Understanding the S Parameter Matrix for Lossless Transmission Lines"

[EEuser]

Homework Statement

What is S(21) for a perfect Transmission Line?

Relevant Equations

See images below

If a perfect transmission line is lossless, then would the S parameter for a perfect transmission line be

?

Homework Equation: S parameter matrix

 

[collinsmark]

Disclaimer: It's been awhile since I've worked with two-port networks, so I might be a little rusty.

Homework Statement:: What is S(21) for a perfect Transmission Line?
Homework Equations:: See images below

If a perfect transmission line is lossless, then would the S parameter for a perfect transmission line be View attachment 255194?

Homework Equation: S parameter matrixView attachment 255195

Yes, you can say that S_{21} = b_2/a_1, but I suspect that's not the whole answer for what is being asked (I think).

You see, S_{21} = b_2/a_1 is always the case, so long as a_2 = 0, because that's how the parameters were measured. Even if the network involves some sort of lossy, complicated transformers and whatnot, that relationship still holds.

But I think you can get more specific. Knowing that the network is supposed to represent a perfect, lossless transmission line (without anything fancy), what is the relationship between a_1 and b_2?

That said, I don't know whether the intended answer is willing to accommodate a phase difference. Even a perfect, lossless transmission line might incur a phase difference if the transmission line is long. But in any case, you should be able to at least say something about the magnitude, | S_{21} |. If you're working with a DC network, ignore this paragraph and give the answer for S_{21} directly. If you're working with AC networks, then the answer might not be so simple since the parameter can be a complex number, but you should at least be able to say something about the parameter's magnitude.

 

[Jody]

My personal answer would just worry about the magnitude.

If I had a voltage source connected to a wire... let's call it a₁ and it's equal to 1V... then what voltage (b₁) would I expect to see other end of a perfect wire before connecting it to a chip that requires 1V?

If the above is confusing or doesn't work, then maybe thinking about this another way might work. If the wire is lossy and imperfect, then what would you not see on the other end?