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Electro-Music Engineer

State Variable Filter

A well known keyboard player recently stated that he was disappointed with the lack of progress in synthesiser design in the last few years. In the context of the interview he was obviously not referring to technical innovations, such as, the numerous polyphonic synthesisers introduced in recent times, the major improvements in stability and reliability or the general trend of offering better value for money. As a musician he was more concerned with the apparent failure to increase the sound capabilities of the instruments.

Undoubtedly most, if not all, manufacturers will disagree with the above particularly in respect of their top models. At the low to medium price bracket, however, they are faced with a dilemma as to whether additional facilities will maintain the 'value for money' concept and would make playing the synthesiser more difficult (an ever present problem). In the writer's view the addition of more filtering capabilities could be justified. After all it is largely the subtractive synthesis technique of removing or attenuating partials from a complex waveform which provides a synthesiser with its wide range of tone colours. Increasing the filtering capabilities would, therefore, increase the range available.

In many synthesisers the only filter used is the low pass type which attenuates the harmonics above its cut-off frequency. Since this effect is characteristic of many acoustic instruments it is clearly the most useful filter. The roll-off rate of such filters has a marked effect on the sound. For example, a 12dB/octave low pass filter produces a more 'electronic' sound because the raw waveform is still noticeable above the cut-off point. While this sound can be useful it can also be unpleasant during extended playing.

The majority of synthesisers now incorporate a 24dB/octave low pass filter and this steeper roll-off gives a more 'natural' character to the sound. The latter filters are also more effective when being swept by an envelope generator to vary both amplitude and tone dynamics during the course of a note.

Figure 1. Response from a 24 dB/octave low pass filter.

Invariably these filters have means to control feedback, or regeneration, of the signal to provide resonance. With a low pass filter the effect of this is to emphasise a band of frequencies at the cut-off point. This is illustrated in Figure 1 which shows the response from a 24dB/octave low pass filter with and without resonance. At low to medium resonance the effect is akin to the resonant filters described in the February 1982 issue of E&MM and although one does not have independent control over the resonant frequency the additional boost is very effective. As the resonance is increased the sound again becomes more 'electronic' but this time the effect arises from ringing, or oscillation, to generate well-worn 'synthesiser' sounds.

To progress beyond the ubiquitous low pass filter one could use a switchable design, as employed in the E&MM 'Spectrum' synthesiser, although to a large extent a single filter with low, high or band pass responses, or combinations of these, is most useful for special effects. The suggestion earlier, however, was to have more than one filter with independent controls and with at least one of them having switched responses. Application of additional treatment to a low pass filtered waveform greatly increases the scope for both imitative and creative synthesis.

Experimentation with different filter types and combinations of filters will prove very rewarding. Furthermore you do not have to discard your existing synthesiser since most make the keyboard control voltage and gate available for driving external equipment. A filter may be treated as an 'effects' unit and used to treat the output signal. It will also be obvious that when one wishes to explore a specific response that is only available on the external filter then the filter incorporated in the synthesiser may be set to pass an untreated waveform. To assist this exploration the design below is for a voltage controlled filter with band pass, low pass and high pass responses at two rates of roll-off which for the latter two types are 12dB/octave and 24dB/octave. The resonance control allows ringing and induced oscillation but the filter will not self oscillate. The design utilises the CEM 3320 voltage controlled filter IC which is configured in what is known as a 'state variable filter'.

Figure 2. Circuit diagram of state variable filter.
(Click image for higher resolution version)

The complete circuit diagram is shown in Figure 2. At first sight it may look complicated but closer inspection reveals that it is simply two state variable filters connected in series. Simplified explanations are always dangerous but an examination of the first stage built around IC1a, IC2a and IC2b will show the general principle. The signal enters via RV1 and R1 and the maximum gain of the circuit is determined by the ratio of R1 to R4. The design is based on a 10V p-p input and for lower signal levels R1 would be reduced proportionately. This would maintain the signal level within the filter at the design level but to maintain a nominal unity gain it will also be necessary to reduce the value of R22. R5 converts the signal into a current required by the gain cells of the CEM 3320 and the first cell is IC2a. The output from this stage is a single pole band pass response, marked B1, and a second integration in IC2b produces a 12dB/octave low pass output (L1). The output from IC2b is inverted with respect to the input signal and it is subtracted from the signal at IC1a to produce a 12dB/octave high pass response (H1).

