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TOPIC 5
FILTERS
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Application of filter
Capacitor filter
Choke input filter
Input capacitor filterresisistance capacitance filter
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Two types of Filter
Passive Filter
Active Filter
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Passive filters
Passive implementations of linear
filters are based on combinations of
resistors(R), inductors(L) and
capacitors(C). These types arecollectively known aspassive filters,
because they do not depend upon an
external power supply and/or they donot contain active components such
as transistors.
http://en.wikipedia.org/wiki/Resistorhttp://en.wikipedia.org/wiki/Inductorhttp://en.wikipedia.org/wiki/Capacitorhttp://en.wikipedia.org/wiki/Capacitorhttp://en.wikipedia.org/wiki/Inductorhttp://en.wikipedia.org/wiki/Resistor8/13/2019 TOPIC 5 - (Filter)Student
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Passive filters
A low-pass electronic filter realised by an RC circuit
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Passive filters
Low-pass filter
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Passive filters
High-pass T filter
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Active filters
Active filtersare implemented using acombination of passive and active(amplifying) components, and require
an outside power source. Operationalamplifiersare frequently used inactive filter designs. These can havehigh Q factor, and can achieve
resonancewithout the use ofinductors. However, their upperfrequency limit is limited by the
bandwidth of the amplifiers used.
http://en.wikipedia.org/wiki/Active_filterhttp://en.wikipedia.org/wiki/Operational_amplifierhttp://en.wikipedia.org/wiki/Operational_amplifierhttp://en.wikipedia.org/wiki/Q_factorhttp://en.wikipedia.org/wiki/Electrical_resonancehttp://en.wikipedia.org/wiki/Electrical_resonancehttp://en.wikipedia.org/wiki/Q_factorhttp://en.wikipedia.org/wiki/Operational_amplifierhttp://en.wikipedia.org/wiki/Operational_amplifierhttp://en.wikipedia.org/wiki/Active_filter8/13/2019 TOPIC 5 - (Filter)Student
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Active filters
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Differentiate between Active filter
and Passive filter
Passive filter Active filter
Structure Used of the passivecomponents likeinductor, capacitor,resistor etc
Used of the active device andresistor and capacitor
Size Big Small
Design Difficult Easy
Signal Operation Load is not isolatedfrom the frequencydeterminingnetwork
Load is isolated from thefrequency determinenetwork
Cost Cheap Expensive
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Passive filters
Application of each passive filters
Low-pass filters(up to 100kHz)
Allow only low frequency signals to pass,
and hold a higher frequencyHigh-pass filters(above 100kHz)
Allow only high frequency signals to passthrough,
Band-pass filters
Allow signals falling within a certainfrequency range to pass through.
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Low-pass filters circuit
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Operation of low-pass filters
circuit
At high frequencies the reverse is true with
Vc being small and Vr being large.
While the circuit above is that of an RC
Low Pass Filter circuit, it can also beclassed as a frequency variable potential
divider circuit similar to the one we looked
at in the Resistorstutorial. The following
equation to calculate the output voltage fortwo single resistors connected in series.
http://www.electronics-tutorials.ws/resistor/res_3.htmlhttp://www.electronics-tutorials.ws/resistor/res_3.html8/13/2019 TOPIC 5 - (Filter)Student
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Operation of low-pass filters
circuit
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Operation of low-pass filters
circuit
We also know that the capacitive reactanceof a capacitor in an AC circuit is given as:
Opposition to current flow in an AC circuitis called impedance, symbol Z and for aseries circuit consisting of a single resistorin series with a single capacitor, the circuitimpedance is calculated as:
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Operation of low-pass filters
circuit
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Operation of low-pass filters
circuit
Then by substituting our equation for
impedance above into the resistive
potential divider equation gives us:
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Example No1
A Low Pass Filtercircuit consisting
of a resistor of 4k7 in series with acapacitor of 47nF is connected across
a 10v sinusoidal supply. Calculate theoutput voltage (Vout) at a frequency
of 100Hz and again at frequency of
10,000Hz or 10kHz.
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At a frequency of 100Hz.
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At a frequency of 10kHz.
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Frequency Response
The Bode Plot shows the Frequency
Responseof the filter to be nearly flat
for low frequencies and all of the input
signal is passed directly to the output,resulting in a gain of nearly 1, called
unity, until it reaches its Cut-off
Frequencypoint ( c ).
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Frequency Response
This is because the reactance of thecapacitor is high at low frequencies andblocks any current flow through thecapacitor. After this cut-off frequency point
the response of the circuit decreases givinga slope of -20dB/ Decade or (-6dB/Octave)"roll-off" as signals above this frequencybecome greatly attenuated, until at veryhigh frequencies the reactance of the
capacitor becomes so low that it gives theeffect of a short circuit condition on theoutput terminals resulting in zero output.
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Frequency Response
For this type of Low Pass Filtercircuit, allthe frequencies below this cut-off, c pointthat are unaltered with little or noattenuation and are said to be in the filtersPass bandzone.
