If you have ever used a tone control on a radio or hi-fi, or guitar, you have used an audio filter.

An audio filter is a circuit that has been designed to let certain frequencies through but block others out; a good example would be the cross-over module in a loudspeaker box, sending low frequency sounds to the woofer and blocking them from destroying the tweeter. Other uses might include blocking low-frequency rumble from a turntable or eliminating hiss from a tape deck, or eliminating mains hum.

There are three main groups of filters:

**Passive**– these use passive components only, such as resistors, capacitors, and inductors, and are suitable to handle high voltage and power levels. Their downfall requires large and expensive components in the cross-over unit and require impedance matching to the inputs and outputs. However, they produce no distortion or electrical noise.

**Digital**– where the signal gets digitized by an analog to digital converter, then processed by a microcontroller, and then sent out again via a digital to analog converter. They are very expensive and complex but can be used in a lot of applications.

**Active**– using active components, could be transistors, but commonly using op-amps. We will look at this group in detail.

Active filters offer some big advantages over passive ones. It has smaller components, no insertion loss, and not dependent on matched input and output impedances. It also has design type families depending on requirements, each having pros and cons—Bessel, Butterworth, Chebyshev, Ellipitical, and Sallen Key.

The designer is faced with many compromises; if he aims at a steep roll-off, he might expect a big pass-band ripple, for example.

The most useful filter with ease of design and best all-around performance with the best control of the compromises is the Sallen Key. And in this tutorial, we will be designing with these. Sallen Key filters are two-pole filters, meaning they have two reactive (capacitors) components.

Their main advantages are they are not fussy about the op-amp’s performance, the phase shift is limited, and reasonable size components (not huge values) can be achieved easily. Their main disadvantage is that they are not really meant to tune and are meant for fixed frequencies.

## Four Types of Filters

**Low Pass**frequencies above a certain point are blocked.

**High Pass**frequencies below a certain point are blocked

**Band Pass**frequencies above and below two points are blocked.

**Notch**frequencies between two points are blocked.

**Low Pass Filte**r

In figure 1 above, you see that frequencies from zero to fc pass without attenuation. But at fc, the signal starts to roll off, and it becomes 3dB down or 0.707 of the original value (0.707 is 1/√2).

As an example, we might want to roll off an amplifier’s response after the audible range (after 20kHz) to prevent oscillations. Shown below in figure 2 is a circuit for such a low pass filter.

Let us design a 20kHz low pass filter. The design is straightforward if some assumptions are made. We make C1=C2 and R1=R2, and Q=0.7 (best flatness at the roll-off point).

Where A is the gain, so A must be 1.6. and the gain is . Choose a value for R4 = 47K then R3 is 27k (using standard values close enough).

The cutoff frequency fc is here. To get a reasonable value, let us experiment and try R1 as 10k.

Where , so for 20kHz, C would work out to 795pF – a very odd value. Let’s put a close standard C value in and see what we get with 680pF.

This gives us 23kHz, which is close enough. It’s not ideal, but if you used a dual gang pot in place of R1 and R2, you could move the cut off a bit.

## High Pass Filter

In figure 3 above, you see that frequencies above fc pass without attenuation. But at fc and below, the signal starts to roll off and becomes ct 3dB down or 0.707 of the original value (0.707 is 1/√2) and continues to roll off as we go down in frequency.

Again, as an example, we might want to roll off an amplifier’s response before the audible range (below 20Hz) to prevent rumble from a turntable. You won’t be able to hear this, but you will see the speaker going in and out! Shown below in figure 4 is a circuit for such a high pass filter.

Let us design a 20Hz high pass filter. The design is straightforward if some assumptions are made. We make C1=C2 and R1=R2, and Q=0.7 (best flatness at the roll-off point)

where A is the gain so A must be 1.6. the gain is . So choose a value for R4=47K then R3 is 27k (using standard values close enough)

The cutoff frequency fc is . Here, you need to experiment a bit so as to get reasonable values so let’s try C1 as 1uF and find R, where and so, for 20Hz, R would work out to 7.9k – a very odd value. Let’s put a close standard R value in and see what we get with 8k2.

This gives us 19.4Hz, which is close enough. It’s not ideal, but if you used a dual gang pot in place of R1 and R2, you could move the cut off a bit.

## Band Pass Filter

In figure 5 above, you see that frequencies between f1 and f2 pass without attenuation. At these points, the signal starts to roll off and in 3dB down or 0.707 of the original value (0.707 is 1/√2) and continues to roll off as we go up or down in frequency.

As an example, we might want to tighten the audio range from a microphone fed into a transmitter to conserve modulation and limit it to a speech band of 300Hz to 3kHz. There is no reason why you can’t cascade a high pass filter set at 300Hz and follow it with a low pass filter set at 3kHz.

Sometimes you might want to pass a narrow band or even just one frequency, for example, a signal generator supplying a test signal of 1kHz and nothing else. Shown in figure 6 below is a narrow band filter for 1kHz.

This is the classic twin t filter, and in the feedback path (from pin 6 to pin 2), there is a low-frequency filter (R2 R3 and C1) and a high-frequency filter (C2 C3 and R5). The two-act together to pass only a narrow band of frequencies, making the gain maximum at the center frequency.

The center frequency fo is , so fo is .

To work properly, the cap in the low-frequency filter should be twice the value of the one in the high-frequency one, and the R in the high frequency one should be half the value in the low-frequency one.

You can easily achieve this by putting two resistors parallel for R5 (halves the value) and two caps in parallel for C1 (doubles the value). The gain is set with R1/R4, i.e., 10. If you wish to make this tunable over a small range, R2 and R3 could be the two gangs of a dual pot.

## Notch Filter

In figure 7, you see that frequencies below f1 and above f2 pass without attenuation. The signal starts to roll-off between these points and in 3dB down or 0.707 of the original value (0.707 is 1/√2) and continues to roll off as we go up or down in frequency. As an example, we might want to get rid of mains borne 60Hz hum in an amplifier.

Shown in figure 8 below is a circuit for a 60Hz notch filter.

This also is a classic twin t filter, and the input and feedback path in the previous circuit have been swapped. There is a low-frequency filter (R2 R3 and C1) and a high-frequency filter (C2 C3 and R5). The two-act together to exclude only a narrow band of frequencies, making the gain minimum at the center frequency.

The center frequency fo is so

The cap in the low-frequency filter should be twice the value of the one in the high-frequency to work properly. The R in the high-frequency one should be half the value in the low-frequency one. You can easily achieve this by putting two resistors parallel for R5 (halves the value) and two caps in parallel for C1 (doubles the value).

The gain is set with R1/R4, i.e., 10. If you wish to make this tunable over a small range, R2 and R3 could be the two gangs of a dual pot.

So that concludes our article on active audio filters. They have so many uses and there is a very nice online calculator here to save you some calculation work.

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