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Active band pass filters are simply
filters constructed by using operational amplifiers as
active devices configured to simulate inductors or what
are known as "gyrators". Active band pass filters are
used largely at audio frequencies where otherwise the
size of the inductor would become prohibitive. The are
many different types of active filters including high
pass, low pass, band reject and there are numerous
responses including multiple feedback band pass (MFBP),
dual-amplifier band pass (DABP) and, state variable
bi-quad all pole circuits. Interestingly all known
filter responses such as Butterworth and Chebyshev may
be synthesised.
Here we will only consider the time
honoured multiple feedback band pass (MFBP) type which
uses capacitors of equal value and leads us to
simplified calculations. Let's look at the basic circuit
in figure 1 below.
Figure 1 - an active band pass filter
Now the calculations are fairly simple.
You need to determine several things first, Ho the gain
per stage, Q the bandwidth and Wo which is 2 * pi * Fc.
Finally pick a convenient value for C
which if reasonably large, leads to smaller values of
resistance and consequently some aid in reducing noise.
Valuable feedback (no pun intended) from
readers using rate-this-page (see below and on every
other page) indicates the following needs clarification:
(a) the 100 uF capacitor above is purely
part of the power supply reservoir and has nothing to do
with the filter itself. The two 10K resistors are part
of the power supply biasing of the op amps because we
are not using positive and negative power supplies.
(b) The capacitor and resistor values
are simply the value of C you choose to use and the
resistor values result from the following calculations.
It's that simple.
We'll proceed with a typical design
example and say we need an audio filter for a CW
receiver. Fc will be 750 Hz, gain per stage we'll fix at
3 and we'll make the bandwidth 150 Hz leading to Q = 750
/ 150 = 5. For convenience C will equal 0.027 uF being a
polyester capacitor we have on hand.
NOTE: If the calculations below look
funny to you in Netscape, just hit the reload button -
just another Netscape "quirk" we poor web designers have
to live with.
Calculate R1 firstly:
R1 = Q / [ Ho * Wo * C ]
= 5 / [ 3 * 4712.4 * 0.027 X 10 - 6 ]
= 5 / 0.0003817 = 13099 or 13K
Next calculate R2:
R2 = Q / [ ( 2 * Q2 - Ho ) * C * Wo ]
= 5 / [ ( 2 * 52 - 3 ) * 0.027 X 10 - 6
* 4712.4 ]
= 5 / [ (50 - 3 ) * 0.000127234 ] = 5 /
.00598 = 836 or 820R
Finally calculate R3:
R3 = 2 * Q / [ C * Wo ]
R3 = 10 / [ 0.027 X 10 - 6 * 4712.4 ]
R3 = 10 / [ 0.000127234 ] = 78,595 or
75K
Resistors in this application could be
typical 5% types but in Australia 1% metal film types in
the E24 series don't cost much more anyway. The
capacitor would be a 5% "Greencap" type. Notice with the
resistors I've gone for the nearest standard E24 value.
The IC could be 741 op amps or for
significantly improved performance select one of the
better quality low noise types such as Philips NE/SA5534
premium low noise operational amplifiers (op-amps).
Pay particular attention to the two 10K
resistors splitting the 12V power supply to correctly
bias the non-inverting (pin 3) input of the op-amps. You
can add as many stages as you wish for sharper cut off
(shape factor) but I don't believe more than two stages
are usually justified
For this kind of active band pass filter
don't try for very high Q's or very high gains, Ho, per
stage. If I receive sufficient feedback (no pun
intended) I might extend the series to other types of
active filters.
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