### Why 50 ohm? - Part 2 of 2

Many years back, I attended a seminar on RF measurment conducted by Agilent Technologies, Innovating the HP Way at the Equatorial Hotel. The presentation material was binded as a nice book having the catch phrase "Strong Basics Today For Tomorrow". The presenter touched a little on this interesting topic too.

First of all, we must not confuse characteristic impedance (Zo) with impedance (Z). The former is a function of the physical cross-section dimension and dielectric constant (Er). It is never a function of length and frequency. Therefore, the characteristic impedance will always remain the same even when length and frequency changes. This is true for all the RF transmission line, which could be coaxial cable, waveguide, micro-strip, strip line, coplanar, wire-over-ground-plane, twisted pair, etc.

The characteristic impedance for a coax line can be caculated using,

Zo = (60/sqrt(Er))*ln(D/d),

where d is the diameter of the center conductor,

and D is the inner diameter of the cable shield.

Characteristic impedance of 30-ohm is found to be the best for maximum power-carrying capability. On the other hand, lowest attenuation can be achieved with the characteristic impedance of 77 ohms. Therefore, 50-ohm is chosen as a compromise between minimum loss and maximum power handling.

From the information gathered from e-panorama.net, it was mentioned that in the early days, the 77-ohm characteristic impedance was acheived using air as the dielectric. Low attenuation is also the over-riding factor for the selection of 77-ohm. This resulted in hardware of certain fixed dimension. When polyethylene, with the dielectric constant of 2.3 is used to fill the air line, the characteristic impedance becomes approximately 51 ohms. For "precision purposes", 50 ohms and 75 ohms are used instead of 51 ohms and 77 ohms.

This also explains why the Ku-pan and the C-kuali on the roof are connected to the decoder using 75-ohm RG-6U coaxial cable.

Well, there is one more reason for the use of coaxial cable with 50-ohm characteristic impedance. A quarter wave antenna with drooping (bent downwards) quarter wave radials at 42 degrees to the horizontal exhibits a feed point impedance of 50 ohms. I was also told that the Marconi antenna (a quarter wave antenna with a perfect ground) is also having an impedance of 50-ohm. Anyway, note that this is impedance, not characteristic impedance.

OK, too much crap for tonight, and it is time to get some sleep. 73.