Equivalent rise time for resonance in power/ground noise estimation

The non-monotonic behavior of power/ground noise with respect to the rise time tr is investigated for an inductive power distribution network with a decoupling capacitor. A time domain solution is provided for the rise time that produces resonant behavior, thereby maximizing the power/ground noise. The sensitivity of the ground noise to the decoupling capacitance Q and parasitic inductance L_g is evaluated as a function of the rise time. Increasing the decoupling capacitance is shown to efficiently reduce the noise for t_r les 2radic(L_gC_d). Alternatively, reducing the parasitic inductance L_g is shown to be effective for t_r ges 2radic(L_gC_d).