{
"metadata": {
"name": "",
"signature": "sha256:22eee2ba9d1da7cc9449ec91cc33a421ca03a319ba4cd73132a5cc29034c4568"
},
"nbformat": 3,
"nbformat_minor": 0,
"worksheets": [
{
"cells": [
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"Chapter12-Network Synthesis"
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex2-pg12.2"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# Network Synthesis : example 12.2 : (pg 12.2)\n",
"import numpy\n",
"p1 = numpy.array([1,0,5,0,4])\n",
"p2 = numpy.array([1,0,3,0])\n",
"[q,r]=numpy.polydiv(p1,p2);\n",
"[q1,r1]=numpy.polydiv(p2,r);\n",
"[q2,r2]=numpy.polydiv(r,r1);\n",
"[q3,r3]=numpy.polydiv(r1,r2);\n",
"print \"\\nEven part of P(s) = (s^4)+(5s^3)+4\"\n",
"print \"\\nOdd part of P(s) = (s^3)+(3s)\"\n",
"print \"\\nQ(s)= m(s)/n(s)\"\n",
"# values of quotients in continued fraction expansion\n",
"print (q);\n",
"print (q1);\n",
"print (q2);\n",
"print (q3);\n",
"print \"Since all the quotient terms are positive, P(s) is hurwitz\";\n",
"\n",
"\n",
"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
"Even part of P(s) = (s^4)+(5s^3)+4\n",
"\n",
"Odd part of P(s) = (s^3)+(3s)\n",
"\n",
"Q(s)= m(s)/n(s)\n",
"[ 1. 0.]\n",
"[ 0.5 0. ]\n",
"[ 2. 0.]\n",
"[ 0.25 0. ]\n",
"Since all the quotient terms are positive, P(s) is hurwitz\n"
]
}
],
"prompt_number": 1
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex3-pg12.2"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Network Synthesis : example 12.3 : (pg 12.2 & 12.3)\n",
"import numpy\n",
"p1=numpy.array([1,0,5,0]) \n",
"p2=numpy.array([4,0,2])\n",
"[q,r]=numpy.polydiv(p1,p2);\n",
"[q1,r1]=numpy.polydiv(p2,r);\n",
"[q2,r2]=numpy.polydiv(r,r1);\n",
"print(\"\\nEven part of P(s) = ((4*s^2)+(2))\");\n",
"print(\"\\nOdd part of P(s) = ((s^3)+(5*(s)))\");\n",
"print(\"\\nQ(s)= n(s)/m(s)\");\n",
"# values of quotients in continued fraction expansion\n",
"print(q);\n",
"print(q1);\n",
"print(q2);\n",
"print(\"\\nSince all the quotient terms are positive, P(s) is hurwitz\");\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
"Even part of P(s) = ((4*s^2)+(2))\n",
"\n",
"Odd part of P(s) = ((s^3)+(5*(s)))\n",
"\n",
"Q(s)= n(s)/m(s)\n",
"[ 0.25 0. ]\n",
"[ 0.88888889 0. ]\n",
"[ 2.25 0. ]\n",
"\n",
"Since all the quotient terms are positive, P(s) is hurwitz\n"
]
}
],
"prompt_number": 2
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex4-pg12.3"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"## Network Synthesis : example 12.4 : (pg 12.3)\n",
"import numpy\n",
"p1=numpy.array([1,0,3,0,12])\n",
"p2=numpy.array([1,0,2,0])\n",
"[q,r]=numpy.polydiv(p1,p2);\n",
"[q1,r1]=numpy.polydiv(p2,r);\n",
"[q2,r2]=numpy.polydiv(r,r1);\n",
"[q3,r3]=numpy.polydiv(r1,r2);\n",
"print(\"\\nEven part of P(s) = ((s^4)+(3*(s)^2)+12)\");\n",
"print(\"\\nOdd part of P(s) = ((s^3)+(2*s))\");\n",
"print(\"\\nQ(s)= m(s)/n(s)\");\n",
"## values of quotients in continued fraction expansion\n",
"print(q);\n",
"print(q1);\n",
"print(q2);\n",
"print(q3);\n",
"print(\"\\nSince two quotient terms are negative, P(s) is not hurwitz\");\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
"Even part of P(s) = ((s^4)+(3*(s)^2)+12)\n",
"\n",
"Odd part of P(s) = ((s^3)+(2*s))\n",
"\n",
"Q(s)= m(s)/n(s)\n",
"[ 1. 0.]\n",
"[ 1. 0.]\n",
"[-0.1 -0. ]\n",
"[-0.83333333 0. ]\n",
"\n",
"Since two quotient terms are negative, P(s) is not hurwitz\n"
