Saturday, 31 August 2019

MEASUREMENTS: Speaker Impedance - Part 2; sealed, ported, and a few of my speakers...


A couple weeks back, I started discussing speaker impedance curves and how one as an audiophile hobbyist might want to measure these ourselves. There are thousands of speaker models out there and while some in the audiophile press do a good job with providing objective results (like Stereophile), sadly, most magazines do not publish the information, and most manufacturers do not openly provide detailed specifications either. What else then can one do but measure it ourselves?!

Today, let's continue to explore the speaker impedance measurement graphs and see what else they can tell us using some of the speakers I use at home regularly...

I. Single speaker in free air...

To start, let's recap what we've looked at so far with this image and graph from last time:



In free air, the speaker impedance allows us to see the natural resonance frequency of the speaker. This is a key property of any driver and is determined by mass and compliance. This frequency represents the balance between the mass and force of the speaker suspension in motion. This property is known as the Fs of the driver / "free air resonant frequency" of the single speaker, or "fundamental resonance"; in this example of the Paradigm 4" midrange, it's around 225Hz and correlates with 0° electrical phase angle.

But that's just a driver itself; not a real speaker which is a much more complex beast consisting of an enclosure (with associated dimensions, alignment, box density, and damping), the drivers, and of course associated circuitry - crossovers in most passive speakers. Each of these components will affect the impedance curve of our speakers.

II. A Typical 2-Way Bookshelf... The Tannoy Mercury mX 2 (circa 2000)


This was one of my first hi-fi speakers purchased just at the turn of the 21st Century. They still work well and I have them connected to my living room TV and receiver for background music mostly. That system BTW has a Chromecast Audio attached and serves as a wireless Roon endpoint; works great.

Notice from the image above that it's a 2-way speaker system in "light maple" veneer, with 25mm (1") soft fabric dome tweeter and 145mm (5.7") ceramic coated paper mid/bass drivers. These small speakers are listed as 8Ω rated impedance, are magnetically shielded, and relatively compact at 330 x 185 x 246mm and 5.1kg each. The sensitivity is a typical 88dB/W/m; my assumption is that this means 88dB/2.83V/m as an 8Ω rated device, but since most specs don't specify, I'll just stick with dB/W/m. Frequency response is published as "48-20kHz", no word on +/- how many dB. And the passive Linkwitz-Riley crossover frequency is reportedly at 2.8kHz.

I think I paid something like CAD$350 for them back in the day and subjectively I still very much enjoy this pair for the nice and smooth treble presentation especially with acoustic music but they're also the most bass-shy of the speakers I listen to regularly. A combination of bookshelves like this plus subwoofer can sound very good.

Here's a look at the back:

Foam speaker port "bungs" came with these speakers, inserted on right speaker. Notice dual multiway speaker connectors for bi-wire/bi-amping. I've identified the HF and LF terminals when you take off the links.
As you can see, these are ported speakers. As opposed to a "sealed box" or tuned "acoustic suspension" enclosures, most box dynamic speakers these days have a "bass reflex port" or are "vented" designs with that hole/port. The principle with the ported design is to make the system into a type of "Helmholtz resonator" with enclosed air in the box and an "aperture" . The resonator can be tuned to a specific "port resonance" based on the driver and size of the enclosure which improves the bass efficiency of the speaker and allows the speaker to extend the useful frequency response below the normal limit for the box. There are "side effects" to this technique such as potential for distortion from the port, time domain changes (low frequency group delay as the air moves through the port), and a ported speaker rolls-off quicker below the port resonance typically by -24dB/octave (4th order filter) compared to the -12dB/octave (2nd order filter) of sealed box designs.

Getting back to our look at impedance measurements then, these Tannoys come with a couple of "bungs" (port plugs) - you can see the picture above where one of the speakers has the port closed off. Doing this could be beneficial to reduce booming when putting the speakers close to rear walls (stop turbulent noise from airflow through the port at the expense of bass extension). This means that one can convert the speakers to a sealed design by doing this... Remember, a pair of rolled up socks in the ports would do the same thing :-).

