{ "metadata": { "name": "", "signature": "sha256:ee8ead130cd20bf208c1745a750e51dbe8ebb757e8693bff3ccfb09c0b5cc29e" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "heading", "level": 1, "metadata": {}, "source": [ "Chapter4:MICROWAVE WAVEGUIDES AND COMPONENTS" ] }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Eg4.1.1:pg-128" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#(a)program to find the cut-off frequency (fc) of an air-filled rectangular waveguide in TE10 mode.\n", "a=0.07 #wave-guide dimension in meters\n", "b=0.035 #wave-guide dimension in meters\n", "f=3.5*(10**9) #operating frequency in Hz \n", "c=3*(10**8) # c is the speed of the light (m/s)\n", "m=1 #Given that guide operates in the dominant mode TE10\n", "n=0\n", "fc=c/(a*2) #since,fc=(c/2)*sqrt(((m/a)**2)+((n/b)**2)). For TE10 mode m=1,n=0,fc=c/2*a \n", "print\"Cut-off frequency for TE10 mode (in GHz)is=\",round(fc/10**9,2),\"GHz\"#print fc ,fc is divided by 10**9 to obtain frequency in GHZ\n", "\n", "#(b) program to find the phase velocity of the wave in the guide at a frequency of 3.5GHZ\n", " \n", "vg=c/(sqrt(1-((fc/f)**2))) #since , phase velocity=c/(sqrt(1-((fc/f)**2))) \n", "print\"Phase velocity for a wave at a frequency of 3.5GHZ (m/s)is=\",\"{:.2e}\".format(vg),\"m/s\" #print the phase velocity\n", "\n", "# (c) program to find the guideD wavelength(lg of the wavE at a frequency of 3.5GHZ)\n", "lo=c/f # lo= wavelength in an unbounded dielectric and lo is in meters\n", "lg_in_metres=lo/(sqrt(1-((fc/f)**2))) #since ,lg=lo/sqrt(1-((fc/f)**2)) guide wavelength(lg) is in meter\n", "lg_in_cm=100*lg_in_metres #guided wavelength (lg) is in centimeters\n", "print\"Guided wavelength for a wave at frequency of 3.5GHZ (cm)is=\",round(lg_in_cm,1),\"cm\" " ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Cut-off frequency for TE10 mode (in GHz)is= 2.14 GHz\n", "Phase velocity for a wave at a frequency of 3.5GHZ (m/s)is= 3.79e+08 m/s\n", "Guided wavelength for a wave at frequency of 3.5GHZ (cm)is= 10.8 cm\n" ] } ], "prompt_number": 32 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Eg4.1.2:pg-133" ] }, { "cell_type": "code", "collapsed": false, "input": [ "from scipy.integrate import dblquad\n", "import math\n", "#Program to find the peak value of the electric field occuring in the guide.\n", "m=1 #given guide transports energy in the TE10 mode.\n", "n=0\n", "f=30*(10**9) #The impressed frequency in Hertz\n", "uo=(4*(math.pi))*(10**-7) #scientific value of permeability of free space\n", "eo=8.854*(10**(-12)) #permittivity of free space in F/m\n", "a=0.02 # dimensions of wave-guide given in metres\n", "b=0.01\n", "energyrate=0.5*746 #given ,the rate of transport of energy =0.5 hp,1 horse power(1 hp)= 746 watts.\n", "kc=math.pi/a #kc is cutoff wave number ,kc=sqrt((m*pi/a)**2+(n*pi/b)**2),For m=1,n=0 we get kc=pi/a\n", "bg=sqrt((((2*math.pi*f)**2)*(uo*eo)) -(kc**2)) #bg is the phase constant in radian/metre, bg=sqrt(((w**2)*(uo*eo))-(kc**2)) where w=2*pi*f\n", "Zg=((2*math.pi*30*(10**9))*uo)/bg #Zg is the characteristic wave impedence ,Zg=(w*uo)/bg where w=2*pi*f\n", "\n", "#Defining the variables\n", "Ex=0 #For TE10 mode Ex=0\n", "#Ey = Eoy*sin((pi*x)/a)*exp(-1j*bg*z) (for TE10 mode) \n", "Ez=0 #For TE10 mode Ez=0 \n", "#since, Hx=(Eoy/Zg)*sin(pi*x)/a)*exp(-1j*bg*z) (for TE10 mode)\n", "Hy = 0 #For TE10 mode Hy=0\n", "#Hz=Hoz*cos((pi*x)/a)*exp(-1j*bg*z) (for TE10 mode).