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46 The PCB Design Magazine • December 2015 The target-impedance concept and these expressions assume a linear and time-invari- ant (LTI) PDN; moreover, assume that the PDN impedance is flat, frequency indepen- dent, from DC up to the BW bandwidth of the excitation. Interestingly, if the impedance profile is not flat, but still stays at or below the Z target limit, the worst-case transient noise gets bigger. For some of the typical PDN impedance profiles, this was shown here [3] . When the impedance profile is not flat and the worst-case transient noise is dif- ferent from what we can expect from the target impedance formula, we need to determine what the excitation pattern that yields worst-case noise is and what its value is. Recently modified target impedance approaches have been pro- posed (for instance [4] ), or as I have written [3] , a conservative correction factor can be used based on the degree of non-flatness of the impedance synthesis method. Using a conservative correc- tion factor from the beginning makes it possible to follow a straightforward design process with- out the need of iterations. For LTI PDNs with flat or any non-flat imped- ance, a process called reverse pulse technique was published in 2002 [5] . Without the need of an optimization loop it provides a guaranteed way to determine the absolute worst-case tran- sient noise and its corresponding excitation pattern, what we still may call rogue wave. To illustrate the power and usefulness of the pro- cess, we take the rogue-wave example circuit in [2] and calculate the worst-case noise with the reverse pulse technique. Figure 1 shows the schematics from [2] , re- drawn in a free circuit simulator [6]. Note that this particular simulator has the capability to repre- sent a full RLC model of a single component, but for sake of clarity the schematic shown here explicitly calls out all parasitic elements and their own parasitics are set to zero. For example, component L 2 , having an inductance value of 2nH, has no series resistance or parallel capaci- tance. The series resistance of L 2 is separately called out by R 2 with 2mOhm value. We can run an AC simulation on this circuit to find out its impedance. For this purpose we run an AC sweep of the I 1 current source with a current magnitude of 1A. The V 2 voltage source with a voltage of zero is included only for con- venience so that we can also plot the current Figure 1: Rogue-wave example circuit from Steve Sandler's DesignCon 2015 paper [2] . quiet power SYSTEMATIC ESTIMATIoN oF WoRST-CASE PDN NoISE

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