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@ingle
Last active May 1, 2019 23:19
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log pixel SNR curve from paper by Spivak et al 2009
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{
"cells": [
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [],
"source": [
"import numpy as np\n",
"from scipy.constants import Boltzmann as k\n",
"from scipy.constants import elementary_charge as q\n",
"import matplotlib.pyplot as plt\n",
"%matplotlib inline"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Initialize all sensor parameters from paper Eq. (8) https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5272465"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [],
"source": [
"T=300 # temperature 300K\n",
"sigr = 96e-6 # 96uV\n",
"Cpd = 10e-15 # 10fF\n",
"Vth_tr = 0.5 # 0.5 V threshold voltage\n",
"sigPRNU_log = 0.0026 \n",
"sigOff_FPN = 0.3/100 # 0.3%\n",
"idc = 0.1e-15 # 0.1fA dark current\n",
"\n",
"iph = np.logspace(-16,-8) # x-axis values from Fig. 5"
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {},
"outputs": [],
"source": [
"numerator = k*T/q * np.log(iph/idc)\n",
"denominator = np.sqrt( sigr**2. + k*T/2./Cpd + (sigPRNU_log**2.) * (iph**2.) + (sigOff_FPN**2.) * (Vth_tr**2.) )"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now calculate SNR from Eq. (8)"
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"/usr/local/lib/python2.7/dist-packages/ipykernel_launcher.py:1: RuntimeWarning: divide by zero encountered in log10\n",
" \"\"\"Entry point for launching an IPython kernel.\n"
]
}
],
"source": [
"SNRdB = 20*np.log10( numerator/(denominator+1e-15) )"
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {},
"outputs": [
{
"data": {
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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"plt.semilogx(iph, SNRdB)\n",
"plt.xlabel('iph [A]')\n",
"plt.ylabel('SNR [dB]')\n",
"plt.grid(True, which='Major')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## This plot does not match Fig. 5 in the paper. For example, the SNR at iph = $10^{-12}$ in the paper is around just below 35 dB. In this plot it is nearly 45 dB.\n",
"<img src=\"https://i.imgur.com/3J1rM0I.png\">"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 2",
"language": "python",
"name": "python2"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 2
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython2",
"version": "2.7.15rc1"
}
},
"nbformat": 4,
"nbformat_minor": 2
}
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