Si44xx Class E matching (Jupyter notebook)

si44xxClE.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Split TX/RX Class-E matching network per AN627 section 5.3 #\n",
    "This iPython notebook implements the transmit matching procedure specified in Silicon Labs AN627.\n",
    "\n",
    "First we load NumPy and set up some useful constants."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "from __future__ import print_function\n",
    "from enum import Enum\n",
    "import numpy as np\n",
    "\n",
    "from ipywidgets import interact, interactive, fixed, interact_manual\n",
    "import ipywidgets as widgets\n",
    "\n",
    "MHz=1e6\n",
    "\n",
    "uF=1e-6\n",
    "nF=1e-9\n",
    "pF=1e-12\n",
    "\n",
    "mH=1e-3\n",
    "uH=uF\n",
    "nH=nF\n",
    "pH=pF\n",
    "\n",
    "mW=mH\n",
    "\n",
    "mA=mH\n",
    "uA=uH\n",
    "\n",
    "class CHIPS(Enum):\n",
    "    Si4060 = 0        # Si4060/Si4460/Si4467\n",
    "    Si4461 = 1        # Si4461\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next we define the design parameters:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Transmit frequency in Hz (\"operating frequency\")\n",
    "FO = 868.0*MHz\n",
    "\n",
    "# RF power supply voltage in Volts\n",
    "VDD_RF = 3.3\n",
    "\n",
    "# set the chip type\n",
    "CHIP = CHIPS.Si4461\n",
    "\n",
    "# Shunt capacitance in Farad\n",
    "if CHIP == CHIPS.Si4060:\n",
    "    CSHUNT = 1.25*pF\n",
    "elif CHIP == CHIPS.Si4461:\n",
    "    CSHUNT = 2.0*pF\n",
    "else:\n",
    "    raise ValueError(\"Invalid chiptype\")\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 5.3.1 -- Step 1: Select a value for L_Choke ##\n",
    "\n",
    "This is based on a straight-line fit of the data given in section 5.3.1."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "112.19959999999999"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lchoke = (-2.803e-16 * FO) + 3.555e-7\n",
    "lchoke/nH"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**TODO: pick the nearest E12 value**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 5.3.2 -- Step 2: Choose/calculate values for L0-C0 series-resonant tank ##\n",
    "\n",
    "Design guidelines:\n",
    "\n",
    "  * The L0-C0 tank must resonate at Fo (FREQ)\n",
    "  * The value of L0 should be chosen to be as large as possible, while:\n",
    "    * Remaining low enough that self-resonance is not an issue\n",
    "    * Close to standard 5%-tolerance values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Resonant frequency: 869.816 MHz\n",
      "Frequency error:    0.209 %\n"
     ]
    }
   ],
   "source": [
    "L0=9.3*nH\n",
    "C0=3.6*pF\n",
    "fresonant = 1./(2.*np.pi*np.sqrt(L0*C0))\n",
    "print(\"Resonant frequency: %0.3f MHz\" % (fresonant/MHz))\n",
    "\n",
    "# calculate error vs. FO\n",
    "ferror = (fresonant - FO) / FO\n",
    "print(\"Frequency error:    %0.3f %%\" % (ferror * 100.0))\n",
    "\n",
    "# impedance at resonance -- Xl and Xc = 0, therefore Z = 0 (in theory)\n",
    "# in practice, Z = parasitic resistance of L and C"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 5.3.3 -- Step 3: Calculate required value for Zload ##\n",
    "\n",
    "Calculate the required value of load impedance to be presented to the output of the resonant tank at the operating frequency (FO)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Load impedance:  (27.0616565534+31.1884365599j) ohm\n"
