Electric Circuits, 9th Edition P79. 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. | 756 Bode Diagrams Example a Compute the transfer function for the circuit shown in Fig. . b Make a straight-line amplitude plot of 20 log10 7 . c Use the straight-line amplitude plot to determine the type of filter represented by this circuit and then estimate its cutoff frequency. d What is the actual cutoff frequency e Make a straight-line phase angle plot of H jco . f What is the value of 0 co at the cutoff frequency from c g What is the actual value of 0 w at the cutoff frequency from which _ 1 a 25 i i 1 - w 10 2 . u 10 iB1 Note that for the quadratic factor u w 10. The amplitude of H jio in decibels is dB 20 log10 l w 25 - 20 logI0 and the phase angle is 250 mH Figure The circuit for Example . 0 w Ai - 3i where tan 1 w 25 co 10 tan 1------------- 1 - co 10 2 Solution a Transform the circuit in Fig. to the s-domain and then perform s-domain voltage division to get Figure shows the amplitude plot. c From the straight-line amplitude plot in Fig. this circuit acts as a low-pass filter. At the cutoff frequency the amplitude of H jio is 3 dB less than the amplitude in the passband. From the plot we predict that the cutoff frequency is approximately 13 rad s. Substituting the component values from the circuit gives 25 v s2 4s 100 b The first step in making Bode diagrams is to put H jco in standard form. Because H s contains a quadratic factor we first check the value of . We find that and iotl 10 so s 25 1 H s --------- 7----------- 1 s 10 2 s 10 dB o rad s Figure The amplitude plot for Example . Phase Angle Plots 757 d To solve for the actual cutoff frequency replace with jo in H s compute the expression for set - 1 V2 1 V3 and solve for a c. First 4 100 O 2 4 100 Then xl V 4 u. 2 1002 1 . 7 V 100 - M2 2 4o . 2 V5 Computing the phase angle we see 0 jl6 . Note the large error in the predicted angle. In general straight-line phase angle plots do not give satisfactory results in the .
