EEVblog Electronics Community Forum
Electronics => Beginners => Topic started by: Dmeads on September 13, 2020, 09:33:24 pm
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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 (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 (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
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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
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Yeah that. :-DD
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 (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