# Chapter : 14 - Phase-Locked Loops (PLL)¶

## Example 14.1 : Page No - 525¶

In :
from numpy import sqrt, pi
#Given data
R_T = 10 # in k ohm
R_T = R_T * 10**3 # in ohm
C_T = 0.005 # in µF
C_T = C_T * 10**-6 # in F
C=10*10**-6 # in F
f_out = 0.25/(R_T*C_T) # in Hz
print "Free Running frequency =",int(f_out*10**-3),"kHz"
# Part (ii)
V=20 # in V
f_L= 8*f_out/V # in Hz
print "Lock range in kHz = ±",int(f_L*10**-3),"kHz"
# Part (iii)
f_C= sqrt(f_L/(2*pi*3.6*10**3*C)) # in Hz
print "Capture range = ±",int(f_C),"Hz"

Free Running frequency = 5 kHz
Lock range in kHz = ± 2 kHz
Capture range = ± 94 Hz


## Example 14.2 : Page No - 532¶

In :
from math import log
#Given data
f_out_max = 200 # in kHz
f_out_min = 4 # in Hz
f_CLK = 2.2*f_out_max # in kHz
print "Frequency of reference oscillation = %0.f kHz" %f_CLK
f_CLK= f_CLK*10**3 # in Hz
# Formula f_out_min= f_CLK/2**n
n=log(f_CLK/f_out_min)/log(2)
print "The number of bits required in the phase accumulator = %0.f" %round(n)

Frequency of reference oscillation = 440 kHz
The number of bits required in the phase accumulator = 17