{
"metadata": {
"name": "",
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"worksheets": [
{
"cells": [
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"Chapter 6 - Noise"
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 1 - pg 281"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#calculate the RMS noise voltage\n",
"import math\n",
"#given\n",
"R = 10.*10**3#resistance of amplifier in ohms\n",
"T = 273.+27#temperature in kelvin\n",
"B = (20.-18)*10**6#bandwidth\n",
"k = 1.38*10**-23#boltzman's constant\n",
"\n",
"#calculations\n",
"V_n = math.sqrt(4*R*k*T*B)*10**6;#rms noise voltage\n",
"\n",
"#result\n",
"print \"Rms noise voltage (muV) = \",round(V_n,2)\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Rms noise voltage (muV) = 18.2\n"
]
}
],
"prompt_number": 1
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 2 - pg 281"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#calculate the RMS noise voltage\n",
"import math\n",
"#given\n",
"R_1 = 300.#equivalent noise resistance\n",
"R_2 = 400.#input resistance\n",
"T = 273+27.#temperature in kelvin\n",
"B = 7.*10**6#bandwidth\n",
"k = 1.38*10**-23#boltzman's constant\n",
"\n",
"#calculations\n",
"R_s = R_1 +R_2#effective resistance in series\n",
"V_nr = math.sqrt(4*k*T*B*R_s)*10**6#rms noise voltage\n",
"\n",
"#result \n",
"print \"Rms noise voltage (muV) = \",round(V_nr,0)\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Rms noise voltage (muV) = 9.0\n"
]
}
],
"prompt_number": 2
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 3 - pg 282"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#calculate the Noise voltage in all cases\n",
"import math\n",
"from math import sqrt\n",
"#given\n",
"R_1 = 20*10**3#resistance one\n",
"R_2 = 50*10**3#resistance two\n",
"T = 273+15#temperature in kelvin\n",
"B = 100*10**3#bandwidth\n",
"k = 1.38*10**-23#boltzman's constant\n",
"\n",
"#calculations\n",
"R_s = R_1 +R_2#series effective resistance\n",
"R_p = (R_1*R_2)/(R_1 + R_2)#parallel effective resistance\n",
"V_1 = sqrt(4*k*T*R_1*B)*10**6#noise voltage in R_1\n",
"V_2 = sqrt(4*k*T*R_1*B)*10**6#noise voltage in R_2\n",
"V_s = sqrt(4*k*T*R_s*B)*10**6#noise voltage when resistance connected in series\n",
"V_p = sqrt(4*k*T*R_p*B)*10**6#noise voltage when resistance connected in parallel\n",
"\n",
"#results\n",
"print \"i.Noise voltage due to R_1 (muV) = \",round(V_1,2)\n",
"print \"ii.Noise voltage due to R_2 (muV) = \",round(V_2,2)\n",
"print \"iii.Noise voltage due to two resistance in series (muV) = \",round(V_s,2)\n",
"print \"iv.Noise voltage due to two resistance in parallel (muV) = \",round(V_p,2)\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"i.Noise voltage due to R_1 (muV) = 5.64\n",
"ii.Noise voltage due to R_2 (muV) = 5.64\n",
"iii.Noise voltage due to two resistance in series (muV) = 10.55\n",
"iv.Noise voltage due to two resistance in parallel (muV) = 4.77\n"
]
}
],
"prompt_number": 3
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 4 - pg 283"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#calculate the Equivalent input noise resistance\n",
"\n",
"#given\n",
"A_1 = 10.#voltage gain for first stage\n",
"A_2 = 25.#volatage gain for second stage\n",
"R_i1 = 600.#input resistance for first stage in ohms\n",
"R_eq1 = 1600.#equivalent noise resistance for first stage \n",
"R_01 = 27.*10**3#Output resistance for first stage \n",
"R_i2 = 81.*10**3#input resistance for second stage\n",
