Issue link: https://iconnect007.uberflip.com/i/615135
48 The PCB Design Magazine • December 2015 ative. Because of the LTI assumption, any DC voltage on the rail can be taken into account as a simple shift. The excitation current is a single current step, stepping up from zero to one ampere with 1 ns rise time. Note that the 1 ns rise time cor- responds to about 300 MHz excitation band- width, where the impedance profile has a ca- pacitive downslope and therefore the actual rise or fall time of the excitation is less critical. The step response is shown up to 200 µs, where it settles out to a -3 mV DC value. This is the result of the series equivalent of R 1 and R 3 . The main signature we see on this scale is a damped sinusoid ringing with approximately 15 µs period; this corresponds to the 67.6 kHz lowest-frequency peak in the impedance pro- file. We see more rapid changes near the left vertical axis, but we don't see any details. To see more details of the faster transients, we need to change the time scale. Figure 4 shows the result. It is the same data, except now we show only the first ten micro- second time interval. On the right half of the plot the step response has a smooth rise; this is the beginning of the 67 kHz ringing. The left half of the response has a damped sinusoidal ringing with approximately 1 µs period; this is originated from the 1.02 MHz impedance peak. We see some further fast transients near the left vertical axis, but on this horizontal scale we still can't see the details. We have to make another adjustment to the horizontal scale to see those details as well. In Figure 5 we further zoom into the wave- form and show only the first one microsecond interval. From 0.1 to 1 µs we see a slow sine wave in the response; this is the 1MHz damped sinusoid. Near the left vertical axis now we see another damped sinusoidal waveform with ap- proximately 20 ns period; this comes from the 51 MHz peak. To see all signatures on the same plot, we need to switch to logarithmic horizontal axis, as shown in Figure 6. The logarithmic time axis, just like the logarithmic frequency axis Figure 3: Simulated step response of the circuit shown in Figure 1. Note that both axes are linear, as it would be shown on an oscilloscope or by a default simulation setup. Horizontal axis shows the full 0 to 0.2 µs time interval. quiet power SYSTEMATIC ESTIMATIoN oF WoRST-CASE PDN NoISE