Most "musical" high-pass corner frequency to remove DC

[synthpark]

In the design of a synth architecture one might have to face the problem of inserting or not inserting a high-pass filter (most likely first order) in the path.

Let's say we have a ladder-filter and it starts with a saturation stage. Driving that filter with a signal after a high-passed filter gives, generally speaking, a different result than for the DC case.

The input signal might be a ring modulated signal with a strong DC. One can restrict the use of HP to the Ring-Mod component only and leave the rest DC.

Another example is a synced signal with a DC component. The most extreme case is a pulse wave with narrow pulse width, although this case is not interesting and should give similar results. But also PWM through a ladder filter should sound different for DC or AC, but I havent tried. Another example is FM modulation, where a strong DC component can develop.

Choosing a cutoff frequency, if first order, results in a settling time of roughly 2.5*tau = 2.5/(2*pi*fc). So for 5 Hz we already get 80ms. If the filter is heavily driven, this may result in a remarkably different sound for the first 80ms until the DC is settled, apart from the effective asymmetrical drive as such.

Does any know if a MiniMoog is DC or AC coupled at the filter input stage? I have seen schematics suggesting AC coupling and also DC coupling.

I understand that there a different design options and each one may be valid, but maybe there is a general agreement which way a hard punch in the sound with a solid, tight, but deep bottom end is realized best.

If there a several DC filters in the path, lets say before the filter, before the final VCA, and maybe somewhere else, for example for a chorus, the deep low end might be seriously weakened (1 dB or more attenuation). One can use of course some EQ to partly restore the low end, but the notch remains. And the resulting phase shift is apparent, most obvious for the pulse wave (but which is not noticable).

One could also use higher AC coupling frequencies for faster DC settling to account for saturators and a final EQ in the end to equalize 30 Hz-100 Hz. Lots of options ...

[mystran]

Classic analog synths generally have DC-blocking capacitors all over the place, often including the feedback loops of filters. With Minimoog in particular, there's plenty of them everywhere. Typically the effective cutoff for these ends up somewhere between 1Hz and 10Hz, but I would really suggest analysing the schematics yourself, especially if you plan on using some approximations cheaper than full MNA.

Something one should be aware of is that once you start modelling this stuff seriously, suspending inactive voices becomes rather problematic, because the DC levels through the circuit tend to be in a constant state of flux. Especially once you throw in some modulation on longer time-scales, you might find that the only reliable way to avoid glitches (or at least transients not present in an analog circuit) at the beginning of notes is to just run every voice all the time.

[mystran]

Then there's the extreme case of TB-303 "bassline" which barely produces any bass whatsoever, thanks to the crazy amount of AC couple going on (well, except the coupling caps in the diode ladder loop actually result in some additional resonance that compensate slightly, but even then below 40Hz or so the thing just won't produce very much of anything).

[synthpark]

Classic analog synths generally have DC-blocking capacitors all over the place, often including the feedback loops of filters. With Minimoog in particular, there's plenty of them everywhere. Typically the effective cutoff for these ends up somewhere between 1Hz and 10Hz, but I would really suggest analysing the schematics yourself, especially if you plan on using some approximations cheaper than full MNA.

Something one should be aware of is that once you start modelling this stuff seriously, suspending inactive voices becomes rather problematic, because the DC levels through the circuit tend to be in a constant state of flux. Especially once you throw in some modulation on longer time-scales, you might find that the only reliable way to avoid glitches (or at least transients not present in an analog circuit) at the beginning of notes is to just run every voice all the time.

Thx. In FPGA all voices may run all the time, since they are physically present as circuits just like in analog (unless you have some lower-sampling-rate sequential architecture where voice might be assigned dynamically). What is MNA by the way?

Maybe some users find a synth to be more "alife" just for the fact that filters have 1 Hz of cutoff?

The feedback path in filters ... do you mean to avoid the loss of low-end for high resonance or simply for some circuit related reasons (like level shifting or DC currents)? For the first thing: I tried to use some filter in the fb path to overcome the thinning but the filter messes with the resonance, so its easier to pre-equalize the input.

