{
"metadata": {
"name": "",
"signature": "sha256:82b1a87e5b1e62f448481647ab7f0e2ca7607ff780f8775431ec8c2b250882dc"
},
"nbformat": 3,
"nbformat_minor": 0,
"worksheets": [
{
"cells": [
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"Chapter 4: Angle Modulation Techniques"
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 4.1, page no. 71"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
" \n",
"# Variable Declaration\n",
"fm1 = 500 # Audio Frequency (Hz)\n",
"Vm1 = 2.4 # AF Voltage (V)\n",
"del_f1 = 4.8*pow(10,3) # Deviation (Hz)\n",
"fm2 = 500 # Audio Frequency (Hz)\n",
"Vm2 = 7.2 # AF Voltage (V)\n",
"fm3 = 200 # Audio Frequency (Hz)\n",
"Vm3 = 10 # AF Voltage (V)\n",
"\n",
"# Calculation\n",
"import math\t # Math Library\n",
"kf = del_f1/Vm1 # Proportionality Constant\n",
"mf1 = del_f1/fm1 # Modulation Index\n",
"del_f2 = kf*Vm2 # Deviation (Hz)\n",
"mf2 = del_f2/fm2 # Modulation Index\n",
"del_f3 = kf*Vm3 # Deviation (Hz)\n",
"mf3 = del_f3/fm3 # Modulation Index\n",
" \n",
"# Result\n",
"\n",
"print \"CASE 1 : Modulation Index, mf1 =\",round(mf1,1)\n",
"print \" Deviation, del_f1 =\",round(del_f1/pow(10,3),1),\"kHz\"\n",
"print \"CASE 2 : Modulation Index, mf2 =\",round(mf2,1)\n",
"print \" Deviation, del_f2 =\",round(del_f2/pow(10,3),1),\"kHz\"\n",
"print \"CASE 3 : Modulation Index, mf3 =\",round(mf3)\n",
"print \" Deviation, del_f3 =\",round(del_f3/pow(10,3),1),\"kHz\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"CASE 1 : Modulation Index, mf1 = 9.6\n",
" Deviation, del_f1 = 4.8 kHz\n",
"CASE 2 : Modulation Index, mf2 = 28.8\n",
" Deviation, del_f2 = 14.4 kHz\n",
"CASE 3 : Modulation Index, mf3 = 100.0\n",
" Deviation, del_f3 = 20.0 kHz\n"
]
}
],
"prompt_number": 1
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 4.2, page no. 71"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"# Variable Declaration\n",
"# GIVEN EXPRESSION : v = 12 sin(6 X 10^(8)t + 5 cos(1250t))\n",
"omega1 = 6.00*pow(10,8) # Angular Velocity (rad/s)\n",
"omega2 = 1250 # Angular Velocity (rad/s)\n",
"mf = 5 # Modulation Index\n",
"A = 12 # Amplitude (V)\n",
"R = 10 # Resistance (Ohms)\n",
"\n",
"# Calculation\n",
"import math\t # Math Library\n",
"fc = omega1/(2*math.pi) # Carrier frequency (Hz)\n",
"fm = omega2/(2*math.pi) # Modulating frequency (Hz)\n",
"del_f = mf*fm # Maximum deviation (Hz)\n",
"P = pow(A/math.sqrt(2),2)/R # Power dissipation (w)\n",
"\n",
"# Result\n",
"print \"Carrier frequency, fc =\",round(fc/pow(10,6),1),\" MHz\"\n",
"print \"Modulating frequency, fm =\",round(fm),\" Hz\"\n",
"print \"Modulation Index, mf =\",round(mf)\n",
"print \"Maximum deviation, del_f =\",round(del_f),\"Hz\"\n",
"print \"Power dissipation, P =\",round(P,1),\"W\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Carrier frequency, fc = 95.5 MHz\n",
"Modulating frequency, fm = 199.0 Hz\n",
"Modulation Index, mf = 5.0\n",
"Maximum deviation, del_f = 995.0 Hz\n",
"Power dissipation, P = 7.2 W\n"
]
}
],
"prompt_number": 2
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 4.3, page no. 73"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"# Variable Declaration\n",
"fm1 = 500 # Audio Frequency (Hz)\n",
"Vm1 = 2.4 # AF Voltage (V)\n",
"del_p1 = 4.8 # Deviation (kHz)\n",
"fm2 = 500 # Audio Frequency (Hz)\n",
"Vm2 = 7.2 # AF Voltage (V)\n",
"fm3 = 200 # Audio Frequency (Hz)\n",
"Vm3 = 10 # AF Voltage (V)\n",
"\n",
"# Calculation\n",
"import math # Math Library\n",
"kp = del_p1/Vm1 # Proportionality Constant\n",
"mp1 = del_p1 # Modulation Index\n",
"del_p2 = kp*Vm2 # Deviation (kHz)\n",
"mp2 = del_p2 # Modulation Index\n",
"del_p3 = kp*Vm3 # Deviation (kHz)\n",
"mp3 = del_p3 # Modulation Index\n",
