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Active Filter Circuits
Z. Aliyazicioglu
Electrical and Computer Engineering Department Cal Poly Pomona
ECE307-
Active Filter Circuits
Introduction
Filter circuits with RLC are passive filter circuit
Use op amp to have active filter circuit
Active filter can produce band-pass and band-reject filter without
using inductor.
Passive filter incapable of amplification. Max gain is 1
Active filter capable of amplification
The cutoff frequency and band-pass magnitude of passive filter
can change with additional load resistance
This is not a case for active filters
We look at few active filter with op amps.
We look at that basic op amp filter circuits can be combined to
active specific frequency response and to attain close to ideal
filter response
ECE 307-10 3
Active Filter Circuits =
Transfer function of the circuit
First-Order Low-pass Filters
( )
f
i
Z H s Z
−
2 2 2
1 1
1 || 1 ( )
R R SC sR C H s R R
− −
= =
R
R
C
Vi (^) Vo
Vi
Zf
Vo
Zi
OUT
2
1 2
( ) ( 1)
R H s R sR C
−
2
1
R
K
R
2
1 c R C
ω =
( ) ( )
c
c
H s K s
ω
ω
= −
The Gain Cutoff frequency
Transfer function in jω
c
H j K
j
Active Filter Circuits
Example
+^ Vo
R
1
C
1F
R
1
Vi
- Find R 2 and C values in the following
active Low-pass filter for gain of 1
and cutoff frequency of 1 rad/s.
2
1
1
R K R
= =
2
1 c^1 R C
ω = =
1 ( )
(1 ) 1
H j
j
ω ω
=
R 2 (^) = R 1 = Ω 1 From the gain
From the cutoff frequency
2
1 C 1 F R
= =
2
ECE 307-10 7
Example
C
0.1 uF
R
200K
Vi
R
20 K Vo
2
1
R
K
R
2
c R C
ω = =
Transfer function in jω
- Find R 2 and R 1 values in the above active High-pass filter
for gain of 10 and cutoff frequency of 500 rad/s.
From the gain
From the cutoff frequency
1
R K
C
R 2 (^) = R 1 10 = 200 K Ω
j
H j
j
1
Active Filter Circuits
Example
>> w=1:10000;
>> h=20log10(10(abs((jw/ )./(1+jw/500)))); >> semilogx(w,h) >> grid on >> xlabel('\omega(rad/s)') >> ylabel('|H(j\omega)| dB') >>
ECE 307-10 9
Scaling
- In filter design, we can transform RLC values in to realistic
values, this process is called scaling
- Two types of scaling, magnitude and frequency scaling
- In magnitude scaling, we multiply all L and R by scaling
factor k m , multiplying all C by 1/k m
m R = k R ' m L = k L '
m
C
C
k
- k m ,is positive real number
Active Filter Circuits
Scaling
- frequency scaling, we multiply all L, C by 1/k f where k f is
scaling factor.
R '= R '
f
L
L
k
f
C
C
k
- A circuit can be scaled in both magnitude and frequency in
simultanously
m R = k R '^
m
f
k L L k
m f
C
C
k k
ECE 307-10 13
- Three components
- A unity gain low-pass filter, cutoff frequency is ωc
- A unity gain high-pass filter , cutoff frequency ωc
- A gain component to provide the desired level
Op Amp Band-Pass Filters
2
1
c
c
Low-pass filter High-pass filter Inverting amp.
Vi Vo
Active Filter Circuits
Vi
RH
Rf CH Rf
Vo
RL
RH
CL
RL
Op Amp Band-Pass Filters
2
2 1
c f
c c i
s R H s
s s R
2
2 1
c
c c
K s H s s s
2 2 1 2 1 2
c
c c c c
K s H s
s s
0
s H s
s s
c 2 c 1
2
c L L
R C
1
c H
R CH
ω = (^0 )
max
f
i
R
H j K R
ECE 307-10 15
Example:
- Design a band-pass filter for a graphical equalizer that has
gain 2 within the frequency between 100 and 10,000 Hz.
Use 0.1 μF capacitors
2
c L L
R C
1
c H
R CH
6 2
L c L
R
ω C π
−
6 1
H c L
R
ω C π
−
f
i
R
K
R
- For upper cutoff frequency from LP filter
- For gain, choose R (^) i=1KΩ
f i
R = R K = = K Ω
- For Lower cutoff frequency from HP filter
Active Filter Circuits
From transfer function
j H j
j j
+^ +^
>> f=10:80000; >> w=2pif; >> H=((- 2pi10000)./(jw+2pi* 10000)).((- jw)./(jw+2pi100))( -2); >> A=20*log10(abs(H)); >> semilogx(f,A) >> grid on; >> ylabel ('A_{dB}') >> xlabel ('F (Hz)')
10 20log | ( ) | dB
A = H j ω
ECE 307-10 19
Example:
- Design an active band-reject filter that has gain 5 and the
stop frequency between 100 and 2000 Hz. Use 0.5 μF
capacitors
1
c L L
R C
2
c H H
R C
2 1 For c c
1 2
c c F = Hz and F = Hz
6 1
L c L
R K
ω C π
−
6 2
H c H
R
ω C π
−
f
i
R
K
R
- For gain, choose R (^) i=1KΩ
f i
R = R K = = K Ω
Active Filter Circuits
>> f=10:80000; >> w=2pif; >> H=(((- 2pi100)./(jw+2pi100)) +((- jw)./(jw+2pi2000)))(- 5); >> A=20*log10(abs(H)); >> semilogx(f,A) >> grid on; >> xlabel ('F (Hz)') >> ylabel ('A_{dB}')
1
1 2
c f
c c i
j R H j
j j R
10 20log | ( ) | dB
A = H j ω
