{ "metadata": { "name": "", "signature": "sha256:060fdcfe827769d224d6e050c45932130de9317b1c6afbcd45de118cee9f7fb4" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "heading", "level": 1, "metadata": {}, "source": [ "Chapter9:MICROWAVE LINEAR-BEAM TUBES(O TYPE)" ] }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Eg9.2.1:pg-377" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math\n", "#(a) Calculate the input gap voltage to give maximum voltage V2\n", "\n", "#For maximum V2, J1(X) must be maximum.This means J1(X)=0.582 at X=1.841. \n", "X=1.841 #bunching parameter\n", "J1X=0.582 \n", "V0=10**3 #dc voltage in Volt\n", "v0=0.593*(10**6)*(sqrt(V0)) #The electron velocity just leaving the cathode\n", "f=3*(10**9) #operating frequency in Hertz\n", "d=1*(10**-3) #Gap spacing in either cavity in meter\n", "w=(2*math.pi*f) #angular frequency in Hertz\n", "Og=(w*d)/v0 #calculation of gap transit angle in radians\n", "Bi=(math.sin(Og/2))/(Og/2) #value of Bi is wrong in book because of calculation mistake\n", "Bo=Bi #value of Bo is wrong in book\n", "L=4*(10**-2) #Spacing between the two cavities in meter\n", "O0=(w*L)/v0 #DC transit angle between the cavaties in radians\n", "V1max=(2*V0*X)/(round(Bi,3)*int(O0)) \n", "print\"The maximum input voltage V1 (in Volts) is =\",round(V1max,1),\"V\" #value of Bi used in book for calculation of V1 is wrong so answer is wrong in book \n", "\n", "#(b) Calculate the voltage gain\n", "R0=40*(10**3) #in Ohms\n", "Rsh=30*(10**3) #Effective shunt impedance excluding beam loading in Ohms\n", "Av=((round(Bo,3)**2)*int(O0)*J1X*Rsh)/(R0*X) #voltage gain\n", "print\"The voltage gain,neglecting the beam loading in the output cavity is =\",round(Av,3) #answer is wrong in book as the value of Bo used is wrong \n", "\n", "#(c)Calculate the efficiency of the amplifier\n", "I0=25*(10**-3) #in ampere\n", "I2=2*I0*J1X \n", "V2=round(Bo,3)*I2*Rsh \n", "efficiency=(round(Bo,3)*I2*int(V2))/(2*I0*V0) \n", "efficiency=100*efficiency \n", "print\"The efficiency of the amplifier,neglecting beam loading =\",round(efficiency,1),\"%\" #calculation mistake in book \n", "\n", "#(d)Calculate the beam loading conductance\n", "G0=25*(10**-6) #G0=I0/V0 is the DC beam conductance in mho\n", "Og=round(Og)\n", "GB=(G0/2)*((round(Bo,3)**2)-(round(Bo,3)*math.cos(Og/2))) \n", "print\"The beam loading conductance GB (in mho) is =\",\"{:.1e}\".format(GB),\"mho\" #answer is wrong in book as the value of Bo in book is wrong\n", "RB=1/GB \n", "print\"Then the beam loading resistance RB (ohm)is =\",\"{:.2e}\".format(RB),\"ohms\"\n", "print('In comparasion with RL and Rsho or the effective shunt resistance Rsh,the beam loading resistance is like an open circuit and thus can be neglected in the preceding calculations') " ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "The maximum input voltage V1 (in Volts) is = 96.1 V\n", "The voltage gain,neglecting the beam loading in the output cavity is = 8.704\n", "The efficiency of the amplifier,neglecting beam loading = 46.6 %\n", "The beam loading conductance GB (in mho) is = 9.6e-07 mho\n", "Then the beam loading resistance RB (ohm)is = 1.04e+06 ohms\n", "In comparasion with RL and Rsho or the effective shunt resistance Rsh,the beam loading resistance is like an open circuit and thus can be neglected in the preceding calculations\n" ] } ], "prompt_number": 4 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Eg9.3.1:pg-385" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math\n", "#(a) Calculate the dc electron velocity\n", "V0=14.5*(10**3) #beam