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let's consider a generic transmission line: enter image description here

Its wave vector Kz is equal to:

enter image description here

where

enter image description here

Then, I read also that it is true that:

enter image description here

where does this relation come from?

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The wavenumber \$k\$ is the result of solving the differential equations of the (general) electromagnetic wave for \$E\$ and \$H\$ in e.g. free space. The result for \$k\$ consists of the material characteristics \$\mu,\epsilon,\sigma\$.

When solving the telegrapher equations for the coaxial cable, you also get \$k\$, but this time \$k\$ consists of an R,L,G & C expression.

So the wavenumber \$k\$ comes either from the definition of a general wave or from the definition of a generic transmission line like e.g. a coaxial cable.

(The phase constant \$\beta\$ is just the imaginary component of \$k\$.)

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  • \$\begingroup\$ But where does the link k= √(YZ) = k = 2π/lambda? Why are they necessarily equal in case of TEM mode? \$\endgroup\$ – Kinka-Byo Nov 16 '19 at 11:39
  • \$\begingroup\$ @Kinka-Byo I refined my anwer to give you a bit more insight \$\endgroup\$ – Stefan Wyss Nov 18 '19 at 5:56

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