By Howard Johnson, PhD - June 22, 2006
A correspondent from the University of Texas—Arlington recently wrote to me with some questions: Most books suggest that overshoot and ringing arise if the signal-rise time is less than the round-trip delay of the transmission line. Does that [suggestion] mean ringing and overshoot cannot occur if the signal-rise time exceeds the round-trip time even though an impedance mismatch exists? I tried the snippet [in Figure 1] in PSpice and found that oscillations exist in the output. How do you explain this scenario?
Here's my response to my correspondent's questions. A line delay that is short compared with the signal rise and fall time does not by itself preclude ringing. A short line—less than one-third the length of the signal rise or fall time—does guarantee that you can model the line as a simple lumped-element circuit known as a pi model. The pi model for suitably short lines accurately mimics the transmission-line performance.
Figure 2 shows the correct pi-model configuration and values for the transmission line in Figure 1. The inductance equals the line delay multiplied by its characteristic impedance, Z0. Each capacitor equals one-half the line delay divided by Z0.
The pi-model circuit, if you drive it as the writer describes with a source impedance of 5Ω and load it with 10 pF, exhibits a high-Q resonance at 260 MHz. The writer sees that resonance.
His choice of driving waveform compounds his difficulties. The sharp corners of the 8-nsec PWL (piecewise-linear) edges kick the circuit with a splash of high-frequency energy on every transition. Those corners overstimulate the resonant behavior at 260 MHz.
A gaussian edge has no sharp corners and, so, better represents a real digital waveform. A gaussian edge with a rise time of 6.4 nsec (10 to 90%) eliminates the phantom ripples in his simulation output (Figure 3).
If my correspondent had used a gaussian edge, he wouldn't have noticed the ringing. Then again, he wouldn't have learned anything new, would he?
In general, at least three factors contribute to ringing: long lines, big capacitive loads, and source impedances much smaller than Z0.
Figure 1 uses a short transmission line but combines the bad factors of a big capacitive load and a small source impedance. Shorten the line delay, and watch the circuit become less sensitive to these two bad factors. Lengthen the delay, and observe an even more squirrelly system.
My "safe-harbor" recommendation for transmission lines works as follows: If the line delay is less than one-sixth of the rise or fall time, and the source impedance is no less than one-third of Z0, you will have little or no trouble with ringing.
I simulate everything else. When I do, I use a gaussian—or at least a parabolic—edge shape.