# Katz's Corner

## Katz's Corner Episode 20: How Insensitive!

This story originally appeared at InnerFidelity.com

How Insensitive! Part 1 of a Series

The Four Questions

1. Is my new headphone as sensitive as my previous headphone—what level will it deliver in comparison?
2. Can my amplifier drive this headphone to an adequate level without introducing audible distortion?
3. Will I hear amplifier noise through my new headphone?
4. Does my amplifier have enough gain to drive an insensitive headphone?

These are basic questions, but headphone and amplifier manufacturers aren't doing much to help people answer them! Not without trying to turn us consumers into engineers. Sure, they publish specs. There's a standard that's supposed to help us, IEC standard 60268-7, which specifies how to report a headphone's SPL* under laboratory conditions. This is known as the headphone's sensitivity. For example, "97 dB/mW" means that the headphone will produce 97 dB SPL when it draws 1 mW of power. Sennheiser, on the other hand, has chosen to display the SPL the headphone will produce when fed 1 Volt at 1 kHz. It is possible to convert between the voltage and the power spec using the headphone's impedance and Ohms law.

Sennheiser's approach allows us to answer question 1, but only for Sennheiser headphones. So if you want to compare Sennheisers with AKGs, you'll have to dig out your calculator. Is it too much for us to ask for a spec that will allow consumers to easily answer all four questions, without having to become an engineer? Seriously, both milliwatts and volts are pretty lame because by themselves they do not let us answer all four questions. The idea of using headphone power consumption (in milliwatts) is silly anyway, how did that get started? A manufacturer has to calculate the power draw only to satisfy the requirements of IEC 60268-7. Using power to specify sensitivity is totally indirect because we have to convert to volts anyway. It's like trying to specify a car's gas mileage as "miles per cubic foot of gas tank volume". Yeah, if you also know the volume of the gas tank, and can calculate the math, you might be able to convert that to miles per gallon. But why not specify performance in a human way that we can use? The IEC spec can only answer question #1, and only if the headphones have the same impedance. But headphone impedances vary all over the map, so that makes the IEC approach pretty lame. The Sennheiser approach is just a bit more useful.

The impedance determines the power drawn, but the voltage determines the SPL!

These specifications confuse consumers, who would be forced to use logarithms and equations to answer the basic questions. We need to make headphone sensitivity and amplifier level specs more user-friendly, useable, interchangeable and effective. So I think it's high time to ditch both sensitivity approaches, and we can do better than both Sennheiser and the IEC if we start thinking outside the box!

A dB is a dB is a dB!
It is totally possible to specify headphone sensitivity and amplifier output so that consumers can easily answer all four critical questions just by reading a spec sheet and sometimes doing simple addition or subtraction. Let's compare some headphone models which have wildly different sensitivity and impedance. Look at the yellow section of Fig. 1, which displays the manufacturer's specifications. Since Sennheiser defines the HD 650 sensitivity at 1 volt, I converted that to watts just to fill a hole in the chart.

Our goal is to evaluate amplifiers and headphones together, so we have to marry them with the same units of measurement. Later we will have to convert amplifier specs from watts to volts. Since manufacturers have not standardized on a single SPL, I converted all the headphone specs to the voltage necessary to produce a common SPL, 97 dB (column 6).

I recommend that an amplifier should be able to deliver at least 110 dB SPL at or just below clipping (nominally 1% THD). Of course that would be 110 dB on momentary peaks, not sustained level, as we do not want to go deaf! I would not advise doing continuous sine wave testing at 110 dB SPL, it could damage some headphones. Notice that only 0.020 watts (20 mW) is necessary to drive an LCD-4 to 110 dB (column 8). We can see that power is the red herring: there no relationship between the wattage and the SPL of headphones with different impedances. Instead, direct your attention to column 6, "Volts @ 110 dB SPL." We can scan the column and observe which headphones require the most and the least voltage to deliver the same SPL. For example, the LCD-4 requires 2 volts to deliver 110 dB. But the one which requires the most voltage (the most insensitive phone) is the Sennheiser HD650, which requires 2.2 volts to deliver 110 dB.

Using voltage and a common SPL is a step forward, but not enough. Voltage is a linear measurement, as opposed to logarithmic decibels. Decibels make our life far more easy. Take a look at the green area of the chart. In the penultimate column I convert voltage to dBu** for 110 dB SPL. We can read dBu directly on any standard audio voltmeter. dBu is so much more useful than volts, because there is a simple relationship between dBu and dB SPL. If we raise the dBu level at the headphone or at the amplifier's input by 1 dB, the headphone SPL will also rise by 1 dB. We can directly (and meaningfully) compare the sensitivities of any headphones when they are expressed in dBu. For example, we see that the LCD-4 requires +8.2 dBu to drive it to 110 dB, and the HD650 requires +9.2 dBu. So the HD650 is 1 dB less sensitive than the LCD-4. The HD650 and the LCD-4 are poor matches for cheap headphone amplifiers, which often overload as they cannot deliver the required level.

