Partial-Fraction Expansion?

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Someone please refresh my memory...

Isn't there some easy way to do a "partial-fraction expansion" of a
transfer function in "S" (Heaviside version of Laplace) and generate
an L-R-C ladder network?
        
                                        ...Jim Thompson
--  
| James E.Thompson                                 |    mens     |
| Analog Innovations                               |     et      |
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Re:Partial-Fraction Expansion?
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I don't know that there's any easy way to do it by hand, no.  
 That's why for the "standard" filter types, someone went to the
 trouble of computing "normalized" filter tables for ladder
 networks.

With something like SciPy or Matlab, if you have a candidate
 filter topology and the transfer function of your filter it
 should be possible to write a program that can find the transfer
 function of the network and solve for the component
 values

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Re: Partial-Fraction Expansion?
On 01/27/2015 07:15 PM, bitrex wrote:
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A partial-fraction expansion will give you a sum of quadratic terms,  
each of which will look like a parallel LRC section.  That leads  
directly to a realization: buffer the tank voltage and sum the results.  
  Getting the ladder realization is tougher, as others have noted.

Cheers

Phil Hobbs


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Dr Philip C D Hobbs
Principal Consultant
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Re: Partial-Fraction Expansion?
On Tue, 27 Jan 2015 16:38:34 -0700, Jim Thompson wrote:

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There's something about alt.binaries.schematics.electronic that either  
Pan or Giganews doesn't like -- if I reply without snipping that from the  
"Newsgroups" line, things quietly fail.

You don't want partial fraction expansion.  Partial fraction expansion  
turns a big transfer function into a sum of a bunch of smaller transfer  
functions.

You would like to be able to factor your transfer function so that you  
could have the product of a bunch of second-order transfer functions,  
each specifying a filter in cascade.  You'd like that, but it only works  
with active filters: with passive filters the stages interact.

Worse, the handbook filters usually don't deal with finite-Q coils, and  
if this is for your Q>100 filter, they'll be useless.

If this were 1950, the answer would be to make pi-wound coils on forms  
inside of cans, with built-in capacitors, with amplifiers between  
stages.  Fancy circuits would use two coils in each can, to get two  
resonators per amplifier.  But even in 1950, no one would try for a  
bandwidth/carrier ratio of 1:100.

--  
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Re: Partial-Fraction Expansion?
On Wed, 28 Jan 2015 20:28:29 -0600, Tim Wescott

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Even with active filters this would be a bear. The stages
may not interact, but the component values and tolerances
get really fiddly.  I liked the "equal-component" Sallen-Key
topology for 2nd-order stages, since it was easier to find
matching values rather than specific quirky ratios to set
the Q.  Then the Q is set by the stage gain, which you can
always trim manually.  Nevertheless, it was way too much
work!

Best regards,


Bob Masta
  
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Re: Partial-Fraction Expansion?
On Thu, 29 Jan 2015 13:37:59 +0000, Bob Masta wrote:

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Jim is pretty consistently ignoring suggestions that a 100:1  
carrier:bandwidth ratio may cause problems.  It's his money.  (Well, it's  
his client's money).

--  
www.wescottdesign.com

Re: Partial-Fraction Expansion?
wrote:

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;-)

But I'm not ignoring.  I'm pulling (:-) the client toward an
injection-locked oscillator.

BTW, Gyrator type filters have non-interacting Q and Fo setting
components.

Sallen-Key should be renamed Sucky-Krap >:-}
        
                                        ...Jim Thompson
--  
| James E.Thompson                                 |    mens     |
| Analog Innovations                               |     et      |
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Re: Partial-Fraction Expansion?
On 01/29/2015 12:17 PM, Jim Thompson wrote:
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If you're trying to do anything fancy, sure, but gentle filters such as  
low-order Bessel and Gaussian work fine--the component value sensitivity  
isn't serious.  I use gentle SKs all the time, because of one shining  
virtue: they have exactly unity DC gain, which sometimes matters a lot.

Cheers

Phil Hobbs


--  
Dr Philip C D Hobbs
Principal Consultant
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Re: Partial-Fraction Expansion?
On Thu, 29 Jan 2015 12:23:29 -0500, Phil Hobbs

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So does a gyrator-based low-pass.
        
                                        ...Jim Thompson
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| James E.Thompson                                 |    mens     |
| Analog Innovations                               |     et      |
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Re: Partial-Fraction Expansion?
On 01/29/2015 01:13 PM, Jim Thompson wrote:
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But it needs twice as many op amps, no?  Those cost money in my world,
whereas good resistors and decent capacitors are cheap, so I don't
usually care about sensitivity factors less than about 3.  A unity-gain
SK isn't bad at all--see e.g.
http://www.maximintegrated.com/en/app-notes/index.mvp/id/738 .

Cheers

Phil Hobbs


--  
Dr Philip C D Hobbs
Principal Consultant
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Re: Partial-Fraction Expansion?
On Thu, 29 Jan 2015 13:26:29 -0500, Phil Hobbs

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Cheap is as cheap does ;-)

OpAmps are free in my world.

Nice tutorial though.  I'll have to commit that to a macro to spit out
quick filter requirements.

        
                                        ...Jim Thompson
--  
| James E.Thompson                                 |    mens     |
| Analog Innovations                               |     et      |
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Re: Partial-Fraction Expansion?
On 01/29/2015 01:43 PM, Jim Thompson wrote:
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There's another one, which I think is somewhat better, at
http://www.ti.com/lit/ml/sprp524/sprp524.pdf .

They show that the 'key' is to use unity gain and equal resistors, which  
gets the sensitivity down to about the level of a biquad.  The main  
issue remaining is that the ratio of the capacitors becomes large if you  
need a Q >~ 5. The TI guys recommend using a biquad for the high-Q  
section (there's usually only one) and low sensitivity SKs for the rest.

Cheers

Phil Hobbs

--  
Dr Philip C D Hobbs
Principal Consultant
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Re: Partial-Fraction Expansion?
wrote:

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[snip]

Must be Pan.  I use Giganews and see no such problems.
        
                                        ...Jim Thompson
--  
| James E.Thompson                                 |    mens     |
| Analog Innovations                               |     et      |
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