Parametric equaliser design:

The parametric equaliser circuit discussed here is a symmetrical constant Q design which makes use of ordinary potentiometers instead of centre tap potentionmeters used in similar circuits.

The parametric equaliser circuit is implemented using the circuit shown in fig. 1. A bandpass filter is connected at V. This bandpass filter determines the centre frequency and Q-factor of the parametric equaliser. The output of the bandpass filter is then send to a variable gain section. The output of this section can either be sent to Vc, to cut frequencies, or Vb to boost frequencies.


Figure 1 - Main signal path

All the resistors except R3 and R5 has the same values. The value of R3 determines the cut ratio, while the value of R5 determines the boost ratio.

If Vc = aZ(s)V and Vb = bZ(s)V

then 

where Z(s) is the transfer function of the bandpass filter. To boost the mid frequencies, a must be 0 while b is adjusted. The opposite is true to cut mid frequencies. Note that for constant-Q operation, the one which is not used, must be zero.

The simplest way to implement the control of a and b with standard potentiometers is to use a dual-gang linear potentiometer. The one half is used to control the gain of the gain stage, while the other half drives a comparator which controls analog switches which either connects the output of the gain stage to Vc or Vb. A standard comparator in combination with a SPDT analog switch can be used to switch between the Vc and Vb inputs. It is advisable to use hysterises in the comparator.

The variable gain stage:

The circuit needed for the gain stage must give maximum gain at the end of the boost/cut control?s travel, while giving zero gain at the centre. Figure 2 shows such a variable-gain circuit.


Figure 2 - Variable gain circuit

The gain of this circuit is as follows:

where RT=(R+gRp)||(R+(1-g)Rp) and g the position of Rp is.

The maximum value of RT, RTmax is when g=0.5, which would also result in Avmin. The minumum value of RT, RTmin is when g=0 or g=1, which would also result in Avmax. Here is the equations for RTmax and RTmin:

RTmax = (2R+Rp)/4

RTmin = (R+Rp)||R

If g=0.5, that is, a flat responce, Av must be 0. To accomplise that R1 must equal RTmin, therefore

For maximum linearity of the boost/cut control, R must not be too small compared to Rp. Note that the larger R is made, the smaller the maximum gain of the gain stage becomes. This circuit shows a deadband in its responce about the centre of Rp. This is actually an advantage, for it gives adequate time for the analog switches to switch from Vc to Vb and vice-versa. It is even possible to give the swithes a dead-band, where the filter and gain section is totally cut-out if Rp is in its centre position.

The first step in designing this circuit is to select a value for Rp. The best choice for R is the same as Rp. This gives the most linear curve, without losing to much gain. After the values of Rp and R have been selected, the value for R1 is calculated.

Next the values the of Avmax and R2 must be calculated. The value of R2 is calculated as follows:

The value of R2 cannot be negative, therefore

RT-R1-AvmaxRT > 0 or 

After the value of Avmax has been selected, the value of R2 can be calculated. It is best to compose R1 of a fixed resistor and preset resistor in series. The circuit can then be balanced to give zero gain at zero boost/cut.

The bandpass-filter:

The type of filter used in modern parametric equalisers is a state-variable active filter. The advantages of such a filter is that the Q-factor and centre frequency is independently adjustable. Figure 3 shows a circuit of a state-variable bandpass filter.

The transfer function of the filter is as follows:

The Q-factor of the filter is adjusted by VR1, while the centre-frequency is adjusted by VR2. Note that for Q values below 1, the amplitude of the hp and lp outputs is 1/Q times higher than the bp output. If such low values of Q is needed, the input signal needs to be attenuated to prevent clipping of the hp and lp outputs. Taking this into account, it may be better to put the variable gain stage before the filter instead of after it. The drawback of putting the stages this way is that the noise generated by the filter will always be present on the output of the equaliser.


Figure 3 - State-variable active filter