Additional Real Poles?

The classic IIR filters have either one or none of the real poles. However
when designing an analog part, it is often possible to stick many additional
1-st order RCs into the schematics. Those realpole RCs can improve the
performance without any side effects.
This seems to be a very typical situation, however I haven't seen any
theoretical considerations about it.
The question is there a canned solution how to make an optimal Butterworth
or Chebyshev like filter, but with the several additional real poles?


Vladimir Vassilevsky
DSP and Mixed signal Consultant
www.abvolt.com

On Sun, 08 Jul 2007 15:16:03 +0000, Vladimir Vassilevsky wrote:

> The classic IIR filters have either one or none of the real poles.

This is correct, whether you're talking about a sampled-time or a
continuous-time system.

> However when designing an analog part, it is often possible to stick
> many additional 1-st order RCs into the schematics.

This is correct.

> Those realpole RCs can improve the performance without any side
> effects.

This is not correct.  There is always a side effect to doing this, the
only question is whether it's going to be significant enough to matter.  If
the amplitude rolloff or phase delay from the inserted RC is in a
frequency band that we care about it must be dealt with.

> This seems to be a
> very typical situation, however I haven't seen any theoretical
> considerations about it.

Usually if it's in the signal path it's done to attenuate noise that's well
above the frequency of interest to keep it from overloading following
stages, or it's done to modify a stage's high-frequency impedance
characteristics, or it's done to enhance the circuit's stability.

Outside the signal path it's done as a matter of course for power supply
decoupling of sensitive circuits, or for other decoupling.

Very rarely is it done with the intent of changing the signal's behavior
in the passband, and when it does the designer can't usually get away with
claiming that his circuit has a "Butterworth response" -- the best he'll
be able to do is claim a "modified Butterworth" or some such.

You do this in the digital domain, too, you just don't think of it in the
same way.  When you oversample, filter, and decimate, you're doing much
the same thing as an analog circuit that has a wide-open front end
followed by a pre-filter and lower-band amplifier.  There are other trick
that one plays with discrete-time systems that are done for design
convenience, and justified as not changing the signal too much, that have
no corresponding technique in the analog world yet are done for the same
reasons of design convenience.

> The question is there a canned solution how to make an optimal
> Butterworth or Chebyshev like filter, but with the several additional
> real poles?
> 
Certainly not that I know of.  The canonical filters are designed so that
in the continuous-time case you can easily choke the filter coefficients
out of the math with a slide rule and a pencil.

I want to make a nice little optimal filter finder in Scilab, for times
just like this -- I want to be able to tell it the amplitude (and possibly
phase) constraints, possibly after sampling and reconstruction, and have
it diddle with coefficients until it comes up with the best filter for the
job, Butterworth, Gauss and Chebychev be damned.

-- 
Tim Wescott
Control systems and communications consulting
http://www.wescottdesign.com

Need to learn how to apply control theory in your embedded system?
"Applied Control Theory for Embedded Systems" by Tim Wescott
Elsevier/Newnes, http://www.wescottdesign.com/actfes/actfes.html

Tim Wescott <tim@seemywebsite.com> wrote in
news:BLidndypmO5nqQzbnZ2dnUVZ_oPinZ2d@web-ster.com: 

One reason you might use a real pole would be to protect from slew rate 
limiting. A digital filter would help you in this case.

Al Clark






> On Sun, 08 Jul 2007 15:16:03 +0000, Vladimir Vassilevsky wrote:
> 
>> The classic IIR filters have either one or none of the real poles.
> 
> This is correct, whether you're talking about a sampled-time or a
> continuous-time system.
> 
>> However when designing an analog part, it is often possible to stick
>> many additional 1-st order RCs into the schematics.
> 
> This is correct.
> 
>> Those realpole RCs can improve the performance without any side
>> effects.
> 
> This is not correct.  There is always a side effect to doing this, the
> only question is whether it's going to be significant enough to
> matter.  If the amplitude rolloff or phase delay from the inserted RC
> is in a frequency band that we care about it must be dealt with.
> 
>> This seems to be a
>> very typical situation, however I haven't seen any theoretical
>> considerations about it.
> 
> Usually if it's in the signal path it's done to attenuate noise that's
> well above the frequency of interest to keep it from overloading
> following stages, or it's done to modify a stage's high-frequency
> impedance characteristics, or it's done to enhance the circuit's
> stability. 
> 
> Outside the signal path it's done as a matter of course for power
> supply decoupling of sensitive circuits, or for other decoupling.
> 
> Very rarely is it done with the intent of changing the signal's
> behavior in the passband, and when it does the designer can't usually
> get away with claiming that his circuit has a "Butterworth response"
> -- the best he'll be able to do is claim a "modified Butterworth" or
> some such. 
> 
> You do this in the digital domain, too, you just don't think of it in
> the same way.  When you oversample, filter, and decimate, you're doing
> much the same thing as an analog circuit that has a wide-open front
> end followed by a pre-filter and lower-band amplifier.  There are
> other trick that one plays with discrete-time systems that are done
> for design convenience, and justified as not changing the signal too
> much, that have no corresponding technique in the analog world yet are
> done for the same reasons of design convenience.
> 
>> The question is there a canned solution how to make an optimal
>> Butterworth or Chebyshev like filter, but with the several additional
>> real poles?
>> 
> Certainly not that I know of.  The canonical filters are designed so
> that in the continuous-time case you can easily choke the filter
> coefficients out of the math with a slide rule and a pencil.
> 
> I want to make a nice little optimal filter finder in Scilab, for
> times just like this -- I want to be able to tell it the amplitude
> (and possibly phase) constraints, possibly after sampling and
> reconstruction, and have it diddle with coefficients until it comes up
> with the best filter for the job, Butterworth, Gauss and Chebychev be
> damned. 
> 



-- 
Al Clark
Danville Signal Processing, Inc.
--------------------------------------------------------------------
Purveyors of Fine DSP Hardware and other Cool Stuff
Available at http://www.danvillesignal.com

Tim Wescott wrote:
> 
>>The question is there a canned solution how to make an optimal
>>Butterworth or Chebyshev like filter, but with the several additional
>>real poles?
>> 
> Certainly not that I know of.

