LC ladder filter questions

[Roy McCammon]

OK, is it really the case that many-section LC filters have less
component sensitivity than a cascaded-section, buffered filter of
equivalent transfer function?

yes, on the average

Suppose that you start off with two filters
that implement the same poles and zeroes; one is
in LC ladder and the other is Active biquads.
It should be obvious that if all the L's and C's
are high by exactly 10% then both implementations
produce the same results. But give the components
random changes uniformly distributed over +/- 10%
then the poles of the LC ladder have a smaller
variation.

The explantion that I have heard is that in the
LC ladders multiple components contribute to each
pole, so that each pole tends to see the average
component tolerance. I've run enough spice monte
carlo trials to convince myself its true.

 

[Roy McCammon]

OK, is it really the case that many-section LC filters have less
component sensitivity than a cascaded-section, buffered filter of
equivalent transfer function?

But there is an active filter topology known as the "leap frog"
filter that shares many of the advantages of an LC ladder.

 

[Peter O. Brackett]

John:

[snip]

An explanation! Thank you. :
:
So, one last question: given, say, an 8-pole lossless LC Butterworth
lowpass, would component sensitivities be less if the filter were a
single LC network, as opposed to two cascaded (buffered) 4-poles? Both
cases would seem to satisfy your sensitivity-zero-at-nominal-value
explanation.

John

[snip]

No.

Two cascaded buffered 4-poles would in general have higher
"average" sensitivities than a single 8-pole network.

Nonetheless, even though the two 4-poles design has higher average
sensistivities across the passband, both the 8-pole and the two 4-poles
would indeed have exactly zero sensitivites *at* the reflection zeros which,
since you have chosen the Butterworth approximation, would all occur at the
same frequency. i.e. the spot frequency sensitivities would be the same.

However the average sensitivity across the passband would be higher
in the cascaded 4-pole case.

If you wish to quantify these effects exactly you will find that there are a
couple
of remarkable formuae that give predictions of such sensitivites for doubly
terminated lossless networks.

One such celebrated formula was found by Meyer Blostein and the other by
Gabby Temes and John Orchard.

M. L. Blostein, "Sensitivity analysis of parasitic effects in resistance
terminated LC filters", IEEE Trans. Vol. CT-14, pp.21-25, Mar. 1967.

G. C.Temes and H. J. Orchard, "First order sensitivity and worst-case
analysis of doubly terminated reactance two ports", IEEE Trans. Vol. CT-20,
pp. 567-571, Sept. 1973.

A good account of all of this is given in:

Adel S. Sedra and Peter O. Brackett, "Filter Theory and Design: Active
and Passive", Matrix Publishers, Champaign IL, 1978.

Incidently, it was John Orchard who first put forth the, non-mathematical,
heuristic
argument for the low sensitivity of matched lossless filter networks that I
repeated
in an earlier posting a little further back along this thread.

Regards,

 

[John Larkin]

No.

Two cascaded buffered 4-poles would in general have higher
"average" sensitivities than a single 8-pole network.

Nonetheless, even though the two 4-poles design has higher average
sensistivities across the passband, both the 8-pole and the two 4-poles
would indeed have exactly zero sensitivites *at* the reflection zeros which,
since you have chosen the Butterworth approximation, would all occur at the
same frequency. i.e. the spot frequency sensitivities would be the same.

However the average sensitivity across the passband would be higher
in the cascaded 4-pole case.

If you wish to quantify these effects exactly you will find that there are a
couple
of remarkable formuae that give predictions of such sensitivites for doubly
terminated lossless networks.

One such celebrated formula was found by Meyer Blostein and the other by
Gabby Temes and John Orchard.

M. L. Blostein, "Sensitivity analysis of parasitic effects in resistance
terminated LC filters", IEEE Trans. Vol. CT-14, pp.21-25, Mar. 1967.

