Sunday, 11 August 2019

MEASUREMENTS: Speaker Impedance - Part 1; measurement box, dummy loads and single speakers...

As you know, speaker impedance is not a "flat" resistance across the audio spectrum as one would find with a resistor. Rather when we measure the speaker load, we see fluctuations affected by the voice coils and crossover networks inside that speaker "box".

Remember that the electrical signal that represents "sound" are alternating waveforms. Thus we are in the domain of AC analysis when talking about the electrical properties of speakers which are typically "seen" by amplifiers as low impedance and complex "reactive" loads that will unevenly affect current and voltage due to capacitance and inductance. (For a good review with some math on the concept of impedance, check out the series of videos here.) As you've probably seen over the years, an important speaker measurement that can help us understand performance and the demand from amplifiers is the impedance curve (and the derived electrical phase angle).

As a hobbyist, measuring speaker impedance with excellent resolution is not difficult these days. We are blessed with free/user-supported software like Room EQ Wizard (REW) that can get the job done quickly and accurately. What we do need to do is to rig up a "sense resistor" to an ADC measurement device for the software to do its "magic". Here's a little black box I put together recently to get it done:

Nothing fancy, just a plastic project box with a few holes drilled out for the RCA connectors, solder some wires and an effective 100-ohm resistor (I had 2 x 200-ohm 1% resistors in parallel). I followed the instructions found here for the hookup (diagram reproduced for convenience):

As you can see, I labeled the various ins and outs for the box between the speaker, headphone out from the DAC as well as the ADC input; one can use the same audio interface box or soundcard for the in/out.

With this hooked up and a speaker connected, it looks like this with my Focusrite Forte ADC/DAC. Laid out on the dining room table temporarily of course! :-)

There's another black box in the far right... We might talk about that one another time.
The benefit to using the Focusrite Forte for this purpose is that I can do all this portably since this ADC/DAC box can be powered using the laptop USB. In the picture above, I have an old Sony SS-H1600 speaker hooked up. These speakers came from an old Sony mini desktop system I used back in the college days.

I would highly recommend the new versions of Room EQ Wizard 5.20 (currently in beta 18 as I publish) for these measurements. Kudos to the software developer John Mulcahy -  clearly improved impedance measurement module of the software including easier calibration plus a nicer and more intuitive interface that looks like this:

Notice the calibration of 0.21Ω for R[Lead] which accounts for resistance in all the wiring, connectors and cables. My black box above has a measured 100.2Ω resistance for R[Sense], and R(input) is the line-in for the Focusrite Forte which has a published impedance of 44kΩ. Depending on how you hook up your sense resistor, you might need to adjust the "Input" and "Output" selections.
As per the screenshot above, I've been using 192kHz sample rate, 2M-sample sweep length with 8 repetitions which will improve noise level of the measurement through averaging the results (3dB improvement with each doubling, so that's about a 9dB improvement with 8 repetitions). I'll measure from 0-48kHz; more than enough. Because the Focusrite Forte has some noise out at 37kHz or so, I'll usually examine the results to 35kHz which is more than enough. Use "Check levels" to confirm that the configuration works. With these parameters, a measurement takes <90 seconds once you click "Start".

For completeness, here's the set-up for the Focusrite Forte using the ASIO driver if you're using this or a similar device:

So, let's do a few measurements today to just show some "basics"... Next time in this series, we'll actually have a look at "real" loudspeaker results.

First, let's just look at power resistors. As you can imagine, this won't be too exciting but it's good foundation to cover. As a hobbyist, in the future once I get some other gear together and finalize a standard procedure, just like with DACs, it'll be nice to get some amplifier measurements done myself without the need for tens of thousands of dollars worth of Audio Precision gear. :-)

For amplifier measurements, we of course need a dummy load of the appropriate resistance / impedance and power handling ability so that the experiment doesn't end up in sparks and puffs of smoke!

As you've undoubtedly seen, most of the time amplifiers are measured using 8Ω or 4Ω loads. In real life one should expect "8Ω compatible" speakers to dip below 8Ω, and in fact they often drop significantly further. As such, I figured for amplifier measurements I likely will do in the future, I might as well just target 4Ω which will put more demand on the amplifier's ability to provide adequate current. These days, even relatively inexpensive amplifiers can handle 4Ω, and even 2Ω .

