John Fields wrote in message . ..
On 16 Jan 2004 14:32:02 -0800, (Dick Pierce)
wrote:
John Fields wrote in message . ..
On 16 Jan 2004 06:40:38 -0800, (Svante)
wrote:
And, if you describe the ratio of the original to its distortion
products in dB rather than in percentage, what do you care?
A THD of 1% means the amplitudes differ by a factor of 100:1,
their powers differ by 10000:1, but it's 40 dB in both cases.
That's the entire point: A RATIO between two signals is EXACTLY
the same whether you describe the RATIO of the voltage, the RATIO
of the power or the LOGS of those ratios (assuming the impedance
is the same in all cases, which is a prefectly reasonable assumption).
---
Except that decibels describing the ratio of one power to another
P1
is dB = 10 log ---- , while for voltages or currents it's _20_ times
P2
the log of the ratio.
But WHY? It's simply because power is proportional to the square of
the voltage, thus since:
dB = 10 log P1/Pref
and since
P prop V^2
and thus:
dB = 10 log V1^2/Vref^2
or
dB = 10 log (V1/Vref)^2
and
dB = 2 * 10 log (V1/Vref)
thus
dB = 20 log V1/Vref
QED.
So, it stands that 40 dB is 40 dB, whether we started with the
ratio of two voltages, or the ratio of the equivalent powers
of those two voltages.