Analog modeling: SD1 vs TS9

There are so many different distortion/overdrive/fuzz guitar pedals, and some have a better reputation than other. Two of them have a reputation of being closed (one copied on the other), and I already explained how one of these could be modeled (and I have a plugin with it!). So let’s work on comparing the SD1 and the TS9.

Global comparison

I won’t focus on the input and output stage, although they can play a role in the sound (especially since the output stage is the only difference between the TS9 and the TS808…).

Let’s have a look at the schematics:

SD1 annotated schematic
SD1 annotated schematic

TS9 schematic
TS9 schematic

The global circuits seem similar, with similar functionalities. The overdrives are heavily closed, and actually without the asymmetry of the SD1, they would be identical (there are versions of SD1 with the 51p capacitor or a close enough value). The tone circuits have more differences, with the TS9 having an additional 10k resistor and a “missing” capacitor around the AOP. The values are also quite different, but based on a similar design.

Now, the input stages are different. SD1 has a higher input capacitor, but removes around 10% of the input signal compared to 1% for TS9 (not accounting for the guitar output impedance). Also there are two high pass filters on SD1 with the same cut frequency at 50Hz, whereas the TS9 has “only” one at 100Hz. They more or less end up being similar. For the output, the SD1 ditches 33% of the final signal before the output stage that also has a high pass filter at 20Hz and finally another one at 10Hz. The TS9 has also a 20Hz high pass but it is followed by another 1Hz high pass. All things considered, except for the overdrive and the tone circuits, there should be not audible difference on a guitar, but I wouldn’t advice either pedal for a bass guitar, the input stages are chopping off too much.

Overdrive circuit

The overdrive circuits are almost a match. The only difference is that the potentiometer has double resistance on the SD1 and there is 2 diodes in one path (the capacitor has no impact according to the LTSpice simulation I ran). And leads to exactly what I expected for similar drive value:

SD1 and TS9 behavior on a 100Hz signal
SD1 and TS9 behavior on a 100Hz signal

This is the behavior for all frequencies. The only difference is the slightly small voltage on the down part of the curve. This shows up more clearly on the spectrum:

SD1 sine sweep with an oversampling x4
SD1 sine sweep with an oversampling x4

TS9 sine sweep with an oversampling x4
TS9 sine sweep with an oversampling x4

To limite the noise in this case, I ran the sine sweep again, with an oversampling of x8. The difference with the additional even frequencies in SD1 is obvious.

SD1 sine sweep with an oversampling x8
SD1 sine sweep with an oversampling x8

TS9 sine sweep with an oversampling x8
TS9 sine sweep with an oversampling x8

Tone

The tone circuit is a nightmare to compute by hand. The issues are with the simplification of the potentiometer in the equations. I did it for the SD1 tone circuit, and as the TS9 is a little bit different, I had to start over (several years after solving SD1 :/).

I won’t display the equations here, the coefficients can be found in the pedal tone stack filters in Audio Toolkit. Suffice to say that TS9 can be a high pass filter whereas SD1 is definitely an EQ. The different behavior is obvious in the following pictures:

SD1 tone spectrum
SD1 tone transfer function

TS9 tone spectrum
TS9 tone transfer function

The transfer functions are different even if their analog circuit is quite similar. This is definitely the difference that people hear between SD1 and TS9.

Conclusion

The two pedals are quite similar when checking the circuit, and even if SD1 is labelled as an asymmetric overdrive, the actual sound different between the two pedals may be more related to the tone circuit than the overdrive.

Now that these filters are available in Audio Toolkit, it is easy to try different combinations!

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