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diff --git a/Microwave_engineering__by_D.M.Pozar_/Chapter_6_MICROWAVE_RESONATORS.ipynb b/Microwave_engineering__by_D.M.Pozar_/Chapter_6_MICROWAVE_RESONATORS.ipynb new file mode 100644 index 00000000..e6a37416 --- /dev/null +++ b/Microwave_engineering__by_D.M.Pozar_/Chapter_6_MICROWAVE_RESONATORS.ipynb @@ -0,0 +1,328 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Chapter 6 MICROWAVE RESONATORS" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example:6.1 page.no:309" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Qair = 2379.5\n", + "Qteflon = 1217.7\n", + "conclusion: Qair is almost twice that of Qteflon\n" + ] + } + ], + "source": [ + "#program to compare the Q of an air filled and teflon filled coaxial line resonator .\n", + "from math import pi,sqrt,log\n", + "\n", + "sigma=5.813*10**7;muo=4*pi*10**-7;f=5*10**9;eta=377;a =1*10**-3;b=4*10**-3;\n", + "omega=2*pi*f;ko=104.7;B=104.7;alpha=0.022;\n", + "Rs=sqrt((omega*muo)/(2*sigma));\n", + "alphaca=(Rs/(2*eta*log(b/a)))*((1/a)+(1/b)); # attenuation due to conductor loss for air filled line .\n", + "eipsilar=2.08;tandelta=0.0004; # for teflon filled line .\n", + "alphact=((Rs*sqrt(2.08)*0.01)/(2*eta*log(b/a)))*((1/ a)+(1/b)); # attenuation due to conductor loss for teflon filled line .\n", + "alphada=0; # for air filled line .\n", + "alphadt=ko*(sqrt(eipsilar)/2)*tandelta;\n", + "Qair=B/(2*alpha);\n", + "B=B*sqrt(eipsilar);\n", + "alpha =0.062;\n", + "Qteflon=B/(2*alpha);\n", + "print \"Qair = %.1f\"%Qair\n", + "print \"Qteflon = %.1f\"%Qteflon\n", + "print \"conclusion: Qair is almost twice that of Qteflon\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example:6.2 page.no:312" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "length of the line in meter = 0.0219\n", + "Q of the resonator = 525.9\n" + ] + } + ], + "source": [ + "# program to compute the length of the line for resonance at 5 GHZ and the Q of the resonator .\n", + "from math import sqrt,pi\n", + "\n", + "W=0.0049;c=3*10**8;f=5*10**9;Zo=50;eipsilar=2.2;ko =104.7;tandelta =0.001;\n", + "Rs=0.0184; # taken from example 7.1.\n", + "eipsilae=1.87; # effective permittivity .\n", + "l=c/(2*f*sqrt(eipsilae)); # resonator length .\n", + "B=(2*pi*f*sqrt(eipsilae))/c;\n", + "alphac=Rs/(Zo*W);\n", + "alphad=(ko*eipsilar*(eipsilae -1)*tandelta)/(2*sqrt(eipsilae)*(eipsilar -1));\n", + "alpha=alphac+alphad;\n", + "Q=B/(2*alpha);\n", + "print \"length of the line in meter = %.4f\"%l\n", + "print \"Q of the resonator = %.1f\"%Q" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example:6.3 page.no:317" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "d in meter = 0.0465\n", + "Q1 = 1437\n", + "Q2 = 1518\n" + ] + } + ], + "source": [ + "# program to find required length ,d and Q for l=1 and l=2 resonator mode.\n", + "from math import sqrt,pi\n", + "\n", + "a=0.04755;b=0.02215;eipsilar=2.25;tandelta=0.0004;f =5*10**9;c=3*10**8;\n", + "k=(2*pi*f*sqrt(eipsilar))/c # wave number .\n", + "for l in range(1,2):\n", + " d=(l*pi)/sqrt((k**2)-((pi/b)**2)); # m=1 & n=0 mode .\n", + " print \"d in meter = %.4f\"%d\n", + "eta=377/sqrt(eipsilar);\n", + "Qc1=3380.;# l=1.\n", + "Qc2=3864.;# l=2.\n", + "Qd=2500.; # Q due to dielectric loss only .\n", + "Q1=((1./Qc1)+(1./Qd))**-1; # for l =1.\n", + "Q2=((1./Qc2)+(1./Qd))**-1; # for l =2.\n", + "print \"Q1 = %.0f\"%Q1\n", + "print \"Q2 = %.0f\"%Q2" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example:6.4 page.no:323" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "a in meter = 0.0395\n", + "Qc = 42364.227\n" + ] + } + ], + "source": [ + "# program to find dimension and Q;\n", + "from math import pi,sqrt\n", + "\n", + "f=5.