voltage in Volt\n", "v0=0.593*(10**6)*sqrt(V0) #dc electron velocity \n", "print\"The dc electron velocity(in m/s)is =\",\"{:.2e}\".format(v0),\"m/s\"\n", "\n", "#(b) Calculate the dc phase constant\n", "f=(10*(10**9)) #operating frequency in Hertz\n", "Be=(2*math.pi*f)/v0 #angular frequency in Hertz \n", "print\"The dc phase constant(in rads/m) is =\",\"{:.2e}\".format(Be),\"rads/m\"\n", "\n", "#(c)Calculate the plasma frequency\n", "po=1*(10**-6) #dc electron charge density in C/m**3\n", "wp=sqrt((1.759*(10**11)*po)/(8.854*(10**-12))) \n", "print\"The plasma frequency(in rad/s)is =\",\"{:.2e}\".format(wp),\"rad/s\"\n", "\n", "#(d) Calculate the reduced plasma frequency for R=0.4\n", "R=0.4 \n", "wq=R*wp \n", "print\"The reduced plasma frequency for R=0.4 (in rad/s) is =\",\"{:.2e}\".format(wq),\"rad/s\" \n", "\n", "#(e)Calculate the dc beam current density\n", "J0=po*v0 \n", "print\"The dc beam current density(in A/m2) is =\",round(J0,1),\"A/m2\" \n", "\n", "#(f) Calculate the instantaneous beam current density\n", "p=1*(10**-8) #RF charge density in C/m**3\n", "v=1*(10**5) #velocity perturbation in m/s\n", "J=(p*v0)-(po*v) \n", "print\"The instantaneous beam current density (in A/m2) is =\",round(J,3),\"A/m2\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "The dc electron velocity(in m/s)is = 7.14e+07 m/s\n", "The dc phase constant(in rads/m) is = 8.80e+02 rads/m\n", "The plasma frequency(in rad/s)is = 1.41e+08 rad/s\n", "The reduced plasma frequency for R=0.4 (in rad/s) is = 5.64e+07 rad/s\n", "The dc beam current density(in A/m2) is = 71.4 A/m2\n", "The instantaneous beam current density (in A/m2) is = 0.614 A/m2\n" ] } ], "prompt_number": 6 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Eg9.3.2:pg-386" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math\n", "#(a) Calculate the dc electron velocity\n", "V0=18*(10**3) #beam voltage in Volt\n", "v0=0.593*(10**6)*sqrt(V0) \n", "print\"The dc electron velocity(in m/s)is =\",\"{:.2e}\".format(v0),\"m/s\" \n", "\n", "#(b) Calculate the dc electron phase constant\n", "f=(10*(10**9)) #Operating frequency in Hertz\n", "w=2*math.pi*f #angular frequency in Hertz\n", "Be=w/v0 \n", "print\"The dc electron phase constant(in rads/m) is =\",\"{:.3e}\".format(Be),\"rads/m\" \n", "\n", "#(c) Calculate the plasma frequency\n", "po=1*(10**-8) #dc electron beam current density in C/m**3\n", "wp=sqrt((1.759*(10**11)*po)/(8.854*(10**-12))) \n", "print\"The plasma frequency(in rad/s) is =\",\"{:.2e}\".format(wp),\"rad/s\"\n", "\n", "#(d) Calculate the reduced plasma frequency for R=0.5\n", "R=0.5 \n", "wq=R*wp \n", "print\"The reduced plasma frequency for R=0.5 (in rad/s)is =\",\"{:.2e}\".format(wq),\"rad/s\" \n", "\n", "#(e) Calculate the reduced plasma phase constant\n", "Bq=wq/v0 \n", "print\"The reduced plasma phase constant(in rad/m) is =\",round(Bq,3),\"rad/m\"\n", "\n", "#(f) Calculate the transit time across the input gap\n", "d=1*(10**-2) #gap distance in m\n", "t=d/v0 \n", "t=t*(10**9) \n", "print\"The transit time across the input gap(in ns) is =\",round(t,4),\"ns\" \n", "\n", "#(g) Calculate the electron velocity leaving the input gap\n", "V1=10 #signal voltage in Volt\n", "Bi=1.0 #beam coupling coefficient\n", "Vt1=v0*(1+(((Bi*V1)/(2*V0))*math.sin(w*round(t,4)*(10**-9)))) \n", "print\"the electron velocity leaving the input gap(in m/s)is =\",\"{:.2e}\".format(v0),\"+\",\"{:.2e}\".format(v0*(((Bi*V1)/(2*V0))*math.sin(w*round(t,4)*(10**-9)))),\"m/s =\",\"{:.2e}\".format(Vt1),\"m/s\" " ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "The dc electron velocity(in m/s)is = 7.96e+07 m/s\n", "The dc electron phase constant(in rads/m) is = 7.897e+02 rads/m\n", "The plasma frequency(in rad/s) is = 1.41e+07 rad/s\n", "The reduced plasma frequency for R=0.5 (in rad/s)is = 7.05e+06 rad/s\n", "The reduced plasma phase constant(in rad/m) is = 0.089 rad/m\n", "The transit time across the input gap(in ns) is = 0.1257 ns\n", "the electron velocity leaving the input gap(in m/s)is = 7.96e+07 + 2.21e+04 m/s = 7.96e+07 m/s\n" ] } ], "prompt_number": 7 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Eg9.3.3:pg-388" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math\n", "#(a)Calculate the plasma frequency\n", "po=1*(10**-6) #dc electron beam current density in C/m**3\n", "e0=8.854*(10**-12) #permittivity of free space in F/m\n", "wp=sqrt((1.759*(10**11)*po)/e0) \n", "print\"The plasma frequency(in rad/s)is =\",\"{:.2e}\".format(wp),\"rad/s\"\n", "\n", "#(b) Calculate the reduced plasma frequency for R=0.5\n", "R=0.5 \n", "f=8*(10**9) #operating frequency in Hertz\n", "w=2*math.pi*f #angular frequency in Hertz\n", "wq=R*wp \n", "print\"The reduced plasma frequency for R=0.5(in rad/s)is =\",\"{:.2e}\".format(wq),\"rad/s\" \n", "\n", "#(c) Calculate the induced current in the output cavity\n", "V0=20*(10**3) #beam voltage in Volt\n", "I0=2 #beam current in ampere\n", "V1=10 #Signal voltage in Volt\n", "Bo=1 #Beam coupling coefficient\n", "I2=(I0*w*(Bo**2)*V1)/(2*V0*wq) \n", "print\"The induced current in the output cavity(in Ampere)is =\",round(I2,4),\"A\" \n", "\n", "#(d) Calculate the induced voltage in the output cavity\n", "Rshl=30*(10**3) #total shunt resistance including load in Volt\n", "V2=round(I2,3)*Rshl \n", "V2=V2/1000 #in KV\n", "print\"The induced voltage in the output cavity(in KV)is =\",V2,\"KV\"\n", "\n", "#(e) Calculate the output power delivered to the load\n", "Rsh=10*(10**3) #shunt resistance of the cavity\n", "Rshl=30*(10**3) #total shunt resistance including load\n", "Pout=(round(I2,3)**2)*Rshl \n", "Pout=Pout/1000 \n", "print\"The output power delivered to the load(in KW)is =\",round(Pout,2),\"KW\"\n", "\n", "#(f) Calculate the power gain\n", "powergain=(((I0*w)**2)*(Bo**4)*Rsh*Rshl)/(4*((V0*wq)**2)) \n", "powergain=10*math.log10(powergain) #powergain in dB\n", "print\"The power gain is =\",round(powergain,1),\"dB\"\n", "\n", "#(g) Calculate the electronic efficiency\n", "n=(Pout*1000)/(I0*V0) \n", "n=n*100 \n", "print\"The electronic efficiency (in %)is =\",round(n,1),\"%\" " ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "The plasma frequency(in rad/s)is = 1.41e+08 rad/s\n", "The reduced plasma frequency for R=0.5(in rad/s)is = 7.05e+07 rad/s\n", "The induced current in the output cavity(in Ampere)is = 0.3566 A\n", "The induced voltage in the output cavity(in KV)is = 10.71 KV\n", "The output power delivered to the load(in KW)is = 3.82 KW\n", "The power gain is = 55.8 dB\n", "The electronic efficiency (in %)is = 9.6 %\n" ] } ], "prompt_number": 8 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Eg9.3.4:pg-390" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math\n", "#(a) Calculate the plasma frequency\n", "po=5*(10**-5) #dc electron beam current density in C/m**3\n", "wp=sqrt((1.759*(10**11)*po)/(8.854*(10**-12))) \n", "print\"The plasma frequency(in rad/s)is =\",\"{:.2e}\".format(wp),\"rad/s\" \n", "\n", "#(b) Calculate the reduced plasma frequency for R=0.6\n", "R=0.6 \n", "f=4*(10**9) #operating frequency in Hertz\n", "w=2*math.pi*f #angular frequency in Hertz\n", "wq=R*wp \n", "print\"The reduced plasma frequency for R=0.6(in rad/s)is =\",\"{:.2e}\".format(wq),\"rad/s\" \n", "\n", "#(c) Calculate the induced current in the output cavity\n", "Rsh=10*(10**3) #shunt resistance of the cavity in Ohms\n", "Rshl=5*(10**3) #total shunt resistance including load in Ohms\n", "V0=10*(10**3) #beam voltage in volt\n", "I0=0.7 #beam current in ampere\n", "V1=2 #Signal voltage in volt\n", "Bo=1 #Beam coupling coefficient\n", "I4=(((I0*w)**3)*(Bo**6)*V1*(Rsh**2))/(8*((V0*wq)**3)) \n", "print\"The induced current in the output cavity(in Ampere)is =\",round(I4,4),\"A\"\n", "\n", "#(d) Calculate the induced voltage in the output cavity\n", "V4=I4*Rshl \n", "V4=V4/1000 #in KV\n", "print\"The induced voltage in the output cavity(in KV)is =\",round(V4,2),\"KV\"\n", "\n", "#(e) Calculate the output power delivered to the load\n", "Pout=(I4**2)*Rshl \n", "Pout=Pout/1000 #in KW\n", "print\"The output power delivered to the load(in KW)is =\",round(Pout,2),\"KW\" " ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "The plasma frequency(in rad/s)is = 9.97e+08 rad/s\n", "The reduced plasma frequency for R=0.6(in rad/s)is = 5.98e+08 rad/s\n", "The induced current in the output cavity(in Ampere)is = 0.6366 A\n", "The induced voltage in the output cavity(in KV)is = 3.18 KV\n", "The output power delivered to the load(in KW)is = 2.03 KW\n" ] } ], "prompt_number": 9 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Eg9.4.1:pg-399" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math\n", "#(a) Calculate the value of the repeller voltage\n", "V0=600 #beam voltage in volt\n", "n=2 #mode=2\n", "fr=9*(10**9) #operating frequency in Hertz\n", "w=2*math.pi*fr #angular frequency in Hertz\n", "L=1*(10**-3) #in meter\n", "em=1.759*(10**11) #em=e/m is the charge to mass ratio of electron\n", "x=((em)*(((2*math.pi*n)-(math.pi/2))**2))/(8*(w**2)*(L**2)) #x=V0/(V0+Vr)**2\n", "y=V0/x #y=(V0+Vr)**2\n", "z=sqrt(y) #z=V0+Vr\n", "Vr=z-V0 \n", "print\"The value of the repeller voltage(volts)is =\",int(round(Vr)),\"V\" \n", "\n", "#(b)Calculate the direct current necessary to give a microwave gap voltage of 200V\n", " #Assume that Bo=1\n", " #V2 = I2*Rsh = 2*I0*J1(X)*Rsh \n", "V2=200 #gap voltage in volt\n", "Rsh=15*(10**3) #shunt resistance of te cavity in ohms\n", "X=1.841 #bunching parameter\n", "J1X=0.582 \n", "I0 = V2/(2*J1X*Rsh) \n", "I0=I0*1000 #in mA\n", "print\"The direct current necessary to give a microwave gap voltage of 200V(in mA)is =\",round(I0,2),\"mA\" \n", "\n", "#(c) Calculate the electronic efficiency \n", "efficiency=(2*X*J1X)/((2*math.pi*n)-(math.pi/2)) \n", "efficiency=efficiency*100 \n", "print\"The electronic efficiency(in %)is =\",round(efficiency,2),\"%\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "The value of the repeller voltage(volts)is = 250 V\n", "The direct current necessary to give a microwave gap voltage of 200V(in mA)is = 11.45 mA\n", "The electronic efficiency(in %)is = 19.49 %\n" ] } ], "prompt_number": 10 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Eg9.5.1:pg-415" ] }, { "cell_type": "code", "collapsed": false, "input": [ "import math\n", "#(a) Calculate the gain parameter\n", "I0=30*(10**-3) #Beam current in ampere\n", "V0=3*(10**3) #Beam voltage in volt\n", "Z0=10 #characteristic impedance of the helix in ohms\n", "C=(((I0*Z0)/(4*V0))**(1/3.0)) \n", "print\"The gain parameter is =\",\"{:.2e}\".format(C) \n", "\n", "#(b) Calculate the output power gain in dB\n", "N=50 #Crcular length\n", "Ap=-9.54+(47.3*N*round(C,4)) \n", "print\"The