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diff --git a/Engineering_Circuit_Analysis_by_W_Hayt/18-Fourier_Circuit_Analysis.ipynb b/Engineering_Circuit_Analysis_by_W_Hayt/18-Fourier_Circuit_Analysis.ipynb new file mode 100644 index 0000000..0e972cc --- /dev/null +++ b/Engineering_Circuit_Analysis_by_W_Hayt/18-Fourier_Circuit_Analysis.ipynb @@ -0,0 +1,183 @@ +{ +"cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Chapter 18: Fourier Circuit Analysis" + ] + }, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 18.1: Trigonometric_form_of_the_Fourier_Series.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clear\n", +"close\n", +"clc\n", +"//Example 18.1\n", +"//From the figure 18.2\n", +"disp('The equation of v(t) considering one period can be written as')\n", +"disp('v(t)=Vm*cos(5*%pi*t) for -0.1<=t<=0.1')\n", +"disp('v(t)=0 for 0.1<=t<=0.3')\n", +"//Assuming the value of Vm is 1\n", +"Vm=1;\n", +"//Evaluating the constants an and bn\n", +"//bn=0 for all n\n", +"//an=(2*Vm*cos(n*%pi/2))/(%pi*(1-n^2))\n", +"//a0=Vm/%pi\n", +"t=-1:0.02:1\n", +"v0t=Vm/%pi\n", +"v1t=(1/2)*(Vm*cos(5*%pi*t))\n", +"v0t_v1t=v0t+v1t\n", +"v2t=(2/(3*%pi))*(Vm*cos(10*%pi*t))\n", +"v0t_v1t_v2t=v0t+v1t+v2t\n", +"v3t=(2/(15*%pi))*(Vm*cos(20*%pi*t))\n", +"v0t_v1t_v2t_v3t=v0t+v1t+v2t-v3t\n", +"figure\n", +"a = gca ();\n", +"a. y_location = 'origin';\n", +"a. x_location = 'origin';\n", +"a. data_bounds =[ -1,0;1 0.5];\n", +"plot (t,v0t)\n", +"xtitle('vot vs t','t in s','vot')\n", +"figure\n", +"a = gca ();\n", +"a. y_location = 'origin';\n", +"a. x_location = 'origin';\n", +"a. data_bounds =[ -1,-0.5;1 0.5];\n", +"plot (t,v0t_v1t)\n", +"a. y_location = 'origin';\n", +"a. x_location = 'origin';\n", +"a. data_bounds =[ -1,-0.5;1 0.5];\n", +"plot (t,v0t_v1t_v2t,'r.->')\n", +"a. y_location = 'origin';\n", +"a. x_location = 'origin';\n", +"a. data_bounds =[ -1,-0.5;1 0.5];\n", +"plot (t,v0t_v1t_v2t_v3t,'d')\n", +"xtitle('v(t)','t in s','v(t) in V')" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 18.5: Definition_of_the_Fourier_Transform.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc;\n", +"//Example 18.5\n", +"//Let amplitude be 1 \n", +"A=1;\n", +"Dt=0.01;\n", +"T1=4;\n", +"t=0:Dt:T1/4;\n", +"for i=1:length(t)\n", +" xt(i)=A\n", +"end\n", +"//Calculate Fourier Transform\n", +"Wmax=2*%pi*1;\n", +"K=4;\n", +"k=-(2*K):(K/1000):(2*K);\n", +"W=k*Wmax/K;\n", +"xt=xt';\n", +"XW=xt*exp(-sqrt(-1)*t'*W)*Dt;\n", +"XW_Mag=real(XW);\n", +"W=[-mtlb_fliplr(W),W(2:1001)];\n", +"XW_Mag=[mtlb_fliplr(XW_Mag),XW_Mag(2:1001)];\n", +"subplot(2,1,1);\n", +"a=gca();\n", +"a.data_bounds=[0,0;1,1.5];\n", +"a.y_location='origin';\n", +"plot(t,xt);\n", +"xlabel('t in sec.');\n", +"title('v(t)vs t');\n", +"subplot(2,1,2);\n", +"a=gca();\n", +"a.y_location='origin';\n", +"plot(W*%pi/2,abs (XW_Mag));\n", +"xlabel('Freq in rad/sec');\n", +"ylabel('|F(jw)|')\n", +"title('|F(jw)| vs t');" + ] + } +, +{ + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example 18.6: Physical_significance_of_Fourier_Transform.sce" + ] + }, + { +"cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], +"source": [ +"clc\n", +"syms s t\n", +"printf('Given')\n", +"disp('v(t)=4*exp(-3*t)*u(t)')\n", +"v=4*exp(-3*t)\n", +"\n", +"F=4*(integ(exp(-(3+%i*1)*s),s,0,%inf))\n", +"//The secind term tends to zero\n", +"disp(F,'F=')\n", +"//Let W be the total 1 ohm energy in the input signal\n", +"W=integ(v^2,t,0,%inf)\n", +"disp(W,'W=')\n", +"//Let Wo be the total energy\n", +"//As the frequency range is given as 1 Hz<|f|<2 Hz\n", +"//Considering symmetry\n", +"Wo=(1/%pi)*integ((16/(9+s^2)),s,2*%pi,4*%pi)\n", +"disp(Wo,'Wo=')\n", +"\n", +"\n", +"" + ] + } +], +"metadata": { + "kernelspec": { + "display_name": "Scilab", + "language": "scilab", + "name": "scilab" + }, + "language_info": { + "file_extension": ".sce", + "help_links": [ + { + "text": "MetaKernel Magics", + "url": "https://github.com/calysto/metakernel/blob/master/metakernel/magics/README.md" + } + ], + "mimetype": "text/x-octave", + "name": "scilab", + "version": "0.7.1" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} |