*10**9;c=3.*10**8;p01=3.832;sigma=5.813*10**7;muo=4.*pi*10** -7;\n", + "eipsilar =2.25;\n", + "# mode TE011 . and d=2a .\n", + "omega=2*pi*f;\n", + "eta =377.;\n", + "lamda=c/f;\n", + "k=(2.*pi)/lamda;\n", + "# f=(c/(2⇤pi))⇤sqrt((p01/a)ˆ2+(%pi/(2⇤a))ˆ2); as d=2a given\n", + "a=sqrt((p01)**2+(pi/2)**2)/k;\n", + "Rs=sqrt((omega*muo)/(2.*sigma))\n", + "Qc=(k*a*eta)/(2.*Rs); # for m=l =1,n=0 and d=2a .\n", + "print \"a in meter = %.4f\"%a\n", + "print \"Qc = %.3f\"%Qc" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example:6.5 page.no:309" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "f1 in GHZ= 2.853\n", + "f2 in GHZ= 27.804\n", + "approx. value of Q due to dielectric loss = 1000\n" + ] + } + ], + "source": [ + "# program to find the resonant frequency and Q for TE01delta mode .\n", + "from math import sqrt,pi,tan\n", + "\n", + "delta=0.001;eipsilar=95.;a=0.413;L=0.008255;c=3.*10**8;\n", + "#tan((B⇤L)/2)=alpha/beta.\n", + "ko=2.405\n", + "alpha=(sqrt((2.405/a)**2-(ko)**2));\n", + "B=sqrt((eipsilar*(ko)**2) -(2.405/a)**2); # beta\n", + "f1=((c*2.405)/(2*pi*sqrt(eipsilar)*a))*10**-7;\n", + "f2=((c*2.405)/(2*pi*a))*10**-7;\n", + "print \"f1 in GHZ= %.3f\"%f1\n", + "print \"f2 in GHZ= %.3f\"%f2\n", + "Q=1/tan(delta);\n", + "print \"approx. value of Q due to dielectric loss = %.0f\"%Q" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "collapsed": true + }, + "source": [ + "## Example:6.6 page.no:336" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "coupling capacitor in pF = 433773.991\n", + "frequency in GHZ= 3.66602230334e-07\n" + ] + } + ], + "source": [ + "# program to find the value of the coupling capacitor required for critical coupling .\n", + "from math import pi,sqrt,atan\n", + "\n", + "l=0.02175;Zo=50;eipsilae=1.9;c=3*10^8;\n", + "fo=c/(2*l*sqrt(eipsilae)); # first resonant frequency will occur when the resonator ia about l=lamdag/2 in length .\n", + "lamdag=c/fo;\n", + "alpha=1/8.7; # in Np/m.\n", + "Q=pi/(2*l*alpha);\n", + "bc=sqrt(pi/(2*Q));\n", + "C=bc/(2*pi*fo*Zo)*10**12;\n", + "print \"coupling capacitor in pF = \",C\n", + "C=bc/(2*pi*fo*Zo);\n", + "w1=atan(2*pi*fo*C*Zo)*c/(l*sqrt(eipsilae)); # from equation tan (B⇤l) =bc ;\n", + "w1=w1*10**-8;\n", + "print \"frequency in GHZ= \",w1" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Example:6.7 page.no:342" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "on taking sin (2⇤pi )=0 ,w becomes= A**2*a*c*d*t/4\n", + "fractional change in resonant frequency= 2*(-A**2*a*b*d*eo/2 + A**2*a*c*d*t/4)/(A**2*a*b*d*eo)\n" + ] + } + ], + "source": [ + "# program to derive an expression for the change in resonant frequency .\n", + "from sympy import symbols,sin,cos,integrate,limit\n", + "from math import pi\n", + "\n", + "Ey,Hx,Hz,A,Zte,n,a,p,i,x,z,d,j,k,t,y,er,eo,c,wo,w,b=symbols('Ey,Hx,Hz,A,Zte,n,a,p,i,x,z,d,j,k,t,y,er,eo,c,wo,w,b')\n", + "Ey=A*sin((pi*x)/a)*sin((pi*z)/d);\n", + "Hx=((-j*A)/Zte)*sin((pi*x)/a)*cos((pi*z)/d);\n", + "Hz=((j*pi*A)/(k*n*a))*cos((pi*x)/a)*sin((pi*z)/d); \n", + "Ey=Ey**2; #c=(er1)⇤eo;\n", + "w=c*integrate(integrate(integrate(Ey,(z,0,d)),(y,0,t)),(x,0,a));\n", + "# as sin (2⇤ pi )=0; then last term of above result will be:\n", + "w=(c*A**2*a*t*d)/4;\n", + "print \"on taking sin (2⇤pi )=0 ,w becomes= \",w\n", + "wo=((a*b*d*eo)/2)*A**2;\n", + "deltaw=(w-wo)/wo;\n", + "print \"fractional change in resonant frequency= \",deltaw" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 2", + "language": "python", + "name": "python2" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 2 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython2", + "version": "2.7.10" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} |