# Science and Math for Audio Humans – Volts and Power

by Danny Maland

Brace yourself for the disclaimer: Everything that I set before you should be read with the idea that “this is how I've come to understand it.” If somebody catches something that's flat-out wrong, or if you just think that an idea is debatable, please take the time to start a discussion via the comments.

In the last installment, life was just about to get useful. I was explaining the inner workings of expressing measurements in decibels - and then I swerved aside. The problem we had encountered was that decibels are really meant as an expression of power ratios, but in pro audio we also apply the decibel to voltage ratios. When we do that, though, our decibel conversion math changes from Figure 1 (power) to Figure 2 (voltage).

• That's all fine and good, but why the change in the math? It all comes down to how voltage translates into power. To get there from here, the freeway entrance ramp is Ohm's Law.
• Figure 3 depicts a very simple electrical circuit. There's a source of 1 Volt, and the current produced by that 1 Volt potential is flowing across a 1 Ohm resistor. It's true that the diagram is depicting a direct current, or DC circuit, and it's also true that audio folks actually use AC, or alternating current, but this will get us “plenty close enough.”

In this circuit, the relationship between voltage (which may also be called electromotive force, or ε, or electrical potential ), current (which is Amperes or I), and resistance (which is Ohms, or R, or Ω) works out to being the exact representation of Ohm's Law:

In other words, 1 Volt across 1 Ohm equals 1 Ampere of current. If we increase the voltage and keep the resistance constant, more current will flow through the circuit. If we increase the resistance and keep the voltage constant, then the current flow will decrease.

You can think of this in terms of water. The voltage source is like a pump, the resistor is like a turbine or water wheel, and the current is how much water is flowing through the system. If we keep the pump as it is, but put in a turbine that requires more force to turn at a certain rate, then we would intuitively expect less total water flow through the system. If we then got ahold of a stronger pump, we could increase the water pressure and restore the total amount of flow.

So, how does power figure into all this? Well, Joule's Law lets us get a mathematical equation that relates power (watts or P) with two items that we're familiar with from Ohm's Law, namely voltage and current.

That being the case, our simple circuit from Figure 3 gives us 1 watt of power. We have 1 Volt flowing across 1 Ohm, which gives us 1 Ampere, and 1 Ampere multiplied by 1 Volt gives us 1 watt. That's simple enough, but what happens to the power when we double that voltage? Take a look at Figures 6 and 7.

By doubling the voltage, we've gotten four times the power. In terms of decibels and power, that works out to this:

To get an equivalent decibel answer when working with voltage, then, we would need to multiply by 2. Thus, “decibel math” with voltages requires us to multiply the logarithm result by 20 (2 X10) instead of 10.

“Alright, alright! We get it! Give us a list of handy decibel references, already!”

No problem. Please note that the reference points listed are the needed value for a 0 dB measurement:

dB SPL (Sound Pressure Level, referenced to 20 micro Pascals rms. Usually coupled with some description of the weighting curve used when measuring, such as A, C, or Z, and should also be coupled with some description of whether the measurement used a slow or fast average.)

dBu (Referenced to 0.775 volts rms)

+4 dBu (1.23 Volts rms, the "pro audio" standard reference voltage for VU meters - see below.)

dBVU (Referenced to +4 dBu, unless somebody has decided to calibrate the meter to something else. It is quite common to have the VU meters on professional, analog, multitrack tape machines calibrated to something other than +4 dBu.)

dBV (Referenced to 1 volt rms)

-10 dBV (The “consumer” audio voltage reference or 0.316 Volts rms. A very common mistake is to say that “consumer level” is 14 dB below “professional,” but this is incorrect. If the “professional” level is 1.23 Volts rms, then 20 times the base 10 logarithm of 1.23 over 0.316 is actually 11.8 dB, referenced to “consumer” level.)

dBFS (Referenced to “full scale.” This is commonly found in digital systems, as it is a very handy indicator of exactly how close you are to clipping a digital signal path or converter. Some systems are able to determine how far above full scale a clipped signal would have gone, and so you may encounter situations where a meter will read positive dBFS numbers. The signal is still clipped, of course – it's just that you have an indication of the reduction in gain required to avoid that clipping.)

Of special note are the decibel numbers used for faders. On a fader, the 0 dB reference point is not tied to any specific voltage. Rather, 0 dB (or “unity”) indicates that the fader is neither attenuating or boosting the signal it is acting upon. That signal may be very small, or it may be in hard clipping. The fader markings only indicate what the fader is doing to that signal's level, so you need to rely on other metering to determine how strong that signal actually is.