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26 DESIGN007 MAGAZINE I NOVEMBER 2022 movement of EM fields and not on the flow of electrons. is also applies to DC analysis of the power distribution network. Rather than considering the current capacity of a conduc- tor, one should allow for the amount of field energy that the conductor can confine. Key Points • Energy does not flow in the copper traces of a PCB, but rather the energy follows the traces acting as a waveguide and prop- agates through the dielectric material. • e lumped element model assumes that the attributes of the circuit—resistance, capacitance, and inductance—are concen- trated into idealized electrical components connected by a network of perfectly conducting wires. • A distributed system disperses elements through the substrate along the entire length of the transmission line and is characterized by delay and scattered reflections. • Forget what you were taught in circuit theory and instead think in terms of electromagnetic field theory. We must focus on the movement of EM fields and not on the flow of electrons. • An EM carrier wave can transport information, or it can supply energy to power an IC. • When information is carried, the propaga- tion of the wave alters the timing of the data and must be added to the delay of the circuit. • Electric fields exist at all frequencies including DC. • e velocity of electrons in copper is extremely slow. In a typical geometry, the average velocity is less than 1 cm/s. • e fields associated with traces over a conducting plane are located under the traces. • At frequencies below a kilohertz, the series inductive reactance between two points is lower than the resistance. erefore, at low frequencies, current patterns are controlled by conductor resistance. • Electromagnetic energy moving through the dielectric induces current to flow in the conductors. • e trace and the plane bound the energy and thus it is the energy density between the conductors that determines the current density in the trace geometry. • e wider and thicker the conductor, the more energy can be contained in the field. • If the trace is too narrow, then the contained energy will dissipate as heat. • A DC power integrity simulator highlights areas of high current density, which will lead to higher temperatures. • e trace also cools by conduction through the substrate. • e skin effect applies to digital circuits, where currents flow very near the surface of the conductors. DESIGN007 Resources 1. Beyond Design by Barry Olney: The Wavelength of Electromagnetic Energy, The Big Bang-Lumped Element to Distributed System, Surface Roughness. 2. An interview with Rick Hartley discussing Ralph Morrison by Judy Warner. 3. "Fast Circuit Boards" by Ralph Morrison 4. "The Energy Density of Electromagnetic Waves" by Cadence. Barry Olney is managing director of In-Circuit Design Pty Ltd (iCD), Australia, a PCB design service bureau that specializes in board-level simulation. The company developed the iCD Design Integrity software incorporat- ing the iCD Stackup, PDN, and CPW Planner. The software can be downloaded at www.icd.com.au. To read past columns or contact Olney, click here.