{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Renormalizing S-parameters "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This example demonstrates how to use skrf to renormalize a Network's s-parameters to new port impedances. Although trivial, this example creates a matched load in 50ohms and then re-normalizes to a  25ohm environment, producing a reflection coefficient of 1/3."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Ok lets do it"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "import skrf as rf\n",
    "from skrf.instances import wr10\n",
    "\n",
    "%matplotlib inline\n",
    "\n",
    "rf.stylely()\n",
    "\n",
    "# this is just for plotting junk\n",
    "kw = dict(draw_labels=True, marker = 'o', markersize = 10)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Create a one-port ideal match Network, (using the premade media class wr10 as a dummy)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "match_at_50 = wr10.match()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note that the z0 for this Network defaults to a constant 50ohm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "match_at_50"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Plotting its reflection coefficient on the smith chart, shows its a match"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "match_at_50.plot_s_smith(**kw)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now, renormalize the port impedance from 50 -> 25, thus the previous 50ohm load now produces a reflection coefficient of \n",
    "\n",
    "\n",
    "$$ \\Gamma^{'} = \\frac{50-25}{50+25} = \\frac{25}{75} = .333 $$\n",
    "\n",
    "\n",
    "Plotting the renormalized response  on the Smith Chart"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "match_at_50.renormalize(25)\n",
    "match_at_50.plot_s_smith(**kw)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Complex Impedances "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You could also renormalize to a complex port impedance if you're crazy. For example, renormalizing to 50j, one would expect:\n",
    "$$\n",
    "\\Gamma^{'} = \\frac{50-50j}{50+50j} = 50\\frac{1-j}{1+j} = -50j\n",
    "$$\n",
    "\n",
    "However, one finds an unexpected result when plotting the Smith chart:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "match_at_50 = wr10.match()\n",
    "match_at_50.renormalize(50j)  # same as renormalize(50j, s_def='power')\n",
    "match_at_50.plot_s_smith(**kw)  # expect -1j"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This is because the default behaviour of scikit-rf is to use _power-waves_ scattering parameter definition (since it is the most popular one is CAD software). But the _power-waves_ definition is [known to fail in such a case](https://www.nist.gov/system/files/documents/2017/05/09/MicrowaveCircuitTheory-proof.pdf). This is why scikit-rf also implement the _pseudo-waves_ scattering parameters definition, but you have to specify it using the `s_def` parameter:  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "match_at_50 = wr10.match()\n",
    "match_at_50.renormalize(50j, s_def='pseudo')\n",
    "match_at_50.plot_s_smith(**kw)  # expect -1j"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Which gives the expected result. "
   ]
  }
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