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
f=30            #rad/s, frequency
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 wc is",round(wc/10000,2),"krad/s"
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
f=80            #Krad/s  cutoff 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