November 20, 1997

Taming nonlinear transmission lines

Ron Mancini

Reflections occur on transmission lines when the lines are long enough for their propagation delay to equal the pulse-transition time.

It was 1967. The air in the RCA computer systems' circuits lab was electric with excitement. The circuits group had recommended a new saturated-logic IC--TTL--and was about to test it. The air of excitement soon turned into a cloud of despair, however, when the TTL would not drive moderately short lines without multiple pulsing. Necessity being the mother of invention, the group solved the problem by adding a diode from the input of the gate to ground. The diode clamped the negative edge to a diode drop below ground, thus preventing the transmission line from ringing back into the TTL threshold. The group incorporated this diode into the substrate, and, thanks to the RCA engineers, all TTL now contains the diode.

Reflections occur on transmission lines when the lines are long enough for their propagation delay to equal the pulse-transition time. If the drivers and receivers are resistive, the system is linear, and you can eliminate reflections by line matching. In analog signal-transmission systems, the signal current is low, so for video you put a 75 ohm resistor in series with the line-driver output. The receiver at the end of the line has a high input impedance, so you terminate the receiver in 75 ohms. Because the characteristic impedance of the line is 75 ohms, the pulse transition sees a pure 75 ohm system, and no reflections occur. However, the price you pay for distortionless transmission is signal strength, because the termination impedances halve the signal.

TTL can't match the transmission-line impedances, because the input and output of TTL gates are nonlinear impedances, and the high, low-level currents prevent the use of matching resistors. Z_IN for TTL is a function of the input voltage; at a TTL high, the input transistor is off, so the wiring sets the impedance at about 90 to 200 ohms. At a TTL low, the input looks into the forward-biased emitter of a common-base transistor that has an impedance of about 20 ohms. You can't match both impedances, so reflections occur. The TTL output impedance is a function of the logic state and ranges from 5 to 20 ohms, so adding a series matching resistor isn't an option.

A logical zero-to-one transition's reflection drives the input voltage higher than the source, and the reflection rings around the source voltage. The input voltage does not ring low enough to get below the threshold for a TTL high (2.0V), so it does no harm. A logical one-to-zero transition's reflection drives the input voltage lower than the source (ground), and the input voltage rings around ground. The clamp diode comes into play because it clamps the negative ringing to about ­0.7V, severely limiting the ringing's energy. The input voltage does not ring high enough to get above the threshold for a TTL low (0.8V), so again it does no harm.

My next column will use feedback theory to explain why amplifiers oscillate and why oscillators amplify.

References

1. De Falco, JA, "Reflections and crosstalk in logic circuit interconnections," IEEE Spectrum, July 1970.

2. Singleton, RS, "No need to juggle equations to find reflections--Just draw three lines," Electronics, Oct 28, 1968.

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