\n", "p=dblquad(lambda x, y :(sin((math.pi*x)/a))**2, 0, b, lambda x:0 ,lambda x:a )\n", "p=p[0]\n", "c=(bg*p)/(4*math.pi*f*uo)\n", "p=c*(eoy)**2\n", "p=373.\n", "eoy=sqrt(p/c)\n", "print\"The peak value of the electric intensity is=\",\"Eoy=\", round(eoy/1000,2),\"KV/m\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "The peak value of the electric intensity is= Eoy= 53.87 KV/m\n" ] } ], "prompt_number": 35 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Eg4.2.1:pg-144" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math\n", "# (a) program to find the cut off frequency (fc) of circular waveguide in TE11 mode\n", "radius=0.05 #Given .Here radius is in meters. \n", "f=3*(10**9) #operating frequency in Hertz\n", "uo=(4*(math.pi))*(10**-7) #scientific value of permeability of free space \n", "eo=8.85*(10**(-12)) #permittivity of free space in F/m\n", "n=1 #Given that a TE11 mode is propagating.\n", "p=1 \n", "X=1.841 #For TE11 mode in circular waveguide X= (kc*radius) =1.841\n", "kc=X/radius #cut-off wave number\n", "fc=kc/((2*math.pi)*(sqrt(uo*eo))) #since fc=kc/((2*pi)*(sqrt(uo*eo))) \n", "print\"Cut-off frequency for TE11 mode (in Hz)is=\",\"{:.3e}\".format(fc),\"Hz\" \n", "\n", "# (b) program to find the guide wavelength(lg) of the wave at operating frequency of 3GHZ\n", "bg=sqrt((((2*math.pi*f)**2)*(uo*eo)) - (kc**2)) #bg is the phase constant in radian/metre, bg=sqrt(((w**2)*(uo*eo))-(kc**2)) where w=2*pi*f\n", "lg_in_metres=(2*math.pi)/bg #Guide wavelength is in meters\n", "lg_in_cm=100*lg_in_metres #Guide wavelength is in centimeters\n", "print\"Guide wavelength for a wave at a frequency of 3GHz(in cm)is=\",round(lg_in_cm,1),\"cm\" # print Guide wavelength for TE11 mode\n", "\n", "# (c) program to find the wave impedance zg in the guide\n", "zg=(2*math.pi*f*uo)/bg #Zg is the characteristic wave impedence ,Zg=(w*uo)/bg where w=2*pi*f\n", "print\"Wave impedance zg in the wave guide(in ohm)=\",int(round(zg)),\"ohm\" #print wave impedance in the wave guide" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Cut-off frequency for TE11 mode (in Hz)is= 1.757e+09 Hz\n", "Guide wavelength for a wave at a frequency of 3GHz(in cm)is= 12.3 cm\n", "Wave impedance zg in the wave guide(in ohm)= 465 ohm\n" ] } ], "prompt_number": 4 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Eg4.2.2:pg-147" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math\n", "#program to find all the TE(n,p) and TM(n,p)modes for which energy transmisssion is possible.\n", "\n", "radius=0.02 #Given. Here radius is in metres. \n", "uo=(4*(math.pi))*(10**-7) #scientific values of permeability of free space\n", "eo=8.85*(10**(-12)) #permittivity of free space in F/m\n", "f=(10**10) #operating frequency in Hertz\n", "wc=(2*math.pi*f) #since, wc=(2*pi*f) is the angular frequency in Hertz\n", "kc=wc*sqrt(uo*eo) #kc is cut-off wave number \n", "X=kc*radius #the product X=(kc*radius) for a given mode is constant\n", "print\"The value of the product X=(kc*radius)is =\",round(X,2) #print the product X=(kc*a)\n", "print\"Any mode having a product (kc*radius) less than or equal to 4.19 will propagate the wave with a frequency of 10 GHZ .This is \\n\",\"(kc*radius)< =4.19\"\n", "print\"The