active band pass filter - op-amp band pass filter

8/18/2019 Active Band Pass Filter - Op-Amp Band Pass Filter

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► Active Filter Design

► What Is Band Pass Filter

► Low Pass Filter

Band stop Notch filtersMany already designed bandstops, & Notch filters, custom designs

Active Band Pass Filter

Active Band Pass Filter

As we saw previously in the Passive Band Pass Filter (http://www.electronics-tutorials.ws/filter/filter_4.ht

tutorial, the principal characteristic of a Band Pass Filter or any filter for that matter, is its ability to pa

frequencies relatively unattenuated over a specified band or spread of frequencies called the “Pass Band”.

For a low pass f ilter this pass band starts from 0Hz or DC and continues up to the specified cut-off frequency point

-3dB down from the maximum pass band gain. Equally, for a high pass filter the pass band starts from this -3dB cut-

frequency and continues up to infinity or the maximum open loop gain for an Active Filter (http://amazon.in/s/?fie

keywords=Understand+Electronic+Filters).

However, the Active Band Pass Filter is slightly different in that it is a frequency selective filter circuit used

electronic systems to separate a signal at one particular frequency, or a range of signals that lie within a certain “ban

of frequencies from signals at all other frequencies. This band or range of frequencies is set between two cut-off

corner frequency points labelled the “lower frequency” ( ƒ ) and the “higher frequency” ( ƒ ) while attenuating a

signals outside of these two points.

Simple Active Band Pass Filter can be easily made by cascading together a single Low Pass Fil

(http://www.electronics-tutorials.ws/filter/filter_2.html) with a single High Pass Filter (http://www.electroni

tutorials.ws/filter/filter_3.html) as shown.

L H

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2/15

The cut-off or corner frequency of the low pass filter (LPF) is higher than the cut-off frequency of the high pass fi

(HPF) and the difference between the frequencies at the -3dB point will determine the “bandwidth” of the band pa

filter while attenuating any signals outside of these points. One way of making a very simple Active Band Pass Filte

to connect the basic passive high and low pass filters we look at previously to an amplifying op-amp circuit as shown

Active Band Pass Filter Circuit

This cascading together of the individual low and high pass passive filters produces a low “Q-factor” type filter circ

which has a wide pass band. The first stage of the filter will be the high pass stage that uses the capacitor to block a

DC biasing from the source. This design has the advantage of producing a relatively flat asymmetrical pass ba

frequency response with one half representing the low pass response and the other half representing high pa

response as shown.

The higher corner point ( ƒ ) as well as the lower corner frequency cut-off point ( ƒ ) are calculated the same as bef

in the standard first-order low and high pass filter circuits. Obviously, a reasonable separation is required between t

two cut-off points to prevent any interaction between the low pass and high pass stages. The amplifier also providisolation between the two stages and defines the overall voltage gain of the circuit.

The bandwidth of the filter is therefore the difference between these upper and lower -3dB points. For examp

suppose we have a band pass filter whose -3dB cut-off points are set at 200Hz and 600Hz. Then the bandwidth of

filter would be given as: Bandwidth (BW) = 600 – 200 = 400Hz.

The normalised frequency response and phase shift for an active band pass filter will be as follows.

H L


3/15

Active Band Pass Frequency Response

While the above passive tuned filter circuit will work as a band pass filter, the pass band (bandwidth) can be quite wi

and this may be a problem if we want to isolate a small band of frequencies. Active band pass filter can also be ma

using inverting operational amplifier. So by rearranging the positions of the resistors and capacitors within the filter

can produce a much better filter circuit as shown below. For an active band pass filter, the lower cut-off -3dB poin

given by ƒ while the upper cut-off -3dB point is given by ƒ .

Inverting Band Pass Filter Circuit

C2 C1


4/15

This type of band pass filter is designed to have a much narrower pass band. The centre frequency and bandwidth

the filter is related to the values of R1, R2, C1 and C2. The output of the filter is again taken from the output of the o

amp.

