Midrange equalisation

The response of the HM100Z0 midrange unit has a 2dB trough in it, centred at around 1kHz, and extending between around 500Hz and 2kHz. This can be more or less removed by using a biquad filter of the form:

,

which has the functional form of unity plus a bandpass filter. The gain at the centre frequency w0 is a/b, and the width of the bandpass increases with b. If the coefficient of the second term is made variable, the amount of boost at the bandpass centre frequency is variable, which is a useful feature.

The simplest implementation of the equalisation, and the one I settled for, is to use a bandpass filter circuit, and then to sum the output of this with its input. I used the following bandpass circuit:

The transfer function of this is

where .

If C1=C2=C, and R1=R2=R3=R, then

where and .

Hence and .

At w=w0, the transfer function is , so the gain of the circuit needs to be adjusted accordingly.

If w0=2 pi x 1kHz, and C=22nF, this gives the following component values:

R1 = R2 = R3 = 10.23 kohms R4 = 7.015 kohms R5 = 15.092 kohms

I used 10 kohms for R1, R2 and R3, 8.2 kohms in parallel with 15 kohms for R4, and 15 kohms for R5. This choice of R1 - R3 detunes the centre frequency by 1.8%, but I didn't find this changed the modelled response of the driver much.

To adjust the size of the response peak at w0, the bandpass circuit was followed by an attenuator and a buffer, so that a fraction of its output could be added to its input:

The buffer is necessary to make sure that changing Ra and Rb does not change the output level outside the midrange. The output must, of course, be followed by a high-impedance input. The whole circuit then looks like this:

I initially implemented Ra and Rb as a 10K linear potentiometer, but I later adjusted the circuit to give as near as possible to a 2dB boost at 1kHz, and substituted fixed resistors.