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+{
+"cells": [
+ {
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "# Chapter 6: Antenna Arrays"
+ ]
+ },
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 6.10_1: Find_the_Directivity.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"//Example No. 6.10.1\n",
+"clc;\n",
+"clear;\n",
+"close;\n",
+"format('v',6);\n",
+"n=10;//no. of elements\n",
+"//d=lambda/4;(spacing)\n",
+"dBYlambda=1/4;///(Spacing/wavelength)\n",
+"//Broadside array\n",
+"D=2*n*dBYlambda;//unitless(Directivity)\n",
+"D=10*log10(D);//dB(Directivity)\n",
+"disp(D,'Directivity for broadside array in dB : ');\n",
+"//Endfire array\n",
+"D=4*n*dBYlambda;//unitless(Directivity)\n",
+"D=10*log10(D);//dB(Directivity)\n",
+"disp(D,'Directivity for Ordinary endfire array in dB : ');"
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 6.10_2: Design_ordinary_endfire_array.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"//Example No. 6.10.2\n",
+"clc;\n",
+"clear;\n",
+"close;\n",
+"format('v',6);\n",
+"D=20;//dB(Directivity)\n",
+"//d=lambda/4;(spacing)\n",
+"dBYlambda=1/4;//(spacing/wavelength)\n",
+"D=10^(D/10);//unitless(Directivity)\n",
+"n=D/4/dBYlambda;//no. of elements\n",
+"disp(n,'(i) No. of elements : ');\n",
+"LBYlambda=(n-1)*dBYlambda;//(length/wavelength)\n",
+"disp('(ii) Length of the array is '+string(LBYlambda)+'*lambda');\n",
+"HPBW=2*acosd(1-1.391/%pi/n/dBYlambda);//degree(HPBW)\n",
+"disp(HPBW,'(iii) HPBW in degree : ');\n",
+"SLL=-13.46;//dB(Side lobe level)\n",
+"disp(SLL,'(iv) SLL in dB : ');\n",
+"Beta_into_lambda=2*%pi;//(temorary calculatuion)\n",
+"//alfa=-Beta*d;//for theta=0\n",
+"//alfa=Beta*d;//for theta=180\n",
+"alfa1=-Beta_into_lambda*dBYlambda;//radian////for theta=0\n",
+"alfa1=alfa1*180/%pi;//degree(angle)\n",
+"alfa2=Beta_into_lambda*dBYlambda;//radian////for theta=180\n",
+"alfa2=alfa2*180/%pi;//degree(angle)\n",
+"disp(alfa2,alfa1,'(v) Progressive phase shift, α for theta equals to 0° & 180° are : ');"
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 6.14_1: Four_Element_broadside_array.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"//Example No. 6.14.1\n",
+"clc;\n",
+"clear;\n",
+"close;\n",
+"format('v',6);\n",
+"SLL=19.1;//dB(Side Lobe Level)\n",
+"//d=lambda/2;(spacing)\n",
+"dBYlambda=1/2;//(Spacing/wavelength)\n",
+"n=4;//(no. of elements)\n",
+"r=round(10^(SLL/20));//(ratio of main lobe to side lobe)\n",
+"m=n-1;//(degree )\n",
+"//T3(x0)=r=4*x0^3-3*x0;\n",
+"x0=roots([4 0 -3 -r]);//(Coefficient)\n",
+"x0=x0(1);//taking real value(Coefficient)\n",
+"//E4(z)=T3(x)=4*x^3-3*x=4*a1*z^3-3*a1*z+a0*z\n",
+"//4*a1*z^3=4*x^3 where z^3=(x/x0)^3\n",
+"a1=4*x0^3/4;//(Coefficient)\n",
+"//a0*z-3*z*a1=-3*x\n",
+"a0=(3/x0*a1-3)*x0;//(Coefficient)\n",
+"disp(a0,a1,'Coefficients of array polynomial a1 & a0 are : ');\n",
+"disp(a0/a1,a1/a1,'Relative current amplitudes are :');"
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 6.2_1: Relative_field_patter.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"//Example No. 6.2.1\n",
