At an early stage of their development, the wireless communication systems (HAM, CB, Police, Fire, Walki Talkies etc) standardized on 50 ohm impedance.
Later inventions of Cell/Mobile Phone and WiFi also followed the suite and adopted this system.
The free to air TV originally had 300 ohm system, and used 300 ohm receivers, 300 ohm antennas & 300 ohm twin-lead between antenna & receiver. With advent of Cable TV and Satellite TV, the standard changed to 75 ohms, and is the current standard for TV.
The Receiver we use for ADS-B receiving is DVB-T i.e. “Digital Video Broadcast - Terrestrial” and is therefore designed as a digital TV receiver. It therefore has an input impedance of 75 ohms (see schematic below).
If DVB-T receiver is used with a 50 ohm antenna and 50 ohm coax, there is a impedance mismatch at the receiver-coax interface.
If DVB-T receiver is used with a 50 ohm antenna and 75 ohm coax, there is a impedance mismatch at the antenna-coax interface.
As far as I know, the ProStick’s front end rf pre-amplifier has 50 ohms input/output impedance, and there will be no mismatch if 50 ohm coax and 50 ohm antenna are used. However there is a hidden mismatch: the RTL chip inside is still 75 ohms, and pre-amplifier is 50 ohms, so there is an internal impedance mismatch (unless Flightaware has included some sort of impedance matching circuit between pre-amplifier and RTL tuner chips).
Apart from all above discussion, the effect of 50 to 75 ohms mismatch is negligible, as shown below.
The impedance mismatch between 50 ohm & 75 ohm results in:
reflection coefficient 0.2
mismatch loss 0.177 dB
power reflected 4%, power reaching the load 96%.
When 50 ohm mixed with 75 ohm,
Reflection Coefficient Γ = (75-50)/(75+50) = 0.2
VSWR = (1+Γ)/(1-Γ) = (1+0.2)/(1-0.2) = 1.2 / 0.8 = 1.5
Mismatch Loss in dB = -10 log (1 - Γ²) = -10 log (1 - 0.2²) = -10 log 0.96 = 0.177 dB
Impedance mismatch is important and costly in case of transmitters as power transferred from transmitter to antenna is in tens or hundreds of watts. In case of receiving, power transferred from antenna to receiver is in micro watts, and the loss is made up easily by front end amplifier or the tuner/receiver chips.