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Old 17th May 2004, 10:20 AM   #1
sfx is offline sfx  Germany
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Question "Which linearity" is the best? Current, Voltage, Power?

While testing my class D amp I just finished (see this thread , or here ), I came across some very basic and general questions.

What does linearity mean? Obviously we measure something and plot it against frequency, and get a more or less flat curve. The question is what we measure exactly, voltage, current, or maybe power? On a resistive load it doesn't make a difference, but speakers have frequency-dependent impedance, and resonance effects. I noticed that the output voltage rms is linear into a resistor, and also into a speaker without enclosure, but in a sealed 60l 12" Subwoofer box, the voltage rises a bit around 120Hz. Nevertheless, according to my ears, the sound level remains constant throughout the sweep. The amplifier is a simple non-feedback class D amp in the BCA topology (Balanced Current Amplifier, see Crown Audio website). My questions are not about my amp, but more general, this is just how I got the idea.

Obviously it is impossible on an inductive load to keep rms voltage and rms current linear in frequency at the same time. So which is in principle better? Or should the power be linear? Ultimately, the sound amplitude in air should be linear, but how does that correlate to voltage, current, power into a speaker, especially around resonance frequencies?

When using feedback, should we feed back the voltage or current? Does anyone know if the known topologies A, AB, D are current amplifiers or voltage amplifiers? How do they usually behave on inductive loads?

Please educate me, or write me your opinions!

Cheers,
Felix
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Old 17th May 2004, 11:15 AM   #2
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The industry standard for speakers is to receive a voltage. Voltage matters (not current or power).

By the way, you are using the term "linear" in a way that is correct but unusual. You are asking about the linearity of the plot of amplitude vs frequency. This is usually refered to as the "frequency response" or "gain response". You'd normally talk about the frequency response being flat flat from 20Hz to 20kHz. The term "linear" is most often associated with the plot of output vs input, eg: output V vs input V.
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Old 17th May 2004, 01:42 PM   #3
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Dynamic woofers do not have a flat impedance curve (impedance vs. frequency--go look at the spec sheets for some drivers to see examples). The changes in voltage/current are not your amplifier's fault--it's simply responding to your speaker.
Measure your amplifier's output into a resistive load. As long as it isn't clipping or current limiting, it will do a pretty good job of delivering power to a real world speaker. The dips and peaks in the impedance curve for the driver even out as far as acoustic power delivered into the room.
You're doing fine.

Grey
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Old 17th May 2004, 07:06 PM   #4
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Ideally you want to have linearity in acoustic power (spl averaged all around the speaker) and in acoustic power density (spl measured on the speaker axis). Between amp and air that's the job of the speaker manufacturer. Mostly they succeed only on-axis.

They in turn normally presume (industry standard, cfr supra) the input voltage is a precise measure of the acoustic output power (pressure actually) you want. So, your amplifier should have a linear frequency response in terms of output voltage. That is, while the speaker is attached. A nice flat frequency response is of little value when it goes awry when it has to work into a speaker. This translates into low output impedance.

If your amp has no feedback emanating after the output filter, the output impedance at high frequencies is (too) high. To get round this problem, you should measure frequency response with the speaker attached (<1W, mind the tweeter) and tailor the result using RC networks connected across the speaker (ie. modify the speaker´s impedance such that at HF it resembles an ohmic load into which the output filter is flat).
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Old 18th May 2004, 08:04 AM   #5
sfx is offline sfx  Germany
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Thanks a lot for your answers. I assume it is common to measure frequency responses into resistive loads, or, when measuring into speakers, taking the voltage.
I'm still a bit confused. Sure, the standard is voltage, and the ideal speaker is proportional in rms input voltage vs. output spl, regardless of the frequency. But this ideal speaker doesn't exist. Also, phase shifts between current and voltage have to be considered, which makes it more complicated. And, as far as I know, the force on a given coil in a magnetic field depends on the current flowing through it.

So, the question is, given a real, non-perfect speaker with "bumps" in the impedance, and an amp like mine, which is linear into a resistive load, but which output voltage responds to the varying impedance of the speaker:
Would it be better to force the "voltage" frequency response to be flat, also into inductive loads like a speaker, by using feedback? I'm not talking about THD here, only frequency response.
The basic question is, given a non-perfect, resonant speaker with an "impedance bump" around frequency f_0:
What happens to the SPL during a sweep around f_0, if I keep the rms voltage constant, and what if I keep the rms current constant, or the rms power?

I got the impression that the "bump" comes from acoustic resonance effects, since it occured when I sealed the enclosure shut. So what happens to the efficiency of a complete speaker vs. frequency? Any rules of thumb?

Something to think about:
Imagine a sealed speaker box as a pipe, closed on one end, and the membrane on the other end.
I can see two cases of "ideal" resonance, in terms of standing waves inside the pipe.
In case 1, the membrane acts like a closed end, hardly moving, and keeping the resonance inside the pipe alive by tiny little movements, but with a lot of force/pressure.
Case 2, at 1/2 of the frequency, is the membrane acting like an open end, moving in and out with the air in the pipe, with hardly any pressure on it. Obviously, in the first case, almost no outside air is moved, but the membrane has to work against a lot of force (=high current through the coil). In the second case, the force on the membrane from the inside is low, but a lot of outside air is moved.
So now I keep the voltage constant, and change the frequency. What happens to the current in case 1, and what in case 2? What about the efficiency, electric power, and the produced SPL? How does it compare to case 3=no resonance?
I'm very confused now... just in case you really read so far, does anyone have an idea?
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Old 19th May 2004, 10:16 AM   #6
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What happens on an impedance bump can be a bit confusing at first. Indeed, the bump signals a resonance. This resonance is part of the high-pass function a driver in a box represents. For a closed box, a third order HPF is realised. Two of these orders form a resonant peak that "straighten up" the corner to get the widest flat response (e.g. butterworth response).
Suppose you superimposed 3 first-order responses cutting off at 50Hz. The asymptotes of this function would still cross over at 50Hz, but the attenuation would already be -9dB. You'd prefer -3dB. So, you combine two orders to create a complementary pair of imaginary poles that resonate at 50Hz and have a boost of 6dB there.
Overall you don't see the boost unless you look at the difference between the actual response and the imagined triple first order version.

Now, the precise tuning presumes that you have a constant-voltage source. As the impedance goes up, this physically means acoustic efficiency increases as well (same output, less power in). If the frequency response at the amplifier terminals isn't flat, the same response error will be added to what you get at the speaker.

It is of course possible that the non-perfect speaker just happens to interact with a non--perfect amplifier to produce a better result, but unless the two are co-designed this is unlikely. For that reason a standard is agreed: the amplifier's response should be flat when the speaker is connected.

Now, whether you straighten up the frequency response using feedback (reduce output impedance), using extra passive parts placed in parallel with the speaker (to make its input impedance ohmic) or using an equaliser before the amplifier is not material in this respect. Having a low output impedance is simply the most consistent way, in that the effort still pays off when you swap speakers.

Cheers,

Bruno
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Old 25th May 2004, 02:50 AM   #7
sfx is offline sfx  Germany
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Hi,

Thanks, Bruno, I think that answered my question. My next amp will probably use feedback. Maybe I can also use other filter coils with lower resistance and inductivtiy, to lower the output impedance.

Felix
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