Coax, Connections, Calculations, Coils and CATV Cable

I’ve been using a spool of RG-6 CATV cable of dubious quality for quite a while as my go-to source of antenna feed line because I happened to have the spool in my junk collection. Using the 75 Ω cable got me thinking about why we care what impedance the cable is and how matching is really a two-sided affair. What I found through my own experimentation, and running numerous NEC models is that there is little intrinsic value in sticking to 50 Ω cable. The main advantage for using 50 ohm cable is that you don’t have to think much about the length of the cable run because, if terminated in 50 Ω at the transmitter, any wave reflected from the transmitter will be absorbed at the transmitter and not re-reflected, so its a one-way affair.  However, as soon as you put an antenna tuner at the transmitter, this one advantage goes away; with the tuner the cable is no longer terminated with its characteristic impedance, so it will happily support standing waves.

What should affect your choice of cable?  Here are my criteria in order:

  1. Voltage handling capability
  2. Cost
  3. Loss characteristics of the cable.
  4. Jacket Dielectric
  5. Characteristic Impedance

Cable Table

Dielectrics: PE = polyethylene; F-PE = foamed polyethylene; FEP = Teflon; S-PE spiral hollow polyethylene.

Lets start by looking at a co-ax cable chart.  This is one I compiled over the years and have distilled to a few essential numbers to be better able to compare cables for HF and VHF applications. The chart is arranged in order of increasing cable size.  What you notice in general is that the voltage capability tends to increase and the losses tend to decrease as you make the cable diameter bigger.  However, there are exceptions to this general trend that relate to the specific form of the dielectric insulation used in the cable and the cable impedance.  Lower impedance cable has a relatively larger center conductor than higher impedance cable.  Hence you would expect slightly lower resistive losses on lower impedance cable.  Solid polyethylene (PE) is commonly used when voltage handling is important, however, using foamed polyethylene (F-PE) will significantly reduce dielectric losses in the cable.  In addition, it turns out that for a given outer diameter cable, if you increase the dielectric constant you have to make the inner conductor smaller to maintain the same impedance.   Smaller inner conductor has smaller circumference and higher skin resistance.  Hence the advantage for using foamed dielectrics with lower ε.  For frequencies up to a few hundred MHz, the dominant loss mechanism is resistive loss in the skin current layer.  The penetration depth of the current becomes smaller as the frequency increases, causing the losses to scale as the √f .  At higher frequencies, the dielectric loss tangent comes into play and generates losses that are proportional to f.  For the HF bands, using just the √f scaling will get you mighty close.

The F-PE dielectrics are almost more like air than plastic, so the speed of propagation is faster in those cables as well. If you are running 100 W or less, then just about any cable can handle the RF voltage including the foamed varieties. When running power you have to be more careful.  RF and DC are different beasts; how well you make connections matters a lot when operating near the voltage limits of cables.  Avoiding high SWR is also required to avoid voltage multiplication in the cable.

Playing around a little bit with LTspice, it is possible to model cable line losses, impedance mismatches, etc.  The most important loss mechanism for the HF bands is the skin effect, which is modeled in my circuit as just a simple series resistance with a frequency dependence that varies as √f.  Here is the model results for a one hundred foot run of RG-8X.

The typical power loss with increasing frequency is seen in the power delivered to the load (green).  With the cable matched on each end with a characteristic impedance match, there is no unusual frequency dependent features that  depend on the time delay in the coaxial cable.  That situation is not the norm, as we will see  when we discuss mismatches below.

CATV 75 Ω Cables

If cost is a driver in your choice of coax, as it often is, then one should look at CATV cable types.  Thousands of miles of this type of cable has been manufactured, so the economy of scale helps us here.  What matters to the CATV folks is not to have to boost the signal too much, so low loss is important at TV frequencies (VHF and up). To keep cost down, there is no copper in this stuff other than the coating on the steel center conductor, otherwise just aluminum.  It is hard to find comparable low loss cables for less than at least three times the cost of the RG-6 and RG-11 aluminum CATV varieties.  These cables are often not voltage rated at all or will declare a 300 VRMS rating.  The best comparison is to look at LMR400 which is also a F-PE dielectric type and observe that his cable which, is about the same size as RG-11 types, is rated at 2500 VDC and good from 1600 W at 100Mhz.

The other issue using CATV aluminum cable types is making the connections.  Fortunately, we have crimp connectors.  It used to be difficult to find PL-259 type crimp connectors for RG-6, but now they can be found easily on E-bay from China.  Crimp connectors for RG-11 are the same as those used for RG-8, are plentiful, and cost a couple dollars each.  Some of the best CATV types are meant for burial and are “flooded” with a gooey gel to prevent water from wicking along the cable, and often have PE jackets.

Crimp Connectors

The figure on the right shows how I gauge how far to cut back the insulation using the actual connector as a guide.  In the background is the GOO GONE I use to get rid of the flooding goo.  Snip the braid back leaving just enough to extend over the connector ferrule.  Then remove the insulation to reveal the center conductor. Electrically, the weak spot is break down from the center conductor, tracking along the cut insulation to the outer conductor.  I increase that path a little by cutting back the foil so the breakdown track would have to go around the corner.  I know some folks who taper the insulation into a cone for even better tracking resistance.

Now it is just a matter of sliding everything together and crimping.  When soldering the center conductor on the PL-259, use a hot iron, and work quickly with the connector level.  You do not want a blob of hot solder running down to the insulation, nor do you want to melt the insulation with too much heat. Get the solder on and then quench with a damp sponge.

