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

[Richie Burnett]

> Also my point is that dB to me seems like an arbitrary unit, it makes
> more sense to me to see on a plot a drop of 1 unit per octave
> (incidentally which is another power of 2) for a 1 pole filter, or a
> rise of 1 unit per octave for a 1 pole high pass filter, 1 pole = 1
> doubling / halving per octave. It just makes things easier to count in
> my head instead of having to multiply and divide by 6 all the time.

I totally agree, Andy.  As an EE I have to deal with things in dB all the 
time, so have just gotten used to it.  But for students learning I get them 
to plot their bode-plots on log-log paper where the y-axis is amplitude in 
volts, and the x-axis is frequency in Hertz.  Then we talk about 1st order 
(1-pole) low-pass filters having a stop-band slope of minus one, 2nd order 
low-pass having a slope of minus two, high-pass filters having a positive 
stop-band slope, etc...

As you said, one factor of 2 change in amplitude for a factor of 2 change in 
frequency for a 1-pole filter, or two factors of 2 change in amplitude for a 
factor of 2 change in frequency for a 2-pole filter.  It is more intuitive 
than saying -6dB/octave or -12dB/octave, but that's what they will encounter 
in EE circles so they need to know about that too.  And then to confuse them 
even more there's slopes quoted as 20dB/decade, etc...

-Richie,

PS. Tim Stinchcombe those 3D animated root-locus plots are cool.  I only 
just realised you could click on them and make them come to life!