So, as a start, let's get a measurement of one of the speakers with the "bung" in place. Let's imagine this is some sort of sealed "pseudo" acoustic suspension speaker. Here are the impedance and electrical phase curves for the right speaker in the image above:

Impedance graph highlighted.
While the "bung" will significantly impede the airflow through the port, it's not perfect (notice the low-level hump to the left). I could have sealed the port better to stop any air flow for a cleaner result. One sees 2 main peaks, the closed box resonance of the woofer on the left at 387Hz (also called the Fc; unless I opened and took out the driver to measure in free air, I would not know the exact Fs), and a second peak on the right is a result of the crossover.

As you can see, while this speaker is labeled as "8Ω", in reality the impedance drops down to about 4.2Ω below 40Hz and around 1kHz! Remember from Part 1, the IEC 60268-5 definition is that the minimum impedance should not drop below 80% of nominal value (more precisely rated impedance = minimum impedance x 1.25). Therefore, these speakers would not be formally 8Ω based on that definition... They're more like "5Ω" speakers. (The lowest impedance measured is not affected by having the port plug in place BTW.)

Now then, let's remove the "bung" and see what the impedance and electrical phase look like for a bass reflex speaker with an unimpeded port. Here's the same right speaker:


Notice now that there are clearly 2 impedance peaks showing up in the bass/woofer region. I've labeled the low and high peaks Fl (port resonance frequency) and Fh (woofer resonance), with the nadir of the valley between these peaks, corresponding with 0° electrical phase Fb, also known as the "box resonance frequency". Another little tidbit discussed here is that we can correlate the driver's "free air" resonance Fs based on the relative heights of Fh and Fl. In the example of the Tannoy mX 2 here, we see that Fh is higher than Fl which suggests that the box resonant frequency Fb is lower than the woofer's Fs.

For this speaker, the Fb is just over 200Hz. This is atypically high compared to other speakers, even small bookshelves.

I've annotated the electrical phase angle plot with some values for the extremes. The angles do encroach towards 45° but notice that at these phase angle extremes, impedance is nowhere close to the lowest 4.2Ω level (this is good, easier for amplifier to drive the speakers).

There are little kinks at 550Hz and 1.3kHz in both the electrical phase and impedance plots, suggesting some box resonances (related to the dimensions of the enclosure) at those frequencies.

Since these speakers can be bi-wired/bi-amped, we can also look at the impedance measurement through the LF (low-frequency) and HF (high-frequency) speaker terminals that are usually hooked up in parallel. By looking at this, we can get a sense of the relative load when we're biamping (the benefits of biwiring dubious):


As you can see, the combination of the two impedance curves at the intersection of the high-pass and low-pass filters meeting at 7.5kHz causes that hump we see on the right. Again, what's a bit unusual is that the crossover frequency is supposed to be around 3kHz according to the specs so the intersection point seems much higher than I expected. (Here's a nice page explaining crossover impedance in more detail.)

I mentioned in Part 1, since speakers are sold in pairs, it's worth comparing how consistent the R and L speakers are to get an idea of speaker "matching"; here then are my pair of Tannoy mX 2s:


While there's some inter-speaker variance in the lower frequencies, both speakers have a minimum impedance down at around 4.2Ω. Notice the 1.3kHz "wrinkle" in the curve is at exactly the same spot and amount in both speakers suggesting this resonance is typical of the design rather than some imperfection found only in one of the speakers.

One last thing before leaving these speakers. While we may know the impedance curve and some of the design parameters of the box and crossovers, remember that this doesn't necessarily reflect exactly in the frequency response in an actual room. For example, here's the frequency response of the Tannoys using a calibrated Dayton Audio EMM-6 measurement microphone placed 50" away, on axis at tweeter level in my sound room 4' off the ground and with at least 5' away from side walls or large objects, 1/6 octave smoothing applied:


The graph is a demonstration of what happens comparing the open bass reflex port and when the "bung" is in place. At 92Hz, we're seeing about 2.2dB boost in amplitude with port open, but a steeper decline into the low bass which is to be expected. (Ported speakers can achieve around +3dB bump in efficiency at the tuning frequency.)

