I debated whether I should introduce radiated pickup by the DM loop area next and then dismissed it so that I could continue with radiated emission from common mode (CM) currents. These tend to be very mysterious because they are typically caused by unbalanced differential mode (DM) currents. Often these are caused by a few extra grounds floating around somewhere in the circuit. As a result I decided to do neither and discuss, instead, how the enigmic grounds get there. It was going to be a brief discussion, but there are a couple of things that we take for granted that at RF do not exist. These are (1) the open circuit and (2) the short(ed) circuit.
A short across the ends of two conductors or from one conductor to ground simply connects them together increasing the total conductor length. Also, the short may cause DC and low frequency resistance to suddenly decrease, resulting in a significant increase in current. At RF, it’s a completely different story. There may not have been any change at all. Conductors have inductance. which means that any changing current in the conductor will induce a voltage in the conductor that is related to how fast the current changes.
We know the law as V= L di/dt. The symbol L for inductance was chosen to honor an early physicist named Heinrich Lenz, but if you ask any budding young science student what L stands for, they will probably answer L stands for length. Good answer, because inductance is so dependent on conductor length that almost all other dimensional characteristics pall by comparison.
Whatever inductance the conductors had before the short, they still have after the short; so as the frequency increases (di/dt increasing), so does the voltage developed across the conductor. Shorting the circuit to ground to eliminate a high frequency RF problem probably will not work, especially with long conductor lengths because the conductor impedance is Z = R + jωL and L (inductance) is highly dependent on L (length). Additionally, at any given frequency when the length L = λ/4, the conductor looks like an open circuit, NOT a short. This is the primary reason that the length of bonding straps and grounding systems is restricted to L = λ/20 at the highest frequency of interest. If it’s “gonna” work it’s “gotta” be short!
The open circuit is the inverse of the short circuit. In this case, two conductors are separated by a dielectric, probably air; but it could be the wiring insulation, the PCB material, or any other non-conductor . . . so instead of having an inductor, we have a capacitor. At DC the open circuit is truly open; but as the frequency increases, the impedance Z= 1/ jωC becomes smaller and smaller until the two conductors may as well be connected together.
How bad is it? Suppose we have two 0.1 inches wide flat conductors crossing each other at 90 degrees with a 10 mil (0.00025 m) spacing. For reference, 0.1 inches is the diameter of number 10 AWG wire. An inch is approximately 1/40th of a meter, so the projected capacitive coupling area A = (1/400)2 = 0.00000625 sq meters. It’s not a very big area, but it still forms a measurable air dielectric capacitor:
C = ε A /d = (8.84pF/m) (0.00000625)/(0.00025) = 0.221 pF
– Ron Brewer