It seems like Learjeff, and I expect many others too, know how to do it, but for those who don’t, and if anyone is interested, here’s the method.
Gizmo’s guide to thinking logarithmically.
First, memorize a set of log tables, then…………….
Or, you can try it the easy way. 
(dB is a ratio, but to make the explanation simpler, I’ll take a reference level here of 0dB as 1W. But if you’re using dBm then just substitute milliWatts. Or take any reference value you want, or just stick to simple ratios.)
You have to remember 3 things.
(1) dBs add (or subtract), Watts multiply (or divide).
If that doesn’t make sense then you might find it helpful to study up on dBs and logarithms. But you don’t have to. I hope it’ll become clear, so just accept it for now.
(2) +10dB is 10 times the power (10W). And -10dB is a tenth the power (1/10W)
So that means that +20dB (10+10) is 100W (10x10).
+30dB (10+10+10) is 1000W (10x10x10)
+40dB (10+10+10+10) is 10000W (10x10x10x10)
and so on.
(3) +3dB is twice the power, (2W). And -3dB is half the power, (½ W). (That’s not exactly true, but it’s near enough.)
So that means that +6dB (3+3) is 4W (2x2)
+9dB (3+3+3) is 8W (2x2x2)
+12dB (3+3+3+3) is 16W (2x2x2x2)
+15dB (3+3+3+3+3) is 32W (2x2x2x2x2)
and so on.
So let’s get complicated.
We can also start at 10dB, and count down in 3dB steps, each time halving the power.
So, 10dB is 10W
7dB (10-3) is 5W (10÷2)
4dB (10-3-3) is 2.5W (10÷2÷2)
1dB (10-3-3-3) is 1.25W (10÷2÷2÷2)
We now know or know how to quickly figure the values for: 1dB, 3dB, 4dB, 6dB, 7dB, 9dB and 10dB. So let’s find the missing numbers.
You can use the fact that 1dB is 1.25, and multiply by that factor to raise by 1dB, or you can start at 20dB and work down. Do whatever is easiest.
20dB is 100W
17dB (20-3) is 50W (100÷2)
14 dB (20-3-3) is 25W (100÷2÷2)
11dB (20-3-3-3) is 12.5W (100÷2÷2÷2)
8dB (20-3-3-3-3) is 6.25W (100÷2÷2÷2÷2)
and 5dB is 3-and-a-tad W, and 2dB is near enough 1.5W
Now you can take any dB value, and calculate the power ratio in your head (but I tend to count on my fingers too.)
+33dB? It’s easy:
33dB is (10+10+10+3), and that converts to (10x10x10x2) = 2000W
24 dB? (10+10+10-3-3) = (10x10x10÷2÷2) = 250W
This all may seem complicated to start with, but when you do it a couple of times it becomes second nature. It’s just a question of figuring out the right combination of 10’s and 3’s. And you can always use the fact that 1dB =1.25 if you’re stuck.
To summarize:
You convert your dB figure into a sum of 10’s and 3’s.
To convert to Watts: + becomes x, - becomes ÷, 10 stays as 10, and 3 turns into 2.
Voltages or currents:
It’s the same thing. The only difference is that +20dB is ten times the Voltage, and +6dB is twice the Voltage.
Or you can half the dB figure, then use 10’s and 3’s as usual.
So, assuming that 0dB is 1V, what is the voltage at +26dB?
First, halve 26 to give 13.
13 is (10+3), which converts to (10x2) = 20V
Easy ain’t it?
80.6 %
| Quote (Gizmo @ Nov. 19 2006,14:35) |
| 0/10 Learjeff. As my college prof used to say, “if you don’t show the figuring, you don’t earn the points!”
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At least I got the answers right. You get a bad student rating for not stating the ground rules. No tenure for you, but I’ll still get my sheepskin!
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| Yeah, let’s go rate Gizmo on Ratemyprofessor.com. |
I think I’d score a zero on there Tom.
OK, I’ll keep my useless tips to myself in future.
It was a great tip! We just didn’t like the grade curve. Everyone wants an A, y’know.
I think the test is flawed. After reviewing the answers, one of the phrases was definitely different when the answer stated it was the same. Only 47% of people answered that it was the same.
A couple of the phrases have the same melody but a difference of one harmony note, which is difficult to hear because of the mix and small pc speakers.
The ear can be trained to better recognize intervals. Memory can also be trained. The test does not measure an innate ability.
I’m consistently in the 75% ballpark. Oh well. I usually do pretty good on these things but I know my ears aren’t what they use to be. Either I’m hearing differences at aren’t there or am not hearing differences that are there. (well…duh)
If the test is making answers wrong then it’s pointless…except it’s fun trying.