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Improving nonlinear distortion of a full DSP loudspeaker system by adding passive speaker-level filter networks

You and I clearly have different interpretations of the data. Noise dominates at very low frequencies, so that's mostly what you're looking at below ~40Hz at 96dB and 103dB, or ~70Hz at 86dB. The 2nd harmonic is not strongly affected, but is generally slightly lower with the filters except around 2kHz. The 3rd and 5th harmonics are significantly lower at most frequencies above 350Hz at 86dB and 96dB, with the exception of around 1kHz at 96dB (due to a mechanical nonlinearity in the compression driver, I believe). The woofer's 3rd harmonic drops nearly 10dB in the top octave of its passband (500Hz-1kHz), while the tweeter's 3rd harmonic drops ~5dB above 2kHz. There seems to be less difference at 103dB compared to the lower levels. At the moment I'm not entirely sure why this is.

A small note regarding perceived sound quality:
First, this is just based on sighted listening so I fully accept that what I heard could be entirely the result of bias. I didn't expect much audible difference besides a reduction in hiss (which was mostly inaudible anyway) as the measured harmonic distortion (>H2, anyway) was already pretty low. However, the more I listen the more I'm (cautiously) convinced that the sound quality is improved. In particular, I've long noticed a low-level "grit" in the sound which was particularly noticeable with certain instruments—piano perhaps being the worst offender, especially if the recording had a generally dark/warm tonal balance. This impression persisted across multiple systems that I built, all having only digital filters. With the added passive networks, this "grit" seems to be absent or at least notably reduced. So what's going on? My guess is that the dominant factor in this case is a reduction in hysteresis-related distortion. Or I'm fooling myself. Could be either.
Yeah, sorry I looked at them with a phone first, but now on a computer (with TV as a screen) and I can see the differences better. The HDs of nth orders are different for sure and some are lower as well with the passive filter. Also the THD seems to be lower on average for mids, although part of the highs have slightly more distortion. The 2nd is the dominant and 3rd is high enough to be audible in some parts. As always, pushing down odd orders is recommendable. Anyway, if the goal is to reduce HD, shouldn't THD be lower too, otherwise there would be no point in doing it, right? It would make the graphs more readable if you left out the highest order HDs, because it's so low anyway. Maybe up to 4th would suffice?

Also another thing. The Purifi article is about filtering out resonance peaks. And to be precise, filtering them with series resistance (reducing current at desired frequency) instead of shorting to ground with a parallel filter (directing the current elsewhere). That surely is theoretically the better approach of the two. That can also be done with a DSP, if you got dedicated DSP channel for each driver. When creating notch filter equivalent with DSP peaking filter of high Q, you get essentially the same effect. Even group delay and phase will be similar if the transfer functions match. Also since DSP works in reducing the signal (reducing current), it should reap the same benefits as series notch filter for taming resonance peaks, because instead of resisting, there is less current to begin with. Can you test this theory out? It should behave in the same manner as in the Purifi article, so if you add multiple peak filters for multiple frequency points, you need to start with the lowest and measure each step.

And one more thing. During current drive experimentation, some have said that woofers sound quality suffers from series resistance. That can be due to the damping factor being lower and the woofers inertia is less controlled. I fail to sees how this does not apply to mids and highs as well, maybe the excursion distance is critical there. But it's nevertheless worth experimenting on if you got time. I can see you have made quite complex passive crossover considering you still have the active filters backing you up. Intuition suggests that reducing the number of passive components would give better results. I would suggest trying simply nothing but series resistors (something in order of 20-40 Ohms for an 8 Ohm driver) and then again added with DSP resonance control and see how they do.
 
That can also be done with a DSP, if you got dedicated DSP channel for each driver. When creating notch filter equivalent with DSP peaking
no, only the linear frequency response can be the same. The effect on the nonlinear current is not the same due to the changed impedance. It’s explained in the blog post.
 
or use REW which has recently baked FSAF in I think
I'm planning to try FSAF at some point. The residuals with and without the passive filters should be interesting and may give me a better idea of whether or not the improvements I hear are only in my head :).
Just in case someone here is looking for it in REW: the current stable release (V5.31.3) doesn't have FSAF, but the beta version does (starting with V5.40 beta 32).

Anyway, if the goal is to reduce HD, shouldn't THD be lower too, otherwise there would be no point in doing it, right?
Not necessarily because nonlinearities differ in audibility/annoyance depending on their order and underlying cause. One good example is the difference between Kms(x) vs Bl(x) nonlinearity, which Purifi covered here. Harmonic distortion for the two examples is very similar, but the intermodulation distortion (and the sound) is very different.

That can also be done with a DSP, if you got dedicated DSP channel for each driver. When creating notch filter equivalent with DSP peaking filter of high Q, you get essentially the same effect.
This was discussed previously. The effect on the linear part can be the same, but the effect on the nonlinear part is not. As @Lars Risbo (the author) says, this is explained in the Purifi application note. Also see posts #4, #5, #7, #8, #10, and #11 in this thread.

