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Signals and Systems with MATLAB Computing and Simulink Modeling, Fourth Edition 11 5 Copyright © Orchard Publications Basic Analog Filters (11.4) The magnitude of (11.4) is (11.5) and the phase angle or argument, is (11.6) We can obtain a quick sketch for the magnitude versus by evaluating (11.5) at , , and . Thus, As , For , and as , We will use the MATLAB script below to plot versus radian frequency . This is shown in Figure 11.6 where, for convenience, we let . Figure 11.6. Magnitude characteristics of the basic RC high pass filter with G j ω () V out V in ---------- j ω RC 1 j ω + ----------------------- j ω ω 2 R 2 C 2 + 1 ω 2 R 2 C 2 + ----------------------------------------- ω RC j ω + 1 ω 2 R 2 C 2 + -------------------------------------- == = = ω RC 1 ω 2 R 2 C 2 + 1 ω 1 tan 1 ω 2 R 2 C 2 + --------------------------------------------------------------------------------------------- 1 11 ω 2 R 2 C 2 + -------------------------------------------- 1 ω 1 tan = = G j ω 1 ω 2 R 2 C 2 + --------------------------------------------- = θ G j ω {} arg 1 ω 1 tan G j ω ω ω 0 = ω 1RC = ω∞ ω 0 G j ω 0 ω = G j ω 12 0.707 G j ω 1 Gj ω ω 1 = 10 -2 10 -1 10 0 10 1 10 2 0 0.2 0.4 0.6 0.8 1 Frequency in rad/sec - log scale Magnitude of Vout/Vin Magnitude Characteristics of basic RC high-pass filter Half power point 1 =

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Chapter 11 Analog and Digital Filters 11 6 Signals and Systems with MATLAB Computing and Simulink Modeling, Fourth Edition Copyright © Orchard Publications w=0:0.02:100; RC=1; magGjw=1./sqrt(1+1./(w.*RC).^2); semilogx(w,magGjw);. .. xlabel('Frequency in rad/sec log scale'); ylabel('Magnitude of Vout/Vin');. .. title('Magnitude Characteristics of basic RC high pass filter'); grid We can also obtain a quick sketch for the phase angle, i.e., versus , by evalu- ating (11.6) at , , , , and . Thus, As , For , For , As , and as , We will use the MATLAB script below to plot the phase angle versus radian frequency . This is shown in Figure 11.7 where, for convenience, we let . w=0:0.02:10; RC=1; phaseGjw=atan(1./(w.*RC)).*180./pi; semilogx(w,phaseGjw);. .. xlabel('Frequency in rad/sec log scale'); ylabel('Phase of Vout/Vin degrees');. .. title('Phase Characteristics of basic RC high pass filter'); grid Figure 11.7. Phase characteristics of an RC high pass filter with θ G j ω () {} arg = ω ω 0 = ω 1RC = ω 1 RC = ω∞ →ω ω 0 θ 0 atan 0 ° ≅≅ ω = θ 1 atan 45 ° == ω 1 = θ 1 atan 45 ° θ∞ atan 90 ° atan 90 ° θω 1 = 10 -2 10 -1 10 0 10 1 0 10 20 30 40 50 60 70 80 90 Frequency in rad/sec - log scale Phase of Vout/Vin - degrees Phase Characteristics of basic RC high-pass filter 1 =
Signals and Systems with MATLAB Computing and Simulink Modeling, Fourth Edition 11 7 Copyright © Orchard Publications Basic Analog Filters 11.2.3 RLC Band Pass Filter The RLC network shown in Figure 11.8 is a basic analog band pass filter.

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