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Decade to Octave Conversion

Discussion in 'Mathematics and Physics' started by dknguyen, Mar 20, 2009.

  1. Tesla23

    Tesla23 Member

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    GdB is simply the gain.

    What it actually means does, however, depend somewhat on the system. An RF amplifier measured in a matched 50 ohm system with 20dB of gain will show a power gain of 100 and an amplitude gain (voltage or current) of 10. An op-amp with high impedance input and low impedance output configured to have a voltage gain of 10 still has 20dB of gain. If the source was low impedance this would supply 100x the power to a load, compared to connecting that same load to the input. However (not wishing to confuse you) you could clearly obtain a power gain of >> 100 simply by lowering the impedance of the load. If the source and load impedances change then you need to be careful, for example a 2:1 transformer can drop the voltage by 2 without changing the power available.

    However in most cases, the simple 10 log power ratios or 20 log amplitude ratios works a treat.
     
  2. Sceadwian

    Sceadwian Banned

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    Tesla.... umm you couldn't be more wrong.

    I'll quote from Wikipedia for a quick reference.
    Please carefully note it is a 'dimensionless unit' which means it has no inherent value in and of itself, only in relation to something else. There db volts, db watts, db current, db ANYTHING. The decibel itself is not a unit of anything, it is the description of a refrence value. Comonly decibel/watts or decibel/volts. Which because power increases logrhythmicaly in respect to voltage they are VERY much not the same.
     
    Last edited: Apr 1, 2009
  3. dougy83

    dougy83 Well-Known Member

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    Oh really? I would have thought power increased exponentially with respect to voltage.

    Also, you may notice that 10log10(P1/P0) is used for power ratios, while 20log10(V1/V0) is used for amplitude ratios. Have you any idea why this is? Maybe because the same dB value is obtained for a given gain, whether you express the ratio as relative amplitude or relative power.
     
    Last edited: Apr 1, 2009
  4. dave

    Dave New Member

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  5. Sceadwian

    Sceadwian Banned

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    Let me please insert my foot in my mouth, thanks dougy =)
    As tesla stated though a DB is not a DB is not a DB.
     
  6. Tesla23

    Tesla23 Member

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    I assume you have examples where a dB isn't a dB, such as where the dB power gain is different from the dB voltage gain etc.

    The point I was trying to make is that the 10log and 20log thing is simply an artifice to measure power ratios - you still get the same dBs. I think if you consult any authoritive reference you will find the bel is defined as log10 of a power ratio. It is then consistent to define it also as 2log10 of an amplitude ratio.

    Of course it is a ratio, and there are many actual quantities measured as dBs relative to a reference level, dBV, dBu, dBm etc.... But the original issue - what is a dB - still only has one answer, and a dB is a dB is a dB in the sense that it doesn't matter whether you are measuring relative amplitudes or powers.
     
  7. Sceadwian

    Sceadwian Banned

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    Tesla, simple example, decibel sound pressure vs decibel power. No device is for acoustical reproduction is completely linear.
     
  8. dknguyen

    dknguyen Well-Known Member

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    Last edited: Apr 1, 2009
  9. Tesla23

    Tesla23 Member

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    Sorry, I still don't understand where the difficulty lies. I'm actually interested, can you give me an example where you get different dB values by considering powers and amplitudes.
     
  10. Tesla23

    Tesla23 Member

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    YES!

    Just to back up what I've been saying, from Fink and Christiansen "Electronic Engineers Handbook":

    The bel, named in honour of Alexander Graham Bell, is defined as the common logarithm of the ratio of two powers P1 and P2. Thus the number of bels Nb is
    Nb = log10(P2/P1)

    for dB add a factor of 10.

    It then goes on to say that in terms of electrical quantities that as P=V^2/R = I^2R then
    dB = 20log10(V2/V1) + 10log(R1/R2)

    and so on.

    So for physical quantities where the impedance level is constant, use 20log amplitude.

    This particular book predates DSP, but I think the analogies with amplitude and power is pretty clear.
     
    Last edited: Apr 1, 2009
  11. Sceadwian

    Sceadwian Banned

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    Is this okay Tesla?
     
  12. Tesla23

    Tesla23 Member

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    Are you saying that in any of those cases that you would get different results by calculating the ratio of amplitudes?
     
  13. Bob Scott

    Bob Scott New Member

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    I also used to be confused about dB, power and voltage relationships.

    This is exactly correct, and it made me instantly understand it years ago.

    If I raise the volume of my stereo by 6dB, I've doubled the voltage going to the speakers and quadrupled the power going to the speakers, and my ears hear a 6dB increase. Power is up by 6dB. Voltage is up by 6dB.

    dB's are handy for plotting filter response graphs, as all we technical types know. If you also have a logarithmic frequency axis, just like the layout of a piano keyboard, it makes your response graph linear. You draw straight lines.

    Also,
    Logarithmic = Exponential.
    There is no difference.
     
    Last edited: Apr 14, 2009
  14. dougy83

    dougy83 Well-Known Member

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    And you're still confused with how to spell it =)

    You will find that the logarithmic and exponential functions are inverses of each other. They are related, but very much different.
     
    Last edited: Apr 13, 2009
  15. Tony Stewart

    Tony Stewart Well-Known Member Most Helpful Member

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    Anything with a controlled impedance is generally defined in dB ratios of power such as all devices, components , filters, amplifiers , Spectrum Analyzers with 50 Ohms.

    - everything else is usually defined in dB for ratios of voltage due to changing impedances in the circuit from high to low.

    - exceptions might include 300 or 600 Ohm phone lines because the impedance changes with the number of phones connected.

    absolute dB readings always have a suffix like dBmV, dBuV, for voltage and dBm or dBW or dBuW for power

    Relative readings of dB are all the same in the context of ratios , but the context is usually implied by a controlled impedance application for inputs and outputs to mean power.

    Otherwise electronics with unknown or differing impedance implies Amplitude and not Power ratio.

    Voltage Ratio in dB differs by a factor of Power dB ratios x2.

    Half voltage is -6dB is not the same as half power @ -3dB = .707V/1V

    So a dB is any log10 ratio. Since deci (-bel) means base 10 logarithm.
    In the context of a controlled impedance like 50 Ohm it is always power, if not specified otherwise.
     
    Last edited: Jul 13, 2015
  16. Ian Rogers

    Ian Rogers Super Moderator Most Helpful Member

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    6 year old thread!!! I doubt any of the above ( apart from Dougy ) come here anymore..
     
  17. steveB

    steveB Well-Known Member Most Helpful Member

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    Lol, my wife does the same thing. - always bringing up issues from the past! ;)
     
  18. AnalogKid

    AnalogKid Well-Known Member

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    Don't think so. In classic active filter design terminology, for example for 1-pole and 2-pole Butterworths, both cutoff frequencies are where the amplitude response is down 3 dB with respect to the passband amplitude, while the attenuation slope is 6 dB or 12 dB per octave depending on the number of poles.

    ak
     
  19. DerStrom8

    DerStrom8 Super Moderator Most Helpful Member

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  20. AnalogKid

    AnalogKid Well-Known Member

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    Historically, I am blind to thread start dates. duh.
     

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