# Chapter 11: Active Filters¶

### Example 11.1 Page No 298¶

In [1]:
#Given
R=10       #Kohm
C=0.001    #microF

#Calculation
wc=1/(R*10**3*C*10**-6)
fc=wc/(6.28)

#Result
print"The cut off frequency is",round(fc/1000,2),"Khz"

The cut off frequency is 15.92 Khz


### Example 11.2 Page No 298¶

In [3]:
#Given
f=2             #Frequency, khz
C=0.005         #MicroF

#Calculation
R=1/(6.28*2*10**3*C*10**-6)

#Result
print"The value of R is",round(R/1000,1),"Kohm"

The value of R is 15.9 Kohm


### Example 11.3 Page No 298¶

In [4]:
#Given
C=0.01          #microF
R=1/(f*10**3*C*10**-6)

#Result
print"The value of R is",round(R/1000,1),"Kohm"

The value of R is 3.3 Kohm


### Example 11.4 Page No 301¶

In [5]:
#Given
f=1             #Khz, cut off frequency
C1=0.01         #MicroF

#Calculation
C2=2*C1
R=0.707/(6.28*f*10**3*C1*10**-6)
Rf=2*R

#Result
print"The value of R is",round(R,0),"ohm"
print"The value of Rf is",round(Rf,0),"ohm"

The value of R is 11258.0 ohm
The value of Rf is 22516.0 ohm


### Example 11.5 Page No 304¶

In [9]:
#given
C3=0.01         #microF, from fig 11.5 (a)
f=1.0             #Khz, cut off frequency

#Calculation
C1=C3/2.0
C2=2*C3
R=1/(6.28*f*10**3*C3*10**-6)

#Result
print"The value of C1=",C1,"microF"
print"The value of C2=",C2,"microF"
print"The value of R=",round(R),"ohm"

The value of C1= 0.005 microF
The value of C2= 0.02 microF
The value of R= 15924.0 ohm


### Example 11.6 Page No 307¶

In [14]:
#Given
C=0.002        #microF, capacitance
fc=10          #Khz, frequency

#Calculation
R=1/(6.28*f*10**3*C*10**-6)

#Result
print"The value of R=",round(R/10000),"kohm"

The value of R= 8.0 kohm


### Example 11.7 Page No 307¶

In [28]:
#Given
R=22.0            #kohm
C=0.001         #microF

#Calculation
import math
wc=1/(R*10**3*C*10**-6)
fc=wc/(2*math.pi)

#Result
print"The value of fc is",round(fc/10,1),"Hz"

The value of wc is 4.55 krad/s
The value of fc is 723.4 Hz


### Example 11.8 Page No 309¶

In [31]:
#Given
C1=0.01         #microF
C2=C1
f=1             #KHz, frequency

#Calculation
#From eq 11.9
R1=1.414/(6.28*f*10**3*C1*10**-6)
R2=R1/2.0

#result
print"The value of R1 is",round(R1/1000,1),"kohm"
print"The value of R2 is",round(R2/1000,1),"kohm"

The value of R1 is 22.5 kohm
The value of R2 is 11.3 kohm


### Example 11.9 Page No 309¶

In [34]:
#Given
C1=125          #pF
C2=C1           #KHz,cut off frequency

#Calculation
#From eq 11.9
R1=1.414/(f*10**3*C1*10**-12)
R2=R1/2.0

#result
print"The value of R1 is",round(R1/1000,0),"kohm"
print"The value of R2 is",round(R2/1000,1),"kohm"

The value of R1 is 141.0 kohm
The value of R2 is 70.7 kohm


### Example 11.10 Page No 311¶

In [42]:
#Given
f=159.0            #Hz, cut off frequency
C=0.1            #microF
C1=C
C2=C
C3=C
wc=1

