topic 5 - (filter)student

8/13/2019 TOPIC 5 - (Filter)Student

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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/Resistor


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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_filter


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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.html


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circuit


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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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circuit


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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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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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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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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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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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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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Shift


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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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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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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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Order Band Pass Filter.

F R f 2 d


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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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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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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.



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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



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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

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