11
Introduction
Filter:-
A filter is a device that passes electric signals at certain frequencies or frequency ranges while preventing the passage of others.
An electric filter is often a frequency selective circuit that passes a specified band of frequencies and blocks or attenuates signals of frequency outside this band.
Classification of filter:-
Ø Analog or Digital
Ø Passive or Active
Ø Audio (AF) or Radio frequency (RF)
The most commonly used filters are:-
Ø Low-pass filter:-
A low pass filter is a circuit offering easy passage to low frequency signals and difficult passage to high frequency signals.
Ø High- pass filter:-
It offers easy passage to higher frequency and difficult passage to low frequency signals.
Ø Band- pass filter:-
There are appliicatios where a particular band, or spread, or frequencies need to be filtered from a wider range of mixed signals. Filter circuits can be designed to accomplish this task by combining the properties of low-pass and high-pass into a single filter. The result is called a band-pass filter.
Ø Band- reject filter:-
The band reject filter also called a band-stop filter. In this filter frequencies are attenuated in the stop band while they are passed outside this band.
Ø All- pass filter
Each of these filters uses an op-amp as the active element and resistor and capacitor as the passive elements. Although the 741 type op-amp works satisfactorily in these filter circuits, high speed op-amp such as the LM318 or IC8017 improve the filter’s performance through their increased slew rate and higher unity gain bandwidth.
Band-pass filter:-
A band-pass filter has a pass band between two cut off frequency fH and fL . any input frequency outside this pass band is attenuated.
signal signal
input output
block frequency block frequency
too high too low
Basically there are two types of band-pass filter:-
Ø Wide band-pass filter
Ø Narrow band-pass filter
In wide band-pass filter if its figure of merit or quality factor Q<10.
Resonant filter orNarrow band-pass filter:-
The narrow band-pass filter using multiple feedback is shown in figure:-
this filter is unique in following aspects:-
Ø The filter use only one op-amp.
Ø The op-amp is used in inverting mode.
Ø It has two feedback path, hence the name multiple feedback filter.
Ø we don’t need an inductor(bulky and expansive at low frequency) to create band-pass shape.
In narrow band-pass filter the output voltage peaks at the central frequency.
Q-factor and Bandwidth:-
The Q, quality factor of a resonant circuit is a measure of the “goodnss”
Or quality of a resonant circuit. A higher value for this figure of merit correspondes to a more narrow bandwidth.
Q = fc = fc
BW fH-fL
where, fc à central frequency
BWà bandwidth
Resonance:-
In physics, resonance is the tendency of a system to oscillate with larger amplitude at some frequencies than at others. These are known as systems resonant frequency.
Resonance occur when a system is able to store and easily transfer energy between two or more different storage modes.
Detailed description
Op-amp:-
Op-amp is a direct coupled high gain (104) amplifier with a differential input and usually a single ended output, to which feedback can be added to control its overall response characteristic.
Ø An op-amp produces an output voltage that is typically hundreds of thousands times larger than the voltage difference between its input terminals.
Ø Operational amplifiers are important building blocks for a wide range of electronic circuits. They had their origins in analog computers where they were used in many linear, non-linear and frequency-dependent circuits.
Ø Op-amps are among the most widely used electronic devices today, being used in a vast array of consumer, industrial, and scientific devices. Many standard IC op-amps cost only a few cents in moderate production volume.
Circuit notation:-
Circuit diagram symbol for an op-amp
The circuit symbol for an op-amp is shown to the right, where:
V- : non-inverting input
V+ : inverting input
Vout : output voltage
V5+ : positive power supply
V5- : negative power supply
THE IC-741 OPERATIONAL AMPLIFIER:-
The Operational Amplifier is probably the most versatile Integrated Circuit available. It is very cheap especially keeping in mind the fact that it contains several hundred components. The most common Op-Amp is the 741 and it is used in many circuits.
The OP AMP is a ‘Linear Amplifier’ with an amazing variety of uses. Its main purpose is to amplify (increase) a weak signal.
