🚀 go-pugleaf

I have been trying to understand a passive loop filter I have twice seen used
in ham radio construction articles.  It looks like this:


     O---VVVVV----+-------+------O
           R1     |       |
                  |       >
                  |       >  R2
                  |       >
                 ---      |
                 --- C1   |
                  |       |
                  |      ---
                  |      --- C2
                  |       |
     O------------+-------+------O

I have been having a great deal of trouble trying to factor out at least
one zero in the denominator of H(s) = F(s)G(s)/[1 + F(s)G(s)], where
F(s) = K/s and G(s) = response of above filter.  I get something like

                 C(as + 1)
     H(s) = ---------------------
               3     2
              s  + ps  + qs + r

where p, q, & r are expressions involving R1, R2, C1, and C2.  It looks
like it ought to be a good performer as long as I could move the poles
to the right place.  When I try to cheat and have an expression manipulator
(such as Mathematica) find the roots, I (deservedly) get an enormous,
intuitively opaque result.

Has anybody out there dealt with this at the design level, or at least
seen a reference to it?  The Egan, Manassewitz, and Gardner books seem
not to address it, but I haven't checked the journals yet.

Thanks in advance,
Marshall Jose  WA3VPZ
mjj%stda@aplcen.apl.jhu.edu  ||  ...mimsy!aplcen!aplvax!mjj