# Chapter 2:Electronics Instruments¶

## Example 2.1,Page no:158¶

In :
import math

#variable declaration
gm     = 0.005;                                #transconductance in siemens
RQ1    = 100*10**3;                            #FET resistance in KΩ
RQ2    = 100*10**3;                            #FET resistance in KΩ
RQ     = 100*10**3;                            #FET resistance in KΩ
Rm     = 50;                                   #meter's resistance in Ω
RD     = 10*10**3;                             #drain resistance in KΩ
v1     = 1;

#calculations
x     = (RQ*RD)/float(RQ+RD);
i     = (gm*x*v1)/float((2*x)+Rm);                  #print'currentt through the PMMC meter(mA)

#result
print'currentt through the PMMC meter is %3.1f'%(i*10**3),'mA';

currentt through the PMMC meter is 2.5 mA


## Example 2.2,Page no:164¶

In :
import math

#variable declaration
e      = 150;          #in V
t      = 3;            #time in s
Kfsin  = 1.11;         #form factor

#calculations
#the sawtooth waveform can be expressed as e = mt
m   = e/float(t);

#e   = 50*t;
#now integration of (50*t)**2 will be 2500*((t**3)/3) with limits ranging 0 to 3 ,solving we get

Erms      = math.sqrt((1/float(9))*((2500)*(t**3)-(0)));   #Erms in V
#now integration of (50*t) will be (50/2)*((t**2)/2) with limits ranging 0 to 3 ,solving we get
Eav       = (1/float(6))*((50)*((t**2)-0));             #Eav in V
Kfsaw     = Erms/float(Eav);                            #form factor
x         = (Kfsin)/float(Kfsaw);                       #ratio of two form factors
e         = ((x-1)/float(1))*100;                       #percentage error

#result
print'percentage error %3.1f'%e,'%'

percentage error -3.9 %


## Example 2.3,Page no:165¶

In :
import math

#vaariable declaration
Kfsin    = 1.11;                                          #form factor  of sine wave

#calculation
#Erms  = math.sqrt((1/T)*(integration(e**2)dt)) with limits from 0 to T is math.sqrt((1/T)*(Emax**2(T-0)))=Emax
#Erms         = Emax;
#Erms      = math.sqrt((1/T)*(integration(e*dt)) with limits from 0 to T is math.sqrt((2/T)*(Emax(T/2-0)))=Emax
#Eav          = Emax;
#Kfsquare    = Erms/float(Emax);       #form factor of squarewave
Kfsquare     = 1;
x            = Kfsin/float(Kfsquare);   #ratio of form factors
e            = ((x-1)/float(1))*100;          #percentage error in %

#result
print'percentage error %3.2f'%e,'%';

percentage error 11.00 %


## Example 2.4,Page no:186¶

In :
import math

#variable declaration
Va    = 2000;                        #anode voltage in V
Id    = 0.02;                        #length of parallel plates in m
d     = 0.005;                        #distance between plates in m
L     = 0.3;                         #distance between screen and plates in m
D     = 0.03;                        #deflect of beam in m
g     = 100;                         #overall gain

#calculations
Vd   = (2*d*Va*D)/float(L*Id);             #voltage in V
Vi   = Vd/float(g);                        #input voltage in V

#result
print'input voltage  %d'%Vi,'V';

input voltage  1 V


## Example 2.5,Page no:186¶

In :
import math

#variable declaration
Va    = 2500;                         #potential difference in V
Id    = 0.025;                        #length of parallel plates in m
d     = 0.005;                        #distance between plates in m
L     = 0.2;                          #distance between screen and plates in m
D     = 0.03;                         #deflect of beam in m

#calculations
Vd   = (2*d*Va*D)/float(L*Id);           #voltage in V
Vi   = D/float(Vd);                      #deflection sensitivity in mm/V

#result
print'deflection sensitivity %2.1f'%(Vi*10**3),'mm/V';

deflection sensitivity 0.2 mm/V


## Example 2.6,Page no:186¶

In :
import math

#variable declaration
Id    = 0.02;               #length of horizontal plates in m
d     = 0.005;              #distance between plates in m
L     = 0.2;                #distance between screen and plates in m
Va    = 2500;               #accelerating voltage in V

