Electric Circuits, 9th Edition P58. 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. | 546 Introduction to Frequency Selective Circuits Figure a A series RLC bandreject filter. b The equivalent circuit for w 0. c The equivalent circuit for w oo. Figure The frequency response plot for the series RLC bandreject filter circuit in Fig. a . before they reach the output at frequencies between the two cutoff frequencies the stopband . Bandpass filters and bandreject filters thus perform complementary functions in the frequency domain. Bandreject filters are characterized by the same parameters as bandpass filters the two cutoff frequencies the center frequency the bandwidth and the quality factor. Again only two of these five parameters can be specified independently. In the next sections we examine two circuits that function as bandreject filters and then compute equations that relate the circuit component values to the characteristic parameters for each circuit. The Series RLC Circuit Qualitative Analysis Figure a shows a series RLC circuit. Although the circuit components and connections are identical to those in the series RLC bandpass filter in Fig. a the circuit in Fig. a has an important difference the output voltage is now defined across the inductor-capacitor pair. As we saw in the case of low- and high-pass filters the same circuit may perform two different filtering functions depending on the definition of the output voltage. We have already noted that at co 0 the inductor behaves like a short circuit and the capacitor behaves like an open circuit but at co oo these roles switch. Figure b presents the equivalent circuit for co 0 Fig. c presents the equivalent circuit for co oo. In both equivalent circuits the output voltage is defined over an effective open circuit and thus the output and input voltages have the same magnitude. This series RLC bandreject filter circuit then has two passbands one below a lower cutoff frequency and the other above an upper cutoff frequency. Between these two passbands
