The Value of Normalized Distortion

Normalized Distortion, or Frequency Normalized Distortion, is a distortion measurement algorithm first proposed by Listen’s president, Steve Temme (then at Bruel and Kjaer) in a 1993 AES paper. Although it’s been available in SoundCheck since 1996, it’s only recently gained traction. This is likely due to a renewed interest in correlating measurements to audibility – something that we’ve always considered important at Listen – and also because it is the only way of accurately measuring some new types of microspeakers. Let’s take a look at how it differs from conventional distortion measurement and why it is valuable for identifying the cause of distortion.

A typical speaker response, shown in Fig. 1, isn’t flat. There are typically amplitude irregularities due to reflections and resonances, and high and low-frequency roll-offs due to the passband nature of the transducer. This introduces some interesting artifacts when we look at harmonic distortion.

 

 

Fig. 2 shows the fundamental, second and third harmonic of a speaker. If we’re measuring harmonic distortion by sweeping from 20 hertz to 20 kHz, to measure the second harmonic, our filter tracks at twice the stimulus frequency and goes out to 40 kHz. Let’s assume that the second harmonic is 20 dB below the fundamental, i.e. 10% distortion. The third harmonic starts at three times the fundamental frequency and goes to 60 kHz, and let’s assume that this harmonic is 40 dB down below the fundamental, or 1% distortion. You can see the bumps and dips in the response align with the fundamental as the harmonics are filtered by the same linear frequency response.

 

 

The problem with conventional THD is that we always plot the harmonics at the stimulus frequency and then we compare the harmonic level to the stimulus level at the stimulus frequency as shown in Fig. 3.

 

 

You can see that the responses are shifted along the x-axis to start at 20 Hz, like the stimulus frequency. This change in alignment between the harmonics and the stimulus causes the irregularities to be offset, and the high and low-pass roll-offs look entirely different.

 

 

When we now calculate THD, (Fig. 4) we get some interesting results. Even though we showed earlier that the second harmonic was uniformly 20 dB down, when we calculate it this way, the distortion appears much higher at low frequencies because the fundamental rolls off sooner. Instead of being -20 dB (or 10%) at 20 Hz, it’s actually only -3 dB, which is equal to 71% distortion.

We see the opposite effect at high frequencies; the distortion rolls off prematurely compared to the stimulus frequency. This means it’s calculated to be -30 dB, or 3.1%, rather than -20 dB (10%).
In the pass-band region, the distortion could be under, or over-estimated, particularly around the resonances and reflections, where the calculation differences are more pronounced. This isn’t limited to the second harmonic; it’s the same for the 3rd and any subsequent harmonics so all these differences stack up.

If you look at a typical THD measurement of a loudspeaker, you’ll notice it’s always high at the lowest frequencies and rolls off at high frequencies. This is because conventional distortion measurement methods tend to over-estimate distortion at low frequencies, and under-estimate it at high frequencies.

So why does this matter? If you want to truly understand what’s causing your distortion, you need to separate the linear from the nonlinear. The good news is that this isn’t difficult – it’s just a small change in the order of operation when the THD is calculated.

What we proposed back in 1993, and I am still a strong advocate for today, is calculating it as follows: Instead of plotting the harmonics at the stimulus frequency and comparing it to the fundamental at the stimulus frequency, reverse the order. Plot the harmonics at the actual measured frequencies, compare it to the fundamental at the harmonic measured frequency, calculate the percent distortion, and then plot it at the stimulus frequency (Fig. 5). This is what we call Frequency Normalized Distortion.

 

 

If you’re wondering why this looks familiar, it’s because the graphs and distortion calculations exactly match the actual distortions shown in Fig 2.

As well as removing the influence of the linear frequency response on the calculated distortion, this method also minimizes the influence of room reflections. This enables you to measure the free field harmonic distortion in a regular untreated room with reflections – a particularly useful technique if you’re measuring somewhere like a car, which is full of reflections. 

Now we’ve covered the theory, let’s examine some real-world examples: a conventional speaker and a piezo-MEMS speaker.

