Working on a project about measurement of DVB-T signals i needed a tunable antenna. The problem with DVB-T in Germany is that the frequencies spread over a wide frequency range. If you like to use good antennas for every channel you have to use more than one antenna. Looking at the channel spectrum and the tv channels that are being broadcasted you will notice that some tv channels are transmitted with more power than others. A compromise need to be found to receive all channels the best way possible.
To be able to experiment with the antenna and to tune it to different frequencies, I decided to build a antenna where the elements can be changed in length.
Looking around the Internet and the "Rothammel" I found that the "sleeve antenna" is ideal. It easy to construct and the elements can be build using expendable antennas from r/c remote controls.

Step 1: Mechanical Construction

Get some extendable antennas from r/c remote controls. I had some lying around from small r/c cars I bought on eBay ( https://www.instructables.com/id/Using-RC-car-parts-as-remote-control/ ). Using a thin coax cable (RG-174), the cable could be feed through the small pipes of the antenna.
Two antennas will be used for the sleeve antenna, being a vertical polarized dipole. The antenna will be small because it is build for a frequency range 470Mhz to 740Mhz. This makes the mechanical construction easy. Just use some heat shrinkable tubing to fix them.
The antenna can be tuned by changing the length of the dipole elements. The antenna can be mounted using a vacuum cup because it doesn't wight much.

All measurement is done in the metric system using meters not inches ... I am German ;-)

Material:
- two r/c remote control antennas
- about 40cm RG-174 coax cable (don't use to much because the damping of this cable is high)
- coax connector that can be plugged into your receiver, i used a bnc blug
- vacuum cup, for easy mounting
- hexagonal brass nut, size M3 (in my case, could be other size for you)

Tools:
- pliers
- soldering iron
- solder
- sharp knife
- hacksaw
- small screw driver
- fine sanding paper
- maybe some silicone spray or oil

Step 2: Calculation

The antenna is basically a vertical polarized dipole antenna using 1/4 wave length elements.
The frequencies used for DVB-T in Germany contain 177,5Mhz to 226,5Mhz (band III, vhf) and 474Mhz to 778Mhz (band IV and V, uhf). The r/c antennas used here are to short for vhf but they work well with uhf. So we will build a uhf only antenna here.
The wave length of a frequency can be calculated using the formula L=c/F. c is a natural constant; c = 300 m/s . Using 470Mhz the wavelength is 0,64m. 1/4 wavelength is 0,16m. The same calculation for 778Mhz leads to a 1/4 wavelength of 0,096m. The result shows that the r/c antennas fit our needs.

The above calculation is not really exact. There is a shortening factor v that depends on the dielectric and the thickness of the elements of the antenna. Rothammel contains a diagram where you can take the shortening factor for a dielectric of air if you got the thickness of the elements. In our case we have to use a mean thickness. Measure the thickness and calculate the thickness ratio. The thickness ratio is defines as follows Ld = length / diameter. In my case the mean diameter is 5mm. The thickness ratio is 127,66 for 470Mhz. Now we can take the shortness factor from the diagram. It is about 0,96 for 470Mhz. The correct length of the element can now be calculated: l = c / F * V / 4 . This leads to 15,32cm for 470Mhz and to 9,2cm for 778Mhz. For the mean frequency of the uhf band of 626Mhz the length is 11,41cm.

Step 3: Preparing the R/c Antennas

Remove the antennas from the r/c remote controllers.

One antenna need to be shortened, because we like to feed the coax cable through it. In my case I needed to cut the two thinnest elements. To find out how much you need to cut, just look for the smallest elements that is big enough to contain the coax cable. Now the mounting base need to be cut off completely so that the coax cable can be feed through the whole antenna.

The other r/c antenna should be left mostly untouched. Only parts of the mounting base should be cut of. This makes it easier to solder the coax cable to it.

Step 4: Assembling

Now you can feed the coax cable through the base antenna. In my case I needed to put some silicone oil on the cable because the tube was very tight.

Cut the outer insulation of the coax cable. Be careful not to cut through the shield. Put the cable through the brass nut. Splice the shielding and bend it backwards. Solder the shielding and the nut to the base of the r/c antenna.

Carefully cut the inner insulation of the coax cable and solder the core wire to the base of the other r/c antenna. Keep the cable length as short as possible.
Be careful not to connect the core wire to the shield. You can check your work with a multimeter.

Put some shrinking tubes over the construction and shrink it to fix the two r/c antennas in place.

Take the vacuum cup, cut a mounting slit into the back and press the antenna into it. You can remove the antenna from the vacuum cup any time you like. You can stick the antenna onto the window of your room, or car ... if you like. Don't stick it on a metal surface. You could use metal surface as a reflector, but the distance between the antenna and the reflector need to be calculated to make that work.