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Basic Analog Filters11.2.3 RLC Band−Pass FilterThe RLC network shown in Figure 11.8 is a basic analog band−pass filter. * We will derive expressionsfor its magnitude and phase.Figure 11.8. Basic band−pass RLC networkApplication of the voltage division expression yields+V in−jωL1 ⁄ jωCR+V out−and thusV out=------------------------------------------- R⋅jωL + 1 ⁄ jωC + RV inGjω ( )V---------- outV in= = -------------------------------------------R= ------------------------------------------------jωRC=jωL + 1 ⁄ jωC + R – ω 2 LC + 1+jωRC-------------------------------------------------------– jω( R ⁄ L)ω 2 – jω( R ⁄ L)– 1⁄LC(11.7)There is no need to express relation (11.7) in magnitude and phase form. We will make use ofthe abs(x) and angle(x) MATLAB functions for the magnitude and phase plots.We will use the MATLAB script below to plot Gjω ( ) versus radian frequency ω . This is shownin Figure 11.9 where, for convenience, we let R = L = C = 1, and thus (11.7) simplifies to:Gjω ( )– jω= --------------------------ω 2 – jω – 1(11.8)w=0:0.02:100; magGjw=abs(−j.*w./(w.^2−j.*w−1)); semilogx(w,magGjw);...xlabel('Frequency in rad/sec − log scale'); ylabel('Magnitude of Vout/Vin');...title('Magnitude Characteristics of basic RLC band−pass filter'); gridThe plot for the magnitude of (11.8) is shown in Figure 11.9.To plot the phase of (11.8), we use the MATLAB script below.w=0:0.02:100; phaseGjw=angle(−j.*w./(w.^2−j.*w−1)).*180./pi; semilogx(w,phaseGjw);...xlabel('Frequency in rad/sec − log scale'); ylabel('Phase of Vout/Vin − degrees');...title('Phase Characteristics of basic RLC band−pass filter'); gridThe plot for the phase of (11.8) is shown in Figure 11.10.* This is the same network as (a) in Exercise 7, Chapter 4, Page 4−22.Signals and Systems with MATLAB ® Computing and Simulink ® Modeling, Fourth EditionCopyright © Orchard Publications11−7