Worst case power/ground noise estimation using an equivalent transition time for resonance

The nonmonotonic behavior of power/ground noise with respect to the transition time t_r is investigated for an inductive power distribution network with a decoupling capacitor. The worst case power/ ground noise obtained with fast switching characteristics is shown to be significantly inaccurate. An equivalent transition time that corresponds to resonance is presented to accurately estimate the worst case power/ ground noise in the time domain. Furthermore, the sensitivity of the ground noise to the decoupling capacitance C_d and parasitic inductance L_g is evaluated as a function of the transition time. Increasing the decoupling capacitance is shown to efficiently reduce the noise for transition times smaller than twice the LC time constant, t_r ≤ 2 √L_gC_d. Alternatively, reducing the parasitic inductance L_g is shown to be effective for transition times greater than twice the LC time constant, t_r ≥ 2√L_gC_d. The peak noise occurs when the transition time is approximately equal to twice the LC time constant, t_r ≈ 2√L_g C_d, referred to as the equivalent transition time for resonance.