+"clc;\n",
+"clear;\n",
+"close;\n",
+"format('v',5);\n",
+"n=2;//(No. of point source)\n",
+"//E=E0*{exp(%i*%pi/2)-exp(-%i*si/2)} where exp(-%i*si)=-1\n",
+"//si=Beta*d*cosd(fi)=2*%pi*cosd(fi)\n",
+"//E=2*%i*E0*sind(%pi*cosd(fi)); But 2*%i*E0=1\n",
+"fi=[0 30 60 90 120 150 180 210 240 270 300 330];//degree(angle)\n",
+"En=sin(%pi*cosd(fi));//Normalized field\n",
+"disp('Different values of fi : ');\n",
+"disp(string(fi));\n",
+"disp('Corresponding normalized field is : ');\n",
+"disp(string(abs(En)));"
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 6.2_2: Radiation_patern.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"//Example No. 6.2.2\n",
+"clc;\n",
+"clear;\n",
+"close;\n",
+"format('v',5);\n",
+"n=2;//(No. of point source)\n",
+"//E=E0*{exp(%i*(%pi/4+si/2))-exp(-%i*(%pi/4+si/2))} as exp(%i*theta)+exp(-%i*theta)=2*cos(theta)\n",
+"//E=2*E0*cos(%pi/4+si/2);\n",
+"//si=Beta*d*cosd(fi)=2*%pi*cosd(fi)\n",
+"//En=cos(%pi/4+Beta*d*cosd(%pi/4)); But 2*E0=1\n",
+"fi=[0 30 60 90 120 150 180 210 240 270 300 330];//degree(angle)\n",
+"En=cos(%pi/4+%pi/4*cosd(fi));//Normalized field\n",
+"disp('Different values of fi : ');\n",
+"disp(string(fi));\n",
+"disp('Corresponding normalized field is : ');\n",
+"disp(string(abs(En)));"
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 6.2_3: Field_patter.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"//Example No. 6.2.3\n",
+"clc;\n",
+"clear;\n",
+"close;\n",
+"format('v',5);\n",
+"//E=cos(fi)+sin(fi)<si;\n",
+"//En=cos(%pi/4+%pi*cosd(fi)) as 2*E0=1\n",
+"fi=[0 30 60 90 120 150 180 210 240 270 300 330];//degree(Angle)\n",
+"si=%pi/2*(cosd(fi)+1);//(Phase)\n",
+"En=cos(%pi/4+%pi*cosd(fi));//Normalized field\n",
+"disp('Different values of fi : ');\n",
+"disp(string(fi));\n",
+"disp('Corresponding normalized field is : ');\n",
+"disp(string(abs(En)));\n",
+"//Answer in the book is wrong."
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 6.6_1: Location_of_first_null.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"//Example No. 6.6.1\n",
+"clc;\n",
+"clear;\n",
+"close;\n",
+"format('v',5);\n",
+"n=80;//(no. of elements)\n",
+"N=1;//for first null\n",
+"//d=lambda/2;(spacing)\n",
+"dBYlambda=1/2;//(spacing/wavelength)\n",
+"fi01=acosd(N/n/dBYlambda);//degree(Angle)\n",
+"Null_1st=(%pi/2*180/%pi)-fi01;//degree(First Null)\n",
+"disp(Null_1st,'Location of 1st null from maxima in degree : ');"
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 6.6_2: Various_parameters_of_isotropic_array.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"//Example 6.6.2\n",
+"clc;\n",
+"clear;\n",
+"close;\n",
+"n=4;//(No. of elements)\n",
+"//d=lambda/2;(Spacing)\n",
+"dBYlambda=1/2;//(Spacing/wavelength)\n",
+"alfa=0;//degree(angle)\n",
+"N=1;//(For first null)\n",
+"disp('Part (i)');\n",
+"theta01=[acosd(+N/2) acosd(-N/2)];//degree(Angle)\n",
+"N=2;//(For second null)\n",
+"theta02=[acosd(+N/2) acosd(-N/2)];//degree(angle)\n",
+"//N=3;//not possible as N/2 is greater than 1\n",
