Download Laplace Transforms Via Matlab - Experiment 6 | CEET 3010 and more Lab Reports Microelectronic Circuits in PDF only on Docsity! Laboratory 6 CEET 3010 Fall 2008 Laplace Transforms via MATLAB Purpose: Introduce Students to MATLAB and some of its computational capabilities. Equipment and Components: • Computer with MATLAB. All computers in the CEET computer lab (B4 408) have MATLAB Preliminary: As circuits and systems continue to increase in complexity, the more difficult the “back of the hand” calculations becomes to perform. This is why engineers are tending to use more computational software packages. MATLAB is effectively a highly programmable mathematical software package that has additional toolboxes that specialize in signal processing, control theory, and symbolic math. Commands can either be entered at the “command line” prompt, edited / save / and run as a “*.m” text file, or graphically manipulated via Simulink. Data is entered and stored in array formats, with spaces or common denoting new columns and ; denoting new rows >> x = [1 2 3 4; 5 6 7 8] x = 1 2 3 4 5 6 7 8 >> with semicolons disabling the echo option. >> x = [1 2 3 4; 5 6 7 8]; >> Sequences of numbers can be specified using sudo C code >> y = 0:0.5:2 y = 0 0.5000 1.0000 1.5000 2.0000 >> Mathematical operations can either be done on a matrix manipulation (+, -, *, /) >> z = [1 2 3]*[4; 5; 6] z = 32 i.e. 1*4 + 2*5 + 3*6 = 32 or an element by element case (+, -, .*, ./ ) >> z = [1 2 3].*[4 5 6] z = 4 10 18 >> i.e. 1*4 2*5 3*6 The element by element case can be used to repeat a sequence of operations on a set of data instead of using “for” or “while” loops. For a complete description of all functions and usage type >> help or >> help [function name] Some other useful commands: >> clear %Clears workspace memory >> edit %Opens text editor >> plot(x, y) %Plots >> linespace(a, b) %Linearly space values from a to b >> abs(a+jb) %Magnitude of a+jb >> angle(a+jb) %Phase of a+jb >> demo %Demonstrations If creating or editing a *.m file it is strongly recommend to include comments after a % i.e. % comments Procedure: 1. Define the following transfer function in MATLAB € F(S) = 8s 3 + 89s2 + 311s+ 300 s4 + 54s3 + 993s2 + 7440s+18500 MATLAB can stores transfer function data as vectors of the coefficients >> N = [an an-1 … ao] >> D = [bm bm-1 … bo] >> F = tf (N, D) where MATLAB assumes that the first element is the coefficient of the largest power of s. In addition, while leading zeros do not change the final result, € [0 4 2] = [4 2]⇒ 4s+ 2 trailing zeros do effect the math. € [3 6 0]⇒ 3s2 + 6s+ 0 2. Find the poles, roots of the denominator, and zeros, roots of the numerator, of the transfer function in part 1. Poles are values of s that cause H(s) → ∞. This can occur when the numerator → ∞ or the denominator to → 0.
