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back-matter - Appendices Appendix A RMS Values of Commonly...

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Appendices
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Appendix A RMS Values of Commonly Observed Converter Waveforms The waveforms encountered in power electronics converters can be quite complex, containing modula- tion at the switching frequency and often also at the ac line frequency. During converter design, it is often necessary to compute the rms values of such waveforms. In this appendix, several useful formulas and tables are developed which allow these rms values to be quickly determined. RMS values of the doubly-modulated waveforms encountered in PWM rectifier circuits are dis- cussed in Section 18.5. A.1 SOME COMMON WAVEFORMS DC, Fig. A.1:
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806 RMS Values of Commonly Observed Converter Waveforms DC plus linear ripple, Fig. A.2: Square wave, Fig. A.3: Sine wave, Fig. A.4: Pulsating waveform, Fig. A.5:
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A.1 Some Common Waveforms 807 Pulsating waveform with linear ripple, Fig. A.6: Triangular waveform, Fig. A.7: Triangular waveform, Fig. A.8:
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808 RMS Values of Commonly Observed Converter Waveforms Triangular waveform, no dc component, Fig. A.9: Center-tapped bridge winding waveform, Fig. A.10: General stepped waveform, Fig. A.11:
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A.2 General Piecewise Waveform 809 A.2 GENERAL PIECEWISE WAVEFORM For a periodic waveform composed of n piecewise segments as in Fig. A.12, the rms value is where is the duty cycle of segment k, and is the contribution of segment k. The depend on the shape of the segments—several common segment shapes are listed below: Constant segment, Fig. A.13: Triangular segment, Fig. A.14:
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810 RMS Values of Commonly Observed Converter Waveforms Trapezoidal segment, Fig. A.15: Sinusoidal segment, half or full period, Fig. A.16: Sinusoidal segment, partial period: as in Fig. A.17, a sinusoidal segment of less than one half-period, which begins at angle and ends at angle The angles and are expressed in radians:
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A.2 General Piecewise Waveform 811 Example A transistor current waveform contains a current spike due to the stored charge of a freewheel- ing diode. The observed waveform can be approximated as shown in Fig. A1.18. Estimate the rms cur- rent. The waveform can be divided into six approximately linear segments, as shown. The and for each segment are 1. Triangular segment: 2. Constant segment: 3. Trapezoidal segment: 4. Constant segment: 5. Triangular segment: 6. Zero segment:
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812 RMS Values of Commonly Observed Converter Waveforms The rms value is Even though its duration is very short, the current spike has a significant impact on the rms value of the current—without the current spike, the rms current is approximately 2.0 A.
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Appendix B Simulation of Converters Computer simulation can be a powerful tool in the engineering design process. Starting from design specifications, an initial design typically includes selection of system and circuit configurations, as well as component types and values. In this process, component and system models are constructed based on vendor-supplied data, and by applications of analysis and modeling techniques. These models, validated by experimental data whenever possible, are the basis upon which the designer can choose parameter values and verify the achieved performance against the design specifications. One must take into account
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This note was uploaded on 01/17/2010 for the course EL 5673 taught by Professor Dariuszczarkowski during the Spring '09 term at NYU Poly.

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back-matter - Appendices Appendix A RMS Values of Commonly...

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