IIa. A more typical looking 2-Way Speaker impedance - Energy C-100B

While it was convenient to show the difference between bass reflex and a "pseudo" closed box speaker and plot out things like the Fb with the Tannoy, notice that I found the frequency values a bit unusual with remarkably high port tuning and even the crossover peak seemed high for published specs. Since the pattern was seen with both speakers, this looks like by design and I'd be curious if other Tannoy mX 2 owners have had a good look inside or measured their speakers to confirm the findings.

To show a more typical impedance graph for a two-way speaker that actually correlates well with the published specs I've seen, here's an Energy C-100B:


This speaker is a rear-vented bass reflex design with a claimed frequency response of 50Hz to 20kHz +/- 3dB. It has an aluminum dome tweeter and 5.5" fiberglass woofer. Impedance is specified as "8Ω nominal / 4Ω minimum" - nice that they published the minimal value. It's a little larger overall than the Tannoy above at 500 x 170 x 250mm, and weighs 9kg each.

Here are the impedance and phase angle curves:


As a bass reflex speaker, we again see the "double hump" in the bass region. Box resonance (Fb) is at a typical value of 67Hz with port resonance down at 48Hz. You can see that the electrical phase angles at most approaches +/-40° with none of the higher angles correlating with the minimum impedance of 4.8Ω; if we use this as 80% of nominal impedance, then this is about a "6Ω" speaker.

There are a few resonances we can make out. There's a subtle one at 180Hz, and another at 300Hz. Finally, around 24kHz, we're probably seeing the "metal-dome resonance" (I've seen Stereophile call this "oil-can resonance") from the aluminum tweeter. Fabric and soft tweeters also have "break-up frequencies" but they're typically less dramatic compared to many metal tweeters (see here for discussion of soft vs. metal tweeters).

We can examine the impedance of the high and low speaker terminals and see that the crossover peak on the right is a result of the intersection at 2kHz which is indeed close to the published crossover point of 2.2kHz.


And if we overlay the impedance curves of the two speakers, we see this rather nice "match" between the two:


This speaker looks like a "textbook" 2-way speaker design and box tuned to typical values for bookshelves. Furthermore, the crossover point appears to be at a typical 2kHz region as published.

Compared with the Tannoy above, we see that this speaker has a little more extended bass (and treble) in my room:


At 75Hz, the Energy C-100B is about 4.6dB louder than the Tannoy mX 2 with the speakers at the same position and measurement microphone again 50" away, on axis at tweeter level 4' off the ground. Both speakers were driven by the same Emotiva XPA-1L amplifier.

Subjectively, although the Tannoy doesn't reach as low down in frequency, I do prefer the Tannoy's smooth treble with acoustic music whereas the Energy can be a bit harsh at times which is why I usually employ them for multichannel Atmos "ceiling bounce" in movies.

III. A 2.5-Way Speaker - the Paradigm Reference Studio 80 v.3

Next, let's move on to another speaker I have. Here's a 2.5-way Paradigm Studio 80.


I bought these guys back around 2002. They sounded great to me in my apartment at the time even after auditioning the Studio 60 and more expensive Studio 100.

Instead of 3-way speakers with woofer, midrange, and tweeter, this type of speaker has a less complex crossover. The high-pass tweeter crossover is the same, but the two woofers act as mid-woofers with low-pass filters only, set to different points and slopes for each driver. There is no "true" midrange with a high-pass filter that prevents it from playing the lowest frequencies.

For this speaker, as you can see, we have a 25mm (1") aluminum dome tweeter, a 210mm (~8.3") mica-polymer mid-woofer, and another 210mm  polypropylene woofer below. The published crossover frequencies for this speaker are at 1.8kHz (3rd order, 18dB/octave) and 400Hz (2nd order, 12dB/octave) for the lower bass driver. Sensitivity of this speaker is rated at 92dB/W/m in room and 89dB/W/m anechoic. These are pretty hefty speakers at 40.5" tall and weighing 90lbs each. Notice that the bass reflex port is coming out the front for this speaker.

Impedance curve and electrical phase angle:

Impedance graph highlighted.
With a minimum impedance down at ~4.5Ω, assuming that's 80% of nominal, this is about a "5.5Ω" speaker. Not surprisingly, Paradigm's literature says this is "compatible with 8 ohms". Having said this, notice just how benign the phase angle is. Nothing approaches +/-45° within the audible spectrum.