#calculation
R3=1/(wc*10**3*C*10**-6)
R1=2*R3
R2=R3/2.0

#Result
print"(a)The value of R3 is",round(R3/1000),"kohm"
print"(b)The value of R1 is",round(R1/1000),"kohm"
print"(c)The value of R2 is",round(R2/1000,0),"kohm"

(a)The value of R3 is 10.0 kohm
(b)The value of R1 is 20.0 kohm
(c)The value of R2 is 5.0 kohm


### Example 11.11 Page No 311¶

In [46]:
#Given
f=60            #kHz, cut off frequency
C=220           #pF
C1=C
C2=C
C3=C

#calculation
R3=1/(6.28*f*10**3*C*10**-12)
R1=2*R3
R2=R3/2.0

#Result
print"(a)The value of R3 is",round(R3/1000,0),"kohm"
print"(b)The value of R1 is",round(R1/1000),"kohm"
print"(c)The value of R2 is",round(R2/1000),"kohm"

(a)The value of R3 is 12.0 kohm
(b)The value of R1 is 24.0 kohm
(c)The value of R2 is 6.0 kohm


### Example 11.12 Page No 313¶

In [1]:
#Given
f1=300      # Hz, lower cutoff frequency
f2=3000     #Hz, upper cutoff  frequency

#Calculation
import math
B=f2-f1
f=math.sqrt(f1*f2)

#Result
print"The bandwidth is",B,"Hz"
print"The frequency is",round(f,1),"Hz"

The bandwidth is 2700 Hz
The frequency is 948.7 Hz


### Example 11.13 Page No 314¶

In [50]:
#Given
fr=950     #Hz, resonant frequency
B=2700     #Hz

#Calculation
import math
fl=math.sqrt(B**2/4.0+fr**2)-B/2.0
fh=fl+B

#Result
print"The lower cutoff frequency is",round(fl,1),"Hz"
print"The upper cutoff frequency is",round(fh,1),"Hz"

The lower cutoff frequency is 300.8 Hz
The upper cutoff frequency is 3000.8 Hz


### Example 11.14 Page No 314¶

In [55]:
#Given
B=2700.0     #Hz
fr=950     #Hz  resonant frequency

#calculation
Q=fr/B

#Result
print"The quality factor",round(Q,2)

if Q<0.5:
print"This filter is classified"
else:
print"This filter is not classified"

The quality factor 0.35
This filter is classified


### Example 11.15 Page No 318¶

In [57]:
#Given
fr=1000         #Hz, resonant frequency
fl=80           #From eq 11.16
fh=1280         #upper frequency
C=0.015         #microF
Q=2.0           #Quality factor

#Calculation
import math
B=fr/Q
fl=math.sqrt(B**2/4.0+fr**2)-B/2.0
fh=fl+B

R=0.1591/(B*C*10**-6)
Rr=R/(2*Q**2-1)

#Result
print"The Rr is",round(Rr/1000,2),"kohm"

The Rr is 3.03 kohm


### Example 11.16 Page No 319¶

In [2]:
#Given
R=21.21*10**3       #ohm,  resiatance
Rr=3.03*10**3
C=0.015*10**-6      #F,  capacitance

#Calculation
import math
#From eq 11.12
fr=0.1125*math.sqrt(1+R/Rr)/(R*C)
B=0.1591/(R*C)

#Result
print"The resonant frequency is",round(fr,0),"Hz"
print"Bandwidth is",round(B,0),"Hz"

The resonant frequency is 1000.0 Hz
Bandwidth is 500.0 Hz


### Example 11.17 Page No 321¶

In [64]:
#Given
fr=120       #Hz  resonant frequency
B=12         #Hz
Q=10         #Quality factor

#Calculation
C=0.33      #MicroF
R=0.1591/(B*C*10**-6)
Rr=R/(2*Q**2-1)

#Result
print"The value of resistance is",round(R/1000,1),"kohm"
print"The value of Rr is",round(Rr,1),"kohm"

The value of resistance is 40.2 kohm
The value of Rr is 201.9 kohm