There was an article in recent issue of ARRL QST, A 20 and 40 meter Vertical on "Autopilot", ...
That article by K6MHE is available here:
http://k6mhe.com/files/DualBandVert.pdf
And here's a blog entry and a corresponding YouTube video by AB8XX for a similar 80m/40m antenna:
http://ab8xx.blogspot.com/2008/12/80m40m-dual-band-vertical.html
This entire system, antenna plus "autopilot" matching network, can be modeled using AutoEZ and the EZNEC "L Networks" feature.
A conventional low pass L network has an inductor in the series branch and a capacitor in the shunt branch. However, EZNEC L networks can have compound components in each branch. Hence the matching network can be modeled like this (from the K6MHE article).
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Here is the AutoEZ L Networks table with variables K-L-M being used for the component C1-L1-C2 values. The source is on V1, the network input port. The network output port is the antenna feedpoint.
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The following extract from the AutoEZ Variables sheet tab shows the initial values for the K6MHE 40m/20m setup. Instructions for setting the initial network component values (variables K-L-M) are found in additional comments on the sheet, not shown.
Note that ground loss due to a less than perfect radial field is simulated using variable D in conjunction with MININEC-type ground; actual radials are not included in the model (although you may add them if you wish and change to High Accuracy ground). Approximate ground loss values are: 4 radials, 29 ohms; 8 radials, 18 ohms; 16 radials, 9 ohms; 32 radials, 4 ohms.
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With the C1-L1-C2 component values as set above, the L network look like this when the model is passed to EZNEC.
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Once the initial network values are set, the AutoEZ optimizer can be used to adjust components C1, L1, and C2 (variables K-L-M) to produce the lowest possible SWR at the two midband frequencies.
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After optimization, here are the final SWR values for seven 40m frequencies and eight 20m frequencies. This is similar to Fig 5 in the K6MHE article except that all frequencies are shown on a single chart. (Blue markup added for clarity.)
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Doing the same kind of analysis for 160m/80m (with radiator length "B" = 132 ft) gives these SWR values, this time shown with a different scale for SWR (on the right). The midband SWR values are fine (remember, right scale) but because of the relatively wider widths of 160 and 80 the band edge SWR values are higher.
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Of course it would be possible to use relays to implement two different "autopilot" matching networks, one for the low end of 160 and 80 and a second for the high end of the bands; I didn't model that.
For those who already have AutoEZ (http://ac6la.com/autoez.html) or who would like to experiment with the free demo version, here is the model used for this study.
http://ac6la.com/adhoc/DualBandVert.weq
Download that file, use the "Open Model File" button, then tab to the Variables sheet to get started. As downloaded, the model is ready to be optimized (Optimize tab, "Start" button) and then calculated over multiple frequencies (Calculate tab, "Calculate All" button). The number of segments has been set to allow use with the free demo version.
I'll be happy to answer any questions even if you are using the demo version of AutoEZ.
One last thing. Nermin, S58DX, has a really cute Golden Retriever:
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Being a dog lover I just had to include that link!
Dan, AC6LA
http://ac6la.com
