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24 DESIGN007 MAGAZINE I NOVEMBER 2022 the signal, energy dissipation, and reflections which are key issues of digital logic design. It incorrectly teaches that: • e conductors carry the energy • e load instantly affects the flow of energy • e transmission line has no losses So now, it is time to forget what you were taught and instead think in terms of electro- magnetic field theory. We must focus on the movement of EM fields and not on the flow of electrons. The first law of thermodynamics states: Energ y can neither b e c reated nor b e destroyed; it can only be transferred from one form to another. When an electromagnetic wave propagates from the source, it transfers energy to objects in its path. Electromagnetic fields transport all the energy on a circuit board. is carrier wave can transport infor- mation, or it can supply energy to power an IC. If information is carried, then the propaga- tion of the wave alters the timing of the data and must be added to the delay of the circuit. e energy supplied to a load is carried in the space between the connecting conductors and not in the conductors themselves. is con- cept applies at all frequencies including DC. EM fields can also move energy in free space but not as DC. Electromagnetic energy travels at the speed of light in a vacuum or air but is delayed by the dielectric materials used to construct multi- layer PCBs. e relative permeability or dielec- tric constant (Dk) of the surrounding materials impacts the velocity of propagation (v) at the speed of light (c). Equation 1 As the dielectric constant of a material increases, the velocity of propagation slows down. With a Dk = 4, the velocity is half the speed of light. If one uses different core and prepreg materials in the substrate, then each layer will have varying speeds depending on the dielectric constant. is will impact the timing of memory buses in particular. What Happens at Low Frequency and DC? Voltage differences can exist between points in space or between conducting surfaces. Elec- tric fields exist at all frequencies including DC. In a field representation, lines of force start on a fixed amount of positive charge and termi- nate on the same amount of opposite charge. When the lines are close together, the forces are the greatest. A small electric field within a conductor is required for current flow. When there is no current flow there is no field. e velocity of electrons in copper is extremely slow. In a typi- cal geometry, the average velocity is less than 1 cm/s. is occurs because the electron den- sity in a conductor is extremely high. What is important is the nature of the electric and mag- netic fields. At low frequencies (below 100 kHz), most of the field generated by a circuit returns to the source. is is a good example of where circuit theory can be put to good use. At DC, the fields are unchanging, and the energy is moving at about half the speed of light. We need to know the value of current flow to calculate voltage drop, power losses, and the magnetic field. e fields associated with traces over a con- ducting plane are located under the traces. At Figure 1: A trace disconnects when there is too much energy in the field.