{
"metadata": {
"name": "Chapter 6"
},
"nbformat": 3,
"nbformat_minor": 0,
"worksheets": [
{
"cells": [
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"Chapter 6: Microwave components"
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 6.2, Page number 234"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"from numpy import array\n",
"import cmath\n",
"import math\n",
"\n",
"#Variable declaration\n",
"S = array([[0,0.3+0.4j], [0.3+0.4j, 0]], dtype=complex)\n",
"B = 34.3 #rad/sec\n",
"\n",
"#Calculations\n",
"phi-1 = [[e^(-j*phi-1), 0]\n",
" [0 1]]\n",
"phi1 = 53.13\n",
"l = math.radians(phi1)/B\n",
"\n",
"#Result\n",
"print \"The distance is\",round(l,5),\"m\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The distance is 0.02703 m\n"
]
}
],
"prompt_number": 17
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 6.3, Page number 236"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"import math\n",
"\n",
"#Variable declaration\n",
"D = 30 #directiviy(dB)\n",
"s = 1 #VSWR\n",
"\n",
"#Calculations\n",
"#since C = -10*log(p1/p4),therefore,\n",
"S41 = math.sqrt(0.1)\n",
"S14=S41 #as matched and lossless\n",
"\n",
"#Now, D = 10*log(p4/p3)\n",
"S31=math.sqrt(S41**2/10**3)\n",
"S13=S31\n",
"\n",
"S11 = ((s-1)/(s+1))\n",
"S22=S11\n",
"S33=S11\n",
"S44=S11\n",
"\n",
"#Let input power be given at port 1\n",
"S21 = math.sqrt(1-S31**2-S41**2)\n",
"S12=S21\n",
"\n",
"S34 = math.sqrt((1+S12**2-10**-1-10**-4)*0.5)\n",
"S43=S34\n",
"\n",
"S23 = math.sqrt(1-10**-4-S34**2)\n",
"S32=S23\n",
"\n",
"S24 = math.sqrt(1-10**-1-S34**2)\n",
"S42=S24\n",
"\n",
"S = array([[S11,S12,S13,S14],[S21,S22,S23,S24],[S31,S32,S33,S34],[S41,S42,S43,S44]])\n",
"\n",
"#Result\n",
"print \"The required S-parameters are:\\n\\n\",S"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The required S-parameters are:\n",
"\n",
"[[ 0. 0.94863059 0.01 0.31622777]\n",
" [ 0.94863059 0. 0.31622777 0.01 ]\n",
" [ 0.01 0.31622777 0. 0.94863059]\n",
" [ 0.31622777 0.01 0.94863059 0. ]]\n"
]
}
],
"prompt_number": 39
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 6.4, Page number 238"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"import math\n",
"\n",
"#Variable declaration\n",
"a1 = 32 #signal power(mW) to port 1\n",
"a2 = 0 #power fed to port 2\n",
"a3 = 0 #power fed to port 3\n",
"s = array([[0.5,-0.5,math.sqrt(0.5)],[-0.5,0.5,math.sqrt(0.5)],[math.sqrt(0.5),math.sqrt(0.5),0]]) #s-matrix for H-plane Tee\n",
"\n",
"#Calculations\n",
"p = array([a1,a2,a3])\n",
"b = (s**2)*p\n",
"print \"[b]=\\n\",b\n",
"\n",
"#Results\n",
"print \"\\nPower at port 1 =\",b[0,0],\"mW\"\n",
"print \"Power at port 2 =\",b[1,0],\"mW\"\n",
"print \"Power at port 3 =\",b[2,0],\"mW\"\n",
"print \"It can be seen that b3=b1+b2\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"[b]=\n",
"[[ 8. 0. 0.]\n",
" [ 8. 0. 0.]\n",
" [ 16. 0. 0.]]\n",
"\n",
"Power at port 1 = 8.0 mW\n",
"Power at port 2 = 8.0 mW\n",
"Power at port 3 = 16.0 mW\n",
"It can be seen that b3=b1+b2\n"
]
}
],
"prompt_number": 59
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 6.5, Page number 239"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"from numpy import array\n",
"\n",
"#Variable declaration\n",
"s = array([[0.5,-0.5,math.sqrt(0.5)],[-0.5,0.5,math.sqrt(0.5)],[math.sqrt(0.5),math.sqrt(0.5),0]]) #s-matrix for H-plane Tee\n",
"b1=10*10**-3 #power at port 1\n",
"b2=10*10**-3 #power at port 2\n",
"\n",
"#Calculations\n",
"rho1=(60.-50.)/(60.+50.)\n",
"rho2=(75.-50.)/(75.+50.)\n",
"P1=0.5*b1**2*(1-rho1**2)\n",
"P2=0.5*b2**2*(1-rho2**2)\n",
"\n",
"#Results\n",
"print \"The solution given in the textbook is incorrect.\\n\"\n",
"print \"Power delivered to port 1 =\",round((P1/1E-3),3),\"mW\"\n",
"print \"Power delivered to port 2 =\",round((P2/1E-3),3),\"mW\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The solution given in the textbook is incorrect.\n",
"\n",
"Power delivered to port 1 = 0.05 mW\n",
"Power delivered to port 2 = 0.048 mW\n"
]
}
],
"prompt_number": 16
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 6.7, Page number 240"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"from numpy import array\n",
"\n",
"#Variable declaration\n",
"Il=0.5 #inserion loss(dB)\n",
"Is = 30 #isolation loss(dB)\n",
"\n",
"#Calculations\n",
"#Il = -20log(S21)\n",
"S21 = 10**(-Il/20)\n",
"#Is = -20log(S12)\n",
"S12 = 10**(-Is/20)\n",
"#Perfectly matched ports\n",
"S11=0\n",
"S22=0\n",
"\n",
"S = array([[S11,S12],[S21,S22]])\n",