Multiple Feedback Band Pass Active FilterWe can improve the band pass response of the above circuit by rearranging the components again to produce

infinite-gain multiple-feedback (IGMF) band pass filter. This type of active band pass design produces a “tuned” circbased around a negative feedback active filter giving it a high “Q-factor” (up to 25) amplitude response and steep ro

off on either side of its centre frequency. Because the frequency response of the circuit is similar to a resonance circ

this center frequency is referred to as the resonant frequency, ( ƒr ). Consider the circuit below.

Infinite Gain Multiple Feedback Active Filter


5/15

This active band pass filter circuit uses the full gain of the operational amplifier, with multiple negative feedbaapplied via resistor, R and capacitor C . Then we can define the characteristics of the IGMF filter as follows:

We can see then that the relationship between resistors, R and R determines the band pass “Q-factor” and

frequency at which the maximum amplitude occurs, the gain of the circuit will be equal to -2Q . Then as the g

increases so to does the selectivity. In other words, high gain – high selectivity.

Active Band Pass Filter Example No1

An active band pass filter that has a gain Av of one and a resonant frequency, ƒr of 1kHz is constructed using an infin

gain multiple feedback filter circuit. Calculate the values of the components required to implement the circuit.

Firstly, we can determine the values of the two resistors, R and R required for the active filter using the gain of

circuit to find Q as follows.

2 2

1 22

1 2


6/15

Then we can see that a value of Q = 0.7071 gives a relationship of resistor, R being twice the value of resistor R . Th

we can choose any suitable value of resistances to give the required ratio of two. Then resistor R = 10kΩ and R

20kΩ.

The center or resonant frequency is given as 1kHz. Using the new resistor values obtained, we can determine the va

of the capacitors required assuming that C = C = C .

The closest standard value is 10nF.

Resonant Frequency PointThe actual shape of the frequency response curve for any passive or active band pass filter will depend upon

characteristics of the filter circuit with the curve above being defined as an “ideal” band pass response. An active ba

pass filter is a 2nd Order type filter because it has “two” reactive components (two capacitors) within its circuit desig

As a result of these two reactive components, the filter will have a peak response or Resonant Frequency ( ƒr ) at

“center frequency”, ƒc. The center frequency is generally calculated as being the geometric mean of the two -3

frequencies between the upper and the lower cut-off points with the resonant frequency (point of oscillation) be

given as:

Where:

ƒ is the resonant or Center Frequency

ƒ is the lower -3dB cut-off frequency point

2 1

1

1 2

r

L


7/15

ƒ is the upper -3db cut-off frequency point

and in our simple example in the text above of a filters lower and upper -3dB cut-off points being at 200Hz and 600

respectively, then the resonant center frequency of the active band pass filter would be:

The “Q” or Quality FactorIn a Band Pass Filter circuit, the overall width of the actual pass band between the upper and lower -3dB corner poi

of the filter determines the Quality Factor or Q-point of the circuit. This Q Factor is a measure of how “Selective”

“Un-selective” the band pass filter is towards a given spread of frequencies. The lower the value of the Q factor t

wider is the bandwidth of the filter and consequently the higher the Q factor the narrower and more “selective” is t

filter.

The Quality Factor, Q of the filter is sometimes given the Greek symbol of Alpha, ( α ) and is known as the alpha-pe

frequency where:

As the quality factor of an active band pass filter (Second-order System) relates to the “sharpness” of the filte

response around its centre resonant frequency ( ƒr ) it can also be thought of as the “Damping Factor” or “Damp

Coefficient” because the more damping the filter has the flatter is its response and likewise, the less damping the fil

has the sharper is its response. The damping ratio is given the Greek symbol of Xi, ( ξ ) where:

The “Q” of a band pass filter is the ratio of the Resonant Frequency, ( ƒr ) to the Bandwidth, ( BW ) between the upp

and lower -3dB frequencies and is given as:

H


8/15

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9/15

Older comments (http://www.electronics-tutorials.ws/filter/filter_7.html/comment-page-1#comments)

RobHello.

Can you comment on the typical bandwidths of each circuit? I am curious to know if one circuit is better suited

for my application based on the pass band. As well, with the IGMF circuit, what is the limit of the bandwith

before the 3dB points start affecting each other?

