EMT212 – Analog Electronic II
Chapter 5
Active Filter
By
En. Rosemizi Bin Abd Rahim
Introduction
Filters are circuits that are capable of passing signals
within a band of frequencies while rejecting or blocking
signals of frequencies outside this band. This property
of filters is also called “frequency selectivity”.
Filter circuits built using components such as resistors,
capacitors and inductors only are known as passive
filters.
Active filters employ transistors or op-amps in addition
to resistors and capacitors.
Advantages of Active Filters over
Passive Filters
1. Active filters can be designed to provide required gain,
and hence no attenuation as in the case of passive filters
2. No loading problem, because of high input resistance
and low output resistance of op-amp.
3. Active Filters are cost effective as a wide variety of
economical op-amps are available.
Applications
Active filters are mainly used in communication and signal
processing circuits.
They are also employed in a wide range of applications
such as entertainment, medical electronics, etc.
Active Filters
There are 4 basic categories of active filters:
1. Low pass filters
2. High pass filters
3. Band pass filters
4. Band reject filters
Each of these filters can be built by using op-amp
as the active element combined with RC, RL or RLC
circuit as the passive elements.
Active Filters
The passband is the range of frequencies that are allowed
to pass through the filter.
The critical frequency, fc is specified at the point where the
response drop -3dB (70.7%) from the passband response.
The stopband is the range of frequencies that have the
most attenuation.
The transition region is the area where the fall-off occur.
Basic Filter Responses
1. Low-pass filter
Allows the frequency from 0Hz to critical frequency.
actual response
Ideal response
The critical frequency can be formula by
1
fc 
2RC
Basic Filter Responses
1. High-Pass filter
Only allowing the frequencies above the critical frequency.
actual response
Ideal response
The critical frequency can be formula by
fc 
1
2RC
Basic Filter Responses
3. Band-pass filter
Allows frequencies between a lower critical frequency (fc1)
and an upper critical frequency (fc2).
Ideal response
actual response
Basic Filter Responses
3. Band-pass filter
Bandwidth, BW = fc2-fc1
center frequency, fo
fo 
f1  f 2
2
Quality factor (Q) is the ratio of center
frequency fo to the BW
Q
fo
BW
The narrower the bandwidth,
the higher the quality factor.
Basic Filter Responses
4. Band-stop filter
Opposite of a band-pass.
Frequencies above and below fc1 and fc2 are passed.
Ideal response
actual response
Animation
A "Group" of waves passing through a Typical Band-Pass Filter
Filter Response Characteristics
Identified by the shape of the response curve
• Passband flatness
• Attenuation of frequency outside the passband
Three types:
1. Butterworth
2. Bessel
3. Chebyshev
Filter Response Characteristics
1. Butterworth Response
•
•
•
Amplitude response is very flat.
The roll-off rate -20 dB per decade.
This is the most widely used.
Filter Response Characteristics
2.
•
•
•
Chebyshev Response
Ripples
The roll-off rate greater than –20 dB
a nonlinear phase response.
Filter Response Characteristics
3.
•
•
Bessel Response
Linear phase response
ideal for filtering pulse waveforms
Filter Response Characteristics
Damping Factor
The damping factor of an active filter determines the type of response
characteristic either Butterworth, Chebyshev, or Bessel.
The output signal is fed back into the filter circuit with negative
feedback determined by the combination of R1 and R2.
Damping factor (DF)
DF  2 
Diagram of an active filter
R1
R2
Filter Response Characteristics
Critical Frequency and Roll-off rate
• Greater roll-off rates can be achieved with more poles.
• Each RC set of filter components represents a pole.
• Cascading of filter circuits also increases the poles which results in
a steeper roll-off.
• Each pole represents a –20 dB/decade increase in roll-off.
First order (one pole) low pass filter
Filter Response Characteristics
The number of filter poles can be increase by cascading
Active Low-Pass Filters
Basic Low-Pass filter circuit
At critical frequency,
Resistance = capacitance
R  Xc
1
R
c C
R
1
2f c C
So, critical frequency ;
1
fc 
2RC
Active Low-Pass Filters
Low Pass Response
Roll-off depends on
number the of poles.
Active Low-Pass Filters
A Single-Pole Filter
Acl  1 
R1
R2
1
fc 
2RC
Active Low-Pass Filters
The Sallen-Key
• second-order (two-pole) filter
• roll-off -40dB per decade
fc 
1
2 RA RB C ACB
For RA=RB=R and
CA=CB=C ;
1
fc 
2RC
Active Low-Pass Filters
Example
• Determine critical frequency
• set the value of R1 for Butterworth response.