Fig. 6 shows the measured harmonics for a dynamic speaker driver. The fundamental starts at 50 Hz and the 2nd and 3rd harmonics are plotted at their measured frequencies, starting at 100 Hz and 150 Hz respectively. The roll-offs are clearly similar at the low frequencies, as expected. At frequencies above around 8 kHz, the shape of the third harmonic is particularly similar to the fundamental, clearly demonstrating its linear filtering effect. Even the second harmonic shows some similar characteristics.

 

 

 

Fig. 7 shows the THD plotted both the conventional way (purple line) and the normalized way (green line). The conventional plot indicates around 10% distortion in the lower frequencies, and a bump around 200 Hz – which could potentially be a problem. The reality, however, is that it’s just the linear response boosting the low frequencies. The conventional plot also has a little bump around 1 kHz, but this is caused by the slight bump in the fundamental curve at higher frequencies. If we now look at the frequency normalized curve, it’s clear that we don’t have a low-frequency issue, although we do have a little bump at resonance around 300 Hz – and that is indeed a nonlinearity. This is much more valuable information if you need to know precisely where the distortion is coming from so that you can design around it.

The differences between conventional and frequency normalized distortion are even more significant with piezo-MEMS transducers. Piezo-MEMS transducers are an interesting new class of miniature transducers that use semiconductor fabrication processes to create actuators with piezoelectric materials that drive a membrane, rather than traditional mechanical components. They behave very linearly in the lower frequencies – you typically don’t see any increase in distortion at all – but often have a little high-frequency resonance. Due to these characteristics, a major vendor of these devices advises their customers that Frequency Normalized Distortion measurements are a critical part of accurately assessing distortion. 

Fig 8. shows the measured fundamental and harmonics of a piezo-MEMS speaker plotted at their measured frequency, and Fig. 9 shows the same harmonics plotted at the stimulus frequency.

 

 

In Fig. 8, the shape of the third harmonic again clearly mirrors the fundamental, and the second harmonic has something going on – maybe a resonance – close to 10 kHz. In Fig. 9 where the harmonics are plotted at the stimulus frequency, the low-frequency distortion, as before, appears a lot more significant than in Fig. 8 where it is plotted at the measured frequency.

 

 

This is clear in Fig. 10, where we compare the conventional and Frequency Normalized THD. Plotted the conventional way, the distortion is calculated at around 20% at 100 Hz, which is quite high. However, when calculated the frequency normalized way, it’s down at 6-7% . It’s also quite flat throughout the 100 to 10 kHz range, which is typical of these drivers. They’re simpler – there are fewer components to cause distortion, and they’re not acting in a nonlinear magnetic field. As with the traditional driver, relying only on conventional THD measurements could lead to a lot of wasted time trying to design around problems that don’t exist.

Whenever I explain this distortion measurement method, most engineers immediately recognize its benefits, and wonder how the conventional method became the norm. I suspect the reason traces back to early measurement practices: in the 1980s, Bruel & Kjaer pioneered the tracking-filter method, and plotting harmonics at their actual measured frequencies simply wasn’t possible with the chart recorders that were in widespread use. That constraint shaped the convention we still use today, even though the technological limitations that created it no longer exist. Perhaps the demands of modern transducer technologies may finally drive the industry to adopt it.

Summary

Conventional and Frequency Normalized distortion measurement methods are compared in Fig. 11. Conventional THD isn’t wrong. If you listen to sine waves it is what you hear. However, we don’t generally listen to sine waves, and Frequency Normalized Distortion correlates better with listener perception of broadband signals such as speech and music. 

More significantly, to correctly identify distortion mechanisms, and design products that address these, it’s essential to separate the linear response from the nonlinear distortion, and this requires Frequency Normalized Distortion.

 

 

Further reading:  How to Graph Distortion Measurements, Steve Temme. Presented at the 94th AES Convention, Berlin, March 16-19, 1993.

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Check out the recording below to learn more on Frequency Normalized Distortion: Why THD Isn’t Enough: