# Chapter 11: Active Filters¶

## Example 11.1, Page 397¶

In :
import math

#Variable declaration
L=1.414;            #Alpha
Ri=1;           #in Ohm

#Calculations&Results
Rf=2-L;
print "The value of Rf is = %.3f Ohm\n"%Rf;
Av=1+Rf/Ri;
print "The pass band gain of  = %.3f \n"%Av;
fc=1000;            #in Hz
W=2*math.pi*fc;
print "The critical frequency is = %.0f radians per seconds\n"%W;
R=1/W;
print "The Resistor required is  = %.6f Ohm\n"%R;
C1=2/L;
print "The capacitor1 required is  = %.3f F\n"%C1;
C2=L/2;
print "The capacitor2 required is  = %.3f F\n"%C2;

The value of Rf is = 0.586 Ohm

The pass band gain of  = 1.586

The critical frequency is = 6283 radians per seconds

The Resistor required is  = 0.000159 Ohm

The capacitor1 required is  = 1.414 F

The capacitor2 required is  = 0.707 F



## Example 11.2, Page 404¶

In :
import math

#Variable declaration
L=1.732;                # Aplha = DAMPING
Kf=1.274;

#Calculations&Results
R1=L/2;
print "The Resistor required is  = %.3f Ohm\n"%R1;
R2=2/L;
print "The Resistor required is  = %.3f Ohm\n"%R2;
F3db=5000;              #in Hz
Fc=F3db/Kf;
print "The critical frequency is = %.0f Hz\n"%Fc;
Wc=2*math.pi*Fc;
print "The Wc is = %.0f radians per seconds\n"%Wc;
R1n=R1/Wc;
print "The value of scaled Resistor R1 is  = %.7f Ohm\n"%R1n;
R2n=R2/Wc;
print "The value of scaled Resistor R2 is  = %.7f Ohm\n"%R2n;

The Resistor required is  = 0.866 Ohm

The Resistor required is  = 1.155 Ohm

The critical frequency is = 3925 Hz

The Wc is = 24659 radians per seconds

The value of scaled Resistor R1 is  = 0.0000351 Ohm

The value of scaled Resistor R2 is  = 0.0000468 Ohm



## Example 11.3, Page 406¶

In :
import math

#Variable declaration
f3db=20;            #In Hz

#Calculations&Results
W3db=2*math.pi*f3db;
print "The desired break frequency, W3db is = %.1f radians per second\n"%W3db;
print "Stage 1";
kf=1.557;
Wc=W3db/kf;
print "The Wc is = %.1f radians per second\n"%Wc;
Rscaled=1/80.7;  #Rscaled value
R=1000*Rscaled;     #Practical Value
print "The scaled Resistor required is  = %.3f Ohm\n"%R;
C=1*10**-6;          #Assumed Value
print "The assumed capacitor  is  = %.f uFarad\n"%(C*10**6);

print "Stage 2";
Alpha=1.775;
R1=Alpha/2;
print "The Resistor R1 required is  = %.4f Ohm\n"%R1;
R2=2/Alpha;
print "The Resistor R2 required is  = %.3f Ohm\n"%R2;
kf1=1.613;
Wc1=W3db/kf1;
print "The required critical frequency ,Wc is = %.1f radians per second\n"%Wc1;
#we will scale the resistor
R1s=R1/Wc1;
R2s=R2/Wc1;
print "The scaled resistor R1 is  = %.4f Ohm\n"%R1s;
print "The scaled resistor R2 is  = %.4f Ohm\n"%R2s;
print "The assumed capacitor  is  = %.f uFarad\n"%(C*10**6);
#for practical values of resistor and capacitor multiplying by 10**6
R1m=R1s*10**6;
R2m=R2s*10**6;
print "The practical value of  resistor R1 is  = %.0f Ohm\n"%R1m;
print "The practical value of  resistor R2 is  = %.0f Ohm\n"%R2m;
print "The assumed capacitor  is  = %.f uFarad\n"%(C*10**6);

print "Stage 3"
Alpha=1.091;
R21=Alpha/2;
R22=2/Alpha;
kf2=1.819;
Wc2=W3db/kf2;
print "The required critical frequency ,Wc is = %.1f radians per second\n"%Wc2;
#Scale resistor by Wc to achive tuning frequency
R21s=R21/Wc2;
R22s=R22/Wc2;
print "The scaled resistor R1 is  = %.5f Ohm\n"%R21s;
print "The scaled resistor R2 is  = %.4f Ohm\n"%R22s;
#for practical values of resistor and capacitor multiplying by 10**6
R21m=R21s*10**6;
R22m=R22s*10**6;
print "The practical value of  resistor R1 is  = %.0f Ohm\n"%R21m;
print "The practical value of  resistor R2 is  = %.0f Ohm\n"%R22m;
print "The assumed capacitor  is  = %.6f Farad\n"%C;

