Lab manual for - City University of Hong Kong Department of Electronic Engineering Course Year EE3118 Linear Systems and Signal Analysis Semester A

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Page. 1/9 City University of Hong Kong Department of Electronic Engineering Course: EE3118 – Linear Systems and Signal Analysis Year: Semester A 2008/09 This laboratory module consists of two main parts: MATLAB programming and LabView Programming. For MATLAB, you are asked to do it individually. For LabView, two students are grouped together. Part 1: Individual work – MATLAB Programming Programming Media: Matlab 6.0 or above with control system toolbox. Background: 1) Before you start, you have to be familiar with the following functions: tf impulse step lsim bode plot title xlabel, ylabel, grid [The detailed description of functions can be obtained by typing “help xxx”, where ‘xxx’ is the function name.] 2) A frequency transfer function is Fourier Transform of the impulse response of a system, expressed as () () () ω φ j e A H = equivalent to the ratio of the complex exponential time waveform at the input of the system to the complex exponential time waveform causing it at the output port. In Matlab, the gain and the phase shift, i.e. ( ) ω A and ( ) ω φ , can be obtained by the function “bode”. Note: The x-axis of Bode Diagram obtained is in ω .
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I. Passive filters (A) First-order Low Pass filter Figure 1 show the first order low-pass filter based on a RC circuit. Its frequency transfer function can be expressed as () () () ( ) () ωτ ω j C j R C j V V H in out + = + = = 1 1 / 1 / 1 where RC = τ is called the time constant. Paper Work Prove that the cut-off frequency (-3dB) is π 2 1 0 = f . Programming Work If R=2k , determine the value of C so that the cut-off frequency is (100+ X ) Hz ( X is the last 2 non- zero digits of your student ID). Plot the bode diagram for verification. (Please refer to Appendix I for the design procedure) (B) First-order high-pass filter Figure 2 shows a first order high-pass filer based on a RC circuit in Fig. 2 is constructed. Its frequency transfer function can be expressed as () () () j j C j R R V V in out + = + = 1 / 1 where RC = is called the time constant, and the cut-off frequency is again 2 1 0 = f . Programming Work If R=2k , determine the value of C so that the cut-off frequency is (1000+ X ) Hz ( X is the last 3 non-zero digits of your student ID). Plot the Bode diagram for verification. (C) Second order band-stop filter Figure 3 shows a band-stop filer based on a RLC circuit. Its frequency transfer function is given as: () () () () () C R j LC LC C j L j R C j L j V V H in out + = + = = 2 2 1 1 / 1 / 1 where the bandwidth is L R BW 2 = Programming Work Let R=1.8k , C=56nF, L=47mH, plot the Bode diagram and describe its characteristics of the filter. Figure 3. RLC band-stop filter Figure 2. RC high-pass filter Figure 1. RC low-pass filter
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This note was uploaded on 01/11/2011 for the course EE 3118 taught by Professor Kitsangtsang during the Spring '08 term at City University of Hong Kong.

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Lab manual for - City University of Hong Kong Department of Electronic Engineering Course Year EE3118 Linear Systems and Signal Analysis Semester A

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