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The need for decibel in analog electronics

  • Author iVenky
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Usually we represent the gain in terms of decibel (db). Have you ever wondered why we are doing like that? I found this while I was reading about Bode plot.

The main reason for working for log is because multiplication becomes addition in log. So this reduces the complexity.

Consider a transfer function

T(s)= s^2= w^2. (s = jw)

This can be written as T(s)= w*w. So that when you increase 'w' say by 10 times then you T(s) increases by 100 times. This number is quite large and can't be drawn in a small graph. Whereas if you work with the log of those we can easily prove that if 'w' increases 10 times its original value then T(s) increases by 40 db. Hence this is a small number. Instead of multiplication here we have added 20 and 20. This reduces the complexity. So it's easier to work in the log domain than in the number domain.

The main aim of mathematics is to reduce complexity.

That's all.



jeet_asic;bt1574 said:
i didn't understand , how it became 40 ?

It's very simple.

T1(s) in db = 20 log w + 20 log w
Now when w increases to 10w We get

T2(s) = 20 log 10w + 20 log 10 w

So that the difference is nothing but T2(s) - T1(s)= 20 log10 + 20 log10= 40 db.

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