1. Filters are circuits that pass signals within a specific band of frequencies while rejecting signals outside of that band, known as frequency selectivity. Filters can be passive, using RC, RL, or RLC circuits, or active, using op-amps.
2. Active filters have advantages over passive filters like providing gain without attenuation, high input impedance preventing loading of sources, and low output impedance preventing loading of outputs. They are also easier to adjust and more cost effective.
3. Common types of active filters include low-pass, high-pass, band-pass, and band-stop filters. The number of poles determines the roll-off rate, with each additional pole providing -20dB/decade
Active filters are type of filters which use the operational amplifier ics for their operation and in this slides any one can get more information in little bit of time. so i recommended if any one want to study filters then must read it.
Active filters are type of filters which use the operational amplifier ics for their operation and in this slides any one can get more information in little bit of time. so i recommended if any one want to study filters then must read it.
Salient Features:
The magnitude response is nearly constant(equal to 1) at lower frequencies
There are no ripples in passband and stop band
The maximum gain occurs at Ω=0 and it is H(Ω)=1
The magnitude response is monotonically decreasing
As the order of the filter ‘N’ increases, the response of the filter is more close to the ideal response
Using Chebyshev filter design, there are two sub groups,
Type-I Chebyshev Filter
Type-II Chebyshev Filter
The major difference between butterworth and chebyshev filter is that the poles of butterworth filter lie on the circle while the poles of chebyshev filter lie on ellipse.
In this presentation we discuss about the active filters and mentioned its frequency response along with block diagrams. Also discussed its pros and cons in this presentation.
low pass filters in detail
Low Pass Filters
RC Low Pass Filter
Critical or cutoff frequency
Response curve
Cutoff frequency of RC LPF
RL Low Pass Filter
Cutoff Frequency of RL LPF
Phase Response in Low Pass Filter
Salient Features:
The magnitude response is nearly constant(equal to 1) at lower frequencies
There are no ripples in passband and stop band
The maximum gain occurs at Ω=0 and it is H(Ω)=1
The magnitude response is monotonically decreasing
As the order of the filter ‘N’ increases, the response of the filter is more close to the ideal response
Using Chebyshev filter design, there are two sub groups,
Type-I Chebyshev Filter
Type-II Chebyshev Filter
The major difference between butterworth and chebyshev filter is that the poles of butterworth filter lie on the circle while the poles of chebyshev filter lie on ellipse.
In this presentation we discuss about the active filters and mentioned its frequency response along with block diagrams. Also discussed its pros and cons in this presentation.
low pass filters in detail
Low Pass Filters
RC Low Pass Filter
Critical or cutoff frequency
Response curve
Cutoff frequency of RC LPF
RL Low Pass Filter
Cutoff Frequency of RL LPF
Phase Response in Low Pass Filter
Immunizing Image Classifiers Against Localized Adversary Attacksgerogepatton
This paper addresses the vulnerability of deep learning models, particularly convolutional neural networks
(CNN)s, to adversarial attacks and presents a proactive training technique designed to counter them. We
introduce a novel volumization algorithm, which transforms 2D images into 3D volumetric representations.
When combined with 3D convolution and deep curriculum learning optimization (CLO), itsignificantly improves
the immunity of models against localized universal attacks by up to 40%. We evaluate our proposed approach
using contemporary CNN architectures and the modified Canadian Institute for Advanced Research (CIFAR-10
and CIFAR-100) and ImageNet Large Scale Visual Recognition Challenge (ILSVRC12) datasets, showcasing
accuracy improvements over previous techniques. The results indicate that the combination of the volumetric
input and curriculum learning holds significant promise for mitigating adversarial attacks without necessitating
adversary training.
Forklift Classes Overview by Intella PartsIntella Parts
Discover the different forklift classes and their specific applications. Learn how to choose the right forklift for your needs to ensure safety, efficiency, and compliance in your operations.
For more technical information, visit our website https://intellaparts.com
Overview of the fundamental roles in Hydropower generation and the components involved in wider Electrical Engineering.
This paper presents the design and construction of hydroelectric dams from the hydrologist’s survey of the valley before construction, all aspects and involved disciplines, fluid dynamics, structural engineering, generation and mains frequency regulation to the very transmission of power through the network in the United Kingdom.
