My wife doesn't think that having tall antennas is acceptable.
Does anyone have a solution for this?
Our house is 16 meter long and 10 meter wide. I have an antenna tuner (if it can help).
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Even though you're asking about "tall antennas," I'm guessing that your wife is more concerned about the appearance of an antenna than its actual height. Search the Internet for "stealth antennas" and you'll find a lot of options for outdoor antennas that aren't very noticeable. Another option is to put an antenna in your attic, if you have one. Either of these options would likely be preferable to putting an HF antenna in your living space because HF antennas tend to be rather large and unpleasant to touch. Also, you'll get better performance if you can get them up high and/or outdoors.
VHF/UHF antennas are a lot easier to fit in your living space, so you could use a J-pole or quarter wave vertical fairly easily. But, there again, you'll get much better performance if you can move them up high and/or outdoors. I put a quarter wave ground plane antenna in my attic that works well, but it would be even better on top of the roof. I hear the VHF/UHF Ventenna antennas work very well without being conspicuous.
Another good resource is ARRL's book Small Antennas for Small Spaces.
J-Pole or vertical dipole are good choices for VHF/UHF. There are good chances that you can reach a local repeater with an antenna right in your shack:
In my case the repeater is ~10 km away and I have no problems reaching it with 5W and a cheap antenna, Nagoya NA-771. Please note that there are many fake NA-771's, see How to identify the genuine and fake antenna?
Speaking of HF you will find many options online. For instance there are shortened vertical antennas (OPEK HVT-400B, OPEK HVT-600, Harvest RH10M, ...) that are no more than 2.5 meters tall. Although these antennas are not most efficient onces, I made plenty of QSOs on my OPEK HVT-400B.
I also have a great experience with antennas described in articles One Stealthy Delta by Steve Ford, WB8IMY and An Easy to Install Vertical Loop for 80-6 Meters by John Reisenauer, KL7JR. Here is my version of "stealthy delta" (full description in Russian):
Note that it's only 6.2 meters tall. This is very little for an antenna that covers 40-10 meters (and 80m too although the antenna doesn't work especially well on this band), doesn't require any counterpoise wires. I made plenty of contacts on 40m and 20m with this antenna, including some transatlantic. The main drawback of my version is that it gathers some QRM from the house on 40m and 80m. I'm going to move it farther from the house.
There are many other options as well, e.g. end-fed antennas. I've been using long wire and Fuchs antenna and they turned out to be quite good. I strongly recommend to read The ARRL Antenna Book for more details.
For VHF/UHF, I did some J-pole's made out of twinlead (old style flat 300 ohm TV antenna cable.) Just google Twinlead J-pole.
For HF, the attic trick is a good one, as is the use of stealth antennas. Flagpoles make good verticals :)
When I lived in the apartment (sometimes called a flat) I had a 40m/15m coaxial dipole strung around the living room. I found the article in the 73 magazine archive. URL below. It was great for CW, and I used it to get my code speed from 5 to 13 WPM so I could upgrade my license. This was back in the early 90s. I had to put ferrite chokes on various things, but I got it to work, and not bother my neighbors. I ran about 10 watts into it and made contact with 20 or so states and canadian provinces. My longest hop was 1000 nautical miles from San Jose CA to Edmonton, AL. Not sure this is the best way, but I wanted to mention it.
Best, Ed Greenberg KM6CG Queensbury, NY USA