EECE 301 Note Set 32 CT Freq Resp and Bode Plots

EECE 301 Note Set 32 CT Freq Resp and Bode Plots - EECE 301...

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1/37 EECE 301 Signals & Systems Prof. Mark Fowler Note Set #32 • C-T Systems: Transfer Function … and Frequency Response • Reading Assignment: Section 8.5 of Kamen and Heck
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2/37 Ch. 1 Intro C-T Signal Model Functions on Real Line D-T Signal Model Functions on Integers System Properties LTI Causal Etc Ch. 2 Diff Eqs C-T System Model Differential Equations D-T Signal Model Difference Equations Zero-State Response Zero-Input Response Characteristic Eq. Ch. 2 Convolution C-T System Model Convolution Integral D-T System Model Convolution Sum Ch. 3: CT Fourier Signal Models Fourier Series Periodic Signals Fourier Transform (CTFT) Non-Periodic Signals New System Model New Signal Models Ch. 5: CT Fourier System Models Frequency Response Based on Fourier Transform New System Model Ch. 4: DT Fourier Signal Models DTFT (for “Hand” Analysis) DFT & FFT (for Computer Analysis) New Signal Model Powerful Analysis Tool Ch. 6 & 8: Laplace Models for CT Signals & Systems Transfer Function New System Model Ch. 7: Z Trans. Models for DT Signals & Systems Transfer Function New System Model Ch. 5: DT Fourier System Models Freq. Response for DT Based on DTFT New System Model Course Flow Diagram The arrows here show conceptual flow between ideas. Note the parallel structure between the pink blocks (C-T Freq. Analysis) and the blue blocks (D-T Freq. Analysis).
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3/37 8.5 Frequency Response Function We have seen that there are two similar tools that relate the output signal to the input signal: Transfer Function: H ( s ) Frequency Response: H ( ω ) ωω . ) ( . ) ( vs H vs H We could just plot over ω > 0, because we know about symmetries In analysis/design of systems and circuits it helps to look at plots of: If the system is stable we know that we can use H ( )as±a±tool… …and we can easily get H ( ) from H ( s ) by replacing s j It is, of course, easy to use computers to compute the data and plot it… Anyone can be trained to do that… good engineers are valuable because they understand what the plots show!!!! Next
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4/37 ) ( t x ) ( t y + Recall: ) / 1 ( ) / ( / 1 ) ( 2 LC s L R s LC s H + + = Example of Computing the Frequency Response Recall the series RLC circuit… Given specific component values: R = 20 Ω L = 1mH C = 1 μ F 9 4 2 9 10 ) 10 2 ( 10 ) ( + × + = s s s H The transfer function then becomes: Or… Use Matlab’s “freqs” routine Now it is possible to replace s j ω and then use general numerical S/W to compute the frequency response…. Next
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5/37 FREQS Laplace-transform (s-domain) frequency response. H = freqs(B,A,w) returns the complex frequency response vector H of the filter B/A: ) ( ... ) 2 ( ) 1 ( ) ( ... ) 2 ( ) 1 ( ) ( ) ( ) ( 2 1 2 1 na a s a s a nb b s b s b s A s B s H na na nb nb + + + + + + = = given the numerator and denominator coefficients in vectors B and A. 0 5 10 15 20 25 30 35 0 0.5 1 1.5 2 f (kHz) |H(f)| 0 5 -4 -3 -2 -1 0 (kHz) <H(f) >> w=0:100:20e4; >> H=freqs(1e9,[1 2e4 1e9],w); >> subplot(2,1,1) >> plot((w/(2*pi))/1e3,abs(H)) >>%%% Plots are vs. f in kHz >> subplot(2,1,2) >> plot((w/(2*pi))/1e3,angle(H)) Create w in units of rad/sec – convert to kHz 9 4 2 9 10 ) 10 2 ( 10 ) ( + × + = s s s H Next
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6/37 0 5 10 15 20 25 30 35 0 0.5 1 1.5 2 f (kHz) |H(f)| Although the previous plots are correct, there are two problems…
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EECE 301 Note Set 32 CT Freq Resp and Bode Plots - EECE 301...

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