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How to Convert 40dB Voltage Gain to Linear Scale Using 20log(Ku) Formula?

rezontor 17112 5
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  • #1 11558836
    rezontor
    Level 15  
    Posts: 210
    Help: 1
    Rate: 13
    The decibel gain from the linear one is calculated by:

    -for tension

    KdB = 20log (Ku)

    -for power

    KdB = 10log (Ku)

    If I have the voltage gain given in the dB scale, e.g. 40dB, then to convert to the linear scale I do this:

    40 = 20log (Ku) / 20
    2 = log (ku)


    because log (10) a = b 10 ^ b = a
    so:
    10 ^ 2 = ku
    100 = ku


    So the linear gain is 100V / V - correct?
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  • #2 11559097
    goldi74
    Level 43  
    Posts: 8058
    Help: 1367
    Rate: 1535
    rezontor wrote:
    So the linear gain is 100V / V - correct?

    No, just 40dB is 10000V / V. 100V / V it is 20dB.
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  • #3 11559226
    13adam13
    Level 29  
    Posts: 1421
    Help: 151
    Rate: 454
    I prefer to convert it like this:
    Ku [V / V] = 10 ^ (Ku [dB] / 20)
    To be sure, I will count
    Ku = 10 ^ 40/20
    Ku = 10 ^ 2
    Ku = 100 [V / V]
    For me it's like that, I don't know, maybe I made a mistake somewhere, but probably not.
    I do not know why goldi74 it turned out differently.
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  • #4 11560362
    rezontor
    Level 15  
    Posts: 210
    Help: 1
    Rate: 13
    So what is the correct solution?
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  • #5 11560480
    goldi74
    Level 43  
    Posts: 8058
    Help: 1367
    Rate: 1535
    13adam13 wrote:
    I prefer to convert it like this:
    Ku [V / V] = 10 ^ (Ku [dB] / 20)
    To be sure, I will count
    Ku = 10 ^ 40/20
    Ku = 10 ^ 2
    Ku = 100 [V / V]
    For me it's like that, I don't know, maybe I made a mistake somewhere, but probably not.
    I do not know why goldi74 it turned out differently.

    Everything is OK with you. The error is with me.

    40dB = 100V / V

    Sorry for the confusion.
  • Helpful post
    #6 11560564
    13adam13
    Level 29  
    Posts: 1421
    Help: 151
    Rate: 454
    If you have round numbers, there is no need to convert:
    10-20dB
    100-40dB
    1000-60dB
    10000-80dB
    and so on .
    Best count yourself this way, goldi74 the zeros are wrong, he gave one 0 too many. :D
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