What difference does the impedance make when receiving with a scanner?
Probably nothing as all scanners impedance are all over the place, as well as most antennas except discone and logperiod types.
If you have a perfect 50 ohm impedance and connect to a perfect 75 ohm impedance, the mismatch will cost you 0,2dB.
Depending of the antenna type it could probably have something like a 20 ohm to 200 ohm impedance within it's advertised frequency range. The same goes for a scanners impedance.
Here's what the measurements are of a yagi antenna designed for 420-450MHz.
17el PMR446 446Mhz (420MHz - 452MHz) Yagi Rear Mount
And here's a Sirio 5/8 wave GP antenna @123MHz
And here are a scanner antenna advertised as 25-1000MHz
And finally a discone that doesn't swing so much in it's impedance but still goes between 30 ohm and 300 ohm, in the green plot.
I sweept the antenna input of my BCD536HP to look at the impedance and filter characteristics. It seems to be 7 filters, some are 2-pole and others 3-pole. Component tolerences are probably 5% at best so at 400MHz it could be a +/-20MHz difference between different BCD536HP scanners. Some...
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As you see there's no point in trying to stick with a 50 ohm coax, thinking it will have an advantage over a 75 ohm coax.
There's also a reason to why all professional RX installations use 75 ohm coax instead of 50 ohm. It is the most effecient impedance for transporting low level signals going from low video frequencies for surveilliance cameras to SHF frequencies at 2000MHz for satellite receivers.
/Ubbe