"R_eq2 = 10.*10**3#Equivalent noise resistance for second stage \n",
"R_02 = 1.*10**6#putput resistance for second case\n",
"\n",
"#calculations\n",
"R_1 = R_i1 + R_eq1\n",
"R_2 = ((R_01*R_i2)/(R_01+R_i2)) + R_eq2\n",
"R_3 = R_02\n",
"R_eq = R_1 + (R_2/A_1**2) + R_3/(A_1**2 *A_2**2);\n",
"\n",
"#results\n",
"print \"Equivalent input noise resistance (Ohms) = \",round(R_eq,0)\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Equivalent input noise resistance (Ohms) = 2519.0\n"
]
}
],
"prompt_number": 4
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 7 - pg 295"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#calculate the output voltage\n",
"import math\n",
"#given\n",
"T = 273. + 17#temperature in kelvin\n",
"Q = 10.#quality factor\n",
"c = 10.*10**-12#capacitance\n",
"f_r = 100.*10**6#resonate frequency\n",
"k = 1.38*10**-23#boltzman's constant\n",
"\n",
"#calculations\n",
"delta_f = f_r/Q#bandwidth of the tuned circuit\n",
"w = 2*math.pi*f_r;#angular frequency\n",
"R = 1/(Q*w*c);#resistance\n",
"V_no = math.sqrt(4*k*Q**2*T*delta_f*R)*10**6 #output voltage\n",
"\n",
"#results\n",
"print \"Output voltge (V) = \",round(V_no,0)\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Output voltge (V) = 16.0\n"
]
}
],
"prompt_number": 5
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 8 - pg 297"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#calculate the Noise figure and Equivalent temperature\n",
"import math\n",
"#given\n",
"R_a = 50.#antenna resistance\n",
"R_eq = 30.#equivalent noise resistance of receiver\n",
"T_0 = 290.#initial temperature in degree kelvin\n",
"#calculations\n",
"F = 1+(R_eq/R_a);#noise figure\n",
"F_dB = 10*math.log10(F)#noise figure in decibels\n",
"T_eq = T_0*(F-1)#equivalent temperature\n",
"\n",
"#results\n",
"print \"i.Noise figure in decibels (dB) = \",round(F_dB,2)\n",
"print \"ii.Equivalent temperature (degree kelvin) = \",T_eq\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"i.Noise figure in decibels (dB) = 2.04\n",
"ii.Equivalent temperature (degree kelvin) = 174.0\n"
]
}
],
"prompt_number": 6
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 9 - pg 302"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#calculate the Noise figure\n",
"import math\n",
"#given\n",
"R_eq = 2518.#equivalent resistance in ohms\n",
"R_t = 600.#input impedence in ohms\n",
"R_a= 50.#output impedencre in ohms\n",
"\n",
"#calculations\n",
"R_eq1 = R_eq - R_t;\n",
"F = 1 + (R_eq1/R_a) #noise figure\n",
"F_dB = 10*math.log10(F)#noise figure in dB\n",
"\n",
"#results\n",
"print \"Noise figure in dB = \",round(F_dB,2)\n",
"print \"Note:Calculation mistake is their in text book in finding noise figure in dB\"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Noise figure in dB = 15.95\n",
"Note:Calculation mistake is their in text book in finding noise figure in dB\n"
]
}
],
"prompt_number": 7
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 10 - pg 305"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#calculate the Overall noise figure\n",
"import math\n",
"from math import exp, log10,log\n",
"#given\n",
"F_1 = 2.#noise figure of first stage in dB\n",
"A_1 = 12.#gain in first stage in dB\n",
"F_2 = 6.#noise figure of second stage in dB\n",
"A_2 = 10.#gain in first second in dB \n",
"\n",
"\n",
"#calculations\n",
"F_1ratio = exp((F_1/10)*log(10));#noise figure of first stage in ratio \n",
"F_2ratio = exp((F_2/10)*log(10));#noise figure of second stage in ratio \n",