G. C.Temes and H. J. Orchard, "First order sensitivity and worst-case
analysis of doubly terminated reactance two ports", IEEE Trans. Vol. CT-20,
pp. 567-571, Sept. 1973.

A good account of all of this is given in:

Adel S. Sedra and Peter O. Brackett, "Filter Theory and Design: Active
and Passive", Matrix Publishers, Champaign IL, 1978.

Incidently, it was John Orchard who first put forth the, non-mathematical,
heuristic
argument for the low sensitivity of matched lossless filter networks that I
repeated
in an earlier posting a little further back along this thread.

Regards,

OK, Peter, thanks.

John

 

[John Larkin]

Probably.......If usenet has done anything it has
shown me that I have a lack of knowlege and little
experience in a number of areas of electronics.

Which is why threads such as this (with expertise
being shown) are so interesting to follow.

*If* you can get the experts to say more than "No" and "You are daft."

John

 

[Tom Bruhns]

...
The explantion that I have heard is that in the
LC ladders multiple components contribute to each
pole, so that each pole tends to see the average
component tolerance. I've run enough spice monte
carlo trials to convince myself its true.

Spice works fine, and perhaps the version you use makes it more
convenient and useful than the one I use, but this is one of the
things I like the freeware RFSim99 for. It's easy to assign a
tolerance to each of the components and run a Monte Carlo analysis,
with a freq. response (and/or return loss) plot building up an
envelope of possible responses. Spice is certainly more flexible,
though. Nice to have both available. And some filter design software
has similar capability.

Cheers,
Tom

 

[Peter O. Brackett]

John:

[snip]

*If* you can get the experts to say more than "No" and "You are daft."

John

[snip]

Jeeeshhhh....

For what you pay for the information on this NG! Be thankful for small
gifts!

BTW... if you had to research and cull out all of the information provided
on this particular
thread by yourself you are probably looking at several months of sole effort
work, providing
you don't come to wrong conclusions!

If you attended a *good* school where the professors actually knew and
taught the stuff
you learned on this thread you would likely have paid up to $20,000 and
taken 12 months
to learn it. Of course you would first have to had gone to the effort to
find a *good* school
where the instructors actually know this particular stuff! There aren't
many!

If you hired an expert consultant, say like myself, my one time retainer and
per diem fees
for this kind of information would have cost you at least a couple of
thousand dollars. Of
course first you would have to go to the effort of finding a qualified and
knowledgeable
consultant with an appropriate track record.

And gee... here you got all this "free" information on lossless LC
ladders...

I know that on the Internet, "information wants to be free"!

But do you really have to "trash" the experts who don't really have to read
questions
and post answers?

For example, the only pay back I get from posting to this NG is the
occasional call usually
from a lurker who actually becomes a client and pays for my services.

I feed my family from "billable hours". Jeesh... my time is valuable, I
don't hang out here
simply to entertain and educate freeloaders!

Especially when they offer only diatribes in return.

"Cool your jets" John.

Regards,

 

[John Woodgate]

I read in sci.electronics.design that Peter O. Brackett <no_such_address
@ix.netcom.com> wrote (in <[email protected]
ink.net>) about 'LC ladder filter questions', on Mon, 12 Apr 2004:

But do you really have to "trash" the experts who don't really have to read
questions
and post answers?

JL is going at the ones who DON'T respond politely. The rule should be,
'If you can't or won't help, DON'T POST.' Unless, of course, you can't
resist a *good* [1] quip, whimsy, gag, etc.

[1] There is no absolute scale of 'good'. Yerron yerrone.

 

[Bill Sloman]

I read in sci.electronics.design that Peter O. Brackett <no_such_address
@ix.netcom.com> wrote (in <[email protected]
ink.net>) about 'LC ladder filter questions', on Mon, 12 Apr 2004:

But do you really have to "trash" the experts who don't really have to read
questions and post answers?

