EDIT: The analogy is wrong if we think of voltage propagation, I confused and in the eletrical signal, it actually happens contrary to what the analogy predicts. However, for current, it holds.
I am doing an experiment for my physics lab course where I have to study the reflections that happen inside it. I tried to look in physics books but I end up getting confused with all the mathematics and some of the physics I don't understand yet (I have no idea what maxwell's equations represent). However I believe it can be understood trough a mechanical analogy. Here it is:
Suppose you have a rope with a mass density per unit lenght $\rho$, wich is attached to another rope of mass density per unit lenght $\alpha$. Now you give a swing at one the end of the rope with density $\rho$, so an impulse of energy will travel along the first rope, but enentually it reaches the point where both ropes meet. And now we have 4 situations:
- if $\alpha =0$, then we have the first rope attached to a massless object which is equivalent to an open end rope, hence the signal is reflected without inversion;
- if $\alpha =\rho$, then it's just like having a continuous rope, hence there is no reflection;
- if $\alpha =\infty$, then it's simply a rope with both "closed" ends, hence there is full reflection with the signal inverted;
- if $\alpha \neq \rho$, then some of the signal is inverted back, and some is passed on to the other rope ( I didn't analyse the cases where $\alpha >\rho$ and $\alpha <\rho$, but it is not relevant for now, I think)
Now for the eletrical coaxial cable. Say I have an impulse generator connected to a coaxial cable, with internal impedance $Z_L$ which is connected to some impedance, $Z_C$. The analogy holds, for when $Z_C$=0 (short circuit) there is full reflection like the open end string, for $Z_C=\infty$ (open circuit) there is full inverted reflection like the "two closed" ends string, for $Z_C=Z_L$ there is no reflection, just like the continuous string, and finnaly for $Z_C\neq Z_L$ there is some refletion, but some signal is still passed on.
Is this analisys valid? If not, where and why does it break? Intuitively, it is easy to see how a wave on a string can be approximated by a number of bodies that perform simple harmonic motions that are connected by a massless string and then we approximate for an infinite number of oscilators. My first intuition is to think that the same is done for eletrical wires/transmission cables with an infinite number of LC coupled oscilators. If that is the case, how can it be explained so that even a child could understand (maybe it's asking too much but still)