{
"metadata": {
"name": "",
"signature": "sha256:c4970c321276b9f7170413d941bf292098cec215a7f4a0308f53e52cf40aad5c"
},
"nbformat": 3,
"nbformat_minor": 0,
"worksheets": [
{
"cells": [
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"Chapter 9: Transmission Lines"
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 9.1, page no. 237"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"# Variable Declaration\n",
"Zo = 75 # Characteristic Impedance (Ohms) \n",
"C = 69.00*pow(10,-12) # Nominal Capacitance (F/m)\n",
"Di = 0.584*pow(10,-3) # Inner core diameter (m)\n",
"k = 2.23 # Dielectric Constant\n",
"\n",
"# Calculation\n",
"import math # Math Library\n",
"L = pow(Zo,2)*C # Inductance per meter (H/m)\n",
"Do = Di*pow(10,Zo*math.sqrt(k)/138) # Outer core diameter (m)\n",
"\n",
"# Result\n",
"print \"Inductance per meter, L =\",round(L/pow(10,-6),3),\"uH/m\"\n",
"print \"Outer Diameter, D =\",round(Do/pow(10,-3),2),\"mm\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Inductance per meter, L = 0.388 uH/m\n",
"Outer Diameter, D = 3.78 mm\n"
]
}
],
"prompt_number": 2
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 9.2, page no. 237"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"# Variable Declaration\n",
"s = 1 # Assumed s (m)\n",
"d = s # Condition for minimum Zo (m)\n",
"\n",
"# Calculation\n",
"import math # Math Library\n",
"Zo_min = 276*math.log10(2*s/d) # Minimum value of characteristic impedance (Ohms)\n",
" \n",
"# Result\n",
"print \"The minimum value of characteristic impedance, Zo_min =\",round(Zo_min),\"Ohms\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The minimum value of characteristic impedance, Zo_min = 83.0 Ohms\n"
]
}
],
"prompt_number": 3
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 9.3, page no. 237"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"# Variable Declaration\n",
"Zo = 2000 # Characteristic Impedance (Ohms) \n",
"Di = 0.025*pow(10,-3) # Inner cable diameter (m)\n",
"k = 2.56 # Dielectric Constant \n",
"\n",
"# Calculation\n",
"import math # Math Library\n",
"Do = Di*pow(10,Zo*math.sqrt(k)/138) # Outer conductor diameter (m)\n",
"\n",
"# Result\n",
"print \"Outer Diameter, D =\",round(Do/pow(10,18),2),\"* 10^(15) km or\",round(Do/(9.44*pow(10,15))),\"light years\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Outer Diameter, D = 3.86 * 10^(15) km or 409.0 light years\n"
]
}
],
"prompt_number": 4
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 9.4, page no. 243"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"# Variable Declaration\n",
"Zo = 200 # Characteristic Impedance of main line (Ohms) \n",
"Zl = 300 # Load Impedance (Ohms)\n",
"\n",
"# Calculation\n",
"import math # Math Library\n",
"Zo1 = math.sqrt(Zo*Zl) # Characteristic impedance of the quarter wave transformer (Ohms)\n",
"\n",
"# Result\n",
"print \"Characteristic impedance of the quarter wave transformer, Zo1 =\",round(Zo1),\"Ohms\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Characteristic impedance of the quarter wave transformer, Zo1 = 245.0 Ohms\n"
]
}
],
"prompt_number": 5
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 9.5, page no. 246"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"# Variable Declaration\n",
"Zl = complex(200,75) # Load Impedance (Ohms)\n",
"Zo = 300 # Characteristic Impedance (Ohms)\n",
"\n",
"# Calculation\n",
"import math # Math Library\n",
"Yl = 1/Zl # Admittance (Mho)\n",
"Bstub = 1/Yl.imag # Reactance of the Stub (Ohms)\n",
"Gl = Yl.real # Real Part of Admittance (Mho)\n",
"Rl = 1/Gl # Resistance (Ohms)\n",
"Zo1 = math.sqrt(Zo*Rl) # Characteristic impedance of the quarter wave transformer (Ohms)\n",
"\n",
"# Result\n",
"print \"Reactance of the stub, Bstub =\",round(Bstub,1),\"Ohms\"\n",
"print \"Characteristic impedance of the quarter wave transformer, Zo1 =\",round(Zo1),\"Ohms\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Reactance of the stub, Bstub = -608.3 Ohms\n",
"Characteristic impedance of the quarter wave transformer, Zo1 = 262.0 Ohms\n"
]
}
],
"prompt_number": 6
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 9.6, page no. 250"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"# Variable Declaration\n",
"Y = complex(0.004,0.002) # Load Susceptance (Ohms)\n",
"Yo = 0.0033 # Ohms - Characteristic Admittance (Ohms)\n",
"f = 150*pow(10,6) # Operating Frequency (Hz)\n",
"vc = 3*pow(10,8) # Speed of light in vacuum (m/s)\n",
"\n",
"# Calculation\n",
"import math # Math Library\n",
"y = Y/Yo # Normalized susceptance required to cancel loads normalized susceptance\n",
