# Chapter 15 Filters¶

## Example 15.1 Page no 547¶

In :
#Given
fH=2000                         #Hz
C=0.01*10**-6                   #F
Af=2                            #gain

#Calculation
import math
R=1/(2.0*math.pi*fH*C)
Rf=Af-1

#Result
print"In this case R1=Rf=10 Kohm is selected."

In this case R1=Rf=10 Kohm is selected.


## Example 15.2 Page no 547¶

In :
wc=20.0                          #K radian/s
C=0.01                          #micro F

#Calculation
R=1/(wc*C)

#Result
print"The value of resistance is ", R,"K ohm"

The value of resistance is  5.0 K ohm


## Example 15.3 Page no 550¶

In :
#Given
fh=2000                         #Hz
C2=0.0033*10**-6                #F
C3=0.0033*10**-6                #F
R0=0.586                        #ohm
R1=10000                        #ohm

#Calculation
import math
R=1/(2*math.pi*fh*C2)
Rf=R0*R1

#Result
print" R2=R3=",round(R*10**-3,0),"Kohm \n C2=C3=",C2 ,"micro F \n Rf=",Rf*10**-3,"Kohm \n R1=",R1*10**-3,"Kohm"

 R2=R3= 24.0 Kohm
C2=C3= 3.3e-09 micro F
Rf= 5.86 Kohm
R1= 10.0 Kohm


## Example 15.4 Page no 553¶

In :
#Given
R=47*10**3                      #ohm
C=0.0022*10**-6                 #F

#Calculation
import math
fl=1/(2.0*math.pi*R*C)

#Result
print"The cutoff frequency is ", round(fl*10**-3,2),"KHz"

The cutoff frequency is  1.54 KHz


## Example 15.5 Page no 557¶

In :
#Given
C=0.01*10**-6                         #f
fh=1000                                #Hz
fl=100

#Calculation
R=1/(2.0*math.pi*fh*C)
R1=1/(2.0*math.pi*fl*C)
fc=math.sqrt(fl*fh)
Q=fc/(fh-fl)

#Result
print"(i) Resistance is ", round(R1*10**-3,0),"Kohm"
print"(ii) The value of Q is ",round(Q,2)

(i) Resistance is  159.0 Kohm
(ii) The value of Q is  0.35


## Example 15.6 Page no 561¶

In :
#Given
C=0.01                          #F
Q=5
Fc=1000                              #Hz
Av0=8
a=1000                             #Hz
b=1.5*10**3                         #Hz

#Calculation
import math
R1=Q/(2.0*math.pi*C*Av0)
R2=(Q/(2.0*math.pi*Fc*C*(2*Q**2-Av0)))*10**3
R3=Q/(math.pi*Fc*C)
Rk=R2*((a/b)**2)

#Result
print"(i) Resistances are \n R1=",round(R1,0),"Kohm \n R2=",round(R2,0),"Kohm \n R3=",round(R3*10**3,0),"Kohm"
print"(ii) The value of resistance is ", round(Rk*10**3,0),"ohm"

(i) Resistances are
R1= 10.0 Kohm
R2= 2.0 Kohm
R3= 159.0 Kohm
(ii) The value of resistance is  842.0 ohm


## Example 15.7 Page no 563¶

In :
#Given
fl=100                            #Hz
fh=1000                            #Hz
R=159                       #Kohm, for low pass filter
C=0.1                     #micro F , for low pass filter
R1=15.9                      # K ohm, for high pass filter
C1=0.01                   #micro F ,  for high pass filter
R2=10.0                        #K ohm
R3=10.0                     #K ohm
R4=10.0                        #K ohm

#Calculation
Rom=(R2*R3*R4)/(R2+R3+R4)*10**-1

#Result
print"Value of resistance is ", round(Rom,1),"Kohm"

Value of resistance is  3.3 Kohm


## Example 15.8 Page no 564¶

In :
#Given
C=0.047                   #micro F
fn=50                             #Hz

#Calculation
import math
R=1/(2.0*math.pi*fn*C)

#Result
print"The value of resistance is ", round(R*10**3,0),"Kohm"

The value of resistance is  68.0 Kohm


## Example 15.9 Page no 566¶

In :
#Given
C=0.01                      #micro F
R=15                        #K ohm
f=2.5                        #K ohm

import math
b=2*math.pi*f*C*R
a=-(2*math.atan(b)*180/3.14)

#Result
print"Phase angle is ", round(a,0)

Phase angle is  -134.0


## Example 15.10 Page no 570¶

In :
#Given
R=316.0                 #ohm
a=10.0
R1=100                              #ohm
F1=1.5 *10**3                       #Hz
c=5.03*10**7
R6=1.8*10**3

#Calculation
R2=R/a
R3=R1/(R*a-1)
R4=c/F1
R7=6*R6
R8=(R6*R7)/(R6+R7)

print"value of external component are \n R2=",R2,"Kohm \n R3=",round(R3*10**2,1),"Kohm \n R4=R5=", round(R4*10**-3,2)
print" R7=",R7*10**-3,"Kohm \n R8=", round(R8*10**-3,3),"Kohm"

value of external component are
R2= 31.6 Kohm
R3= 3.2 Kohm
R4=R5= 33.53
R7= 10.8 Kohm
R8= 1.543 Kohm