## Sharp Edges

Harish from the University of Texas at Arlington writes:

**Figure 1—**Phantom oscillations exist in the output

of this transmission-line circuit.

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 PSpice and found that oscillations exist in the output (Figure 1). How do you explain this scenario?

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, Z_{0}. Each capacitor equals one-half the line delay *divided* by Z_{0}.

**Figure 2—**This pi-model circuit mimics the

behavior of a short transmission line.

The pi-model circuit, if you drive it as the Harish describes with a source impedance of 5Ω and load it with 10 pF, exhibits a high-Q resonance at 260 MHz. Harish is seeing 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 Harish had used a gaussian edge, he wouldn't have noticed the ringing. Then again, he wouldn't have learned anything new, would he?

**Figure 3—**A gaussian edge eliminates the phanton

ripples in the simulation output.

In general, at least three factors contribute to ringing: long lines, big
capacitive loads, and source impedances much smaller than Z_{0}.

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 Z_{0}, 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.