"A_1ratio = exp((A_1/10)*log(10));#gain of first stage in ratio\n",
"A_2ratio = exp((A_2/10)*log(10));#gain of second stage in ratio\n",
"F = F_1ratio + ((F_2ratio - 1)/(A_1ratio));#Overall noise figure \n",
"F_dB = 10*log10(F);#Overall noise figure in dB\n",
"\n",
"#results\n",
"print \"Overall noise figure (dB) = \",round(F_dB ,1)\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Overall noise figure (dB) = 2.5\n"
]
}
],
"prompt_number": 9
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 11 - pg 306"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#calculate the Overall noise figure\n",
"import math\n",
"from math import exp, log10,log\n",
"#given\n",
"F_1 = 9.#noise figure for first stage in dB\n",
"F_2 = 20.#noise figure for second stage in dB\n",
"A_1 = 15.#gain in first stage in dB\n",
"\n",
"#calculations\n",
"F_1ratio = exp((F_1/10)*log(10));#noise figure of first stage in ratio \n",
"F_2ratio = exp((F_2/10)*log(10));#noise figure of second stage in ratio \n",
"A_1ratio = exp((A_1/10)*log(10));#gain of first stage in ratio\n",
"F = F_1ratio + ((F_2ratio - 1)/(A_1ratio));\n",
"F_dB = 10*log10(F);\n",
" \n",
"#results\n",
"print \"Overall noise figure (dB) = \", round(F_dB,2)\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Overall noise figure (dB) = 10.44\n"
]
}
],
"prompt_number": 10
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 12 - pg 307"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#calculate the rms noise voltage\n",
"import math\n",
"#given\n",
"f_1 = 18.*10**6#lower operating frequency in Hz\n",
"f_2 = 20.*10**6#lower operating frequency in Hz\n",
"T = 273. + 17#temperature in kelvin\n",
"R = 10.*10**3#input resistance\n",
"k = 1.38*10**-23#boltzman's constant\n",
"\n",
"#calculations\n",
"B = f_2 - f_1#bandwidth in Hz\n",
"V_n = math.sqrt(4*k*B*R*T)*10**6;#rms noise voltage\n",
"\n",
"#results\n",
"print \"rms noise voltage (muV) = \",round(V_n,1)\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"rms noise voltage (muV) = 17.9\n"
]
}
],
"prompt_number": 11
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 14 - pg 308"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#calculate the Meter reading, resistance\n",
"\n",
"#given\n",
"A = 60.#gain of noiseless amplifier\n",
"V_n1 = 1.*10**-3#output of the amplifier\n",
"B = 20.*10**3#initial bandwidth\n",
"B1 = 5.*10**3#change in bandwidth\n",
"k = 1.38*10**-23#boltzman's constant\n",
"T = 273. + 80#temperature in degree kelvin\n",
"\n",
"#calculaitons\n",
"#since the bandwidth is reesuced to 1/4th of its value,therefore the noise voltage \n",
"#will be V_n proportional to sqrt(B)\n",
"#Hence, the noise voltage at 5KHz will become half its value at 20KHz bandwidth i.e,\n",
"V_n = .5*10**-3#noise voltage in volts\n",
"V_no = V_n1/A;#noise ouput voltage \n",
"R = (V_no**2/(4*k * T * B ));#resistance at 80degree celcius\n",
"\n",
"#results\n",
"print \"i.Meter reading in volts (V) = \",V_n\n",
"print \"ii.Resistance at 80 degree celcius (kohms) = \",round(R/1000.,0)\n",
"print \"Note: There is calculation mistake in textbook in the measurement of resistance they took constant in formula as 1 instead of 4\"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"i.Meter reading in volts (V) = 0.0005\n",
"ii.Resistance at 80 degree celcius (kohms) = 713.0\n",
"Note: There is calculation mistake in textbook in the measurement of resistance they took constant in formula as 1 instead of 4\n"
]
}
],
"prompt_number": 12
