Filters can be passive or active. Passive filters use resistors, capacitors, and inductors while active filters use op-amps in addition to passive components. There are four main types of filters: low-pass filters which pass frequencies below a cutoff frequency, high-pass filters which pass frequencies above a cutoff frequency, band-pass filters which pass a range of frequencies between an upper and lower cutoff, and band-stop filters which reject a range of frequencies. Active filters have advantages over passive filters like reduced size, increased performance, and ability to provide gain.

1. Filters
Ideal Filter Responses
Passive Filters and Active Filters
Active Filters
LOW PASS FILTER
HIGH PASS FILTER
BAND PASS FILTER
BAND STOP FILTER
RAJESH G
Sr. Asst. Prof/ECE

2. Introduction
 Filtersare circuits that are capable of passing signals
within a band of frequencies while rejecting or blocking
signals of frequencies outside this band. Thisproperty of filters is also
called “frequency selectivity”.
Filtercan 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
resistors
in the designan addition to
and capacitors

3. Types of Filters
•
There are two broad categories of filters:
–
–
An analog filter processes continuous-time signals
A digital filter processes discrete-time signals.
• The analog or digital filters can be sub divided
into four categories:
–
–
–
–
Low pass Filters
High pass Filters
Band
Band
stop Filters
pass Filters

4. Analog Filter Responses
H(f) H(f)
0 0f ff fc c
Ideal “brick wall” filter Practical filter

5. Ideal Filters
Lowpass Filter Highpass Filter
c c
Bandstop Filter Bandpass Filter
c1 c2 c1 c2
Stopband Passband Stopband
M( )
Passband Stopband Passband
Stopband Passband
M( )
Passband Stopband

6. Passive Filters
• Made up of passive components - resistors, capacitors
inductors
No amplifying elements (transistors, op-amps, etc)
No signal gain
1st order - design is simple (just use standard equations
find resonant frequency of the circuit)
and
•
•
• to
•
•
•

2n
d
order - complex equations
Require no power supplies
Buffer amplifiers might be required
Desirable to use inductors with high quality factors

7. Inductor - BIG PROBLEM!
•
•
Physical size, and large inductance values are required.
Tuning inductors to the required values is time-consuming
and expensive for larger quantities of filters.
Often prohibitively expensive.•

Difficult
Lossy
to implement at frequencies below 1 kHz.


8. Active Filter
•
•
•
•
•
No inductors
Made up of op-amps, resistors and capacitors
Provides arbitrary gain
Generally easier to design
High input impedance prevents excessive loading
source
of the driving
• Low output impedance prevents the filter from being affected
by the load
Easy to adjust over a wide frequency range without altering the
desired response
•

9. Op Amp Advantages
• Advantages of active RC filters
include:
–
–
–
Reduced size and weight
Increased reliability and improved performance
Simpler design than for passive filters and can realize a
wider range of functions as well as providing voltage gain
In large quantities, the cost of an IC is less than its passive
counterpart
–

10. Op Amp Disadvantages
• Active RC filters also have some disadvantages:
– limited bandwidth of active devices limits the highest
attainable pole frequency and therefore applications
nearby
100 kHz (passive RLC filters can be used up to 500 MHz)
require power supplies (unlike passive filters)
–
– increased sensitivity to variations in circuit parameters
caused by environmental changes
filters.
compared to passive
• For many applications, particularly in voice and data
communications, the economic and performance advantages of
active RC filters far outweigh their disadvantages.

11. Categories of Filters
Low Pass Filters:
Pass all frequencies from
High Pass Filters:
Pass all frequencies thatdc are
up to the upper
frequency.
A
cutoff above its lower
frequency
cutoff
Av(
dB
)
v(
dB
)
{{ -
3d
B
-
3d
B
f
f ff
2
1
High-passresponseLow-passresponse

12. Categories
Band Pass Filters:
Pass only the frequencies
that fall between its values
of the lower and upper
of Filters
Band Stop (Notch) Filters:
Eliminate all signals within
the stop band while passing
all frequencies
band.
outside this
cutoff frequencies.
Av(
dB
)
Av(
dB
)
{{ -
3d
B
-
3d
B
f ff
1
f
2
f
1
f
2
BandPassResponse BandStopResponse

