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OpAmp
Active Filters
Q. What is v0?
Filter
• What is Active filter?
• What is Passive filter?
• What is analog filter?
• What is digital filter?
An analog filter processes continuous-time signals
A digital filter processes discrete-time signals
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What is filter?
Purpose of filter?
Types of filters?
What is cut-off frequency?
Draw frequency responses of 4 filters?
What is pass-band?
• Pros and cons of active filter?
• Pros and cons of passive filter?
Passive Filters
• made up of passive components - resistors, capacitors and
inductors
• no amplifying elements (- transistors, op-amps, etc)
• no signal gain
• 1st order - design is simple (just use standard equations to find
resonant frequency of the circuit)
• 2nd order - complex equations
• require no power supplies
• not restricted by the bandwidth limitations of the op-amps
• can be used at very high frequencies
• can handle larger current or voltage levels than active devices
• They are particularly non-ideal (lossy)
• They are bulky and expensive
Ref:080222HKN
EE3110 Active Filter (Part 1)
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Passive elements : Inductor
• 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 timeconsuming and expensive for larger quantities of filters
• inductors are often prohibitively expensive
EE3110 Active Filter (Part 1)
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Active Filter
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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 opamps
• easy to adjust over a wide frequency range without altering the
desired response
Ref:080222HKN
EE3110 Active Filter (Part 1)
8
• Draw ideal filter responses of 4 types of
filters.
• Draw the same for practical filters.
• Draw the Bessel characteristics of a LPF.
• Draw the same for a HPF.
Bessel Characteristic
• Flat response in the
passband.
• Phase response is
linear.
• Used for filtering pulse
waveforms without
distorting the shape of
the waveform.
Ref:080222HKN
Av
EE3110 Active Filter (Part 1)
f
11
• Draw Butterworth characteristic for HPF.
Butterworth Characteristic
• Very flat amplitude,
Av(dB) , response in the
passband.
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Av
Phase response is not linear.
Used when all frequencies in the
passband must have the same
gain.
Often referred to as a maximally
flat response.
Ref:080222HKN
EE3110 Active Filter (Part 1)
f
13
• Draw Chebyshev characteristic for LPF
• Draw the same for BPF
Chebyshev Characteristic
• Overshoot or ripples
in the passband.
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Av
Role-off rate greater than
20dB/decade/pole.
Phase response is not linear worse than Butterworth.
Used when a rapid roll-off is
required.
Ref:080222HKN
EE3110 Active Filter (Part 1)
f
15
• Draw a passive LPF filter circuit.
• Draw an active LPF filter circuit.
Passive LPF
R
Vo 
XC
Vi
XC  R
Vi
1
1
jC
Vo 
Vi 
Vi
1
1  jCR
R
jC
C
Vo
Active LPF using OpAmp
• What is cut-off frequency for LPF?
• What is ,,, for HPF?
• What is ,,, for BPF?
• What is ,,, for BRF?
• What is dB/decade?
dB/…
• In many situations, the magnitude
attenuation of a signal is given in units of
dB/decade or dB/octave.
• The decibel is defined in terms of a power
(P) ratio, or the magnitude ratio (M).
• A decade is defined as a 10-fold increase
in frequency.
• An octave is defined as a 2-fold increase
(doubling) in frequency.
• How can we improve the performance of a
filter?
Better response? 2nd order?
• Draw a circuit for active HPF.
HPF
• Draw a circuit for 2nd order HPF.
2nd order HPF
• Draw a circuit for BPF.
Two-Stage Band-Pass Filter
C2
R4
+V
R2
R1
+V
+
C4
C3
+
vin
C1
-
R3
-
Rf1
-V
vout
-V
Rf3
Rf2
Rf4
Stage 1
Two-pole low-pass
Stage 2
Two-pole high-pass
Av
Stage 2
response
BW
f1
Ref:080222HKN
Stage 1
response
fo
BW = f2 – f1
Q = f0 / BW
f
f2
EE3110 Active Filter (Part 1)
30
• Draw a model for BRF, BSF, BEF, notch
filter.
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.
Av(dB)
Low pass
filter
f1
vin
High pass
filter
low-pass
high-pass
{
Summing
amplifier
-3dB

vout
f2
f
f1
Block diagram
Ref:080222HKN
f2
Frequency response
EE3110 Active Filter (Part 1)
32
Notch filter
Ref:080222HKN
EE3110 Active Filter (Part 1)
33