Basics of Digital Design--Lumped and Distributed Systems

Basics of Digital Design--Lumped and Distributed Systems

The response of a conducting system to an input signal depends largely on whether the size of the system is smaller than the effective length of the fastest electrical characteristic of the signal, and vice versa.

The effective length of an electrical characteristic, such as a rising edge, is determined by the duration of the characteristic and its propagation delay. As an example, let's analyze the rising edge of a 10KH ECL signal. The rise time of this type of gate circuit is about 1.0NS. When this rising edge propagates along the inner layer of an FR-4 printed circuit board, its effective length is 5.6M: I=TR/D

Where: I = the length of the rising edge, IN

TR = rise time, PS

D = delay, PS/

The series of instantaneous waveforms in Figure 1.3 plot the potential of a signal as it travels along a 10-in straight line. A 1-ms rising edge flows in from the left end of the line. Obviously, as the pulse travels forward along the line, the potential at each point is different. The response of this system to the input pulse is distributed along the line, and we call it a distributed system. The instantaneous waveform of the 4th NS shows that the actual length of this rising edge is 5.6 in.

If the physical size of the system is small enough and all points respond to a uniform potential at the same time, it is called a lumped system. A 1IN line in Figure 1.3 that transmits the same 1NS rising edge shows the response of a lumped system. The potential of each part of the trace is (almost) the same throughout the duration.

Whether a system is distributed or lumped is determined by the rise time of the signal flowing through the system. The distinguishing mark is the ratio of the system size to the effective length of the rise time. For printed circuit board traces, point-to-point connections, and bus structures, if the connection length is less than 1/6 of the effective length of the rise time, the circuit mainly exhibits the characteristics of a lumped system.