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42 The PCB Design Magazine • May 2014 and G (dielectric loss) terms can be assumed to be zero simplifying the equation to: equation 3 The characteristic impedance (Zo), of an ideal transmission line, remains constant at all frequencies. It has no imaginary part and is not frequency dependant. As the electromagnetic energy propagates down a transmission line, current is induced into the conductors as il- lustrated in Figure 5. The current flows along the conductors, charging the first section's parasitic capacitance and then flows back, on the return conductor (reference plane), to the source. The current exists only on the rising edge of the propagating wave and thus charges each section's capacitance as it moves down the line with the return current, from each sec- tion, flowing back to the source. Then as the pulse passes, the falling edge discharges each section's capacitance in turn. By the time the signal wave reaches the load, it has established multiple paths of return current along the PCB planes. Current always flows in a loop. But is does not flow along the transmission line to the end (load) and then return to the source as one would expect with DC. But instead, the signal charges each section in turn as the rising edge propagates along the transmission line on the dielectric material. Although a lossless model is a good repre- sentation of a typical low-frequency transmis- sion line, at high frequencies, the conductor and dielectric losses need to be considered. For this reason, the closed-form equations shown here are approximations only and a 2D field solver, such as that integrated into the ICD Stackup Planner is required to accurately mod- el the impedance of a multilayer PCB transmis- sion line. Points to Remember • In the early 1900s, barbed wire fences were used as an ad hoc, rural telephone system that had no operators, no bills, and no long-distance charges. • Telegrapher's equations still accurately model the propagation of signals along trans- mission lines. • In 1995, Broadcom demonstrated its 100Base-T4 Ethernet chipset operating over barbed wire. • Wideband Corporation later successfully demonstrated 1Gbps over barbed wire. • A transmission line is a series of conduc- tors that guide electromagnetic energy from one point to another. It is the movement of an electromagnetic field or energy—not voltage or current. • The three common transmission line structures of a multilayer PCB are: embedded microstrip, symmetric, and dual asymmetric stripline configurations. • The velocity of propagation in FR-4 is about half the speed of light, or 6 inches per ns. Figure 5: Model of a lossless transmission line indicating current flow. TRANSMISSION LINES continues beyond design