Problems associated with a capacitive load

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lrisbo

Member
Joined 2021
purifi-audio.com
ianbo said:
I really feel like I'm talking to myself, now. I know this is off topic, really, and this thread is in the Solid State forum, and I'm focussing on a point about speaker crossovers. But @steveu made a very significant claim in post 26, so I'm not dropping the issue - yet. Here's what he said:



If it's true that second order filters exaggerate break-up resonances, and may sound brighter than first order filters, that would be a really important discovery for the world of passive crossovers.

But is it true? Here's where I've got to. I can't find anything which backs up those claims. My best guess is that steveu was thinking of the work done by Purifi, linked to above. But if that's the case, then I fear he's misread the Purifi work. The claim in the Purifi work is that a crossover topology which creates a low source impedance at the frequency of a break-up peak can create increased distortion levels, related to that peak. That's not the same as claiming that the resonances will be exaggerated, or the frequency response 'brighter'.

Also, I want to point out something about the Purifi work. It's very impressive work, and the distortion variation they uncover looks pretty significant. But the topology which creates the problem is not just a plain second order network, it's a network with two LC series traps (i.e. L and C in series with each other, shunting the driver), plus a shunt cap damped by a resistor. (Note, the Purifi work calls these two traps parallel notch filters, but that's using terms the opposite way round from what I'm used to, and I'm sticking with my familiar designations.) This topology results in an extremely low source impedance at 5kHz, the frequency of the main break-up peak - around 0.5 ohms. The Purifi work contrasts this with a network that uses a parallel trap to reduce the 5kHz break up peak (they call it a series notch). This creates a big peak in the source impedance, over 40 ohms at the break-up frequency.

Now, I can't really criticise Purifi for using an example that strongly illustrates the problem they've discovered. But I can't help but think that the two circuit examples they've given represent a pretty extreme case. Very few crossover topologies are going to create source impedance dips as low as 0.5 ohms. For one thing, most series notch filters include a resistor, which will limit the dip. Plain vanilla second order networks may bring the source impedance down to a few ohms, but not sub 1 ohm. When I set up Vituixcad the way that the Purifi paper suggests, to show source impedance, and use a second order woofer crossover, I get source impedance of around 10 ohms at 3 kHz (which is where my woofer has its main break-up peak). See the screenshot below. The woofer crossover is shown on the lower left side, and the source impedance appears in the bottom right hand chart of the six-pack. The rest can safely be ignored.

View attachment 1314465

The question which the Purifi work leaves unanswered is about how much extra distortion will be generated if the source impedance at the breakup peak is higher than 0.5 ohms, but less than 40? Say, 10 ohms? I can't really answer that, for the moment, but I'd guess the problem would be far smaller. So, to sum up: panic averted.
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you are doing the analysis correctly. the spl graph shows a notch at 400 Hz where the driver sees into an infinite impedance from the xover. The spl graph shows the transfer function from back EMF distortion to spl. you can add 0.5 ohms or 40ohms and study effect. You can also go to an odd order filter ending with an inductor and see the effect.
 
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ianbo

Member
Joined 2014
Thank you! I really appreciate you responding here. I'm relieved I've got the analysis right (-ish). Is the notch in the SPL graph at 400 Hz a problem? Adding resistance in series with the capacitor reduces it. Adding another inductor to go third order doesn't seem to change it. I was thinking that the notch isn't a problem - it's the correlate of the source impedance peak at that frequency (which is the corner frequency). In your blog post on this topic, linked to above, there's an impedance peak around 1650 Hz with both filters - but you don't seem too bothered about it - you focus on the change in impedance at the breakup peak frequency of 5 kHz.
 
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MarcelvdG

Member
Joined 2003
EdGr said:
Electrostatic speakers are capacitors and need an amplifier designed to drive a capacitor. This is when the output inductor becomes mandatory.
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There is more to it than that: by Walker's equation, flat panel electrostatic loudspeakers meant for listening in the far field actually have to be designed such that the magnitude of the sum of the currents through the stator segments stays constant with frequency over most of their frequency range. Anyway, it's somewhat off topic.
 
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