[JCJR]

In analog audio design it is common to isolate every stage with either coupling caps or more rerely with transformers. Transformers were more common in earlier gear but have their own nonlinearities, hum susceptibility, frequency response issues, hysteresis.

The ac coupling of every stage was at least two-fold necessary--

_1 Very difficult to design a circuit stage that doesn't have at least a little bit of accidental DC offset so if you don't isolate every stage then even if all sub circuit stages are theoretically supposed to be "ground referenced", accidental dc errors get propogated from stage to stage until it can get ridiculous after awhile, stealing much of the available dynamic range. Or maybe some versions of the device would just peg up to a supply rail shortly after turning it on.

_2 Many perfectly good circuit stages can operate "good enough" with fewer parts if you don't care exactly where it's internal dc quiescent point lies, so long as it is close enough to the middle to allow sufficient dynamic range. Maybe sometimes a sub circuit function will even rely on a funky dc level in order to operate as intended.

The "lazy approximate biasing" is often seen in class a tube, fet, or bipolar transistor amp circuits for example. Without ac coupling you just couldn't string several stages of that kinda 'low precision" stuff together with any hope of it working correctly.

There are a few dc coupled high quality devices such as Hardy preamps but they are expensive because lots of money and precision has to be thrown at the problem of getting rid of the coupling caps (or transformers) and still having a functional device.

[mystran]

Thx. In FPGA all voices may run all the time, since they are physically present as circuits just like in analog (unless you have some lower-sampling-rate sequential architecture where voice might be assigned dynamically). What is MNA by the way?

MNA = Modified Nodal Analysis, essentially the gold standard of circuit simulation (eg. Spice and such).

Maybe some users find a synth to be more "alife" just for the fact that filters have 1 Hz of cutoff?

Users find synths more "alive" because they happen to have pretty pixels in their GUI, but low-frequency high-pass poles certainly modulate non-linearities in response to DC transients. When the coupling caps are inside filter loops, the effects are somewhat less predictable as it depends a whole lot on the specific filter.

The feedback path in filters ... do you mean to avoid the loss of low-end for high resonance or simply for some circuit related reasons (like level shifting or DC currents)? For the first thing: I tried to use some filter in the fb path to overcome the thinning but the filter messes with the resonance, so its easier to pre-equalize the input.

With a straight 4-pole cascade, the feedback is normally out of phase at low-frequencies, leading to a decrease in passband gain as the resonance is increased. This can be compensated (to various degrees) either at the input (eg. some CEM chips) or at the output (eg. TB-303). In either case you'll basically just increase the input or output gain to counter the passband losses.

When you place some HP poles into the loop (eg. most transistor and diode ladders; details vary), you'll actually end up decreasing the amount of negative feedback at the low frequencies, which paradoxically enough results in more low frequencies through the ladder proper. This has a non-negligible effect on the non-linearities. Note that the phase-shift from the DC blockers is really the most important component here, as it extends much higher than the actual amplitude response losses.

The added phase-shift also has the side-effect of typically damping the resonance at low frequencies. As a result, a circuit like Minimoog's (or even Voyager's for that matter) doesn't self-oscillate below a certain cutoff (and this point is typically a lot higher than you might think).

[camsr]

With regard to filters, one thing to experiment with is re-introducing the DC side of the equation at a different point in the flow. It won't eliminate the transient, but one goal of a DC blocker before a filter is to get more harmonic tone from it. If the DC component is required for ring modulation or other things, then it's possible to pass the low-passed side from before the filter.
If the filter in question is a low-pass, the signal coming from it ends up as a composite band-pass, and the inverse of the high-pass pre-filter is the lower band that was removed from it.
With that low-band signal, it's possible to do whatever with it, as the non-linear low-pass did not limit it or modulate it.

[mystran]

If the DC component is required for ring modulation or other things, then it's possible to pass the low-passed side from before the filter.

