Since putting together this antenna system I have noticed a fairly good match with the 4:1 balun on 20 meters. I ran the numbers and here are results providing that good match.

I took readings with my uncalibrated AA-600 and 4:1 balun across the HF band and see that the input to the line is 139-j384Ω on 20m. Now this is with the 4:1 balun causing the readings to be normalized to 200Ω. So for practical reasons, I will stay in that 200Ω system for calculating convenience.

The first thing I would like to point out is that 90° transmission lines tranform impedances by the following formula set. The antenna Z I have here is just an example.

Knowing the input impedance of the antenna and line we can insert them into the second formula and arrive at an answer. But like all things in this world exact values are rarely achieved because of the antenna impedances are location dependant because of varying soil conductivity, etc. causing shifts in the readings. What we can see from this experiment is a general range or location of solutions that lie in certain quadrants of the Smith chart. To get close enough to the center is enough to gain an understanding of the sensitivity and direction we would like to go.

The transmission line is approximately 800Ω and the line input Z = 139 - j384Ω (at 200Ω system impedance). My earlier back yard measurements revealed that an 8 inch spacing yields a characteristic impedance of 725Ω, so when it is greater than that, ~10-12 inches, 800Ω is close enough for the math.

Zantenna = 533 +j1474Ω (AA-600 with 4:1 balun behind our line)

Now, the line is approximately 20 feet long and we need to remove it mathematically to see what the antenna input impedance is as well. I generated a spreadsheet table showing the length of various fractions of wavelengths for a line slowed down by 6% due to imperfect effects of the wire and insulation on that wire. My arrival at 94% velocity factor is from an actual measurement.

So a 20m quarter wavelength piece of that line is physically 16.5 feet long. Since we are at about 20 feet I would like to know how electrically long 20 feet will be. So in the last two columns I took that 20 foot piece and calculated the how long (in wavelengths) that piece of feedline is for each band. At 20m it is approximately 0.3 wavelength and I converted to electrical degrees (with each 90° wrap removed for simplicity on the Smith chart) in the last column.

This yields 109° for 20 feet at 14MHz given a velocity of propagation of 0.94.

Adding the antenna impedance, line impedance, and length into the Smith chart one can see that the resulting input impedance is approximately centered.

Since the load can vary a certain amount out in the right quadrant by a somewhat large numerical amount, the amount of area travelled on the Smith chart is relatively small. This means that the other end of the line back at the input varies in the vicinity of the blue VSWR circle. That is why, when the wind blows on the antenna or the open wire line dances around a bit, the actual VSWR doesn't change that much and is close enough to the center to provide a good match. Again, all of these values are at the 4:1 or 200 ohm level through the balun.

The blue circle represents VSWR values of 2.2:1, any value inside that circle is under 2.2:1.

Next, I will run the EZNEC model and see if the input Z matches what I have measured.

-WVØH

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