This was exactly the info I was looking for, thanks so much for taking the time. Just one more ? if I may. Aside from the obvious volume increase, do you think I would get better sound doing this? I would hope that I could get a fuller sound with perhaps better bass, clarity and soundstage at the same listening level just by having an amp with more headroom. Thanks again
The short answer is no, not by virtue of more headroom alone. Not as long as each amplifier is operating within its linear range of operation, and the peak power output levels of the amps are closely matched on one and the same music track.
The long-winded explanation follows. As you say, an increase in volume level is perceived as better sound, up to a point. We can eliminate this factor by matching volume levels (power output levels) between different DAC and amp systems to examine the other factors. Modern DACs, if implemented correctly, are very high-performance, and so different DACs play practically no part in differences in system sound quality. Amps play a larger role, and electric-to-acoustic transducers (headphones and earphones) play by far the largest role in sound differences.
Considering first the soundstage and imaging factor, with stereo reproduction this comes down mainly to channel separation (crosstalk or crossfeed) and room reverberations. Most modern DACs and amps introduce very little extra crosstalk into the music signal, and certainly extra power headroom contributes absolutely nothing to this. The perception of the soundstage built into the stereo signal created by the studio mixing and mastering engineers depends mostly on the headphones, and you will have to research the various headphones for this. Some electronics with poor channel separation (rare) can narrow the soundstage.
The clarity factor (including instrument separation) is also affected far more by the tonality and detail accuracy of the headphones than by the electronics. However, accurate low-distortion headphones like the HD6XX can certainly reveal noise and distortion introduced in the electronics if their levels are high enough. Generally, noise and distortion of the electronics with a SINAD over 100 (THD+N less than -100 dB or 0.001%) will be hard to perceive at normal levels of music listening, which your BTR5 with its ES9218P clears easily. However, when listening with a high volume setting, you may be able to hear a little amp distortion and in very quiet music passages at the same high volume, you may be able to hear a little amp noise. If you are seeking guaranteed audibly transparency of the electronics, a SINAD of 116 dB or higher will give you that, though it is really overkill. The Atom amp is certainly audibly transparent, however when driven by the BTR5, the noise and distortion of the BTR5 passes through to the Atom to the HD6XX. If you really wanted the last iota of accuracy in the electronics, you could replace the BTR5 with the Tempotec or E1DA dongles or else a an audibly transparent desktop DAC. The other aspect of clarity is the tonality. Headphone/IEM FR curves that are boosted in the clarity range where our hearing is the most sensitive and in the treble, give sound that is perceived as clearer, brighter, leaner and more sharp-edged. But this is probably not what you want.
The third factor, regarding the fuller sound and better bass, is dependent both on volume level and on tonality (frequency response). Modern DACs and amps generally have pretty flat frequency response (FR) curves over the audible range of 20 Hz to 20 kHz, and so they have no influence on the tonality. So introducing the Atom downstream of the BTR5, and even replacing the BTR5 with a higher-SQ DAC will do nothing to the tonality, though the Atom will certainly give more volume headroom. Considering first the volume level, the nominal impedance and power conversion efficiency of the HD6XX are 300 ohms and 103 dB at 1 mW. Sustained long-exposure long-term listening at average SPL levels above 85 to 90 dB will damage your hearing. So counting 90 dB average SPL as the maximum you would need, and adding 20 dB headroom for brief loud passages in the music, 110 dB SPL should be the maximum that we would need to hear from our speakers, headphones and IEMs. [If you do not provide that 20 dB headroom for loud music passages, the amp can clip during them, resulting in unpleasant harsh distortion and loss of clarity. More power headroom than the needed 20 dB will not improve the non-clipping SQ.] At their max volume levels, the BTR5+Atom combo can drive the HD6XX to 125 dB, the BAL output of the BTR5 alone to 117 dB, and even the SE output of the BTR5 to 112 dB which all seemingly allow you to reach satisfyingly loud levels with enough headroom for extra loud passages.
I think the reason you find the BTR5's SE to be not loud enough is related to tonality of HD6XX rather than average power delivered by BTR5's SE. The impedance and efficiency values quoted for the HD6XX are either for a 1 kHz tone or averaged over the audible frequency range. The HD6XX have a steep roll-off in FR when going to lower frequencies below 100 Hz (though their response above 500 Hz is pretty neutral and accurate). The response is around 10+ dB lower at 20 Hz and around 15+ dB lower at 10 Hz than the Harman curve preferred by most people for modern music genres such as rock, rap and EDM. Thus at the lowest frequencies the BTR5's max SE output falls short by 8 to 13 dB of providing enough power for strong bass, plus in modern genres the bass tends to be continuously present. A poor way to overcome this is by bumping up the amp's power level such as by cranking up the Atom in High Gain. The bass would become satisfyingly loud, particularly because the perceived difference in loudness between bass and mids lessens at higher volumes (see Fletcher-Munson loudness curves). However, with low-distortion headphones like the HD6XX, the loudness of the upper mids and lower treble can simultaneously rise unnoticed to hearing-damaging levels.
Altering the tonality of the headphones is a preferable strategy for getting a fuller sound and better bass, for which there are a couple of good approaches. To reiterate, raising the power level is not recommended for altering the perceived tonality of the headphones. The approach to try first is to use software EQ in the BTR5 to try and boost the bass to better levels relative to the response at 1 kHz. There is however a limit to how much you can do this before the drivers distort. If the max non-distorting EQ does not make the HD6XX sound full enough or bass-rich enough for your taste, you might consider the second approach of supplementing or replacing the HD6XX with a headphone like the inexpensive yet reasonably accurate AKG K371 which has a FR that closely follows the Harman HP curve.