#calculations
S    = (L*Id)/float(2*d*Va);      #deflection sensitivityin mm/V

#result
print'deflection sensitivity %3.2f'%(S*10**3),'mm/V';

deflection sensitivity 0.16 mm/V


## Example 2.7,Page no:187¶

In :
import math

#variabledeclaration
va   = 2500;                #anode to cathode voltage in V
Id    = 0.015;               #length of parallel plates in m
d     = 0.005;               #distance between plates in m
L     = 0.5;                 #distance between plates and screen in m
m     = 9.109*10**-31;       #mass of electron in kg
e     = 1.602*10**-19;        #charrge of electron in C

#calculations
v   =  math.sqrt((2*e*va)/float(m));       #beam speed in m/s
S   =  (L*Id)/float(2*d*va);               #deflection sensitivity in mm/V

#calculatons
print'beam speed %3.2f'%(v*10**-6),'m/s';
print'deflection sensitivity %3.1f'%(S*10**3),'mm/V';

beam speed 29.65 m/s
deflection sensitivity 0.3 mm/V


## Example 2.8,Page no:187¶

In :
import math

#variable declaration
L    =  0.22;               #distance between screen and plates in m
l    =  0.033;              #width of uniform magnetuc field in m
Va   =  6000;               #anode potential  in V
D    =  0.044;              #deflection on the screen in m
m    = 9.107*10**-31;       #mass of electron in kg
e    = 1.6*10**-19;         #charge of electron in m

#calculations
X    = math.sqrt(e/float(2*m*Va));               #density of magnetic field in Wb/m**2
B    = D/float(L*l*X);

#result
print'density of magnetic field %3.3f'%(B*10**3),'m Wb/m**2';

density of magnetic field 1.584 m Wb/m**2


## Example 2.9,Page no:187¶

In :
import math

#variable declaration
B    = 1.8*10**-4;           #flux density in Wb/m**2
Va   = 800;                  #final anode voltage in V
d    = 0.01;                 #distance ebetween plates in m
m    = 9.107*10**-31;        #mass of electron in kg
e    = 1.6*10**-19;          #charge of electron in C

#calculations
#we have D  = B*L*I*(math.sqrt((e/float(2*m*Va)))
#let us assume x = B*(math.sqrt((e/float(2*m*Va)))
#thus D  = x*L*I
#we also  have D   = L*Vd*l/float(2*d*Va)
#let us assume y = 1/float(2*d*Va)
#thus D  =  L*Vd*l*y
#comparing both D equations we get
x    = B*(math.sqrt((e)/float(2*m*Va)));
y    = 1/float(2*d*Va) ;
Vd   = x/float(y);                       #voltage applied to Y deflection in V

#result
print'voltage applied to Y deflection %3.3f'%Vd,'V';

voltage applied to Y deflection 30.179 V


## Example 2.10,Page no:207¶

In :
import math

#variable declaration
a   = 3;                #vertical attenuation in mV/div
x   = 5;                #one part is sub divided in units

#callculations
s   = 1/float(x);                            #1 subdivision in units
pp  = 2+(a*s);                        #positive peak in units
Vpp = pp+pp;                          #peak to peak voltage in divisions
Vpp1 = a*Vpp;                         #peak to peak voltage in mV
Vmax = Vpp1/float(2);                 #amplitude in mV
Vrms =Vmax/float(math.sqrt(2));       #R.m.s value in mV

#result
print'Peak-to-peak value %3.1f'%Vpp1,'mV';
print'Amplitude %3.1f'%Vmax,'mV';
print'R.m.s value %3.3f'%Vrms,'mV';

Peak-to-peak value 15.6 mV
Amplitude 7.8 mV
R.m.s value 5.515 mV


## Example 2.11,Page no:210¶

In :
import math

#variable declaration
#from figure we note this values
y1   = 1.25;       #vertical axis in divisions
y2   = 2.5;        #maximum vertical value in divisions

#calculations
x    = y1/float(y2);
phi  = math.asin(x);                         #sinphi value
phi1  = 360-((phi*180)/float(math.pi));       #possible phases

#result
print'possible phases are %3.2f'%((phi*180)/float(math.pi)),'°','or %3.2f'%phi1,'°';

possible phases are 30.00 ° or 330.00 °


## Example 2.12,Page no:219¶

In :
import math

#variable declaration
R1   = 20;                #resistance in kΩ
R2   = 30;                #resistance in kΩ
R3   = 80;                #resistance in kΩ