This pass band zone also represents theBandwidthof the filter. Any signalfrequencies above this point cut-off pointare generally said to be in the filters Stopbandzone and they will be greatlyattenuated.
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Cut-off Frequency and Phase
Shift
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Low Pass Filter Summary
So to summarize, the Low Pass Filterhas
a constant output voltage from D.C. (0Hz),
up to a specified Cut-off frequency, ( c )
point.This cut-off frequency point is 0.707 or -
3dB(dB = -20log Vout/Vin) of the voltage
gain allowed to pass. The frequency range
"below" this cut-off point c is generallyknown as the Pass Bandas the input
signal is allowed to pass through the filter.
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Low Pass Filter Summary
A simple 1st order low pass filter can be
made using a single resistor in series with
a single non-polarized capacitor (or any
single reactive component) across an inputsignal Vin, whilst the output signal Vout is
taken from across the capacitor.
The cut-off frequency or -3dB point, can be
found using the formula, c = 1/(2RC).The phase angle of the output signal at cand is -45o for a Low Pass Filter.
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Low Pass Filter Summary
The gain of the filter or any filter for
that matter, is generally expressed in
Decibelsand is a function of the
output value divided by itscorresponding input value and is
given as:
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Operation of high-pass filters
circuit
In this circuit arrangement, the reactance of thecapacitor is very high at low frequencies so thecapacitor acts like an open circuit and blocks anyinput signals at Vin until the cut-off frequency point
(c) is reached.Above this cut-off frequency point the reactance ofthe capacitor has reduced sufficiently as to nowact more like a short circuit allowing all of the inputsignal to pass directly to the output as shown
below in the High Pass Frequency ResponseCurve.
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Frequency Response of a 1st
Order High Pass Filter.
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Frequency Response of a 1st
Order High Pass Filter.
The Bode Plotor Frequency Response
Curve above for a High Pass filter is the
exact opposite to that of a low pass filter.
Here the signal is attenuated or damped atlow frequencies with the output increasing
at +20dB/Decade (6dB/Octave) until the
frequency reaches the cut-off point (c)
where again R = Xc.
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Frequency Response of a 1st
Order High Pass Filter.
It has a response curve that extends down frominfinity to the cut-off frequency, where the outputvoltage amplitude is 1/2 = 70.7% of the inputsignal value or -3dB (20 log (Vout/Vin)) of the input
value. The phase angle ( ) of the output signalLEADSthat of the input and is equal to +45oatfrequency c.The frequency response curve for a high passfilter implies that the filter can pass all signals out
to infinity. However in practice, the high pass filterresponse does not extend to infinity but is limitedby the characteristics of the components used.
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Frequency Response of a 1st
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, but the equation forthe phase shift is modified slightly to
account for the positive phase angle
as shown below.
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Cut-off Frequency and Phase
Shift
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Cut-off Frequency and Phase
Shift
The circuit gain, Av which is given as Vout/Vin (magnitude) and is
calculated as:
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Example No1.
Calculate the cut-off or "breakpoint"
frequency (c) for a simple high passfilterconsisting of an 82pF capacitor
connected in series with a 240kresistor.
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Answer example No1.
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Band Pass Filter Circuit
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Operation of Band Pass Filter
Circuit
A Band Pass Filterspasses signals withina certain "band" or "spread" of frequencieswithout distorting the input signal orintroducing extra noise. This band of
frequencies can be any width and iscommonly known as the filters Bandwidth.Bandwidth is defined as the frequencyrange between two specified frequencycut-off points (c), that are 3dB below the
maximum centre or resonant peak whileattenuating or weakening the othersoutside of these two points.
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Operation of Band Pass Filter
Circuit
Then for widely spread frequencies, we
can simply define the term "bandwidth",
BW as being the difference between the
lower cut-off frequency ( cLOWER ) andthe higher cut-off frequency ( cHIGHER )points. In other words, BW = H - L.Clearly for a pass band filter to function
correctly, the cut-off frequency of the lowpass filter must be higher than the cut-off
frequency for the high pass filter.
O f
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Operation of Band Pass Filter
Circuit
The "ideal" Band Pass Filtercan also be
used to isolate or filter out certain
frequencies that lie within a particular band
of frequencies, for example, noisecancellation. Band pass filters are known
generally as second-order filters, (two-pole)
because they have "two" reactive
component within their circuit design. Onecapacitor in the low pass circuit and
another capacitor in the high pass circuit.
Frequency Response of a 2nd
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Frequency Response of a 2nd
Order Band Pass Filter.
