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DECEMBER 2022 I DESIGN007 MAGAZINE 21 he discovered he did so empirically by experi- menting in the lab. He is credited with devel- oping Faraday's Law of Magnetic Induction 5 in 1831: "A changing magnetic field is accompanied by a changing electric field at right angles to the change of the magnetic field." A Side Note on Magnetic Fields We learned in EE101 that if we send a cur- rent down a trace, a magnetic field is formed around the trace. It takes some energy to cre- ate that field and that energy is stored in the field. But that is only a small portion of the energy flowing down the trace. We know that because the energy in the trace heats the trace due to the I 2 R power dissipation in the trace. If we stop the current flow, the energy in the magnetic field collapses back around the trace and returns to the trace. In a lossless sys- tem, there is no energy lost in the field. Only the "real" term in the impedance expression (the resistance) can result in energy loss 6 . e energy that builds up around (ideal) inductors and capacitors is always returned back to the circuit. The Implications ink about this: We send a (changing) sig- nal down a trace. is causes a "flow" of cur- rent (movement of electrons) along the trace. e electrons, being charged particles, cause a changing electric field along the trace. e changing current, following Ampere's Law, causes a changing magnetic field along the trace. us, there is an electromagnetic field around the trace. So, where exactly is the sig- nal? is is not an either/or question. I have just described a system where the signal is inherent everywhere. It is in the current along the trace. It is in the voltage gradients along the trace. It is in the electromagnetic field around the trace. We know this because: • We can measure the changing current along the trace with a probe • We can measure the changing voltage gradients along the trace caused by IR drops (Ohm's Law) • We can measure the EMI radiated from around the trace • If we cut the trace, the electromagnetic field stops • If we change a characteristic of the trace (physical size or resistance), the current and the electromagnetic field around the trace change • If we change the terminating resistor at the end of the trace, changing the reflection coefficient, the current, signal, and electromagnetic field all change • If we change the e r of the material around the trace (where the field is) the propaga- tion speed of the (signal) current in the trace changes We also know that these elements are not separable. e electric field cannot get out in front of the magnetic field, the magnetic field cannot get in front of the current, and the cur- rent cannot get in front of the electromagnetic field. Conclusion Board designers must pay attention to both the electronic circuit (trace, current, Ohm's Law, etc.) and the physics of the electromag- Figure 4: An example of Ampere's Law.