     ]
    }
   ],
   "source": [
    "ANG_RAD=np.deg2rad(49.0524)\n",
    "zload = (0.2815/(2*np.pi*FO*CSHUNT)) * (np.cos(ANG_RAD)+(1j*np.sin(ANG_RAD)))\n",
    "print(\"Load impedance:  %s ohm\" % zload)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 5.3.4 -- Step 4, estimate the required PA_PWR_LVL register value from the calculated value of a hypothetical voltage-limiting resistor ##"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "V_DD = 1.045 V\n",
      "I_DD = 22.387 mA\n",
      "R_DC = 100.718 Ohms\n"
     ]
    }
   ],
   "source": [
    "POUT = 23.4*mW\n",
    "\n",
    "vdd = np.sqrt(POUT / (2.*(np.pi**2)*FO*CSHUNT))\n",
    "print(\"V_DD = %0.3f V\" % (vdd))\n",
    "\n",
    "idd = 2.*(np.pi**2)*FO*CSHUNT*vdd\n",
    "print(\"I_DD = %0.3f mA\" % (idd / mA))\n",
    "\n",
    "rdc = (VDD_RF - vdd) / idd\n",
    "print(\"R_DC = %0.3f Ohms\" % (rdc))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next we assume the PA is in switched programmable current-source mode (`PA_MODE.PA_MODE` = `SWC` = `1`). This is less efficient but provides better power flatness.\n",
    "\n",
    "We work out a set of `PA_BIAS_CLKDUTY.OB` and `PA_PWR_LVL.DDAC` values which would give the desired PA bias current."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "OB:    17 (0x11)\n",
      "DDAC: 124 (0x7C)\n",
      "I:     22.32 mA\n"
     ]
    }
   ],
   "source": [
    "# Set maximum DDAC value\n",
    "if CHIP == CHIPS.Si4060:\n",
    "    DDAC_MAX = 0x7F    # e.g. Si4461\n",
    "elif CHIP == CHIPS.Si4461:\n",
    "    DDAC_MAX = 0x7F    # e.g. Si4461\n",
    "else:\n",
    "    raise ValueError(\"Invalid chiptype\")\n",
    "\n",
    "# Set maximum OB value\n",
    "OB_MAX   = 0x3F\n",
    "\n",
    "# OB = 0 = 10uA/finger, OB=1=20uA, ...\n",
    "\n",
    "for ob in range(0, OB_MAX):\n",
    "    # Calculate resulting per-finger current\n",
    "    i_ob = (ob + 1) * 10*uA\n",
    "    \n",
    "    # Calculate required DDAC -- round down to avoid exceeding I_DD\n",
    "    ddac = int(idd / i_ob)\n",
    "    \n",
    "    # Does this OB setting result in DDAC <= DDAC_MAX?\n",
    "    if ddac <= DDAC_MAX:\n",
    "        break\n",
    "\n",
    "# Back-calculate the actual current\n",
    "iactual = ((ob + 1) * 10*uA) * ddac\n",
    "\n",
    "        \n",
    "print(\"OB:   %3d (0x%02X)\" % (ob, ob))\n",
    "print(\"DDAC: %3d (0x%02X)\" % (ddac, ddac))\n",
    "print(\"I:    %6.2f mA\" % (iactual/mA))"
   ]
  }
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Useful references:

Matching network design (SiLabs knowledge base)
What is the Si4432 PA output impedance?
What are the advantages and disadvantages of switched current mode?
Class-E power vs. RDC
External PA Matching
RSSI squelching (limiting RX sensitivity)

And some about the chip:
Si4463 patch and startup delay

Alternative power amps:
Maxim MAX2601/MAX2602 (Can't find any S-parameter files)
-- MAX2602 match data for 120MHz
NXP -- ADS data but no S-params
Infineon -- S-param data available, can use with RFSim99

Dev boards:
Si4461 RF Pico Board

4FSK symbol mapping and preamble requirements (FLEX)
Si4x6x errata re. 4FSK
4FSK sync word
Ins and outs of non-standard preamble detection

Si446x DSA notes -- Digital Signal Arrival detector, see https://www.silabs.com/documents/public/data-sheets/Si4468-7.pdf

Unknowns for Class-E matching: the relationship between PA_PWR_LVL and switcher loss/resistance