" \n",
"# Result\n",
"print \"CASE 1 : Modulation Index, mp1 =\",round(mp1,1)\n",
"print \" Deviation, del_p1 =\",round(del_p1,1),\"kHz\"\n",
"print \"CASE 2 : Modulation Index, mp2 =\",round(mp2,1)\n",
"print \" Deviation, del_p2 =\",round(del_p2,1),\"kHz\"\n",
"print \"CASE 3 : Modulation Index, mp3 =\",round(mp3)\n",
"print \" Deviation, del_p3 =\",round(del_p3,1),\"kHz\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"CASE 1 : Modulation Index, mp1 = 4.8\n",
" Deviation, del_p1 = 4.8 kHz\n",
"CASE 2 : Modulation Index, mp2 = 14.4\n",
" Deviation, del_p2 = 14.4 kHz\n",
"CASE 3 : Modulation Index, mp3 = 20.0\n",
" Deviation, del_p3 = 20.0 kHz\n"
]
}
],
"prompt_number": 3
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 4.4, page no. 74"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"# Variable Declaration\n",
"# GIVEN EXPRESSION : v = 12 sin(6 X 10^(8)t + 5 cos(1250t))\n",
"omega1 = 6*pow(10,8) # Angular Velocity (rad/s)\n",
"omega2 = 1250 # Angular Velocity (rad/s)\n",
"mp = 5 # Modulation Index\n",
"A = 12 # Amplitude (V)\n",
"\n",
"# Calculation\n",
"import math\t # Math Library\n",
"fc = omega1/(2*math.pi) # Carrier frequency (Hz)\n",
"fm = omega2/(2*math.pi) # Modulating frequency (Hz)\n",
"del_p = mp # Maximum Deviation (kHz)\n",
"\n",
"# Result\n",
"print \"Carrier frequency, fc =\",round(fc/pow(10,6),1),\" MHz\"\n",
"print \"Modulating frequency, fm =\",round(fm),\" Hz\"\n",
"print \"Modulation Index, mp =\",round(mp),\"radians\"\n",
"print \"Maximum deviation, del_p =\",round(del_p),\"kHz\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Carrier frequency, fc = 95.5 MHz\n",
"Modulating frequency, fm = 199.0 Hz\n",
"Modulation Index, mp = 5.0 radians\n",
"Maximum deviation, del_p = 5.0 kHz\n"
]
}
],
"prompt_number": 4
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 4.5, page no. 75"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"# Variable Declaration\n",
"# GIVEN EXPRESSION FM: v=A sin(omega_c*t + mf cos(omega_m*t))\n",
"# GIVEN EXPRESSION PM: v=A sin(omega_c*t + mp cos(omega_m*t))\n",
"A = 4 # Carrier Voltage (V)\n",
"del_f = 10.00*pow(10,3) # Maximum Frequency Deviation (Hz)\n",
"del_p = 25 # Maximum Phase Deviation (Hz)\n",
"f_c = 25.00*pow(10,6) # Carrier Frequency (Hz)\n",
"f_m1 = 400 # Modulating Frequency 1 (Hz)\n",
"f_m2 = 2000 # Modulating Frequency 2 (Hz)\n",
"\n",
"# Calculation\n",
"import math # Math Library\n",
"omega_c = 2*math.pi*f_c # Angular Velocity of carrier (rad/s)\n",
"omega_m = 2*math.pi*f_m1 # Angular Velocity of Modulating Wave (rad/s)\n",
"mf1 = del_f/f_m1 # Modulation Index for FM\n",
"mf2 = del_f/f_m2 # Modulation Index for FM\n",
"mp = del_p # Modulation Index for PM\n",
"\n",
"# Result\n",
"print \"(a)For FM Case 1, v =\",round(A),\"sin(\",round(omega_c/pow(10,8),2),\"* 10^(8) * t +\",round(mf1),\"cos\",round(omega_m),\"* t )\"\n",
"print \"(b)For PM Case 1, v =\",round(A),\"sin(\",round(omega_c/pow(10,8),2),\"* 10^(8) * t +\",round(mp),\"cos\",round(omega_m),\"* t )\"\n",
"print \"(c)For FM Case 2, v =\",round(A),\"sin(\",round(omega_c/pow(10,8),2),\"* 10^(8) * t +\",round(mf2),\"cos\",round(omega_m),\"* t )\"\n",
"print \"(d)For PM Case 2, v =\",round(A),\"sin(\",round(omega_c/pow(10,8),2),\"* 10^(8) * t +\",round(mp),\"cos\",round(omega_m),\"* t )\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"(a)For FM Case 1, v = 4.0 sin( 1.57 * 10^(8) * t + 25.0 cos 2513.0 * t )\n",
"(b)For PM Case 1, v = 4.0 sin( 1.57 * 10^(8) * t + 25.0 cos 2513.0 * t )\n",
"(c)For FM Case 2, v = 4.0 sin( 1.57 * 10^(8) * t + 5.0 cos 2513.0 * t )\n",
"(d)For PM Case 2, v = 4.0 sin( 1.57 * 10^(8) * t + 25.0 cos 2513.0 * t )\n"
]
