Click here to purchase the entire book in PDF format. dBm When you're measuring sound pressure levels, you use a reference based on the threshold of hearing ($20 * 10^{-6}$ Pa) which is fine, but what if you want to measure the electrical power output of a piece of audio equipment? What is the reference that you use to compare your measurement? Well, in 1939, a bunch of people sat down at a table and decided that when the needles on their equipment read 0 VU, then the power output of the device in question should be 0.001 W or 1 milliwatt (mW). Now, remember that the power in watts is dependent on two things - the voltage and the resistance (Watt's law again). Back in 1939, the impedance of the input of every piece of audio gear was 600$\Omega$. If you were Sony in 1939 and you wanted to build a tape deck or an amplifier or anything else with an input, the impedance across the input wire and the ground in the connector would have to be 600$\Omega$. As a result, people today (including me until my error was spotted by Ray Rayburn) believe that the dBm measurement uses two standard references - 1 mW across a 600$\Omega$ impedance. This is only partially the case. We use the 1 mW, but not the 600$\Omega$. To quote John Woram, ``...the dBm may be correctly used with any convenient resistance or impedance.'' [Woram, 1989] By the way, the m stands for milliwatt. Now this is important: since your reference is in mW we're dealing with power. Decibels are a measurement of a power difference, therefore you use the following equation: $$\textrm{Power (in dBm)} = 10 \log \left ( \frac{\textrm{Power 1}}{ 1 \textrm{ mW}} \right )$$ (3.35) Where Power1 is measured in mW. What's so important? There's a 10 in there and not a 20. It would be 20 if we were measuring pressure, either sound or electrical, but we're not. We're measuring power.