Match making for headphone lovers pt.2

How To

Match making for headphone lovers pt.2

Richard Barclay continues his explorations in the deep waters of headphone tech with an investigation into what really counts in a headphone amplifier.

As a headphone is essentially a miniature loudspeaker, it shouldn’t be surprising that the interactions between headphones and headphone amplifiers are very similar to those between loudspeakers and power amplifiers. Many of us have hopefully developed a pretty good knack for selecting appropriate amplification for our loudspeakers and vice versa, but how confident are we in our abilities to do this for our headphones?  

There are many design variables that affect the performance and perceived synergy of such pairings – not to mention individual taste – so we cannot simply reduce things to a few quantifiable specifications. There are however three attributes that play an important role in the matchmaking process and are often responsible for explaining some of the sonic differences heard between various headphone and amplifier combinations. I discuss each of these in turn in a trio of articles on output power, gain and output impedance. 

Gain
The previous article discussed how output power contributes to the ability of a headphone amplifier to drive a particular headphone, but gain is another very important consideration. Gain is the amplifier’s voltage multiplier, the fixed ratio by which the amp increases an input voltage. Put simply, gain determines how soon your headphones get loud as you turn up the volume, and thus how soon the amplifier’s maximum output power is reached. 

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It is important to note that gain is notan intrinsic indicator of an amplifier’s output power capability. If an amplifier doesn’t have enough gain, our headphones may not get loud enough because, even if the amplifier has enough output power capability, cranking the volume control to max will not achieve the amplifier’s maximum rated output if the input signal is too weak. Conversely, if an amplifier has too much gain, we will be restricted to using only a small portion of the volume range, above which the output will become uncomfortably loud and clip before the volume control reaches its max position. This not only makes it more difficult for the listener to dial in volume adjustments, it can also decrease sonic fidelity in some setups (I’ll expand on this later).

Amplifiers usually have an optimal performance envelope that varies with the design, and the design therefore often influences the amount of gain employed. Higher output voltage amplifiers tend to use higher gain structures because it is necessary to swing the output voltage rails. (You may also see high gains being used in low output amplifiers, this is sometimes a tactic used to give the impression that an amplifier is more powerful than it actually is). There are however two important external factors that must also be taken into consideration when settling upon an appropriate gain ratio, the strength of input signaland the voltage sensitivity of the headphonesto be partnered with the amp. 

Input levels
0dBFS represents the maximum level of a digital audio recording. Source inputs can vary significantly in their maximum output voltage, from as low as 0.5Vrms with some battery-powered mobile devices to 2Vrms normally for a mains-powered line level source. If you include balanced sources, output voltages typically jump to 4Vrms and some are even higher than this; you may encounter 6Vrms or even 8Vrms. The level at which a recording is mastered determines if these output voltages are achieved in practice. A digital recording that has been mastered with levels peaking at 0dBFS will swing 100% of the player’s maximum output voltage, but one that’s mastered quieter with peaks at -6dBFS will swing just half of the player’s maximum output voltage. The chosen gain therefore ought to be compatible with the potentially significant variations in input voltage the amplifier will be presented with. It is important to have high enoughgain to be able to drive the amplifier to its maximum power output capability with plausibly low output sources and recordings.

Digital audio recording with peaks of -0dBFs

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Digital audio recording with peaks of -6dBFs

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However, the gain should also be low enoughto suppress the amplifier’s noise floor to a level that is inaudible (or as close to inaudible as possible) through the headphones partnered with the amp, and to allow a decent portion of the volume control to be used to make volume adjustments easier and (where applicable) minimise fidelity losses. This is dependent on the headphone’s voltage sensitivity. The higher a headphone’s voltage sensitivity, the more easily the amplifier’s noise floor will be heard, and the more restricted the range of volume adjustment will be, thus the lower the amount of gain required.

Due to the above considerations, gain is – or at least ought to be – a cause of great deliberation for headphone amp designers. Not so much historically when there was less variation in source output voltages and headphone sensitivity but certainly in recent years, with the increasing diversity of digital audio devices and proliferation of high-efficiency, low-impedance headphones, where voltage output differences of as much as 24dB among sources and 30dB among headphones are not implausible in extreme cases.

