# Characteristic Impedance of Coax

Discussion in 'Wireless & RF Design' started by Pavlo138, Dec 30, 2009.

1. ### Pavlo138 Thread Starter Member

Feb 26, 2009
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Just out of curiosity, if anybody happens to know this,( I'm sure someone does), what exactly determines the characteristic impedance in coax? I understand that the shielding plays a role; but is it the material of the shielding or the distance of the shielding from the core, plus the dielectric constant of the jacket? If it's a combination of distance and dielectric constant, then it would seem to me to be impedance that is capacitive in nature. Thanks!

2. ### t_n_k AAC Fanatic!

Mar 6, 2009
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Z0 depends upon all the radial physical parameters including the dielectric constant of the insulation between the outer braid and core conductor. However, length doesn't come into the computation for Z0. One can perhaps argue that any length of a given coax has the same Z0.

Provided the load end of the coax is terminated in a value equal to Z0 then there will be no mismatch reflections set up in the cable (operating at RF) and the source will "see" an impedance equal to Z0.

The convention I was taught is that the characteristic impedance of a given coax cable type is the same as that observed when measuring the impedance of an infinite length of that cable.

Any coax has a certain resistance & inductance as well as capacitance per unit length.

Last edited: Dec 31, 2009
3. ### t_n_k AAC Fanatic!

Mar 6, 2009
5,448
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If you are interested there are a number of coaxial calculator programs around.

There is a nice visually interactive application for this function in the free RF calculator AppCAD, which may be downloaded via this link

http://www.hp.woodshot.com/

4. ### Pavlo138 Thread Starter Member

Feb 26, 2009
28
0
That is what I was taught as well; Z0 is the same for any given length of the cable. But thank you, that enforces my suspension that Z0 is determined by the radial properties.( I was thinking of the distance between the conductor and outer shell, the dielectric thickness.) And wow, thanks for the software! Looks really neat, cant wait to try it out. Again thankyou and have a Happy New Year!

Apr 5, 2008
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6. ### steveb Senior Member

Jul 3, 2008
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If you are looking for the actualy formula, here is what I have from the book "Fields and Waves in Communications Electronics", by Ramo, Whinnery and Duzer.

"We will assume the conductor spacing is large enough to neglect internal inductance. Using C [for capacitance per unit length] and L [for inductance per unit length], in $Z_o=\sqrt{{{L}\over{C}}}$ we find"

$Z_o={{ {\rm log_e} b/a }\over {2\pi}}\sqrt{{{\mu}\over{\epsilon}}}$

where $a$ and $b$ are the radii of the inner and outer conductors at the dielectric surfaces, respectively.

Note the previously given formulas in the text.

$C={{2\pi\epsilon}\over{ {\rm log_e} b/a }}$, which is capacitance per unit length in [F/m]

$L= {{\mu}\over{2\pi}} {\rm log_e} b/a$, which is inductance per unit length in [H/m] (assuming high frequency with little penetration into the conductors)

Feb 26, 2009
28
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8. ### Pavlo138 Thread Starter Member

Feb 26, 2009
28
0
This well explains it, thank you.