 

Cable Jacket

Often the cable jacket has no electrical consequences.  It is there just to protect the rest of the cable assembly and hold it all together.  However, in some antenna applications, I like to use the outside of the outer conductor of the coax as part of the active antenna structure, and often will make coils wound of the coax as traps or chokes.  In these circumstances, especially with coils, the jacket material can matter.  There are two common choices for jacket material. Most common is PVC insulation, but you can also find cable jacketed with polyethylene (PE).  What is curious here, is that PE is one of the very best dielectric materials with a loss tangent ~0.0002 whereas PVC is one of the worst dielectric materials with loss tangent ~0.1 !  Why does this matter?  Image making a self resonant coil with the two materials.  Much of the capacitance associated with the self-resonant coil will be due to fields in the jacket dielectric.  The Q of the capacitor formed with such a dielectric is the reciprocal of the loss tangent, so with PE dielectric the potential Q is ~5000, whereas with PVC it is only ~10.  In the worst case, where you are driving power into an antenna load terminated with a resonant trap, you could put a lot of heat into the insulation if it is made of PVC!  Does this happen?  I don’t know, but I’ll go for the PE jacket if I have a choice.

Feedline Coils – Traps and Inductors

This really is an article in itself, but I’ll just mention a few points here.  If you are building a “resonant feedline antenna,” where you are defining the active antenna element with an inductor on the feedline, then Q matters.  The reason is quite simple — you are driving into the end-defining inductor so any losses there are power losses.  Hence the argument above to use PE dielectric cable, but also this should clue you in to be wary of using ferrite cores.  Just as dielectric materials can be lossy, so can magnetic materials.  An efficient resonant feed line antenna will use a high Q trap where both inductance and capacitance combine to give very high impedance at the operating frequency, rather than using a large non-resonant ferrite inductor.

If the point of the feed line inductor is only to block RF currents from coming back to the transmitter, then then you do want to use the ferrite core inductor and should not attempt to block feed line RF on a multi-band antenna with an air core coil.  Losses in this application are your friend, since any RF bouncing back and forth on the way to the transmitter is unwanted.  The narrow band, low inductance, nature of air-core coils tends to make them useless very far from their natural self-resonance.

Modeling shows that two modest size inductors spaced a distance apart are better at killing feedline currents than a single large inductor.  This is because the single inductor can define a current null at the inductor location, yet allow a resonant mode to persist on the remaining length of feedline. Defining two locations for RF current zeros much more effectively eliminates feed line resonances.

Feedline Mismatch and Length

What really goes on when you have a mismatched load, finite lengths of cable with their associated losses, various cable impedances, and lets throw in an antenna tuner to complete the picture?  To put all of this together, I’ve been playing with LTspice models of various feed line configurations.  What I’ve found is worthy of another article, so I’ll just touch on some results from a couple models to wet your appetite.

With multiband dipole antennas, such as GR5V and OCFD designes, the feed impedance at the antenna is often significantly larger than 50 Ω, often between 100 Ω to >200 Ω for some bands and designs.  A section of mismatched cable is much like a tuner in that it can reduce the SWR in the feed line if adjusted correctly.  The figure below illustrates what happens when you have a simple mismatch; in this case in the load is 120 Ω, a value that places the 75 Ω cable, plus its losses, at about the geometric mean of source and load impedance.  The SWR is the brown curve which you can see approaches 1.0 at several frequencies.

At other frequencies, where the SWR is highest, the source and load voltages (red and blue traces) are identical, almost as if the cable was not even there.  These extremes are at odd 1/4 wave multiples or 1/2 wave multiples respectively, of the waves that fit on the transmission line’s electrical length.  The periodic frequency  dependence is the result of fitting the next half-wave on the transmission line.  There are a few “good” transmission line lengths that will tend to have SWR minimums for more than one ham band.  The 122 ns electrical length (36.6m electrical = 30.38m of VF 83% cable = 99.7 ft.) generates happy minimums for 30m, 20m, and 17m ham bands.  Note that if you were running a 50 Ω line to the 120 Ω antenna load, the SWR would be about 2.4; the mismatch of the 75 Ω cable and the 120 Ω load has SWR 1.6.  In general, using the intermediate impedance cable , between source and load impedances, can only help with the power transfer efficiency.

As a final example, here is the case of 50 Ω line driving a bad mismatch, SWR 10, but with a tuner at the source.  In the example the tuner is adjusted to deliver power to the load a about 14 MHz, which you can see by the low SWR at the source (brown) where it almost touches 1.0 near 14 MHz on the graph..

What you can see by all of the resonances that show up on the frequency plots is that there are plenty of standing waves on the coax when there is a tuner between the 50 Ω source and the 50 Ω cable.  Where the tuner allows the source to be well-matched at 14 MHz, the input voltage (red) is properly loaded to about half the open circuit voltage of the source.  Notice that into the mismatch, the output voltage (blue) is more than three times that matched voltage (1.0 V as modeled).  The input (pink) and output power (green) are normalized to the matched case.  Note that maximum power transfer does indeed correspond to the low SWR point where the green and pink curves kiss. Somewhat surprisingly, the power transfer to the load is very good where tuned, despite the high SWR at the load.  There are other frequency values where the power transfer is not too horrible, where the feed line resonances allow it.  As you can see, there is nothing magic about 50 ohms!

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