There are many different types of 50 ohm coax. Some thick, some thin, some rigid, some flexible. They also vary in factors of attenuation and RF leakiness, yet they are all said to be 50 ohm coax.
But what does it mean when we say a coax cable is 50 ohms? If I pull out a multimeter and test the center conductor of a coax jumper from end to end I won’t see 50 ohms of resistance. I will see it as a perfect conductor, with no resistance. Similarly, I could measure the shield end to end and get the same thing. If I touch one lead to the center conductor and the other to the shield, my multimeter reads infinite impedance. Finally, when I short the far end and measure again it now reads zero ohms. I can’t find 50 ohms anywhere!
With a handful of exceptions, which I won’t cover here, we use 50 ohm coax in amateur radio. Our feedline, jumpers, connectors and all of our equipment is designed for a 50 ohm input impedance. Let’s take a deeper dive.
Resistivity is the term used to describe how resistive a given material is. Just as DENSITY describes the mass of a cubic meter of material, RESISTIVITY describes resistance across two opposite faces of a cubic meter of material.
Different materials have different amounts of resistivity. The resistivity of copper is 1.7 × 10-8
Other factors necessary to calculate the resistance of a given wire are its length and its cross sectional area. In other words, yes copper has some resistance that can be measured, but it is so small that you would never ever be able to run a length of coax long enough to accumulate 50 ohms of resistance.
50 ohm coax doesn’t have to be made of copper, but copper is a wildly popular choice due to the combination of low resistivity, availability, its relative ease of processing and low cost.
Velocity Factor is a value we use to calculate how much a given conductor will reduce the speed of RF propagation relative to the speed of light if the RF were in free space. Different materials have different velocity factors at different frequencies. For example, a bare copper wire used as a 70cm antenna has a velocity factor of 0.95. If I were making a half wave or quarter wave 70cm antenna, I would determine the length for my desired frequency of 440 MHz and then multiply by 0.95 to get the ideal length for my antenna, adjusted for velocity factor. As you can see, velocity factor is an interesting topic all its own, but does it have anything to do with the 50 ohm question?
There are many different types of dielectrics with differing permeability. The interesting thing here is that coax is manufactured very intentionally, with great care in the selection of materials, their size and spacing. This all leads us to the answer we are looking for…
There are two definitions we should be familiar with to help us understand what this is.
- Characteristic Impedance is the input impedance of a transmission line when its length is infinite.
- Characteristic impedance is determined by the geometry and materials of the transmission line and is not dependent on its length.
Let’s say we have a coax transmission line coming out of our amateur radio transceiver. Coax has a center conductor and a shield. There will be a certain amount of current flowing on this transmission line when we use our transceiver. Current will flow in both directions, and it will flow on both the center conductor and the shield.
We could measure the current in amperes. Let’s call this I (I = amps).
We could also measure some voltage between the two conductors. Let’s call this E (E = volts).
There will be a difference of potential between the two conductors all along the transmission line. The physical characteristics of the coax, the spacing, the dielectric material, are engineered such that a given ratio will exist between volts and amps. As one of these values changes, the other must change in ratio.
The ratio is E/I = Zo, where Zo is referred to as the Characteristic Impedance.
If our antenna is a half-wave dipole in free space, then theoretically, it should be free of reactance (also known as a resonant antenna). Notwithstanding the tidiness of OHM’S LAW (R = V/I), note that Zo is not the same thing as a purely resistive load (R = resistance).
Other factors of impedance come from REACTANCE, the interplay between Inductance (L) and Capacitance (C). In fact, one of the ways we can determine the characteristic impedance of a given coax is to measure its inductance and capacitance per unit of length. The formula is simple: the square root of L divided by C gives us the characteristic impedance in ohms.
You may be asking, where did that 138 come from in the above formula? Remember the dielectric constant chart we looked at earlier? The formula above expresses the characteristic impedance of a lossless air insulated coax cable.
When coax designers create a recipe for any coax, they have to select a dielectric material which will have a suitable constant as well as velocity factor. They will have to appropriately size the center conductor, dielectric, and shield, and they will have to precisely plan the distance between the conductors in order to achieve the desired ratio for the coax characteristic impedance.
The key takeaway here is that in amateur radio, we have standardized on a characteristic input impedance of 50 ohms. A wide variety of products from many vendors in all parts of the ecosystem adhere to this standard. This fact makes it much easier for us to plan and design well operating systems, where we hope to get as much efficiency as we can with the power that we have. But what happens when something goes wrong?
SWR METERS and IDEAL IMPEDANCE
By using an SWR meter you can measure the voltage standing wave ratio on your transmission line. Remember how we said current would be found on both conductors moving in both directions? What should we expect to happen to voltage measured across these conductors? According to OHM’s LAW there is a relationship between these.
When we look at a VSWR reading we can interpret the result as telling us how close to an ideal impedance we have achieved. This is why, when we have a poor impedance match, we can correct it by using an antenna tuner to add or remove inductance or capacitance. We could also make physical changes to our antenna or other portions of the feed system to affect the real resistance.
A 50 ohm input impedance is a concept. It is a theoretical thing. In practice, we will never have a perfect, ideal system. The fact that all our gear is designed and specified to this characteristic impedance makes it easier for us to get close, or at least as close as we can, to an ideal system.