Active bandpass filters

What are active band pass filters?

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.

Active band pass filter schematic

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 tw1o 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.

Active band pass filter calculations

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

Active band pass filter components

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 tw1o 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 tw1o
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.