April 9, 1998

SIGNAL INTEGRITY
How close is close enough?

Howard Johnson, PhD

Stub delays exceeding one-third of the driver's rise time destroy a termination's effectiveness.

Let's say you can't fit your series termination in the ideal location next to the driver. There just isn't room. So, you have to place it a little farther away than you'd like. Will it still work?

A series-termination resistor is supposed to absorb high-frequency energy, damping reflections on the net. To perform at its best, the resistor must be directly connected to a very-low-impedance source, presumably your driver. Anything placed in series with the termination resistor changes its value, making it less effective. This constraint includes the short pc-board trace, or connection stub, that hooks the
driver to the termination resistor. When designing applications that need very accurate termination, such as clock lines, you should take this effect into account. Fortunately, you can easily calculate the degradation that a connection stub causes. As long as the stub delay does not exceed one-third of the signal rise time, the approximations given below are accurate to within ±25%.

Because the connection stub connects at one end to a low-impedance driver, the connection stub acts like a little inductor, L_STUB. This stub inductance acts in series with the termination resistor, adding to the impedance of the termination. If you add the impedance of the stub, (j2pi)L_STUB, to the resistor value, R_T, you get a reasonable model for the combined termination impedance. Any step waveform hitting this type of termination impedance generates a short reflected pulse, even if the value of R_T exactly matches the line's characteristic impedance. This first reflected pulse amplitude approximately equals 1/2(V_STEP)(L_STUB/Z₀)(1/T_R), where V_STEP is the step amplitude, Z₀ is the transmission-line impe-
dance, and T_R is the 10 to 90% rise time of the step waveform.

That's the theory, except for the following embellishments:

1. The stub inductance may be calculated as L_STUB=(Z₀)DLY, where DLY is the delay of the stub in seconds, and Z₀ is the stub impedance.
2. Add to the stub inductance the parasitic series inductance of the driver package, L_PACKAGE.
3. The stub affects the rise time of the first incident waveform by a tiny amount. By keeping the stub delay less than one-third of the rise time, you hardly see this effect. (Thanks to Tom Giovannini at Applied Signal Technology (www.appsig.com) and Joe Cahill at IBM (www.ibm.com) for reminding me to mention this.)

For example, take a BGA package, L_PACKAGE=6000 pH, with an ideal 70ohms series terminator 1/2 in. (microstrip trace) from the driver package. Assume you have a 3.3V driver with a 1000-psec rise time. We can use embellishment 1 above to estimate L_STUB=1/2(145 pH/in.)(70ohms)=5075 pH. The total inductance equals L_TOTAL=L_PACKAGE+L_STUB=11,075 pH, and the reflected signal amplitude is Refl= 1/2(3.3V){(11,075 pH/70ohms)/1000 psec}=261 mV.

Even though the series-termination resistor had an ideal value, it failed to completely damp the reflections in this example. The implication is that you may need to wait at least one extra round-trip time for the reflections to decay before sampling the signal.

Pay close attention to the length of your connection stub. Stub delays measuring less than one-third of the signal rise time create residual reflections that can be approximated by this simple lumped-element model. Stub delays measuring in excess of one-third of the driver's rise time can create significant resonances, which grow rapidly with increasing trace length. Don't press your luck. If you want 20 dB (or more) of reflected-wave attenuation, use a stub delay that will not exceed more than one-sixth the rise time, a very good low-inductance package, and an accurate, low-inductance, nonetched metal film resistor.

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