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Understanding Sealed Speaker Impedance

Rick Sykora

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As some of you are aware, have been playing around with my Purifi SPK parts and working to determine a final configuration for them. As I have been trying various vented alignments, reminded me that I planned to share some useful observations about speaker impedance measures. I am multitasking projects but Covid just put a damper on going out in public here and thought I would start the thread.

A couple of quick caveats before I start:
  1. While most of what I will present will be generally applicable, will the using the SPK parts to demonstrate some things and so may not be always be applicable to other speakers. The SPK woofer is a 4 ohm, lower Q woofer and the tweeter is a Mundorf AMT with a very flat 4 ohm impedance. The crossover is pretty typical but nothing that would prevent me from using it for this thread.
  2. Some of what I will show may be hard to apply without a baseline for comparison and frankly experience in speaker design. Am hoping to help members better understand some aspects of the impedances shown in Amir's reviews. That said, conditions matter. This includes the measurement voltage. software, environment and condition of the speaker being tested. In my case, my measurements are being done are at room temperature, using REW with a 100 ohm sense resistor using a Sound Blaster Audigy card to drive the speaker at 100 mV.
I have an advantage that Amir usually does not have as Purifi provides a baseline measure...

1659728465758.png


Here is my measurement in comparison...
1659728416992.png


So why do they not match exactly? As I said earlier, conditions matter. Note that I used the Purifi SPK4 as a baseline. My SPK does not have the same damping and has the crossover mounted internally rather than externally. More importantly, I can say the build is essentially valid as the key peaks and valley frequencies match. The key ones being the leftmost peak (port resonant frequency), the next dip (box tuning frequency) and the next peak (driver resonant frequency). The other key inflections also match at 800 Hz, 2000 Hz and 8000 Hz. These indicate a good match of the tweeter and its crossover to the baseline.

Note the impedance magnitude difference is most likely due to my cabinet being a bit leakier than the reference Purifi one. I anticipate I will be able to reduce the box issues in upcoming steps. Also, as will examine later, there is a slight blip in the trace around 240 Hz. As Amir will often point out in his reviews, this indicates a (undesirable) resonance.

For simplicity, want to start a new baseline and offer the first major change by taking the same speaker and sealing the vent closed. If I did not have a published baseline for comparison, this is my next best way to establish one. I then could use a speaker modeling program to verify whether my baseline was a good one. Bear in mind, that that design model would need to include the crossover. If the crossover design is not known, could bypass and measure each driver independently in the cabinet and model without it.

1659729536788.png


While this a larger sealed box than would be suggested for this woofer, for the sake of this experiment, it shows what you would expect. Due to the woofer seeing greater push back as it tries to move against the trapped air, the box resonance frequency is now much higher and so is the impedance peak.
 
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Rick Sykora

Rick Sykora

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The SPK cabinet design incorporates a removable back and experience has shown that (despite best efforts) it will likely leak to some degree. The drivers are all gasketed, but the port and speakon connector will need to be checked too. This leaves the other cabinet joints. While I have a stethoscope to help find leaks, for this exercise, I am returning to my previous method - using painter's tape to seal over the joints.

For the first round, am taping the front baffle seams. Here is a before and after comparison...

1659787750378.png


While difficult to see, this has yielded about a (pretty marginal) 1 ohm improvement in impedance at the peak. If the front baffle leaked worse, then could expect a few or maybe tens of ohms of higher impedance. This is because the air in the cabinet is now pushing harder to impede the woofer's movement. In comparison to another design, the magnitude of the spike could be lower or higher. With the baseline established, we can see the relative change and know that the change is due to a leak.
 
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witwald

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So why do they not match exactly? As I said earlier, conditions matter. Note that I used the Purifi SPK4 as a baseline. My SPK does not have the same damping and has the crossover mounted internally rather than externally. More importantly, I can say the build is essentially valid as the key peaks and valley frequencies match. The keys ones being the leftmost peak (port tuning frequency), the next dip (box tuning frequency) and the next peak (driver tuning frequency).
Doesn't the impedance minimum between the two low-frequency impedance peaks correspond to the port tuning frequency? That's where the motion of the driver is at a minimum, as the port is providing most of the acoustic output, hence the impedance minimum. According to Small (1973), f_B is equal to the frequency at the impedance minimum, f_M, where f_B is defined as the resonance frequency of the vented enclosure.
 
