We’ve been discussing loops all along and we are still at it. The last post looked at DM, this time it’s back to CM. These loops are the worst — big – bad – ugly! Finding the loop may be a problem . . . but where there’s current, there’s a loop. The DM loop is easy, typically a differential pair over a ground plane in a high-speed system, the CM is some synchronous current from unbalanced impedances associated with both the signal and its associated return lead that is conducted via a common reference surface.
All conductors have series inductance (L) and are coupled to the underlying ground plane or other closely coupled conductors via parasitic shunt capacitance (CP). The physical characteristics are not constant. The width or diameter of the conductors change along the length, the insulation or PCB thickness changes, the conductors have uneven lengths, different numbers of turns, and their spacing changes. These varying conductor characteristics unbalance the signal and its return, create the CM loop, and result in differential signal skew. Consequently, small CM currents, called longitudinal mode by telecommunications designers, arise from the unbalanced LC characteristics of the signal and associated signal return leads with respect to any closely coupled underlying return path, usually the chassis or grounding system.
These CM currents travel simultaneously in the same direction on each signal and return conductor and can be visualized as returning via a capacitively coupled return path in the nearby conducting surfaces. At the lower frequencies, this forms an antenna structure very similar to a monopole antenna oriented parallel to the cable runs.
At the higher frequencies where the cable lengths are a wavelength or longer, the structure becomes a traveling-wave antenna. In both of these antenna structures, the loop current is returned via the ground reference.
For an electrically short monopole antenna of length l, the electric field E(θ) radiation created by the CM current on the cable as denoted by Henry Ott is:
E(max) = 4 π ( F * I * l ) sin (θ) / 10 r
By orienting the antenna for maximum emissions, sin (θ) = 1 and simplifying, the equation can be rewritten as:
E(max) = 1.256×104 * F * I * l / r
Where:
E(max) = µV/meter
I = drive current (amps)
l = cable length in centimeters
F= emissions frequency (Hz)
r= measurement distance (meters)
I = drive current (amps)
l = cable length in centimeters
F= emissions frequency (Hz)
r= measurement distance (meters)
The CM-generated EMI levels predicted from this antenna model correspond well with measured data.
Speaking of antennas, all conductors can be antennas. Good conductors can be good antennas, but even poor conductors can be poor antennas. A poor antenna may be all it takes for a product to fail its EMC qualification test.
The amount of RF energy collected by or radiated from an antenna is related to its capture area which is related to its physical area. If the antenna is a microwave horn or a defined loop the physical area can be determined by inspection. With a wire it’s not so obvious, but since area is the product of length times width (A = L x W) keeping wire lengths short reduces the capture area. When designing a high speed system, think small.
– Ron Brewer
