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December 2015 • The PCB Design Magazine 55 2 (126 mOhm at 51.2 MHz) multiplied by 4/p. This is the result of sweeping a periodical cur- rent pulse stream to find the maximum noise deviation. This estimate is 59.6% lower than the true worst case. The rogue-wave optimized value is taken from [2] . It is 4.1% lower than the true worst case. In this particular example, when the imped- ance profile has multiple, almost equal peaks, the difference is dramatic. Estimating the worst- case noise just from the peak deviation or from swept-frequency periodic excitation hugely un- der-estimates the worst-case noise. The rogue- wave optimization, in theory, should be able to find the true worst case, but at a price of signifi- cant run time and potential convergence fail- ures. With a more flat impedance profile, with fewer peaks and smaller peak-valley ratio, the errors in all of the approximations would be lower. Eventually for a perfectly flat impedance profile all four calculation methods would pro- vide the same result. If you want to learn more about the subject, follow [7] and [8] at DesignCon 2016. PCBDESIGN References 1. Larry D. Smith, Raymond E. Anderson, Douglas W. Forehand, Thomas J. Pelc, and Tan- moy Roy, ''Power distribution system design methodology and capacitor selection for mod- ern CMOS technology,'' IEEE Transactions on Advanced Packaging, vol. 22, no. 3, pp. 284– 291, Aug.1999. 2. Steve Sandler, "Target Impedance Limita- tions and Rogue Wave Assessments on PDN Per- formance," paper 11-FR2 at DesignCon 2015, January 27–30, 2015, Santa Clara, CA. 3. Istvan Novak, "Comparison of Power Distribution Network Design Methods: Bypass Capacitor Selection Based on Time Domain and Frequency Domain Performances," DesignCon 2006, February 6–9, 2006, Santa Clara, CA. 4. Jingook Kim, Songping Wu, Hanfeng Wang, Yuzou Takita, Hayato Takeuchi, Kenji Araki, Gang Feng, and, Jun Fan, "Improved Target Impedance and IC Transient Current Measurement for Power Distribution Network Design," proceedings of the IEEE EMC Sympo- sium, July 25–30, 2010, Fort Lauderdale, FL. 5. Drabkin, et al, "Aperiodic Resonant Ex- citation of Microprocessor power Distribution Systems and the Reverse Pulse Technique," pro- ceedings of EPEP 2002, p. 175. 6. Linear Technology device simulation and models, click here. 7. Target Impedance and Rogue Waves, pan- el discussion at DesignCon 2016, January 19– 21, 2016, Santa Clara, CA. 8. Jae Young Choi, Ethan Koether, Istvan Novak, "Electrical and Thermal Consequences of Non-Flat Impedance Profiles," DesignCon 2016, January 19–21, 2016, Santa Clara, CA. Figure 11: Worst-case transient noise estimates of the circuit in Figure 1 based on different calculation methods. All responses assume a sequence of 1A current steps. Dr. Istvan Novak is a distin- guished engineer at oracle, working on signal and power integrity designs of mid-range servers and new technology de- velopments. With 25 patents to his name, Novak is co-author of "Frequency- Domain Characterization of Power Distribu- tion Networks." To read past columns, or to contact Novak, click here. quiet power SYSTEMATIC ESTIMATIoN oF WoRST-CASE PDN NoISE