possible modes are\" \n", "print\"TE11(1.841) TM01(2.405) \\n\",\"TE21(3.054) TM11(3.832) \\n\",\"TE01(3.832)\" \n" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "The value of the product X=(kc*radius)is = 4.19\n", "Any mode having a product (kc*radius) less than or equal to 4.19 will propagate the wave with a frequency of 10 GHZ .This is \n", "(kc*radius)< =4.19\n", "The possible modes are\n", "TE11(1.841) TM01(2.405) \n", "TE21(3.054) TM11(3.832) \n", "TE01(3.832)\n" ] } ], "prompt_number": 16 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Eg4.5.1:pg-170" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#(a)program to find the amount of the power dissipated in the load Zl\n", "PT4=8 #Given.Transmitted power to Bolometer 1 at port 4 in mW\n", "s=2 #Given.VSWR of 2.0 is introduced on arm 4 by Bolometer 1 in mW \n", "r4=(s-1)/(s+1) #reflection coefficient at port 4(r4)\n", "PR4=8/8 #(r4**2)=PR4/PI4=PR4/(PR4+PT4)=PR4/PR4+8=1/9 so we get 8PR4=8 \n", "PI4=PT4 + PR4 #PI4=power incident at port 4 PT4=power transmitted at port 4 PR4=power reflected at port 4 \n", "#Since port 3 is matched and the Bolometer at port 3 reads 2mw ,then 1 mw must be radiated through the holes. \n", "#Since 20 dB is equivalent to a power of 100:1,the power input at port 2 is given by PI2\n", "PI2=100*PI4 \n", "PR2=100.0*PR4 #power reflected from the load at port 2 is given by (mW)\n", "PT2=PI2-PR2 #power dissipated in the load = incident power - reflected power\n", "print\"power dissipated in the load at port 2 is given by (mW) =\",int(PT2),\"mW\" \n", "\n", "#(b)Program to find the VSWR on arm 2\n", "r=sqrt(PR2/PI2) #reflection coefficient at port 2\n", "s=(1+r)/(1-r) #VSWR ON ARM 2 \n", "print\"value of VSWR ON ARM 2 is=\",s " ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "power dissipated in the load at port 2 is given by (mW) = 800 mW\n", "value of VSWR ON ARM 2 is= 2.0\n" ] } ], "prompt_number": 37 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Eg4.5.2:pg-174" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math\n", "#(a)Program to find out the input and output VSWRs.\n", "s11=0 #for balanced amplifier s11=(1/2)*(s11a-s11b) where s11a=s11b is given in question\n", "s=(1+s11)/(1-s11) #Input VSWR\n", "print\"Input vswr=\",s \n", "s22=0 #for balanced amplifier s22=(1/2)*(s22a-s22b) where s22a=s22b is given in question\n", "s=(1+s22)/(1-s22) #output VSWR\n", "print\"Output vswr=\",s \n", "\n", "#(b)Program to find out the output power in watts\n", "Pg=10 #power gain of each GaAs chip(dB)\n", "n=2 #number of GaAs chip\n", "pin=200 #input signal power in mW\n", "PO=pin*Pg*n #output power(PO)=[power input]*[power gain of each GaAs chip]*[n],here n=2\n", "print\"Output POWER (in Watt)=\",PO/1000,\"W\" #print power in watts by dividing PO by 1000\n", "\n", "#(C)Program to find out the linear output power gain in db \n", "GAIN=10*math.log10(2) #BECAUSE TWO CHIPS ARE IN PARALLEL. Gain=(power gain of each GaAs chip)*log(n),n=2.\n", "print\"Linear output power gain (in db)=\",int(round(GAIN)),\"dB\" #print linear output power gain in db" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Input vswr= 1\n", "Output vswr= 1\n", "Output POWER (in Watt)= 4 W\n", "Linear output power gain (in db)= 3 dB\n" ] } ], "prompt_number": 36 } ], "metadata": {} } ] }