JL is going at the ones who DON'T respond politely. The rule should be,
'If you can't or won't help, DON'T POST.' Unless, of course, you can't
resist a *good* [1] quip, whimsy, gag, etc.

[1] There is no absolute scale of 'good'. Yerron yerrone.

But there are relative scales of "good". Your threshold seems to be
lower than most ....

 

[John Fields]

I read in sci.electronics.design that Peter O. Brackett <no_such_address
@ix.netcom.com> wrote (in <[email protected]
ink.net>) about 'LC ladder filter questions', on Mon, 12 Apr 2004:

But do you really have to "trash" the experts who don't really have to read
questions and post answers?

JL is going at the ones who DON'T respond politely. The rule should be,
'If you can't or won't help, DON'T POST.' Unless, of course, you can't
resist a *good* [1] quip, whimsy, gag, etc.

[1] There is no absolute scale of 'good'. Yerron yerrone.

But there are relative scales of "good". Your threshold seems to be
lower than most ....

 

[Tom Bruhns]

Jeeeshhhh....
...

"Cool your jets" John.

And to reiterate and clarify my earlier post, I've seen plenty of
threads that have gotten very impolite and seldom informative. This
one has been quite a contrast to that, with lots of good ideas.
Peter's have been great, but postings from others have _also_ been
quite useful. Being able to look at a problem several different ways
seems to almost always be helpful, and the postings have helped me do
that. I've been able to pick my battles in solving this one; I could
have done it without asking in the first place, but figured that
someone might have some ways of looking at it that I hadn't
considered. Indeed that's been the case. Too bad there's not a
trivial way to accomplish the task, but just learning that some real
experts don't know any trivial ways was useful in itself. Fortunately
there are several ways to "skin this cat" and the "best" one depends
on the resources available.

Thanks again to all who've posted ideas.

Cheers,
Tom
(thinking it's time for this thread to die now...)

 

[Peter O. Brackett]

Te

John:

[snip]

*If* you can get the experts to say more than "No" and "You are daft."

John

[snip]

Jeeeshhhh....

For what you pay for the information on this NG! Be thankful for small
gifts!

BTW... if you had to research and cull out all of the information provided
on this particular
thread by yourself you are probably looking at several months of sole effort
work, providing
you don't come to wrong conclusions!

If you attended a *good* school where the professors actually knew and
taught the stuff
you learned on this thread you would likely have paid up to $20,000 and
taken 12 months
to learn it. Of course you would first have to had gone to the effort to
find a *good* school
where the instructors actually know this particular stuff! There aren't
many!

If you hired an expert consultant, say like myself, my one time retainer and
per diem fees
for this kind of information would have cost you at least a couple of
thousand dollars. Of
course first you would have to go to the effort of finding a qualified and
knowledgeable
consultant with an appropriate track record.

And gee... here you got all this "free" information on lossless LC
ladders...

I know that on the Internet, "information wants to be free"!

But do you really have to "trash" the experts who don't really have to read
questions
and post answers?

For example, the only pay back I get from posting to this NG is the
occasional call usually
from a lurker who actually becomes a client and pays for my services.

I feed my family from "billable hours". Jeesh... my time is valuable, I
don't hang out here
simply to entertain and educate freeloaders!

Especially when they offer only diatribes in return.

"Cool your jets" John.

Regards,

--
Peter
Freelance Professional Consultant
Signal Processing and Analog Electronics
Indialantic By-the-Sea, FL.

Peter, I for one would like to offer you my thanks for your lucid, and IMHO
excellent, posts on this subject. I certainly have learned from your posts,
(which I have archived) and have done some research (unnecessary but I like
to be thorough) to confirm your statements regarding LC ladder filter
sensitivity. I have written and tested a variety of digital filters, and the
LC ladder-like structures certainly do work best; I have also just recently
completed a redesign for a client, in which I replaced an infinite-gain BPF
(Q=10) with a negative-K sallen-key BPF. The original design missed the
target centre-frequency by about 15% due to finite GBW, and component
tolerance (GBW variation was the worst) caused tremendous changes in
pass-band gain, rendering the overall circuit inoperable.