During current drive experimentation, some have said that woofers sound quality suffers from series resistance. That can be due to the damping factor being lower and the woofers inertia is less controlled. I fail to sees how this does not apply to mids and highs as well
See the article @tmuikku linked in post #18. Low driving impedance only offers meaningful control near a driver's LF resonance.
 
Just a note or 2 about the 'sine-cap' filter, also known as capless highpass or RL highpass, that series resistor will get hot being it is the load the amplifier sees. It is not bandwidth limited due to no capacitor, so low frequencies pass and then shunt through the coil. A 50W resistor with heatsink is recommended for this kind of circuit, and externally mounting the resistor to the loudspeaker cabinet is a benefit here to avoid starting a fire with internal damping, etc.

If using a capless highpass is something you want to try, but don't want the heat issues, a passive series xover can get you most of the way there. However, since that kind of xover cannot be biamped, then you can't use DSP or active filters separately for different drivers. This means general EQ is about all you can do there.
 
for a tweeter it’s best to add a series resistor directly in series with the tweeter. this increases the drive impedance and can be used for padding down the tweeter sensitivity. An L pad is very popular but almost the worst solution. The L-R (cap less ) is burning much energy as pointed out and capacitors are typically close to ideal than inductors.
 
@Wolf
In his application (I assume), there will be high-pass filtering elsewhere.........upstream of the amplifier, via the DSP.
So, there will be bandwidth limiting to that network and no low frequencies should be seen by the tweeter or resistor.

But, a good clarification nonetheless.

Dave Reite.
 
for a tweeter it’s best to add a series resistor directly in series with the tweeter. this increases the drive impedance and can be used for padding down the tweeter sensitivity. An L pad is very popular but almost the worst solution. The L-R (cap less ) is burning much energy as pointed out and capacitors are typically close to ideal than inductors.
@Lars Risbo...
There are reasons you prefer the aft resistor, as it reduces distortion as cited in your document. However, an aft resistor will also tilt the response down in the treble the larger the value utilized. It also changes the effective damping Q of the xover to where coils get larger and caps get smaller for the same outcome. Copper is expensive, and can increase parts cost over that of a lesser driver net impedance. Having a resistor out front does not tilt the response in this manner.

A resistor across the tweeter is a bad idea in terms of the back EMF operation, but has so many other positive reasons. It damps the Fs of the tweeter, readjusts to the normal Q range of xover components, and attenuates without tilting the response.

Adding series resistance, while decreasing distortion, can also; take the life out of the driver at times, increase sibilance (if not using the right value or type), and if using too long a speaker cable or too high a DCR coil- make a speaker sound overly muted.

I'm sure you already know all of this. I'm thus far not convinced that reducing HD by added resistance or electrical damping is actually more beneficial than using the network with these other positives in play. It shifts the balance of more benefits in the other direction, IMO.
 
Just a note or 2 about the 'sine-cap' filter [...]
Good points to keep in mind if one intends to use it in a passive system. In this case, the power dissipation falls rapidly below 1kHz because the digital filters on the tweeter channel have a ~12dB/oct high pass response (see the third image in post #1). I use three 30Ω 10W resistors in parallel for the 10Ω series resistance. Massive overkill[1] for this application really, but resistors are fairly cheap.

1: A rough calculation says that if I were to play Bargain by The Who at 95dB(C) avg. RMS (>110dB(C) peaks), the series resistor's average dissipation over the duration of the track would be less than 50mW (~4W instantaneous peak).
 
there are of course pros and cons to adding series resistance. It decreases the electrical damping (increases Qts) which typically increases distortion down closer to the driver fs. In that sense, the shunt inductor offer the advantage of keeping the damping at low frequencies.
 
@Wolf, we're talking DSP/active systems here, so altered response is a non-issue. It really depends on the tweeter which drive impedance vs frequency is optimal. Most tweeters improve in sound/distortion with high source impedance overall, from a simple series R (but keeping the target frequency response the same, of course) but not all.
 
there are of course pros and cons to adding series resistance. It decreases the electrical damping (increases Qts) which typically increases distortion down closer to the driver fs. In that sense, the shunt inductor offer the advantage of keeping the damping at low frequencies.
Yep, I've found some compression drivers really hate high source impedance around resonance, actually they performed best with as much internal feedback as possible (negative drive impedance). My working theory is that the VC (as a motor and as a sensor) is very linear as it is usually underhung but the flat suspension is extremely progressive. Strong internal velocity feedback helps then quite a bit.
 
My working theory is that the VC (as a motor and as a sensor) is very linear as it is usually underhung but the flat suspension is extremely progressive. Strong internal velocity feedback helps then quite a bit.
That mirrors my thoughts, hence why I designed the tweeter filter the way I did.
 
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