making LP filters into HP

[gstopp at fibermux.com]

     There's a thing in some old Electronotes (of course) about how to sum 
     various stages in a cascaded filter to get all the different 
     responses. They said that the big problem with doing it this way is 
     that it's extrememly dependent on precise summing resistor values - if 
     you don't get the ratios exactly right then the responses are 
     inadequate. They actually thought it was such a pain in the ass that 
     it'd be better just to cascade a bunch of state-variables in different 
     ways. I think they also mentioned that changing the resonance screwed 
     things up. If I get the chance I'll look it up....
     
     - Gene


______________________________ Reply Separator _________________________________
Subject: making LP filters into HP
Author:  Christopher List <Christopher_List at sonymusic.com> at ccrelayout
Date:    5/13/96 12:27 PM


Hi List - 
     
I built one of those filters Gene was talking about the other week. The 
Electronotes one with the 4 x (3080->cap->3140) stages. It's 4-pole low-pass. 
It works very well (as Gene described) and it's very easy to layout and put 
together. 
     
Anyway, I was thinking (or maybe I read somewhere) that if you take the output 
of a LP filter, invert it and add it to the original, unfiltered signal you get 
a HP output. I played with this for a little while, and sure enough, it worked. 
The problem is that when the Q changes you have to change the mix of the two 
signals to continue getting a proper HP response.
     
Is there any trick you experienced fellows have run across to avoid this? Like 
inverting the Q feedback and adding it to the whole thing or something? - No 
wait, that would just cancel out the Q all together. I guess what I'm really 
wondering is do state-variable models have to be designed from the ground up as 
state variable or can you "enhance" any LP filter to get a high pass response 
<<with>> adjustable Q?
     
- Thanks,
Chris
     
ps.
Another thing I was playing around with was summing the output with the cosine 
output (second stage). Doesn't really do anything to the original signal, but 
for self oscillation it makes an interesting waveform (Sine + Cos) which has 
points and is more buzzy. This means that the res. at med-high (before self 
oscillation) levels adds a more buzzy tone to the original signal...