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Author Topic: Surge Impedance Calculations  (Read 5862 times)
K9MRD
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Posts: 331




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« on: May 05, 2008, 02:16:43 PM »

Is the formula: Zsurge = 60[ln(4h/d)-1] fairly accurate for small diameters (wire verticals) or is some weighting required as diameter becomes small? If required, is there a table somewhere?

Wayne
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W5DXP
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« Reply #1 on: May 05, 2008, 02:28:02 PM »

The surge impedance of a vertical varies at every point along the vertical since the height (H) is continuously changing. Would you mind explaining why surge impedance in a vertical is important to you?
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73, Cecil, w5dxp.com
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73, Cecil, www.w5dxp.com
The purpose of an antenna tuner is to increase the current through the radiation resistance at the antenna to the maximum available magnitude resulting in a radiated power of I2(RRAD) from the antenna.
K9MRD
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Posts: 331




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« Reply #2 on: May 05, 2008, 03:01:57 PM »

Hi Cecil,
Yes, I know the surge impedance changes with height, that's why there is an 'h' in the equation. The reason for my question is surge impedance is required to design cap hats and loading coils for verticals. I just wondered if the equation remains accurate for diameters ranging from 10-15" for a tower to .064" for #14 wire. Seems like a very wide range.

Wayne
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W5FYI
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« Reply #3 on: May 05, 2008, 04:36:22 PM »

The ARRL Antenna Book uses essentially the same formula for mobile antenna calculations, and they can have relatively thick base sections and thin whips for very short verticals. I've compared the formula with other programs, and it compares favorably. However, I can see where an oddly shaped diameter, such as a triangular Rohn, may have to have the diameter "smoothed" to an equivalent circular shape.
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W5DXP
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« Reply #4 on: May 06, 2008, 08:36:15 AM »

> K9MRD wrote: I just wondered if the equation remains accurate for diameters ranging from 10-15" for a tower to .064" for #14 wire.

The equation is a ballpark approximation of limited accuracy, not designed for precise results. No matter how accurate your inputs, trim&try tuning will be required unless you are extremely lucky.
--
73, Cecil, w5dxp.com
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73, Cecil, www.w5dxp.com
The purpose of an antenna tuner is to increase the current through the radiation resistance at the antenna to the maximum available magnitude resulting in a radiated power of I2(RRAD) from the antenna.
W5FYI
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Posts: 1046




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« Reply #5 on: May 06, 2008, 09:51:21 AM »

I did some more research and found a reference in the 1959-1960 edition of the Handbook of Chemistry and Physics. While it doesn't directly address surge impedance, it does have a formula for inductance that takes into account a calculation called sigma which adjusts for conductor diameter, frequency, and temperature, and another factor, ยต, the permeability of the conductor. These corrections are quite small, and the text states "For wires other than iron, whose length is 100,000 times the diameter the inductance at infinite frequency is about 2% less than at zero frequency."

Of course, surge impedance can be calculated from SQRT(L/C), so the slight change in L will yield a somewhat insignificant change in surge impedance. That is probably why the Handbook and other sources omit the sigma calculation.
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K9MRD
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« Reply #6 on: May 06, 2008, 10:25:20 AM »

Thanks FYI & DXP!

I am writing a vertical software design tool for those that don't use modeling.  So I have been trying to be as accurate as possible.

DXP - You are so right - the formulas get you in the ballpark, but there are so many environmental factors that 'cut & try' is usually (always!) required. By the way, very interesting web site! I really like your transmission line matching setup.

FYI - As you suggested, there is an equation to 'normalize' a triangular tower to its 'round' equivalent.  Thanks for finding the reference to sigma. For all practical purposes, it looks like diameter weighting is not a consideration.

It has been a long time since college, so I am trying to clear the cobwebs!

Wayne

 

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