I posted this earlier today, but I think it deserves to be put in the blog - if nothing else so I can find it again next time ... and there always seems to be a next time when it comes to calculating headphone amplifier gains.

Starting at the beginning, the encoded data on a CD goes from 0 to 1 in 2^16 steps, but in a typical CD player or soundcard, the DAC output is -2.8 V to 2.8 V or 2 V rms or 6 dB. Many sources, such as phono stages and portable audio, are lower, perhaps as low as 250 mV.

How loud the sound is depends on the source signal amplitude, the position of the volume control, the circuit gain, and the impedance and sensitivity of the headphones.

As a practical matter, most people would want the volume control at the 9-10 o'clock position for "normal" listening.

For standard "line level" source, the gain required to keep the volume control at a 9-10 o'clock varies depending on the impedance...

Biggest changeover in many years.

Denon DP-2000, DA-307, DL-103 turntable/tonearm/cartridge
Phonoclone 3 with 160 VA Plitron power supply
47 Labs "Treasure" model 0247 preamplifier
47 Labs "Treasure" model 0347 amplifier
Onkyo D-605SR speakers
Cables by oyaide, mostly.
(photo: Pentax K10D, Pentax FA 31mm F1.8 AL Limited)

If we accept that conventional wisdom that the audio bandwidth extends from 20 Hz to 20 kHz, a good rule of thumb for the f(-3 dB) high and low cutoff points of the frequency response of each audio circuit element is 5x the bandwidth, or 4 Hz to 100 kHz. In practice most designs tend to shift that range a little to the higher frequencies, so perhaps 5 Hz - 200 kHz, or 4 - 250 kHz.

Personally I "tune" my circuits to 4 Hz. That is, the time constants are adjusted to about 4 ms. Capacitance is usually cheap enough to go even longer, but the influence on sonics is typically net negative.

The high frequency side is more interesting, since many circuit elements naturally run into the megahertz range, the the question is do you actively try to prevent that, and if so, where and how?

The biggest issue is bypassing: a small value electrolytic (100 uF) is probably fine up to 100 kHz or so, but quite useless at 2 Mhz. The textbook solution is...

Having recently actually bought some new (not used, not my own design, and relatively expensive) audio gear, and from 47 Labs no less, the following question has been occupying my thoughts of late:

How much would you pay to not have a component installed in the audio equipment you buy?

The traditional price scheme for audio equipment is [BOM-times-X], where BOM is the cost of the parts used to make it, and X is a multiple to cover fabrication and distribution costs, as well as profit for the various parties involved. My understanding is that for consumer audio "X" is about 4, though companies with strong brand recognition can get away with higher multiples. And do.

The basic problem is this: how much it costs to build and how good it sounds are not the same thing. There is some correlation: a large, high quality transformer is pretty much guaranteed to improve the sound quality, but for the rest, stuffing a pretty box with many cheap...