]
}
],
"prompt_number": 3
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex5-pg12.3"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"## Network Synthesis : example 12.5 : (pg 12.3 & 12.4)\n",
"import numpy\n",
"p1=numpy.array([1,0,2,0,2])\n",
"p2=numpy.array([1,0,3,0])\n",
"[q,r]=numpy.polydiv(p1,p2);\n",
"[q1,r1]=numpy.polydiv(p2,r);\n",
"[q2,r2]=numpy.polydiv(r,r1);\n",
"[q3,r3]=numpy.polydiv(r1,r2);\n",
"print(\"\\nEven part of P(s) = ((s^4)+(2*(s)^2)+2)\");\n",
"print(\"\\nOdd part of P(s) = (s^3)+(3s)\");\n",
"print(\"\\nQ(s)= m(s)/n(s)\");\n",
"## values of quotients in continued fraction expansion\n",
"print(q);\n",
"print(q1);\n",
"print(q2);\n",
"print(q3);\n",
"print(\"\\nSince two terms are negative, P(s) is not hurwitz\");"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
"Even part of P(s) = ((s^4)+(2*(s)^2)+2)\n",
"\n",
"Odd part of P(s) = (s^3)+(3s)\n",
"\n",
"Q(s)= m(s)/n(s)\n",
"[ 1. 0.]\n",
"[-1. -0.]\n",
"[-0.2 0. ]\n",
"[ 2.5 0. ]\n",
"\n",
"Since two terms are negative, P(s) is not hurwitz\n"
]
}
],
"prompt_number": 4
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex6-pg12.4"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"## Network Synthesis : example 12.6 : (pg 12.4)\n",
"import numpy\n",
"p1=numpy.array([2,0,6,0,1])\n",
"p2=numpy.array([5,0,3,0])\n",
"[q,r]=numpy.polydiv(p1,p2);\n",
"[q1,r1]=numpy.polydiv(p2,r);\n",
"[q2,r2]=numpy.polydiv(r,r1);\n",
"[q3,r3]=numpy.polydiv(r1,r2);\n",
"print(\"\\nEven part of P(s) = ((2*s^4)+(6*(s)^2)+1)\");\n",
"print(\"\\nOdd part of P(s) = ((5*s^3)+(3*s))\");\n",
"print(\"\\nQ(s)= m(s)/n(s)\");\n",
"## values of quotients in continued fraction expansion\n",
"print(q);\n",
"print(q1);\n",
"print(q2);\n",
"print(q3);\n",
"print(\"\\nSince all the quotient terms are positive, P(s) is hurwitz\");\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
"Even part of P(s) = ((2*s^4)+(6*(s)^2)+1)\n",
"\n",
"Odd part of P(s) = ((5*s^3)+(3*s))\n",
"\n",
"Q(s)= m(s)/n(s)\n",
"[ 0.4 0. ]\n",
"[ 1.04166667 0. ]\n",
"[ 2.45106383 0. ]\n",
"[ 1.95833333 0. ]\n",
"\n",
"Since all the quotient terms are positive, P(s) is hurwitz\n"
]
}
],
"prompt_number": 5
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex7-pg12.4"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"## Network Synthesis : example 12.7 : (pg 12.4 & 12.5)\n",
"import numpy\n",
"p1=numpy.array([1,0,6,0,8])\n",
"\n",
"p2=numpy.array([7,0,21,0])\n",
"[q,r]=numpy.polydiv(p1,p2);\n",
"[q1,r1]=numpy.polydiv(p2,r);\n",
"[q2,r2]=numpy.polydiv(r,r1);\n",
"[q3,r3]=numpy.polydiv(r1,r2);\n",
"print(\"\\nEven part of P(s) = ((s^4)+(6*(s)^2)+8)\");\n",
"print(\"\\nOdd part of P(s) = (7*(s^3)+(21*s))\");\n",
"print(\"\\nQ(s)= m(s)/n(s)\");\n",
"## values of quotients in continued fraction expansion\n",
"print(q);\n",
"print(q1);\n",
"print(q2);\n",
"print(q3);\n",
"print(\"\\nSince all the quotient terms are positive, P(s) is hurwitz\");\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
"Even part of P(s) = ((s^4)+(6*(s)^2)+8)\n",
"\n",
"Odd part of P(s) = (7*(s^3)+(21*s))\n",
"\n",
"Q(s)= m(s)/n(s)\n",
"[ 0.14285714 0. ]\n",
"[ 2.33333333 0. ]\n",
"[ 1.28571429 0. ]\n",
"[ 0.29166667 0. ]\n",
"\n",
"Since all the quotient terms are positive, P(s) is hurwitz\n"
]
}
],
"prompt_number": 6
