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I am on vacation this month, but Roger is here with you and in this month’s Roger’s Corner we will be talking about decibels. I am kind of glad I took this month off because after reading the article myself I was pretty much at a loss for what to write for the introduction. Those of you that are mathematically inclined, or those of you who want to take a shot at being mathematically inclined can have some fun with Roger on this one. Just be sure to have the martinis close at hand. Good luck and see you next month.

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Having Fun with Decibels,
By Roger A. Modjeski

Having fun with what? Do you think I am some kind of nerd? Well, I have fun with decibels and I am no nerd. I love to go to audiophile cocktail parties and demonstrate how many drinks I can have and still do decibels in midair, no calculator, no chart, and no props at all. I assure you I have not memorized the table many of you use nor have I converted my brain to a logarithmic computer. I still think quite linearly, well at least about decibels. I started the practice some ten years ago out of some simple observations about decibels. You will have to memorize four simple things and understand what the reasoning behind decibels is about. That is probably the most beneficial part of the trick as you will truly understand decibels when you are done with this. You will also be able to pick out the multitude of errors in publications and become a decibel proofreader if you like.

Now let us get a few things straight. I insist that all my students develop the proper language in speaking about electronic matters. I do this because right language promotes right thinking. First, there are no such things as voltage decibels and power decibels, there are simply decibels. That is the elegance of the system. There is indeed a relation for deriving decibels from voltage and another one for power, but once in decibel form, the number stands alone in its simplicity. The formula for decibels is dB=20logV1/V2 which is spoken, “Twenty times the log (base ten) of voltage one over voltage two. Well, I do not talk like that around my house. Besides I may be able to divide two numbers in my head but how am I going to figure out the base 10 log in my head. What is a base 10 log anyway? For those of you that care it is simply the exponent of the number 10 that yields the number you are concerned with in our common base 1 number system. It is like a converter between a base 1 number system and a base 10 system.

So, what are decibels and how are they useful? As engineers we want a way of specifying things in a relative way. Ratios are useful things and easier to deal with than absolute numbers. It is easier to say, "I have half as much," than to say, "Well I first had this much and now I have this much," or to say, "The voltage decreased 10%," instead of, "The voltage went down from 120 volts to 108 volts." If I make a 10 watt amplifier that is 5 watts shy of its rated output, you should be upset with me for cheating you out of half of what was promised. If I make a 250 watt amplifier that is 5 watts shy, I hope to be forgiven for being off by 2%. My experience those of you who have accounting type minds tend to count every bean where those of us with science type minds are happier with the percentage to which things are accurate. If you are an accountant, try my little game on the other side of your brain.

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