output power gain (in dB) is =\",round(Ap,2),\"dB\"\n", "\n", "#(c) Calculate the four propagation constants\n", "f=10*(10**9) #frequency in Hertz\n", "V0=3*(10**3) #beam voltage in volt\n", "w=2*(math.pi)*f #nagular frequency in Hertz\n", "v0=0.593*(10**6)*sqrt(V0) \n", "Be=w/v0 \n", "Be=int(Be/10)\n", "Be=Be*10\n", "r1=(-1*Be*round(C,4)*(round((sqrt(3)/2),2)))+1j*Be*(1+(round(C,4)/2)) \n", "X=round(r1.real,2)\n", "Y=int(r1.imag)\n", "r1=X+1j*Y\n", "print\"The four propagation constants are:\"\n", "print\"\\nThe first propagtaion constant is =\",r1 #value of imaginary part is wrong in book\n", "r2=(Be*round(C,4)*(round((sqrt(3)/2),2)))+1j*Be*(1+(round(C,4)/2))\n", "X=round(r2.real,2)\n", "Y=int(r2.imag)\n", "r2=X+1j*Y\n", "print\"The second propagtaion constant is =\",r2 #value of imaginary part is wrong in book\n", "r3=1j*Be*(1-round(C,4)) \n", "print\"The third propagtaion constant is =\",r3 #answer is wrong in book\n", "r4=(-1*1j*Be*(1-((C**3)/4)))\n", "r4=0+1j*round(r4.imag)\n", "print\"The fourth propagtaion constant is =\",r4" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "The gain parameter is = 2.92e-02\n", "The output power gain (in dB) is = 59.52 dB\n", "The four propagation constants are:\n", "\n", "The first propagtaion constant is = (-49.03+1958j)\n", "The second propagtaion constant is = (49.03+1958j)\n", "The third propagtaion constant is = 1873.644j\n", "The fourth propagtaion constant is = -1930j\n" ] } ], "prompt_number": 15 }, { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Eg9.7.1:pg-427" ] }, { "cell_type": "code", "collapsed": false, "input": [ "#(a) Calculate the number of electrons returned per second\n", "Ir=0.85 #returned current in ampere\n", "q=1.6*(10**-19) #electronic charge in C\n", "Nr=Ir/q \n", "print\"The number of electrons returned (per second) is =\",\"{:.2e}\".format(Nr),\"electrons/s\" \n", "\n", "#(b)Calculate the Energy associated with these returning electrons in 20ms\n", "V=-11*(10**3) #overdepreesion collector voltage in volt\n", "V=-1*V\n", "t=20*(10**-3) #in seconds\n", "W=V*Nr*t \n", "print\"The Energy associated with these returning electrons in 20ms(in eV) is =\",\"{:.3e}\".format(W),\"eV\"\n", "\n", "#(c) Calculate the Power for returning electrons\n", "P=V*Ir \n", "P=P/1000 #in KW\n", "print\"The Power for returning electrons(in KW)is =\",P,\"KW\" \n", "\n", "#(d) Calculate the Heat in calories associated with the returning electrons(a factor for converting joules to calories is 0.238)\n", "t=20*(10**-3) #in seconds\n", "H=0.238*P*1000*t \n", "print\"The Heat associated with the returning electrons(in calories)is =\",round(H,2),\"calories\"\n", "\n", "#(e) Calculate the temperature\n", "mass=250*(10**-3) #mass of heated iron pole piece in gram\n", "specific_heat=0.108 \n", "T=round(H,2)/(mass*specific_heat) \n", "print\"The temperature(in degree Celsius)is =\",round(T,2),\"degree celsius\"\n", "\n", "#(f) Calculate whether the output iron pole piece is melted\n", "print\"The output iron pole piece is melted\"" ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "The number of electrons returned (per second) is = 5.31e+18 electrons/s\n", "The Energy associated with these returning electrons in 20ms(in eV) is = 1.169e+21 eV\n", "The Power for returning electrons(in KW)is = 9.35 KW\n", "The Heat associated with the returning electrons(in calories)is = 44.51 calories\n", "The temperature(in degree Celsius)is = 1648.52 degree celsius\n", "The output iron pole piece is melted\n" ] } ], "prompt_number": 16 } ], "metadata": {} } ] }