¿Qué significa que una señal tenga una amplitud inferior a 0 dB?

Soy un desarrollador de software (que usa lenguajes de alto nivel como .NET, C, C ++, etc.) tratando de entender cómo funcionan las computadoras en un nivel inferior.

Entiendo que la amplitud siempre es positiva porque se calcula por (arriba-abajo) / 2. Sin embargo, no entiendo qué es realmente una amplitud negativa, es decir, qué significa si la onda cae por debajo del equilibrio (0).

Los valores negativos que parecen confusos se dan en decibelios (dB).

Esta es probablemente una pregunta más física, pero estoy tratando de entender los circuitos analógicos.

Un decibel ($dB$) es una forma de expresar una razón. La mayoría de los usos prácticos de los decibelios miden algo en relación con otro. Un número negativo de decibelios indica que la cosa que se está midiendo es menor que la referencia.

Consideremos como un ejemplo $dBm$, una unidad que mide una potencia $p$ relativo a $1mW$. Así:

$P_{dB} = 10 \log_{10}\left(\dfrac{p}{1mW}\right)$

Entonces 1mW es:

$10 \log_{10}\left(\dfrac{1mW}{1mW}\right) = 10 \log_{10}(1) = 0 dBm$

Qué pasa $100mW$?

$10 \log_{10}\left(\dfrac{100mW}{1mW}\right) = 10 \log_{10}(100) = 20 dBm$

Qué pasa $2\mu W$?

$10 \log_{10}\left(\dfrac{2\mu W}{1mW}\right) = 10 \log_{10}(0.002) \approx -26.99 dBm$

Cuando consideramos algo como el voltaje, es habitual considerar la relación de los cuadrados de los valores, porque la potencia es proporcional al cuadrado de amplitud. Por ejemplo,$1V$ en un $1\Omega$ la carga es $(1V)^2 / 1\Omega = 1W$, pero si el voltaje es de 2V entonces $(2V)^2 / 1\Omega = 4W$. Creo que esta es una convención aturdidora, y si quieres que tus medidas expresadas en decibelios sean como potencia, entonces debes medir la potencia. Pero es la convención, y probablemente puedas culpar a los ingenieros que desarrollaron la red telefónica.

De todos modos, consideremos $dBV$, que usa 1V como referencia. Aquí hay un ejemplo con$1V$:

$10 \log_{10}\left(\dfrac{(1V)^2}{(1V)^2}\right) = 20 \log_{10}\left(\dfrac{1V}{1V}\right) = 20 \log_{10}(1) = 0 dBV$

Notice that rather than squaring both voltages in the fraction, we can multiply the logarithm by 2. The two are mathematically equivalent, but multiplying by 2 is easier than squaring.

$20 \log_{10}\left(\dfrac{120V}{1V}\right) = 20 \log_{10}(120) \approx 41.58 dBV$

$20 \log_{10}\left(\dfrac{3mV}{1V}\right) = 20 \log_{10}(0.003) \approx -50.47 dBV$

The level for something like a sine wave is generally given as the RMS (Root Mean Square) value, which (for a sine wave) is 0.707 of the peak value.

For example, 240VAC mains voltage is actually (1/0.707) * 240V = 340V peak to peak - the RMS is used as this is the equivalent of the DC value power wise (i.e. 240VDC would provide the same power as 340VAC pk-pk) Since the RMS value is usually assumed, if you mean peak tp peak you should write e.g. 240VAC pk-pk if the highest pont is +/- 240V

Negative amplitude means the signal is attenuated relative to a reference point, so if you see e.g. -20dB, it means the signal is 1/10th of the reference value. dB on it's own is unitless, so you will see things like dBm (relative to 1mW → 0dB = 1mW), or dBV (relative to 1V → 0dB = 1V)

So if you see -3dBV, this means the level is 0.707 * 1V = 0.707V and -20dBV would be 0.1V.

