dB to percentages

[edba]

Hi

I have a bit of basic question which is just confusing completely this morning. I have a spec stating the voltage gain of an amplifier is x10 +/-0.9 dB. Don't ask me why the limits are in dB they just are!

So I convert 0.9 dB to a percentage which is 10^(0.9/20) = 1.1092, whilst 10^(-0.9/20) = 0.9016, so the gain could be 11.092 to 9.016 or 10 +1.092 / -0.984. Why are the limits not symmetrical anymore, as with +/-0.6 dB? I am forgetting some of my mathematics rules from 40 years ago! It maybe a senior moment!

Br

Edba

[PGPG]

Why are the limits not symmetrical anymore

Because dB expresses deviation as exact value being changed by the factor and not by value.
It is like saying that gain is 10 but can be 2 times higher or 2 times lover giving you 10 +10/-5.

Such information is closer to real live. If gain of 10 is very not accurate it is more normal to expect it being 2 times smaller or 2 times higher than being ±10 giving you 0 at one and. What with gain being 10 ±15 where with + we don't have a big problem but having the phase reversed by inaccuracy is rather not expected.

There are many values that are very not accurate. For example transistor beta varying from 100 to 600.

[radiolistener]

dB for voltage and current is 20*log(ratio).
dB for power is 10*log(ratio)

since your specification is voltage gain 10x ±0.9 dB, it's more easy to convert 10x to dB: 20*log(10) = 20 dB.
So, your specification is voltage gain +20 dB ± 0.9 dB = 19.1 ... 20.9 dB range.
Now you can convert back to linear ratio:
10^(19.1/20) = 9.02
10^(20.9/20) = 11.09

As result your voltage gain should be within 9.02 ... 11.09 range.

It is not symmetrical because your error specification is in dB which is logarithmic scale.

[edba]

Ok thanks for the answers. Yes the easiest way is to convert the gain to dB, so expressed in the same units, then convert the + and - limits back to linear gain.

[TimFox]

dB are a ratio, percentages are an increment.
For quantities like gain, you should use dB:  if you increase something by 20%, and then decrease it by 20% you do not get back to the start.
1.200 x 0.800 = 0.960, not 1.000
If you increase something by 3 dB, and then decrease it by 3 dB, you get 0 dB which is back to the start.