# Riddle me this, CAD man: when is a transmission line not a transmission line?

THE SHORT ANSWER is, never. A transmission line is always a transmission line and always behaves like a transmission line, no matter how long or how short it is.

One of the important properties of a transmission line is the reflection of signals that occurs at the ends of unterminated lines. This will happen if the driver has a low impedance and the receiver has a high impedance.

However, if the transmission line's time delay is short compared to the rise time of the signal, the reflections that might occur at the ends will still happen, but will be smeared out during the rising or falling edge of the signal. We may not see them or their effects. This is not to say the transmission line will not act like a transmission line; it's just that the reflections may not cause a problem.

FIGURE 1 shows the signal at a receiver located on the end of a 50 [ohms] transmission line with a low impedance driver driving the line. The rise time of the driver is 0.5 nsec and the length of the line is increasing in each of the simulations. When the time delay is 20% of the rise time, the reflections are almost imperceptible. As the length of the line, or its time delay, increases, the reflections begin to appear.

[FIGURE 1 OMITTED]

This suggests a simple rule of thumb. If the transmission line's time delay is shorter than roughly 20% of the rise time of the signal, the reflections will be smeared out, and the reflection noise may be insignificant. The electrical effects of the transmission line can always be modeled in a simulator, using an ideal transmission line circuit model.

If the trace is in FR-4, with a dielectric constant of about 4, the speed of a signal will be about 6 in/nsec. If the rise time is RT, in nsec, and the time delay is TD, in nsec, then the condition for the transmission line being so short that the reflections will smear out is TD < 20% x RT. See FIGURE 2.

[FIGURE 2 OMITTED]

The physical length of the line, Len, in inches is related to the TD of the line by: TD = Len/vel, with vel = 6 in/nsec. With a little algebra, we find the maximum length of a transmission line, where the reflections smear out, to be Len < RT, with Len in inches and RT in nsec.

In other words, the rule of thumb is that if we can keep the length in inches shorter than the rise time in nsec, reflections may not cause a problem.

For example, if the rise time is 1 nsec, by keeping transmission lines shorter than 1 inch we will minimize reflections. If the rise time were 0.5 nsec, the critical length would be 0.5 in. Clearly, with the current state-of-the-art drivers, with rise times shorter than 0.5 nsec, virtually all interconnects on a board are longer than this critical length, and all interconnects will behave like transmission lines, and probably should be terminated.

The way to think about a transmission line is as a brand-new type of circuit element that is not a bunch of lumped inductors and capacitors, but a new type of circuit element on which a signal sees a constant, instantaneous impedance each step it takes moving down the line. A signal does not see a capacitor, followed by an inductor and then a capacitor. It sees a constant impedance each step, until it hits the ends, where it reflects.

You can never go wrong thinking about every interconnect as a transmission line, and designing for a target controlled impedance.

REFERENCES

The principle covered in this column is reviewed in detail in Signal Integrity- Simplified (Prentice Hall) and online at www.BogEnt.com.

ERIC BOGATIN is the CTO at IDI (www.idi.net), a high-volume manufacturer of high-performance interconnects. He is scheduled to speak at PCB Design Conference East in October. Bogatin can be reached at eric@BogEnt.com.
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