Calculating gain
Gain is most often represented as a decibel ratio or voltage ratio, and one can be derived from the other using an online calculator or the following formulae:

 
   

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The following table lists some of the gain factors likely to be found in headphone amplifiers and shows the corresponding dB equivalent (rounded to the nearest half dB):

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A gain factor of 1x or 0dB is known as unity gain because the output voltage equals the input voltage, i.e. the amp passes the input signal to the output without changing it. Gain factors of less than 1x indicate that the output voltage is less than the input voltage, i.e. the global gain stage effectively becomes a global attenuation stage, but these are rarely used in practice. It’s more likely you’ll see a local attenuation stage being used on a specific input that’s expected to receive a voltage stronger than the other inputs. An amp that provides inputs for line level and balanced sources, for example, may provide an attenuation switch for the balanced input as a means of levelling the inputs.

 

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Until fairly recently, headphone amplifiers typically had one ‘catch-all’ gain setting that was fixed and couldn’t be changed. Many still do, including the Arcam rHead that I referenced in the previous article. The rHead’s gain is 7x (+17dB), which delivers its maximum output voltage (approximately 6.5Vrms) with an input of just over 0.9Vrms. Manufacturers are however increasingly acknowledging the benefits of providing a choice of gains that can be selected by the listener to best suit their connected ancillaries. Increasing compatibility broadens appeal, a win/win for manufacturers and consumers. Examples of headphone amps with more than one gain setting include: Audeze’s Deckard (0dB, +10dB or +20dB); Audio-Technica’s flagship AT-HA5050H (+2dB or +14dB); all Schiit Audio offerings (ratios vary with model, e.g. Mjolnir: 0dB or +18dB, Jotunheim: +6dB or +14dB).

If we know how much output voltage a headphone needs to reach a certain SPL and the output voltage of our source, it is possible to estimate the minimum gain required for that headphone. It is advisable to allow some gain headroom to accommodate a ‘worst case scenario’, that is an amount of gain in excess of what should be required in typical conditions. The amount that should be added depends on the reason for wanting headroom. If it’s just to account for quietly-mastered recordings, a few dB extra should suffice. If however it’s also to improve compatibility with sources that have weaker output voltages and/or allow the use of headphones with lower sensitivities, the extra gain must compensate for how many dB weaker the other source input is and/or how many dB less sensitive the other headphone is.

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Two into one
Let’s imagine we are buying a headphone amplifier for the Focal Utopia, an audiophile headphone with high sensitivity of 115dB/1V. We will use two input sources with the amp, a mains-powered CD player and portable audio player with output voltages of 2Vrms and 1Vrms, respectively. We are also thinking about purchasing the Sennheiser HD800S, an audiophile headphone with moderate 102dB/1V sensitivity, in the near future and wish to use the same amplifier. We want enough gain for peak SPLs of 110dB (we’ll assume that the amplifier has enough output power to achieve these SPLs before clipping). A significant portion of our music library contains recordings that peak at only -6dBFS. We therefore desire a gain that will swing enough output voltage for peak SPLs of 110dB through either headphone with an input voltage as low as 0.5Vrms.

 
   

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Thus in order to satisfy all of the above requirements, we must look for a headphone amplifier with gain of 5x (+14dB), which is 13dB more than what would be needed if we were only going to be partnering the amp with Utopia. 

Controlling volume
Let’s now demonstrate how the above levels of gain affect the user experience with the two headphones mentioned. It is beyond this article’s scope to cover all types of volume control so we’ll focus on the two most commonly used analogue devices, potentiometers and stepped attenuators; the former provides continuous adjustment of output voltage and the latter adjusts the output in discrete increments or ‘steps’. Stepped attenuators tend to offer superior sonic transparency and channel matching, potentiometers can suffer from tracking errors (channel imbalances) which often widen towards maximum attenuation i.e. minimum output. Pots on the other hand allow the user to reduce the output seamlessly in theory all the way to zero, stepped attenuators present audible jumps in output level and abruptly cut off the output below their minimum setting, making it more difficult to finely tune to the desired output level.

