# will Characteristic impedance of a TX line depends on frequency

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#### hioyo

Dear team

I read in many places characteristic impedance of a TX line does not depend on frequency.
But the below equation you can see frequency term(w)

Then why it does not depend on frequency Regards
HARI

For an IDEAL transmission line, it is assumed R and G are zero. Thus, the characteristic impedance is:

z=sqrt(L/C). The frequency term disappears. Like magic!

Ok but,for a real transmission line will it depend on frequency

Ok but,for a real transmission line will it depend on frequency
But for real cable parameters, only slightly for the frequencies it's designed for.
Typically R is low and G is high compared to the reactive values.
At low frequencies the value approaches the DC value of R/G.

But for real cable parameters, only slightly for the frequencies it's designed for.
Typically R is low and G is high compared to the reactive values.
At low frequencies the value approaches the DC value of R/G.
Which is why there are different cables for different frequencies.

Actually the lossy line model in post #1 doesn't reflect the behaviour of real transmission lines because R and G are also frequency dependent. The dominant loss parameter is conductor skin effect which results in R ~ sqrt(f) for those frequencies with a skin depth < conductor radius.

All in all, transmission line characteristic impedance is always frequency dependent, the variation is however small in frequency range of interest.

Hi,

You think in low frequency, where the wavelength of the signal is longer than the cable.
In your case the overall trace resistance, imepdance, capacitance... counts.
But this is not the "characteristic" impedance. It´s the total cable impedance.
For sure the total cable impedance depends on frequency .. and btw on cable length, too.

The characteristic impedance however is when the cable length is bigger than the signal wavelength.
Then the signal (edge) of interest maybe is just 0.2m in length while the cable may be is 10m in total.
So for the signal only the 0.2m is of interest.

For a better understanding you may look for videos about "characteristic impedance" or "traveling wave" or similar.

Klaus

From Eric Bogatians Signal and power integrity simplified it defines characteristic impedance as shown below It says characteristic impedance is inversely proportional to CL = the capacitance per length of the line, in pF/inch.

So in my understanding characteristic impedance depends on
1)Trace width
2)Height above the dielectric
3) Dielectric constant

It does not depend on frequency, length

Please correct me if I am wrong

It's correct within the scope of your question. Lossless or almost lossless transmission line and frequency independent dielectric medium. In terms of post #1 and #4 negligible R and G values, constant R and L.

• hioyo

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