# CHAPTER 14: SINUSOIDAL OSCILLATORS¶

## Example 14.1 : Page number 371-372¶

In :
from math import sqrt
from math import pi

#Variable declaration
L1=58.6;                #Inductance, micro henry
C1=300.0;               #Capacitance, pF

#Calculation
f=(1/(2*round(pi,2)*sqrt(L1*10**-6*C1*10**-12)))/1000;         #Frequency of oscillation, kHz

#Result
print("frequency of oscillation=%dkHz"%f);

#Note : The frequency has been calculated in the text  as 1199kHz but here the answer gets approximated to 1200kHz.

frequency of oscillation=1200kHz


## Example 14.2 : Page number 372¶

In :
from math import pi

#Variable declaration
L1=1.0;                     #Inductance , mH
f=1.0;                      #frequency of oscillation, GHz

#Calculation
#Since, f=1/(2*pi*sqrt(L1*C1)),
C1=(1/(L1*10**-3*(f*10**12*2*pi)**2))*10**12;               #Capacitance, pF

#Result
print("The Capacitance of the capacitor of the LC oscillator=%.2epF"%C1);

The Capacitance of the capacitor of the LC oscillator=2.53e-11pF


## Example 14.3 : Page number 373-374¶

In :
from math import pi
from math import sqrt

#Variable declaration
L=15.0;                 #Inductance, microhenry

#Calculation
CT=C1*C2/(C1+C2);               #Total capacitance

#(i) Operating frequency
f=(1/(2*pi*sqrt(CT*10**-6*L*10**-6)))/1000;             #Operating frequency, kHz

#(ii) Feedback fraction
mv=C1/C2;                                   #Feedback fraction

#Result
print("(i)  The operating frequency=%dkHz"%f);
print("(ii) The feedback fraction=%.1f"%mv);

#Note : The operating frequency is calculated in the text as 1361kHz but here it has been approximated to 1362kHz

(i)  The operating frequency=1362kHz
(ii) The feedback fraction=0.1


## Example 14.4 : Page number 374: Page number¶

In :
from math import pi

#Variable declaration
mv=0.25;                    #Feedback fraction
L=1.0;                      #Inductance, mH
f=1.0;                      #Operating frequeny, MHz

#Calculation
#Since, f=1/(2*pi*sqrt(L*C))
CT=round((1/(L*10**-3*(2*pi*f*10**6)**2))*10**12,1);              #Total capacitance, pF

#Since, mv=C1/C2 and CT=C1*C2/(C1+C2) or CT=C2/(1+ (C2/C1)),
#From the above equations, substituting value of mv and calculaing value of C2,
C2=CT*(1+(1/mv));               #Capacitance of C2 capactior, pF
C1=mv*C2;                       #Capacitance of C1 capacitor, pF

#Result
print("C1=%.1fpF and C2=%.1fpF"%(C1,C2));

C1=31.6pF and C2=126.5pF


## Example 14.5 : Page number 375-376¶

In :
from math import sqrt
from math import pi

#Variable decalaration
L1=1000.0;                  #Inductance of L1 inductor, microhenry
L2=100.0;                   #Inductance of L2 inductor, microhenry
M=20.0;                     #Mutual inductance, microhenry
C=20.0;                     #Capacitance, pF

#Calculation
LT=L1+L2+2*M;                   #Total inductance, microhenry

#(i) Operating frequency
f=(1/(2*pi*sqrt(LT*10**-6*C*10**-12)))/1000;           #Operating frequency, kHz

#(ii)
mv=L2/L1;                   #feedback fraction

#Result
print("(i)  The operating frequency=%dkHz."%f);
print("(ii) The feedback fraction=%.1f."%mv);

#Note : The operating frequecy has been calculated in the text as 1052kHz but here it gets approximated to 1054kHz

(i)  The operating frequency=1054kHz.
(ii) The feedback fraction=0.1.


