Control Engineering

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Why are the impedances of coaxial and twisted wire lines 50, 100, and 120 Ohms?
January 14, 2008

As far as I know, there’s no technical reason to favor one surge impedance over another for transmission lines. It’s like whether you drive on the left or right side of the road: it makes no difference as long as everyone involved does the same thing. Having no clue myself as to why those particular impedances might be favored, I asked my friend Jack Smith, managing editor of Plant Engineering, who provided the following:

In a nutshell the characteristic impedance of a coax cable is the square root of the per unit length inductance divided by the per unit length capacitance. For coaxial cables, the characteristic impedance will be typically between 20 and 150 Ω. The length of the cable makes no difference in the characteristic impedance.

If the impedances are not matched, part of the waves in the cable will be reflected back on the cable connections, distorting the outbound waves. When these reflected waves hit the wave generator, they are again reflected and mingle with the outbound waves so that it is difficult to tell which waves are original and which are re-reflections. Of course, there are phase differences, which can (and usually do) result in the dreaded standing wave.

The most typical coaxial cable impedances used are 50 and 75 Ω. The 50 Ω coaxial cables are probably the most commonly used coaxial cables. They are commonly used with radio transmitters, radio receivers, laboratory equipment and in Ethernet networks.

The 75 Ω coaxial cable is used primarily in video applications, in CATV networks, in TV antenna wiring, and in telecommunication applications.

600 Ω is a typical impedance for open-wire balanced lines for telegraphy and telephony. Twisted pairs of 22 gauge wire with reasonable insulation on the wires comes out at about 120 Ω for the same mechanical reasons that the other types of transmission lines have their own characteristic impedances.

Twin-lead cable used in some antenna systems are 300 Ω to match to a folded dipole in free space impedance. However, when that folded dipole is part of a Yagi (beam) antenna, the impedance is usually quite a bit lower, in the 100-200 Ω range typically.

Different impedance values are optimum for different parameters. Maximum power-carrying capability occurs at a diameter ratio of 1.65 corresponding to 30 Ω impedance. Optimum diameter ratio for voltage breakdown is 2.7 corresponding to 60 Ω impedance (incidentally, the standard impedance in many European countries).

Power carrying capacity on breakdown ignores current density, which is high at low impedances such as 30 Ω. Attenuation due to conductor losses alone is almost 50% higher at that impedance than at the minimum attenuation impedance of 77 Ω (diameter ratio 3.6). This ratio, however, is limited to only one half maximum power of a 30 Ω line.

In the early days, microwave power was hard to come by, and lines could not be taxed to capacity. Therefore low attenuation was the overriding factor leading to the selection of 77 (or 75) Ω as a standard. This resulted in hardware of certain fixed dimensions. When low-loss dielectric materials made the flexible line practical, the line dimensions remained unchanged to permit mating with existing equipment.

The dielectric constant of polyethylene is 2.3. Impedance of a 77 Ω air line is reduced to 51 Ω when filled with polyethylene. Fifty-one Ohms is still in use today, though the standard for precision is 50 Ω.

Attenuation is minimal at 77 Ω; the breakdown voltage is maximum at 60 Ω and the power-carrying capacity is maximum at 30 Ω.

Another thing that might have lead to 50 Ω coax is if you take a reasonably sized center conductor and put a insulator around that and then put a shield around that and choose all the dimensions so that they are convenient mechanically and look good aesthetically, then the impedance will come out at about 50 Ω. To raise the impedance, the center conductor's diameter needs to be tiny with respect to the overall cable's size. To lower the impedance, the thickness of the insulation between the inner conductor and the shield must be made very thin. Since almost any coax that “looks” good just happens to come out at close to 50 Ω anyway, there was a natural tendency to standardize at exactly 50 Ω.

Many engineers question the significance of 52 or 75 Ω characteristic impedance. The best coaxial cable impedances to use in high-power, high-voltage, and low-attenuation applications were experimentally determined in 1929 at Bell Laboratories to be 30, 60, and 77 Ω respectively. Cable with 30 Ω impedance is exceedingly hard to make, however, so a compromise between 30 Ω and 60 Ω was reached at 52 Ω, which has persisted. This corresponds very closely to the drive impedance of a half wave dipole antenna in real environments, and it provides an acceptable match to the drive impedance of quarter wave monopoles as well. A center-fed dipole antenna in free space (approximated by very high dipoles without ground reflections) matches exactly 73 Ω, so 75 was adopted as a compromise between 73 and 77 Ω.

As a matter of convention, there is a tendency for many coaxial cables to be designed and manufactured to have an impedance of either 75 Ω (used by TV and video industry) or 50 Ω (used by scientists and engineers for instrumentation and communications, and many radio transmitters).

Engineers use a variety of types and impedances of cables. At RF, use of 300 Ω twin feed is fairly common, and 600 on is often used at audio frequencies. In modern telecommunications, cables are typically 100 Ω (modern structured cabling), or 120 Ω (many in-ground telephone cables) unshielded twisted pair. Standard values tend to be adopted for convenience in a given application area as this makes it easier for people to build systems from compatible elements.

Jack also turned up an answer specifically for 50 Ω coax from Harmon Banning of W.L. Gore & Associates, Inc.
For more on impedance, also see Ask Charlie entries from Jan. 7, 2008, and Dec. 31, 2007.

Posted by Charlie Masi on January 14, 2008 | Comments (0)