Author: Robbie Edward Sayers
Collaborators and co editors: Charlie Sims and Connor Healey.
(C) 2024 Robbie E. Sayers
Water scarcity is the lack of fresh water resources to meet the standard water demand. There are two type of water scarcity. One is physical. The other is economic water scarcity.
Quality defects in TMT Bars, Possible causes and Potential Solutions.PrashantGoswami42
Maintaining high-quality standards in the production of TMT bars is crucial for ensuring structural integrity in construction. Addressing common defects through careful monitoring, standardized processes, and advanced technology can significantly improve the quality of TMT bars. Continuous training and adherence to quality control measures will also play a pivotal role in minimizing these defects.
Explore the innovative world of trenchless pipe repair with our comprehensive guide, "The Benefits and Techniques of Trenchless Pipe Repair." This document delves into the modern methods of repairing underground pipes without the need for extensive excavation, highlighting the numerous advantages and the latest techniques used in the industry.
Learn about the cost savings, reduced environmental impact, and minimal disruption associated with trenchless technology. Discover detailed explanations of popular techniques such as pipe bursting, cured-in-place pipe (CIPP) lining, and directional drilling. Understand how these methods can be applied to various types of infrastructure, from residential plumbing to large-scale municipal systems.
Ideal for homeowners, contractors, engineers, and anyone interested in modern plumbing solutions, this guide provides valuable insights into why trenchless pipe repair is becoming the preferred choice for pipe rehabilitation. Stay informed about the latest advancements and best practices in the field.
Event Management System Vb Net Project Report.pdfKamal Acharya
In present era, the scopes of information technology growing with a very fast .We do not see any are untouched from this industry. The scope of information technology has become wider includes: Business and industry. Household Business, Communication, Education, Entertainment, Science, Medicine, Engineering, Distance Learning, Weather Forecasting. Carrier Searching and so on.
My project named “Event Management System” is software that store and maintained all events coordinated in college. It also helpful to print related reports. My project will help to record the events coordinated by faculties with their Name, Event subject, date & details in an efficient & effective ways.
In my system we have to make a system by which a user can record all events coordinated by a particular faculty. In our proposed system some more featured are added which differs it from the existing system such as security.
Hybrid optimization of pumped hydro system and solar- Engr. Abdul-Azeez.pdffxintegritypublishin
Advancements in technology unveil a myriad of electrical and electronic breakthroughs geared towards efficiently harnessing limited resources to meet human energy demands. The optimization of hybrid solar PV panels and pumped hydro energy supply systems plays a pivotal role in utilizing natural resources effectively. This initiative not only benefits humanity but also fosters environmental sustainability. The study investigated the design optimization of these hybrid systems, focusing on understanding solar radiation patterns, identifying geographical influences on solar radiation, formulating a mathematical model for system optimization, and determining the optimal configuration of PV panels and pumped hydro storage. Through a comparative analysis approach and eight weeks of data collection, the study addressed key research questions related to solar radiation patterns and optimal system design. The findings highlighted regions with heightened solar radiation levels, showcasing substantial potential for power generation and emphasizing the system's efficiency. Optimizing system design significantly boosted power generation, promoted renewable energy utilization, and enhanced energy storage capacity. The study underscored the benefits of optimizing hybrid solar PV panels and pumped hydro energy supply systems for sustainable energy usage. Optimizing the design of solar PV panels and pumped hydro energy supply systems as examined across diverse climatic conditions in a developing country, not only enhances power generation but also improves the integration of renewable energy sources and boosts energy storage capacities, particularly beneficial for less economically prosperous regions. Additionally, the study provides valuable insights for advancing energy research in economically viable areas. Recommendations included conducting site-specific assessments, utilizing advanced modeling tools, implementing regular maintenance protocols, and enhancing communication among system components.
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In today’s fast-changing business environment, it’s extremely important to be able to respond to client needs in the most effective and timely manner. If your customers wish to see your business online and have instant access to your products or services.
