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{
"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": {
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"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",
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|
