[sdiy] Ladder filters and gain drop, that old chestnut

Andrew Simper andy at cytomic.com
Mon Aug 31 05:27:14 CEST 2015


On 31 August 2015 at 00:09, Richie Burnett <rburnett at richieburnett.co.uk> wrote:
>
> It's an EE thing again, and just a commonly used convention.  It comes from
> the "half power" definition.  If the voltage amplitude is down to -3dB, then
> the power is halved.  It doesn't work for everything though.  For instance
> you could have a Chebyshev filter with 5dB of passband ripple - It's
> passband response would cross the -3dB line several times before finally
> disappearing into the stopband.  So clearly -3dB is not a good definition
> for this filter.

And a point to note is the half power point is not -3 dB exactly, as
dB isn't exactly related to powers of 2:

20*log(10, sqrt(1/2)) ~= -3.0102

where ~= means approximately equal to.

powers of 2 make much more sense:

log(2, sqrt(1/2)) = -1/2

I always use the power of 2 scale in my calculations, not dB, and to
my plots in power of 2 scale as well as doubling and halving makes
much more sense and is exact.

> -Richie,
>
> PS. Apologies for the long post to anyone not finding this discussion
> interesting.

Thanks for the long posts Richie!

Cheers,

Andy


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