Phased array animation

environment.yml

name: py37
dependencies:
  - python=3.7
  - numpy
  - matplotlib
  - ipywidgets
  - ipympl

Phased Array Animation.ipynb

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    "# Phased array example\n",
    "In this example, we are observing an array of 5 antennas radiating at 10GHz from above, and looking at the radiated electric fields in the near-field.\n",
    "\n",
    "1. Run the notebook by Selecting **Run->Run All Cells** from the menu\n",
    "2. **Adjust the sliders for the phase shift phi and spacing d** of the phased array, to observe beam steering and the appearance of grating lobes in the plot\n",
    "\n",
    "You may observe that for large steering angles, the results diverge a little from the theory. However, such large steering angles are not used in practice."
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    "%matplotlib widget\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from ipywidgets import interact, FloatSlider\n",
    "from itertools import count\n",
    "from collections import OrderedDict\n",
    "\n",
    "# fixed parameters\n",
    "f = 10e9 # operating frequency\n",
    "c = 3e8 # speed of light\n",
    "lam = c/f\n",
    "k = 2*np.pi*f/c\n",
    "N = 5 # number of elements in array\n",
    "\n",
    "# points in x-y plane to display\n",
    "points_x = 200\n",
    "points_y = 180\n",
    "x_range = np.linspace(0.001, 0.5, points_x)\n",
    "y_range = np.linspace(-0.2, 0.2, points_y)\n",
    "\n",
    "scaling_val = 20/(4*np.pi*np.sqrt(x_range[-1]-x_range[0])) # scaling factor so all of plot can be seen\n",
    "\n",
    "def calculate_array(N, d, phi):\n",
    "    \"\"\"Calculate field from a phased array\n",
    "    N: number of elements\n",
    "    d: element spacing in meters\n",
    "    phi: phase between elements in degrees\n",
    "    \n",
    "    returns:\n",
    "    E: electric field in 2D plane\n",
    "    antenna_y: location of antennas\n",
    "    lobe_angles: dictionary containing angle of main lobe and any grating lobes in degrees\n",
    "    \"\"\"\n",
    "    phi_rad = phi*np.pi/180\n",
    "    E = np.zeros((points_y, points_x), np.complex64)\n",
    "    antenna_y = (np.arange(N+1)-0.5*N)*d\n",
    "    phi_range = np.arange(N+1)*phi_rad\n",
    "    x, y = np.meshgrid(x_range, y_range)\n",
    "\n",
    "    for y_0, phi_n in zip(antenna_y, phi_range):\n",
    "        R = np.sqrt(x**2 + (y-y_0)**2)\n",
    "        E += np.exp(1j*k*R)/(4*np.pi*np.sqrt(R))*np.exp(1j*phi_n)\n",
    "\n",
    "    sin_theta_0 = phi_rad/(k*d)\n",
    "    lobe_angles = OrderedDict()\n",
    "    lobe_angles[0] = np.arcsin(sin_theta_0)*180/np.pi\n",
    "\n",
    "    for n in count(1):\n",
    "        sidelobe_n = False\n",
    "        negative_lobe = sin_theta_0 - n*lam/d\n",
    "        if abs(negative_lobe) <= 1.0:\n",
    "            lobe_angles[-n] = np.arcsin(negative_lobe)*180/np.pi\n",
    "            sidelobe_n = True\n",
    "\n",
    "        positive_lobe = sin_theta_0 + n*lam/d\n",
    "        if abs(positive_lobe) <= 1.0:\n",
    "            lobe_angles[n] = np.arcsin(positive_lobe)*180/np.pi\n",
    "            sidelobe_n = True\n",
    "            \n",
    "        if not sidelobe_n:\n",
    "            break\n",
    "        \n",
    "    return E, antenna_y, lobe_angles\n",
    "\n",
    "fig = plt.figure(figsize=(8, 6))\n",
    "im = plt.imshow(np.zeros((points_y, points_x)), interpolation='nearest', \n",
    "                origin='lower', \n",
    "                vmin=-scaling_val, vmax=scaling_val, \n",
    "                extent = (x_range[0], x_range[-1], y_range[0], y_range[-1]),\n",
    "               )\n",
    "\n",
    "antenna_plots, = plt.plot(0, 0, 'rx', markeredgewidth=2)\n",
    "plt.xlabel('x (m)')\n",
    "plt.ylabel('y (m)')\n",
    "ti = plt.title(\"\")\n",
    "plt.show()\n",
    "\n",
    "#@interact(phi=(-180, 180, 5), d=(0.005, 0.05, 0.001))\n",
    "@interact(phi = FloatSlider(value=0, min=-180, max=180, step=5, continuous_update=False, readout_format=\".0f\", description=\"phi (deg)\"),\n",
    "          d = FloatSlider(value=0.02, min=0.005, max=0.05, step=0.001, continuous_update=False, readout_format=\".3f\", description = \"d (m)\"))\n",
    "def update_plot(phi=0, d=0.02):\n",
    "    E, antenna_y, lobe_angles = calculate_array(N, d, phi)\n",
    "    im.set_data(E.real)\n",
    "    antenna_plots.set_data(np.zeros_like(antenna_y), antenna_y)\n",
    "    title_text = fr\"$d/\\lambda={d*f/c:.2f}$\"\n",
    "    for order, angle in lobe_angles.items():\n",
    "        title_text += fr\", $\\theta_{{{order}}}={angle:.1f}^\\circ$\"\n",
    "    ti.set_text(title_text)"
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