This document discusses different types of filters including low pass, high pass, band pass, and band stop filters. It explains the basic components used in filters including resistors, capacitors, and inductors. It provides examples of low pass filter and high pass filter designs, discussing how to calculate the cutoff frequency. Active filters are introduced as having advantages over passive filters like no loading effect. Formulas for calculating gain and cutoff frequency are presented. Higher order filters and their steeper roll-off rates are covered. Finally, it discusses homework problems involving designing various filter circuits.

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Filters
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Unit 6: Active filters
• Filter may be classified on a number of ways.
• Analog or digital
• Passive or active
• Audio or radio frequency
http://nptel.ac.in/courses/117107094/15
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Types of filters
• Low pass filters
• High pass filter
• Band pass filter
• Band reject filter.
• All pass filter
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RLC Basic components
• Resistor (R)
– R
• Capacitor (C)
– Pass AC, block DC
– Impedance of capacitor = -j/ωC = -j/(2πfC)
– Capacitor current: Ic = CdV/dt
• Inductor (L)
– BlockAC, pass DC
– Impedance of inductor = jωL = j(2πfL)
– Inductor Voltage: V = LdI/dt
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LPF (Low Pass Filter )
• Pass low frequency
• Attenuate high
frequencies
• Xc=1/2πfC
• f↓ = Xc↑
• f ↑ = Xc↓
• Cut off frequency
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LPF
fc= 1/(2πRC)
fc=1/(2π*1.2*100μ)
fc=1326 Hz
-3dB = 0.707
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HPF (High Pass Filter)
• High Frequencies are pass
• Low frequencies are
attenuated
• Xc=1/2πfC
• f↓ = Xc↑
• f ↑ = Xc↓
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HPF
fc= 1/(2πRC)
fc-=1/(2π*15*10 μ)
fc=1061 Hz
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• LPF
• HPF
• BPF
• BSF
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Gain on Y axis (Voltage / db)
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Gain / Attenuation
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Active filters using OPAMP
• Passive filter  Attenuation due to passive
components
• Passive filters may have Loading effect
• Inductors are not used often in electronic circuits due
to their size, their susceptibility to parasitic effects
(esp. magnetic fields)
• Active filters  Required gain.
• In active filters, no loading problem as OPAMP has
high input resistance and low output resistance.
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• A simple cascade connection
• No amplification
• No loading problem
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ƒ = the frequency of the input signal in Hertz, (Hz)
ƒc = the cut-off frequency in Hertz, (Hz)
Gain of Active LPF is function of frequency
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Design a low pass filter at a cutoff frequency of
1 kHz with a pass band gain of 2.
• Given fc = 1 kHz. Let C = 0.01 µF.
• Therefore, R can be obtained as
• A 20 kΩ potentiometer can be used to set the
resistance R.
• Since the pass band gain is 2, R1 and RF must
be equal. Let R1 = R2 = 10 kΩ.
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---Home work ----
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A) Design a low pass filter at a cutoff frequency of 1
KHz with a pass band gain of 3. (assume suitable data,
if necessary).
B) For Vin = 1 Vpp, Calculate the Vout at frequencies
1) 100Hz, 2) 700Hz 3) 1000Hz 4) 1500Hz , 5) 5000Hz ,
10,000Hz , 7) 30000Hz 8) 10,000Hz,9) 1MHz 10) 10 Mhz
C) Draw the frequency response of the LPF with
a) Vout on Y- axis , b) Gain in db on Y-axis, c) Attenuation on Y-axis
use semi log paper.
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• Design a non-inverting active low pass filter
circuit that has a gain of ten at low frequencies,
a high frequency cut-off or corner frequency of
159Hz and G =10
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Af=10
• Fc= 159 Hz
• Assume C1=100nF
• fc= 1/(2πRC)
• R3= 10kΩ
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Assume R1=1kΩ, So, R2 = 9 kΩ
Gain in dB= 20 log A =20 log 10 = 20dB
Check the Gain
First order high pass filter
• The cut-off frequency point for a first order
high pass filter can be found using the same
equation as that of the low pass filter
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LPF HPF
Xc=1/2πfC
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ƒ = the frequency of the input signal in Hertz, (Hz)
ƒc = the cut-off frequency in Hertz, (Hz)
Roll Off
• Roll off rate for first order filter
is -20dB / decade (10X)
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Roll-off rate
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• Nth order filter will have a roll-off rate of 20n dB/decade.
• First-order filter = 20dB/decade.
• Second-order filter = 40dB/decade.
• Fourth-order filter =80dB/decade .
• High-order filters, such as third, fourth, and fifth-order are usually
formed by cascading together single first-order and second-order filters.
Second order Low Pass Filter
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Second order High Pass Filter
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Active Band Pass Filter
• Simple Active Band Pass Filter can be easily
made by cascading together a single Low Pass
Filter with a single High Pass Filter as shown
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Low Pass Filter
High Pass Filter
Band Pass Filter
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Filters : Quality Factor
• Depends on the bandwidth of the pass band.
• Q = f_center/Bandwidth
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Active Band Stop Filter
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All pass filter
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• RC= 2 π F Tan (Φ/2)
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HW
• Design wideband pass filter having FL= 1kHz
and FH= 6 KHz with pass band gain is 3
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Reference:
1. George Clayton and Steve Winder, “Operational
Amplifiers”, 5th Edition Newnes.
2. Sergio Franco, “Design with Operational Amplifiers
and Analog Integrated Circuits”, Tata McGraw Hill.
3. Bali, “Linear Integrated Circuits”, Mc Graw Hill
2008.
4. Gray, Hurst, Lewise, Meyer, “Analysis & Design of
Analog Integrated Circuits”, Wiley Publications.
5. https://electronicspost.com/what-is-a-band-stop-
filter-draw-and-explain-the-frequency-response-of-a-
band-stop-filter/
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Thank You…
- V K Bairagi
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