Cheers

April 7th, 2015 (http://www.electronics-tutorials.ws/filter/filter_7.html/comment-page-2#comment-6499)Reply (/filter/filter_7.html?replytocom=6499#respond)

Wayne Storr (http://www.electronics-tutorials.ws)

This is a very open question. A filters passband is dependant upon what you set as the corner or cut-off

frequencies. It can be very narrow and selective or very wide and flat with ripple in the pass band or stop

band, also the roll-off either side of the -3dB points depending on what order the filter is and whether its a

Butterworth, Chebyshev or Bessel design.

April 8th, 2015 (http://www.electronics-tutorials.ws/filter/filter_7.html/comment-page-2#comment-6502)Reply (/filter/filter_7.html?replytocom=6502#respond)

kaya

is there any reason for having HPF>AMP>LPF configuration could you not for instance have HPF>LPF>AMP etc

March 25th, 2015 (http://www.electronics-tutorials.ws/filter/filter_7.html/comment-page-2#comment-6398)Reply (/filter/filter_7.html?replytocom=6398#respond)


Yes you could do that if you wished, or any combination you want. As explained in the text, the purpose of the

op-amp is to isolate the two filters and stop them having a loading effect on each other.


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10/15

Jack

Hi Wayne

Is there a way that you can have two separate band pass filters in the same circuit? For instance if I wanted a

band pass filter that is close to 800Hz and then another for 970Hz? Obviously two band pass filters wouldn’t

work because they would block each other, but is there something else similar?

Thankyou for the help



Hello Jack, yes you can do that with a single circuit. For example, keep the same value capacitor and switch

between two different resistors, one sets the center frequency at 800Hz and the other at 970Hz, just switch

between the two. A quick calculation suggests with a common 10nF capacitor, switching between a 20k

resistor will give 800Hz and a 16k5 resistor will give 970Hz, more or less.


Eric

In ‘Active Band Pass Filter Example No1′ the resonant frequency, Fr is given as 1kHz but further down you

calculate an Fr of 346Hz by taking the geometric mean of 200 and 600. Can you explain this difference and also

where 200 and 600 came from? Thanks.

February 1st, 2015 (http://www.electronics-tutorials.ws/filter/filter_7.html/comment-page-2#comment-5767)Reply (/filter/filter_7.html?replytocom=5767#respond)


Hello Eric, in the tutorial text above the filters normalised frequency response curve, I make reference to a

theoretical filter having a Bandwith or 400Hz (600Hz – 200Hz). The same lower and upper frequencies are then

used again to show that for this filter its center frequency would be 346Hz. Example No1 is another filter

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11/15

calculation. I appologise if it was confusing and have ammended the text to hopefully make it more clearer.

February 1st, 2015 (http://www.electronics-tutorials.ws/filter/filter_7.html/comment-page-2#comment-5768)Reply (/filter/filter_7.html?replytocom=5768#respond)

Mohammad

Hello.

I am an electronics engineer. I need to separate the different frequencies of sound, hence I need to have my

filter design with minimal elements.

Please help me.

November 13th, 2014 (http://www.electronics-tutorials.ws/filter/filter_7.html/comment-page-2#comment-4865)Reply (/filter/filter_7.html?replytocom=4865#respond)

rafi13

Can anyone tell me what kind of filters are used in commercial devices like microphone or speaker??

October 23rd, 2014 (http://www.electronics-tutorials.ws/filter/filter_7.html/comment-page-2#comment-4587)Reply (/filter/filter_7.html?replytocom=4587#respond)

Mark

Why is the term “infinite gain” used, when the gain is limited by the feedback itself? I’m curious as to how that

terminology came about.

Thank you for the tutorial.

September 29th, 2014 (http://www.electronics-tutorials.ws/filter/filter_7.html/comment-page-2#comment-2182)Reply (/filter/filter_7.html?replytocom=2182#respond)


Hello Mark. Infinite Gain Multi Feedback filters are so called because they use a single op-amp as an infinite

gain voltage amplifier with an RC network to provide the required negative feedback. In this case the amplifier

is assumed to be ideal, (i.e., infinite input impedance, infinite gain, and zero output impedance) as it uses the

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12/15

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13/15

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