• Critical frequency
fc 
1
 7.23kHz
2RC
• Butterworth response
from table 15.1 floyd, page 744
R1/R2 = 0.586
R1  0.586R2
R1  586k
Active Low-Pass Filters
Cascaded LPF – Three pole
• cascade two-pole and single-pole
• roll-off -60dB per decade
Active Low-Pass Filters
Cascaded LPF – Four pole
• cascade two-pole and two-pole
• roll-off -80dB per decade
Active Low-Pass Filters
Example
• Determine the capacitance values required to produce a critical
frequency of 2680 Hz if all resistors in RC low pass circuit is
1.8k
fc 
1
2RC
C
1
 0.033F
2f c R
CA1=CB1=CA2=CB2=0.033µf
Active High-Pass Filters
Basic High-Pass circuit
At critical frequency,
Resistance = capacitance
R  Xc
1
R
c C
R
1
2f c C
So, critical frequency ;
1
fc 
2RC
Active High-Pass Filters
High Pass Response
Roll-off depends on
number the of poles.
Active High-Pass Filters
A Single-Pole Filter
Acl  1 
R1
R2
1
fc 
2RC
Active High-Pass Filters
The Sallen-Key
• second-order (two-pole) filter
• roll-off -40dB per decade
fc 
1
2 RA RB C ACB
Lets RA=RB=R and
CA=CB=C
fc 
1
2RC
Active High-Pass Filters
Cascaded LPF – Six pole
• cascade 3 Sallen-Key two-pole stages
• roll-off -120 dB per decade
Active Band-Pass Filters
A cascaded of a low-pass and high-pass filter.
Active Band-Pass Filters
f c1 
1
2 RA1RB1C A1CB1
fc2 
1
2 RA2 RB 2C A2CB 2
f0 
f c1 f c 2
Active Band-Pass Filters
Multiple-Feedback BPF
• The low-pass circuit consists of R1 and C1.
• The high-pass circuit consists of R2 and C2.
• The feedback paths are through C1 and R2.
center frequency
f0 
1
2 R1 // R3 R2C1C2
Active Band-Pass Filters
State-Variable BPF is widely used for band-pass applications.
• It consists of a summing amplifier and two integrators.
• It has outputs for low-pass, high-pass, and band-pass.
• The center frequency is set by the integrator RC circuits.
• R5 and R6 set the Q (bandwidth).
Active Band-Pass Filters
The band-pass output peaks sharply the center frequency
giving it a high Q.
Active Band-Stop Filters
The BSF is opposite of BPF in that it blocks a specific
band of frequencies.
The multiple-feedback design is similar to a BPF with
exception of the placement of R3 and the addition of R4.
Assignment on Active Filters
Due date : 30th Sept 2005
Refer to Floyd text book
page 766 – 770
Q5, Q10, Q15, Q16, Q19
Quiz on Active Filters
i)
Name the type of circuit. Determine the critical frequency.
ii) Modify the circuit to increase roll-off to -120dB/dec.
iii) Convert the circuit to become a high pass filter.
Filter Response Measurements
Measuring frequency response can be performed with
typical bench-type equipment.
It is a process of setting and measuring frequencies
both outside and inside the known cutoff points in
predetermined steps.
Use the output measurements to plot a graph.
More accurate measurements can be performed with
sweep generators along with an oscilloscope, a
spectrum analyzer, or a scalar analyzer.
Summary
 The bandwidth of a low-pass filter is the same as the
upper critical frequency.
 The bandwidth of a high-pass filter extends from the
lower critical frequency up to the inherent limits of the
circuit.
 The band-pass passes frequencies between the lower
critical frequency and the upper critical frequency.
 A band-stop filter rejects frequencies within the upper
critical frequency and upper critical frequency.
 The Butterworth filter response is very flat and has a
roll-off rate of –20 B.
Summary
 The Chebyshev filter response has ripples and overshoot in
the passband but can have roll-off rates greater than –20 dB.
 The Bessel response exhibits a linear phase characteristic,
and filters with the Bessel response are better for filtering
pulse waveforms.
 A filter pole consists of one RC circuit. Each pole
doubles the roll-off rate.
 The Q of a filter indicates a band-pass filter’s selectivity.
The higher the Q the narrower the bandwidth.
 The damping factor determines the filter response
characteristic.