Online Grocery Store is an e-commerce website, which retails various grocery products. This project allows viewing various products available enables registered users to purchase desired products instantly using Paytm, UPI payment processor (Instant Pay) and also can place order by using Cash on Delivery (Pay Later) option. This project provides an easy access to Administrators and Managers to view orders placed using Pay Later and Instant Pay options.
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About
Indigenized remote control interface card suitable for MAFI system CCR equipment. Compatible for IDM8000 CCR. Backplane mounted serial and TCP/Ethernet communication module for CCR remote access. IDM 8000 CCR remote control on serial and TCP protocol.
• Remote control: Parallel or serial interface.
• Compatible with MAFI CCR system.
• Compatible with IDM8000 CCR.
• Compatible with Backplane mount serial communication.
• Compatible with commercial and Defence aviation CCR system.
• Remote control system for accessing CCR and allied system over serial or TCP.
• Indigenized local Support/presence in India.
• Easy in configuration using DIP switches.
Technical Specifications
Indigenized remote control interface card suitable for MAFI system CCR equipment. Compatible for IDM8000 CCR. Backplane mounted serial and TCP/Ethernet communication module for CCR remote access. IDM 8000 CCR remote control on serial and TCP protocol.
Key Features
Indigenized remote control interface card suitable for MAFI system CCR equipment. Compatible for IDM8000 CCR. Backplane mounted serial and TCP/Ethernet communication module for CCR remote access. IDM 8000 CCR remote control on serial and TCP protocol.
• Remote control: Parallel or serial interface
• Compatible with MAFI CCR system
• Copatiable with IDM8000 CCR
• Compatible with Backplane mount serial communication.
• Compatible with commercial and Defence aviation CCR system.
• Remote control system for accessing CCR and allied system over serial or TCP.
• Indigenized local Support/presence in India.
Application
• Remote control: Parallel or serial interface.
• Compatible with MAFI CCR system.
• Compatible with IDM8000 CCR.
• Compatible with Backplane mount serial communication.
• Compatible with commercial and Defence aviation CCR system.
• Remote control system for accessing CCR and allied system over serial or TCP.
• Indigenized local Support/presence in India.
• Easy in configuration using DIP switches.
2. 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 can be passive or active filter.
Passive filters: The circuits built using RC, RL, or RLC circuits.
Active filters : The circuits that employ one or more
op-amps in the design an addition to
resistors and capacitors
3. Passive elements : Inductor
BIG PROBLEM!
High accuracy (1% or 2%), small physical size, or large
inductance values are required ??
Standard values of inductors are not very closely spaced
Difficult to find an off-the-shelf inductor within 10 percent
of any arbitrary value .
Adjustable inductors are used.
Tuning such inductors to the required values is time-
consuming and expensive for larger quantities of filters.
Inductors are often prohibitively expensive.
4. Active Filter
No inductors
Made up of op-amps, resistors and capacitors
Provides virtually any arbitrary gain.
Generally easier to design.
High input impedance prevents excessive loading of the
driving source .
Low output impedance prevents the filter from being
affected by the load
At high frequencies is limited by the gain-bandwidth of
the op-amps
Easy to adjust over a wide frequency range without
altering the desired response
5. Advantages of Active Filters over Passive Filters
Active filters can be designed to provide required gain,
and hence no attenuation as in the case of passive filters
No loading problem, because of high input resistance
and low output resistance of op-amp.
Active Filters are cost effective as a wide variety of
economical op-amps are available.
6. 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.
7. Active Filters
1. Low-pass filters
2. High-pass filters
3. Band-pass filters
4. Band-reject filters
5. All-pass 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.
There are 4 basic categories of active filters:
8. Actual response
Vo
A low-pass filter is a filter that passes frequencies from 0Hz to
critical frequency, fh and significantly attenuates all other frequencies.
Ideal response
Ideally, the response drops abruptly at the critical frequency, fH
roll-off rate
9. Stopband is the range of frequencies that have the most attenuation.
Critical frequency, fc, (also called the cutoff frequency) defines the
end of the passband and normally specified at the point where the
response drops – 3 dB (70.7%) from the passband response.
Passband of a filter is the
range of frequencies that are
allowed to pass through the
filter with minimum
attenuation (usually defined
as less than -3 dB of
attenuation).