The desired break frequency, W3db is = 125.7 radians per second

Stage 1
The Wc is = 80.7 radians per second

The scaled Resistor required is  = 12.392 Ohm

The assumed capacitor  is  = 1 uFarad

Stage 2
The Resistor R1 required is  = 0.8875 Ohm

The Resistor R2 required is  = 1.127 Ohm

The required critical frequency ,Wc is = 77.9 radians per second

The scaled resistor R1 is  = 0.0114 Ohm

The scaled resistor R2 is  = 0.0145 Ohm

The assumed capacitor  is  = 1 uFarad

The practical value of  resistor R1 is  = 11392 Ohm

The practical value of  resistor R2 is  = 14463 Ohm

The assumed capacitor  is  = 1 uFarad

Stage 3
The required critical frequency ,Wc is = 69.1 radians per second

The scaled resistor R1 is  = 0.00790 Ohm

The scaled resistor R2 is  = 0.0265 Ohm

The practical value of  resistor R1 is  = 7896 Ohm

The practical value of  resistor R2 is  = 26536 Ohm

The assumed capacitor  is  = 0.000001 Farad



## Example 11.4, Page 412¶

In :
import math

#Variable declaration
L=1.414;            #Alpha
fc=800;         #In Hz

#Calculations&Results
Rf=2-L;
print "The value of Rf is = %.3f Ohm\n"%Rf;
Wc=2*math.pi*fc;
print "The critical frequency is = %.0f radians per seconds\n"%Wc;
R=1/Wc;
print "The value of scaled Resistor R1 is  = %.3e Ohm\n"%(R*10**-4);

print "The value of scaled Resistor and capacitor is  = %.0f Ohm and 10nF \n"%(R*10**8);

The value of Rf is = 0.586 Ohm

The critical frequency is = 5027 radians per seconds

The value of scaled Resistor R1 is  = 1.989e-08 Ohm

The value of scaled Resistor and capacitor is  = 19894 Ohm and 10nF



## Example 11.5, Page 419¶

In :
import math

#Variable declaration
f2=1200;                #in Hz
f1=800;                 #in Hz

#Calculations&Results
BW=f2-f1;
print "The Bandwidth is %.f Hz\n"%BW;
fo=(f1*f2)**0.5;
print " fo is %.0f Hz\n"%fo;
Q=fo/BW;
print " Q is %.2f \n"%Q;
Av=-2*Q*Q;
print "Av is %.0f \n"%Av;
fut=10*Av*fo;
print "funity is %.0f Hz\n"%fut;
R2=2*Q;
print "R2 is %.1f Ohm\n"%R2;
R1b=Q/(2*Q*Q-1);
print "R1b is %.4f Ohm\n"%R1b;
W=2*math.pi*fo;
print "The  frequency is = %.0f radians per seconds\n"%W;
C=1/W*10**6;
print "C is %.1f uF\n"%C;
#practical component value
print "R and C are %.0f Ohm and %.3f F\n"%(R2*10,C/10);

The Bandwidth is 400 Hz

fo is 980 Hz

Q is 2.45

Av is -12

funity is -117576 Hz

R2 is 4.9 Ohm

R1b is 0.2227 Ohm

The  frequency is = 6156 radians per seconds

C is 162.4 uF

R and C are 49 Ohm and 16.244 F



## Example 11.6, Page 424¶

In :
import math

#Variable declaration
Q=25;
fo=4300;            #in Hz

#Calculations&Results
Rd=3*Q-1;           #R damping
print "Rdamping is %.1f Ohm\n"%Rd;
W=2*math.pi*fo;
print "The  frequency is = %.0f radians per seconds\n"%W;
C=1./W*10**6;
print "C is %.f uF\n"%C;
#practical component value
print "Rdamping and C are %.0f Ohm and %.1f nF\n"%(Rd*5000,C/5000*10**3);
#remaining other Resistor are of 5K Ohm

Rdamping is 74.0 Ohm

The  frequency is = 27018 radians per seconds

C is 37 uF

Rdamping and C are 370000 Ohm and 7.4 nF



## Example 11.7, Page 427¶

In :
import math

#Variable declaration
Q=30;
fo=60;            #in Hz

#Calculations&Results
Rd=3*Q-1;           #R damping
print "Rdamping is %.1f Ohm\n"%Rd;
W=2*math.pi*fo;
print "The  frequency is = %.0f radians per seconds\n"%W;
C=1/W*10**3;
print "C is %.2f F\n"%C;

Rdamping is 89.0 Ohm

The  frequency is = 377 radians per seconds

C is 2.65 F