{
"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": {}
}
]
}