I didnt even have to figure out the component sensitivity formulae, as its
all been published before, and a little bit of research showed the original
topology was the worst possible choice.....SPICE Monte-Carlo simulations
confirmed this (in order to model GBW i used a laplace block with a
first-order model, and adjusted Aol and Fo manually - changes in Aol made
very little difference (as expected), but changes in Fo were quite dramatic;
the 1st-order model behaved very like the opamp models, but was easier to
modify).

Correcting the original design for nominal GBW didnt help much, although
using $$ 0.1% discretes tamed the design, except for GBW variations....which
a minimum GBW of 20MHz fixed nicely. In this case cost was the driver, so a
lower sensitivity design (higher pass-band gain, lower Q) allowed me to use
a cheaper opamp, and slightly fewer discretes (1% R, 2% C), yet attain much
better performance (over time, temperature and tolerance - the three "T's" )
than the expensive reworked original design.

It would appear that many "designers" dont take the three T's into account
at all, and are thus blissfully unaware of sensitivity analysis.

cheers
Terry

 

[Peter O. Brackett]

Terry:

Great! It's nice to see others appreciate and can use the results of
sensitivity analysis.

Regards,

--
Peter

John:

[snip]

*If* you can get the experts to say more than "No" and "You are daft."

John

[snip]

Jeeeshhhh....

For what you pay for the information on this NG! Be thankful for small
gifts!

BTW... if you had to research and cull out all of the information provided
on this particular
thread by yourself you are probably looking at several months of sole effort
work, providing
you don't come to wrong conclusions!

If you attended a *good* school where the professors actually knew and
taught the stuff
you learned on this thread you would likely have paid up to $20,000 and
taken 12 months
to learn it. Of course you would first have to had gone to the effort to
find a *good* school
where the instructors actually know this particular stuff! There aren't
many!

If you hired an expert consultant, say like myself, my one time retainer and
per diem fees
for this kind of information would have cost you at least a couple of
thousand dollars. Of
course first you would have to go to the effort of finding a qualified and
knowledgeable
consultant with an appropriate track record.

And gee... here you got all this "free" information on lossless LC
ladders...

I know that on the Internet, "information wants to be free"!

But do you really have to "trash" the experts who don't really have to read
questions
and post answers?

For example, the only pay back I get from posting to this NG is the
occasional call usually
from a lurker who actually becomes a client and pays for my services.

I feed my family from "billable hours". Jeesh... my time is valuable, I
don't hang out here
simply to entertain and educate freeloaders!

Especially when they offer only diatribes in return.

"Cool your jets" John.

Regards,

--
Peter
Freelance Professional Consultant
Signal Processing and Analog Electronics
Indialantic By-the-Sea, FL.

Peter, I for one would like to offer you my thanks for your lucid, and IMHO
excellent, posts on this subject. I certainly have learned from your posts,
(which I have archived) and have done some research (unnecessary but I like
to be thorough) to confirm your statements regarding LC ladder filter
sensitivity. I have written and tested a variety of digital filters, and the
LC ladder-like structures certainly do work best; I have also just recently
completed a redesign for a client, in which I replaced an infinite-gain BPF
(Q=10) with a negative-K sallen-key BPF. The original design missed the
target centre-frequency by about 15% due to finite GBW, and component
tolerance (GBW variation was the worst) caused tremendous changes in
pass-band gain, rendering the overall circuit inoperable.

I didnt even have to figure out the component sensitivity formulae, as its
all been published before, and a little bit of research showed the original
topology was the worst possible choice.....SPICE Monte-Carlo simulations
confirmed this (in order to model GBW i used a laplace block with a
first-order model, and adjusted Aol and Fo manually - changes in Aol made
very little difference (as expected), but changes in Fo were quite dramatic;
the 1st-order model behaved very like the opamp models, but was easier to
modify).