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 16 - pg 309"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#calculate the Overall noise figure\n",
"import math\n",
"from math import exp, log10,log\n",
"#given\n",
"A_1 = 10.#gain in first stage in dB\n",
"A_2 = 10.#gain in second stage in dB\n",
"A_3 = 10.#gain in third stage in dB\n",
"F_1 = 6.#noise figure for first stage in dB\n",
"F_2 = 6.#noise figure for second stage in dB\n",
"F_3 = 6.#noise figure for third stage in dB\n",
"\n",
"#calculations\n",
"F_1ratio = exp((F_1/10)*log(10));#noise figure of first stage in ratio \n",
"F_2ratio = exp((F_2/10)*log(10));#noise figure of second stage in ratio \n",
"F_3ratio = exp((F_3/10)*log(10));#noise figure in third stage in ratio \n",
"A_1ratio = exp((A_1/10)*log(10));#gain of first stage in ratio\n",
"A_2ratio = exp((A_2/10)*log(10));#gain of second stage in ratio\n",
"A_3ratio = exp((A_3/10)*log(10));#gain of third stage in ratio\n",
"F = F_1ratio + ((F_2ratio - 1)/(A_1ratio)) + ((F_3ratio - 1)/(A_2ratio*A_1ratio));#Overall noise figure\n",
"\n",
"#results\n",
"print \"Overall noise figure of three stage cascaded amplifier = \",round(F,2)\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Overall noise figure of three stage cascaded amplifier = 4.31\n"
]
}
],
"prompt_number": 13
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 17 - pg 310"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#calculate the Overall noise figure\n",
"import math\n",
"from math import exp, log10,log\n",
"#given\n",
"G_1 = 10.#gain in first stage in dB\n",
"#noise figure for both the stages are same\n",
"F_1 = 10.#noise figure for first stage in dB\n",
"F_2 = 10.#noise figure for second stage in dB\n",
"\n",
"#calculations\n",
"F_1ratio = exp((F_1/10)*log(10));#noise figure of first stage in ratio \n",
"F_2ratio = exp((F_2/10)*log(10));#noise figure of second stage in ratio \n",
"G_1ratio = exp((G_1/10)*log(10));#gain of first stage in ratio\n",
"F = F_1ratio + ((F_2ratio - 1)/(G_1ratio));#Overall noise figure\n",
"F_dB= 10*log10(F)##Overall noise figure in dB\n",
"\n",
"#results\n",
"\n",
"print \"Overall noise figure (dB) = \", round(F_dB,2)\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Overall noise figure (dB) = 10.37\n"
]
}
],
"prompt_number": 14
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 18 - pg 310"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#calculate the overall noise figure and overall gain\n",
"import math\n",
"from math import exp, log10,log\n",
"#given\n",
"G_1 = 4.#gain in first stage in dB\n",
"G_2 = 10.#gain in second stage in dB\n",
"F_1 = 10.#noise figure for first stage in dB\n",
"F_2 = 10.#noise figure for second stage in dB\n",
"\n",
"#calculations\n",
"F_1ratio = exp((F_1/10)*log(10));#noise figure of first stage in ratio \n",
"F_2ratio= exp((F_2/10)*log(10));#noise figure of second stage in ratio \n",
"G_1ratio = exp((G_1/10)*log(10));#gain of first stage in ratio\n",
"G_2ratio = exp((G_2/10)*log(10));#gain of second stage in ratio\n",
"F = F_1ratio + ((F_2ratio - 1)/(G_1ratio));#Overall noise figure \n",
"G = log10(G_1ratio *G_2ratio );\n",
"F_dB= 10*log10(F)##Overall noise figure in dB\n",
"\n",
"#results\n",
"print \"i.Overall noise figure (dB) = \",round(F_dB,2)\n",
"print \"ii.Overall gain (dB) = \",G \n",
"print \"Note:There is mistake in calculation of overall gain in textbook\"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"i.Overall noise figure (dB) = 11.33\n",