Usually you don't really want DC components for ring-mod as such, but rather the ring-modulation itself will produce DC (or very low frequency) components if the two signals have partials are frequencies close to each other. With other signals, like oscillator sync (with the frequency ratio under modulation), even just computing the exact DC offset might be rather tricky.

[synthpark]

With a straight 4-pole cascade, the feedback is normally out of phase at low-frequencies, leading to a decrease in passband gain as the resonance is increased. This can be compensated (to various degrees) either at the input (eg. some CEM chips) or at the output (eg. TB-303). In either case you'll basically just increase the input or output gain to counter the passband losses.

When you place some HP poles into the loop (eg. most transistor and diode ladders; details vary), you'll actually end up decreasing the amount of negative feedback at the low frequencies, which paradoxically enough results in more low frequencies through the ladder proper. This has a non-negligible effect on the non-linearities. Note that the phase-shift from the DC blockers is really the most important component here, as it extends much higher than the actual amplitude response losses.

The added phase-shift also has the side-effect of typically damping the resonance at low frequencies. As a result, a circuit like Minimoog's (or even Voyager's for that matter) doesn't self-oscillate below a certain cutoff (and this point is typically a lot higher than you might think).

A year ago I simulated some compensation schemes for the low end. I wasn't very lucky with the suggestion to place some filter into the feedback path, due to the phase shift it causes. Most success came from boosting the low end in advance using a kind of lowshelf filter. Just boosting flat results in brighter sound, not desirable in my point of view.

[mystran]

The classic compensation approach is just to adjust the overall gain in a frequency independent way depending on the resonance setting, to correct the perceived drop in overall volume. This overall drop in gain actually also makes a ladder more linear with higher resonance, which can be avoided by boosting the gain at input side. Compensating on the output side on the other hand doesn't really affect the filter behaviour in any way, it just adjusts the gain for the next stage.

The DC blockers in the feedback loop are a different thing, with typically little effect on the overall gain, but rather changing the way the filter distorts.

[synthpark]

The classic compensation approach is just to adjust the overall gain in a frequency independent way depending on the resonance setting, to correct the perceived drop in overall volume. This overall drop in gain actually also makes a ladder more linear with higher resonance, which can be avoided by boosting the gain at input side. Compensating on the output side on the other hand doesn't really affect the filter behaviour in any way, it just adjusts the gain for the next stage.

The DC blockers in the feedback loop are a different thing, with typically little effect on the overall gain, but rather changing the way the filter distorts.

Yeah thats the flat-gain compensation curve in the diagram. But the sound gets brighter. Using a lowshelf instead preserves a mallower or "warmer" HF frequency response while removing the loss of bottom. A matter of taste. The lowshelf can be applied after the filter also.

[mystran]

But the sound gets brighter. Using a lowshelf instead preserves a mallower or "warmer" HF frequency response while removing the loss of bottom. A matter of taste. The lowshelf can be applied after the filter also.

If you compensate flat gain at the output, there is no change in tone, only gain. If you compensate flat gain at the input, then you will drive any non-linearities in the filter harder with resonance, so you will get more distortion (with resonance).

Note that in a traditional transistor ladder, the pass-band losses mean that the distortion is a LOT lower when resonance is high, because there is no compensation on the input side. On the other hand, some IC chips (eg. CEM3372) do compensate (at least partially; only compensating for half the dB losses can actually be quite nice) on the input, so the distortion levels are somewhat more consistent with varying resonance.

[synthpark]

If you compensate flat gain at the output, there is no change in tone, only gain. If you compensate flat gain at the input, then you will drive any non-linearities in the filter harder with resonance, so you will get more distortion (with resonance).

Note that in a traditional transistor ladder, the pass-band losses mean that the distortion is a LOT lower when resonance is high, because there is no compensation on the input side. On the other hand, some IC chips (eg. CEM3372) do compensate (at least partially; only compensating for half the dB losses can actually be quite nice) on the input, so the distortion levels are somewhat more consistent with varying resonance.

