antenna-theory.com

[AZ]

Hello,

I read most of the tutorials a few months ago and I am sure I have read this information somewhere here. However, now I am unable to find this information again.

I remember it was derived from an equation but where ?

Any clue or even better, any link ?

[admin]

Not derived from any equation. An antenna should be matched to it's transmission line or receiver - typically 50 Ohms.

TV antennas usually need to be about 300 Ohms, hence a folded dipole is often used.

There is no universal reason on why 50 Ohms is used.

[keepmoving]

there are some reasons:
1. 35 ohm, the coax can transmit maximum power;
2 73 ohm, the coax can be minimum attenuation;

so, we choose 50 ohm.
hope it can help you.

[admin]

That is interesting. Do you have a reference?

I believe the max power and minimum attenuation values would be highly dependent on the type of transmission line (and for that matter, size/type/material of coaxial cable), so I'm not sure that would be a universal rule.

For instance, if minimum attenuation always occurred at 73 ohms for transmission lines, then gps transmission lines should be set at 73 ohms, as they don't transmit any power. But gps receivers are 50 ohms as well.

Let me know if you have more info on this. Thanks

[keepmoving]

I'm sorry..
maybe I don't say clearly. what I said is just about coaxial without medium..

[doug]

73 ohms gives the minimum attenuation. if you stuff it full of Teflon you get 50 ohms. maybe that's why we generally use 50 ohms

[NSmith]

Microwaves101.com has a great write up on this topic found here...
http://www.microwaves101.com/encyclopedia/why50ohms.cfm

The short version is that they derive air core numbers for the optimum for power(30ohm) and loss (77ohm). Arithmetic mean of 53 and geometric mean of 48. They suggest a convenient compromise led to the 50 ohm standard.

I wont spoil there conclusion on the PTFE filled coax for CATV because its an interesting read.

-Nick-

[admin]

Good link, and I'll say I stand corrected.

However it also looks like these derivations depend on the materials of the transmission line (conductivity of dielectric and conductors), so they probably aren't universal

[NSmith]

I agree that it does depend on the insulating material. Keep in mind that the author speaks to this standard being in place based on air insulator construction. Any time these sort of things come up it makes you wonder what the analysis would be with modern materials and would the standard be different if it was re-addressed and legacy support was not an issue.

-Nick-

[R. Fry]

The equation for the characteristic impedance of coaxial transmission line is:

Zo = (138/e^1/2) * log(D/d)

e = dielectric constant
D = inside diameter of outer conductor
d = outside diameter of inner conductor
(log to the base 10)

EIA standard coax line having a nominal outside diameter of 3-1/8" is commonly used by broadcast stations. The inside diameter of its outer conductor is 3.027", and the outer diameter of its inner conductor is 1.315". The inner conductor is supported by perforated Teflon rings at intervals along the line. For dry air within the line, the dielectric constant is very close to unity (space), and the velocity of propagation is about 0.997c. Its Zo based on these values is 49.9679602 ohms.

Coax using solid polyethylene has a dielectric constant of 2.25, so for Zo = 50 ohms, the outer diameter of its inner conductor would need to be reduced by about 1/3 from the value producing 50 ohms for an air dielectric. Its velocity of propagation is about 0.66c, typically.