I do have some large ceramic power resistors, but for convenience, what we have in the picture below are some inexpensive "100W" power resistors you should be able to find at many places locally or online. The larger one on the right is heftier and rated as 4Ω, up to 100W.

The small green one on the left is a very inexpensive 8Ω, supposedly 100W resistor I got online. While it can tolerate 100W for short durations, I would not recommend these small inexpensive ones during prolonged testing due to limited heat dissipation. Since I had a couple of small metal 8Ωs, I decided to just run them 2x8Ω parallel like this for an effective 4Ω load:

Yeah, I know, it ain't pretty and looks a little like some kind of badly done improvised explosive device. But as a dummy load, it works. And now I have two 4Ω loads that I can use for testing with 2-channels driven.

Remember that values like "8-ohms" speakers are referring to "nominal" impedance which pretty well just means an "acceptable" amount around that spec. Based on the IEC60268-3 definition of "rated value", an 8Ω speaker's impedance must not drop below 80% nominal which is 6.4Ω. Likewise, a 4Ω speaker could have dips down to 3.2Ω by this definition.

Using my little 100Ω "black box" and REW software, here's what the single larger gold-colored 4Ω "dummy load" measurement looks like connected to the rig:

I highlighted the impedance graph just above the 4Ω marker. Notice that I've put the marker over 1kHz horizontally and we see that at this frequency, impedance (resistance) is 4.13Ω, phase angle 0.3 degrees.
And here is the impedance and electrical phase angle curve for the 2x8Ω load:

With the marker over 1kHz, impedance (resistance) is 3.87Ω, phase angle 0.3 degrees using the 2 parallel 8Ω resistors.
Looking at the graphs above using REW, we've got impedance vs. frequency from 10Hz to 35kHz. I've put in a small amount of 1/48-octave smoothing. Notice that the rig is measuring an impedance (resistance) of 4.13Ω for the "gold" resistor and slightly lower at 3.87Ω with the parallel 8Ω resistors (to make 4Ω). Commonly, wire-would resistors like these have 5% tolerance which could be +/-0.2Ω and we see the results here fall within the predicted range (exactly +/-0.13  on either side).
As for electrical phase angle, notice that they're benign as expected for power resistors.

You can read more about phase angle curves at Audioholics. Basically it comes to this... Amplifiers are constant voltage devices that tries to maintain the output voltage to the speakers proportionate to the input voltage from the source. To do this, the current varies depending on the demand from the speaker load. Because the speaker has both inductive and capacitive elements, the amount of current the device uses will vary in the following ways:

Capacitance requires that the current must flow and build up ahead of voltage - this is defined as a negative phase angle in relation to voltage.

Inductance results in the development of back EMF thus resisting and delays the change in current - this is defined as a positive phase angle in relation to voltage.

As discussed in the Audioholics article, the key phase angle (denoted as Greek phi Φ) to keep in mind is +/-45°. This is the point where the amplifier must dissipate double the power compared to just a purely resistive load while the speaker receives only half the power. On either side of that key phase angle, the amplifier demand is reduced. Knowing this allows the amplifier designers to ensure that they can deliver adequate power and maintain the temperature of the devices at safe levels. I've seen my own speakers vary between +/-70° at the extremes with +/-60° being more common.

As you can see, electrical phase angle for a dummy resistive load is essentially zero across the frequency range. Notice that the measurement does deviate a little bit in the higher frequencies due to slight inductance in the wire-wound resistor. Like the flat impedance measurement, this "flatness" of the phase angle also is a gross simplification as we'll see once we measure real speakers.

No doubt, the use of a simple resistive load as a "dummy" speaker is a simplification for amplifier measurements as no real-life speakers present themselves like this. Nonetheless, "flat" power resistors like these do provide a standard for amplifier measurements so long as we're aware of the limitations and allows us to target how many watts of power is being demanded of the amplifier.

