endof-

More documents

Recommendations

Info

Chapter 4Circuit Analysis with Laplace TransformsThis chapter presents applications of the Laplace transform. Several examples are presentedto illustrate how the Laplace transformation is applied to circuit analysis. Complex impedance,complex admittance, and transfer functions are also defined.4.1 Circuit Transformation from Time to Complex FrequencyIn this section we will show the voltage−current relationships for the three elementary circuitnetworks, i.e., resistive, inductive, and capacitive in the time and complex frequency domains.They are shown in Subsections 4.1.1 through 4.1.3 below.4.1.1 Resistive Network TransformationThe time and complex frequency domains for purely resistive networks are shown in Figure 4.1.Time DomainComplex Frequency Domain+v R () t = Ri R () t+V R ( s) = RI R ( s)v R () t R i R () t vi R () t R () tV R ( s) R I R ( s)V= ------------I R ( s)R ( s)= --------------−RR−Figure 4.1. Resistive network in time domain and complex frequency domain4.1.2 Inductive Network TransformationThe time and complex frequency domains for purely inductive networks are shown in Figure 4.2.+v L () t−LTime Domaini L () t v L () t Ldi L= -------dti L () t=t--1vL ∫ L dt–∞Figure 4.2. Inductive network in time domain and complex frequency domain4.1.3 Capacitive Network TransformationThe time and complex frequency domains for purely capacitive networks are shown in Figure 4.3.+V L ( s)−sLComplex Frequency Domain+ −I L( s)Li L ( 0 −)V L ( s) = sLI L ( s) – Li L ( 0 −)I L ( s)V L ( s)i------------- L ( 0 −)= + --------------Ls sSignals and Systems with MATLAB ® Computing and Simulink ® Modeling, Fourth EditionCopyright © Orchard Publications4−1
Using the Simulink Transfer Fcn Block0-0.2-0.4-0.6-0.8-10 2 4 6 8 10Figure 4.23. Plot of v out () t for Example 4.8.Figure 4.24. Simulink model for Example 4.8Figure 4.25. Waveform for the Simulink model of Figure 4.24Signals and Systems with MATLAB ® Computing and Simulink ® Modeling, Fourth EditionCopyright © Orchard Publications4−19
Page 7: 4.2 Complex Impedance Z(s).........
Page 10 and 11: 8.6.4 The Transform of ft () = Acos
Page 12 and 13: 11.2.1 RC Low−Pass Filter .......
Page 14 and 15: MATLAB ComputingPages D−3, D−4,
Page 16 and 17: The Unit Step FunctionThus, the pul
Page 18 and 19: Chapter 1 Elementary Signals6. To d
Page 20 and 21: Chapter 2 The Laplace Transformatio
Page 22 and 23: Chapter 2 The Laplace Transformatio
Page 24 and 25: Chapter 3 The Inverse Laplace Trans
Page 28 and 29: Solutions to End−of−Chapter Exe
Page 30 and 31: Chapter 5 State Variables and State
Page 32 and 33: A: [−1 −1; 3/4 0]B: [1 0]’C:
Page 38 and 39: Chapter 7 Fourier Seriesthat is, th
Page 40 and 41: Chapter 8 The Fourier Transform8.2
Page 42 and 43: Chapter 8 The Fourier TransformExam
Page 44 and 45: Chapter 9 Discrete−Time Systems a
Page 46 and 47: num=[0 1 0 0];% The coefficients of
Page 48 and 49: Chapter 10 The DFT and the FFT Algo
Page 50 and 51: The Fast Fourier Transform (FFT)The
Page 52 and 53: Basic Analog Filters11.2.3 RLC Band
Page 54 and 55: Chapter 11 Analog and Digital Filte
Page 56 and 57: Digital Filters1Four signals separa
Page 58 and 59: Chapter 11 Analog and Digital Filte
Page 60: Appendix E Window Functionsh[n]A(f)
Page 63 and 64: Appendix E Window FunctionsMH 1 ( z
Page 65 and 66: IndexSymbols Cauchy’s residue the
Page 67 and 68: Fourier transform - properties of f
Page 69 and 70: S for discrete-time systems 9-45 St

endof-

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?