and Zoc, the test circuit is used to find an unknown impedance.
I am a simple person, so I think you can solve the test circuit using a phasor diagram, but it is a bit complicated. Take Ii as the reference, as it is a series circuit, and then V50, Vrm and V2 will add up vectorially to Vs. V50 and Vrm are in phase with Ii and are found from Ii using Ohm's Law. Then the complex ratio of V2/Ii give the cable input impedance.
2) The question is very weak on the matter of dielectric, because the conductors have only a thin covering and are not embedded in the dielectric. So we presume Er may lie somewhere between air=1 and polyethylene=2.3.
You have my total sympathy with this laborious question.

 

[TheRedDevil18]

No none else answering yet, this is my best shot:-
1) One of the methods of finding Zo is from Zo = SQRT (Zoc * Zsc)
To find Zsc and Zoc, the test circuit is used to find an unknown impedance.
I am a simple person, so I think you can solve the test circuit using a phasor diagram, but it is a bit complicated. Take Ii as the reference, as it is a series circuit, and then V50, Vrm and V2 will add up vectorially to Vs. V50 and Vrm are in phase with Ii and are found from Ii using Ohm's Law. Then the complex ratio of V2/Ii give the cable input impedance.
2) The question is very weak on the matter of dielectric, because the conductors have only a thin covering and are not embedded in the dielectric. So we presume Er may lie somewhere between air=1 and polyethylene=2.3.
You have my total sympathy with this laborious question.

Thanks for the reply, I have a few questions,

By V50, You mean the the signal generator impedance voltage ?
V2 is measuring the input voltage to the transmission line or the input impedance voltage ?
And what voltage is V1 measuring ?

 

[tech99]

Thanks for the reply, I have a few questions,

By V50, You mean the the signal generator impedance voltage ?
V2 is measuring the input voltage to the transmission line or the input impedance voltage ?
And what voltage is V1 measuring ?

V50 is the voltage across Rs.
V2 is the voltage across the line at its input point.
V1 is the voltage across the output terminals of the signal generator.

 

[rude man]

Though I'm not sure what to use for Er. On the site it says
εR=(c/v)^2
but I don't know the velocity of the signal

Assume air as the dielectric. What is ε_r for air?
Also assume lossless line.
There is a formula stating that V₂ = V₂(V₃, θ, Z₂, Z₀).
θ = βx, γ = jβ and x = physical line length. So θ is unknown.
But you know V₂, V₃ and Z₂ for 2 cases so you have 2 equations and 2 unknowns so you can solve for γ and Z₀.

These of course are all phasors, i.e. voltages with attendant phase shifts.

 

[tech99]

Assume air as the dielectric. What is ε_r for air?
Also assume lossless line.
There is a formula stating that V₂ = V₂(V₃, θ, Z₂, Z₀).
θ = βx, γ = jβ and x = physical line length. So θ is unknown.
But you know V₂, V₃ and Z₂ for 2 cases so you have 2 equations and 2 unknowns so you can solve for γ and Z₀.

These of course are all phasors, i.e. voltages with attendant phase shifts.

I don't think we are given the line length and velocity factor.

 

[TheRedDevil18]

Can't I just use a voltage divider ?

V2 = Vs*(Zin)/(Zin+Rs+Rm)

Since we know V2, Vs, Rs and Rm we can calculate Zin

 

[tech99]

Can't I just use a voltage divider ?

V2 = Vs*(Zin)/(Zin+Rs+Rm)

Since we know V2, Vs, Rs and Rm we can calculate Zin

This not accurate because Zin is possibly reactive.

 

[rude man]

I don't think we are given the line length and velocity factor.

As I said, line length x is an unknown. But you will solve for θ so forget x. x and θ are related per what I gave you.

 

[rude man]

Can't I just use a voltage divider ?

V2 = Vs*(Zin)/(Zin+Rs+Rm)

Since we know V2, Vs, Rs and Rm we can calculate Zin

How do you propose to solve for Z₀ and γ?

 

[rude man]

This not accurate because Zin is possibly reactive.

It's "accurate" but it's no help.

 

[TheRedDevil18]

How do you propose to solve for Z₀ and γ?

I forgot to note that the length of the transmission line is known, 56m. Their is a formula for calculating Zo

So Zsc would be the input impedance I measure when the load is short circuited. And Zoc would be the input impedance I measure when their is no load

And for a open circuit line,

And for short circuit,

So once I have found Zoc and Zsc and hence Zo, I can use one of the above equations to calculate Beta = Gamma

 

[rude man]

How do you propose to get β?

 

[TheRedDevil18]

How do you propose to get β?

By finding the input impedance, for example Zsc using the voltage divider equation
V2 = Vs*(Zin)/(Zin+Rs+Rm)

Then finding Zoc, using the same equation but for open circuit

Then Zo, using this equation

And since I have Zsc and Zoc, I can use either of the equations I listed above to solve for Beta

I have the length of the line = 56m

 

[rude man]

I forgot to note that the length of the transmission line is known, 56m. Their is a formula for calculating Zo
View attachment 104974

So Zsc would be the input impedance I measure when the load is short circuited. And Zoc would be the input impedance I measure when their is no load

View attachment 104970

View attachment 104971

And for a open circuit line,
View attachment 104972

And for short circuit,
View attachment 104973

So once I have found Zoc and Zsc and hence Zo, I can use one of the above equations to calculate Beta = Gamma

Looks good now RedDevil!

 

[TheRedDevil18]

Thanks guys