"\n",
"#Result\n",
"print \"The scattering matrix is:\\n\",S\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The scattering matrix is:\n",
"[[ 0. 0.01 ]\n",
" [ 0.94406088 0. ]]\n"
]
}
],
"prompt_number": 24
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 6.9, Page number 241"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"from numpy import array\n",
"\n",
"#Variable declaration\n",
"Il= 0.5 #inserion loss(dB)\n",
"Is = 20 #isolation loss(dB)\n",
"S = 2 #VSWR\n",
"\n",
"#Calculations\n",
"#Il = -20log(S21)\n",
"S21 = 10**(-Il/20)\n",
"#For circulator,\n",
"S32=S21\n",
"S13=S21\n",
"\n",
"#Is = -20log(S12)\n",
"S12 = 10**(-Is/20)\n",
"#For circulator,\n",
"S23=S12\n",
"S31=S12\n",
"\n",
"rho = (S-1.)/(S+1.)\n",
"#For circulator,\n",
"S11=rho\n",
"S22=rho\n",
"S33=rho\n",
"\n",
"#Results\n",
"S = array([[S11,S12,S13],[S21,S22,S23],[S31,S32,S33]])\n",
"print \"[S]=\\n\",S\n",
"#For a perfectly matched, non-reciprocal, lossless 3-port circulator, [s] is given by,\n",
" [S21 0 0 ]\n",
"#The terminal planes are such that phase angles of S13=S21=S32=1\n",
"S13_new=1\n",
"S21_new=1\n",
"S32_new=1\n",
"S_new = array([[0,0,S13_new],[S21_new,0,0],[0,S32_new,0]])\n",
"print \"\\nThe scattering matrix now becomes [S]=\\n\",S_new"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"[S]=\n",
"[[ 0.33333333 0.1 0.94406088]\n",
" [ 0.94406088 0.33333333 0.1 ]\n",
" [ 0.1 0.94406088 0.33333333]]\n",
"\n",
"The scattering matrix now becomes [S]=\n",
"[[0 0 1]\n",
" [1 0 0]\n",
" [0 1 0]]\n"
]
}
],
"prompt_number": 15
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 6.10, Page number 242\n"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"import math\n",
"\n",
"#Variable declaration\n",
"Pi = 90. #power source(W)\n",
"C = 20 #dB\n",
"D = 35 #dB\n",
"Is = 0.5 #insertion loss(dB)\n",
"\n",
"#Calculations\n",
"#C = 20=10log(Pi/Pf)\n",
"Pf = Pi/(10**(20./10.))\n",
"#D=350=10log(Pf/Pb)\n",
"Pb = Pf/(10**(35./10.))\n",
"Pr = Pi-Pf-Pb #received power\n",
"Pr_db = 10*math.log10(Pi/Pr)\n",
"Pr_dash=Pr_db-Is\n",
"\n",
"#Result\n",
"print \"The output power at the port is\",round(Pr_dash,3),\"dB\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The output power at the port is -0.456 dB\n"
]
}
],
"prompt_number": 34
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 6.11, Page number 243"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"import math\n",
"\n",
"#Variable declaration\n",
"[S] = [[0.05/_30 0.96/_0 0.1/_90 0.05/_90]\n",
" [0.96/_0 0.05/_30 0.05/_90 0.1/_90 ]\n",
" [0.1/_90 0.05/_90 0.05/_30 0.96/_0 ]\n",
" [0.05/_90 0.1/_90 0.96/_0 0.05/_30]]\n",
"\n",
"#Calculations\n",
"#Coupling = C=10log(P1/P3)=-20log|S13|\n",
"C = -20*math.log10(0.1)\n",
"#Directivity = D=10log(P3/P4)=20log(|S13|/|S14|)\n",
"D = 20*math.log10(0.1/0.05)\n",
"#Isolation =I=10log(P3/P4)=10log(P1/P4)=-20log|S14|\n",
"I = -20*math.log10(0.05)\n",
"\n",
"#Results\n",
"print \"Coupling =\",C,\"dB\"\n",
"print \"Directivity =\",round(D,2),\"dB\"\n",
"print \"Isolation =\",round(I,2),\"dB\"\n",
"\n",
" "
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Coupling = 20.0 dB\n",
"Directivity = 6.02 dB\n",
"Isolation = 26.02 dB\n"
]
}
],
"prompt_number": 43
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 6.12, Page number 244"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"import math\n",
"\n",
"#Variable declaration\n",
"lamda2 = 3.5 #distance between 2 minimas(cm)\n",
"lamda_g = 7 #guided wavelength(cm)\n",
"d2_1 = 2.5*10**-1 #distance between minimum power points(cm)\n",
"\n",
"#Calculation\n",
"S = lamda_g/(math.pi*d2_1)\n",
"\n",
"#Result\n",
"print \"VSWR =\",round(S,4)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"VSWR = 8.9127\n"
]
}
],
"prompt_number": 46
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 6.13, Page number 244"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"import math\n",
"\n",
"#Variable declaration\n",
"lamda_g = 7.2 #guided wavelength(cm)\n",
"rn = 10.5 #position of reference null(cm)\n",
"rn_new = 9.3 #new position of reference null due to component(cm)\n",
"\n",
"#Calculations\n",
"pd = rn - rn_new #path difference due to component(cm)\n",
"ps = (2*math.pi*pd)/lamda_g #phase shift introduced\n",
"\n",
"#Result\n",
"print \"The phase shift component is\",round(ps,3)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The phase shift component is 1.047\n"
]
}
],
"prompt_number": 48
}
],
"metadata": {}
}
]
}