#calculations
Rx  = (R2*R3)/float(R1);        #unknown resistance in kΩ

#result
print'unknown resistance %d'%Rx,'kΩ';

unknown resistance 120 kΩ


## Example 2.13,Page no:222¶

In :
import math

#variable declaration
R3    = 100.03*10**-6;                     #standard resistance in uΩ
l     = 100.31;                     # inner ratio arm resistance  in Ω
m     = 200;                        # inner ratio arm resistance in Ω
R1    = 100.24;                     #outer ratio arm resistance in Ω
R2    = 200;                        #outer ratio arm resistance in Ω
Ry    = 680*10**-6;                        #unknown resistor in uΩ

#calculation
x   = (R1*R3)/float(R2);                        #resistance in Ω
y   = (m*Ry)/float(l+m+Ry);                      #resistance in Ω
z   = ((R1/float(R2))-(l/float(m)));               #unknown resistanc in Ω
Rx  = x+(y*z);

#rresult
print'unknown resistance %3.3f'%(Rx*10**6),'uΩ';

unknown resistance 49.977 uΩ


## Example 2.14,Page no:224¶

In :
import math

#variable declaration
Z1  = 50;                         #inductive resistance in Ω
Z2  = 125;                        #pure rresistance  in Ω
Z3  = 200;                        #inductive resistance in Ω
theta1  = 80;
theta2  = 0;
theta3  =  30;

#calculations
Z4  = (Z2*Z3)/float(Z1);                   #unknown resistance in Ω
theta4 = theta2+theta3-theta1;             #unknowm angle in °

#result
print'unknown resistance %d'%Z4;
print 'unknowm angle %d'%theta4,'°';

unknown resistance 500
unknowm angle -50 °


## Example 2.15,Page no:28¶

In :
import cmath

#variable declaration
R1   = 225;                                    #resistance in Ω
R2   = 150;                                    #resistance in Ω
C2   = 0.53*10**-6;                            #capacitance in F
R3   = 100;                                    #resistance in Ω
L    = 7.95*10**-3;                            #inductance in H
f    = 1000;                                   #frequency in Hz

#calculations
Z1   = R1;
w    = 2*cmath.pi*f;
x    = (1/float(w*C2));
Z2   = complex(R2,-x);
y    = w*L;
Z3   = complex(R3,y);
Z4   = (Z2*Z3)/float(Z1);                      #unknown arm
Z41  = complex(Z4)
C4   = (1/float(2*cmath.pi*f*100));            #imaginary value is 100 from Z4
c    = (Z4);

#result
print' R4 = %05f'%(Z4.real);
print'capacitance %3.2f'%(C4*10**6),'uF'

 R4 = 133.333333
capacitance 1.59 uF


## Example 2.16,Page no:226¶

In :
import math

#variable declaration
w    = 7500;              #frequency in radians/sec
R2   = 140;               #resistance in Ω
R3   = 1000;              #non-reactive resistance of Ω
R4   = 1000;              #non-reactive resistance of Ω
C2   = 0.0115;            #capacitance in uF

#calculations
R1   = (R2*R3)/float(R4);        #shuntless resistance in Ω
C1   = (C2*R4)/float(R3);        #capacitor of imperfect condenser in F

#result
print'shuntless resistance %d'%R1,'Ω';
print'capacitor of imperfect condenser %3.4f'%C1,'uF';

shuntless resistance 140 Ω
capacitor of imperfect condenser 0.0115 uF


## Example 2.17,Page no:228¶

In :
import math

#variable declaration
R1      = 235;                 #resistance in kΩ
R2      = 2.5;                 #resistance in kΩ
R3      = 50;                  #resistance in kΩ
C1      = 0.012;               #capacitance in uF

#calculations
Rx    = (R2*R3)/float(R1);        #unknown resistance in Ω
Lx    = C1*R2*R3;                 #unknown inductance in H

#result
print'unknown resistance %3.2f'%Rx,'kΩ';
print'unknown inductance  %3.1f'%Lx,'H';

unknown resistance 0.53 kΩ
unknown inductance  1.5 H


## Example 2.18,Page no:230¶

In :
import math

#variable declaration
w    = 3000;                  #frequency in radians/sec
R2   = 9000;                  #resistance in Ω
R1   = 1800;                  # resistance of Ω
R3   = 900;                   # resistance of Ω
C1   = 0.9*10**-6;            #capacitance in F