+"disp(theta01,'Null directions for N=1 : theta01(degree) ');\n",
+"disp(theta02,'Null directions for N=2 : theta02(degree) ');\n",
+"disp('Part (ii)');\n",
+"m=0;//for maxima\n",
+"theta_m=acosd(m/dBYlambda);//degree(angle)\n",
+"disp(theta_m,'Direction of maxima : theta_m(degree) ');\n",
+"disp('Part (iii)');\n",
+"S=1;//for side lobe maxima\n",
+"//S=2 & onwards not possible\n",
+"theta_S=[acosd((2*S+1)/2/n/dBYlambda) acosd(-(2*S+1)/2/n/dBYlambda)];//degree(angle for side lobe)\n",
+"disp(theta_S,'Side lobe maxima : theta_S(degree) ');\n",
+"disp('Part (iv)');\n",
+"HPBW=2*[90-acosd(1.391/%pi/n/dBYlambda)];//degree(HPBW)\n",
+"disp(HPBW,'HPBW(degree) ');\n",
+"disp('Part (v)');\n",
+"FNBW=2*[90-acosd(1/n/dBYlambda)];//degree(FNBW)\n",
+"disp(FNBW,'FNBW(degree) ');\n",
+"disp('Part (vi)');\n",
+"SLL=-13.46;//dB////for isotropic sources array(Side lobe level)\n",
+"disp(SLL,'Side lobe level(dB) ');"
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 6.8_1: Ordinary_endfire_array.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"//Example No. 6.8.1\n",
+"clc;\n",
+"clear;\n",
+"close;\n",
+"format('v',5);\n",
+"n=4;//(No. of elements)\n",
+"//d=lambda/2;(spacing)\n",
+"dBYlambda=1/2;//(spacing/wavelength)\n",
+"theta=0;//degree(angle)\n",
+"//Beta=2*%pi/lambda\n",
+"disp('Part (i)');\n",
+"Beta_into_lambda=2*%pi;//(Coefficient)\n",
+"//alfa=-Beta*d\n",
+"alfa=-Beta_into_lambda*dBYlambda;//radian(Progressive phase shift)\n",
+"alfa=alfa*180/%pi;//degree(Progressive phase shift)\n",
+"disp(alfa,'Progressive phase shift(degree) ');\n",
+"disp('Part (ii)');\n",
+"N=1:3;//as N=4 is not allowed\n",
+"theta01=acosd(1-N(1)/n/dBYlambda);//degree(angle)\n",
+"theta02=acosd(1-N(2)/n/dBYlambda);//degree(angle)\n",
+"theta03=acosd(1-N(3)/n/dBYlambda);//degree(angle)\n",
+"disp(theta03,theta02,theta01,'Null directions, theta01, theta02 & theta03 in degree are : ');\n",
+"disp('Part (iii)');\n",
+"m=0:1;//as m=2 & onwards is not allowed\n",
+"theta0=acosd(1-m(1)/dBYlambda);//degree(angle)\n",
+"theta1=acosd(1-m(2)/dBYlambda);//degree(angle)\n",
+"disp(theta1,theta0,'Maxima directions, theta0, theta1 in degree are : ');\n",
+"disp('Part (iv)');\n",
+"FNBW=2*acosd(1-1/n/dBYlambda);//degree(FNBW)\n",
+"disp(FNBW,'FNBW in degree : ');\n",
+"disp('Part (v)');\n",
+"HPBW=2*acosd(1-1.391/n/%pi/dBYlambda);//degree(HPBW)\n",
+"disp(HPBW,'HPBW in degree : ');"
+ ]
+ }
+,
+{
+ "cell_type": "markdown",
+ "metadata": {},
+ "source": [
+ "## Example 6.8_2: Half_Power_Beam_Width.sce"
+ ]
+ },
+ {
+"cell_type": "code",
+ "execution_count": null,
+ "metadata": {
+ "collapsed": true
+ },
+ "outputs": [],
+"source": [
+"//Example No. 6.8.2\n",
+"clc;\n",
+"clear;\n",
+"close;\n",
+"format('v',6);\n",
+"n=16;//no. of point source\n",
+"//d=lambda/4;(spacing)\n",
+"dBYlambda=1/4;//(Spacing/wavelength)\n",
+"HPBW=2*acosd(1-1.391/n/%pi/dBYlambda);//degree(HPBW)\n",
+"disp(HPBW,'HPBW in degree : ');"
+ ]
+ }
+],
+"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
+}
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