(Editor's Note: It's important to note that Bob's article is based on published specs and not measurements taken on the same system. My measurements show the LCD-4 as being less sensitive than the HD 650. In my opinion, this discrepancy is yet more evidence that the IEC spec needs a tune-up along the lines Bob is drawing. Even though his numbers may not reflect reality, his logic is sound and his point is on target.)

Without using dBu, these facts would not be obvious from the manufacturer's published specs without rolling out your logarithms. Our chart does this for you. Manufacturers may not have anything to hide, but by using ineffective units, they are hiding the obvious facts from us. For example, in the last column, by using the LCD-4 as the reference, we can immediately see that the Oppo PM-3 is a whopping 14 dB more sensitive than the LCD-4 and the new Audeze LCD-MX4 is 18 dB more sensitive! 18 dB is the difference between a shout and a whisper. This clearly reveals an imminent danger: If you plug an LCD-MX4 into your headphone amplifier after listening to the LCD-4 without changing your volume control, you will damage your ears! It will be 18 dB higher! With any headphone amplifier, turn down the headphone volume when switching headphones.

In summary, we need to know that an amplifier can deliver a particular voltage into the load of the headphone, and we need to express that voltage in dBu. If manufacturers and reviewers specify headphone sensitivity and amplifier capability in dB SPL and dBu, then we can directly compare amplifier and headphone performance by simple addition or subtraction. So I urge every manufacturer to provide dBu specifications. This should not be hard. Then eventually I hope that the IEC will revise its standards to use dBu for the reasons I describe here.

For example, let's say that Audeze and Pass employ or include dBu in each of their specs:

Audeze LCD-4 Sensitivity: 97 dB SPL at -4.8 dBu

Pass HPA-1: Maximum output: 22.2 dBu

Let's look at the Amplifier and DAC chart.

Fig. 2. Amplifiers, DACs and Headphone SPL (work in Progress)

For the Pass HPA-1 I used John Atkinson's measurements from his Stereophile Magazine review. Let's see if this headphone amplifier can drive the most insensitive headphone to a satisfactory listening level. In other words, does it have adequate voltage gain? I feel that -12 dBu (0.2 v) is a reasonable "typical" unbalanced analog output level of a DAC at -20 dBFS. I recommend that an amplifier must have enough gain to drive an insensitive headphone to at least 85 dB SPL with -12 dBu input. I recommend that a DAC with built-in headphone amplifier be able to drive an insensitive headphone to at least 85 dB SPL at -20 dBFS. This ensures that the quietest, most dynamic music (such as a well-recorded classical symphony) can be reproduced adequately loud.

For example, as seen in green on the above chart, the Pass HPA-1 can deliver 97 dB SPL from the Sennheiser HD650 with a -12 dBu input, with volume control at maximum. So it has about 12 dB more gain than my minimum recommendation, which is probably a good thing since it accommodates occasional lower level sources, and situations where a listener needs to bring up soft passages while editing or recording. The extra gain also helps accommodate EQ plugins which may include some digital attenuation.

The Prism Callia's headphone jack, shown in the green section of the chart, can produce 99 dB SPL at -20 dBFS from an HD650 at maximum headphone volume. That's about 14 dB more output than my minimum recommendation. So both amplifiers can produce more than adequate level with the most insensitive headphones using any reasonable musical source.

The Callia DAC has a DIP switch in the back that sets the headphone amp gain. The manual attempts to simplify the process by describing the switch settings in terms of headphone impedance, low, medium, and high. But this misleads, since this is just a gain setting: Its "high impedance" (actually "high gain") setting is specified as +18 dBu at 0 dBFS. I then subtracted 20 dB to arrive at the level the Callia would produce at -20 dBFS (column 4). The output impedance of the Prism remains at a constant 4 ohms. The user may leave the switch in the so-called high impedance setting, even when using low impedance headphones, just adjust the headphone volume control accordingly. Change the dip switch only if the adjustment range of the volume control becomes crowded or you hear amplifier hiss when the headphone volume is turned all the way down.

Another useful paradigm is to express an amplifier's noise floor in dB SPL, shown in yellow in Fig. 2. I calculated the SPL of the amplifier's noise with a very sensitive and a very insensitive headphone. You can see that the Pass would produce only 18 dB SPL (wide band) with the LCD-4 and 32 dB with the Oppo PM-3. Both noise floors are probably inaudible except in an extremely quiet room. Especially, 18 dB SPL (measured wideband) would be insignificant. When I get a Pass for review I'll listen to its noise with the sensitive Oppo cans and verify if it is truly inaudible. These values were easy to calculate with simple subtraction: For example: +8.2 dBu is required to drive the LCD-4 to 110 dB SPL. The amp's THD+Noise floor is -83.8 dBu. Thus, 110 - 8.2 - 83.8 = 18 dB SPL. See how easy decibels are to work with!