The normal method of obtaining resonance with a state variable filter is to feed the band pass output back to the non-inverting input of the first stage, IC1a. The CEM 3320, however, requires a reference current of about 63uA into each cell and in this design the current is established by injecting a bias voltage of about 6V8 into the non inverting input of IC1a from the resistive divider formed by R2 and R3. The bias voltage is converted to the required current by R5. The output of IC2a will retain the bias voltage which in turn provides the current for IC2b via R10. Since the non inverting input is otherwise engaged an alternative for resonance control is to create a feedback loop around IC2a using a CEM 3335 voltage controlled amplifier. The latter device is a simplified version of the CEM 3330 used in the 'Spectrum' insofar as it only has exponential control inputs. The use of an exponential gain control is ideal for resonance since it gives the right 'feel' to the control. C3 blocks the DC voltage and R6 converts the signal to a current to the signal input of IC3a, one half of the CEM 3335. IC4a is an inverting current to voltage converter to restore the signal to its original phase while R9 converts the voltage back into a current for feeding back to the input of IC2a. C5 is for stability as it removes any DC offsets developed in IC3a and IC4a. R7, C4 and D1 are usual components on the signal input to the CEM 333X VCAs and are for compensation and to prevent latch up.

The above completes the first part of the filter and so far we have only used two of the gain cells in the CEM 3320. We can now take any of these first stage outputs (B1, L1, H1) from the pole of switch S1a and feed them into another identical filter section. The result is to produce the higher roll-off responses mentioned earlier and these are marked B2, L2 and H2 at switch S1b. Any of the six outputs may be selected using S1b and output via a buffer formed around IC5. One could consider having all of the outputs available simultaneously but since the filters are all acting on the same signal(s) and have the same cut-off frequency and resonance level there are only a few circumstances when two or more simultaneous responses may be useful. The choice is left to the user.

The other connections to the CEM 3320 and CEM 3335 are shown below the main circuit. On the former, R27, RV3, R28 and R29 allow the filter to be accurately scaled to one volt per octave at the input to R25 and these components plus R24, which sets the control input in the correct range, should be 1% metal film resistors and cermet multiturn as appropriate. The signal and frequency control inputs are both summing nodes and so other inputs may be added as desired. In the circuit diagram the number has been reduced for clarity. The resonance control input to pins 2 and 11 of the CEM 3335 could also be preceded by a summing stage to allow for both manual and external voltage control of resonance.

One may question the use of a relatively expensive VCA in the feedback loop instead of, say, an LM 13600. There are a number of reasons governing the choice. One has already been mentioned, namely, an exponential response to resonance is more realistic although this could have been achieved with an appropriate potentiometer. Another is the desire to retain the high signal to noise ratio inherent in the CEM 3320 especially if the filter is to be used as a post treatment to the synthesiser. Not least, however, is the importance of avoiding complicated setting up procedures, whenever practical, since not all constructors are fortunate enough to have sophisticated test equipment. A particular advantage of this design is the absence of signal or feedthrough trimmers which will ensure that many more constructors will get it operating correctly. In fact, the only adjustment required is the 1V/octave scaling which cannot be avoided if accurate tracking is required. This scale is, however, easily adjusted by reference to the voltage controlled oscillator.

As regards construction, ICs 1, 4 and 5 should be BIFET op-amps, such as TL081 and LF351 or their dual versions TL082 and LF353, whereas the control input, IC6, and a summer for resonance if fitted, may be the 741-type. One precaution, which applies to most circuits, is to achieve a neat lay-out and in this connection it may be simpler to use single op-amps for IC1 instead of the dual type indicated in Figure 2.

Finally, reverting to the roll-off rate of low pass filters we note that a number of polyphonic synthesisers use a 12dB/octave filter although there is at least one which provides both 12 and 24 dB/octave responses. We guess the former must be due to restrictions on available space but we would be pleased to receive comments on the application of the different roll-off rates in both monophonic and polyphonic synthesisers. In fact, when one considers the dramatic effect filtering has on tone colour it does seem to be a neglected one in synthesis and deserving of more documentation in the context of music making.

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Electronics & Music Maker - Copyright: Music Maker Publications (UK), Future Publishing.


Electronics & Music Maker - May 1982

Feature by Charles Blakey

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