Published by Eric Bogatin on 25 Oct 2012 at 09:14 am
It’s Signal Integrity Which Keeps the Universe from Blowing Up
I teach two classes in which I introduce essential principle #5, that whenever the instantaneous impedance the signal sees changes, a reflected signal is created. Almost without fail, at the end of the class, some brave soul, usually a younger engineer, comes up to me and asks that very important question, “Why?”
The flip answer is that if there were no reflected signal created when the instantaneous impedance the signal encounters changes, the universe would blow up. The reflected signal is created to keep the universe in harmony.
To see the problem, look at the figure to the left. The instantaneous impedance defines the ratio of the propagating voltage to the current in each region. If the instantaneous impedance in the two regions is different, the ratio of the voltages to currents in the two regions must be different.
Think about the incident voltage that hits the interface and continues to the other side. If there were no reflections, and the incident and transmitted voltages were different, there would be an electric field between two points on either side of the interface. The closer these two points get, the larger the electric field.
If we bring the two points really, really close but still sitting in the different impedances, the field could become extremely large, and the universe could blow up.
So, maybe the voltages have to be the same. But, if the impedances are different, the ratios of the voltages to the currents in the two regions have to be different different. If the voltages are the same, the currents into the interface must be different. But, if there is more current going into the interface than transmitted out, charge will build up and if we wait long enough, the universe will explode at the interface.
These two conditions, of the voltages being continuous and the net current into the interface being 0, are called boundary conditions. They cannot both be met without a reflected signal being created. The details of how the reflected signal helps to keep the universe in harmony and the derivation of the reflection coefficient and transmission coefficient can be found in the brief article I wrote for PCD&F magazine.
So we see that the most common signal integrity problem, the creation of reflections from impedance changes and the signal distortion that results from multiple reflections, is really a good thing. Without it, the universe would blow up.
boson on 15 Dec 2012 at 10:54 am #
Hi Eric,
What you give is an example that transmission line approximation to Maxwell’s equations cannot explain adequately. At the location of discontinuity higher order modes will be excited which can only be accounted for by a full-wave solution of Maxwell’s equations. Reflection and transmission according to impedance mismatch will be a low frequency approximation to a more complicated situation.
As for the blow-up of the universe, the inflation theory predicts its outer edges are already expanding faster than the speed of light. But if your sensational title is only meant for getting lost in a black hole or something that will not happen, either. There’s a much deeper level of physics below classical Maxwell theory that has to be considered here. Indeed, according to quantum physics there’s a finite probability that all photons pass the discontinuity without being reflected, just like the probability that all photons be reflected without any transmission, at all. Those cases bode well with the physics that govern our visible universe. So don’t worry, with or without the reflection on your structure the universe is not going to not blow up.
Eric Bogatin on 16 Dec 2012 at 11:38 am #
Boson-
Thanks for your comment. I would counter that the transmission line approximation to Maxwell’s equations does indeed provide a basis to predict reflections from impedance discontinuities. Why is Maxwell’s equations correct, and seem to obey boundary conditions? I would go with the the Anthropic Principle that suggests if they were not correct, we would not be here to use them. If the speed of light were off, or static E and M fields did not drop off like 1/r^2, stars, matter and life as we know it would not exist.
While the universe may be blowing up at the fringes, and eventually will locally, if there were no reflections at interfaces, I think we would accelerate the blowup.