1{
2 "metadata": {
3  "name": "",
4  "signature": "sha256:ff1c36b9112c525d961d4a72ae907a41e125fd4f11589f8fc766d7e823e1dedd"
5 },
6 "nbformat": 3,
7 "nbformat_minor": 0,
8 "worksheets": [
9  {
10   "cells": [
11    {
12     "cell_type": "code",
13     "collapsed": false,
14     "input": [
15      "from lcapy import Circuit, j, omega\n",
16      "cct = Circuit()\n",
17      "cct.add(\"\"\"\n",
18      "Vi 1 0_1; down\n",
19      "L 1 2; right, size=1.5\n",
20      "R 2 0; down\n",
21      "W 0_1 0; right\n",
22      "W 0 0_2; right, size=0.5\n",
23      "P1 2_2 0_2; down\n",
24      "W 2 2_2;right, size=0.5\"\"\")\n"
25     ],
26     "language": "python",
27     "metadata": {},
28     "outputs": [],
29     "prompt_number": 2
30    },
31    {
32     "cell_type": "code",
33     "collapsed": false,
34     "input": [
35      "cct.draw()"
36     ],
37     "language": "python",
38     "metadata": {},
39     "outputs": [
40      {
41       "metadata": {
42        "png": {
43         "height": 100,
44         "width": 200
45        }
46       },
47       "output_type": "display_data",
48       "png": 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csHCDVc+or01ud5/jm/UxHTmH5/jaRKDdhCYPWRgVywMRHYTB6QYH83gJwtHtkWNlkws/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\n"
49      }
50     ],
51     "prompt_number": 3
52    },
53    {
54     "cell_type": "code",
55     "collapsed": false,
56     "input": [
57      "H = (cct.R.V / cct.Vi.V).simplify()"
58     ],
59     "language": "python",
60     "metadata": {},
61     "outputs": [],
62     "prompt_number": 4
63    },
64    {
65     "cell_type": "code",
66     "collapsed": false,
67     "input": [
68      "H(j * omega)"
69     ],
70     "language": "python",
71     "metadata": {},
72     "outputs": [
73      {
74       "latex": [
75        "$\\frac{R_{}}{i L_{} \\omega + R_{}}$"
76       ],
77       "metadata": {},
78       "output_type": "pyout",
79       "prompt_number": 5,
80       "text": [
81        "    R    \n",
82        "\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n",
83        "\u2148\u22c5L\u22c5\u03c9 + R"
84       ]
85      }
86     ],
87     "prompt_number": 5
88    },
89    {
90     "cell_type": "code",
91     "collapsed": false,
92     "input": [
93      "H(j * omega).rationalize_denominator()"
94     ],
95     "language": "python",
96     "metadata": {},
97     "outputs": [
98      {
99       "latex": [
100        "$\\frac{- i L_{} R_{} \\omega + R_{}^2}{L_{}^2 \\omega^2 + R_{}^2}$"
101       ],
102       "metadata": {},
103       "output_type": "pyout",
104       "prompt_number": 11,
105       "text": [
106        "            2\n",
107        "-\u2148\u22c5L\u22c5R\u22c5\u03c9 + R \n",
108        "\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n",
109        "   2  2    2 \n",
110        "  L \u22c5\u03c9  + R  "
111       ]
112      }
113     ],
114     "prompt_number": 11
115    },
116    {
117     "cell_type": "code",
118     "collapsed": false,
119     "input": [
120      "H(j * omega).real_imag"
121     ],
122     "language": "python",
123     "metadata": {},
124     "outputs": [
125      {
126       "latex": [
127        "$- \\frac{i L_{} R_{} \\omega}{L_{}^2 \\omega^2 + R_{}^2} + \\frac{R_{}^2}{L_{}^2 \\omega^2 + R_{}^2}$"
128       ],
129       "metadata": {},
130       "output_type": "pyout",
131       "prompt_number": 12,
132       "text": [
133        "                    2    \n",
134        "   \u2148\u22c5L\u22c5R\u22c5\u03c9         R     \n",
135        "- \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500 + \u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n",
136        "   2  2    2    2  2    2\n",
137        "  L \u22c5\u03c9  + R    L \u22c5\u03c9  + R "
138       ]
139      }
140     ],
141     "prompt_number": 12
142    },
143    {
