AudioBanter.com - View Single Post

(Stewart Pinkerton) wrote in message ...
On 17 Jan 2004 02:02:57 -0800, (Svante)
wrote:

However, this would actually speak against
using dB as a measure of distorsion, since dB is fundamentally
intended to measure a POWER ratio.

The dB was originally a measure of sound pressure level, and the
logarithmic scale is used simply becuause our ears respond to sound in
a logarithmic fashion.

Nope. Think a bit. "deci" is a tenth. Why would mister Bell have
defined a Bel as TWO times the logarithm of the ratio between two
voltages/pressures/currents?
The original definition of Bel is simply (ONE time) the tenth
logarithm of a power ratio. Then, if we want to end up with the same
number measuring voltages, we will have to take the logarithm of the
SQUARE of the voltage ratio, which is the same as TWO times the
logarithm of the voltage ratio. Or:

Bel = log(p/pref) = log((u/uref)^2 = 2 * log(u/uref)
or:
deciBel= 10 * log(p/pref) = 10 * log((u/uref)^2 = 20 * log(u/uref)

....given that pref and uref corresponds to the same power in the
resistance in question.

The "2 (* log...)" is a simple by-product of the square in P=U^2/R

So I guess it is safe to assume that the fundament of the deciBel
rests on a power ratio.

3. The measuring equipment measures ratios of voltages. It does not
measure power delivered to the load.

So... A spectral display based on voltage measurement should not
really be allowed to display "dB" on the y axis, unless we know that
we have a constant, resistive load?

Not at all, since a voltage ratio of 2:1 is approximately 6dB,
regardless of current flow. This is why voltage, not power, is used
as a standard measure of speaker sensitivity, since it is independent
of the load impedance.

Not if the decibel indicates the power ratio.

I mean, the fundaments of dB
assumes that we measure a power ratio.

No, it doesn't. It is simply a useful logarithmic ratio.

Indeed, the Bel is a useful logarithm of a power ratio.

The equation for "voltage dBs"
(20*log(u/uref)) is a derivation based on that p~u^2 neglecting the
effects of varying load resistance. It simply assumes that the load
resistenace is constant.

It assumes no such thing.

If you get back to the fundaments, it does. But I know what you mean,
I am just trying to point out that on the way to the voltage ratio,
somewhere, the resistance has been ignored.