Transition region shows the
area where the fall-off occurs.
roll-off rate
10. At low frequencies, XC is very high and the capacitor circuit
can be considered as open circuit. Under this condition, Vo =
Vin or AV = 1 (unity).
At very high frequencies, XC is very low and the Vo is small as
compared with Vin. Hence the gain falls and drops off gradually
as the frequency is increased.
Vo
11. The bandwidth of an ideal low-pass filter is equal to fc:
cfBW
The critical frequency of a low-pass RC filter occurs when
XC = R and can be calculated using the formula below:
RC
fc
2
1
12. A high-pass filter is a filter that significantly attenuates or rejects
all frequencies below fL and passes all frequencies above fL.
The passband of a high-pass filter is all frequencies above the
critical frequency.
Vo
Actual response Ideal response
Ideally, the response rises abruptly at the critical frequency, fL
13. The critical frequency of a high-pass RC filter occurs when
XC = R and can be calculated using the formula below:
RC
fc
2
1
14. A band-pass filter passes all signals lying within a band
between a lower-frequency limit and upper-frequency limit
and essentially rejects all other frequencies that are outside
this specified band.
Actual response Ideal response
15. The bandwidth (BW) is defined as the difference between
the upper critical frequency (fc2) and the lower critical
frequency (fc1).
12 cc ffBW
16. 21 cco fff
The frequency about which the pass band is centered is called
the center frequency, fo and defined as the geometric mean of
the critical frequencies.
17. The quality factor (Q) of a band-pass filter is the ratio of
the center frequency to the bandwidth.
BW
f
Q o
The quality factor (Q) can also be expressed in terms of the
damping factor (DF) of the filter as :
DF
Q
1
The higher value of Q, the narrower the bandwidth and the
better the selectivity for a given value of fo.
(Q>10) as a narrow-band or (Q<10) as a wide-band
18. Band-stop filter is a filter
which its operation is opposite to
that of the band-pass filter
because the frequencies within
the bandwidth are rejected, and
the frequencies above fc1 and fc2
are passed.
Actual response For the band-stop filter,
the bandwidth is a band of
frequencies between the 3
dB points, just as in the
case of the band-pass filter
response.
Ideal response
19. There are 3 characteristics of filter response :
i) Butterworth characteristic
ii) Chebyshev characteristic
iii) Bessel characteristic.
Each of the characteristics is identified by the shape of the response
curve
Comparative plots of three types
of filter response characteristics.
20. The damping factor (DF) of an active filter determines which
response characteristic the filter exhibits.
This active filter consists of
an amplifier, a negative
feedback circuit and RC circuit.
The amplifier and feedback
are connected in a non-inverting
configuration.
DF is determined by the
negative feedback and defined
as :
2
1
2
R
R
DF General diagram of active filter
21. The value of DF required to produce a desired response
characteristics depends on order (number of poles) of the filter.
A pole (single pole) is simply one resistor and one capacitor.
The more poles filter has, the faster its roll-off rate
22. The critical frequency, fc is determined by the values of R
and C in the frequency-selective RC circuit.
Each RC set of filter components represents a pole.
Greater roll-off rates can be achieved with more poles.
Each pole represents a -20dB/decade increase in roll-off.
One-pole (first-order) low-pass filter.
23. For a single-pole (first-order) filter, the critical frequency is :
RC
fc
2
1
The above formula can be used for both low-pass and high-
pass filters.
24. The number of poles determines the roll-off rate of the filter. For
example, a Butterworth response produces -20dB/decade/pole.
This means that:
One-pole (first-order) filter has a roll-off of -20 dB/decade
Two-pole (second-order) filter has a roll-off of -40 dB/decade
Three-pole (third-order) filter has a roll-off of -60 dB/decade
25. The number of filter poles can be increased by cascading.
To obtain a filter with three poles, cascade a two-pole with
one-pole filters.
Three-pole (third-order) low-pass filter.
26. Advantages of active filters over passive filters (R, L, and C
elements only):
1. By containing the op-amp, active filters can be designed to
provide required gain, and hence no signal attenuation
as the signal passes through the filter.
2. No loading problem, due to the high input impedance of
the op-amp prevents excessive loading of the driving
source, and the low output impedance of the op-amp
prevents the filter from being affected by the load that it is
driving.