144     "cell_type": "code",
145     "collapsed": false,
146     "input": [
147      "H(j * omega).magnitude\n"
148     ],
149     "language": "python",
150     "metadata": {},
151     "outputs": [
152      {
153       "latex": [
154        "$\\frac{R_{}}{\\sqrt{L_{}^2 \\omega^2 + R_{}^2}}$"
155       ],
156       "metadata": {},
157       "output_type": "pyout",
158       "prompt_number": 6,
159       "text": [
160        "       R       \n",
161        "\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n",
162        "   ____________\n",
163        "  \u2571  2  2    2 \n",
164        "\u2572\u2571  L \u22c5\u03c9  + R  "
165       ]
166      }
167     ],
168     "prompt_number": 6
169    },
170    {
171     "cell_type": "code",
172     "collapsed": false,
173     "input": [
174      "H(j * omega).phase_degrees"
175     ],
176     "language": "python",
177     "metadata": {},
178     "outputs": [
179      {
180       "latex": [
181        "$\\frac{180.0}{\\pi} \\operatorname{atan2}{\\left (- L_{} \\omega,R_{} \\right )}$"
182       ],
183       "metadata": {},
184       "output_type": "pyout",
185       "prompt_number": 7,
186       "text": [
187        "180.0\u22c5atan2(-L\u22c5\u03c9, R)\n",
188        "\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n",
189        "         \u03c0          "
190       ]
191      }
192     ],
193     "prompt_number": 7
194    },
195    {
196     "cell_type": "code",
197     "collapsed": false,
198     "input": [
199      "H1 = H.subs('L',1).subs('R',1e3)\n",
200      "H1(j * omega)"
201     ],
202     "language": "python",
203     "metadata": {},
204     "outputs": [
205      {
206       "latex": [
207        "$\\frac{1000.0}{i \\omega + 1000.0}$"
208       ],
209       "metadata": {},
210       "output_type": "pyout",
211       "prompt_number": 8,
212       "text": [
213        "   1000.0   \n",
214        "\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n",
215        "\u2148\u22c5\u03c9 + 1000.0"
216       ]
217      }
218     ],
219     "prompt_number": 8
220    },
221    {
222     "cell_type": "code",
223     "collapsed": false,
224     "input": [
225      "from numpy import logspace\n",
226      "w = logspace(1, 6, 500)\n",
227      "%matplotlib inline\n",
228      "H1(j * omega).dB.plot(w, log_scale=True)"
229     ],
230     "language": "python",
231     "metadata": {},
232     "outputs": [
233      {
234       "metadata": {},
235       "output_type": "display_data",
236       "png": 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jLaltsBoYl2MjjgnA+FwPKMFSftZRLJxcYtGund2f8eGHcNJJsH598O2Kgj4XwfHTYTyO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\nRERERERERERERERERERK1f8HmcQCFnRNfeEAAAAASUVORK5CYII=\n",
237       "text": [
238        "<matplotlib.figure.Figure at 0x7f9bf2f7d8d0>"
239       ]
240      }
241     ],
242     "prompt_number": 9
243    },
244    {
245     "cell_type": "code",
246     "collapsed": false,
247     "input": [
248      "H1(j * omega).phase_degrees.plot(w, log_scale=True)"
249     ],
250     "language": "python",
251     "metadata": {},
252     "outputs": [
253      {
254       "metadata": {},
255       "output_type": "display_data",
256       "png": 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ABwGnAucCx6YwrqqoD0MC9dVXttDS/Pmwzz5hRyOSmCDGYbQAHgAOBX4APsNG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\nsC3AZrQt26GXzQpQLmIKUC5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257       "text": [
258        "<matplotlib.figure.Figure at 0x7f9bf0499790>"
259       ]
260      }
261     ],
262     "prompt_number": 10
263    },
264    {
265     "cell_type": "code",
266     "collapsed": false,
267     "input": [],
268     "language": "python",
269     "metadata": {},
270     "outputs": [],
271     "prompt_number": 10
272    }
273   ],
274   "metadata": {}
275  }
276 ]
277}