Thank you everybody.
I am particularly interested in understanding this properly:
an atu (be it a pi, l,t ... match) will have losses, a good antenna with a proper impedance transformer (and proper grounding/choking) will have lower losses
what is the reason? Can you point to some general argument/calculations that would help me reach the same conclusion regarding T-match VS transformer? I haven't been able to find much.
In your case the antenna (wire) is directly connected to the tuner, so either a transformer or a matching unit will make little difference from the loss/efficiency standpoint; the only problem (let me call it so) is that with that config you will have "RF in the shack" since part of the ratiating element (the antenna) is inside; that's why it's usually better to either use a remote antenna matching unit sitting at the (external) antenna feedpoint or a transformer (again, at the feedpoint) and feeding the antenna using some coax (with proper choking/grounding).
As for simulating the antenna, you may have a look at the free 4NEC2 program which you can download
here it will allow you to create a model of your antenna and then perform a number of simulations; for a primer on 4NEC2, see
this and
this (you can find more guides/manuals/primers on the net)
in your case, you have two main issues, first of all your 7 meters antenna is too short for the 20 meters band (14MHz), second, you lack a counterpoise, the latter may even be a piece of wire hanging down from the window and connected to the gnd of your matching unit (or transformer); as I already wrote, my suggestion is to start by going
here and selecting from the GREEN numbers list the longest length of wire which will fit your available space, next build a 9:1 UnUn like
this one (the toroid may be smaller given that you'll use low power); done so, pick up some length of coax to connect it between the UnUn and the wire and connect a second run of wire hanging down from the UnUn "gnd" connector; use a piece of rope to hold the UnUn and the wires as far from the building as possible and a second one to hold it at the far end; that will give you a pretty decent antenna, sure it won't be a Yagi or whatever, but it will at least be better than the current one
Willing to go for a resonant antenna, you may consider putting up a resonant dipole, in such a case the calculation is pretty simple/straightforward
Lambda = 300000 / KHz
HalfWave = Lambda / 2
WireLength = HalfWave * 0.954
ArmLength = WireLength / 2
with the above infos in your hands, cut two wires at ArmLength and connect their center point to a 1:1 BalUn (yes, you want a BalUn there since it's a balanced antenna) like
this and connect the balun to the coax, hang the center as far as possible from the building (using a piece of rope) and hang the two arm ends (through ropes) to a couple supports outside, the dipole will then have an "inverted V" shape but will work w/o problems; to bring it to resonance you may just fold back (a bit at a time) the wire ends over themselves until you'll find the sweet spot
Ok, enough I think, hope it will be of some help
[edit]
The 0.954 factor I used is the velocity factor for "phosphor/bronze" wire, I prefer using that since, even if it will give you a (slightly) longer value, it's easier to shorten the wire than to lengthen it
[edit 2]
As for the "random wire" lengths, the table below shows them in meters, the first colum shows the "lowest" band which a given length will cover, the second one the length of the wire in meters, knowing the band of interest, pick the longest length which will cover the desired band (or a lower one) and fits your available space; notice that while laying out the antenna in a straight line would be the best setup, it's not mandatory, the antenna wire may be sloping or zig-zagging (horizontally and/or vertically) as long as the angles described are above 100 degrees, sure that will alter the radiation pattern, but it will allow to fit the wire into your available space
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lowest band wire (meters)
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20 8.8392
40 10.8204
40 12.4968
40 17.6784
80 21.6408
80 25.6032
80 32.6136
80 36.2712
160 45.1104
160 61.8744
160 105.7660
160 124.0540
160 128.9300
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