Wednesday, September 21, 2005

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, 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.

Tuesday, September 20, 2005

Why 50 ohm? - Part 1 of 2

Back in the old days where people had just started to have Local Area Network in the office, the Thin Ethernet was the popular choice. It was widely used becuase it was one of the simplest and cheapest implementations. It is also known as the 10 Baseband 2 or the IEEE 802.3a. All computer are connected to each other on RG-58 coaxial cable using the BNC T-connector. One end of the bus is terminated with a grounded 50-ohm terminator, while the other end has an ungrounded 50-ohm terminator. On Saturdays, I followed some friends, who owned a small "IT solution" company, to perform LAN installation at those small/medium industry (SMI) companies. That was back in the year 1993 ~ 1995.

RG-58 coaxial cable has been long enough before the invention of Thin Ethernet. As you and I know, it is the transmission cable used by many hams. It is the life line between the rig and the antenna. Besides RG-58, there are RG-174, RG-223, RG-8, Belden 9913, etc. Other than they are all coaxial cables, they share one thing in common, i.e. they are all having the characteristic impedance of 50 ohms.

When I started to involve in this ham radio hobby, the "why 50-ohm" question is revisited. In the quest for an explanation, I never stop asking people on this topic. Many tried their best to share, thank you very much. Some, on the other hand, tried to bull shit or tried to beat around the bush.

seh-jai-ming: Why do we use 50-ohm coaxial cable?

dai-mah-seng: It is for matching purpose. If you use coaxial cable with other value, your SWR will be high.

seh-jai-ming: Why they choose the value of 50-ohm ?

dai-mah-seng: Because it is the standard.

seh-jai-ming: How do they come out with such a standard?

dai-mah-seng: All the cable manufacturer decided to standardize it.

seh-jai-ming: Why don't they choose other value?

dai-mah-seng: It is because 50-ohm is the output impedance of the transceiver.

seh-jai-ming: Why the output impedance of the tranceiver must be 50-ohm?

dai-mah-seng: So that, there will be no reflection of the transmitted power.

seh-jai-ming: Why not make everything to be, let's say, 40-ohm?

dai-mah-seng: No, because 50-ohm gives the lowest SWR.

seh-jai-ming: If everything is 40-ohm, then you will also get the lowest SWR too, won't you?

dai-mah-seng: Where can you find 40-ohm coaxial cable?

seh-jai-ming: If you make 40-ohm as the standard, I am sure you will be able to get 40-ohm coax.

dai-mah-seng: Lima Lima coming in, talk to you later.

seh-jai-ming: 73.