Published by Eric Bogatin on 28 Oct 2008
One of the most common questions I get asked in my Essential Principles class is why does everyone use 50 Ohms? what’s so special about 50 Ohms? The answer, like so many standards we use today, has its origin in a practical application at the time which may not apply today.
50 Ohms had its origin in the early days when transmission lines were first getting popular, with radio and radar system. When the generation and transmission of an rf signal is not very efficient, every milliwatt of power is precious. To minimize the losses in the cables from the rf generator to the transmitting antenna, you want to use the lowest loss cable you can.
In a coax cable, what is the impedance to use that gives the lowest loss per length?
The losses in a coax cable are dominated by the conductor loss, which depends on the series resistance of the inner conductor and outer conductors. Since above about 1 MHz, all the current is skin depth limited, it is the circumference of the conductors that influence the series resistance. The larger the circumference, the lower the series resistance.
But, the attenuation depends on the series resistance divided by the characteristic impedance. If the outer diameter of the cable is fixed- you use the largest diameter you can- then the only parameter to adjust is the diameter of the inner conductor.
If you increase the inner diameter, the series resistance decreases, which is good, but the characteristic impedance decreases, which is bad. As you sweep the inner diameter from really small to close to the outer conductor diameter, and ask, how does the attenuation vary, there is a minimum value. What is the impedance of the cable when the attenuation is a minimum?
It’s very easy to “put in the numbers” using the simple approximations for attenuation and the impedance of a coax cable found in my book. When you plot the attenuation vs characteristic impedance of a coax cable, as shown to the left, you find there is an impedance that gives the lowest attenuation. When the dielectric constant is 2, this is just about 50 ohms. Even if the dielectric constant is higher, closer to 4, it is still close to 50 ohms.
Of course, few high speed digital systems are limited by attenuation in coax cables. But the same principles can be used to find the optimum impedance for lowest loss, or lowest power dissipation, or lowest cross talk, or thinnest dielectric layers. Depending on which of these features is the most important for your design, the optimum impedance will range from around 40 ohms to 80 ohms single ended, or 80 to 150 ohms differential impedance.
The details on performing these trade offs is covered in our High Speed Design Principles class. Hope to see you there sometime.