Speaker Impedance Measurements

[Draft--revisions coming]

In late 2018 a plug-in was added for making speaker impedance measurements. This post takes a look at additional hardware requirements to be aware of and the impact of those requirements on impedance accuracy.

First, take a look at the topology for measuring speaker impedance in the diagram below. This picture is also available in the "SPKR Impedance" plug-in help menu:

Let's recap how the measurement works: The left channel measures the voltage across the speaker (and only the speaker) differentially, and the right channel measures the voltage across a sense resistor in series with the speaker. From the second measurement, we can learn the current flowing in the resistor and speaker, and using a complex division with the speaker voltage, the impedance and phase of the speaker can be learned.

The setup for the impedance measurement using the plug-in is shown below:

Above we are specifying the sense resistor value, the desired output level for the chirp, any external gain that might be present, how much smoothing we'd like, and then a few options related to phase and calculations.

The key to this topology working is the CMRR, or common mode rejection ratio of the QA401 when measuring the sense resistor voltage. When you apply identical signals to the + and - inputs of the QA401, then the result should be zero. That is, if you apply an identical sine wave to both inputs of the QA401 left channel, you should see no signal at the sine frequency. But in fact that's not the case: Every differential circuit has a CMRR short of ideal and it's usually due to resistor variations between the channels. 

In the QA401, a representative set of plots were made with the attenuator on and off for both the left and right channels at both 100 Hz and 1 kHz.

In panel #1, the difference between left and right channel is around 7 dB, and the CMRR attenuation could be expressed as "80 to 90 dB." This figure will vary from unit to unit. In panel #2, the attenuator is engaged. This introduces additional resistors into the signal path, along with the uncertainty they bring. Here we might state the CMRR with the attenuator engaged is "60 to 70 dB".

At 1 kHz, the measurements are pretty similar to the 100 Hz condition.

Key Point: To maximize CMRR, setup your measurement to ensure the attenuator needn't be engaged. This means ensuring the levels are comfortably (2-3 dB) below the +6 dBV limit. 

Drive Level

In the picture above, it's might not be clear on first inspection, but the right channel sees the full amplitude of the speaker output drive voltage. That is, if you are driving the speaker with 1VRMS then the input to the current sense channel (right channel) is 1Vrms. With the attenuator off, the max input signal needs to be limited to around 2Vrms. Using a 1Vrms limit, this puts the max power into the speaker at 250 mW (4 ohms) and 1250 mW (8 ohms). At 2Vrms, that grows to 1W (4 ohms) and 500 mW (8 ohms).

You can test speakers at higher power levels, but doing so will require the attenuator to be engaged. Yes, that hurts your CMRR, but if your sense resistor is large enough, that OK.

It's interesting to look at how a speaker's resonant frequency and peak amplitude might change based on drive. Driving a speaker harder can result in a slight downward shift of the resonant peak (up to 10%) and a drop in the measured impedance at resonance (about 5%). This shouldn't be a surprise, as inductor and capacitor behavior changes based on applied current and voltage (respectively). 

Key Point: You probably want to pick a speaker drive level that is somewhat representative of the target power levels. Your measurement amp will limit you somewhat here. But as a good starting point, pick a power level that is 1/10th to 1/100th the design limit of the speaker. 

Sense Resistor Value

The sense resistor needs to strike a balance: If too small, then the current signal becomes too small to measure reliably. And if too large, then it becomes too hard to drive lower impedances at a higher power levels. 

The plot below shows some measurements using a 0.01 ohm sense resistor and fixed load resistors. In the picture, notice that 1 and 2 ohm measurements are rock solid. But that degrades your measurement approaches 10 ohms. The measurement error at 10 ohms is under 5%, but quickly becoming significant. At 50 ohms, you have nearly 25% error. 

If we assume 10 ohms and above is degrading quickly, then that suggests a good rule of thumb is our sense resistor must be greater than the expected max load impedance divided by 100. 

The same measurement is repeated below, but this time with a 1 ohm sense resistor. In this case, a 100 ohm resistor has about 3% error, improving to 1% error at 50 ohms. The error gets even smaller for lower values.

Key Point: Use a sense resistor that is no smaller than about 100X than the largest impedance you expect to measure. If you want to measure an amp input with a 10k nominal input Z, you'd want a sense resistor no smaller than 100 ohms. 

A Current Sense Test Jig

Below is a schematic and layout of a simple board to allow you to easily insert an arbitrary resistor value in-line with a signal. You then connect across the resistor differentially via J3. These are low-cost boards to build, and it makes it easy to have several boards with values ranging from 1 ohm, 10 ohm, 100 ohm, etc. This let you measure anything from a 2 ohm speaker up to a 10k (or larger) amplifier input.

Key Point: It's hard to measure a wide range of impedances with a single setup. You'll need some different setups for measuring 4 ohms speakers, 600 ohm headphones and 10K amp inputs.

FFT Size

The size of the FFT matters to a point. Smaller FFTs take less time, but they can under-report the peak impedance as shown below:

Key Point: Use a 64K or higher FFT at 48Ksps. This will yield a chirp that is just over 1 second, and it's accuracy at resonance will be within a few % of the value seen with a 128K or 256K FFT.

Using the QA460

The QA460 is a transducer driver with a buit-in current sense resistor. The value of the QA460 sense resistor is 0.01 ohms, and the reference designator is R107. It's location on the PCB is shown below. Swapping the resistor, which is a 1206 footprint, is a straightforward task. If your aim is measuring most speakers, then a 0.1 ohm resistor will generally suffice here.

Key Point: The QA460 is designed precisely to help you make speaker measurements, but you might want to increase the shunt resistor to 0.1 ohms or even 1 ohm, depending on the accuracy you need to see in the resonant peak amplitude. It's not uncommon to see resonant peaks of 20 or 40 ohms when measuring speakers. The good news is the sense resistor doesn't have an impact on resonant frequency--just the accuracy at peak resonance. 

DATS Comparison

DATS is widely used for measuring speakers. The same speaker was measured at "high drive" (0 dBV = 1Vrms into speaker) and "low" drive (-26 dBV = 50 mVrms) into the speaker. Using a scope, the drive level from DATS was measured to be about 50 mVrms, with a fair bit of variation due to what is likely a higher value sense resistor. 

The DATS plot of the speaker is shown below. Note the resonance peak at about 93 Hz, and the impedance at resonance is about 14.2 ohms. At 20 kHz, the impedance is approaching 7 ohms, and at 10 Hz it's about 3.5 ohms

Looking at the plot from the QA401 at "low drive" we have the following:

At comparable drive levels, the measurements between the QA401 and DATS agree very well.

Next, take a look at the "high drive" level from the QA401:

At the higher drive level, we see the resonant frequency has dropped about 3%, and the resonance at peak has also dropped from about 14.5 ohms to 13.5 ohms, which is about 7%. These changes are fairly modest, but they are something to keep in mind.

In the low-drive case, the speaker was driven with about half a mW of power. In the high-drive case, the speaker was driven with about 250 mW of power.

Conclusion

The QA401, when augmented with the QA460 or a similar amp with shunt measurement abilities, provides a robust means for measuring speaker impedances at a range of drive levels.

The post hopefully described the various tradeoffs to be made when attempting to measure low-value reactive loads with the QA401 and its impedance plug-in.

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