LAB_18 - Filters and Resonant Circuits

LAB_18 - Filters and Resonant Circuits - Lab 18 Filters and...

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Lab 18 197 Filters and Resonant Circuits Summary The behavior of many circuits may be described by considering the entire circuit as a unit and concentrating on only the input and the output (Figure 1). The input is called the excitation and the output is the response. Many characteristics such as amplitude, frequency, phase, and power dissipation of the response are of interest to the designer. The frequency response of an AC circuit describes the behavior or response to input signals at different frequencies. The study of how the output changes with respect to changes in the frequency of the input is called frequency analysis. The characteristics of the circuit that relates output to input as a function of frequency is called the transfer function, H ( j ω ). Educational Objectives 1 . Measure the frequency characteristics of some basic filters. 2 . Construct Bode plots for these filters. "Physical concepts are free creations of the human mind, and are not, however it may seem, uniquely determined by the external world." - Albert Einstein Figure 1 - An electric circuit may be studied in terms of its input and output relationships.
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Lab 18 198 Background Information Filters are frequency selective circuits which utilize combinations of different circuit elements whose impedances vary with frequency in such a way that certain signals will be suppressed while other signals will appear at the output. The circuit of Figure 2 is called a lowpass filter. If the input to this circuit is the voltage applied across the series connection of the resistor R and the capacitor C while the output is the voltage V out across the capacitor, then the transfer function for this filter is: This is a complex valued function, whose magnitude and angle are given in equations (2) and (3): Plots for |H ( j ω ) | and H ( j ) are provided in Figures 3 and 4 for a filter with RC = 1. Figure 2 - A lowpass filter. (1) (2) (3) Figure 3 - The magnitude of the transfer function for the lowpass filter of figure 2 with RC = 1. Hj jR C RC ( +( ) ) = 1 1 2 (+ ( ) ωω )( ) = 1 2 1 2 ∠= ( ) tan 1
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Lab 18 199 Inspection of Figure 3 reveals why the circuit is called a lowpass filter. The magnitude of the transfer function decreases as ω increases, meaning signals of high frequency are suppressed by this cir- cuit. If the positions of the resistor and the capacitor are interchanged (Figure 5), the resulting circuit would be a highpass filter with the transfer function in magnitude and phase given in equations (4) and (5) and their plots in Figures 6 and 7. One frequency of interest for both the highpass and the lowpass filter is that at which the magni- tude of the transfer function is one divided by the square root of two times its maximum. This is the fre- quency at which the power output of the filter has diminished to half its power output at frequencies of Figure 4 - The phase angle of the transfer function for the filter in figure 2 with the RC = 1.
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LAB_18 - Filters and Resonant Circuits - Lab 18 Filters and...

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