Can I use 50 ohm cable with 75 ohm antenna (without any adapter)?
I found on the internet that 75 ohm cable can be a problem with 50 ohm antenna, but does vice versa make the same problem? Or the combination of the 50 ohm cable with the 75 ohm antenna is more tolerant?
A portion of a signal passing down a transmission line, such as a coaxial cable, will be partially reflected if there is a mismatch between the characteristic impedance of the transmission line, and the load.
The ratio of the voltage (or current) of the signal moving in the forward direction and the reflected signal is known as the reflection co-efficient, and is represented by the Greek letter \$\Gamma\$.
If \$Z_0\$ is the characteristic impedance of the transmission line, and \$Z_L\$ is the impedance of the load, then the reflection co-efficient is given by.
$$\Gamma=\frac{Z_0-Z_L}{Z_0+Z_L}$$
So, for a 75 \$\Omega\$ coax fed into a 50 \$\Omega\$ load, the reflection co-efficient will be
$$\Gamma=\frac{75-50}{75+50} = \frac{1}{5}$$
The signal that is reflected will travel backward to the source. If the source impedance is also mismatched with the characteristic impedance of the coaxial cable, the signal will be partially reflected again. This new reflection will be travelling in the same direction as the original signal, but will be delayed from the original signal (and lower in amplitude).
In analog video, this delayed signal will cause "ghosts". That is weaker images that are shifted from the original image. In digital video, the delayed signal will shift the voltage levels, but whether or not this has a noticeable effect will depend upon whether the delayed signal adds enough noise, together with noise from other sources, to shift the signal to a different logic level. If the signal plus noise has the same logic levels as the original signal, then the noise will not have a noticeable effect. If the signal plus noise has a different logic level than the original signal, the result may be completely garbled video.
The takeaway? If you are in an analog environment, a mismatched cable (75 \$\Omega\$ instead of 50 \$\Omega\$) will seriously degrade your analog signal. If you are in a digital environment, a mismatched cable will cost you something in your noise budget, but this may or may not have noticeable effects.
With both antenna and TV tuner input impedance being 75 Ω, the ideal choice of coaxial cable impedance would be 75 Ω.
However, with a strong local station, a 50 Ω cable with matching connectors would hardly make any difference to the received signal.
If I did my math right, a 50 ohm/75 ohm mismatch equates to a loss of less than 0.2 dB. This amount of loss is inconsequential in all but the most sensitive or demanding applications.