F R f 2 d
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Frequency Response of a 2nd
Order Band Pass Filter
The Bode Plotor frequency response curve above showsthe characteristics of the band pass filter. Here the signal isattenuated at low frequencies with the output increasing at aslope of +20dB/Decade (6dB/Octave) until the frequencyreaches the "lower cut-off" point L. At this frequency theoutput voltage is again 1/2 = 70.7% of the input signal valueor -3dB(20 log (Vout/Vin)) of the input. The output continuesat maximum gain until it reaches the "upper cut-off" point Hwhere the output decreases at a rate of -20dB/Decade(6dB/Octave) attenuating any high frequency signals. Thepoint of maximum output gain is generally the geometricmean of the two -3dB value between the lower and upper
cut-off points and is called the "Centre Frequency" or"Resonant Peak" value r. This geometric mean value iscalculated as being r2 = (upper)x (lower).
F R f 2 d
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Frequency Response of a 2nd
Order Band Pass Filter
The upper and lower cut-off frequency
points for a band pass filter can be
found using the same formula as that
for both the low and high pass filters,For example.
1
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Examp le No1.
A second-order band pass filteris to
be constructed using RC components
that will only allow a range of
frequencies to pass above 1kHz(1,000Hz) and below 30kHz
(30,000Hz). Assuming that both the
resistors have values of 10ks,calculate the values of the twocapacitors required.
A f l N 1
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Answer fo r example No1.
The High Pass Filter Stage.
The value of the capacitor C1
required to give a cut-off frequency Lof 1kHz with a resistor value of 10kis calculated as:
Answer for example No1
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Answer for example No1.
The Low Pass Filter Stage.
The value of the capacitor C2
required to give a cut-off frequency
H of 30kHz with a resistor value of10k is calculated as:
Completed Band Pass Filter
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Completed Band Pass FilterCircuit
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Types of active filter
a. Low- Pass Filter
b. High-Pass Filterc. Band- Pass Filter
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Low pass filter circuit
Operation of lo pass filters
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Operation of low-pass filters
circuit
This first-order low pass active filter,consists simply of a passive RC filterstage providing a low frequency path
to the input of a non-invertingoperational amplifier.
The amplifier is configured as avoltage-follower (Buffer) giving it a DC
gain of one, Av = +1 or unity gain asopposed to the previous passive RCfilter which has a DC gain of less than
unity.
Frequency Response of a 1st
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Frequency Response of a 1st
Order Low Pass Filter
Gain of a first order low pass
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Gain of a first-order low pass
filter
Gain of a first order low pass
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Gain of a first-order low pass
filter
Magnitude of Voltage Gain in
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Magnitude of Voltage Gain in
(dB)
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Example No1
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 159Hzand an input impedance of 10K.
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Solution:
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Second order Low Pass Active
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Second-order Low Pass Active
Filter
As with the passive filter, a first-order lowpass active filter can be converted into asecond-order low pass filter simply byusing an additional RC network in the input
path.The frequency response of the second-order low pass filter is identical to that ofthe first-order type except that the stop
band roll-off will be twice the first-orderfilters at 40dB/decade (12dB/octave).Therefore, the design steps required of thesecond-order active low pass filter are the
same.
Second order Active Low Pass
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Second-order Active Low Pass
Filter Circuit
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The High Pass Filter Circuit
Operation of high-pass filters
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Operation of high-pass filters
circuit
When the closed loop response of the op ampintersects the open loop response. A commonlyavailable operational amplifier such as the uA741has a typical "open-loop" (without any feedback)DC voltage gain of about 100dB maximum
reducing at a roll off rate of -20dB/Decade (-6db/Octave) as the input frequency increases. Thegain of the uA741 reduces until it reaches unitygain, (0dB) or its "transition frequency" ( Ft ) whichis about 1MHz. This causes the op-amp to have afrequency response curve very similar to that of a
first-order low pass filter
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Gain for an Active High Pass Filter
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Magnitude of Voltage Gain in (dB)
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Example No1
A first order active high pass filter has
a pass band gain of two and a cut-off
corner frequency of 1kHz. If the input
capacitor has a value of 10nF,calculate the value of the cut-off
frequency determining resistor and
the gain resistors in the feedbacknetwork. Also, plot the expected
frequency response of the filter.
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Second-order High Pass Active
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Second order High Pass Active
Filter
As with the passive filter, a first-order highpass active filter can be converted into asecond-order high pass filter simply byusing an additional RC network in the input
path. The frequency response of thesecond-order high pass filter is identical tothat of the first-order type except that thestop band roll-off will be twice the first-
order filters at 40dB/decade (12dB/octave).Therefore, the design steps required of thesecond-order active high pass filter are thesame.
Second-order Active High Pass
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Second order Active High Pass
Filter Circuit
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Cascading Active High Pass Filters
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B d P Filt
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Band Pass Filter
This cascading together of the individuallow and high pass passive filters producesa low "Q-factor" type filter circuit which hasa wide pass band. The first stage of the
filter will be the high pass stage that usesthe capacitor to block any DC biasing fromthe source. This design has the advantageof producing a relatively flat asymmetrical
pass band frequency response with onehalf representing the low pass responseand the other half representing high passresponse
Band Pass Frequency Response
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Band Pass Frequency Response