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Probe.ipynb
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260
Probe.ipynb
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{
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"cells": [
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{
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"cell_type": "code",
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"execution_count": 1,
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"id": "731fc261",
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"metadata": {},
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"outputs": [],
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"source": [
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"from numpy import *"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 15,
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"id": "fb15ea05",
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"metadata": {},
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"outputs": [],
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"source": [
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"%matplotlib inline\n",
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"import matplotlib.pyplot as plt\n",
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"e0 = 8.8541878188e-12"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 103,
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"id": "ec2633de",
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"metadata": {},
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"outputs": [],
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"source": [
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"def capacitor(ri, ra, l, er=9):\n",
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" C = 2*pi*er*e0*l/log(ra/ri)*1e12\n",
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" #print(f\"{C:.2f}pF\")\n",
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" return C*1e-12"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 104,
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"id": "5193496d",
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"metadata": {},
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"outputs": [],
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"source": [
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"def capacitor_query(ri, ra, l, er=9):\n",
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" C_min = capacitor(ri,ra,l,er=1)\n",
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" C_mid = capacitor(ri,ra,l/2,er=1) + capacitor(ri,ra,l/2,er=er)\n",
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" C_max = capacitor(ri,ra,l,er=er)\n",
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" print(\"----Params----\")\n",
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" print(f\"ri = {ri*1e3:.2f}mm\\nra = {ra*1e3:.2f}mm\\nl = {l*1e3:.2f}mm\\ner = {er:.1f}\")\n",
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" print(\"----Result----\")\n",
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" print(f\"C_min = {C_min*1e12:.2f}pF\")\n",
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" print(f\"C_max = {C_max*1e12:.2f}pF\")\n",
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" print(f\"C_mid = {C_mid*1e12:.2f}pF\")"
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]
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},
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{
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"cell_type": "markdown",
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"id": "1517377f",
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"metadata": {},
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"source": [
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"Capacitor\n",
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"========\n",
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"First we need to know the capacitor and the range we have available,\n",
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"we need the inner and outer diameter $r_i$, $r_a$, length $l$, and $\\epsilon_r$"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 148,
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"id": "e68edb6a",
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"----Params----\n",
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"ri = 4.00mm\n",
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"ra = 8.00mm\n",
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"l = 100.00mm\n",
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"er = 2.0\n",
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"----Result----\n",
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"C_min = 8.03pF\n",
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"C_max = 16.05pF\n",
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"C_mid = 12.04pF\n"
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]
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}
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],
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"source": [
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"capacitor_query(4e-3,8e-3,10e-2,2)"
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]
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},
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{
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"cell_type": "markdown",
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"id": "1188809f",
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"metadata": {},
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"source": [
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"Resonance frequency of an LC circuit:\n",
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"$f_0 = \\frac{1}{2\\pi\\sqrt{LC}}$\n",
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"\n",
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"Solve for L:\n",
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"\n",
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"$L_{RF}= \\frac{1}{(2\\pi f_0)^2C}$"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 143,
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"id": "5ceee5f8",
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"metadata": {},
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"outputs": [],
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"source": [
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"def probe_design(f0, C_mid=12e-12):\n",
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" L_RF = 1e6/((2*pi*f0)**2*C_mid)\n",
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" print(f\"L_RF={L_RF:.2f}µH\") \n",
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" L_duplex = 50/(2*pi*f0)*1e6\n",
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" print(f\"L_duplex={L_duplex:.2f}µH\") \n",
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" C_duplex = 1/(2*pi*f0*50)*1e12\n",
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" print(f\"C_duplex={C_duplex:.2f}pF\") \n",
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" \n",
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" return L_RF*1e6\n",
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"\n",
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"def probe_range(L_RF, C_min, C_max):\n",
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" f_min = 1/(2*pi * sqrt(C_max*L_RF))\n",
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" f_max = 1/(2*pi * sqrt(C_min*L_RF))\n",
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" print(f\"f_min = {f_min:.1f}MHz\\nf_max = {f_max:.1f}MHz\")"
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]
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},
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{
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"cell_type": "markdown",
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"id": "92577356",
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"metadata": {},
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"source": [
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"Now we can calculate the needed coil inductance for the resonance circuit. Here, we also calculate the $\\Pi$-circuit C and L paramters for the duplexer (the \"$\\lambda/4$\" lumped circuit)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 150,
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"id": "44c4a308",
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"L_RF=3.37µH\n",
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"L_duplex=0.32µH\n",
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"C_duplex=127.32pF\n"
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]
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}
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],
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"source": [
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"L_RF = probe_design(25e6, C_mid=12.04e-12)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 147,
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"id": "181a4255",
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"metadata": {
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"scrolled": true
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},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"f_min = 21.7MHz\n",
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"f_max = 30.6MHz\n"
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]
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}
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],
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"source": [
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"probe_range(L_RF, 8e-12, 16e-12)"
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]
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},
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{
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"cell_type": "markdown",
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"id": "cdecc4f3",
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"metadata": {},
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"source": [
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"Coil64\n",
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"=====\n",
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"Calculate the coil windings:\n",
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"\n",
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"Give the wire diameter, incl. isolation thickness, former diameter (5mm)\n",
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"\n",
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"Coil64 v2.2.32 - One layer close-winding coil\n",
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"\n",
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"Input:\n",
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"=====\n",
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" Inductance L: 3.38 microH\n",
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" Frequency f: 25 MHz\n",
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" Former diameter D: 5 mm\n",
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" Wire diameter d: 0.3 mm\n",
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" Wire diameter with insulation k: 0.436 mm\n",
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" Wire material Mt: Copper\n",
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"\n",
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"Result:\n",
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"======\n",
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"\n",
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" Number of turns of the coil N = 56.719 \n",
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" Length of wire without leads lw = 96.894 cm\n",
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" Length of winding l = 25.165 mm\n",
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" Weight of wire m = 0.614 g\n",
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" DC resistance of the coil Rdc = 0.236 Ohm\n",
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" Reactance of the coil X = 530.929 Ohm\n",
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"\n",
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" Self capacitance Cs = 0.356 pF\n",
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" Coil self-resonance frequency Fsr = 218.021 MHz\n",
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" Coil constructive Q-factor Q = 171 \n",
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" Loss resistance ESR = 2.67 Ohm\n",
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"\n",
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" Additional results for parallel LC circuit at the working frequency:\n",
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" => Circuit capacitance: Ck = 11.635 pF\n",
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" => Characteristic impedance: ρ = 531 Ohm\n",
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" => Equivalent resistance: Re = 77.531 kOhm\n",
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" => Bandwidth: 3dBΔf = 171.199 kHz\n",
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"\n",
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" Input data for LTSpice:\n",
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" Inductance: 3.380μ\n",
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" Series resistance: 236.334m\n",
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" Parallel resistance: 78.065k\n",
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" Parallel capacitance: 0.356p\n",
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"\n"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "ff03bfb4",
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"metadata": {},
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"outputs": [],
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"source": []
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}
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],
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"metadata": {
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"kernelspec": {
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"display_name": "Python 3 (ipykernel)",
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"language": "python",
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"name": "python3"
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},
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"language_info": {
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"codemirror_mode": {
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"name": "ipython",
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"version": 3
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},
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"file_extension": ".py",
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"mimetype": "text/x-python",
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"name": "python",
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"nbconvert_exporter": "python",
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"pygments_lexer": "ipython3",
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"version": "3.11.2"
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}
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},
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"nbformat": 4,
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"nbformat_minor": 5
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}
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