Chebyshev Transfer function (odd order)

[Dmeads]

Hullo!

I working on Chebyshev filter for the first time using this link: http://www.simonbramble.co.uk/techarticles/active_filters/active_filter_design.htm

Im working through the design of the 5th order HP Cheby (1dB ripple passband) with fc = 1 KHz.

I am trying to figure out the denominator for the normalized transfer function. Since the filter is 5th order, it has two 2nd order stages cascaded with a 1st order stage. The first order polynomial is where i am having trouble.

The pole tables say that the real pole for a LP cheby with 1db ripple 5th order is -0.28 http://www.simonbramble.co.uk/techarticles/active_filters/active_filter_pole_locations.pdf

Given the Transfer function for a single pole normalized (Resistors/caps set to 1) HP RC filter:   1/(1 + 1/s)

if we replace the 1 in the denominator with the real pole from the table:  -0.28 + 1/s = 0

then invert: -3.5714 + s = 0

and divide all terms by -3.5714 to normalize:  1 - 0.28s = 0

is (1 - 0.28s) the third polynomial in the denominator for the normalized transfer function (in additon to the two second order polynomials I already found were correct)?

Thanks,

-Dom

[Dmeads]

actuall if the pole is at s = -1/(R*C),

then the 1st order polynomial would be (s + 0.28).

than answers my question never mind

[T3sl4co1l]

Yeah that.

I don't worry so much about the polynomials, as they're a solved problem, and there are calculators to transform their solutions into the approximate RLC values I need (that, because of factors not accounted for, often need further tweaking anyway).  I'm satisfied with knowing the underlying mechanics: poles on a circle/ellipse/etc. for the various conditions, or some variation on that for other purposes (there are many other possible optimization goals; some even just arise from what's convenient in a given topology).

But I will add in regards to that, you can get a 3-pole single stage pretty easily.  The values are screwed up, it's not simply putting an RC in front of a 2-pole stage; but they can still be calculated, and have enough freedom to allow for most (all?) Q factors a stage might need.
http://sim.okawa-denshi.jp/en/Fkeisan.htm
Note that the response still depends on source impedance, so it may be desirable after all to put a buffer in front, which still ends up needing 3 op-amps; but this is better than the 4 that would be needed for a buffered 1/2-pole chain.  Heh, also not that it saves much in practical terms, given that amps come in duals and quads, but this can be helpful in stereo/multichannel systems.

Tim