#calculations
a     = ((w**2)*(R1**2)*(C1**2));
Rx     = ((w**2)*(C1**2)*R1*R2*R3)/float(1+a);                  #equivalent resistance in KΩ
Lx     = (R2*R3*C1)/float(1+((w**2)*(R1**2)*(C1**2)));          #equivalent inductance in H

#result
print'equivalent resistance %3.2f'%(Rx*10**-3),'KΩ';
print'equivalent inductance %3.3f'%Lx,'H';
print'Note:calculation mistake in textbook';

equivalent resistance 4.32 KΩ
equivalent inductance 0.296 H
Note:calculation mistake in textbook


## Example 2.19,Page no:232¶

In :
import math

#variable declaration
R1    = 1.5*10**3;                       #resistance in Ω
R2    = 3000;                            #resistance in Ω
C1    = 0.4*10**-6;                      #capacitance in F
C3    = 0.4*10**-6;                      #capacitance in F
f     = 1000;                            #frequency in Hz

#calculations
w      = 2*math.pi*f;
Rx     = (R2*C1)/float(C3);       #resistance in kΩ
Cx     = (R1*C3)/float(R2);       #capacitance  in F
D      = w*Cx*Rx;                 #dissipation factor

#result
print'resistance %d'%Rx,'kΩ';
print'capacitance %3.2f'%(Cx*10**6),'uF';
print'dissipation factor %3.2f'%D;

resistance 3000 kΩ
capacitance 0.20 uF
dissipation factor 3.77


## Example 2.20,Page no:234¶

In :
import math

#variable declaration
Q  = 1000;                 #resistance in Ω
S  = 1000;                 #resistance in Ω
P  = 500;                  #resistance in Ω
C  = 0.5*10**-6;           #capacitance in uF
r  = 100;                  #resistance in  Ω

#calculations
R    = (P*Q)/float(S);                         #resistance in Ω
L    = ((C*P)*((r*(Q+S))+(Q*S)))/float(S);     #inductance in H

#result
print'resistance %d'%R,'Ω';
print'inductance %3.1f'%L,'H';

resistance 500 Ω
inductance 0.3 H


## Example 2.21,Page no:235¶

In :
import math

#variable declaration
R2  = 1000;                 #resistance in Ω
R4  = 1000;                 #resistance in Ω
R3  = 500;                  #resistance in Ω
C   = 3*10**-6;             #capacitance in uF
r   = 100;                  #resistance in  Ω

#calculations
R    = (R2*R3)/float(R4);                            #resistance in Ω
L    = ((C*R2)*((r*(R3+R4))+(R3*R4)))/float(R4);     #inductance in H

#result
print'resistance %d'%R,'Ω';
print'inductance %3.2f'%L,'H';

resistance 500 Ω
inductance 1.95 H


## Example 2.22,Page no:237¶

In :
import math

#variable declaration
R2    = 100;                     #resistance in Ω
R3    = 834;                     #resistance in Ω
C4    = 0.1*10**-6;              #capacitance in F
C3    = 0.124*10**-6;            #capacitance in F
f     = 1000;

#calculations
L1   = R2*R3*C4;                        #inductance in H
R1   = (R2*C4)/float(C3);              #resistance in Ω
X1   = 2*math.pi*2*f*L1;               #reactance of specimen in Ω
Z1   = math.sqrt((R1**2)+(X1**2));     #impedance of specimen in Ω

#result
print'inductance of specimen %3.2f'%(L1*10**3),'Ω';
print'resistance of specimen %3.2f'%R1,'Ω';
print'impedance of specimen %3.3f'%Z1,'Ω';

inductance of specimen 8.34 Ω
resistance of specimen 80.65 Ω
impedance of specimen 132.240 Ω


## Example 2.23,Page no:243¶

In :
import math

#variable declaration
M   = 18.35*10**-3;             #mutual inductance in H
R1  = 200;                      #non-reactive resistance in Ω
L1  = 40.6*10**-3;              #inductance in mH
R2  = 119.5;                    #non-reactive resistance in Ω
R4  = 100;                      # resistance in Ω

#calculations
C2  = M/float(R1*R4);                #capacitance in F
R3  = (R4*(L1-M))/float(M);          #resistance in Ω
R   = R3-R2;                         #series resistance of capacitor in  Ω

