One of the joys of technical writing is the opportunity it gives to chew over ideas and basic principles. Often these deliberations lead to experimental circuits which in turn enhance one's understanding and experience in electronics.

This month I have been engaged in writing an article on how to design one's own sub bass woofer. Much of the thrust of speaker technology has been directed at the problem of gaining as much bass as possible from existing enclosure types. The manufacturers suffer from the drawback of having little influence over the electronics used to drive their creations.

This is just the area in which the electronics enthusiast can make his mark. Existing Hi-Fi installations can easily be manipulated by the addition of external circuitry to compensate for the shortcomings of speakers etc.

The obvious example of this is the graphic equaliser which seems to be doing better in the American market than here. One of the reasons for this is probably the fundamental dichotomy between the design-philosophies of the British and Americans.

Our friends across the 'pond' are almost conditioned to accept that the more EQ that can be fitted into a preamp the better. We, of course, tend to be more conservative about these things arguing that if the system is flat from the microphone to the speaker then all will be well.

It is interesting to note that several American speaker manufacturers employ active EQ boxes designed to be used with their speaker systems. One of the most obvious uses of such an EQ box would be to boost the deep bass response.

As part of the research for the above mentioned bass article I designed just such a box for use with I.B. enclosures. Most speakers encountered nowadays are of this variety and in consequence most could use a little judicious bass boost.

Normal tone controls are useless for this particular application because they are mainly designed for the maximum effect. In practice this means that they start to boost the signal just below 1kHz. In consequence the mid-range is boosted as well and the whole signal becomes severely coloured if the lift is advanced far enough to counter-the roll-off of the speaker system.

A better solution is to design a filter that gives a known amount of boost at a very low frequency with a response that complements the speaker's own roll-off.

The most important information, where to start boosting the response can be obtained from the data included with the speaker. This will quote the low frequency -3dB limit. Once this information is known it is a relatively simple matter to design a filter with the right characteristics.

Figure 1a shows just such a circuit. Since the roll-off of I.B. enclosures is some 12dB/octave the circuit contains two separate 6dB/octave boost sections. Each section works as follows.

With reference to Figure 1c, A1 is a conventional op-amp connected as a non-inverting amplifier. This means that the output signal is in phase with the input signal which is applied to the +, non-inverting input. It is a characteristic of an op-amp connected in this manner that the voltage gain is equal to R_f/R1. So even if R_f were to be a short circuit the gain cannot fall below unity.

At high frequencies the capacitor, C1, will appear to be a short circuit and as this is shunting the signal across R_f it follows that for practical purposes the amp's gain will be unity. As the input signal's frequency is lowered there will come a point at which the impedance of the capacitor is equal in value to the resistance of R_f. This is the much vaunted '3dB point' in the frequency response of the amp. As the input frequency is lowered towards DC, C1's impedance rises. Eventually it is large compared to R_f and the amps gain becomes as predicted by the above equation.

The impedance of a capacitor can be defined by the following simple equation, Z = 1/(2πfC). C is in Farads, f in Hz, and Z in ohms. To take a practical example let's suppose that we want our amplifier response to be +3dB up at 50Hz. In order not to upset the power amp unduly it's a good idea to keep the maximum gain to 6dB, 4 times. This sets the ratio between the value of R_f and R1 at 3 times. For the sake of example let's make R_f 47k. The nearest standard value for R1 is then 47/3 = 15k. Having settled this the next stage is to determine the value of C1. For 3dB at 50Hz we need to choose a value which will have an impedance of 47k at 50Hz.

Rearranging the equation for impedance we obtain C = 1/2πfZ [10^-8] = 6.77 x 10^-8F, i.e. 68nF.

When such a single stage amp is placed between the pre and power amp feeding the speaker the results are quite dramatic. For starters the rapid 12dB per octave roll-off is halved instead of being 12dB down at 25Hz the response is only 6dB down. The result is an increase of deep bass without detriment to the rest of the frequency range.

A still more elegant solution is to cascade two such circuits in series. This will extend the -3dB point down by half an octave. Our speaker will then be 3dB down at 38Hz! This will allow bass drums, for example to be reproduced at their proper volume.

For this return to Figure 1a. Here the resistor values have been adjusted to give a maximum gain of 2 per stage, 4 in total. The capacitor values have also to be changed in order to ensure that the response is 1.5dB up at the selected frequency in each stage.

Keeping the feedback resistor at 47k the right value for C can be determined from the table. Other values can be determined by using the equation C = (4.8 x 10⁶) / f (C is expressed in Farads). The circuit can easily be built on a piece of Veroboard and mounted in a suitable, preferably metal, box. A PP3 gives a reasonable life. Only one channel is shown, the other is identical.