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Rick Sykora

Rick Sykora

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Doesn't the impedance minimum between the two low-frequency impedance peaks correspond to the port tuning frequency? That's where the motion of the driver is at a minimum, as the port is providing most of the acoustic output, hence the impedance minimum. According to Small (1973), f_B is equal to the frequency at the impedance minimum, f_M, where f_B is defined as the resonance frequency of the vented enclosure.

Yes, Small defines f_B as the box tuning and is used that way to this day AFAIK. He only defines the peaks as fL and fH (frequency Low and frequency High). My posted definition for the peaks came from Bassbox Pro and have not read anything that would contradict those definitions. I did adjust the wording to be "resonance" rather than "tuning" as this seemed more accurate.

The Bassbox software is based on Small's work on both bass reflex and passive radiator designs. The software also refers to fL as the resonant frequency of the passive radiator. Given a port and a passive radiator are roughly equivalent, Bassbox is consistent at the very least. :)
 
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Do you find that the purefi woofers perform differently than models in general? I know when scanspeak introduced some of the high excursion illuminators, they commented that conventional T/S simulation didn't really tell the whole story.
 
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Rick Sykora

Rick Sykora

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Do you find that the purefi woofers perform differently than models in general? I know when scanspeak introduced some of the high excursion illuminators, they commented that conventional T/S simulation didn't really tell the whole story.

This is a broader topic than just impedance, so going to suggest you start another thread or maybe can discuss on my SPK thread. Thanks!

P.S. Just as a sneak peak, the answer on impedance is yes (at least for VituixCAD)
 
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Rick Sykora

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Have taped all the seams that could have major leaks and only continued to see marginal improvements up to a point of diminishing returns. The major area of concern was the back baffle and it yielded about another ohm. So did a quick cross check against my VituixCad model and matches closely as you can see here (note the tweeter portion is not in the model)...

1659822333484.png
 
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Rick Sykora

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Circling back to the simple case where a sealed box is leaking, wanted to show this is a more controlled manner, so I loosened the speakon connector and you can see the result in red below...

1659888460924.png


This will look much different for a vented box, but here is simply a case of less air cushion and so lowered the impedance peak by about 10 ohms. In any case, might be difficult to determine without another speaker, modeling it or supplied vendor baseline. If the baseline is coming from another source, remember that conditions matter. Here I took the same speaker and simply reduced the input voltage to 25 mV...

1659888988155.png


In this case with less force coming from the speaker, the impedance is higher by 8 ohms. Looks as though I could make the leak go away simply by reducing the voltage! Seems rather obvious (like a leaky tire), but thought it was a useful visual to share.:)
 

DonH56

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Very interesting seeing how a small effect can cause such a big impedance change.
 
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Rick Sykora

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So, for all the earlier sealed measurements, there has been some polyfill in the area behind the woofer. This time, I have added about 100 grams of cotton damping material to the upper back part of the cabinet. Here is how that changed the impedance...

1659905132979.png


Remember, baseline is blue. So the purple trace is after I added more damping material and you can see it lowered the peak impedance about 5-6 ohms.
 
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Rick Sykora

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Inspired by a member's request for help, am adding how a simple low pass crossover can affect impedance. Let's start with a new baseline using the popular Dayton RS-225. Here shown simulated in a standard sealed box using VituixCAD.

1695732118226.png

So, a pretty typical sealed impedance curve (for a woofer with higher inductance voice coil). The voice coil inductance causes the impedance to rise after 1 kHz. Now let's add a simple LR2 low pass crossover at 600 Hz. Like so...

1695770640111.png

This changes the impedance, like so...