Fb (box resonance) appears to be down around 22Hz.

We can also examine the impedance curves of the HF and LF speaker terminals for bi-wiring/bi-amping with crossing point at 2.5kHz (close to the 1.8kHz published crossover point):


Finally, how well matched do the right and left speaker pairs measure?


Looks great with the impedance values diverging at most 0.5Ω suggesting good consistency of the crossovers, speaker drivers, and enclosure construction. It appears that my left speaker impedance is just marginally lower than the right one; about 4.2Ω left vs. 4.4Ω right at the lowest point. Notice there's an anomaly up at 26.5kHz. Since this is an aluminum dome tweeter, this is likely representative of the aluminum tweeter's "metal-dome resonance" like in the Energy.

IV. A 3-Way Speaker - Paradigm Reference Signature S8 v.3


Here's my main speaker in the sound room (with the Sub 1 to the left, turned off); Paradigm's Signature S8 v.3. That's a lot of drivers! :-)

It's a 3-way system described again by Paradigm as "compatible with 8 ohms". It's quite tall at 48.5" and heavy at ~100lbs each. On-axis frequency response rated as 39Hz - 45kHz (+/-2dB) of moderate sensitivity at 92dB/W/m in room and 89dB/W/m anechoic.

Speaker drivers include the 25mm (1") beryllium dome tweeter, 178mm (7") "cobalt-infused" aluminum midrange, and the lower four are 178mm (7") polypropylene woofers. As you can see, there's also a front port.

Crossover frequencies are listed as 3rd order (18dB/octave) at 2kHz and 2nd order (12dB/octave) at 230Hz for the bass drivers.

Impedance graph highlighted.
As you can see with a 3-way crossover and more complex arrangement of drivers, we also have a more complex impedance and phase angle graph than the ones above. Box resonance frequency Fb is down at 32Hz. Lowest impedance is around 3.6Ω from about 80-120Hz and then again up around 20kHz. Despite this being listed as "8Ω compatible", think 4Ω when you're selecting an amplifier.

The phase angles here are certainly also more challenging than the other speakers above ranging from +49° down to -60°. The most difficult area is around 70Hz where we see a phase angle of -45° while the impedance is down at around 4.8Ω.

There is a tiny "wrinkle" at 180Hz, perhaps some kind of internal resonance. Notice the lack of the "metal dome resonance" with the beryllium tweeter up to 35kHz compared to the Studio 80 and Energy C-100's aluminum tweeters. This is to be expected as the "ringing"/"break up" frequency of beryllium is higher than aluminum (remember that shape and dampening also have roles to play). Theoretically at least, as a material for tweeters, a well constructed beryllium tweeter should achieve better linearity than soft domes without the resonant harshness close to the audible frequencies one might see with titanium or aluminum (bad parts about beryllium are price and toxicity); again, remember that the material itself is only part of the equation.

Here is the impedance of the high and low-frequency speaker terminals if one were to bi-wire/bi-amp. Notice crossing over around 1.5-2kHz mark which is consistent with the published 2kHz crossover point for the tweeter:


And finally, how "coherent" are the impedance curves comparing my right and left speakers?


Hmmm... Above the 2kHz crossover area, we see some variation, the largest deviation I found was at 3.6kHz with about 1.4Ω variation between the two speakers around the 10Ω mark. I don't like this and suspect that we have a problem here - will get in touch with Paradigm and follow up on this in another post once I take a look at the tweeter assembly and crossover in those speakers. Otherwise, the precise overlay of impedance up to 2kHz for these Signature S8's is excellent.

V. In Summary...

I think it's fair to say that when manufacturers say a pair of speakers are "8Ω", this is a relatively meaningless specification. All 4 of the speakers above are supposed to be 8Ω "compatible" yet notice just how different they are when impedance and electrical phase are measured out fully! Whereas the Signature S8's impedance varies significantly in the audio band from 3.8-25Ω, the Studio 80 shows a remarkably tame series of 4-10Ω rolling hills. Even then, the S8's impedance range isn't actually all that remarkable... I'll show you some other speakers another time with an even greater range!

