Recording - July 2014 - 8

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Sensitive to the subject of Sensitivity
This month I'm handing Talkback over to Mike Rivers, who
addresses my reviews of various headphones in our March
2014 issue and discusses the tricky subject of sensitivity and
how it relates (and doesn't relate) to a headphone's performance. Take it away, Mike.-MM
I admired Mike Metlay's seemingly infinite patience to report
on all those headphones in the March 2014 issue of
Recording-he says he really likes listening with headphones,
and I guess he really must. However, I questioned a statement
that he made regarding one of the headphones: "Its sensitivity
of 101 dB/mW means it will have good transient response
when properly driven." This seems to be a non-sequitur since
sensitivity (how loud the headphone gets when a specified
power level is applied) of a headphone has little if anything to
do with its transient response.
A headphone's transient response is primarily a function of the
design of the driver element. It's true that a headphone's impedance can have an effect on the apparent sensitivity, and its
impedance, in theory, can also have an effect on transient
response. But as a great man once said: "In theory, theory and
practice are the same. In practice, they often aren't."
A characteristic known as damping factor (crudely, how quickly a driver starts moving when hit with a signal, or settles to rest
after the signal stops) can degrade transient response if it's too
far off from what the headphone designer expected. Damping
factor is the impedance of the load (in this case, the headphone)
divided by the output impedance of the amplifier driving it.
Since a typical power amplifier has an output impedance of
very near zero, it doesn't matter whether you're dividing 120
ohms or 16 ohms by nearly zero. So in the practical world, the
headphone's sensitivity (which can be a function of its impedance) has little if any effect on transient response.
Sensitivity isn't well understood by non-engineers; it's a useful
number whose practical effect is confused by differences in
impedance. Here's how.
If you know the specified sensitivity of a headphone-for
example, 100 dB/mW-then you know that with 1 milliwatt of
power driving the heaphone, you'll get an acoustical output of
100 dB SPL (Sound Pressure Level), which is pretty darn loud.
For loudspeakers, the SPL for the specified input power is usually measured at a distance of 1 meter. For headphones, SPL is
usually measured using an artificial ear (a HATS, or Head And
Torso Simulator) positioned very close to the diaphragm.
Sensitivity is a function of the electromechanical efficiency of
the earphone-how much electrical power (from the amp) gets
converted to acoustical power (moving the drivers). But how do
you know how much power you're putting into the headphones?
This is where the headphone's impedance comes into play.

If we know the impedance of the headphones and ignore the
output impedance of the amplifier (a reasonable assumption for
most amplifiers-nearly zero, remember?), we can calculate
power by measuring the voltage across the headphone terminals. More voltage results in more power, which means more
SPL. All's well as long as the amplifier is capable of giving the
headphone all the voltage and current that it needs to get to the
desired SPL.
Keeping with the assumption that the amplifier's output impedance is essentially zero, all the voltage that the amplifier produces
will be delivered to the headphones regardless of their impedance. Ohm's Law tells us that current is inversely proportional to
impedance, so a low impedance headphone will draw more current from the amplifier than a higher impedance one. More current at a given voltage means more power... so when comparing
headphones, with an ideal amplifier applying a known voltage
to a headphone of known sensitivity (dB SPL at a specified power
level), lower impedance phones will be louder. From this, we
might conclude that the lower-impedance headphones are "more
sensitive" because they sound louder for the same amount of
power... but that's not what sensitivity really is.
Traditionally, headphones were designed with an impedance
of 150 to 2000 ohms because that was a pretty good match for
most big amplifiers. Then along came mobile devices that were
battery powered, usually from 1.5 to 3 volts. You can't get 10
or 15 volts out of an amplifier that has only a 3 volt power supply... but if your headphone has a sensitivity of 100 dB/mW
(and the vast majority of them have sensitivities very close to that
number), you still need that 1 mW of power to get that nominal
100 dB SPL.
By lowering the impedance of the headphones, we can get
the same power from a lower output voltage, so a portable
device can make a low-impedance headphone sound as loud as
an AC powered amplifier driving a medium- or high-impedance
headphone.
It takes only about 0.125 volts to get 1 mW into a 16 ohm
headphone (and hear 100 dB SPL), but it takes about 0.35 volts
to get that same 1 mW into a 120 ohm headphone. Connected
to the same device, the 120 ohm phone will have to have its volume cranked up to get the same loudness as you'd hear in the
16 ohm phone. This leads to the conclusion that the 16 ohm
phone is "more sensitive," but actually, both have the same sensitivity in terms of power required for a given SPL.-MR

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