"Just a Few dB" (When it Matters, and When it REALLY Matters)

First, this write-up is going to cover two topics that share at least one thing in common: “A few dB” (do they matter?). The first topic is related to hearing and hearing loss, and should be of interest to those who are involved in hearing science, audiology, or sound generally. The second topic dives into a discussion that could be of interest to those involved with test and measurement, or electronics generally. In the second part, I’ll be revealing a type of measurement “error” that’s not a consequence of component tolerance, uncalibrated equipment, or mathematical miscalculations. I’ll explain this problem using actual data and, best of all, provide a “fix” to mitigate such errors. The circuit I use in the demo is simple, but the measurement technique is equally applicable to your Qualcomm Snapdragon SoC-based product as well as vintage electronics (I enjoy working with tubed equipment).

The title, “A few dB”, goes back to a comment an audiologist (as I recall) made after reading an Outdoor Life article titled “The Big Bang!”. Because I had something to do with this article (see pics below), I was also the person who often responded to questions and comments. Briefly, the impetus for the article had to do with firearms equipped with muzzle brakes (sporting arms or weaponry--take your pick--I'm not an expert on firearms). On a perceptual basis, firearms with muzzle brakes were considerably louder than those without muzzle brakes. But when sound pressure levels (SPLs) were measured using conventional sound level meters (SLMs), there was little--sometimes zero--difference between the readings. To add to this story, a few shooters incurred hearing loss after firing one or two rounds from a muzzle brake equipped rifle. These shooters didn’t experience hearing loss when firing the same rifle, same ammo, from their rifle prior to attaching a muzzle brake. Something about the sound level measurements seemed amiss. Originally, the reason for the difference in subjective loudness and measured SPL would have seemed apparent: It comes down to the averaging = meter ballistics (FAST vs SLOW vs IMPULSE) as well as weighting (A, C) of SLMs intended for “OSHA type” sound surveys. The equipment used to show measureable SPL differences among various firearms was to use a microphone preamplifier with a fast rise time and a storage oscilloscope. Using an oscilloscope, it was easy to capture the peak of the blast noise (very brief in duration, and probably half a cycle before decay), and convert from the recorded voltage to pressure (in Pa), and then to peak SPL. For the Outdoor Life article, I reported numbers as PPL, or peak pressure level.

For people who have studied audiology or psychoacoustics, you know that “loudness” is more than a function of frequency and SPL (following the equal loudness, or Fletcher-Munson curve); loudness perception is also a function of a sound’s duration. Tones presented for very brief periods (say less than 200ms) won’t appear to be as loud as the same tones when presented for a longer time period (but only up to a point). You can probably understand the importance of this when it comes to hearing tests: Presentation tones need to be at least 200ms in duration (which is fairly brief), plus fade-ins and fade-outs are needed to avoid audible “clicks” that occur from abrupt transitions. In general, I prefer to present test tones as intermittent bursts: Intermittent beeps help the listener identify a test tone from continuous tinnitus and possible background noise. Considering all of this, and getting back to firearms and muzzle blasts, we might question the importance of capturing the peak of a waveform that’s very brief in duration. Also, after careful measurements, the PPLs for a given rifle (and ammo) with a muzzle brake were rarely more than “a few dB” greater than the recorded PPLs for the rifle minus its muzzle brake. One person (the aforementioned audiologist) commented: “Why all the fuss over a few dB?” My thought (with numbers, explained below, as well as evidence) was: “It’s the difference between a (possible) temporary threshold shift and acute acoustic trauma.” Really? Read on.

Another curious thing about sound (referring to hearing, not a tree-in-the-forest) has to do with our ability to discern changes in SPL. A lot of published data focuses on tones, as tonal stimuli are easy to replicate. Some folks might initially guess that as a tone grows louder, an even greater difference in dB SPL is needed to discern a change in level (volume). The ear doesn’t work this way, and there are known “compressive nonlinearities” when it comes to normal-ear physiology and hearing. For soft sounds, you may have to increase a quiet tone’s level by 3 dB to notice a change in level, but a change of 1 dB is noticeable for louder tones and complex sounds. (By the way, I don’t like stepped attenuators when the step is a gross 1.5 dB because it’s either “too loud” or “not loud enough” when switching between steps.) There’s little research for REALLY loud sounds because subjecting people to high SPLs isn’t exactly ethical (you can find interesting data by digging into pre-WWII archives). Getting back to firearms (again): A few dB could be “painfully” louder than an already loud 130 dB SPL. But what about the physiological damage from “a few dB”?

