It's pretty brute-force, I didn't have time to be elegant. Each "voice" consisted of an Oscillator, a Waveform Generator, a Waveform Selector, a Waveform D/A converter, a Multiplying D/A converter for amplitude control and an Envelope Generator for modulation. The analog output of each voice could be sent through a Multimode Analog Filter or bypass the filter and a final Multiplying D/A converter provided overall manual volume control.
As I recall, the Oscillator is a 24-bit phase-accumulating design of which the lower thelower 16-bits are programmable for pitch control. [1] The output of the accumulator goes directly to a D/A converter through a waveform selector. Normally, the output of a phase-accumulating oscillator would be used as an address into memory which contained a wavetable, but SID had to be entirely self-contained and there was no room at all for a wavetable on the chip.
The Sawtooth waveform was created by sending the upper 12-bits of the accumulator to the 12-bit Waveform D/A.
The Triangle waveform was created by using the MSB of the accumulator to invert the remaining upper 11 accumulator bits using EXOR gates. These 11 bits were then left-shifted (throwing away the MSB) and sent to the Waveform D/A (so the resolution of the triangle waveform was half that of the sawtooth, but the amplitude and frequency were the same).
The Pulse waveform was created by sending the upper 12-bits of the accumulator to a 12-bit digital comparator. The output of the comparator was either a one or a zero. This single output was then sent to all 12 bits of the Waveform D/A.
The Noise waveform was created using a 23-bit pseudo-random sequence generator (i.e., a shift register with specific outputs fed back to the input through combinatorial logic). [2] The shift register was clocked by one of the intermediate bits of the accumulator to keep the frequency content of the noise waveform relatively the same as the pitched waveforms. The upper 12-bits of the shift register were sent to the Waveform D/A. Since all of the waveforms were just digital bits, the Waveform Selector consisted of multiplexers that selected which waveform bits would be sent to the Waveform D/A. The multiplexers were single transistors and did not provide a "lock-out", allowing combinations of the waveforms to be selected. The combination was actually a logical ANDing of the bits of each waveform, which produced unpredictable results, so I didn't encourage this, especially since it could lock up the pseudo-random sequence generator by filling it with zeroes. [3] [Actually, the result isn't a logical ANDing at all. -TechEd]
The output of the Waveform D/A (which was an analog voltage at this point) was fed into the reference input of an 8-bit multiplying D/A, creating a DCA (digitally-controlled-amplifier). The digital control word which modulated the amplitude of the waveform came from the Envelope Generator.
The Envelope Generator was simply an 8-bit up/down counter which, when triggered by the Gate bit, counted from 0 to 255 at the Attack rate, from 255 down to the programmed Sustain value at the Decay rate, remained at the Sustain value until the Gate bit was cleared then counted down from the Sustain value to 0 at the Release rate.
A programmable frequency divider was used to set the various rates (unfortunately I don't remember how many bits the divider was, either 12 or 16 bits). A small look-up table translated the 16 register-programmable values to the appropriate number to load into the frequency divider. Depending on what state the Envelope Generator was in (i.e. ADS or R), the appropriate register would be selected and that number would be translated and loaded into the divider. Obviously it would have been better to have individual bit control of the divider which would have provided great resolution for each rate, however I did not have enough silicon area for a lot of register bits. Using this approach, I was able to cram a wide range of rates into 4 bits, allowing the ADSR to be defined in two bytes instead of eight. The actual numbers in the look-up table were arrived at subjectively by setting up typical patches on a Sequential Circuits Pro-1 and measuring the envelope times by ear (which is why the available rates seem strange)!
In order to more closely model the exponential decay of sounds, another look-up table on the output of the Envelope Generator would sequentially divide the clock to the Envelope Generator by two at specific counts in the Decay and Release cycles. This created a piece-wise linear approximation of an exponential. I was particularly happy how well this worked considering the simplicity of the circuitry. The Attack, however, was linear, but this sounded fine.
A digital comparator was used for the Sustain function. The upper four bits of the Up/Down counter were compared to the programmed Sustain value and would stop the clock to the Envelope Generator when the counter counted down to the Sustain value. This created 16 linearly spaced sustain levels without havingto go through a look-up table translation between the 4-bit register value and the 8-bit Envelope Generator output. It also meant that sustain levels were adjustable in steps of 16. Again, more register bits would have provided higher resolution.
When the Gate bit was cleared, the clock would again be enabled, allowing the counter to count down to zero. Like an analog envelope generator, the SID Envelope Generator would track the Sustain level if it was changed to a lower value during the Sustain portion of the envelope, however, it would not count UP if the Sustain level were set higher.
The 8-bit output of the Envelope Generator was then sent to the Multiplying D/A converter to modulate the amplitude of the selected Oscillator Waveform (to be technically accurate, actually the waveform was modulating the output of the Envelope Generator, but the result is the same).
Hard Sync was accomplished by clearing the accumulator of an Oscillator based on the accumulator MSB of the previous oscillator. [4] Ring Modulation was accomplished by substituting the accumulator MSB of an oscillator in the EXOR function of the triangle waveform generator with the accumulator MSB of the previous oscillator. [5] That is why the triangle waveform must be selected to use Ring Modulation.
The Filter was a classic multi-mode (state variable) VCF design. There was no way to create a variable transconductance amplifier in our NMOS process, so I simply used FETs as voltage-controlled resistors to control the cutoff frequency. An 11-bit D/A converter generates the control voltage for the FETs (it's actually a 12-bit D/A, but the LSB had no audible affect so I disconnected it!).
Filter resonance was controlled by a 4-bit weighted resistor ladder. Each bit would turn on one of the weighted resistors and allow a portion of the output to feed back to the input. The state-variable design provided simultaneous low-pass, band-pass and high-pass outputs. Analog switches selected which combination of outputs were sent to the final amplifier (a notch filter was created by enabling both the high and low-pass outputs simultaneously).
The filter is the worst part of SID because I could not create high-gain op-amps in NMOS, which were essential to a resonant filter. In addition, the resistance of the FETs varied considerably with processing, so different lots of SID chips had different cutoff frequency characteristics. I knew it wouldn't work very well, but it was better than nothing and I didn't have time to make it better.
Analog switches were also used to either route an Oscillator output through or around the filter to the final amplifier. The final amp was a 4-bit multiplying D/A converter which allowed the volume of the output signal to be controlled. By stopping an Oscillator, it was possible to apply a DC voltage to this D/A. Audio could then be created by having the microprocessor write the Final Volume register in real-time. Game programs often used this method to synthesize speech or play "sampled" sounds.
An external audio input could also be mixed in at the final amp or processed through the filter.
The Modulation registers were probably never used since they could easily be simulated in software without having to give up a voice. For novice programmers they provided a way to create vibrato or filter sweeps without having to write much code (just read the value from the modulation register and write it back to the frequency register). These registers just give microprocessor access to the upper 8 bits of the instantaneous value of the waveform and envelope of Voice 3. Since you probably wouldn't want to hear the modulation source in the audio output, an analog switch was provided to turn off the audio output of Voice 3.