Dual Band Dipole
This is a simple dipole built for two-band operation that I made for portable use with my 20 and 40 meter QRP rigs.  It was built to take along camping so I would only have to take & put up one antenna instead of two.

The antenna consists of a regular 40 meter dipole using a 1:1 balun at the feedpoint.  Connected to the same feedpoint is the 20 meter element.  The spacers are made out of 1/2" PVC pipe, cut 7" long.  I used a balun as the feedpoint since I had a spare one and it has an eye bolt sticking out the top, which I use to hoist the antenna to use it as an inverted-V.  A straight to-coax connection can also be used, such as shown
here.  Once the antenna is built, the longer elements should be trimmed to find a good match first, then the shorter elements.  The parallel elements should be spaced at least 2 to 4 inches apart. 

An antenna like this can be made for any two bands, and additional elements can be added for other bands to make a multi-band antenna.  An antenna like this works on multiple bands because the antenna presents a high impedance on the elements that aren't resonant, allowing the resonant elements to radiate.  In other words, the radio virtually ignores the non-resonant elements, and uses the elements that provide a 50-Ohm match.   The antenna doesn't rely on the two bands being harmonically related, so other bands such as 30, 17, 15, or 12 meters can be added.

One might think that one could build an antenna for each HF band, and could conceivably add elements for all frequency bands between 2 and 30 MHZ.  However, the elements will react inductively to each other, and the more elements that are added, the narrower the bandwidth for each band.  A fan dipole is a similar antenna to this, except that the elements on each end are spaced at an angle to the others.  I have heard from others who constructed fan dipoles that trimming one element may affect the VSWR on the other elements.  The longer elements should be trimmed before the shorter ones.
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