Active Filter DsD Lecture Slide
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Transcript of Active Filter DsD Lecture Slide
![Page 1: Active Filter DsD Lecture Slide](https://reader034.fdocuments.in/reader034/viewer/2022051019/5695d45b1a28ab9b02a12c7a/html5/thumbnails/1.jpg)
D i d S h iDesign and Synthesis ofof
Active Filter
R fReferences: H. Lam, “ANALOG AND DIGITAL FILTERS: Design and Realization”W K Chen “Passive and Active Filters: Theory and Implementations”W. K. Chen, Passive and Active Filters: Theory and ImplementationsV. K. Aatre, “Network Theory And Filter Design”
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What is a Filter?What is a Filter?
• An electric filter is a frequency selective• An electric filter is a frequency selectivecircuit that passes a specified band off i d bl k tt tfrequencies and blocks or attenuatessignals of frequencies outside this band.
• Filter modifies signals in frequencyf g f q ydomain – both in amplitude and phase.
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•Analog filters are designed to process analog signals.
Di it l filt l i l i di it l t h i•Digital filters process analog signals using digital techniques.
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•Elements used in the passive filters : resistors, inductors, capacitors.•Elements used in the active filters : Transistors or Op‐Amps in additiont i t d itto resistors and capacitors
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Most commonly used filtersMost commonly used filters
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Most commonly used filtersMost commonly used filters
?
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Low pass FilterLow pass Filter
• Passes low frequency components andPasses low frequency components and attenuates high frequency components
Ideal Characteristics of Low pass filter
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Low pass FilterLow pass Filter
• Passes low frequency components andPasses low frequency components and attenuates high frequency components
Actual Characteristics of Low pass filter
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High pass FilterHigh pass Filter
• Passes high frequency components andPasses high frequency components and attenuates low frequency components
Ideal Characteristics of High pass filter
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High pass FilterHigh pass Filter
• Passes high frequency components and asses g eque cy co po e ts a dattenuates low frequency components
Actual Characteristics of High pass filter
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Band pass FilterBand pass Filter
• Passes certain band of frequencies and• Passes certain band of frequencies andattenuates frequencies outside this band.
• Has pass‐band between two stop‐bands
• Bandwidth= (ωH ‐ ωL)Bandwidth (ωH ωL)
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Band pass FilterBand pass Filter
Id l Ch t i ti f B d filtIdeal Characteristics of Band pass filter
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Band pass FilterBand pass Filter
A t l Ch t i ti f B d filtActual Characteristics of Band pass filter
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Band stop FilterBand stop Filter
Ideal Characteristics of Band stop filter
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Band stop FilterBand stop Filter
Actual Characteristics of Band stop filter
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Narrow Band‐pass filter: known as Tuned Filter N B d fil k N h FilNarrow Band‐stop filter: known as Notch Filter
Tuned Filter Notch Filter
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Filter Transfer FunctionFilter Transfer Function
m = number of zeros and n = number of poles
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First Order FilterFirst Order Filter
For Low-pass Filter:
Pass-band gain = (a0 / b0)Cut-off frequency = b rad/secCut-off frequency b0 rad/sec
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First Order FilterFirst Order FilterFor Low-pass Filter:
P b d i ( / b )Pass-band gain = (a0 / b0)Cut-off frequency = b0 rad/sec
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First Order FilterFirst Order Filter
For High-pass Filter:For High pass Filter:
P b d iPass-band gain = a1Cut-off frequency = b0 rad/sec
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Second Order FilterSecond Order Filter
For Low-pass Filter:For Low pass Filter:
Pass-band gain = a0 / b0Cut-off frequency of the filter = rad/s
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Second Order FilterSecond Order Filter
For High-pass Filter:For High pass Filter:
Pass-band gain = a2Cut-off frequency of the filter = rad/s
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Second Order FilterSecond Order Filter
For Band-pass Filter:For Band pass Filter:
Pass-band gain = a1 / b1Centre frequency of the filter = rad/s
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Second Order FilterSecond Order Filter
For Band-stop Filter:For Band stop Filter:
[a2 = a0 / b0]
Pass-band gain = a2Centre frequency of the filter = rad/s
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Schematic of Band-stop Filter:Schematic of Band stop Filter:
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Schematic of Band-stop Filter:Schematic of Band stop Filter:
a1 /b1 = 1a1 /b1 1
Pass-band gain = 1Pass band gain 1 Centre frequency of the filter = rad/s
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Filter Circuit ComponentsBasic Building Blocks:
Resistors, Capacitors & 0p‐Amps, p p p
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Filter Circuit ComponentsSecondary Building Block:
V lt C t ll d V lt S (VCVS)Voltage Controlled Voltage Source (VCVS)
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First Order Low‐pass Filter
Pass-band gain = a0/b0 = KPass band gain a0/b0 KCut-off frequency b0 = 1/R1C2
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First Order High‐pass Filter
Pass band gain = a =KPass-band gain = a1=KCut-off frequency b0 = 1 / R2C1
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Second Order Filter Circuit
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Second Order Filter Circuit
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Second Order Low‐pass Filter
P b d i /b K VCVS iPass-band gain = a0/b0 = K=VCVS gain
Cut-off frequency =
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Second Order High‐pass Filter
Pass-band gain = a2 =K = VCVS gainPass band gain a2 K VCVS gain
Cut-off frequency = 4321/1 RRCC
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Band‐pass Filter Circuit
Pass-band gain = a1/b1 =
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Band‐pass Filter Circuit
Center/ cut-off frequency = =