Compared to some speaker measurements I've seen, the 4 I have here are actually relatively "tame". Nothing here even goes below 3Ω :-).

With the data in hand, we can appreciate this variability by overlaying the impedance curves for all 4 speakers in one graph...

"Left" speaker of each pair.
About the only thing similar between each speaker is the fact that they are all ported (did not include the curve of the port-plugged Tannoy), so there are double-humps in the bass region although the box resonance frequencies are quite different, and we can make out that for each, the double peaks Fh > Fl suggesting that the box resonant frequency (Fb) is lower than the bass driver's natural free-air resonant frequency (Fs); not uncommon but we can see the opposite as well in some speakers.

It's also good to have a look at some of the subtle anomalies like little resonance "wrinkles" in the graphs, and things like the ultrasonic "metal dome resonance" that might be there (at least up to 35kHz as shown in these graphs). Knowing these potentially problem frequencies will help when doing acoustic measurements to focus on whether anomalies can be detected/heard.

I think it's also good to be able to compare the right and left speakers to see how well the impedances match. As I noted above, I don't recall seeing this kind of comparison done by Stereophile over the years just as a measure perhaps of quality control. (Even if this comparison were made, I think it's fair to keep in mind that prominent magazines typically have samples loaned to them for testing from the company which may be specially selected samples compare to what consumers buy off the regular retail channels as I have here.)

One interesting comment I read on John Atkinson's Stereophile article on speaker measurements from 1998 suggested that European speaker companies tended to have minimum impedance in higher treble frequencies compared to US (North American) companies situating the minimum impedance in the low midrange. While not exactly at the frequencies identified by Atkinson, we do see that a European-designed speaker like my Tannoy had an impedance minimum around 1kHz while both the Canadian Paradigms and Energy had minima down around 100-150Hz. I'll keep an eye on this with other speakers.

Ultimately, knowing the impedance of one's speakers and the phase angle will allow us to appreciate the load being placed on our amplifiers and give us an idea of which speaker models are more demanding. Looking at these 4 speakers I routinely use around the home, it's quite clear to me that my amplifiers should be able to handle 4Ω loads. In fact, I've measured a number of other speakers and almost every one will have some portion of the impedance graph dip below 6Ω in the audible spectrum. A nice remainder that in the days ahead when I measure amplifiers, I really should be focusing on performance across a 4Ω load rather than 8Ω, and 2Ω would be significantly lower than typical.

Another implication of the low impedance at certain frequencies plus challenging phase angle is for anyone connecting two speakers to the same amplifier terminal. Obviously one should not assume that connecting two "8Ω" speakers in parallel would result in a simple "4Ω" load to the amp when in fact one could easily see 2Ω impedance for substantial portions of the audible spectrum! Just be cautious.

There's a ton of interesting material on speaker design on the Internet to research! For example, here's an interesting study on vented port designs including port length, size, whether flanged, etc. We could perhaps in time talk about passive radiators, horns, dipoles... There are all kinds of great pages for calculating cabinets and crossovers (also here). Online 3D subwoofer box designs (especially useful for those car audio guys!). Also there are many software packages for design of speakers, crossovers, and measurements. Examples of this include LspCAD, and free crossover design with XSim. There are of course books out there like Designing, Building, and Testing Your Own Speaker System with Projects. Much to learn and maybe even try out one day for audio hobbyists wanting to dip their toes into DIY speaker construction.

One last thing...

Here's a frequency response comparison to show the difference between the small 2-way bookshelves and the full-range Signature S8 (all were measured with microphone 50" away, on axis, tweeter height, 1/6 octave smoothing, each powered by the same Emotiva XPA-1L monoblock amp):


While there are room effects and I didn't place the S8 at the exact same position as the two bookshelves, what is clear is that the full-range speaker is able to extend lower (there's a dip from 100-200Hz likely positioning related since the S8 was closer to the side and rear walls). Plus, the S8 also has a flatter treble response out to 20kHz.