3. Easy to adjust over a wide frequency range without
altering the desired response.
27. RC
fc
2
1
cXR
Figure below shows the basic Low-Pass filter circuit
Cf
R
c2
1
C
R
c
1
At critical frequency,
Resistance = Capacitance
So, critical frequency ;
29. The op-amp in single-pole filter is connected as a
noninverting amplifier with the closed-loop voltage gain in the
passband is set by the values of R1 and R2 :
1
2
1
)(
R
R
A NIcl
The critical frequency of the single-pole filter is :
RC
fc
2
1
30. Ch7 Operational Amplifiers and Op Amp Circuits
7.3 Active Filter
Low-Pass Filter
2
)(31
1
)(
)(
)(
RCjRCj
A
jV
jV
jA VF
i
O
Second-order (two-pole) Filter
VA
-20dB/decade
1
1
R
Rf
RC
f
2
1
0
0
-40dB/decade
0
1
1 fR
V V
R
1
1
1
1 1
/ /
i
f
V
R j c
R
R R
j c j c
31. Ch7 Operational Amplifiers and Op Amp Circuits
fRR
R
VV
3
3
7.3 Active Filter
Low-Pass Filter
Voltage-controlled voltage
source
(VCVS) filter A
For simplicity, RRR 21 CCC 21
0
2
0
2
1
)(1
)()3(1
f
f
Q
j
f
f
A
RCjRCjA
A
V
V
A
f
f
f
i
o
3
1
3
1
R
R
A
A
Q
f
f
f
32. f
f
o AV
R
R
VV
3
1
fRR
R
VV
3
3
7.3 Active Filter
Low-Pass Filter
Voltage-controlled voltage
source
(VCVS) filter A
For simplicity, RRR 21
CCC 21
fo AVVV
21
Ch7 Operational Amplifiers and Op Amp Circuits
cj
R
cj
R
cj
VV
cj
R
cj
cj
RR
cj
cj
RR
VV
1
//
1
1
1
1
1
//
1
1
//
12
01
f
f
o AV
R
R
VV
3
1
Using super position:
34. Sallen-Key is one of the most common configurations for a
second order (two-pole) filter.
Basic Sallen-Key low-pass filter.
There are two low-pass
RC circuits that provide a
roll-off of -40 dB/decade
above fc (assuming a
Butterworth characteristics).
One RC circuit consists of
RA and CA, and the second
circuit consists of RB and CB.
35. The critical frequency for the Sallen-Key filter is :
BABA
c
CCRR
f
2
1
For RA = RB = R and CA = CB = C, thus the critical frequency :
RC
fc
2
1
36. 21 586.0 RR
kR 5861
• Determine critical frequency
• Set the value of R1 for Butterworth response by giving
that Butterworth response for second order is 0.586
kHz
RC
fc 23.7
2
1
• Critical frequency
• Butterworth response given
R1/R2 = 0.586
37. A three-pole filter is required to provide a roll-off rate of -60
dB/decade. This is done by cascading a two-pole Sallen-Key low-
pass filter and a single-pole low-pass filter.
Cascaded low-pass filter: third-order configuration.
38. Cascaded low-pass filter: fourth-order configuration.
A four-pole filter is required to provide a roll-off rate of -80
dB/decade. This is done by cascading a two-pole Sallen-Key low-
pass filter and a two-pole Sallen-Key low-pass filter.
39. RC
fc
2
1
• Both stages must have the same fc. Assume equal-value of capacitor
F
Rf
C
c
033.0
2
1
CA1=CB1=CA2=CB2=0.033µf
• Determine the capacitance values required to produce a critical
frequency of 2680 Hz if all resistors in RC low pass circuit is
1.8k
40. RC
fc
2
1
cXR
Figure below shows the basic High-Pass filter circuit :
Cf
R
c2
1
C
R
c
1
At critical frequency,
Resistance = Capacitance
So, critical frequency ;
41. In high-pass filters, the roles of the capacitor and resistor are
reversed in the RC circuits as shown from Figure (a). The negative
feedback circuit is the same as for the low-pass filters.
Figure (b) shows a high-pass active filter with a -20dB/decade roll-off
Single-pole active high-pass filter and response curve.