#result
print'capacitance %3.4f'%(C2*10**6),'uF';
print'series resistance of capacitor %3.2f'%R,'Ω';

capacitance 0.9175 uF
series resistance of capacitor 1.75 Ω


## Example 2.24,Page no:245¶

In :
import math

#variable declaration
R1    = 2.8*10**3;           #resistance in Ω
C1    = 4.8*10**-6;          #capacitance in uF
R2    = 20*10**3;            #resistance in Ω
R4    = 80*10**3;            #resistance in Ω
f     = 2000;                #frequency in Hz
w     = 12.57*10**3;
R3    = 11.2*10**3;

#calculations
x     = 1/float((w**2)*(C1**2)*(R1));
y     = R1+x;
z     = R4/float(R2);
R3    = z*(x+y);                                       #equivalent resistance in KΩ
a     = (w**2)*C1*R1*R3;
C3    = 1/float(a);                                   #equivalent capacitance in F

#result
print'equivalent resistance %3.2f'%(R3*10**-3),'KΩ';
print'equivalent capacitance %3.2f'%(C3*10**12),'pF';

equivalent resistance 11.20 KΩ
equivalent capacitance 42.04 pF


## Example 2.25,Page no:246¶

In :
import math

#variable declaration
L1     = 52.6;                #inductance in mH
R2     = 1.68;                 #resistance in MHz
r1     = 28.5;                 #resistance in MHz

#calculations
#at balance of bridge (r1+jwL1)=((R2+r2)+jwL2)
#comparing both real and imaginary terms we get

r2    = r1-R2;                #resistance in Ω
L2    = L1;                   #inductance in H

#result
print'resistance %3.2f'%r2;
print'inductance %3.2f'%L1,'mH';

resistance 26.82
inductance 52.60 mH


## Example 2.26,Page no:246¶

In :
import cmath

#variable declaration
R3   = 300;                                    #resistance in Ω
R2   = 500;                                    #resistance in Ω
C1   = 0.2*10**-6;                            #capacitance in F
C3   = 0.1*10**-6;                            #capacitance in F
f    = 1000;                                   #frequency in Hz

#calculations
w    = 2*(cmath.pi)*f;                            #angular frequency
z   = (1/float(w*C1));
Z1  = complex(0,-z);
Z2   = R2;
x    = 1/float(R3);
y    = w*C3;
Y3   = complex(x,y);
Z4   =  (Z2)/complex(Z1*Y3);
L   = ((182.19)/float(2*cmath.pi*f));            #imaginary value is 182.12 from Z4

#result
print'R4  = %03f'%(Z4.real),'Ω';
print'inductance %3.0f'%(L*10**3),'mH';

R4  = 34.311470 Ω
inductance  29 mH


## Example 2.27,Page no:247¶

In :
import cmath

#variable declaration
R1   = 200;                                    #resistance in Ω
R2   = 200;                                    #resistance in Ω
C2   = 5*10**-6;                               #capacitance in F
C3   = 0.2*10**-6;                               #capacitance in F
R3   = 500;                                    #resistance in Ω
f    = 1000;                                   #frequency in Hz

#calculations
Z1   = R1;
w    = 2*cmath.pi*f;                             #angular frequency
x    = (1/float(w*C2));
Z2   = complex(R2,-x);
y    = 1/float(w*C3);
Z3   = complex(R3,-y);
Z4   = (Z2*Z3)/float(Z1);                        #unknown arm
C4   = (1/float(2*cmath.pi*f*875.3));             #imaginary value is 100 from Z4

#result
print'R4 = %05f'%(Z4.real),'Ω';
print'capacitance %3.2f'%(C4*10**6),'uF';

R4 = 373.348520 Ω
capacitance 0.18 uF


## Example 2.28,Page no:248¶

In :
import cmath

#variable declaration
R1   = 600;                                    #resistance in Ω
R2   = 100;                                    #resistance in Ω
C1   = 1*10**-6;                               #capacitance in F
R3   = 1000;                                   #resistance in Ω
f    = 1000;                                   #frequency in Hz

#calculations
w    = 2*cmath.pi*f;                   #angular frequency
x    = 1/float(R1);
y    = w*C1;
Y1   = complex(x,y);
Z2   = R2;
Z3   = R3;
Z4   = Z2*Z3*Y1;                         #unknown arm
L    = (628.3/float(2*cmath.pi*f));       #inductance in H

#result
print'R4 = %05f'%(Z4.real),'Ω';
print'inductance %3.2f'%L,'H';