1695770904073.png

Ignore the data kink at 1.2 kHz, but can see the major change increase in impedance at frequencies above 200 Hz and a lesser decrease centered around 100 Hz compared to the original (green dotted line). So, one question is how does the inductor contribute to the filter vs the capacitor? So, removing the cap, we get a simple 1st order crossover. The resulting impedance looks like so...

1695772868426.png


So, still get the major rise in impedance around 300 Hz, but the decrease is gone. If we short the inductor and re-insert the (parallel) cap, we can see why...

1695773095751.png

As you can see the capacitor is having a significant impact on the system impedance by decreasing it mainly after 1.3 kHz. Please note, this could present an ugly load to an amplifier. If you did miswire your crossover and hooked this load to an amplifier, it might shutdown or worse. These are simulated examples for illustrative purposes. Not suggesting anyone wire them up and hook them up to an amplifier.
 

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Trdat

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This was very educational. Apologize if I missed it but it's not very clear what the improvements are and what that translates to?

You mention a slight decrease in resonant peak, what is that improving exactly?
 
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Rick Sykora

Rick Sykora

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This was very educational. Apologize if I missed it but it's not very clear what the improvements are and what that translates to?

You mention a slight decrease in resonant peak, what is that improving exactly?

Please elaborate the context for the claims in question. Am not sure. Thanks!
 
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Rick Sykora

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A shorted inductor and shunted capacitor is no longer a first-order filter. You're aware of this, right?
I'm not sure what your point is with this exercise.

May have confused you. I started with an LR2 low pass. By removing the cap, it is a first order low pass. For completeness, just showed how a shunt capacitor affects impedance in the last example.
 
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Rick Sykora

Rick Sykora

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No, I'm not confused. :)
Xc goes low at high frequencies, so you'd just be shorting your amplifier. It's not a practical example.

The point was to show the effect. This could happen if you were wiring this crossover and connected the input to the wrong side of the inductor. Seems practical enough to me.:)

p.s. Agree on the shunt cap being a potentially ugly load, so added note that my example is simulated (and NOT measured).
 
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pma

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Please let me comment on woofer impedance (component alone) and woofer inside the vented box (bassreflex)

woofer_imp_vented.png


This of course depends on box resonant frequency. Here the box resonant frequency is near to woofer resonant frequency. Due to phase inversion there is a minimum of impedance in the vented box.
 
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Rick Sykora

Rick Sykora

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Please let me comment on woofer impedance (component alone) and woofer inside the vented box (bassreflex)

View attachment 315198

This of course depends on box resonant frequency. Here the box resonant frequency is near to woofer resonant frequency. Due to phase inversion there is a minimum of impedance in the vented box.

Thanks Pavel, but really would be more appropriate in my …Vented Speaker… thread.;)
 

Trdat

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Please elaborate the context for the claims in question. Am not sure. Thanks!

Amatuer hour apologize, I think I wrote my question before full understanding the thread. But in post 10 you mention adding polyfill which brings the resonanat frequency down by an ohm or two, what is the benefit of that? If the resonant frequency is the same but at a different ohms I am curious how that effects the speaker?
 
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Rick Sykora

Rick Sykora

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Amatuer hour apologize, I think I wrote my question before full understanding the thread. But in post 10 you mention adding polyfill which brings the resonanat frequency down by an ohm or two, what is the benefit of that? If the resonant frequency is the same but at a different ohms I am curious how that effects the speaker?

Was showing how much impedance is affected by the damping material. Thought I mentioned somewhere but the intent of the thread is to help members visualize how certain conditions affect the speaker impedance. If I try to explain every aspect of design, will be a book...

Damping material can have several effects on speaker performance. The typical sealed case is to increase the compliance of the enclosure. You will often hear it explained as being comparable to increasing the volume of the box. The impact depends on the driver, box size, and the amount and type of damping. Post #10 was meant to briefly show how damping might compare to the earlier leaky box case. Many more use cases are needed to really do the topic justice. :)
 

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Do box modellers simulate the frequency shift accurately? I don't think it's particularly impactful in most designs but I'm curious if bassbox or whatever captures it.
 
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