Characteristic Impedance vs Frequency

Question

I am reading this paper and I see that characteristic impedance does not take frequency into account. I am surprised by this as I figured different rise time signals would have different frequency content and see different impedances. Z0 is proportional to sqrt(L/C) and I figured those values change at different frequencies.

Are these characteristic impedance equations only valid for certain frequency range or am I wrong in assuming that characteristic impedance will have a frequency dependency?

https://www.polarinstruments.com/support/cits/IPC1999.pdf

Answer 1

I am reading this paper and I see that characteristic impedance does not take frequency into account.

At frequencies above about 100 kHz to 1 MHz, the characteristic impedance can be said to be \$\sqrt{L/C}\$ but, this doesn't account for lower frequencies where the characteristic impedance is: -

$$Z_0 = \sqrt{\dfrac{R+j\omega L}{G+j\omega C}}$$

_{Where R is the series resistance per unit length and G is the parallel conductance per unit length.}

• So, at really low frequencies we can say that \$Z_0\$ is \$\sqrt{R/G}\$.
• At mid-audio frequencies we can say that \$Z_0\$ is \$\sqrt{R/j\omega C}\$.

Here's an example of telephone cable that I calculated myself using excel: -

Extracted from my answer here.

Are these characteristic impedance equations only valid for certain frequency range or am I wrong in assuming that characteristic impedance will have a frequency dependency?

It has a frequency dependency for sure but, for track impedance calculations we are normally only interested in frequencies that are significantly above 1 MHz hence, \$Z_0 = \sqrt{L/C}\$.