For all the small variation we might hear between DACs, argue if "bits are bits", debate "best" digital filter setting, promote hi-res audio, or God forbid we obsess over cables, just look at the magnitude of the differences between speakers! How many orders of magnitude difference is that compared to the above controversies?! Remember folks, at the end of the day, focus on your room and speakers, because that is truly the heart of your sound system hardware, and within reason, all other hardware is peripheral. Speakers and the room are where money should be primarily allocated for "good sound".

Enjoy, and remember to not sweat the small stuff, friends...

Hope you're all enjoying the music! Welcome to September.

Oh yeah... Speaking of speakers, physics, and interesting measurements. Here are a few more unpublished pictures from last September when I met up with Mitch to check out the "KleinHorns" (see Mitch's report here).

I wondered what the impedance measurements and frequency response would have looked like for these speakers in that room!





3 comments:

  1. Hey Arch, awesome two parter on speaker impedance. Very well explained with several real world speaker examples. Kudos! It is great to see phase angle getting equal consideration.

    Thanks for the linkage to the Kleinhorn article and additional pics. It was fun hanging out together man!! Listening to those behemoths as art was wild! Would be interesting to see their measured impedance for sure. Nelson applied a Zobel network to his Kelinhorns. Wonder what that does to the impedance…

    Keep up the great writings!
    Cheers,
    Mitch

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    Replies
    1. Hey Mitch... Yeah, amazing that the art install was a year ago! Time flies!

      Yeah, would have been fun to take the impedance measurement rig over and peek into how the artist had put that together :-).

      Great conversation and drinks that evening as well...

      All the best!

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  2. Hi! I have been reading your posts and I noticed some little mistakes on your análisis of electrical impedance curves.

    Firt of all, sorry for my english, I'm from Argentina! I'll try my best.
    I'm studying sound engineering at Universidad Nacional de Tres de Febrero or UNTREF, and everything I'll say its based on the Leo. L. Beranek's book "Acoustics: Sound Field and Transducers" and my personal studies of that work.

    When you show the second vented box impedance curve of the "Tannoy mX2" without the "bung" you identify the first impedance peak as a result of the presence of the vented box (or Helmholtz resonator). And altough thats correct, the actual increase of the impedance it's not caused by the resonator itself (as an actual resonance peak as shown in the first picture, caused by the FEM at the "fs" of the mass-spring system) but the presence of the Helmholtz causing a low impedance at its ressonance frequency. I explain myself. If we understand the loudspeaker as a series resonant circuit (RLC), and a very important detail: with a roll-off by -12 dB/oct (2nd order filter) detailed in the book that I mentioned before, and from the same work, the Helmholtz resonator can be understood as an parallel resonant circuit. Those together gives the -24 dB/oct roll-over (4th order filter) but that parallel resonant circuit have its LOWEST impedance at its fs. Doing a brief explanation on the Q factors will finally crack this mistery.

    Basically, as you can know from the TS parameters of a loudspeaker, its QTS value will be from 0,2 to 1,sth but not that much further. That mean that it will be a "skinny" peak. On the other hand, the Q value of the Helmholtz resonator will have much larger values, going up to 20 or 30 in most cases. That means that it will "substract" impedance at its fs. If we tune the fs at the same resonance frequency of the speaker, finally, we can see that really the minimum in between the two peaks we find the resonance frequency of the box. But not only the box, the Helmholtz resonator with the port, both together have a unique resonance frequency and both acting as a resonator. Without the port, the box by its own its an acoustic compliance.

    In fact, from this point of view, now, the difference between the two peaks can be interpreted as how much the speaker and the box are "coupled" together as you mentioned. If both have the same fs, the peaks will be equal (at both sides of that fs) because of the substraction that the parallel circuit makes to the natural peak impedance of the "free air" resonance.

    So, neither the Fl nor Fh are the port resonance and woofer, respectively. I think that its a bad interpretation of the article from audiojudgement.com that you made. They refer to the Fb as the "box resonance" but you made a free interpretation that the first peak correspond to the "port" frequency. Their mistake too because of not using the right words I think.

    I hope you can understand everything I've said and let me know if thats not the case and I will try my best again! I appreciate the work you have done.

    Best regards from Argentina!

    EAING

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