1、The Basic Elements and Phasors,OBJECTIVES,Become familiar with the response of a resistor, an inductor, and a capacitor to the application of a sinusoidal voltage or current. Learn how to apply the phasor format to add and subtract sinusoidal waveforms. Understand how to calculate the real power to
2、resistive elements and the reactive power to inductive and capacitive elements. Become aware of the differences between the frequency response of ideal and practical elements. Become proficient in the use of a calculator to work with complex numbers.,DERIVATIVE,To understand the response of the basi
3、c R, L, and C elements to a sinusoidal signal, you need to examine the concept of the derivative in some detail.If x fails to change at a particular instant, dx = 0, and the derivative is zero.,DERIVATIVE,FIG. 14.1 Defining those points in a sinusoidal waveform that have maximum and minimum derivati
4、ves.,DERIVATIVE,FIG. 14.2 Derivative of the sine wave of Fig. 14.1.,DERIVATIVE,FIG. 14.3 Effect of frequency on the peak value of the derivative.,RESPONSE OF BASIC R, L, AND C ELEMENTS TO A SINUSOIDAL VOLTAGE OR CURRENT,Resistor Inductor Capacitor,FIG. 14.4 Determining the sinusoidal response for a
5、resistive element.,RESPONSE OF BASIC R, L, AND C ELEMENTS TO A SINUSOIDAL VOLTAGE OR CURRENT,FIG. 14.5 The voltage and current of a resistive element are in phase.,RESPONSE OF BASIC R, L, AND C ELEMENTS TO A SINUSOIDAL VOLTAGE OR CURRENT,FIG. 14.6 Defining the opposition of an element to the flow of
6、 charge through the element.,FIG. 14.7 Defining the parameters that determine the opposition of an inductive element to the flow of charge.,RESPONSE OF BASIC R, L, AND C ELEMENTS TO A SINUSOIDAL VOLTAGE OR CURRENT,FIG. 14.8 Investigating the sinusoidal response of an inductive element.,FIG. 14.9 For
7、 a pure inductor, the voltage across the coil leads the current through the coil by 90.,RESPONSE OF BASIC R, L, AND C ELEMENTS TO A SINUSOIDAL VOLTAGE OR CURRENT,FIG. 14.10 Defining the parameters that determine the opposition of a capacitive element to the flow of charge.,RESPONSE OF BASIC R, L, AN
8、D C ELEMENTS TO A SINUSOIDAL VOLTAGE OR CURRENT,FIG. 14.11 Investigating the sinusoidal response of a capacitive element.,FIG. 14.12 The current of a purely capacitive element leads the voltage across the element by 90.,RESPONSE OF BASIC R, L, AND C ELEMENTS TO A SINUSOIDAL VOLTAGE OR CURRENT,FIG. 1
9、4.13 Example 14.1(a).,FIG. 14.14 Example 14.1(b).,RESPONSE OF BASIC R, L, AND C ELEMENTS TO A SINUSOIDAL VOLTAGE OR CURRENT,FIG. 14.15 Example 14.3(a).,FIG. 14.16 Example 14.3(b).,RESPONSE OF BASIC R, L, AND C ELEMENTS TO A SINUSOIDAL VOLTAGE OR CURRENT,FIG. 14.17 Example 14.5.,FIG. 14.18 Example 14
10、.7.,FREQUENCY RESPONSE OF THE BASIC ELEMENTS Ideal Response,Resistor R Inductor L Capacitor C,FREQUENCY RESPONSE OF THE BASIC ELEMENTS Ideal Response,FIG. 14.19 R versus f for the range of interest.,FIG. 14.20 XL versus frequency.,FREQUENCY RESPONSE OF THE BASIC ELEMENTS Ideal Response,FIG. 14.21 Ef
11、fect of low and high frequencies on the circuit model of an inductor.,FREQUENCY RESPONSE OF THE BASIC ELEMENTS Ideal Response,FIG. 14.22 XC versus frequency.,FREQUENCY RESPONSE OF THE BASIC ELEMENTS Ideal Response,FIG. 14.23 Effect of low and high frequencies on the circuit model of a capacitor.,FRE
12、QUENCY RESPONSE OF THE BASIC ELEMENTS Practical Response,Resistor R Inductor L Capacitor C ESR,FREQUENCY RESPONSE OF THE BASIC ELEMENTS Practical Response,FIG. 14.24 Typical resistance-versus-frequency curves for carbon composition resistors.,FREQUENCY RESPONSE OF THE BASIC ELEMENTS Practical Respon
13、se,FIG. 14.25 Practical equivalent for an inductor.,FIG. 14.26 ZL versus frequency for the practical inductor equivalent of Fig. 14.25.,FREQUENCY RESPONSE OF THE BASIC ELEMENTS Practical Response,FIG. 14.27 Practical equivalent for a capacitor; (a) network; (b) response.,FREQUENCY RESPONSE OF THE BA
14、SIC ELEMENTS Practical Response,FIG. 14.28 ESR. (a) Impact on equivalent model; (b) Measuring instrument.,AVERAGE POWER AND POWER FACTOR,FIG. 14.29 Demonstrating that power is delivered at every instant of a sinusoidal voltage waveform (except vR = 0V).,AVERAGE POWER AND POWER FACTOR,FIG. 14.30 Powe
