We got a question from Lauren, who asked me to post it on her behalf. Let's see if we can help her out! She wrote:
I am a young engineer from New Hampshire. I was wondering whether
could be used to define the characteristic impedance of a transmission line instead of
and if NOT, why? What is the fundamental difference between a "uniform material" and a transmission line? A transmission line also has a permittivity and a permeability... why can't we use them to calculate impedance? Another point of confusion: intrinsic and characteristic impedance seem to be used analogously for propagating EM signals in a uniform medium and on a TL, respectively, so why would they be defined differently?
If eta CAN be used in place of Zo, this seems to imply that in a transmission line, the ratio of permeability to permittivity is the same as the ratio between the per-meter inductance to capacitance. Why?
And tangentially, how do we measure / design for per-meter inductance and capacitance in real life (e.g., how do we ensure that our 50 ohm TL is as close to 50 ohms as possible)?
Thank you so much, and thank you for your wonderful website!
Your first equation works for a plane wave. In other transmission lines, you need a version of the second equation. This is actually a complex question. I would start with "A general waveguide circuit theory" by Roger Marks and myself.
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