Chapter 10: Phase locked loop

Example 10.1, Page No: 429

In [1]:
#Variable Declaration:
fs=20000.0                 #Signal frequency in hertz
fr=21000.0                 #Free running frquency in hertz
VCOf=4000.0                #V/F transfer coefficient of VCO in Khz/V

#Calculation:
Vcd=(fr-fs)/VCOf           #Calculating change in DC control voltage

#Result:
print('Vcd= %.2f V'%Vcd)

Vcd= 0.25 V

Example No. 10.2, Page No: 430

In [2]:
#Part A
#Variable Ceclaration:
R1=15.0*10**3                #Resistance in ohm
R3=15.0*10**3                #Resistance in ohm
R2=2.2*10**3                 #Resistance in ohm
C1=0.001*10**-6              #Capacitance in farad
Vcc=12.0                     #Voltage in volt

#Calculations:
Vc=Vcc*(R3/(R2+R3))          #Calculating volatage in Vc
fo1=2*(Vcc-Vc)/(C1*R1*Vcc)   #Calculating frequency
fo1n=fo1/1000.0              #Calculating frequency

#Results:
print('\nVc= %.3f V'%Vc)
print('\nFo= %.2f kHz'%fo1n)

#Part B
#Variable Declaration:
Vc1=7.0
Vc2=8.0

#Calculation:
fo2=2*(Vcc-Vc1)/(C1*R1*Vcc)  #Calculating frequency
fo2n=fo2/1000.0              #Calculating frequency

fo3=2*(Vcc-Vc2)/(C1*R1*Vcc)  #Calculating frequency
fo3n=fo3/1000.0              #Calculating frequency

fch=fo2n-fo3n                #Calculating chane in output frequency
 
#Results:
print('\nFo= %.3f kHz'%fo2n)
print('\nFo= %.3f kHz'%fo3n)
print('\nChange in output frequency= %.3f kHz'%fch)

Vc= 10.465 V

Fo= 17.05 kHz

Fo= 55.556 kHz

Fo= 44.444 kHz

Change in output frequency= 11.111 kHz

Example No. 10.3, Page No: 438

In [3]:
#Variable Declaration:
import math
fo=100.0*10**3                            #Frequency in hertz
C=2.0*10**-6                              #Capacitance in farad
Vcc=6.0                                   #Voltage in volt

#Calculations:
fld=7.8*fo/(2*Vcc)                        #Calculating lock frequency
fldn=fld/1000.0                           #Calculating lock frequency
LR=2.0*fldn                               #Calculating lock range

fcd=math.sqrt(fld/(C*2*math.pi*3.6*10**3))#Calculating capture frequency 
fcdn=fcd/1000.0                           #Calculating capture frequency
CR=2*fcdn                                 #Calculating capature range 

R1=12.0*10**3
C1=1.2/(4*R1*fo)                          #Calculating value of capacitance  
C1n=C1*10**12                             #Calculating value of capacitance

#Results:
print('\nDelta FL= +/- %d kHz'%fldn)
print('\nLock Range= %d kHz'%LR)
print('\nDelta FC= +/- %.3f kHz'%fcdn)
print('\nCapture Range= %.3f kHz'%CR)
print('\nC1= %d pF'%C1n)

Delta FL= +/- 65 kHz

Lock Range= 130 kHz

Delta FC= +/- 1.199 kHz

Capture Range= 2.397 kHz

C1= 250 pF

Example No. 10.4, Page No: 438

In [3]:
#Variable Declaration:
import math
R1=15000.0                      #Resistance in ohm
C1=0.01*10**-6                  #Capacitance in farad
C=1*10**-6                      #Capacitance in farad
V=12.0                          #Voltage in volt

#Calculations:
fo=1.2/(4*R1*C1)                #Calculating output frequency 
fon=fo*10**-3                   #Calculating output frequency
LR=7.8*fo/V                     #Calculating lock range
LR1=LR/1000.0                   #Calculating lock range
fcd=math.sqrt(LR/(C*2*math.pi*3.6*1000)) #Calculating delta for capture frequency

#Results:
print('\nCentre frequency of VCO is= %.2f kHz'%fon)
print('\nLock Range = +/- %.1f kHz'%LR1)
print('\nDelta FC= %.2f Hz'%fcd)

Centre frequency of VCO is= 2.00 kHz

Lock Range = +/- 1.3 kHz

Delta FC= 239.73 Hz

Example No. 10.5, Page No: 439

In [5]:
#Variable Declaration:
import math
C1=470.0*10**-12                 #Capacitance value in farad
C=20.0*10**-6                    #Capacitance value in farad
V=12.0                           #Voltage in volt
R1=15000.0                       #Resistance in ohm

#Calculations:
fo=1.2/(4*R1*C1)                 #Calculating centre frequency of the VCO
fon=fo/1000.0                    #Calculating centre frequency of the VCO

LR=7.8*fo/V                      #Calculating lock range 
LR1=LR/1000.0                    #Calculating lock range
fcd=math.sqrt(LR/(C*2*math.pi*3.6*1000)) #Calculating capture range 

#Results:
print('\nCentre frequency of VCO is= %.3f kHz'%fon)
print('\nLock Range = +/- %.2f kHz'%LR1)
print('\nDelta FC= +/- %.2f Hz'%fcd)

Centre frequency of VCO is= 42.553 kHz

Lock Range = +/- 27.66 kHz

Delta FC= +/- 247.27 Hz

Example No. 10.6, Page No: 439

In [4]:
#Variable Declaration:
fr=300.0                  #Free running frequency in hertz
bw=50.0                   #Bandwidth in hertz
ip=320.0                  #input signal frequency in hertz

#Calculations:
pdop=fr+ip                #Calculating phase detector output
difr=ip-fr                #Calculating difference frequency

#Results:
print('\nPhase detector output= %d kHz'%pdop)
print('\nDifference Frequency= %d kHz'%difr)
print('\nAs Bandwidth is greater than difference frequency,')
print('\nPLL can acquire lock')

Phase detector output= 620 kHz

Difference Frequency= 20 kHz

As Bandwidth is greater than difference frequency,

PLL can acquire lock

Example no. 10.7, Page No: 440

In [5]:
#Variable Declaration:
import math
C1=0.01*10**-6                       #Capacitance value in farad
C=0.04*10**-6                        #Capacitance value in farad
V=12.0                               #Voltage in volt
R1=10000.0                           #Resistance in ohm

#Calculations:
fo=120/(4*R1*C1)                     #Calculating centre frequency of the VCO
fon=fo/1000.0                        #Calculating centre frequency of the VCO

fld=7.8*fo/(V)                       #Calculating Lock range
fldn=fld/1000.0                      #Calculating Lock range
       
fcd=math.sqrt(fld/(C*2*math.pi*3.6*10**3)) #Calculating capture range
fcdn=fcd/1000.0                            #Calculating Capture range

#Results:
print('\nCentre frequency of VCO is= %.1f kHz'%fon)
print('\nLock Range= %d kHz'%fldn)
print('\nCapture Range= %.2f kHz'%fcdn)

Centre frequency of VCO is= 300.0 kHz

Lock Range= 195 kHz

Capture Range= 14.68 kHz