}
],
"prompt_number": 5
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 4.6, page no. 79"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"# Variable Declaration\n",
"del1 = 10.00*pow(10,3) # Maximum Deviation (Hz)\n",
"fm = 2.00*pow(10,3) # Modulating frequency (Hz)\n",
"H = 8 # Highest Needed Sideband from Table 4.1\n",
"\n",
"# Calculation\n",
"import math # Math Library\n",
"mf = del1/fm # Modulation Index\n",
"delta = fm*H*2 # Bandwidth required for the FM signal (Hz)\n",
"\n",
"# Result\n",
"print \"Bandwidth required for the FM signal, delta =\",round(delta/pow(10,3)),\"kHz\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Bandwidth required for the FM signal, delta = 32.0 kHz\n"
]
}
],
"prompt_number": 6
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 4.7, page no. 88"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"# Variable Declaration\n",
"gm = 12.00* pow(10,-3) # Transconductance (Siemens) \n",
"f = 5.00*pow(10,6) # Frequency (Hz)\n",
"n = 9 # Constant, from X_GS = (1/9)X_GD\n",
"\n",
"# Calculation\n",
"import math # Math Library\n",
"XCeq = n/gm # Capacitive Reactance of the FET (Ohms)\n",
"\n",
"# Result\n",
"print \"Capacitive reactance of the FET, XCeq =\",round(XCeq),\"Ohms\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Capacitive reactance of the FET, XCeq = 750.0 Ohms\n"
]
}
],
"prompt_number": 7
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 4.8, page no. 89"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"# Variable Declaration\n",
"gm = 9.00*pow(10,-3) # Transconductance (Siemens) \n",
"f = 50.00*pow(10,6) # Frequency (Hz)\n",
"n = 8 # Constant, from R_GS = (1/8)XC_GD\n",
"C = 50.00*pow(10,-12) # Capacitance (F)\n",
"\n",
"# Calculation\n",
"import math # Math Library\n",
"Cn = 0 # Minimum Equivalent Capacitance of FET (F)\n",
"Cx = gm/(2*math.pi*f*n) # Maximum Equivalent Capacitance of FET (F)\n",
"fx_by_fn = math.sqrt(1+Cx/C) # Maximum to Minimum Frequency Ratio\n",
"delta = (fx_by_fn-1)*f/(fx_by_fn+1) # Total frequency variation of FET (Hz)\n",
"\n",
"# Result\n",
"print \"Total frequency variation of FET =\",round(2*delta/pow(10,6),2),\"MHz\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Total frequency variation of FET = 1.73 MHz\n"
]
}
],
"prompt_number": 8
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 4.9, page no. 90"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"# Variable Declaration\n",
"gm_max = 830.00*pow(10,-6) # Max. Transconductance (Siemens)\n",
"gm_min = 320.00*pow(10,-6) # Min. Transconductance (Siemens) \n",
"f = 88.00*pow(10,6) # Frequency (Hz)\n",
"n = 10 # Constant, from R_GS = (1/10)XC_GD\n",
"delta = 75*pow(10,3) # Maximum Deviation (Hz)\n",
"Vgs1 = -2 # Gate Source Voltage (V)\n",
"Vgs2 = -0.5 # Gate Source Voltage (V)\n",
"\n",
"# Calculation\n",
"import math # Math Library\n",
"Vm_rms = -(Vgs1-Vgs2)/(2*math.sqrt(2)) # RMS value of required voltage modulating voltage (V)\n",
"Cn = gm_min/(2*math.pi*f*n) # Minimum Equivalent Capacitance of FET (F)\n",
"Cx = Cn*gm_max/gm_min # Maximum Equivalent Capacitance of FET (F)\n",
"C = (Cx-Cn)*f/(4*delta)-Cn # Capacitance (F)\n",
"L = 1/(4*pow(math.pi*f,2)*C) # Inductance (H)\n",
"\n",
"# Result\n",
"print \"(a) RMS value of required modulating voltage, Vm_rms =\",round(Vm_rms,2),\"V\"\n",
"print \"(b) Capacitance, C =\",round(C/pow(10,-12)),\"pF\"\n",
"print \" Inductance, L =\",round(L/pow(10,-6),3),\"uH\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"(a) RMS value of required modulating voltage, Vm_rms = 0.53 V\n",
"(b) Capacitance, C = 27.0 pF\n",
" Inductance, L = 0.121 uH\n"
]
}
],
"prompt_number": 9
}
],
"metadata": {}
}
]
}