This thread is full of discussion about 50 ohms. What exactly is the "magic" to 50 ohms? In a world full of numbers, why is 50 ohms special? Could someone explain?
50 ohms is a common impedance for coax cables, but there are many other impedances around like 75 ohm coax and 100 ohm twisted pair.
In a way it is pretty "magic" and "special" because what is actually happening in these cables is amazing.
As you probably know, when two wires are near each other, these is a capacitance between them, so a very long cable has lots of capacitance. This is a bad thing as capacitance tends to attenuate AC.
All wire also has a self inductance, so the longer the wires, the more inductive impedance which again attenuates signals.
Now if you have a pair of wires that are separated with a constant spacing, such as in coax or twisted pair, then at one particular ratio of voltage to current, the self inductance exactly counters the effect of the capacitance. So no attenuation except for resistive and dielectric dissipative losses, even for very high frequencies. This explains why you are able to send a 1GHz signal down a 10 meter coax cable with little attenuation, even though from the apparent capacitance, there should be massive signal loss. This one particular ratio of voltage to current is the cable impedance and so if it is terminated at the far end by a resistor of the same impedance, a signal can travel down the cable with almost no deformation or attenuation.
What is actually happening is that each microscopic slice of the cable with its inductance and capacitance is temporarily storing the energy from the previous slice, and then passes all the energy on to the next slice at somethings a bit less then the speed of light. So each microscopic slice is actually a bit like a memory, as each different slice could have a different voltage. This sequence of differing voltages get faithfully passed from one slice to the next down the cable.
As an example, analogue oscilloscopes need to delay waveforms in the the channels by something like 5 - 100nS so that they can have the trigger firing before the edge you want to look at reaches the screen. The way they used to do this was to have a long coiled length of 50 ohm coax. If the sweep rate was set to 1 nSec per division, the complete waveform you see on the screen was stored at one point in the delay cable.
Why it is magical is that with discrete inductors and capacitance, their impedance only cancels out exactly at one frequency. With the case of the distributed inductance and capacitance in a coax cable, it surprisingly cancels out at every frequency.
This is incredibly lucky for us. Without this, the phone system wouldn't work and it would be very hard to get the signal from your TV antenna to your TV.
Richard