[sdiy] Voltage divider with RC filter - help with the basics, please

[cheater00 .]

Hi Russell,

On Tue, Jul 23, 2013 at 4:27 PM, Russell McClellan
<russell.mcclellan at gmail.com> wrote:
> Hey Tom,
>
> Richie already gave a complete and accurate response, but maybe you'd
> be interested in a standard, general technique for this sort of
> passive network.
>
> First, I convert everything to "impedances" - this means treated the
> capacitor as an "impeder" with impedance 1/sC.  The units of impedance
> are ohms, and resistors translate directly - their impedance is R.
> Don't worry about what the "s" "means" other than that it depends on
> frequency (it's a fancy math thing called a "laplace variable").  The
> cool thing about impedances is that they behave and combine exactly
> like resistors - you can use the 1/R_parallel = 1/R_1 + 1/R_2 rule for
> parallel impedances and you can use addition to find serial impedance.
>  Using these two tools you can quickly build up your whole network
> into a single equation - this equation is called the "Transfer
> Function" of your system.  Interpreting this transfer function is
> where your lack of formal training may get you into trouble - but, if
> you've correctly made a low-pass filter, your function should look
> like x/(1 + ys) where x and y are combinations of R and C values.  If
> you can't use algebra to turn your equation into that form, it isn't a
> lowpass filter.  As richie mentioned, if it's something like (1 +
> xs)/(1+ys), it could be a shelf filter or an allpass filter (i.e., a
> phasor).  In the lowpass case above, the cutoff is just 1/(y*2Pi).  Of
> course there's deeper reasons why these equations work the way they
> do, but that's probably out of scope for an e-mail exchange.
>
> The reason I prefer to use this slightly pedantic method to analyze
> even relatively simple networks of capacitors and resistors is I don't
> have very much intuition.  This method wouldn't be used directly by
> experienced folks except in relatively complicated situations.  For
> me, it can be hard to guess whether your network even is a low-pass
> filter just by looking at it.  Calculating the "cut-off" doesn't mean
> much if you don't even know whether it's a low-or-high pass!

That's the most amazing, down-to-earth description of obtaining
transfer functions I've seen. I feel I finally stand a chance of
understanding the process! Thanks!

D.