# mechanical analogy to signal propagation on coaxial cable

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)

## 1 Answer

I think your analogy is a good one. I have used it in the past and found it to be an excellent visualization tool.

Regarding the electrical analogy, it is valid for transmission lines in the limit where the number of individual "lumped" elements becomes large.

Many years ago I saw an excellent visualization analogy for transmission lines which consisted of a cable with fixed ends and a series of slender rods attached to it at right angles and at even intervals. the rods furnished rotary inertia and the cable segments between them furnished torsional compliance, so you could wiggle the end of one rod and send torsional waves down the cable which the rods made visible. Each rod-and-cable unit was one "lumped element" representation of the transmission line.

I have no idea where to procure one but have wanted to build one for years.