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Stepped attenuator
The effect of gain on a stepped attenuator is easy to visualise. Turned fully clockwise an attenuator provides no (0dB) attenuation (full voltage output), and each counter-clockwise step reduces the output by thedB increment the attenuator is specified with. Attenuators can be specified with particular increments and are ultimately limited by the finite number of steps that can be accommodated. Designers must weigh the provision of increments small enough for fine volume adjustment against increments large enough when cumulated to allow the output to be reduced to a sufficiently quiet level. 

Increments of 2dB on a 24-step attenuator, for example, permit a -46dB total reduction before the output is silenced, while 3dB increments allow the level to be attenuated by a total of -69dB. To provide both sufficient attenuation and a fine degree of adjustment, it is not uncommon for stepped attenuators to be specified with a combination of increments of, for example, 1dB gradually widening to 6dB as the attenuator is turned counter-clockwise.

We ideally want to be able to access as much of the stepped attenuator’s rotational range as possible, especially if the steps are steeper at the bottom, as this will give us more control over the output level. However, the excess gain to accommodate variations in input voltages and headphone sensitivities will inevitably restrict us to a fraction of this. The following tables show the SPLs produced by each headphone with 0.5Vrms, 1Vrms and 2Vrms input voltages and +1dB and +14dB gains, using stepped attenuators with 2dB and 3dB increments providing -46dB and -69dB attenuation at their lowest positions, respectively.

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With +1dB gain applied to Utopia and +14dB gain applied to HD800S, the tables show that our desired absolute maximum SPL of 110dB is achieved with the attenuators set between -0dB (for 0.5Vrms input) and -12dB (for 2Vrms input). Maximum SPLs of between 41dB (for 0.5Vrms input) and 53dB (for 2Vrms input) are obtained with the -69dB attenuator set to its lowest position, while maximum SPLs of between 64dB (for 0.5Vrms input) and 76dB (for 2Vrms input) are attained with the -46dB attenuator set to its lowest position.

Applying HD800S’s suggested gain of +14dB to Utopia effectively increases Utopia’s SPLs at any step on the attenuators by 13dB. Our desired absolute maximum SPL of 110dB is now achieved with the stepped attenuators set between -13dB and -25dB.  Maximum SPLs of between 54dB and 66dB are now obtained with the -69dB attenuator set to its lowest position, and maximum SPLs of between 77dB and 89dB are now attained with the -46dB attenuator set to its lowest position. This not only renders a substantial upper portion of the attenuators’ rotational range unusable, it also significantly raises the lowest volume threshold at which Utopia can be listened.

 
   

 

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Potentiometer
Potentiometers are trickier to model since they have an attenuation taper that approximates a logarithmic curve for the most part followed by a linear walk-off to zero. Pots are manufactured with different resistance ratios to provide different levels of attenuation at the midway (12 o'clock) position to suit different applications. 10% and 15% are common ratios for audio amplifiers. The following formulae can be used to approximatethe proportion of voltage output and thus attenuation in dB that a given rotation of the pot will provide:

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Again, we ideally want to be able to access as much of the pot’s rotational range as possible, as this will provide more control over output level and minimise the audibility of tracking errors but, as with the stepped attenuators, the excess gain to accommodate variations in input voltages and headphone sensitivities will restrict us to a fraction of this. We should generally aim to have our headphones provide the desired listening levels with the volume pot set beyondthe first quarter-turn, as this will improve adjustment controllability and will in many cases improve sonic fidelity. (Potentiometer tracks typically have 270-degrees of rotation, so a quarter-turn visually equates to 10 o’clock). 

A pot that outputs 10% of the voltage input at mid-rotation should output 2.5% at a quarter-rotation clockwise and therefore provides -20dB and -32dB attenuation at these respective positions. A pot that outputs 15% of the voltage input at mid-rotation is expected to output  4.4% at a quarter-rotation clockwise and therefore provides -16.5dB and -27dB attenuation at these positions.

