1. CHAPTER 3: Active Filter
analogue electronics
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2. Chapter Outcomes
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analogue electronics
 Describe the frequency response of basic filters
 Describe the three basic filter response characteristics
 Analyze low-, high- and band-pass filters
 Design active filter

3. Introduction
PASSIVE FILTER ACTIVE FILTER
•RC, RL and RLC circuits •Active components + passive components
•Transistors or op-amps + RC/RL/RLC
•Provides frequency selectivity •Provides voltage gain
•Advantage: simple •Advantage: Loading effect is minimal
-o/p independent of the load
driven
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 Filters are circuits that are capable of passing signals with
certain selected frequencies while rejecting signals with
other frequencies
 2 types of filter

4. Introduction
Types of active filter:
Low-Pass Filter
High-Pass Filter
Bandpass Filter
o Cascaded Low-Pass and High-Pass Filter
o Multiple-Feedback Band-Pass Filter
o State-Variable Filter
o Biquad Filter
Bandstop Filter
o Multiple-Feedback Band-Stop Filter
o State-Variable Band-Stop Filter
The op-amp active filter provides controllable
cutoff frequencies and controllable gain
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5. Frequency Response
 Pass Band: The range of
frequency seen in the
filter output. Has the
same meaning as the
bandwidth (BW) of the
filter
 Stop Band: The range of
frequency blocked by the
filter. These frequency are
not see in the filter
output
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AV (dB)
f (Hz)
f (Hz)
AV (dB)
3dB
Ideal
Practical
AV (dB)
AV (dB)
f (Hz)
f (Hz)
3dB
Ideal
Practical
Pass Band
Stop Band
Transition
Region

Transition region: The
frequency between the pass
band and the stop band

Cut off Frequency : The
highest or lowest frequency
that is allowed to pass or
determines the pass band.
The cutoff frequency of real
filter is the -3 dB frequency
of that filter

6. Decibel (dB)
 This is a relative power unit. At audio frequencies a change
of one decibel (abbreviated dB) is just detectable as a change
in loudness under ideal conditions.
 For a given power ratio the decibel change is calculated as:
dB = 10 log P2/P1
 If we used voltage or current ratios instead then it becomes:
dB = 10 log (V2
2
/ R)/(V1
2
/ R)
= 20 log V2/V1
= 20 log AV
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7. Basic Diagram of An Filter
 Inverting or non-inverting??
 Which part is the filter?
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_
+Vin
R1
R2
Vo
+V
-V
RC Circuit
Gain
Frequency
1
2
1V
R
A
R
= +

8. Cut-Off Frequency
 In electronics, cut-off frequency (fc) is the frequency at
which the gain on a frequency-response plot is 3 dB less
than at mid-band gain
 The cutoff frequency often called 3-dB frequencies
 Also called the knee frequency, due to a frequency
response curve's physical appearance.
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AV(dB)
-3.012dB
fc=1Hz
Slope =20dB/decade
f=1Hz,
Av(dB)=-3dB
f=10Hz,
Av(dB)=-20dB
f=100Hz,
Av(dB)=-40dB

10. 3dB
 At -3dB, the output power is half of the output power at
pass band
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V@passband
V@passband
V@passband
20 log A -20 log 2
20 log A -10log 2
20 log A 3.012
=
=
= −
2
@
outP
out passband
V
P
R
=
2 2
@
@ 3
2 2
out passband outP outRMS
out dB
P V V
P
R R
− = = =
@ 3
2
outP
o dB outRMS
V
V V− = =
@
@ 3
2 2
V passbandoutP
V dB
in
AV
A
V
− = =

11. Filter Response Characteristics
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The Butterworth characteristic
response is very flat. The roll-off rate
-20dB per decade. This is the most
widely used.
The Chebyshev characteristic
response provides a roll-off rate
greater than -20dB but has ripples in
the passband and a non-linear phase
response.
The Bessel characteristic response
exhibits the most linear phase response
making it ideal for filtering pulse
waveforms with distortion.

