[sdiy] Transfer Functions

[David G. Dixon]

> I've realised it would be a struggle for me to learn the mathematics
> involved. I'm pushed for time as it is and would rather spend it doing
> something I enjoy, and that level of maths is not something I enjoy. I
> generally understand how circuits work and know what to fiddle with to
> change them so I should be able to get by without knowing what a Laplace
> transform is.

That's too bad, because you don't even need to know what a Laplace transform
is to derive transfer functions for filters.  All you need are a couple of
impedance formulas, Kirchhoff's current law, and some basic algebra (i.e.,
equation rearranging) skills.  To draw filter response plots, you only need
to separate the real and imaginary parts of both the numerator and
denominator of the transfer function, square each part, add them together
and take the square root of the sum, then take the log of the whole mess,
multiply it by 20, and plot the result vs f or w (omega).

Really, the math you need to do basic filter analysis can be mastered in
about half an hour.  That's not really going to cut into your
circuit-building time, now, is it?