SmithDemo_v2.ipynb

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    "# A Smith Chart Demo\n",
    "\n",
    "Written by Michael Lamoureux, September 2020.\n",
    "With guidance from Matt Yedlin and Sam Ng on how to use a Smith chart.\n",
    "\n",
    "Run the two cells below, or hit Run All under the \"Kernel\" menu.\n",
    "\n",
    "There are two sliders where you can input the normalized impednace values (real and imaginary parts).\n",
    "\n",
    "The code does all the plotting of various points, curces, and lines, as per Sam's instructions. \n",
    "\n",
    "Use the check boxes to see the various curves. (A pedogogical tool to help the students see the steps.)\n",
    "\n",
    "Note the Smith chart here is something I grabeed off the internet. Probably we can input a higher resolution one./ "
   ]
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   "source": [
    "import plotly.graph_objects as go\n",
    "import numpy as np\n",
    "from ipywidgets import HTML, HBox, VBox, BoundedFloatText, Checkbox, interact, interactive\n"
   ]
  },
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       "interactive(children=(FloatSlider(value=0.8, description='Z_real', max=10.0, min=0.1), FloatSlider(value=-1.2,…"
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       "interactive(children=(Checkbox(value=True, description='Show_Point'), Checkbox(value=False, description='Show_…"
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       "FigureWidget({\n",
       "    'data': [{'marker': {'color': '#ff0000'},\n",
       "              'name': 'Box',\n",
       "              'type'…"
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   "source": [
    "# define some colors because I am lazy\n",
    "Red = '#ff0000'\n",
    "Green = '#00ff00'\n",
    "Blue = '#0000ff'\n",
    "\n",
    "# define the mobius transformation, in a convenient form for plotting\n",
    "def mob(x,y):\n",
    "    z = (x+1j*y -1)/(x+1j*y +1)\n",
    "    return [np.real(z),np.imag(z)]\n",
    "\n",
    "\n",
    "# The initial impedance (from Sam's example)\n",
    "X0,Y0 = 0.8,-1.2 \n",
    "\n",
    "# set up the figure, with the bounding box. In red\n",
    "fig = go.FigureWidget([go.Scatter(x=[-1, 1,1,-1,-1], y=[-1,-1,1,1,-1],name='Box')])\n",
    "theBox = fig.data[0]\n",
    "theBox.marker.color = Red\n",
    "fig.layout.hovermode = 'closest'\n",
    "\n",
    "\n",
    "# Add the data point (impedance)\n",
    "fig.add_trace(\n",
    "    go.Scatter(x=[mob(X0,Y0)[0]], y=[mob(X0,Y0)[1]], mode='markers', name='The Point')\n",
    ")\n",
    "thePoint = fig.data[1]\n",
    "thePoint.marker.color = Red\n",
    "thePoint.marker.size = [20]\n",
    "\n",
    "# Add the constant resistance circle\n",
    "x = X0\n",
    "y = np.geomspace(0.01,50,100) # geometric spacing looks better\n",
    "y = np.append(-np.flip(y),y) # include the negative values\n",
    "fig.add_trace(\n",
    "    go.Scatter(\n",
    "        visible=False,\n",
    "        line=dict(color=Green, width=3),\n",
    "        name='Const R',\n",
    "        x=mob(x,y)[0],\n",
    "        y=mob(x,y)[1]\n",
    "        )\n",
    "    )\n",
    "theCurve_R = fig.data[2]\n",
    "\n",
    "# Add the constant impedance curve\n",
    "x = np.geomspace(0.01,50,100) # geometric spacing looks better\n",
    "y = Y0\n",
    "fig.add_trace(\n",
    "    go.Scatter(\n",
    "        visible=False,\n",
    "        line=dict(color=Green, width=3),\n",
    "        name='Const C',\n",
    "        x=mob(x,y)[0],\n",
    "        y=mob(x,y)[1]\n",
    "        )\n",
    "    )\n",
    "theCurve_C = fig.data[3]\n",
    "\n",
    "# Add the circle curve\n",
    "t = np.linspace(0,2*np.pi,100) \n",
    "r = np.sqrt(mob(X0,Y0)[0]**2 + mob(X0,Y0)[1]**2)\n",
    "\n",
    "fig.add_trace(\n",
    "    go.Scatter(\n",
    "        visible=False,\n",
    "        line=dict(color=Blue, width=3),\n",
    "        name='Circle-1',\n",
    "        x=r*np.cos(t),\n",
    "        y=r*np.sin(t)\n",
    "        )\n",
    "    )\n",
    "theCircle = fig.data[4]\n",