"Lambda = vc/f # Wavelength (m)\n",
"Length = 0.337*Lambda # Length from Smith Chart (m)\n",
"\n",
"# Result\n",
"print \"Normalized susceptance required to cancel loads normalized susceptance = +j *\",round(y.imag,2)\n",
"print \"Length =\",round(Length*100,1),\"cm\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Normalized susceptance required to cancel loads normalized susceptance = +j * 0.61\n",
"Length = 67.4 cm\n"
]
}
],
"prompt_number": 7
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 9.7, page no. 250"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"# Variable Declaration\n",
"Z = complex(100,50) # Load Impedance (Ohms)\n",
"Zo = 75 # Characteristic Impedance (Ohms)\n",
"\n",
"# Calculation\n",
"import math # Math Library\n",
"z = Z/Zo # Normalized Load Impedance (Ohms)\n",
"Zg = 39.8 # Resistance at Distance = 0.184* Lambda, from Smith Chart (Ohms)\n",
"Zo_dash = math.sqrt(Zg*Zo) # Impedance of the transformer (Ohms)\n",
"\n",
"# Result\n",
"print \"(a) From Smith Chart the Distance = 0.184 * Lambda\"\n",
"print \"(b) Zo_dash for the transformer, Zo' =\",round(Zo_dash,1),\"Ohms\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"(a) From Smith Chart the Distance = 0.184 * Lambda\n",
"(b) Zo_dash for the transformer, Zo' = 54.6 Ohms\n"
]
}
],
"prompt_number": 8
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 9.8, page no. 253"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"# Variable Declaration\n",
"Z = complex(450,-600) # Load Impedance (Ohms)\n",
"Zo = 300 # Characteristic Impedance (Ohms)\n",
"\n",
"# Calculation\n",
"import math # Math Library\n",
"z = Z/Zo # Normalized Load Impedance (Ohms)\n",
"s = 4.6 # Standing Wave Ratio\n",
"L = 1/(2*math.pi)*math.atan(math.sqrt(s)/(s-1)) # (* Lambda) Stub Length (m)\n",
"\n",
"# Result\n",
"print \"Normalized load Impedance = \",z\n",
"print \"From Smith Chart the Distance to the stub = 0.130 * Lambda\"\n",
"print \"Stub Length =\",round(L,3),\"* Lambda\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Normalized load Impedance = (1.5-2j)\n",
"From Smith Chart the Distance to the stub = 0.130 * Lambda\n",
"Stub Length = 0.086 * Lambda\n"
]
}
],
"prompt_number": 9
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 9.9, page no. 254"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"# Variable Declaration\n",
"Z = complex(450,-600) # Load Impedance (Ohms)\n",
"Zo = 300 # Characteristic Impedance (Ohms)\n",
"f1 = 10 # Old frequency (MHz)\n",
"f2 = 12 # New frequency (MHz)\n",
"\n",
"# Calculation\n",
"import math # Math Library\n",
"z = Z/Zo # Normalized Load Impedance (Ohms)\n",
"z1 = z.imag * f1/f2 # Intermediate Impedance (Ohms)\n",
"z = complex(z.real,z1) # Normalized Load Impedance (Ohms)\n",
"s = 4.6 # Standing Wave Ratio\n",
"L = 1/(2*math.pi)*math.atan(math.sqrt(s)/(s-1))*f2/f1 # (* Lambda')Stub Length (m)\n",
"\n",
"# Result\n",
"print \"Normalized load Impedance = \",z\n",
"print \"From Smith Chart the Distance to the stub = 0.156 * Lambda'\"\n",
"print \"Stub Length =\",round(L,3),\"* Lambda'\"\n",
"print \"From Smith chart SWR = 2.2\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Normalized load Impedance = (1.5-1.66666666667j)\n",
"From Smith Chart the Distance to the stub = 0.156 * Lambda'\n",
"Stub Length = 0.103 * Lambda'\n",
"From Smith chart SWR = 2.2\n"
]
}
],
"prompt_number": 10
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 9.10, page no. 256"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"# Variable Declaration\n",
"Z = 200.00 # Load Impedance (Ohms)\n",
"Zo = 300.00 # Characteristic Impedance (Ohms)\n",
"\n",
"# Calculation\n",
"import math # Math Library\n",
"z = Z/Zo # Normalized Load Impedance (Ohms)\n",
"L1_by_Lambda = 0.311 # Ratio from Smith Chart\n",
"L2_by_Lambda1 = L1_by_Lambda*1.1 # Ratio\n",
"\n",
"# Result\n",
"print \"(a) Normalized load Impedance = \",round(z,2)\n",
"print \" From Smith Chart the Distance to the stub = 0.11 * Lambda\"\n",
"print \" From Smith Chart the Length of stub = 0.311 * Lambda\"\n",
"print \"(b) New Length of stub =\",round(L2_by_Lambda1,3),\"* Lambda'\"\n",
"print \" From Smith chart SWR = 1.3\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"(a) Normalized load Impedance = 0.67\n",
" From Smith Chart the Distance to the stub = 0.11 * Lambda\n",
" From Smith Chart the Length of stub = 0.311 * Lambda\n",
"(b) New Length of stub = 0.342 * Lambda'\n",
" From Smith chart SWR = 1.3\n"
]
}
],
"prompt_number": 11
}
],
"metadata": {}
}
]
}