Measurement and Instrumentation
ACTIVE FILTERS and its
applications
Dr. Tayab Din Memon
Assistant Professor
Dept of Electronic Engineering, MUET, Jamshoro.
Objectives
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Discuss about the Active filters,
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Filter Approximations
Order of Filter
Categories of Filter Responses
Active Lowpass Filter
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Single order highpass filter, Second order highpass filter
Unity gain and variable gain highpass filter.
K Values Table & its discussion
Bandpass Filter
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Single Order Lowpass Filter & Double Order Lowpass Filter
Unity Gain and Variable Gain
Active Highpass Filter
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its use and applications.
Types of filters
Important terminologies of Active Filters.
Order of Filter
Wideband & Narrowband
Band stop Filter
Session-II Lab Work
Design and simulation of circuits.
Filters: An Introduction
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Filters can be defined as:
filters are electrical networks that have been
designed to pass alternating currents generated at
only certain frequencies and to block or attenuate all
others.
Filters have a wide use in electrical and electronic
engineering and are vital elements in many
telecommunications and instrumentation systems
where the separation of wanted from unwanted
signals – including noise – is essential to their
success.
Filters Applications
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Filter circuits are used in a wide variety of applications.
In the field of telecommunication, band-pass filters are used in the
audio frequency range (0 kHz to 20 kHz) for modems and speech
processing.
High-frequency band-pass filters (several hundred MHz) are used for
channel selection in telephone central offices.
Data acquisition systems usually require anti-aliasing low-pass filters as
well as low-pass noise filters in their preceding signal conditioning
stages.
System power supplies often use band-rejection filters to suppress the
60-Hz line frequency and high frequency transients.
Types of Filters
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Passive Filters
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Incorporates only passive components like; capacitors, resistors,
inductors.
Passive filters are difficult to design.
Further inductors are difficult to handle. Not only are they
expensive, bulky and heavy; they are prone to magnetic field
radiation unless expensive shielding is used to prevent unwanted
coupling
Used for high frequencies (>MHz)
Active Filters
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Along with passive components capacitors and resistors,
Additionally it incorporates active components particularly like; opamp.
Due to inductor property at low frequencies, active filters are Used
at low frequencies.
It overcomes the inductor problems in passive filter.
Important terminologies in Filters
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Frequency Response of Filter is the graph of
its voltage gain versus frequency.
Passband: Those frequencies that are passed
by a filter without attenuation.
Stopband: Those frequencies that are
rejected by filter after cutoff.
Transition: The roll-off region between
passband and the stopband.
Attenuation: Attenuation refers to the loss of
signal.
Order of a Filter
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The order of an active filter depends on
the number of RC circuits called poles it
contains.
If an active filter contains 8 RC circuits,
n=8.
In active filters simple way to determine
the order is to identify the number of
capacitors in the circuit.
n= #of capacitors.
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What is the advantage of increasing
Order?
Answer!!
Filter Approximation
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Butterworth Approximation
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Chebyshev Approximation
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The butterworth approximation is sometimes called the maximum flat
approximation.
Roll off =20n dB/decade
An equivalent roll of in terms of octaves is: Roll-off = 6n dB/octave
In Chebyshav approximation ripples are present in passband, but its
roll off rate is greater than 20dB/decade for a single pole.
The number of ripples in the passband of a Chebyshav filter are equals
to the half of the filter order:
#Ripples = n/2
Inverse Chebyshav Approximation
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In applications in which flat response is required as well as the fast
roll-off, a designer may choose Inverse Chebyshav.
It has flat passband and rippled stopband.
Inverse Chebyshav is not a Monotonic (No Stop Band ripples)
Approximation.
Filter approximation
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Elliptic Approximation
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If rippled passband and rippled stopband are accepted
designer must choose elliptic approximation.
Its major advantage is its highest roll-off rate in transition
region.
Bessel Approximation
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Bessel approximation has a flat passband and a monotonic
stopband similar to those of the Butterworth approximation.
For the same filter order, however, the roll-off in the
transition region is much less with a Bessel filter than with a
Butterworth filter.
The major advantage of the Bessel Filter is that it produces
the least distortion of non-sinusoidal signals.
No phase change.
Butterworth Approximation
Chebyshav Approximation
Elliptic Approximation
Bessel Approximation
Damping Factor
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Peaking action at resonant frequency is to
use the damping factor defined as:
 
1
Q
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For Q=10, the damping factor is 0.1.
Categories of filters
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Lowpass
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Highpass
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It passes all frequencies after cutoff.
Bandpass
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It passes frequencies before cutoff.
It passes all the frequencies in a specific band.
Bandstop
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It rejects all the frequencies of a specific band.
Response Curves of All types of Filters
Fig. Lowpass Filter
Fig. Highpass Filter
Filter Response Curves of all types
Fig. Bandpass Filter
Fig. Bandstop Filter
First Order Stage
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First order stages can only be
implemented using Butterworth
response.
Why?
Active Lowpass Filter (unity Gain)
R1
+
AC
C1
Gain is Av  1
Cutoff frequency fc 
A
Fig. Single pole lowpass
filter.
1
1   f 
 fc 
2
1
2R 1C1
Active Lowpass Filter (Variable Gain)
Rf
Ri
R1
+
AC
C1
Gain is Av  1 
Cutoff frequency fc 
A
Fig. Single pole lowpass
filter.