There is a plethora of established “dB” references, to include dBm, dBV, dBu, dBA, dB SPL, and dB HL (the latter, “Hearing Level”, is used in hearing assessments). Regardless of the suffix, all dB measurements are based on a ratio. The difference is generally the metric for the 0-dB reference: dBm is 1mW with a 600-ohm load (power), dBV is 1Vrms, and dB SPL in air is 20 μPa (micro pascal). For sake of discussion, we could make weight (in grams, ounces, pounds) a reference; after all, pressure is force (e.g., weight on Earth) per unit area. The area is fixed; e.g. inch^2 for psi, or pounds per square inch. The same applies to SPL, noting SPL is not a static pressure, but a pressure that varies with time (yielding frequency or perceived pitch). From this, we could easily calculate the applied force on an eardrum as a function of SPL. So now let’s look at what “a few dB” means as decibels increase.

Assume our 0 dB reference is 1 pound (easy to perceptualize if you lift weights). This makes “20 dB re 1 lb.” equivalent to 10 pounds. Increasing by 3 dB gives us 23 dB, which is 14 pounds, an uneventful 4-pound increase from 10 pounds. This doesn’t sound daunting when it comes to weights. Now let’s say you’re doing barbell curls with 100 pounds, and this is near your maximum weight (for curls). Adding an additional 20 pounds makes the weight too heavy to curl for a single repetition. However, this is only a 1.58 dB increase in weight (or force over an area, such as your hands). A 6.02 dB increase in weight means going from 100 to 200 lbs. Now you’re going from a 100 lb. weight you can curl to a 200 lb. weight you can’t easily lift off the rack (but still a warmup weight for my friends Daniel Harris and Andy Davies). Instead of a 4-pound difference in force on your hands (10 to 20 lbs.), you’re increasing it by 100 lbs. (noting linear versus logarithmic). Insofar as force on the eardrum goes, what does all of this mean?

Let’s use psi the analogy, and assume the area of the eardrum = 0.8 cm^2 = 0.124 square inches (based on the tympanic membrane being 1cm in diameter). The force on the eardrum using our “0 dB re 1 lb.”, then, would be 0.124 lbs. at 0 dB. When we go to 20 dB, this is 1.24 pounds on the eardrum (from 10 lbs. and 0.124 square inches). Increasing by 3 dB equates to 1.75 lbs., a 0.51-pound jump in linear units. Let’s move up to 80 dB, a 10,000X increase in weight (and pressure): Now we have 1240 lbs. on the eardrum. Increasing this by “a few dB” means 1750 lbs., a 510 lb. increase. So, first we have a 0.51 lb. increase (going from 10 to 13 dB lbs), and now we see a 510 lb. jump (going from 80 to 83 dB lbs), noting that both "jumps" are 3 dB increases.

Firearm blasts can easily exceed 160 dB PPL at the shooter’s ear (approaching an actual 1 psi!). In our analogy, what would this mean in linear pounds? 160 dB would be 12,400,000 lbs. on the eardrum (major ouch!), and 163 dB means adding an additional 510,000 lbs. to our load for total of 17,500,000 lbs. Ok, these numbers seem ridiculous, but the analogy is sound. For the same dB scale, we see a 0.51 lb. increase, then a 510 lb. increase, and finally a monstrous 510,000 lb. increase (latter is the increase going from 160 dB lbs to 163 dB lbs); all being 3 dB increases. From a mechanical perspective, we might not be concerned with the sheer force or tensile strength of a material at 0.510, or even 510 lbs., but the 510,000 lbs. ought to be a major concern. Similarly, think of the eardrum: At some point you’ll encounter rupture (“it’s just a few dB”). Even worse, you could exceed the elasticity of the basilar membrane (inner ear), and the deleterious consequence would be acute acoustic trauma resulting in a permanent, profound hearing loss! By the way, one pascal is 0.000145038 psi; similarly, one psi is 6895 Pa, or 170.75 dB SPL re 20 μPa. A few dB my derriere!

That was fun, but let’s move to a whole other topic: Electronics measurements and a mysterious “few dB” difference between mathematical (or Spice models) as well as variations in data when using different makes of precision test equipment.

Converted to volts, a few dB is easily the difference between Pass/Fail on an assembly line. In hearing (at normal levels) and for augmentative reality (AR) devices, we’d have gross lateralization or spatialization errors resulting from as little as 1 dB error. Same goes for phase shift: A few degrees matter, whether an AR or active noise cancellation (ANC) device. So, as you develop your next-generation product, you probably expect accurate test results. You buy the fancy stuff: Audio Precision, Brüel & Kj?r (HBK), GRAS, NI, Keysight, Rohde & Schwarz, etc. You believe the numbers. You use Spice models, again, expecting numbers to align with actual measurements. But what if the measured results are off by a few dB? This, of course, is unacceptable. Where did these errors come from? Component variations (e.g. resistor or capacitor tolerances), faulty test equipment, defective circuitry, bad technique, or a misspent youth?