Correcting the original design for nominal GBW didnt help much, although
using $$ 0.1% discretes tamed the design, except for GBW variations....which
a minimum GBW of 20MHz fixed nicely. In this case cost was the driver, so a
lower sensitivity design (higher pass-band gain, lower Q) allowed me to use
a cheaper opamp, and slightly fewer discretes (1% R, 2% C), yet attain much
better performance (over time, temperature and tolerance - the three "T's" )
than the expensive reworked original design.

It would appear that many "designers" dont take the three T's into account
at all, and are thus blissfully unaware of sensitivity analysis.

cheers
Terry

 

[John Larkin]

John:

[snip]

*If* you can get the experts to say more than "No" and "You are daft."

John

[snip]

Jeeeshhhh....

For what you pay for the information on this NG! Be thankful for small
gifts!

I probably answer 5 or 10 questions here for each one that I ask. But
I don't answer with monosyllables, or tell people "go Monte Carlo the
circuits and see for yourself". I try to be helpful. Hell, I send
people parts. And beer. And grits. And I post some great recipes.

BTW... if you had to research and cull out all of the information provided
on this particular
thread by yourself you are probably looking at several months of sole effort
work, providing
you don't come to wrong conclusions!

If you attended a *good* school where the professors actually knew and
taught the stuff
you learned on this thread you would likely have paid up to $20,000 and
taken 12 months
to learn it. Of course you would first have to had gone to the effort to
find a *good* school
where the instructors actually know this particular stuff! There aren't
many!

If you hired an expert consultant, say like myself, my one time retainer and
per diem fees
for this kind of information would have cost you at least a couple of
thousand dollars. Of
course first you would have to go to the effort of finding a qualified and
knowledgeable
consultant with an appropriate track record.

And gee... here you got all this "free" information on lossless LC
ladders...

I know that on the Internet, "information wants to be free"!

But do you really have to "trash" the experts who don't really have to read
questions
and post answers?

I didn't trash your useful explanation, I said "thanks."

For example, the only pay back I get from posting to this NG is the
occasional call usually
from a lurker who actually becomes a client and pays for my services.

If you want to make a lot of money, I sincerely suggest you avoid
watching TV or playing on newsgroups. I consider this to be goofing
off.

I feed my family from "billable hours". Jeesh... my time is valuable, I
don't hang out here
simply to entertain and educate freeloaders!

Freeloaders? Unavoidable. The whole world can read this newsgroup.

Especially when they offer only diatribes in return.

Like "thanks"?

"Cool your jets" John.

I am cool. Geez, this is only a newsgroup; it doesn't matter.

Wanna try some grits? Grits matters.

John

 

[John Jardine]

John:

[snip]

*If* you can get the experts to say more than "No" and "You are daft."

John [snip]

Jeeeshhhh....

[snip]
For example, the only pay back I get from posting to this NG is the
occasional call usually
from a lurker who actually becomes a client and pays for my services.

I feed my family from "billable hours". Jeesh... my time is valuable, I
don't hang out here
simply to entertain and educate freeloaders!

Especially when they offer only diatribes in return.

"Cool your jets" John.

Regards,

--
Peter
Freelance Professional Consultant
Signal Processing and Analog Electronics
Indialantic By-the-Sea, FL.

Surely there's more noble rewards in this short life of ours than money?.
I get lots of payback from these groups but it's in terms of specialist
knowledge and general amusement, given freely, by the likes of JL and many
others.
Indeed, the groups are exactly that; just places to 'hang out'. It's the
random influx of different people, ideas, attitudes wot makes life worth
savouring.
regards
john

 

[John Woodgate]

I read in sci.electronics.design that Bill Sloman <[email protected]>

But there are relative scales of "good". Your threshold seems to be
lower than most ....

That's just your miserable opinion.

 

[Peter O. Brackett]

John:

Even though I was not born in Dixie I consider myself an
adopted Southerner. I have lived in the deep South lo these
many years, and...

Hey I love grits, don't trash grits!

Do you do "hominy" as well?

Now there's a great question for another thread.

What exactly is the difference between hominy and grits?

And why is the soil in Alabama red?

Bye ya'll...

--
Peter

John:

[snip]

*If* you can get the experts to say more than "No" and "You are daft."

John

[snip]

Jeeeshhhh....

For what you pay for the information on this NG! Be thankful for small
gifts!

I probably answer 5 or 10 questions here for each one that I ask. But
I don't answer with monosyllables, or tell people "go Monte Carlo the
circuits and see for yourself". I try to be helpful. Hell, I send
people parts. And beer. And grits. And I post some great recipes.

BTW... if you had to research and cull out all of the information provided
on this particular
thread by yourself you are probably looking at several months of sole effort
work, providing
you don't come to wrong conclusions!

If you attended a *good* school where the professors actually knew and
taught the stuff
you learned on this thread you would likely have paid up to $20,000 and
taken 12 months
to learn it. Of course you would first have to had gone to the effort to
find a *good* school
where the instructors actually know this particular stuff! There aren't
many!

If you hired an expert consultant, say like myself, my one time retainer and
per diem fees
for this kind of information would have cost you at least a couple of
thousand dollars. Of
course first you would have to go to the effort of finding a qualified and
knowledgeable
consultant with an appropriate track record.

And gee... here you got all this "free" information on lossless LC
ladders...

I know that on the Internet, "information wants to be free"!

But do you really have to "trash" the experts who don't really have to read
questions
and post answers?

I didn't trash your useful explanation, I said "thanks."

For example, the only pay back I get from posting to this NG is the
occasional call usually
from a lurker who actually becomes a client and pays for my services.

If you want to make a lot of money, I sincerely suggest you avoid
watching TV or playing on newsgroups. I consider this to be goofing
off.

I feed my family from "billable hours". Jeesh... my time is valuable, I
don't hang out here
simply to entertain and educate freeloaders!

Freeloaders? Unavoidable. The whole world can read this newsgroup.

Especially when they offer only diatribes in return.

Like "thanks"?

"Cool your jets" John.

I am cool. Geez, this is only a newsgroup; it doesn't matter.

Wanna try some grits? Grits matters.

John

 

[John Woodgate]

I read in sci.electronics.design that Peter O. Brackett <no_such_address
@ix.netcom.com> wrote (in <[email protected]
ink.net>) about 'LC ladder filter questions', on Tue, 13 Apr 2004:

And why is the soil in Alabama red?

Let us hope that it is due to the iron content, not arsenic or mercury!

 

[Bill Sloman]

I read in sci.electronics.design that Peter O. Brackett <no_such_address
@ix.netcom.com> wrote (in <[email protected]
ink.net>) about 'LC ladder filter questions', on Mon, 12 Apr 2004:

But do you really have to "trash" the experts who don't really have to
read questions and post answers?

JL is going at the ones who DON'T respond politely. The rule should be,
'If you can't or won't help, DON'T POST.' Unless, of course, you can't
resist a *good* [1] quip, whimsy, gag, etc.

[1] There is no absolute scale of 'good'. Yerron yerrone.

But there are relative scales of "good". Your threshold seems to be
lower than most ....

Not true. About 10% of John Woodgate's quips, whimsys and gags and
gags are genuinely funny - which puts him streets ahead of you - but
the others are no more than semi-plausible excuses for wit.

 

[Bill Sloman]

I read in sci.electronics.design that Bill Sloman <[email protected]>


That's just your miserable opinion.

I'm certainly more miserly than you in my judgment of the comic value
of your quips, whimsys and gags. You do come up with some genuinely
comic comments, but you strike out more often than not. Other posters,
who try for comedy less often, do seem to achieve a better batting
average - Spehro Pefhany comes to mind.