## Example 14.6 : Page number 376¶

In :
from math import pi

#Variable declaration
C=1.0;                  #Capacitance, pF
f=1.0;                  #Frequency, MHz
mv=0.2;                 #Feedback frequency

#Calculation
LT=(1/(C*10**-12*(2*pi*f*10**6)**2))*1000;               #Total inductance, mH

#Since, mv=L2/L1 or L2=mv*L1 and L1+L2=LT or L1(1+mv)=LT,
L1=LT/(1+mv);                   #Inductance of L1 inductor, mH
L2=L1*mv;                       #inductance of L2 inductor, mH

#Result
print("L1=%.1fmH and L2=%.2fmH."%(L1,L2));

L1=21.1mH and L2=4.22mH.


## Example 14.7 : Page number 378¶

In :
from math import sqrt
from math import pi

#Variable declaration
R1=1.0;                 #Resistor R1, mega ohm
R2=R1;                  #Resistor R2, mega ohm
R3=R1;                  #Resistor R3, mega ohm
C1=68.0;                #Capacitor C1, pF
C2=C1;                  #Capacitor C2, pF
C3=C1;                  #Capacitor C3, pF

#Calculation
R=R1*10**6;                   #Resistance of the resistors of phase shift circuit, ohm
C=C1*10**-12;                 #Capacitance of the capacitors of phase shift circuit, F
fo=1/(2*pi*R*C*sqrt(6));      #Frequency of oscillation, Hz

#Result
print("The frequency of oscillation=%dHz"%fo);

#Note: The frequency of oscillation had been calculated in the text as 954Hz, but here it gets approximated to 955 HZ.

The frequency of oscillation=955Hz


## Example 14.8 : Page number 378¶

In :
from math import pi
from math import sqrt

#Variable declaration
C=5.0;                      #Capacitance of the capacitors of phase shift circuit, pF
fo=800.0;                    #Required frequency of oscillation, kHz

#Calculation
#Since, fo=1/(2*pi*R*C*sqrt(6))
R=(1/(2*pi*C*10**-12*fo*10**3*sqrt(6)))/1000;                   #Resistance of the resistors of phase shift circuit, kilo ohm

#Result
print("R=%.1f kilo ohm."%R);

R=16.2 kilo ohm.


## Example 14.9 : Page number 380¶

In :
from math import pi

#Variable declaration
#Resistance of R1 and R2 resistors of the R-C bridge circuit
R1=220.0;                           #kilo ohm
R2=220.0;                           #kilo ohm

#Capacitance of C1 and C2 the capacitors of the R-C bridge circuit
C1=250.0;                           #pF
C2=250.0;                           #pF

#Calculation
#Since, R1=R2 and C1=C2, R1=R2 is taken as R and C1=C2 is taken as C
#And, f=1/(2*pi*sqrt(R1*R2*C1*C2))is transformed to f=1/(2*pi*R*C).
R=R1*10**3;                                   #kilo ohm
C=C1*10**-12;                                   #pF
f=1/(2*pi*R*C);           #Frequency of oscillation, Hz

#Result
print("The frequency of oscillation=%dHz."%f);

#Note : The frequency of oscillation is calculated in the text as 2892Hz but here it gets approximated to 2893 Hz.

The frequency of oscillation=2893Hz.


## Example 14.11 : Page number 384¶

In :
from math import sqrt
from math import pi

#Variable declaration
#a.c equivalent values of the crystal:
L=1.0;                          #Inductance , H
C=0.01;                         #Capacitance , pF
R=1000.0;                       #Resistance , ohm
Cm=20.0;                        #Mounting capacitance, pF

#Calculation
fs=(1/(2*round(pi,2)*sqrt(L*C*10**-12)))/1000;               #Series resonant frrequency, kHz
CT=(C*Cm/(C+Cm));                                            #Total capacitance, pF
fp=(1/(2*round(pi,2)*sqrt(L*CT*10**-12)))/1000;              #Prallel resonant frequency, kHz

#Result
print("fs=%.0fkHz and fp=%.0fkHz."%(fs,fp));

#Note: fs and fp are calculated in the text as 1589kHz and 1590kHz, but here it gets approximated to 1592kHz and 1593kHz

fs=1592kHz and fp=1593kHz.

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