    "\n",
    "# add the 1st straight line\n",
    "r = np.sqrt(mob(X0,Y0)[0]**2 + mob(X0,Y0)[1]**2)\n",
    "y1 = np.sqrt(4 + 25*r**2)-2\n",
    "y1 = np.sqrt(y1) # a second square root as we are solving a quartic\n",
    "x = mob(1,y1)[0]\n",
    "y = mob(1,y1)[1]\n",
    "a = max(np.abs(x),np.abs(y))\n",
    "fig.add_trace(\n",
    "    go.Scatter(\n",
    "        visible=False,\n",
    "        line=dict(color=Blue, width=3),\n",
    "        name='Line-1',\n",
    "        x=[0,x,x/a],\n",
    "        y=[0,y,y/a]\n",
    "        )\n",
    "    )\n",
    "theLine_1 = fig.data[5]\n",
    "\n",
    "# add the 2nd straight lines\n",
    "# use same y1 value as above\n",
    "x = mob(1,-y1)[0]\n",
    "y = mob(1,-y1)[1]\n",
    "a = max(np.abs(x),np.abs(y))\n",
    "fig.add_trace(\n",
    "    go.Scatter(\n",
    "        visible=False,\n",
    "        line=dict(color=Blue, width=3),\n",
    "        name='Line-2',\n",
    "        x=[0,x,x/a],\n",
    "        y=[0,y,y/a]\n",
    "        )\n",
    "    )\n",
    "theLine_2 = fig.data[6]\n",
    "\n",
    "\n",
    "## update all the curves when X0,Y0 change\n",
    "def update_curves(X,Y):\n",
    "    X0 = min(max(X,0),50)\n",
    "    Y0 = min(max(Y,-50),50)\n",
    "    # update the point\n",
    "    thePoint.x = [mob(X0,Y0)[0]]\n",
    "    thePoint.y = [mob(X0,Y0)[1]]\n",
    "    # update the R curve\n",
    "    x = X0\n",
    "    y = np.geomspace(0.01,50,100) \n",
    "    y = np.append(-np.flip(y),y)\n",
    "    theCurve_R.x=mob(x,y)[0]\n",
    "    theCurve_R.y=mob(x,y)[1]\n",
    "    # update the C curve\n",
    "    x = np.geomspace(0.01,50,100) \n",
    "    y = Y0\n",
    "    theCurve_C.x=mob(x,y)[0]\n",
    "    theCurve_C.y=mob(x,y)[1]\n",
    "    # update the circle\n",
    "    t = np.linspace(0,2*np.pi,100) \n",
    "    r = np.sqrt(mob(X0,Y0)[0]**2 + mob(X0,Y0)[1]**2)\n",
    "    theCircle.x = r*np.cos(t)\n",
    "    theCircle.y = r*np.sin(t)\n",
    "    # update the lines\n",
    "    r = np.sqrt(mob(X0,Y0)[0]**2 + mob(X0,Y0)[1]**2)\n",
    "    y1 = np.sqrt(4 + 25*r**2)-2\n",
    "    y1 = np.sqrt(y1) # a second square root as we are solving a quartic\n",
    "    x = mob(1,y1)[0]\n",
    "    y = mob(1,y1)[1]\n",
    "    a = max(np.abs(x),np.abs(y))\n",
    "    theLine_1.x =[0,x,x/a]\n",
    "    theLine_1.y = [0,y,y/a]\n",
    "    x = mob(1,-y1)[0]\n",
    "    y = mob(1,-y1)[1]\n",
    "    a = max(np.abs(x),np.abs(y))\n",
    "    theLine_2.x =[0,x,x/a]\n",
    "    theLine_2.y = [0,y,y/a]\n",
    "\n",
    "\n",
    "    \n",
    "\n",
    "# Add image in the background\n",
    "fig.add_layout_image(\n",
    "        dict(\n",
    "            source=\"smith00.png\",\n",
    "            xref=\"x\",\n",
    "            yref=\"y\",\n",
    "            x=-1.16,\n",
    "            y=1.15,\n",
    "            sizex=2.3,\n",
    "            sizey=2.3,\n",
    "            sizing=\"fill\",\n",
    "            opacity=1.0,\n",
    "            layer=\"below\")\n",
    ")\n",
    "\n",
    "fig.update_layout(\n",
    "    width = 1000,\n",
    "    height = 1000,\n",
    "    title = \"Smith Chart Display\",\n",
    "    yaxis = dict(\n",
    "      scaleanchor = \"x\",\n",
    "      scaleratio = 1,\n",
    "    )\n",
    ")\n",
    "\n",
    "\n",
    "\n",
    "@interact(Z_real = (0.1,10.0,.1),Z_imag=(-20,20,.1))\n",
    "def g1(Z_real=X0, Z_imag=Y0):\n",
    "    update_curves(Z_real,Z_imag)\n",
    "    return\n",
    "\n",
    "@interact(Show_Point=True,Show_Const_R=False,Show_Const_C=False,Show_Circle_1=False,Show_Line_1=False,Show_Line_2=False)\n",
    "def g2(Show_Point,Show_Const_R,Show_Const_C,Show_Circle_1,Show_Line_1,Show_Line_2):\n",
    "    thePoint.visible = Show_Point\n",
    "    theCurve_R.visible = Show_Const_R\n",
    "    theCurve_C.visible = Show_Const_C\n",
    "    theCircle.visible = Show_Circle_1\n",
    "    theLine_1.visible = Show_Line_1\n",
    "    theLine_2.visible = Show_Line_2\n",
    "    return\n",
    "\n",
    "fig"
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