High Frequency Measurements
Douglas C. Smith
Address: P. O. Box 1457, Los Gatos,
Technical Tidbit - March 2004
Coupling Effects Between Equipment Enclosures (interactions with grounding conductors)
Two Cabinets with Separate Ground Connections
(figure from "Computer Simulation of ESD and Lightning Events," see below)
Abstract: Metal planes in close proximity, whether circuit boards or sheets of metal,
are tightly coupled at high frequencies. The frequencies involved
need not be all that high in some instances. Adjacent equipment cabinets
are one such case. Computer simulation is used to show that noise or EMI
arriving at one cabinet over equipment cables can strongly couple to an adjacent
cabinet, possibly affecting operation.
Discussion: Many computer and equipment rooms place large racks
and cabinets of equipment close to each other. Figure 1 illustrates two cabinets
located adjacent to each other. Such an arrangement can produce a relatively
large capacitance between the cabinets. For the purposes of this article,
a spacing of 1 cm and a total equipment side area of 2 square meters is assumed.
Such dimensions produce about 1800 pF of capacitance between the cabinets,
a significant amount of capacitance.
Sometimes adjacent equipment cabinets, such as those in Figure 1, are
grounded through individual conductors and not connected to each other. Safety
implications aside, such an attempt at producing a "single point" ground
can have unintended consequences. If three meter grounding cables are used
to connect the cabinets to building ground, the inductance of the cables
could be in the neighborhood of 2 1/2 microhenries. Then the equipment in
Figure 1 actually represents a parallel plate capacitor connected to a 5
microhenry inductor that is center tapped to building ground. For simplicity,
assume other cables are not present, coupling between the cabinets and other
structures is not significant, and we can neglect the free space capacitance
of the cabinets themselves. The cabinets and the grounding conductors form
a resonant circuit at about 1.7 MHz. There is very little loss in the circuit,
so the resonance will be reasonably high Q.
Let's assume that cabinet 0, on the left, is driven by a normalized
1 Volt source with a source impedance of 150 Ohms and 3/4 of a microhenry
of inductance, on the order of a meter of cable. Such a source is not a particularly
strong EMI source and could represent the common mode noise current on a
cable shield connected to the cabinet. Figure 2 shows cable currents for
the source cable (black), the grounding cable of cabinet 0 (blue), and the
grounding cable of cabinet 1 (red).
Figure 2. Source and Cable Currents vs. Frequency
At low frequencies, below 1 MHz, the source current is
just the short circuit current of a 1 volt source and 150 Ohms (6.7 mA) and
the current is flowing mostly in the grounding conductor of cabinet 0. At
about 1.7 MHz, the resonant frequency of the cabinets and grounding
conductors, an interesting phenomena results. The currents in both grounding
conductors are nearly equal and reach almost 40 mA. If the source had been
10 Volts, the grounding conductors would have carried almost 400 mA of current!
The cabinet 1 grounding conductor current actually exceeds the current at resonance in the
cabinet 0 grounding conductor by a few percent (not easily seen on the log
scale used). It is interesting to note that the current in the grounding conductor
of the "isolated" cabinet is slightly greater than the current in the grounding conductor
of the cabinet with the applied signal.
At frequencies above resonance, the source current divides equally between
the grounding conductors and is decreasing at 20 dB/decade due to the inductance
of the grounding conductors.
Conclusion: The example presented here of two adjacent equipment
cabinets again points out that metal planes in close proximity
are strongly coupled to each other. Thus, single point grounding at frequencies
significantly higher than power line frequencies is not possible.
Other articles on this website on coupling between metal planes:
Equipment used in this article includes:
- Mac OS X (FreeBSD "Unix") running on a dual G4 MacIntosh computer
- MI-SUGAR circuit simulation program version 0.4.4 for Mac OS X (Spice with a graphical interface, free!) Click here
to download the program for Mac OS X - not available for Windows. If you
would like more information on MI-SUGAR, click here to send email to Berk Ozer, the program's author. Berk's latest version, 0.5.2, now includes schematic capture.
Figure 1 is taken from one of my early published papers, "Computer Simulation
of ESD and Lightning Events" published in 1986 at the EOS/ESD Symposium. Although simulations and
design techniques have change significantly over the nearly 20 years since
that paper was written, the conclusions are still valid and support the conclusion
in this article. The original paper treats the subject in the time domain as opposed
to the viewpoint of this article in the frequency domain. Click here
to download the 1986 paper in pdf format.
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Copyright © 2004 Douglas C. Smith