Then I will try to derive it analytically.

> I want to make a nice little optimal filter finder in Scilab, for times
> just like this -- I want to be able to tell it the amplitude (and possibly
> phase) constraints, possibly after sampling and reconstruction, and have
> it diddle with coefficients until it comes up with the best filter for the
> job, Butterworth, Gauss and Chebychev be damned.

Quite often I have to do it in that way too. The only difference is that 
the optimizer is done in the plain C++. But this is a shamanistic 
approach and it is always better to have the full understanding.

Vladimir Vassilevsky

DSP and Mixed Signal Design Consultant

http://www.abvolt.com

Tim Wescott wrote:


>>However when designing an analog part, it is often possible to stick
>>many additional 1-st order RCs into the schematics.
>>Those realpole RCs can improve the performance without any side
>>effects.
> 
> 
> This is not correct.  There is always a side effect to doing this, the
> only question is whether it's going to be significant enough to matter.  If
> the amplitude rolloff or phase delay from the inserted RC is in a
> frequency band that we care about it must be dealt with.
> 

By the side effects I mean the highly sensitive tolerances and/or the 
weird values of the components. That's what happens if one tries to 
build a higher order filter around one opamp. To the contrary, the first 
order poles are simple and forgiving everything.

Vladimir Vassilevsky

DSP and Mixed Signal Design Consultant

http://www.abvolt.com

Tim Wescott wrote:

   ...

> I want to make a nice little optimal filter finder in Scilab, for times
> just like this -- I want to be able to tell it the amplitude (and possibly
> phase) constraints, possibly after sampling and reconstruction, and have
> it diddle with coefficients until it comes up with the best filter for the
> job, Butterworth, Gauss and Chebychev be damned.

Butterworth, Gauss and Chebychev and the rest are more-or-less 
sophisticated design approaches for approximating desired 
characteristics. The best that can be said for them is that they work 
with tractable math. "Tractable" means a grubby engineer can specify one 
with a slide rule. They share that character with T- and pi section 
filters with M-derived (and double-M-derived) end sections.

Now that we have computers capable of completing a recursive (ala 
Parks-McClellan) approximation faster than I can get my slide rule out 
of its case, they are historically interesting points on a continuum at 
best and obsolete specifications at worst. One could even make a case 
that they are an example of how theory impedes practice.

Jerry
-- 
Engineering is the art of making what you want from things you can get.
¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯

On Sun, 08 Jul 2007 14:03:22 -0500, Tim Wescott <tim@seemywebsite.com>
wrote:

>
>I want to make a nice little optimal filter finder in Scilab, for times
>just like this -- I want to be able to tell it the amplitude (and possibly
>phase) constraints, possibly after sampling and reconstruction, and have
>it diddle with coefficients until it comes up with the best filter for the
>job, Butterworth, Gauss and Chebychev be damned.

Doesn't Parks-McClellan/Remez Exchange do that?

Eric Jacobsen
Minister of Algorithms
Abineau Communications
http://www.ericjacobsen.org

On Jul 8, 11:16 am, "Vladimir Vassilevsky"
<antispam_bo...@hotmail.com> wrote:

> The classic IIR filters have either one or none of the real poles. However
> when designing an analog part, it is often possible to stick many additional
> 1-st order RCs into the schematics. Those realpole RCs can improve the
> performance without any side effects.

Can you please be more specific?  I'm familiar with adding finite
zeros ("loss poles") to standard analog transfer functions to improve
stopband attenuation, but I'm not certain that's what you're
discussing here.

Greg Berchin

Greg Berchin wrote:

>>The classic IIR filters have either one or none of the real poles. However
>>when designing an analog part, it is often possible to stick many additional
>>1-st order RCs into the schematics. Those realpole RCs can improve the
>>performance without any side effects.
> 
> 
> Can you please be more specific?  I'm familiar with adding finite
> zeros ("loss poles") to standard analog transfer functions to improve
> stopband attenuation, but I'm not certain that's what you're
> discussing here.

When designing an analog part which has to do some frequency filtering, 
it is often possible to stick many RCs of the 1st order into it. Those 
RCs come as a "free" addition to the "main" analog filter; they may not 
even require any extra parts. If those RCs are designed correctly, that 
can improve the stopband attenuation and the flatness of the passband.

But I don't know of any analytical approximation for a filter with the 
several real and complex poles.  The common way to deal with that is the 
brute force optimization. That doesn't seem right to me.


> 
> Greg Berchin
> 

VLV

Vladimir Vassilevsky <antispam_bogus@hotmail.com> wrote in news:I0uki.37519
$YL5.37108@newssvr29.news.prodigy.net:

> If those RCs are designed correctly, that 
> can improve the stopband attenuation and the flatness of the passband.
> 

RC's can be hard to design "correctly", as caps have poor tolerance.  I 
don't believe that an RC can improve flatness in the passband.  Of course 
it can improve stopband attenuation, but so can upping the order of your 
filter.  

-- 
Scott
Reverse name to reply