Similarly 20dBV would mean 10V.

(In the below calculations log10 refers to the base 10 logarithm, as opposed to the natural logarithm or e.g. log2 for base 2 logarithm) The calculation for dB is 20 * log10(signal/ref), so for the above:

20 * log10(10/1) = 20dBV

For the 0.707 case:

20 * log10(0.707) = -3dBV

1mV in dBV would be:

20 * log10(0.001/1) = -60dBV

For measurements of power, the calculation is:

10 * log10(power_level/ref_power_level) so for example, 100W in dBW would be:

10 * log10(100/1) = 20dBW

So a negative amplitude means a reduction in amplitude relative to a reference point.

See the Wikipedia page on Decibels.

The question is a little unclear to me : but if you mean, how is amplitude measured or defined while the signal is below 0V, then remember the difference between speed and velocity : amplitude (like speed) is a magnitude, and is either zero or positive.

The signal (like velocity) is a vector : velocity is defined by speed and direction; signal (restricting the discussion to cosines for the moment) is defined by amplitude and phase. Thus the negative peak -V of the signal is defined as amplitude V and phase Pi (or 180 degrees).

More complex signals can be represented as a sum of different cosine waves with different frequencies, amplitude and phases, the Fourier transform is a technique for translating an arbitrary waveform into such a representation (and back again)

Decibels describe the ratio of signal strengths, according to how many factors of ten a new signal (such as some circuit's output) is compared to the original or some standard reference signal.

When the output is smaller than the input, you'll have to divide by some factors of ten -- the same as multiplying by 1/10, which is (10)^(-1). Thus negative decibels.

In the illustration, the big signal is an input to some gadget, and I made up the value 15.0V for its peak (from zero) amplitude. For a sine, the RMS voltage is 1/sqrt(2) of the peak amplitude. The peak-to-peak is double. The second sine wave has a smaller amplitude. If we imagine applying these sine waves to a simple load (the resistor), currents will flow in proportion to the voltages.

Power is voltage times current, so the smaller signal's power (heating the resistor) is (0.4)^2 of the original's power. This power ratio is what engineers usually care about.

Engineers, being fond of slide rules and easy math, use base ten logarithms for a lot of things. A chain of amplifiers and lossy filters can be dealt with more easily by adding logarithms of gains and losses, instead of multiplying the gains and loss factors. A factor of 10 is one "Bel" but since we're often dealing with fractional quantities like 0.3 Bel (a doubling of power), for ages we've been using decibels to shift that decimal point over.

Note that dB always (usually) refer to power and not voltages. Note also that it doesn't matter if we use peak amplitude, peak-to-peak, or RMS, as long as we're consistent measuring the input and output the same way.

Zero decibels means unity gain, or no change in signal level, because $10^0 = 1$.

Decibels are usually some relative measure, like output related to input.Positive decibel values are increases in signal level (amplification), and negative decibel values are decreases (attenuation).

I recently created a panel where some knobs are labeled as going from $-\infty$ to $0$ decibels, with a gradation of negatively valued ticks in between. This reflects the fact that the knob is a linear potentiometer which attenuates the input signal. $-\infty$ means that the signal is completely trimmed to zero, and $0$ means that the full signal is passed through. The midpoint is marked $-6$ because the voltage is cut in half. Voltage cut in half means power is reduced to a quarter, which is about six decibels down: $20\times\log_{10}(0.5)$.

There exist scales of measure in which decibels are associated with some absolute level. In those scales, zero decibels will refer to a specific absolute voltage or wattage or other quantity. For example, in the dBm scale, 0 dB is one milliwatt. In the dBu scale, zero decibels is 0.775 VRMS.

Regarding $-\infty$ dB: that's a bit of an abuse of notation that appears on instrumentation, which everyone understands. Logarithms are not defined for zero, but grow large as their argument approaches zero from above. Of course, infinity is not a number, and a zero signal has no defined decibel value.