In a recent example (below), taking the input impedance of the measurement devices into account didn’t compensate for the errors (e.g., 100kohm for my Audio Precision ATS-2 and 200kohm for the NI USB-4431). Additionally, I added low-noise preamps with 100Mohm input impedances to the mix, but continued to have mixed (and aberrant) results. The circuit I’ll describe is ultra-simple, but the problem applies to your most sophisticated electronics. First, let’s take a peek at the phase lag circuit, shown below. For the sake of simplicity, I solved for a single frequency. The frequency, 3183.1 Hz may appear odd, but it’s simply 2*pi*f = 20k rad/sec, making the reactance of the 0.1 μF cap (C1) = 500 ohms. Remember that V across C1 lags V across R1 by 90 deg, but this isn’t our measured phase shift when comparing Vout to Vin (the latter phase shift is frequency-dependent).

It’s easy to understand that putting any resistance across C1 will make a whole mess of things (unity gain buffers are often used if we want to look at the voltage across C1), but this isn’t the problem. Let’s continue our circuit with the following, which shouldn’t make the circuit particularly sensitive to resistive loading:

Because we’ve added R2 to the circuit, we can easily model the effects of loading (again, 200kohm for my NI USB-4431, etc.). And again, we compare the measured results to our model. Holy cow! Those results are way off the mark! About the only agreement among curves was the phase response as measured by the AP ATS-2 and NI USB-4431, but neither agree with the modeled response. All components were carefully measured using an LCR meter with 4-arm test leads. Bad model? (Answer to this is “Nope”, but my math should always be checked.) Looking at slopes, I imagine many of you recognize the culprit.

Below is a more “complete” circuit, but this merely allows me to include more components. Of course, you can do this with Spice software, but that doesn’t give you the same insight (nor does it resolve the problem we’re seeing).

The next photo is a major hint, and directly related to what you probably suspected:

I teach electronics at a local college, and stress the importance of probe compensation. Without a properly compensated probe (generally 10X probes), high frequency measurements should be scrutinized. In general, this is less of a concern with low-impedance sources and loads, to include many audio devices (e.g., loudspeakers, power amplifier, line drivers with low internal impedances). But for higher impedance devices, measured voltages at high frequencies (e.g., 10kHz) could be in error. The ubiquitous 10X oscilloscope probes are designed for a 1Mohm input impedance (standard for o’scopes). For 50- or 75-ohm o’scope input impedances (which would load any high-z circuit), a 10X probe isn’t used. So, as a question, how many of you use compensated or active probes with your Audio Precision (for example) test equipment? As mentioned above, 10X probes are designed for a 1Mohm input z, and my AP ATS-2 has input z = 100kohm. Furthermore, would adding such a probe curtail the problem I’m describing?

Because my modified “vintage” ultra-low noise preamps have a high input z (100Mohm in parallel with 15 pF), it’s easy to “convert” them to have 1Mohm at the input. You can see the addition of 1Mohm resistors in the photo below:

Additionally, the 10X probe’s 20 dB loss is easily made up with the preamp gain, and can be further trimmed to produce 0 dB loss using a 10X probe. The output impedance of the preamps is low enough not to be affected by test lead or cable capacitance, which is our culprit when using uncompensated probes or test leads. (Side: The photo below shows my LCR meter for accurately obtaining C1’s value. To the right is the NI USB-4431 and AP ATS-2. Note the oscilloscope probes: They’re being compared against one another to ensure accurate channel balance.)

Finally, let’s look at measured results when using the capacitance-compensated system (noting it presents a 10Mohm resistance across the DUT). Looking at the image below, we see that the measured results align almost perfectly with either model (my “Extended Model” and “Thevenin Model”). The roll-off is exactly what it should be.

Ok, perhaps this seems like a lot of work for just “a few dB”, but you had better be on the mark for your AR/VR/HRTF and ANC to work well. And if you do legal work (e.g., expert witnessing and consulting services), you better be able to stand trial with your equipment and measurements. The next photo shows the frequency response of a simple divider circuit that should have a perfectly flat response and 0 deg phase shift. Also, note the photo to the right: I have presented data and auditory demos as testimony during trials. You have to show how your numbers were obtained, but keep it simple for the non-technical jurors (demos work well).

The graph above shows some discrepancy in phase (but not attenuation) when using my test setup. This was for a simple, resistive voltage divider (noting high resistances). What would this look like had I bypassed the probes? As you can see below, big measurement errors resulted despite top-notch test equipment and a simple circuit. The gray (flat) line was the measurement made with compensated probes.

I suppose you know my feelings on “a few dB” by now. It’s reasonable to say a fraction of a dB has little bearing on acoustical measurements (temperature variations alone result in measurable differences). But when it comes to a few dB, I start asking questions as to “why?”. For hearing assessments that go up/down in 5 dB steps (and also depend on the tester and listener’s attentiveness), I suppose a few dB doesn’t matter. But for electronics and noise abatement, I’ll challenge anyone who proposes that a few decibels don’t matter. I also encourage everyone to double-check measurements against models; not only does test equipment affect results, so can circuitry that’s upstream of the components being evaluated. Cheers! ELC