42. The op-amp in single-pole filter is connected as a
noninverting amplifier with the closed-loop voltage gain in the
passband is set by the values of R1 and R2 :
1
2
1
)(
R
R
A NIcl
The critical frequency of the single-pole filter is :
RC
fc
2
1
43. Components RA, CA, RB, and CB form the second order (two-
pole) frequency-selective circuit.
The position of the resistors and capacitors in the frequency-
selective circuit are opposite in low pass configuration.
The response
characteristics can be
optimized by proper
selection of the feedback
resistors, R1 and R2.
Basic Sallen-Key high-pass filter.
There are two high-pass
RC circuits that provide a
roll-off of -40 dB/decade
above fc
44. The critical frequency for the Sallen-Key filter is :
BABA
c
CCRR
f
2
1
For RA = RB = R and CA = CB = C, thus the critical frequency :
RC
fc
2
1
45. As with the low-pass filter, first- and second-order high-pass
filters can be cascaded to provide three or more poles and thereby
create faster roll-off rates.
A six-pole high-pass filter consisting of three Sallen-Key two-pole
stages with the roll-off rate of -120 dB/decade.
Sixth-order high-pass filter
46. R A 1
R B 1
R A 2 R B 2
C A 1
C B 1
C A 2
C B 2
R 1
R 2
R 3
R 4
V in
V out
Two-pole high-pass Two-pole low-pass
Band-pass filter is formed by cascading a two-pole high-pass and
two pole low-pass filter.
Each of the filters shown is Sallen-Key Butterworth configuration,
so that the roll-off rate are -40dB/decade.
47. A v (dB)
0
3
Low-pass response High-pass response
f c 1 f c 2f o
f
The lower frequency fc1 of the passband is the critical frequency
of the high-pass filter.
The upper frequency fc2 of the passband is the critical frequency
of the low-pass filter.
48. 210 cc fff
1111
1
2
1
BABA
c
CCRR
f
2222
2
2
1
BABA
c
CCRR
f
The following formulas express the three frequencies of the
band-pass filter.
If equal-value components are used in implementing each filter,
RC
fc
2
1
49. R1
R2
R3
C1
C2
Vin
Vout
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;
21231
0
//2
1
CCRRR
f
50. The maximum gain, Ao occurs at the center frequency.
1
2
2R
R
Ao
321
31
0
2
1
RRR
RR
C
f
ooCAf
Q
R
2
1
By making C1 = C2 =C, yields
The resistor values can be found by using following formula
Cf
Q
R
o
2
)2(2 23
oo AQCf
Q
R
51. Ref:080222HKN EE3110 Active Filter (Part 1) 51
Band-Stop (Notch) Filter
The notch filter is designed to block all frequencies that fall within its
bandwidth. The circuit is made up of a high pass filter, a low-pass filter
and a summing amplifier. The summing amplifier will have an output
that is equal to the sum of the filter output voltages.
f1
f2
vin vout
Low pass
filter
High pass
filter
Summing
amplifier
-3dB{
f
f2
f1
Av(dB)
low-pass high-pass
Block diagram Frequency response
52. A parallel op amp
bandreject filter
(a) The block diagram
(b) The circuit
Band reject Filters
53. R 1
R 2
R 3
R 4
C 1
C 2
Vin
Vout
The configuration is similar to the band-pass version BUT R3
has been moved and R4 has been added.
The BSF is opposite of BPF in that it blocks a specific band of
frequencies
54. 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.
55. 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.
56. 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
The Chebyshev filter response has ripples and
overshoot in the passband but can have roll-
off rates greater than –20 dB
57. 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.
60. Standard Transfer Functions Butterworth
Flat Pass-band.
20n dB per decade roll-off.
Chebyshev
Pass-band ripple.
Sharper cut-off than Butterworth.
Elliptic
Pass-band and stop-band ripple.
Even sharper cut-off.
Bessel
Linear phase response – i.e. no signal distortion in pass-band.
61. Ch7 Operational Amplifiers and Op Amp Circuits
7.3 Active Filter
Basic Filter Responses
)(
)(
)(
sv
sv
sA
i
O
voltage gain
)()(
)(
)(
)(
jjA
jV
jV
jA
i
o
jS
Basic Filter Responses
bandwidth
cutoff frequency
Transition region
stopband region
Low-Pass Filter
Filter .. Vo(t)Vi(t)
62. Ch7 Operational Amplifiers and Op Amp Circuits
7.3 Active Filter
Low-Pass Filter
2
0
0
0
1
1
1
1
1
/1
j
j
cj
R
cj
V
V
A
i
O
450
0
1
tg
)
1
(
RC
O
63. Ch7 Operational Amplifiers and Op Amp Circuits
7.3 Active Filter
High-Pass Filter
o
i
O
j
Rcjcj
R
R
V
V
A
1
1
1
1
1
1
64. Ch7 Operational Amplifiers and Op Amp Circuits
7.3 Active Filter
Advantages of Filter
L
L
L
L
L
L
iL
Li
cRj
R
R
cRj
R
cj
R
R
cj
R
VR
cj
R
cj
RV
A
1
1
1
1
)//
1
(
)
1
//(
1
1
)1)((
RR
cRjR
RR
R
L
L
L
L
'
1'1
)/(
O
v
L
LL
j
A
cRj
RRR
)( LLV RRRA
CRL
O
'
1
'where
RL
1|| max
A
65. Ch7 Operational Amplifiers and Op Amp Circuits
7.3 Active Filter
High-Pass Filter
H
SRC
SRC
L A
SRC
RCj
A
1
1
1
1
1
1
• Transfer functions:
• Circuit: R↔C
• Frequency domain
66. Ch7 Operational Amplifiers and Op Amp Circuits
7.3 Active Filter
Band-Pass Filter
Low-Pass High-
Pass
iV
oV
A
Af AfAf
1
ωL ωH ωωH ω
1
A
ωL ω
A
Lower-frequency Upper-frequency
fA
A
fA
A
fA
A
67. Ch7 Operational Amplifiers and Op Amp Circuits
7.3 Active Filter
Band-Stop Filter
A A
Af
ωh ωL ω ωh ωL ω
AfAf
A
1
Low-Pass
High-
Pass
iV
oV
fA
A
fA
A
fA
A
68. Ch7 Operational Amplifiers and Op Amp Circuits
7.3 Active Filter
Example 2 For the circuit shown, show that what it is filter?
(a)
1// R
v
ZR
v i
Cf
O
o
VF
f
f
f
fCf
i
o
j
A
cRjR
R
cj
R
cj
R
R
R
ZR
V
V
A
1
1
1
1
1
1
//
1
11
The Inverting First-order Low-Pass Filter.
69. Ch7 Operational Amplifiers and Op Amp Circuits
7.3 Active Filter
Example 2 For the circuit shown, show that what it is filter?
(b)
C
i
f
o
ZR
v
R
v
1
o
VF
f
f
i
C
f
i
i
o
j
A
CRjR
R
cj
R
R
V
ZR
R
V
V
V
A
1
1
/11
1
1
1
11
1
1
The Inverting First-order High-Pass Filter.
70. Ch7 Operational Amplifiers and Op Amp Circuits
7.3 Active Filter
Example 2 For the circuit shown, show that what it is filter?
(c)
The Non-Inverting Band-Stop Filter(Second-order).
71. Ch7 Operational Amplifiers and Op Amp Circuits
7.3 Active Filter
Example 2 For the circuit shown, show that what it is filter?
The Inverting Band-Pass Filter.
(Second-order)
The Inverting High-Pass Filter.
(Second-order)
72. Filter response is characterized by
flat amplitude response in the
passband.
Provides a roll-off rate of -20
dB/decade/pole.
Filters with the Butterworth
response are normally used when
all frequencies in the passband
must have the same gain.
73. Filter response is characterized
by overshoot or ripples in the
passband.
Provides a roll-off rate greater
than -20 dB/decade/pole.
Filters with the Chebyshev
response can be implemented
with fewer poles and less
complex circuitry for a given
roll-off rate
74. Filter response is characterized by a
linear characteristic, meaning that the
phase shift increases linearly with
frequency.
Filters with the Bessel response are
used for filtering pulse waveforms
without distorting the shape of
waveform.