15、r versus time for a purely resistive load.,AVERAGE POWER AND POWER FACTOR,FIG. 14.31 Determining the power delivered in a sinusoidal ac network.,AVERAGE POWER AND POWER FACTOR,FIG. 14.32 Defining the average power for a sinusoidal ac network.,AVERAGE POWER AND POWER FACTOR,Resistor Inductor Capacito
16、r Power Factor,AVERAGE POWER AND POWER FACTOR,FIG. 14.33 Purely resistive load with Fp = 1.,FIG. 14.34 Purely inductive load with Fp = 0.,AVERAGE POWER AND POWER FACTOR,FIG. 14.35 Example 14.12(a).,FIG. 14.36 Example 14.12(b).,AVERAGE POWER AND POWER FACTOR,FIG. 14.37 Example 14.12(c).,COMPLEX NUMBE
17、RS,A complex number represents a point in a two-dimensional plane located with reference to two distinct axes. This point can also determine a radius vector drawn from the origin to the point. The horizontal axis is called the real axis, while the vertical axis is called the imaginary axis.,COMPLEX
18、NUMBERS,FIG. 14.38 Defining the real and imaginary axes of a complex plane.,RECTANGULAR FORM,The format for the rectangular form is:,RECTANGULAR FORM,FIG. 14.39 Defining the rectangular form.,FIG. 14.40 Example 14.13(a).,RECTANGULAR FORM,FIG. 14.41 Example 14.13(b).,FIG. 14.42 Example 14.13(c).,POLA
19、R FORM,The format for the polar form is:,POLAR FORM,FIG. 14.43 Defining the polar form.,FIG. 14.44 Demonstrating the effect of a negative sign on the polar form.,POLAR FORM,FIG. 14.45 Example 14.14(a).,FIG. 14.46 Example 14.14(b).,POLAR FORM,FIG. 14.47 Example 14.14(c).,CONVERSION BETWEEN FORMS,Rect
20、angular to Polar Polar to Rectangular,FIG. 14.48 Conversion between forms.,CONVERSION BETWEEN FORMS,FIG. 14.49 Example 14.15.,FIG. 14.50 Example 14.16.,CONVERSION BETWEEN FORMS,FIG. 14.51 Example 14.17.,FIG. 14.52 Example 14.18.,MATHEMATICAL OPERATIONS WITH COMPLEX NUMBERS,Complex Conjugate Reciproc
21、al Addition Subtraction Multiplication Division,MATHEMATICAL OPERATIONS WITH COMPLEX NUMBERS,FIG. 14.53 Defining the complex conjugate of a complex number in rectangular form.,FIG. 14.54 Defining the complex conjugate of a complex number in polar form.,MATHEMATICAL OPERATIONS WITH COMPLEX NUMBERS,FI
22、G. 14.55 Example 14.19(a).,FIG. 14.56 Example 14.19(b).,MATHEMATICAL OPERATIONS WITH COMPLEX NUMBERS,FIG. 14.57 Example 14.20(a).,FIG. 14.58 Example 14.20(b).,MATHEMATICAL OPERATIONS WITH COMPLEX NUMBERS,FIG. 14.59 Example 14.21(a).,FIG. 14.60 Example 14.21(b).,CALCULATOR METHODS WITH COMPLEX NUMBER
23、S Calculators,FIG. 14.61 TI-89 scientific calculator.,CALCULATOR METHODS WITH COMPLEX NUMBERS Calculators,FIG. 14.62 Setting the DEGREE mode on the TI-89 calculator.,CALCULATOR METHODS WITH COMPLEX NUMBERS Calculators,Rectangular to Polar Conversion,FIG. 14.63 Converting 3 + j 5 to the polar form us
24、ing the TI-89 calculator.,CALCULATOR METHODS WITH COMPLEX NUMBERS Calculators,Polar to Rectangular Conversion,FIG. 14.64 Converting 53.1 to the rectangular form using the TI 89 calculator.,CALCULATOR METHODS WITH COMPLEX NUMBERS Calculators,Mathematical Operations,FIG. 14.65 Performing the operation
25、 (10 50)(2 20).,CALCULATOR METHODS WITH COMPLEX NUMBERS Calculators,FIG. 14.66 Performing the operation (53.1)(2 + j 2).,FIG. 14.67 Verifying the results of Example 14.26(c).,PHASORS,FIG. 14.68 Adding two sinusoidal waveforms on a point-by-point basis.,PHASORS,FIG. 14.69 (a) The phasor representatio
26、n of the sinusoidal waveforms of part (b); (b) finding the sum of two sinusoidal waveforms of v1 and v2.,PHASORS,FIG. 14.70 Adding two sinusoidal currents with phase angles other than 90.,PHASORS,FIG. 14.72 Example 14.29.,PHASORS,FIG. 14.73 Solution to Example 14.29.,PHASORS,FIG. 14.74 Example 14.30
27、.,PHASORS,FIG. 14.75 Solution to Example 14.30.,COMPUTER ANALYSIS PSpice,FIG. 14.76 Using PSpice to analyze the response of a capacitor to a sinusoidal ac signal.,COMPUTER ANALYSIS PSpice,FIG. 14.77 A plot of the voltage, current, and power for the capacitor in Fig. 14.76.,COMPUTER ANALYSIS Multisim,FIG. 14.78 Using Multisim to review the response of an inductive element to a sinusoidal ac signal.,
