2. INTRODUCTION
Filters are circuits that are capable of passing
signals within a band of frequencies while rejecting
or blocking signals of frequencies outside this
band.
This property of filters is also called “frequency
selectivity”.
3. TYPES OF FILTER
There are two broad categories of filters:
Analog or digital
Passive or active
Analog filters: designed to process
analog signals
Digital filters: process analog signals using
digital signals
4. Passive filters
Passive filters use resistors, capacitors, and
inductors (RLC networks).
To minimize distortion in the filter characteristic,
it is desirable to use inductors with high quality
factors
practical inductors includes a series resistance.
They are particularly non-ideal
They are bulky and expensive
5. ACTIVE FILTERS
Active filters: The circuits that employ one
or more op-amps in the design an addition to
resistors and capacitors
Active filters replace inductors using op-amp
based equivalent circuits.
Most commonly used filters:
o Low-pass Filters
o High-pass Filters
o Band-pass Filters
o Band-reject Filters
6. LOW PASS FILTERS
A LOW-PASS FILTER IS A FILTER THAT PASSES
SIGNALS WITH A FREQUENCY LOWER THAN A
CERTAIN CUTOFF FREQUENCY AND ATTENUATES
SIGNALS WITH
FREQUENCIES HIGHER THAN THE CUTOFF
FREQUENCY.
FIRST ORDER LOW PASS FILTER
7. Thus, the operation of a low pass active filter can be verified
from the frequency gain equation above as:
1. At very low frequencies, ƒ < ƒc , Vout/vin = Af
2. At the cut-off frequency, ƒ = ƒc , Vout/vin = .707 Af
3. At very high frequencies, ƒ > ƒc , Vout/vin < Af
v
Frequency response curve
8. APPLICATION OF ACTIVE LOW -PASS FILTER
ACTIVE LOW PASS FILTERS ARE IN AUDIO AMPLIFIERS, EQUALIZERS
OR SPEAKER SYSTEMS TO DIRECT THE LOWER FREQUENCY BASS
SIGNALS TO THE LARGER BASS SPEAKERS OR TO REDUCE ANY HIGH
FREQUENCY NOISE OR “HISS” TYPE DISTORTION. WHEN USED LIKE
THIS IN AUDIO APPLICATIONS THE ACTIVE LOW PASS FILTER IS
SOMETIMES CALLED A “BASS BOOST” FILTER.
HIGH-PASS FILTER
HIGH-PASS FILTER (HPF) ATTENUATES CONTENT BELOW A CUTOFF
FREQUENCY, ALLOWING HIGHER FREQUENCIES TO PASS THROUGH
THE FILTER.
9. FIRST ORDER HIGH-PASS FILTER
THE OPERATION OF A HIGH PASS ACTIVE FILTER CAN BE VERIFIED
FROM THE FREQUENCY GAIN EQUATION ABOVE AS:
10. 1. AT VERY LOW FREQUENCIES, Ƒ < ƑC VOUT/VIN < AF
2. AT THE CUT-OFF FREQUENCY, Ƒ = ƑC VOUT/VIN = .707AF
3. AT VERY HIGH FREQUENCIES, Ƒ > ƑC VOUT/VIN = AF
Frequency Response Curve
11. APPLICATION OF ACTIVE HIGH-PASS FILTER
ACTIVE HIGH PASS FILTERS ARE IN AUDIO AMPLIFIERS,
EQUALIZERS OR SPEAKER SYSTEMS TO DIRECT THE HIGH
FREQUENCY SIGNALS TO THE SMALLER TWEETER SPEAKERS OR TO
REDUCE ANY LOW FREQUENCY NOISE OR “RUMBLE” TYPE
DISTORTION. WHEN USED LIKE THIS IN AUDIO APPLICATIONS THE
ACTIVE HIGH PASS FILTER IS SOMETIMES CALLED A “TREBLE
BOOST” FILTER.
BAND –PASS FILTER
It is a frequency selective filter circuit used in electronic
systems to separate a signal at one particular frequency, or a
range of signals that lie within a certain “band” of
frequencies from signals at all other frequencies. This band
or range of frequencies is set between two cut-off or corner
frequency points labelled the “lower frequency” ( ƒL ) and the
“higher frequency” ( ƒH ) while attenuating any signals
outside of these two points.
12. ACTIVE BAND-PASS FILTER
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
13. BAND-STOP FILTER
THE BAND STOP FILTER, ALSO KNOWN AS A BAND REJECT FILTER,
PASSES ALL FREQUENCIES WITH THE EXCEPTION OF THOSE WITHIN A
SPECIFIED STOP BAND WHICH ARE GREATLY ATTENUATED.
14. IF THIS STOP BAND IS VERY NARROW AND HIGHLY ATTENUATED OVER
A FEW HERTZ, THEN THE BAND STOP FILTER IS MORE COMMONLY
REFERRED TO AS A NOTCH FILTER, AS ITS FREQUENCY RESPONSE
SHOWS THAT OF A DEEP NOTCH WITH HIGH SELECTIVITY (A STEEP-
SIDE CURVE) RATHER THAN A FLATTENED WIDER BAND.
THE BAND STOP (BAND REJECT OR NOTCH) FILTER IS A SECOND-
ORDER (TWO-POLE) FILTER HAVING TWO CUT-OFF FREQUENCIES,
COMMONLY KNOWN AS THE -3DB OR HALF-POWER POINTS PRODUCING
A WIDE STOP BAND BANDWIDTH BETWEEN THESE TWO -3DB POINTS.
16. Advantages of active filters over passive filters (R, L, and C
elements only):
1. By containing the op-amp, active filters can be designed to
provide required gain, and hence no signal attenuation as
the signal passes through the filter.
2. No loading problem, due to the high input impedance of
the op-amp prevents excessive loading of the driving source,
and the low output impedance of the op-amp prevents the
filter from being affected by the load that it is driving.
3. Easy to adjust over a wide frequency range without
altering the desired response.
17. ACTIVE RC FILTERS ALSO HAVE
SOME DISADVANTAGES:
LIMITED BANDWIDTH OFACTIVE DEVICES LIMITS
THE HIGHEST ATTAINABLE FREQUENCY (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 COMPARED TO PASSIVE FILTERS
FOR MANY APPLICATIONS, PARTICULARLY IN VOICE
AND DATA COMMUNICATIONS, THE ECONOMIC AND
PERFORMANCE ADVANTAGES OFACTIVE RC
FILTERS FAR OUTWEIGH THEIR DISADVANTAGES.
