Introduction to Signal Integrity - Understanding Signal Integrity - page 6

0 5n 10n 15n 20n

0 5n 10n 15n 20n

(a) fo only (b) fo + h3

0 5n 10n 15n 20n 0 5n 10n 15n 20n

(d) fo + h3 + h5 + h7
Figure 1.3 Reconstructing a 10-ns pulse stream from the fundamental and the fi rst three odd harmonics.
The progressive improvement in the pulse appearance is apparent as more harmonics are added.

(c) fo + h3 + h5

A second relationship is shown in Figure 1.4. The solid circles represent the
spectra of the 100-MHz square wave when the rise time is zero. This is identical to
Figure 1.2 and is included for comparison with the hollow circles, which show the
spectra when the same pulse has a rise time of 1.5 ns. The fundamental frequencies
are seen to be the same, but the amplitude is lower for the 1.5-ns case, and some
even harmonics are now present (for instance, at 200 MHz and 400 MHz). We
further notice that for the 1.5-ns rise time case the amplitudes are essentially zero
for frequencies of roughly 600 MHz and higher. In contrast, when the rise time is
zero, the amplitude is still significant up to 1.3 GHz and beyond.
Apparently the zero rise time pulse requires more harmonics than an identical
pulse having a slower rise time. In the frequency domain this means the zero rise
time pulse requires more bandwidth than the 1.5-ns rise-time pulse for distortion
free transmission. Alternatively, we can say that less bandwidth is needed for dis-
tortion free transmission of a long rise time pulse than an identical, sharper pulse.
Pulse shaping (including rise time control) is an important aspect of high-speed
I/O design [9-12], but is outside the scope of this topic. What is relevant to us is the