Distortion Measurement in Decibels
Just like linear volts, linear % distortion really doesn't tell us the magnitude. That's why it's helpful to express THD and noise specs in decibels, even better in dB SPL of each partial for a particular headphone. We can estimate whether a hum component will be audible or the audible importance of harmonics. A further refinement would be to weight the spectral graph according to the equal loudness curves, which I may attempt to do sometime in the future. Even more powerful would be to calculate psychoacoustic masking of fundamentals, harmonics, and noise. But masking calculations are beyond my current knowledge. Worldwide, I think there are only a handful of psychoacousticians capable of intelligently quantifying masking perception.

The Final Proof is in the Listening
In part 2 of this series, I'll refine these spreadsheets and present more amplifier measurements. We're also going to verify these recommendations by critical listening. I'm a self-confessed headroom junkie: personally I've found that, in general, the more powerful amplifiers sound best, even if we never play them loud. To my ears they seem to have more impact, perhaps because they are not compressing musical peaks. Is a half watt amp enough? If so, then why does Audeze recommend between 2 and 4 watts to drive the LCD-4, even though the charts show that only 20 mW will drive the cans to 110 dB SPL? I intend to find out the reasons for this discrepancy, and present recommendations that we can quantify and help you make educated choices.

Here's a photo of "Amplifier Jungle" chez Katz. I hope to have two more representative contenders on loan for review so we can compare amps from the smallest to the biggest, with the least and most sensitive headphones. Stay tuned!

Fig. 3. Amplifier Jungle. From left to right, top to bottom. JDS Labs O2, Audeze Deckard, Mjolnir KGSS Carbon HV, AMB M3 (Katz custom build), Prism Callia DAC/Amp, Mjolnir Pure Bipolar

Footnote: The Meaning of Sensitivity
Keep in mind that headphone sensitivity is an approximation. It's usually measured using a sine wave tone. 500 or 1 kHz. Of course sensitivity will vary according to the headphone's response at other frequencies unless the headphone is perfectly flat (and none of them are). But 1 kHz is a useful place to compare one headphone's sensitivity with another's. Impedance is also a nominal value: Planar-magnetic headphones usually exhibit a very even impedance across the spectrum, so if the manufacturer says "200 ohms", it's likely to be maintained across the audible range. But moving coil headphones' impedance varies across the spectrum, often significantly.

As long as an amplifier has a reasonably low output impedance, headphone impedance variations should not cause a problem. Many say 1 ohm is acceptable. Headphone amplifiers built into gear like receivers and integrated amplifiers often employ buildout resistors, as much as 80 Ohms or more in some cases. This is an outdated philosophy, it ruins damping factor and makes insensitive headphones harder to drive. Even when the headphone is direct coupled to the output stage, manufacturer's philosophies differ. Some advocate having super low output impedance, which requires large amounts of negative feedback, but I feel that extreme negative feedback can lower the total distortion so much that auditory unmasking begins to take place: bad harmonics might become audible when they are no longer masked by the good ones.

Both Mjolnir and Pass's philosophy for their discrete amplifiers is that the amp should perform with reasonable distortion (say, under 0.1 % THD at normal listening levels, assuming the major harmonic contributions are 2nd and possibly 3rd). Both manufacturers point out that super low distortion (say, 0.003%) can produce harsh or bright sounding results because of masking and unmasking. I personally prefer an amplifier which sounds just a little on the warm side versus one that's subjectively cold, dry, bright, or harsh. As long as the amp doesn't sound too warm or artificially "tubey". Loose, unregulated power supplies can make an amplifier sound "flubby" and thick, like some tube amp designs of the early 50s. We have a lot to learn, and in this series I will try to sonically compare the sound of amplifiers which have vanishingly low distortion and high negative feedback versus those with more reasonable distortion.

* SPL, Sound Pressure Level is not loudness! It is a measurable physical quantity, but loudness is a perceived quantity. SPL is related to loudness, as a higher SPL is usually perceived as louder. But to quantify the human perception of loudness requires knowledge of frequency content (among many other things). Here's a chart of SPLs of typical sound sources.

** dBu stands for "dB unterminated." dBu is voltage expressed in dB with a reference of 0.7746 volts, usually rounded to 0.775. I believe the term was coined by Neve Corporation when matched impedances began going out of style. Most audio-rated voltmeters can read dBu directly. The scale may read "dBm reference 600 ohms", but it's actually reading voltage in dB with a 0.775 volt reference. dBm is a measurement of power that once was very relevant but not for many years.

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