13. Filter
Av
Response Characteristics
f
Butterworth
Bessel
Chebyshev

14. ACTIVE LOW PASS FILTER
Passive filter

15. ACTIVE LOW PASS FILTER
Passive filter and its frequency response

16. ACTIVE LOW PASS FILTER
Passive filter and its frequency response

17. ACTIVE LOW PASS FILTER
This first-order low pass active filter, consists simply of a passive RC filter stage providing a
low frequency path to the input of a non-inverting operational amplifier. The amplifier is
configured as a voltage-follower (Buffer) giving it a DC gain of one, Av = +1 or unity gain as
opposed to the previous passive RC filter which has a DC gain of less than unity.
The advantage of this configuration is that the op-amps high input impedance prevents
excessive loading on the filters output while its low output impedance prevents the filters cut-
off frequency point from being affected by changes in the impedance of the load.
While this configuration provides good stability to the filter, its main disadvantage is that it
has no voltage gain above one. However, although the voltage gain is unity the power gain is
very high as its output impedance is much lower than its input impedance. If a voltage gain
greater than one is required we can use the following filter circuit.

18. ACTIVE LOW PASS FILTER
Active First order Low Pass Filter with Amplification

19. ACTIVE LOW PASS FILTER
Active First order Low Pass Filter

20. ACTIVE LOW PASS FILTER
Analysis

21. ACTIVE LOW PASS FILTER

22. 6/21/2020

23. ACTIVE LOW PASS FILTER
Active second order Low Pass Filter

24. ACTIVE LOW PASS FILTER
Active second order Low Pass Filter
The main feature of the 2nd order LPF is, the frequency response falls
at the rate of 40dB/Decade above the cutoff frequency.

25. ACTIVE LOW PASS FILTER
Active second order Low Pass Filter
•At lower frequencies C1 and C2 are more
so, no effect on the circuit operation.
V0 = Vi , Av = 1.
•At higher frequencies ,
• C1 & R2 causes the o/p to fall of
@ 20dB/D as the frequency
increases.
•Phase lag produced by R2 & C1
and Phase lead is produced by
combined C2 and [R1 + R2] .
•The result of these phase
differences is that the feedback via
C2 produces further fall of 20dB/D.
•Thus total roll off rate is 40db/D

26. ACTIVE LOW PASS FILTER
Design Procedure of 2nd Low Pass Filter
•Rmax = R1 + R2 =
•R1 = R2 and R3 = R1 + R2
•
•C2 = 2*C1 @ fh and
Design of 2nd order LPF with a cutoff frequency of 100Hz.
Draw the circuit diagram.

28. ACTIVE HIGH PASS FILTER
1ST order HPF

29. ACTIVE HIGH PASS FILTER

30. ACTIVE HIGH PASS FILTER

31. ACTIVE HIGH PASS FILTER
Design 1st order HPF for the cutoff frequency
1KHz.Draw the Circuit diagram.

32. ACTIVE HIGH PASS FILTER
2nd order HPF

33. ACTIVE HIGH PASS FILTER
•At higher frequencies C1 and C2 are
more so, no effect on the circuit
operation.
C1 & C2 << R1 & R2 , so
V0 = Vi , Av = 1.
•At lower frequencies ,
• C2 & R2 causes the o/p to fall
of @ 20dB/D as the frequency
increases.
•Phase lead produced by R2 & C2
and Phase lag is produced by
combined R2 and [C1 + C2 ] .
•The result of these phase
differences is that the feedback
via R2 produces further fall of
20dB/D.
•Thus total roll off rate is 40db/D

34. ACTIVE HIGH PASS FILTER
Design 2nd order HPF for the cutoff frequency
120KHz.Draw the Circuit diagram.

38. The “Q” or Quality Factor
In a Band Pass
Filter circuit, the overall
width of the actual pass band
between the upper and lower
-3dB corner points of the
filter determines the Quality
Factor or Q-point of the
circuit. This Q Factor is a
measure of how “Selective”
or “Un-selective” the band
pass filter is towards a given
spread of frequencies. The
lower the value of the Q
factor the wider is the
bandwidth of the filter and
consequently the higher the
Q factor the narrower and
more “selective” is the filter.