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Electric Circuits, 9th Edition P78. Designed for use in a one or two-semester Introductory Circuit Analysis or Circuit Theory Course taught in Electrical or Computer Engineering Departments. Electric Circuits 9/e is the most widely used introductory circuits textbook of the past 25 years. As this book has evolved over the years to meet the changing learning styles of students, importantly, the underlying teaching approaches and philosophies remain unchanged. | 746 Bode Diagrams d See Fig. E.5. e As we can see from the Bode plot in Fig. E.5 the value of AdB at co 500 rad s is approximately -12.5 dB. Therefore A io -12-5 20 0.24 and V no A1K - 0.24 5 1.19 V. We can compute the actual value of 7 w by substituting o 500 into the equation for x 0.11 y500 H 500 ------- 0.22 -77.54 . 7 l 50 l 5 2-------- Thus the actual output voltage magnitude for the specified signal source at a frequency of 500 rad s is v m I4K - 0.22 5 l.l V. E.3 More Accurate Amplitude Plots We can make the straight-line plots for first-order poles and zeros more accurate by correcting the amplitude values at the corner frequency one half the corner frequency and twice the corner frequency. At the corner frequency the actual value in decibels is dBc - 20 logiojl l 20 logl0V2 3 dB. E.13 The actual value at one half the corner frequency is dBc 2 - 20 logl0 I j 20 logjo V5 4 l dB. At twice the corner frequency the actual value in decibels is AdB c 20 logl0 l 2 20 logl0V5 7 dB. E.U E.15 In Eqs. E.13-E.15 the plus sign applies to a first-order zero and the minus sign applies to a first-order pole. The straight-line approximation of the amplitude plot gives 0 dB at the corner and one half the corner frequencies and 6 dB at twice the corner frequency. Hence the corrections are 3 dB at the corner frequency and l dB at both one half the corner frequency and twice the corner frequency. Figure E.6 summarizes these corrections. A 2-to-l change in frequency is called an octave. A slope of 20 dB decade is equivalent to 6.02 dB octave which for graphical purposes is equivalent to 6 dB octave. Thus the corrections enumerated correspond to one octave below and one octave above the corner frequency. E.4 Straight-Line Phase Angle Plots 747 2 Figure E.6 Corrected amplitude plots for a first-order zero and pole. If the poles and zeros of H s are well separated inserting these corrections into the overall amplitude plot and achieving a reasonably accurate curve is relatively .
