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50 The PCB Design Magazine • December 2015 on the impedance plot, allows us to see very different signatures on the same plot. We now clearly see side by side all three damped sinu- soid responses. With the step response data in Figures 3 through 6 we can continue the process of the reverse pulse technique. (Note that Figures 3–6 show the same exact data only in different forms.) Next, we have to identify the steady state and the peaks and valleys in the step re- sponse. We have to do it in reverse order, start- ing with the right-most first extremum (peak or valley) and step through the peaks and valleys one by one from right to left until we reach the excitation time instance. Figure 7 shows the time stamps and voltage values of the peaks and valleys identified in the step response. Note that in simulated waveforms, like in this case, iden- tifying the peaks and valleys automatically is relatively easy; it would become more difficult when we need to process step response wave- forms obtained by measurements. The measure- ment noise makes the peak/valley identification a little trickier. With the data points in Figure 7 we can continue in two different ways. If we do not need to identify the pattern of the rogue wave excitation and we need only the worst- case transient noise magnitude, we just need to sum up the peaks and valleys and take the difference. The sum of the peaks is -78 mV; the sum of the valleys is -275 mV. The dif - ference is -197 mV. The -197 mV value is the absolute worst-case one-sided noise when an arbitrary sequence of 1A current steps hits the PDN. The worst-case two-sided transient noise is twice of this value minus the DC steady-state value (-3 mV in this case). These numbers give us 391 mVpp worst-case tran - sient noise. The other possible way of con- tinuing with the data points from Figure 7 is to determine the time-domain sequence of excitation edges creating the worst-case noise (the rogue wave) and to actually simulate the time-domain noise. With the timing sequence from Figure 7, Figure 8 shows the simulated waveforms on logarithmic horizontal scale. The blue wave- Figure 6: Simulated step response of the circuit shown in Figure 1. vertical axis is linear; the horizontal axis is logarithmic. quiet power SYSTEMATIC ESTIMATIoN oF WoRST-CASE PDN NoISE