### A Look At How Short Coax Can Act As Lumped Elements At Low Frequencies

The dilemma of getting a balanced wire or ladderline into the shack has perplexed a few hams over the years. Common solutions to the problem is to run a short piece of high quality coax, such as RG-213, through the wall and attach the ladderline to the coax that goes through the wall. The advice goes on to say to run a balun or just attach the balanced tuner output to the coax that is on the inside of the shack. Hmm, this has always bothered me because of the shortness of the coax not acting like coax at all on low frequencies but a capacitor with low Q. I didn't realize how bad this could be until now, let alone the trickery involved in getting rid of the common mode current.

### Some Smithing To Get Us Started

Interesting link on QRZ forum,

Dan shows that the contribution of the lengths of transmission lines affect the transformed impedance in baluns.

One thing that always bothered me is that coax at extremely low frequencies relative to physical length behaves as lumped components with real values of Q causing a shift in the results.

I recreated the Z in SimSmith using Dan’s impedance and 2 sections
of TL line just like he has, 2.75 feet total. I then replaced those sections of line with a series L (211.75nH)
and C (84.7pF) if I did the maths right.

This creates an input Z of 21.6 - j124 ohms.

This creates an input Z of 21.6 - j124 ohms.

Then I switched over to lumped elements with infinity Q,

About the same input Z, 21.4 - j123 ohms.

But since coax exhibits non-ideal Q I did a search for what
the Q of coax would be and retrieved this off the internet: http://www.wetterlin.org/sam/SA/Operation/CoaxStubs.pdf

His Q of 25 seems reasonable so I plugged in Q of 25 into
the SS model and got this:

A different result, 29.9 - j122 ohms. Meh, not that different.

A different result, 29.9 - j122 ohms. Meh, not that different.

### Try a High Z Load

While the previous example is for terminating impedances near the characteristic impedance of the TL, what happens when we throw a high Z load at the same circuit? Say a really high impedance of 5192 - j2100 ohms, a typical impedance with an 80m doublet fed on 40m at the input to 55 feet of JSC #1318 ladderline. (Okay, I upped the Q to 50).I set the source Zo(a) to be 100 Watts to show how much power get burned up in each element when you have a high Z load hanging on the end of that 2.75 foot piece of RG-213 coax.

The reveal below shows how pretty much all of your 100Watts gets burned up in the capacitance of the coax.

Zooming in on the details, we see that the capacitance within the coax is burning up 88W, almost all of the power while the inductance within the coax is dissipating little RF power, for a coax Q of 50.

The "up" arrow is mnemonically remembered as "burned up" in that element. If you add up the powers dissipated in each element, it should total the input power from the generator on the right. As well, the "right arrow" in from the left indicates the power coming in from the previous element when you left click on the W symbol you cycle through all the selections.

### A Better Approach

Get some brass rod or at least some 3/16 to 1/4 inch threaded rod. Commonly called all thread or reddy-rod and drill two small holes through the shack wall (about an inch or more apart) and continue the balanced line from outside to in by affixing the balanced TL on the outside to the two rods and likewise on the inside. Done.

73

Myron

WV0H

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