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December 2015 • The PCB Design Magazine 51 form on the bottom is the excitation waveform; the black waveform on the top is the transient response. The peak-to-peak transient value is 391 mVpp, exactly matching the value that we calculated just from the peaks and valleys of the step response. Note that to achieve the worst-case transient noise, we used 37 current steps and their spacing does not exactly follow the three resonance frequencies. This straight- forward process yields the worst-case noise very fast, without the need of an optimization loop and it guarantees to provide the worst-case noise. In this particular example the true worst- case noise is 391 mVpp/A as opposed to the 375 Figure 7: Peak and valley time stamps and voltages identified in the step response of the circuit shown in Figure 1. mVpp/A predicted by the rogue-wave optimiza- tion from [2] . We can also look at the transient noise by another popular test method: using a repetitive stream of current steps with 1A magnitude and tune the repetition frequency (and possibly also the duty cycle) until we observe the maximum noise. We just change the definition of the I 1 current source to a stepped-frequency square- wave and run the simulations again. As we change the repetition frequency, we find that we get the maximum noise magnitude when the repetition frequency matches one of the peak frequencies. Figure 9 shows the result when we quiet power SYSTEMATIC ESTIMATIoN oF WoRST-CASE PDN NoISE