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DDRR antenna - Part 2
The math
In first part I talked about modeling the two ring DDRR and patterns. I received so many inquiries about a program to compute the dimensions that I decided to write a second section explaining the math behind the DDRR and wrote a program to do the calculations below.
You may need to refer to the ARRL antenna handbook for some explanations about antennas as transmission lines, "characteristic impedance" etc... but if you master the calculations below you will be able to use them to design also vertical antennas because the math are almost the same. The vertical post characteristic impedance is the one used for verticals and I will post some day something on short verticals, loaded with coil and top caps.
You have below, all the math needed to redesign a DDRR from scratch, starting with the vertical post dimensions, length and diameter, the diameter of the tube used for the horizontal sections, referred as the "loading section", and the maximum and minimum frequency that you want to cover. The results are the dimensions of horizontal sections, and the min and max values for the tuning capacitor.
But, you are going to tell me, these equations are for a one ring DDRR! What about the two ring DDRR equations? The same equations seems to work for the two ring DDRR. After all, the one ring DDRR is in fact a 2 ring when we consider the reflection in the perfect ground below. The vertical post is doubled in length that is true, but differences are minor and can be corrected with the tuning capacitor.
Tony, VE2DLJ, and Alex, VE2AMT (no they don't have email addresses) who build already 2 ring-DDRRs used these equations to compute the length of the horizontal sections and they had good results.
The single ring DDRR math
If we "unfold" the DDRR in a vertical plane we get something that looks like the picture on the right. It is basically a rectangle of height h and length L (My L goes to the capacitor but you can take L as the horizontal dimension only).
On the left you have the vertical post of height h with the source at the base, on the right another vertical post with the tuning capacitor. They are separated by a tube of length L. To keep thing more general we will assume that the vertical post has a diameter of d and the horizontal section a diameter of d1. This will allow you to change these dimensions depending on the material you use.
Equivalent electrical circuit
The equivalent electrical circuit is represented here as a short vertical attacked at the base, and a "loading section" made of a horizontal transmission line loaded at the end by a tuning capacitor Cx. The horizontal transmission line and capacitor will create and equivalent Xc placed at the extremities of the vertical post. The problem is to find the correct combination of L and Cx that will make the vertical post resonant.
Input parameters:
- Fmax = 4 Mhz
- h = 6 feets
- d = 4 in
- d1 = 4 in
There was a mistake in the calculation of Phi min below because of presence of frst Xc but this is corrected here. So our final results are:
You will notice that a mere 28 pF is enough to cover from 3.5 Mhz to 4 Mhz so you need some demultiplication on the capacitor to adjust the resonance.
- For a 6 feet high post, 4 in diameter and horizontal line 4 in diameter
- Length of loading line: 54.675 ft
- Capacitor minimum value (measured) : 8 pF will tune the DDRR for : 4 Mhz
- Capacitor maximum value: 38pF, will tune the DDRR to 3.5Mhz
The next step is to match that to 50 ohms. The impedance at the base of the vertical post is too low (and the shorter the post smaller it is) so the technique is to attack the ring at some distance from the vertical post between ring and ground (or between the two rings). Start near the vertical post and adjust C to resonate then measure, increase the distance and readujst C etc until you find a good compromise for SWR. For 3.795 Mhz that distance was around a foot in the models build by VE2DLJ and VE2AMT.
Good luck !
Madjid
VE2GMI
DOS Program
for double ring DDRR
Patents: US Patent (J.M. Boyer) #3,151,329; #3,247,715; RD26196 all assigned to Northrop Corporation
Note: Tony, VE2DLJ haunts the 75 DX window at sunrise and sunset EST time.
If you have questions, comments, critics, suggestions click here: art@orionmicro.com
This document is Copyright (C) 1997-2001 Madjid BOUKRI - VE2GMI