The following tables show the SPLs obtained through each headphone with the volume pot set a full-turn clockwise (-0dB), a half-turn clockwise and a quarter-turn clockwise with 0.5Vrms, 1Vrms and 2Vrms input voltages and +1dB and +14dB gains, using volume pots with 10% and 15% resistance ratios.

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With +1dB gain applied to Utopia and +14dB gain applied to HD800S, the tables show that our desired absolute maximum SPL of 110dB is achieved with the potentiometers set between fully clockwise (-0dB) for 0.5Vrms input and just under two thirds of a turn clockwise (between the 1 o’clock and 2 o’clock positions) for 2Vrms input. Maximum SPLs of between 78dB for 0.5Vrms input and 95dB for 2Vrms input are obtained with the potentiometers set to a quarter-turn clockwise. 

Applying HD800S’s suggested gain of +14dB to Utopia effectively increases Utopia’s SPLs at any pot rotation by 13dB. Our desired absolute maximum SPL of 110dB is now achieved or even exceeded with the potentiometers set to a half-turn clockwise, rendering the remaining half-turn unusable. The potentiometers must also now be set much lowerthan a quarter-turn clockwise to attain the same previous SPLs of 78dB to 95dB, significantly restricting controllability and possibly resulting in an audible loss of fidelity.

Compromised performance 
Gain optimised for Utopia is unable to deliver the maximum desired SPL of 110dB with HD800S while, for amplifiers that use a traditional stepped attenuator or potentiometer to control volume, gain optimised for HD800S is likely to result in a sub-optimal listening experience with Utopia. The further apart two headphones are in sensitivity, and the further apart the minimum and maximum source input voltages are, the more detrimental the compromise will be. Thus the more likely a better outcome will be obtained by either: purchasing two headphone amps with fixed gains suited to each headphone’s respective sensitivity or; a single headphone amp that provides more than one gain setting. 

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Pragmatic solutions
It is often useful to have a headphone amp with gain of or near 1x (0dB) as this ensures compatibility with earspeakers at the most sensitive end of the spectrum including IEMs, and another headphone amp with gain between 3x (+9dB) and 6x (+15dB) as this provides good usability with high impedance headphones of low-to-moderate sensitivity. Very high gain ratios tend only to be required for the few headphones on the market that have unusually low sensitivities. I personally prefer headphone amps that provide the flexibility of multiple gains, that way you can optimise on the fly. By raising the gain for weaker sources and/or less sensitive headphones and lowering it for stronger sources and/or more sensitive headphones, you not only maximise the usable range of the volume control but also potentially lower the noise floor whenever high gain isn’t needed.

Amplifiers with low gain structures often measure superior to their high gain counterparts. Low gain is typically achieved with negative feedback, and this tends to result in a lower noise floor, lower THD and lower output impedance than high gain structures, which operate with less or no negative feedback. As was explained earlier however, amplifiers may have an optimal performance envelope that favours a particular amount of gain, so it is too simplisticto unconditionally advocate selection of the lowest gain that achieves the maximum desired SPL (particularly as some consider negative feedback to the work of the devil - Ed.). 

There are also headphone amps that control volume in a way that mitigates some of the previously discussed disadvantages of having a gain that is higher than that required for your headphone. Arcam’s rHead, for example, uses a resistor-ladder volume control to provide an impressive -80dB attenuation in fine 1dB increments and has near-perfect channel matching throughout its entire operating range.

Listener preferences should also be taken into consideration, each of us may have different priorities and a different set of compromises we are willing to accept. For example, even though I can usually achieve loud enough SPLs through Sennheiser’s HD600 and HD800S with my headphone amplifier set to unity (0dB) gain, I personally prefer the presentation via the amp’s high (+14dB) gain setting. To my ears, these two ‘phones sound more alive and immersive this way and, in exchange, I am happy to sacrifice some of my potentiometer’s turning range. There are however Sennheiser users who prefer the ‘blacker background’ from low gain; subjectivity is what makes this hobby so fascinating! Provided the gain levels are workable with your ancillaries, I’d choose whichever gain sounds best to you with your particular headphone.