R4 = 166.666667 Ω
inductance 0.10 H


## Example 2.29,Page no:249¶

In :
import math

#variable declaration
C2     = 106*10**-12;               #capacitance in F
R4     = 1000/float(math.pi);       #resistance in
C4     = 0.55*10**-6;               #capacitance in F
R3     = 270;                      #resistance in
e0     = 8.854*10**-12;            #absolute permittivity
t      = 0.005;                    #thickness of bakelite in m
d      = 12*10**-2;                       #diameter in m
f      = 50;                           #frequency in Hz

#calculations
R4     = 1000/float(math.pi);       #resistance in
A      = (math.pi/float(4))*((d)**2);     #area of electrodes in m**2
w      = 2*math.pi*f;                    #angular frequency
R1     = (R3*C4)/float(C2);               #resistance in
C1     = (R4*C2)/float(R3);               #apacitance in pF
P      = w*R1*C1;                         #power factor
er     = (C1*t)/float(e0*A);              #relative permittivity

#result
print'capacitance = %3.2f'%(C1*10**12),'pF';
print'power factor = %3.3f'%P;
print'relative permittivity = %3.2f'%er;

capacitance = 124.97 pF
power factor = 0.055
relative permittivity = 6.24


## Example 2.30,Page no:260¶

In :
import math

#variable declaration
f1   = 2*10**6;                   #frequency in Hz
C1   = 420*10**-12;               #capacitance in F
C2   = 90*10**-12;                #capacitance in F
f2   = 4*10**6;                   #frequency in Hz

#calculations
Cd   = (C1-(4*C2))/float(3);         #distributed capacitance in pF

#result
print'distributed capacitance %d'%(Cd*10**12),'pF';

distributed capacitance 20 pF


## Example 2.31,Page no:260¶

In :
import math

#variable declaration
f1   = 2*10**6;          #frequencyin Hz
f2   = 5*10**6;          #frequencyin Hz
C1   = 410*10**-12;       #capacitance in F
C2   = 50*10**-12;       #capacitance in F

#calculations
x  = f2/float(f1);
Cd  = (C1-((x**2)*(C2)))/float((x**2)-1);      #distributed capacitance

#result
print'distributed capacitance %3.3f'%(Cd*10**12),'pF';

distributed capacitance 18.571 pF


## Example 2.32,Page no:261¶

In :
import math

#variable declaration
C1     = 190*10**-12;            #capacitance in F
Q1     = 75;                     #quality factor
C2     = 170*10**-12;            #capacitance in F
Q2     =  45;                     #quality factor
f      = 200*10**3;               #frequency in Hz

#calculations
Rx    = ((C1*Q1)-(C2*Q2))/float(2*math.pi*f*C1*C2*Q1*Q2);     #resistive in Ω
Xx    = (C1-C2)/float(2*math.pi*f*C1*C2);                      #reactive components in Ω

#result
print'resistive %3.2f'%Rx,'Ω';
print'reactive components %3.2f'%Xx,'Ω';

resistive 48.18 Ω
reactive components 492.74 Ω


## Example 2.33,Page no:261¶

In :
import math

#variable declaration
R   = 4;                                 #resistance in Ω
f   = 500*10**3;                         #frequency in Hz
C   = 110*10**-12;                      #capacitance in F
x   = 0.02;                             #resistance across oscillatory circuit in Ω

#calculations
Qtrue     = 1/float(2*math.pi*f*C*R);
Qindicated  = 1/float(2*math.pi*f*C*(R+x));
e           = ((Qtrue-Qindicated)/float(Qtrue))*100;    #percentage error in %

#result
print'percentage error %3.1f'%e,'%';

percentage error 0.5 %


## Example 2.34,Page no:262¶

In :
import math

#variable declaration
f1       = 600*10**3;            #frequency in Hz
f2       = 2*10**6;               #frequency in Hz
C1       = 100*10**-12;          #capacitance in F

#calculations
Cd    = ((f1**2)*C1)/float((f2**2)-(f1**2));    #self-capacitance in F

#calculations
print'self-capacitance %3.2f'%(Cd*10**12),'pF';

self-capacitance 9.89 pF


## Example 2.35,Page no:263¶

In :
import math

#variable declaration
f    = 400*10**3;                          #frequency in kHz
C    = 220*10**-12;                        #capacitance in F
Rsh   = 0.8;                               #resistance in Ω
Q     = 110;                               #quality factor

