As IC clock frequencies approach the GHz range, the distribution of the clo
ck signals becomes more critical in terms of controlling both skew and sign
al attenuation. Moreover, inductance effects are evident since RC transmiss
ion lines will overly attenuate these high-frequency clock signals. To faci
litate accurate optimization of clock tree performance and skew requires si
mple metrics which capture these high-frequency effects,
In this paper, we derive simple metrics and bounds for the phase delay and
the attenuation of a periodic [RC(L)] tree response as a function of the fu
ndamental frequency of the clock signal, These metrics are based on the fir
st two moments of the impulse response, and are shown to further provide a
mechanism for control of underdamped responses (reflections), An important
result of this work is the clear demonstration that once the attenuation of
the clock signal is controlled, the phase delay can be accurately captured
in terms of the first-moment. Furthermore, the form of these metrics and t
heir relationship to one another provides an excellent foundation for vario
us forms of clock tree optimization.