12.  The damping factor of an active filter determines the type
of response characteristic
 The output signal is fed back into the filter circuit with
negative feedback determined by the combination of R1
and R2
 The negative feedback ultimately determines the type of
filter response is produced. The equation below defines
the damping factor
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DF = 2 – R1/R2

13.  List of the roll-off rates, damping factors, and feedback
resistors for up to six order Butterworth filters
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Back

14. 1. Low Pass Filter
 Low-pass filter passes low
frequencies well, but attenuates
(or reduces) frequencies higher
than the cutoff frequency
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a) 1st
Order
R1
R2
_
+Vin
+V
-V
RA CA
Vo
AV (dB)
AV(max)
AV(max) - 3
fc 10fc100fc
AV(max) - 20
AV(max) - 40
-20dB/dec
f (Hz)
 The capacitor CA in
conjunction with the resistor
RA provides the filtering action,
while the op-amp with its
associated resistor R1 and R2
function as non-inverting
amplifier and provides the
needed gain
BW

15. Analysis
 It is low pass filter if
No s at numerator
V+
= VC
 It is 1st
order system if
The highest order is s1
Only one pair RC at +input of op-
amp
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Vo = 1+ V+
R1
R2
_
+Vin
+V
-V
RA CA
Vo
V+
= Vi
1
sCA
1
sCA
+RA
R1
R2
Vo = 1+
R1
R2
Vi
V+
= Vi
1
sRACA+1
1
V+
= VcA
AV = = 1+
R1
R2Vi
1Vo
sRACA+1
sRACA+1

16. Analysis
 At 0 < f < fc, low pass filter will pass
the frequencies because XCA=∞, thus,
V+
=VCA =Vi
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analogue electronics
AV (dB)
AV(max)
AV(max) - 3
fc 10fc100fc
AV(max) - 20
AV(max) - 40
-20dB/dec
f (Hz)
AV(max) = 1+
R1
R2
 At f = fc, the gain is
0.707AV(max) or in dB AVdB(max)-3.
The magnitude of the
capacitive reactance, XCA
equals the resistance of the
resistor, RA
 At f > fc, low pass filter will
attenuate the frequencies at
roll-off of -20dB/decade
because XCA is reducing to 0.
When XCA=0,
V+
=VCA=0
A = 0
1
2πfcCA
= RA
fc = 1
2πRACA

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b) 2nd
Order (Sallen-Key)
 One of the most common configurations for 2nd
order filter
 There are two pairs of RC that provide roll-off of -40dB/dec
 The capacitor CA provides feedback for shaping the response
near the edge of the pass band (-3dB not -6dB)
Vo
R1
R2
_
+
Vin
+V
-V
RA
CA
RB
CB
1
2
1
22
1
1
1 1
1
A B A Bo
in
B B A B A A
A B A B A B A B
R
R R R C CV
V R
R C R C R C
R
s s
R R C C R R C C
 
+ ÷
 =
   
+ + − + ÷ ÷ ÷ ÷   + +

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R1=10kΩ, R2=17.2k Ω, RA=RB=3.18kΩ, CA=CB=0.01µF

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AV (dB)
AV(max)
AV(max) - 3
fc 10fc100fc
AV(max) - 40
AV(max) - 80
-40dB/dec
f (Hz)
BW
AV(max) = 1+
R1
R2
1
2π RARBCACB
fc = fAfB
1
2πRACA
1
2πRBCB
•=
=

20. Higher Order Low Pass Filter
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R1
R2
_
+
Vin
+V
-V
RA
CA
RB
CB
R3
R4
_
+
+V
-V
RC CC
Vo
R1
R2
_
+
Vin
+V
-V
RA
CA
RB
CB
Vo
R3
R4
_
+
+V
-V
RC
CC
RD
CD
Table for Butterworth response
3rd
order system
4th
order system

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• By adding more RC networks the roll-off can be made steeper