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex8-pg12.5"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"## Network Synthesis : example 12.8 : (pg 12.5)\n",
"import numpy\n",
"p1=numpy.array([1,0,5,0,10])\n",
"\n",
"p2=numpy.array([5,0,4,0])\n",
"[q,r]=numpy.polydiv(p1,p2);\n",
"[q1,r1]=numpy.polydiv(p2,r);\n",
"[q2,r2]=numpy.polydiv(r,r1);\n",
"[q3,r3]=numpy.polydiv(r1,r2);\n",
"print(\"\\nEven part of P(s) = ((s^4)+(5*(s)^2)+10)\");\n",
"print(\"\\nOdd part of P(s) = (5*(s^3)+(4*s))\");\n",
"print(\"\\nQ(s)= m(s)/n(s)\");\n",
"## values of quotients in continued fraction expansion\n",
"print(q);\n",
"print(q1);\n",
"print(q2);\n",
"print(q3);\n",
"print(\"\\nSince two terms are negative, P(s) is not hurwitz\");\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
"Even part of P(s) = ((s^4)+(5*(s)^2)+10)\n",
"\n",
"Odd part of P(s) = (5*(s^3)+(4*s))\n",
"\n",
"Q(s)= m(s)/n(s)\n",
"[ 0.2 0. ]\n",
"[ 1.19047619 0. ]\n",
"[-0.5313253 -0. ]\n",
"[-0.79047619 0. ]\n",
"\n",
"Since two terms are negative, P(s) is not hurwitz\n"
]
}
],
"prompt_number": 7
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex9-pg12.6"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"## Network Synthesis : example 12.9 : (pg 12.6)\n",
"import numpy\n",
"p1=numpy.array([1,0,3,0,2,0])\n",
"p2=numpy.array([5,0,9,0,2])\n",
"[q,r]=numpy.polydiv(p1,p2);\n",
"[q1,r1]=numpy.polydiv(p2,r);\n",
"[q2,r2]=numpy.polydiv(r,r1);\n",
"[q3,r3]=numpy.polydiv(r1,r2);\n",
"[q4,r4]=numpy.polydiv(r2,r3);\n",
"print(\"\\n P(s) = ((s^5)+(3*(s^3))+(2*s))\");\n",
"print(\"\\n d/ds.P(s)= ((5*(s^4))+9*(s^2)+2)\");\n",
"print(\"\\nQ(s)=P(s)/d/ds.P(s)\");\n",
"## values of quotients in continued fraction expansion\n",
"print(q);\n",
"print(q1);\n",
"print(q2);\n",
"print(q3);\n",
"print(q4);\n",
"print(\"\\nSince all the quotient terms are positive, P(s) is hurwitz\");\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
" P(s) = ((s^5)+(3*(s^3))+(2*s))\n",
"\n",
" d/ds.P(s)= ((5*(s^4))+9*(s^2)+2)\n",
"\n",
"Q(s)=P(s)/d/ds.P(s)\n",
"[ 0.2 0. ]\n",
"[ 4.16666667 0. ]\n",
"[ 0.51428571 0. ]\n",
"[ 4.08333333 0. ]\n",
"[ 0.28571429 0. ]\n",
"\n",
"Since all the quotient terms are positive, P(s) is hurwitz\n"
]
}
],
"prompt_number": 8
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Ex10-pg12.6"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"## Network Synthesis : example 12.10 : (pg 12.6 & 12.7)\n",
"import numpy\n",
"p1=numpy.array([1,0,1,0,1,0])\n",
"p2=numpy.array([5,0,3,0,1])\n",
"[q,r]=numpy.polydiv(p1,p2);\n",
"[q1,r1]=numpy.polydiv(p2,r);\n",
"[q2,r2]=numpy.polydiv(r,r1);\n",
"[q3,r3]=numpy.polydiv(r1,r2);\n",
"[q4,r4]=numpy.polydiv(r2,r3);\n",
"print(\"\\n P(s) = ((s^5)+((s^3))+(s))\");\n",
"print(\"\\n d/ds.P(s)= ((5*(s^4))+3*(s^2)+1)\");\n",
"print(\"\\nQ(s)=P(s)/d/ds.P(s)\");\n",
"## values of quotients in continued fraction expansion\n",
"print(q);\n",
"print(q1);\n",
"print(q2);\n",
"print(q3);\n",
"print(q4);\n",
"print(\"\\nSince two quotient terms are negative, P(s) is not hurwitz\");\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"\n",
" P(s) = ((s^5)+((s^3))+(s))\n",
"\n",
" d/ds.P(s)= ((5*(s^4))+3*(s^2)+1)\n",
"\n",
"Q(s)=P(s)/d/ds.P(s)\n",
"[ 0.2 0. ]\n",
"[ 12.5 0. ]\n",
"[-0.05714286 -0. ]\n",
"[-8.16666667 0. ]\n",
"[ 0.85714286 0. ]\n",
"\n",
"Since two quotient terms are negative, P(s) is not hurwitz\n"
]
}
],
"prompt_number": 9
}
],
"metadata": {}
}
]
}