Published by Eric Bogatin on 25 Oct 2012 at 09:14 am
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.