Rf
Ri
1
1   f 
 fc 
2
1
2R 1C1
Active Lowpass Inverting with variable gain.
C1
Rf
Ri
+
AC
Gain is Av  
Rf
Ri
Cutoff frequency fc 
A
Fig. Active Lowpass Inverting Circuit.
1
1   f 
 fc 
2
1
2R2C1
Single pole Highpass unity gain Filter
C1
+
AC
Gain is Av  1
Cutoff frequency fc 
R1
A
Fig. Single Pole Highpass
Filter.
1
1   fc 
 f
2
1
2R1C1
Single pole Highpass with variable gain
Rf
Ri
C1
+
Gain is Av  1 
AC
R1
Rf
Ri
Cutoff frequency fc 
A
1
1   fc 
 f
2
1
2R1C 1
Sallen Key Approach (VCVS)
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Second order or 2-pole stages are the most
common because they are easy to build and
analyze.
Higher order filters are usually made by
cascading second order stages. Each secondorder stage has a resonant frequency and Q
to determined how much peaking occurs.
Sallen Key approach is also known as VCVS
(Voltage Controlled Voltage Source) because
the opamp is used as a voltage-controlled
voltage source.
VCVS Double Pole Lowpass Filter (Butterworth
and Bessel)
C2
R
R
+
-
AC
C1
Gain is Av  1
Cutoff frequency fp 
Q  0.5
C2
,A 
C1
1
2R C1C 2
1
 fc 4
1 f
Butterwort :
Q  0.707, Kc  1
Bessel : Q  0.577, Kc  0.786
Double Pole Lowpass Peaked Response
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Peaked Response can be calculated using following
three frequencies:
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f0=K0fp
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fc=Kcfp
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f3dB=K3fp
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f0 is the resonant frequency where peaking appears,
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fc is the edge frequency, &
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f3dB is the cutoff frequency.
K values and Ripple depth of Second-Order
Stages (Table 1)
Q
0.577
K0
Kc
K3
Ap(dB)
----
----
1
--
0.707
---
1
1
---
0.75
0.333
0.471
1.057
0.054
0.8
0.476
0.661
1.115
0.213
0.9
0.620
0.874
1.206
0.688
1
0.78
1
1.277
1.25
2
0.935
1.322
1.485
6.3
3
0.972
1.374
1.532
9.66
4
0.984
1.391
1.537
12.1
5
0.99
1.4
1.543
14
10
0.998
1.410
1.551
20
100
1
1.414
1.554
40
Discussion of the Table
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Table gives us K and Ap values versus
Q.
The Bessel and Butterworth have not
noticeable frequency, So K0 and Ap
values does not apply.
When Q is greater than 0.707, a
noticeable resonant frequency appears
and all K an Ap values are present.
Equal Component Values Second Order
Lowpass Filter
C
R
R
+
-
AC
Rf
C
R1
Av  1 
Rf
R1
1
Q
3  Av
1
fc 
2RC
VCVS Second Order Unity Gain High Pass
Filters
R2
C
C
+
-
AC
R1
Av  1
Q  0 .5
fp 
R1
R2
1
2C R1R 2
VCVS Highpass Filter with Voltage gain greater
than unity.
R
C
C
+
-
AC
Rf
R
R1
Av  1 
Rf
R1
1
3  AV
1
fp 
2CR
Q
Bandpass Filter
A Bandpass filter has a center frequency and a
bandwidth.
BW  f 2  f 1
f0 
Q 
f1 f
2
f0
BW
When Q is less than 1, the filter has a wideband
response. In this case bandpass filter is designed by
cascading lowpass and highpass filter.
When Q is greater than 1, the filter has a narrowband
response and a different approach is used.
Solution!
Vin
HIGH PASS
fc=300Hz
LOWPASS
fc=3.3KHz
Fig. Wideband Filters uses cascade
of lowpass and highpass stages.
Vout
Narrowband Filters
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When Q is greater than 1, we use Multiple Feedback (MFB) filter
shown in fig.
The input signal is at Inverting terminal.
Two feedbacks one from capacitor & resistor.
Operation: At low frequencies capacitor appears to be open.
Therefore, the input signal cannot reach the opamp, and the
output is zero.
At high frequencies, the capacitors appear to be shorted. In this
case, the voltage gain is zero because feedback capacitor has
zero impedance.
Between the low and high extremes in frequency, there is a
band of frequencies where the circuit acts like an inverting
amplifier.
Narrowband Filters (cont….)
Av 
-R 2
2 R1
The Q of t he circuit
Q  0 .5
is:
R2
R1
which is e quivalent
Q  0 .707
to:
-A v
For ins tan ce, if A
Q  0 .707
v
 -100
100  7 .07
A v is direct ly proport ional to Q .
The center
f0 
frequency
1
2 πC
R1 R 2
is:
C1  C2
Narrowband Filter Typical Circuit
Notch Filter
Av 
f0 
Q 
R2
1
R1
1
2 RC
0 .5
2  Av
VCVS Sallen Key Band stop Filter circuit
All pass filters
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All pass filter is widely used in industry.
This is called phase filter.
It shifts the phase of the output signal
without changing the magnitude.
Time delay filter.
Summary
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Note that in Inverting and Non-Inverting
Opamp modes, feedback is – ve.
The only difference is that; input is
applied at different terminals.
Output is 1800 out of phase with input in
Inverting whereas in Non-Inverting
Output is in phase with Input.