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3 dB bandwidth

Discussion in 'Electronic Design' started by [email protected], Jun 21, 2005.

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  1. Guest

    Why do we measure the bandwidth of any amplifier as 3 dB down from the
    gain value at DC? Why 3dB? Why not 2dB or 1dB?
    I am not able to find a correct answer as to why did we choose this

    Thank You
  2. keith

    keith Guest

    3dB ~ half-power
  3. Hi,
    A voltage gain of -3dB is a voltage gain of 1/sqrt(2). Since power is
    relative to the square of the voltage, this implies a power transfer
    ratio of 1/2. So basically the -3dB point is the frequency where the
    output power of the circuit is half of the power in the passband.

  4. Guest

    Why half power? Why not 1/4th power? why do we choose half power?

  5. For a single pole low-pass filter, that drop (3.01 dB, actually)
    occurs at the frequency where the straight-line projection of the
    passband intersects the asymptote of the stopband. For a
    series R/shunt C filter, it also where the magnitude of drop
    across the R equals the magnitude on the C. So it is readily
    calculated by hand, (as things were when that standard arose).
  6. keith

    keith Guest

    Why not?
    That would be 6bB. Choose it if you so desire.
    Two is such a nice number. Besides, two is the loneliest number
    since the number one and the 0db "point" doesn't tell us much.
  7. And the issue isn't the measuring point, but that the point be consistent.
    One can come up with really good filter specs, but it means nothing if it
    turns out they were measuring at the 1.5dB point rather than the 3dB point.
    Use an odd reference point, and at the very least you'd better be sure to
    specify it. And even then, it can make for complicated comparisons with other
    such units, and might even be considered outright misleading.

  8. Phil Hobbs

    Phil Hobbs Guest

    And besides, if you're going to pick a single frequency as the boundary
    between the passband and the stopband, it's natural to pick the point at
    which half the power gets through.


    Phil Hobbs
  9. Joerg

    Joerg Guest

    Hello Keith,
    Actually that is done for many filters when they characterize the
    roll-off at the 6dB and the 60dB points.
    13 is more lonely...

    Regards, Joerg
  10. Joerg

    Joerg Guest

    Hello Larry,
    Hey, they still are. I have one calculator in my drawer (HP11C) but
    several slide rule calculators. No abacus though.

    Thing is, if the power goes out I can keep going. A long time ago they
    pestered me about it at a client's lab and one of the engineers bragged
    about a new calculator with "continuous memory" that didn't fail when
    the battery died. I told him my slide rule had continuous memory as
    well. The slider...

    Then one day a company came out with a slide rule calculator that had an
    LCD and buttons. That almost made me sick.

    Regards, Joerg
  11. Pooh Bear

    Pooh Bear Guest

    3dB down is half power. It's kinda 'traditional' to measure this.
    In audio ( for one ) it's no longer the standard it was. Not least since
    if you put say 10 devices in series, the signal will then be 30dB down at
    the frequency in question !

    With the higher performance available from modern circuit design and
    components bandwidth in pro-audio is often now specced at -1dB or even

  12. Pooh Bear

    Pooh Bear Guest

    Nicely put.

    Reactive and real component of the filter are equal. It's as good an
    explanation as I need. ;-)

  13. Guy Macon

    Guy Macon Guest

    Addiators work better for addition and subtraction, and are still
    100% mechanical. There are usually a few on eBay cheap because
    many were made and few people collect them. (Always contact the
    seller and confirm that the slides move freely and that the numbers
    are still readable).
    I remember that one. The calc only added and subtracted. There was a
    sliderule with an addiator on the back too.

    Back to the topic, 3DB is also the amount of drop you get when you
    have the output impedence and the input impedence matched, which was
    common in the days of transformer-balanced audio lines.
  14. Lissajoooze figures on a scope

  15. Pooh Bear

    Pooh Bear Guest

    Nooooo ! That's a 6dB drop.

    Thank God we got rid of so-called 'matched impedance working' and went for
    'voltage matching' in audio a long long time ago.

    I can recall seeing 600 ohm variable attenuators though in an antique studio
    when I was a young 'un. I expect they'd cost around £1000 to make today. Just
    to control the 'volume'. Wow !

  16. A Larry said, the -3.01 db value falls out of the maths. For a single RC
    combination, phase moves between 0 and 90 degrees : at -3.01 db the phase is
    half way - 45 degrees.

    Also, -3db frequency in radians per sec = 1/( C R )
    { farads, ohms )

    When you sketch a Bode diagram, for example when checking the stability of a
    feedback loop, you just draw straight lines to the -3db frequency asymptote
    intersection points Larry mentioned, and you are close enough in engineering

    So we got 70+ good years out of the -3db concept and that value still pops
    out at me when I am writing the transfer function for some network on paper.
    However, programs like Spice present a mass of result data and those special
    frequencies are less special to us.

    Engineering is all about getting a feel for the thing you work with, and
    the -3db frequency is like this : its an *interesting* frequency for an
    engineer. You generally know your circuit resistance- an estimate of your
    capacitance and you calculate the "hot frequency" at -3db. At 3db changes
    are happening : rolloff slopes are starting or finishing.

    This was especially so in the valve/tube days where you would increase gain
    by increasing load resistance, to the point where the -3db frequency was as
    low as you could allow.

    3 db was a nice fit with the audio world too, because tests on humans showed
    that a 3 db change was just discernable to the ordinary listener. Of
    course, many careful listeners can do better than that.

    Roger Lascelles
  17. keith

    keith Guest

    Sure, if those parameters are of particular interest. That was sorta my
    Not according to Nilsson.
  18. keith

    keith Guest

    I have a slip-stic in my office and and HP45 around somewhere. The
    batteries in the '45 have long gone to their maker though.
    Putting the slip-stic in its scabbard was tended to clear the memory.
    I see it as someone with a sense of humor. I hope the PHB that
    funded the development didn't expect to make much money on it though.
  19. Pooh Bear

    Pooh Bear Guest

    I have carefully 'lined up' audio tape recorders to an accuracy of better than
    0.5dB 'by ear'.

    3 dB is a dumbfuck 'standard'.

  20. Depends what you mean by "modern". -0.5dB performance was trivially and
    cheaply achievable 25 years ago.

    Kevin Aylward
    SuperSpice, a very affordable Mixed-Mode
    Windows Simulator with Schematic Capture,
    Waveform Display, FFT's and Filter Design.
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