# Art of Electronics example 1.11

Discussion in 'Homework Help' started by Mookie809, Jul 17, 2015.

1. ### Mookie809 Thread Starter New Member

Jul 16, 2015
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0
Hello, all!
I have a question from The Art of Electronics. I'll start by giving just the question, it reads: Determine the voltage and power ratios for a pair of signals with the following decibel ratios: a) 3dB, b) 6dB, c) 10dB, d) 20 dB. Relevant information would be: dB=20log(base 10)(A2/A1) and dB=10log(base 10)(P2/P1)

Basically, I was wondering if anyone could interpret what "pair" of signals this question is referring to (because there's 4). If you interpret it as like "what is the ratio of 3dB to 6dB?", that seems to go without saying... So I feel I'm missing something, unless this is just an algebra problem where you isolate (A2/A1) and solve for it with the left side of the equation being 3dB for part a) and so on, but even then I feel like this example is hinting at something more important and obvious.

2. ### crutschow Expert

Mar 14, 2008
13,028
3,237
dB is the ratio of two quantities, which here is two separate ratios, voltage (A2/A2) and power (P2/P1).

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3. ### WBahn Moderator

Mar 31, 2012
17,757
4,800

The bel is defined as the base-10 log of the ratio of two powers.

So if P1 is 1 W and P2 is 100 W, the ratio of them is 2 B (2 bels).

Because more than a few bels would represent very large ratios, we work in decibels (dB) where 10 dB = 1 B.

So if P1 is 1 W and P2 is 100 W, the ratio is 20 dB.

If one signal is twice the power of another signal (or if the power of one signal in increased by a factor of two), that the ratio is 3 dB (not exactly, but extremely close).

The reason for the 20 in the ratio of voltages is because power is related to the square of the voltage and decibels are about power.

So you have P1 = G·V1² and P2 = G·V2² (where G is some conductance) and so you have

X dB = 10·log10(P2/P1)
X dB = 10·log10(G·V2²/G·V1²)
X dB = 10·log10(V2²/V1²)
X dB = 10·log10((V2/V1)²)
X dB = 20·log10(V2/V1)

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4. ### DickCappels Moderator

Aug 21, 2008
2,658
632
The editor must have been asleep at the wheel. There is no obvious answer to your question. If the answer is provided in the book and you want to test your understanding, you can try all pairs from the four figures.

Alternatively, you can answer with respect to these two pairs and somebody here will check your result:
Pairs
a) 3dB, 6dB,
c) 10dB, 20 dB.

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5. ### WBahn Moderator

Mar 31, 2012
17,757
4,800
I don't think there's a problem with the question. You have a pair of signals, One has an amplitude of A1 and a power of P1 and the other has an amplitude of A2 and a power of P2.

a) If the signals have a decibel ratio of 3 dB, what is the voltage ratio, A2/A1 of these two signals? What is the power ratio of these two signals?
b) If the signals have a decibel ratio of 6 dB, what is the voltage ratio, A2/A1 of these two signals? What is the power ratio of these two signals?
c) If the signals have a decibel ratio of 10 dB, what is the voltage ratio, A2/A1 of these two signals? What is the power ratio of these two signals?
d) If the signals have a decibel ratio of 20 dB, what is the voltage ratio, A2/A1 of these two signals? What is the power ratio of these two signals?

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6. ### DickCappels Moderator

Aug 21, 2008
2,658
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@WBhan, You are correct. Some of us aren't very good at reading questions.

"Determine the voltage and power ratios for a pair of signals with the following decibel ratios..."

7. ### WBahn Moderator

Mar 31, 2012
17,757
4,800
If I'm better than most, it's only because I've got a long history of writing questions that people have found multiple reasonable ways to interpret and have gotten much better over time at not doing that as often.

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8. ### Mookie809 Thread Starter New Member

Jul 16, 2015
2
0
Ooooooh. Thanks for the replies , guys. It's pretty obvious now. WBahn, you explained it clear as day. It may have seemed like a dumb question, but skipping over it would have bothered me to no end.

9. ### KL7AJ AAC Fanatic!

Nov 4, 2008
2,040
287
Remember if you're working with voltage or current, the formula is dB=20 log (V1/V2).....AND this only works if the input and output impedances are the same. Otherwise you can conclude (erroneously, of course) that a step up transformer has power gain!