#calculations
Lcoil    = 1/float(((2*math.pi*f)**2)*C);     #inductance in H
x        = (2*math.pi*f*Lcoil)/float(Q);
Rcoil    = x-Rsh;                        #resistance in Ω

#calculations
print'inductance %3.2f'%(Lcoil*10**6),'uH';
print'resistance %f'%Rcoil,'Ω';

inductance 719.61 uH
resistance 15.641626 Ω


## Example 2.36,Page no:271¶

In :
import math

#variable declaration
Cs   = 210*10**-12;                    #capacitance in F
Cv   = 6*10**-12;                      #capacitance in F
f1    = 2*10**6;                       #frequency in  Hz
f2    = 4*10**6;                       #frequency in  Hz

#calculations
#we have Cs+Cv  = 1/(4*(math.pi**2)*(f2**2)*L
#we have  C+Cv  = 1/(4*(math.pi**2)*(f2**2)*L
L   = 1/float(4*(math.pi**2)*(f2**2)*(Cs+Cv));              #inductance in uH
C   = (1/float((4*(math.pi**2)*(f1**2)*L)))-Cv;             #capacitance in pF

#result
print'inductance L  = %3.2f'%(L*10**6),'uH';
print'capacitance C  = %3.3f'%(C*10**12),'pF';

inductance L  = 7.33 uH
capacitance C  = 858.000 pF


## Example 2.37,Page no:271¶

In :
import math

#variable declaration
C1   = 40*10**-12;              #capacitance in pF
C2   = 48*10**-12;              #capacitance in pF
f    = 4*10**6;        #frequency in Hz
R1    = 60;              #resistance in Ω

#calculations
Co   = (C1+C2)/float(2);
L    = 1/float(4*(math.pi**2)*(f**2)*Co);     #inductance in H
#we have I = E/math.sqrt((R**2)+((w*l)-((1/w*C1))**2))
#we also have I   = E/(R+R1)
#comparing we get and solving we get R**2 + 2*R1*R +R1**2  = R**2 + ((w*l)-((1/w*C1))**2)
w    = 2*math.pi*f;        #angular frequency
x    = w*L;
y    = 1/float(w*C2);
Y     =  ((x-y)**2);
R   = (Y-(R1**2))/float(2*R1);     #resistance in Ω

#result
print'inductance L = %3.3e'%(L),'uH';
print'resistance R  = %3.1f'%(R),'Ω';
print'calculation mistake in textbook assuming approximate values'

inductance L = 3.598e-05 uH
resistance R  = 17.3 Ω
ccalculation mistake in textbook assuming approximate values


## Example 2.38,Page no:272¶

In :
import math

#variable declaration
C       = 160*10**-12;                        #capacitancein pF
f0      = 1.2*10**6;                         #frequency in Hz
f01     = 6*10**3;                           #frequency in Hz

#calculations
f1      = f0+f01;                           #frequency in Hz
f2      = f0-f01;                           #frequency in Hz
f       = f1-f2;                           #frequency in Hz
Q       = f0/float(f);                      #Q factor
R       = f/float(2*math.pi*f0*f0*C);       #effective resistance in Ω

#result
print'Q factor %d'%Q;
print'effective resistance %3.2f'%R,'Ω';

Q factor 100
effective resistance 8.29 Ω


## Example 2.39,Page no:274¶

In :
import math

#variable declaration
C1    = 200*10**-12;               #capacitance in F
C2    = 40*10**-12;               #capacitance in F

#calculations
f1     = (2/float(math.pi))*10**6;      #frequency in Hz
f2     = 2*f1;                          #frequency in Hz
x1     = 4*(math.pi**2)*(f1**2);
x2     = 4*(math.pi**2)*(f2**2);
#L = 1/(x1*(C+Cd));
# L  = 1/(x2*(C+Cd));
#comparing we get following equation for Cd
Cd     = ((x1*C1)-(x2*C2))/float(x2-x1);    #capacitance in pF
c      = C1+Cd;
L      = 1/float(x1*(c));                  #inductance in H

#result
print'self-capacitance of the coil = %3.2f'%(Cd*10**12),'pF';
print'inductance = %3.2f'%(L*10**6),'uH';

self-capacitance of the coil = 13.33 pF
inductance = 292.97 uH