"ii.Overall gain (dB) = 1.4\n",
"Note:There is mistake in calculation of overall gain in textbook\n"
]
}
],
"prompt_number": 15
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 19 - pg 310"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#calculate the Overall noise figure\n",
"import math\n",
"from math import exp, log10,log\n",
"#given\n",
"G_1 = 15.#gain in first stage in dB\n",
"F_1 = 9.#noise figure for first stage in dB\n",
"F_2 = 20.#noise figure for second stage in dB\n",
"\n",
"#calculations\n",
"F_1ratio = exp((F_1/10)*log(10));#noise figure of first stage in ratio \n",
"F_2ratio = exp((F_2/10)*log(10));#noise figure of second stage in ratio \n",
"G_1ratio = exp((G_1/10)*log(10));#gain of first stage in ratio\n",
"F = F_1ratio + ((F_2ratio - 1)/(G_1ratio));#Overall noise figure \n",
"F_dB= 10*log10(F)##Overall noise figure in dB\n",
"\n",
"#results\n",
"print \"Overall noise figure (dB) = \", round(F_dB,2)\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Overall noise figure (dB) = 10.44\n"
]
}
],
"prompt_number": 16
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 20 - pg 311"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#calculate the Noise temperature and overall noise temperature\n",
"import math\n",
"from math import exp, log10,log\n",
"#given\n",
"F_2 = 20.#noise figure of receiver in dB\n",
"G_1 = 40.#gain of low noise amplifier in dB\n",
"T_e1 = 80.#noise temperature of low noise amplifier in degree kelvin\n",
"T_0 = 300.#room temperature\n",
"\n",
"#calculations\n",
"F_2ratio = exp((F_2/10)*log(10));#noise figure of receiver in ratio \n",
"G_1ratio = exp((G_1/10)*log(10));#gain of low noise amplifier\n",
"T_e2 = (F_2ratio-1)*T_0#noise temperature of the receiver in degree kelvin\n",
"T_e = T_e1 +(T_e2/G_1ratio)#overall noise temperature in degree kelvin\n",
"\n",
"#results\n",
"print \"i.Noise Temperature of the receiver (degkelvin) = \",T_e2\n",
"print \"ii.Overall noise temperature (degkelvin) = \",T_e\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"i.Noise Temperature of the receiver (degkelvin) = 29700.0\n",
"ii.Overall noise temperature (degkelvin) = 82.97\n"
]
}
],
"prompt_number": 17
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 21 - pg 311"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#calculate the overall noise temperature and noise figure\n",
"import math\n",
"#given from the figure\n",
"G_1ratio = 1000.#gain of master amplifier \n",
"G_2ratio = 100.#gain of TWT\n",
"G_3ratio = 10000.#gain of mixer and IF amplifier\n",
"F_2ratio = 4.#noise figure of TWT \n",
"F_3ratio = 16.#noise figure of mixer and IF amplifier\n",
"T_0 =273 + 17.#ambident temperature in degree kelvin\n",
"T_e1 = 5.#temperature of master amplifier in degree kelvin\n",
"\n",
"#calculaitons\n",
"F_1 = 1 + (T_e1/T_0);#noise figure of master amplifier\n",
"F = F_1 + ((F_2ratio - 1)/(G_1ratio)) + ((F_3ratio - 1)/(G_2ratio*G_1ratio));#Overall noise figure\n",
"F_dB = 10*math.log10(F);#overall noise figure in dB\n",
"T_e = (F - 1)*T_0;#overall noise temperature of the receiver \n",
"\n",
"#results\n",
"print \"i.Overall noise temperature of the receiver (degreekelvin) = \",round(T_e,0)\n",
"print \"ii.Overall noise figure (dB) = \", round(F_dB,5)\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"i.Overall noise temperature of the receiver (degreekelvin) = 6.0\n",
"ii.Overall noise figure (dB) = 0.08767\n"
]
}
],
"prompt_number": 18
}
],
"metadata": {}
}
]
}