Shure, I agree that the loss of bottom gives headroom for the resonance, of course. I started once with the Nordlead 2 and always hated the resonance on that machine for the 24 dB filter (although there is a trick: make the volume to be dependent on mod wheel and resonance also, a way to get more gain for high resonance). Maybe they just make the input quieter to get even more headroom. On a Juno 60 it is done right. I dont know if Juno 60 has output gain compensation or how they do it.

Anyways, I will experiment with what I find sounding best. Just output gain compensation, or lowshelf input or output compensation, or adjustable lowshelf input compensation by the user from uncompensated to fully compensated etc. Also a question of drive. You can drive the filter quieter for high reso to get headroom and apply an input LF boost and still get self resonance which is independent of input level anyway, combined with some output compensation. The filter stages do not have to be unity gain. There are quite a few variables ...

There are so many options that it is surprising that manufacturers of VAs didn't come up with filter models, where you can change more than cutoff/resonance and maybe number of poles.

Also the question is how well tuned the first order analog filter stages are. If there are small deviations, some resonance gain is lost, but the resonance gets a broader ... not shure anyone models this.

[Fender19]

Choosing a cutoff frequency, if first order, results in a settling time of roughly 2.5*tau = 2.5/(2*pi*fc). So for 5 Hz we already get 80ms. If the filter is heavily driven, this may result in a remarkably different sound for the first 80ms until the DC is settled, apart from the effective asymmetrical drive as such.

It's a common question on mixing forums, "how come adding a high pass filter caused my peak levels to go up? Why did REMOVING part of the signal make it bigger?"

I have explained many times that it is due to what you noted here - a DC level shift/bounce. Many natural sound sources, like human voice, are asymmetric. Removing low frequencies (even those much higher than "DC") can cause that entire curve to shift up/down on the amplitude axis because HPF creates a new average DC amplitude.

So yes, "DC blocking filters" - intended to be below audible frequencies - CAN affect audible frequencies. That first 80mS you note is a transient response/difference in sound created by the DC blocking filter.

The next question is, how low is "DC"? Technically it's 0Hz but in practice we filter at 1Hz, 2Hz, 5Hz, etc. Again, those "inaudible" filters can have audible effects.

[JCJR]

At severe risk of foolish captain obvious explanation: Some biquad filter transfer functions give "natural unadjusted" gain at the center frequency == Q.

In such situation an un-adjusted-gain lowpass filter with Q of 10 would have gain of 10 at Fc. Un-adjusted-gain filter with Q of 0.5 would have gain of 0.5 at Fc. But either case would have gain approaching unity well below Fc.

So if you expect input signals approaching full-scale and you don't want the input to clip at any input frequency or filter Fc, with this kind of filter you would adjust the filter gain as the inverse of Q (in cases where Q > 1.0). That way the filter gain is always unity at the highest-gain location in the filter response curve. But of course with high-resonance filters, that means the bass passband is lacking in gain. You get a good clean non-clipping signal in vicinity of Fc by losing overall (below Fc) bass gain.

If you don't want to lose bass gain, just leave the filter gain un-adjusted, so that resonance gain would be +20 dB if Q = 10 or or +40 dB if Q = 100 or whatever. Then you set up the filter to soft-clip, to distort in a "musical-sounding" fashion. That way you don't lose bass, but the filter distorts heavily as it sweeps thru loud harmonics of the signal. Which is the way some analog filters behave. The Operational Transconductance Amps (OTA's) in many kinds of analog VCFs tend to have nice mellow overdrive sound. Below Fc Bass gain stays at unity and some kind of "musical sounding" softclipping prevents the filter from getting louder than dammit when a high-Q, high-gain filter sweep passes thru loud input signal harmonics.

Moog ladder filter distortion to my ear was harsher than some of the OTA VCFs and I didn't like it as much. That is old Moog ladders from decades ago. I don't know if modern Moog ladder filters sound the same as the old ones when overdriven. I have not heard any modern Moog filters and do not know if they behave the same. But many people liked the sound of the old overdriven Moog transistor ladder. I just didn't care much for it. Was too gritty and harsh for my taste.