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Active Filters are very much important in Electrical Enginering.
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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”
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.
•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.
•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
Most commonly used filtersMost commonly used filters
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
Low pass FilterLow pass Filter
• Passes low frequency components andPasses low frequency components and attenuates high frequency components
Actual Characteristics of Low pass filter
High pass FilterHigh pass Filter
• Passes high frequency components andPasses high frequency components and attenuates low frequency components
Ideal Characteristics of High pass filter
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
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)
Band pass FilterBand pass Filter
Id l Ch t i ti f B d filtIdeal Characteristics of Band pass filter
Band pass FilterBand pass Filter
A t l Ch t i ti f B d filtActual Characteristics of Band pass filter
Band stop FilterBand stop Filter
Ideal Characteristics of Band stop filter
Band stop FilterBand stop Filter
Actual Characteristics of Band stop filter
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
Filter Transfer FunctionFilter Transfer Function
m = number of zeros and n = number of poles
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
First Order FilterFirst Order FilterFor Low-pass Filter:
P b d i ( / b )Pass-band gain = (a0 / b0)Cut-off frequency = b0 rad/sec
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
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
Second Order FilterSecond Order Filter
For High-pass Filter:For High pass Filter:
Pass-band gain = a2Cut-off frequency of the filter = rad/s
Second Order FilterSecond Order Filter
For Band-pass Filter:For Band pass Filter:
Pass-band gain = a1 / b1Centre frequency of the filter = rad/s
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
Schematic of Band-stop Filter:Schematic of Band stop Filter:
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
Filter Circuit ComponentsBasic Building Blocks:
Resistors, Capacitors & 0p‐Amps, p p p
Filter Circuit ComponentsSecondary Building Block:
V lt C t ll d V lt S (VCVS)Voltage Controlled Voltage Source (VCVS)
First Order Low‐pass Filter
Pass-band gain = a0/b0 = KPass band gain a0/b0 KCut-off frequency b0 = 1/R1C2
First Order High‐pass Filter
Pass band gain = a =KPass-band gain = a1=KCut-off frequency b0 = 1 / R2C1
Second Order Filter Circuit
Second Order Filter Circuit
Second Order Low‐pass Filter
P b d i /b K VCVS iPass-band gain = a0/b0 = K=VCVS gain
Cut-off frequency =
Second Order High‐pass Filter
Pass-band gain = a2 =K = VCVS gainPass band gain a2 K VCVS gain
Cut-off frequency = 4321/1 RRCC
Band‐pass Filter Circuit
Pass-band gain = a1/b1 =
Band‐pass Filter Circuit
Center/ cut-off frequency = =
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