Why 50-ohms Mailbag

(Originally published in EDN Magazine, January 4, 2001)
 

Regarding my article "Why 50W?" (EDN, Sept 14, 2000, pg 30), I received some interesting justifications for the use of 50W coaxial cabling:

In the early days of solid-conductor, high-power, coaxial cables, a common impedance was 51.5V. This impedance was partially due to the use of standard sizes of copper pipe for the inner and outer conductors.— Bob Stroupe

Back in my school days nearly 40 years ago, I was told that a 50 W coax delivered the maximum power for given limits on current density on the conductors (or perhaps only the inner conductor) and voltage gradient in the dielectric.—Bruce Carsten

The 50W value is a compromise between high power (30W), high voltage (66W), and minimum insertion loss (75W). —Raymond P Meixner

A half-wave dipole in free space has a feed-point impedance of approximately 73W. A quarter-wave antenna with a ground plane has a feed-point impedance of approximately 37W. A compromise between the two, ratiometrically, is 51.97W, which produces an SWR of 1.404-to-1 either way.—James C Bach

Some readers recognized the minimum-loss-impedance theorem but remembered only the historical value for an air-dielectric cable:

Hate to be the bearer of bad news, but the minimum-loss Z₀ for coax is about 70W, not 50. This was first derived during the World War II era.—Jim Rautio

Pre-World War II coax transmission lines often used an air dielectric, because the alternative available dielectric materials all had too much dielectric loss. Small insulating "holders" spaced every so often along the line supported the center conductor. The overall structure was rigid and could not be easily bent.

The development of polyethylene changed everything: Polyethylene made possible the production of cheap, flexible coaxial cables, which in turn enabled the deployment of military radar, which helped win World World II.

If you are building an air-dielectric transmission line =1.00), then 76.6W is the minimum-loss impedance value. That theorem is the one that so many people remember. For cables having a solid-polyethylene dielectric ( =2.25), 51.1W is the minimum-loss impedance value. You can also get a foamed polyethylene dielectric, or cellular polyethylene, whose properties fall between solid polyethylene and air. Figure 1 plots the relative-loss properties of all three materials.

I received several questions about impedances other then 50 and 75 W:

Why 93W coax?—Craig Miller

IEC Publication 78 (1967) defines standard coaxial-cable impedances of 50, 75, and 100W. The 50 and 75W values remain popular, but the 100W value fell out of fashion. Today, the highest commonly available impedance for coaxial cable is 93 W. IEC Publication 78 provides no rationale for the values selected. Standards publications rarely do, because each member of the standards committee usually harbors his or her own reasons for supporting the final solution.

In my experiences, 50W is a good low-loss value for use with cheap, solid-polyethylene dielectrics. It works with most test equipment. Ethernet went with 50 rather than 75W coax, because 50 W is more tolerant of the capacitive loading effects of the transceiver taps.

If you can afford a rigid-air dielectric cable, 75W works best. The 75W impedance also closely matches the input impedance of a half-wave dipole antenna, which accounts for its popularity with RF engineers. Why do video folks use 75W cables? I can only assume that they inherited this preference from their radio-engineering roots.

I've never heard any plausible explanation for 93W except to say that wimpy drivers appreciate higher impedance transmission lines.

Why 150W shielded twisted pair? —Silence Dogood

I consider IBM's selection of 150W a goof. IBM would have achieved less skin-effect loss using a 100W differential impedance within the same jacket. When this cable was developed, IBM's engineers touted 75W coax as optimal. So, they reasoned, when you put two center conductors in the same jacket, the best differential impedance has to be 150 W. Unfortunately, the math supports that conclusion only for an air dielectric. With the dielectric IBM chose, a 100W differential impedance would have been a better choice. Or, for the same loss, they could have designed a smaller, more easily handled cable.

All Publications by Dr. Howard Johnson except as noted.
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