The OP-AMP has two inputs:
Ø INVERTING ( - ) :-
If the voltage goes into pin two then it is known as an INVERTING AMPLIFIER.
Ø NON-INVERTING (+):-
If the voltage goes into pin three then the circuit becomes a NON-INVERTING AMPLIFIER.
THE 741 IS USED IN TWO WAYS
1. An inverting amplifier. Leg two is the input and the output is always reversed.
In an inverting amplifier the voltage enters the 741 chip through leg two and comes out of the 741 chip at leg six. If the polarity is positive going into the chip, it negative by the time it comes out through leg six. The polarity has been ‘inverted’.
2. A non-inverting amplifier. Leg three is the input and the output is not reversed.
In a non-inverting amplifier the voltage enters the 741 chip through leg three and leaves the 741 chip through leg six. This time if it is positive going into the 741 then it is still positive coming out. Polarity
IC-741 pin diagram
IC-741 s 8 pin Ic. Every IC should be supplied with +ve and –ve dc voltages
Of +12v and -12v respectively.
Pin no. 7 à +12v should be supplied
Pin no. 4 à -12v should be supplied
Pin no. 2 à Inverting input
Pin no. 3 à Non inverting input
Pin no. 6 à output
Pin no. 1 & 5 à for output offset voltage compensation
Resistor:-
A resistor is a component of an electrical circuit that resists the flow of electrical current .A resistor has two terminals across which electricity must pass , and is designed to drop the voltage of the current as it flows from on terminal to the . A resistor is primarily used to create and maintain a known safe current within an electrical component.
Every resistor falls into on the two categories
1. Fixed resistor.
2. Variable resistor.
A fixed resistor has a predetermined amount of resistance to current, while a variable resistor can adjusted to give different levels of resistance. Variable resistors are also called as potentiometers and are commonly used as volume controls on audio devices. A rheostat is a variable resistor made especially for use with high current.
We have used both variable and fixed resistance in the circuits symbols are given below:-
Figure: Fixed resistor Figure: Variable resistors
Capacitor:-
A capacitor is a device for storing large quantity of electric charge.
A conductor can store a small amount of charge two or more conductors are arranged to form a capacitor. Thus, a capacitor possesses a large capacitance to store charges and that too in a small space.
Dual power supply:-
An op-amp requires a power supply with +ve and –ve outputs as well as zero volts. This is called a dual power supply.
Dual power supply is used to bios the internal differential amplifiers transistors in active region.
For equal magnitude (balanced) supply the centre point is always zero volt and output voltage will swing between ~ +Vcc to –Vcc from this centre point. This means the swing is equal on both sides.
If supply is not balanced, the swing on one side will be less than the other side and may cause clipping in the output waveforms. Also this will add DC offset to output.
Design method
To design a filter, four things must be known in advance:
Ø The power supplies available: positive / negative—or only positive (single supply)
Ø The frequencies that need to be passed and those that need to be rejected.
Ø A transition frequency, the point at which the filter starts to work—or—a center frequency around which the filter is symmetrical.
Ø An initial capacitor value—pick one somewhere from 100 pF for high frequencies to 0.1 μF for low frequencies. If the resulting resistor values are too large or too small, pick another capacitor value.
Generally, the narrow band-pass filter is designed for specific value of center frequency fc and Q or fc and bandwidth.
Q = fc = fc
BW fH-fL
The circuit components are determined from following relationships.
Design procedure:-
è Pick c1 = c2 =c
è Calculate R1 = Q
2*Ω*fc*c*Af
è Calculate R2 = Q
2*Ω*fc*c*(2*Q2 -Af)
è Calculate R3 = Q
Ω*fc*c
è Calculate Af = R3
2*R1
Where, Af is gain at fc .
è The gain Af must satisfy the condition
Af 2*Q2
Components and specific values:-
Here, we designed narrow band-pass filter or resonant filter fc=15.92 kHz and Af=10, Q=3.
Ø Pick c1 = c2 = c =0.01µF
Ø R1= 300Ω
Ø R2= 375Ω
Ø R3=6.00kΩ
Circuit diagram