The graph above is an overlay of impedance for both 4Ω resistive loads to demonstrate that the ugly parallel 8Ω x 2 load and the single 4Ω resistor are equivalent except for a consistent +/-0.13Ω variance from 4Ω. It's nice to be able to easily overlay impedance graphs to compare different "speakers". As mentioned above, with reasonably closely matched verified loads, I could drive both stereo channels for amplifier measurements.

Speaking of impedance overlays, measurements of speakers in magazines over the years generally just show the results from a single speaker. Since speakers are typically sold in pairs, I've often wondered if the pair would be precisely matched. Obviously, the more precise the match, this speaks to better quality control off the production line. Therefore, when I measure my speakers, I'll make it a point to have a look at how closely speaker pairs are matched.

Moving on then... Going beyond resistive dummy loads, let's now put in an actual speaker. Here's a simple one:

An Epiphone Electar 10 electric guitar practice amp. Let's see how that single 6" paper cone speaker inside measures in terms of impedance. The back of the box is open so I can easily just attach the wires from my tester box to the speaker. This is what the impedance and electrical phase look like:

Now we're beginning to see how actual speakers measure. This is what a single speaker looks like without any passive crossover and in "free air". Notice that 14Ω peak at ~108Hz - this is the speaker's resonant frequency, the natural frequency you'd hear if you (gently!) tap on the cone like the skin of a drum. I'm showing the impedance up to 45kHz and you see that there is rising inductance (increasing electrical phase) into the higher frequencies accompanied by the increasing impedance.

The amplifier driving this speaker would see the lowest impedance as just below 5Ω. The electrical phase remains significantly below +/-45° which as discussed above is easier for an amplifier to drive. By the way, notice that at the resonant frequency, the electrical phase is 0°.

Remember that the electromechanical speaker not only acts to create sound waves, but they can also act as microphones. Check this out...

While a single measurement is being captured, if I clap my hands nearby or lightly tap on that box at around the same frequency during the sweep, I can affect the impedance and electrical phase measurements. This means that not only can we use the impedance/phase graph to look at the speaker's electrical properties, but physical anomalies as well such as a highly resonant cabinet that would result in sonic "coloration" at certain frequencies can show up. When severe enough, this would affect the smoothness of the graphs at those frequencies. You can read more about this in Stereophile's article from a number of years back. Another implication of this is that during measurements of impedance, one has to make sure the room is quiet. Random noise can be dealt with by averaging a number of measurement repetitions.

One final single-speaker example before we end today...

More than a year back, I blew out the tweeter on my Paradigm Signature C3 v3 center channel :-(. The replacement from the company was a combo assembly with both a midrange and tweeter as you can see above (by the way, if anyone has a replacement tweeter voice coil for one of these Paradigm C3 speakers, let me know!).

So what does that single Paradigm "Cobalt-Infused Pure-Aluminum" midrange 4" cone's impedance look like?

Impedance highlighted in yellow for clarity.
The fundamental resonant frequency is at 225Hz, +/-35° phase angle, minimum impedance of 7.5Ω with a peak ~31Ω at the resonance frequency which is also the frequency of maximal efficiency.

Notice in the graph above there are a couple of irregularities at ~2.7kHz and ~10kHz. If this speaker were inside its box in a quiet room, I suppose we could wonder if these are some kind of vibrational modes but given that the speaker is just sitting precariously on my kitchen table, there could have been a number of causes of vibration during the measurement!

Anyhow, I'm sure what I've posted is "old hat" to many out there. It's just some foundational and I hope practical thoughts on how to do this and how to interpret the squiggles.

For those who haven't thought of this stuff, I hope it's good to know that with free software these days, one can measure for oneself and recognize that there's complexity here which the layman audiophile can also explore. For those not familiar with graphs like this, when you're reading magazines like Stereophile, I hope the discussion here will increase your curiosity and you'll have a better look at those speaker impedance/phase graphs... As usual, objective results can provide a way for us to tell if the device (eg. speaker) we're interested in is engineered well.

Next time in Part 2 of this series, let's start looking at actual speakers inside enclosures and with crossovers :-).

Hope you're all enjoying the music!


  1. Thanks Arch,
    I like where this is going.

    1. Hi Mark,
      Yeah, I figure it's time to diversify where I can and see what other cool stuff can be done as a home hobbyist!