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16 DESIGN007 MAGAZINE I DECEMBER 2019 The simplistic approach to analyzing elec- tronic circuits is to use the lumped element model. This methodology assumes that the at- tributes of the circuit—resistance, capacitance, and inductance—are concentrated into ideal- ized electrical components connected by a net- work of perfectly conducting wires. However, in reality, that is not the case. As the frequency and rise time increase, these elements become distributed continu- ously through the substrate along the entire length of the trace. The copper trace and the adjacent dielectric materials become a trans- mission line, the skin effect forces current into the outer regions of the conductor, and fre- quency-dependent losses impact on the qual- ity of the signal. The PCB trace now behaves as a distributed system with parasitic induc- tance and capacitance characterized by delay and scattered reflections. The behavior we are now concerned about occurs in the frequency domain. In this month's column, I will discuss the difference between the lumped element model and the distributed system (Figure 1). In my previous column, "The Frequency Do- main," we saw that impedance is defined in both the time and frequency domains. In the time domain, the impedance of a resistor (R) can be represented by a relationship between voltage and current (Ohm's Law). Similarly, an ideal capacitor (C) has a relationship be- tween the stored charge and the voltage across its plates. And the behavior of an ideal induc- tor (L) is defined by how fast the current trav- eling through it changes in the time domain. We group these three elements (RLC) in a category called lumped circuit elements, in the sense that their properties can be lumped into The Big Bang: Lumped Element to Distributed System Beyond Design by Barry Olney, IN-CIRCUIT DESIGN PTY LTD / AUSTRALIA Figure 1: (a) Lumped element; (b) distributed system.