topic Re: dB in Mathcad

dB

ValeryOchkov — Thu, 27 Apr 2023 01:39:54 GMT

It is necessary to express the power of the power plant in decibels.
I go online and find out that bel is the decimal logarithm of the ratio of two physical quantities, the second of which (the denominator of the fraction) is called a certain base. In the same place on the Internet you can find the corresponding formula for the calculation.
Here's how such a calculation might look like in Mathcad 15 with the help of tools for separating variable and function names into styles using different font colors (black, green, blue and white - invisible).
If one watt is taken as the base, then the power of the largest Russian thermal power plant, Surgutskaya GRES-2, will be 96.812 decibels (see please the picture and the attach).

We solve the inverse problem: given the power in decibels, it is necessary to calculate the power in the usual watts.

Question. Why are decibels called decibels and not decabels? After all, if we multiply the logarithm by ten, and not by one tenth.

See please also decibel

Re: dB

LucMeekes — Thu, 27 Apr 2023 12:17:35 GMT

Answer is simple.

How do you get from 1 metre to decimeters? By multiplying the amount in metres with 10.

1 m = 10 dm

likewise:

1 B is 10 dB

Success!
L:uc

Re: dB

ValeryOchkov — Thu, 27 Apr 2023 16:33:58 GMT

Thank you Luc for lifting a burden from my soul!

But

1 dB is 0.1 B

Re: dB

LucMeekes — Thu, 27 Apr 2023 19:36:23 GMT

Correct.

1 db = 0.1 B

Multiply each side of the equation with 10, you get:

10 dB = 1 B

Thus: 1 B is 10 dB.

Success!
Luc

Re: dB

ValeryOchkov — Sun, 30 Apr 2023 15:39:14 GMT

1 db = 0.1 B

Multiply each side of the equation with 10, you get:

10 dB = 1 B

Thus: 1 dB is 0.1 B or 1 dB is 0.1 log(var/base) not 1 dB is 10 log(var/base)

Re: dB

ValeryOchkov — Sun, 30 Apr 2023 17:02:24 GMT

Cut me into pieces, eat me with butter, but if I want to get a decimeter, I divide the meter by 10, not multiply the meter by 10. If I multiply the bel by ten, then I get a decabel, not a decibel.
Cut me into pieces, eat me with butter!

Re: dB

LucMeekes — Sun, 30 Apr 2023 20:57:40 GMT

Correct, if you want to get a decimetre, you divide the metre by 10, That is answering the question: How long is a decimetre?

BUT.

If you have a rope with a length of 100 cm, then its length is 1 m, or 10 dm. That is: to express the length in dm instead of in m, you have to multiply the value in front of the metre with 10 and replace the m with dm.

Remember where we came from. You (implicitly) asked the question: if we want to express a ratio in dB (instead of B), why do we multiply with 10 (instead of dividing by 10).

Success!
Luc