path: root/Antenna_and_Wave_Propagation_by_S_Wali/6-Antenna_Arrays.ipynb

{
"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 :  ');"
   ]
   }
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