|
There is quite a lot of literature and software for designing filters using idealized xtals, but so far as I can find, no one has presented selecting which N xtals from a set of P xtals will best match a specified N pole response. All the treatments I've found use the N xtals which most closely match the idealized design values.
A VNA makes measuring the phase and amplitude response of xtals very simple. And the nanoVNA has made it cheap. This suggests simply multiplying the transfer functions of each possible section and using linear programming to solve for the set of N of P xtals which most closely give the desired response. The general term for this is "basis pursuit".
Though NP hard on the surface, in fact, the optimal (L0) choice can be computed in L1 time using linear programming. David Donoho of Stanford proved this in 2004. L0 is combinatorially intractable. L1 is more easily handled, even very large problems which would be combinatorially impossible.
Does anyone know of prior work on selecting which of a set of measured xtals will most closely match the required amplitude and phase response?
Have Fun!
Reg
|
Reg,
I apologize for this being off topic.?
I am afraid I cannot be of any help with the design of crystal filters as my only experience with them has been to use a resistance-loaded 100 MHz crystal to clean up sub-harmonics from a multiplier.? However, when you mentioned "linear programming," a long standing question came to mind.? By linear programming are you referring to the methods utilized for business computations such as finding approximations to the Traveling Salesman problem?? Or you talking about linear algebra.
I was an engineer in an earlier life and later went back to school for a business degree.? There we learned to use linear programming methods -? first computational and graphical, then a computer program, to solve various business problems and to perform optimizations.? I never really understood the underlying theory behind these business methods as they did not involve matrices, yet the school I attended required competence in linear algebra and calculus for entry.
Regards,
Bruce, KG6OJI?
-----Original Message-----
From: Reginald Beardsley via groups.io <pulaskite@...>
To: [email protected]; [email protected]
Sent: Sat, Jun 12, 2021 11:41 am
Subject: [qex] Optimal Crystal Filter Design
There is quite a lot of literature and software for designing filters using idealized xtals, but so far as I can find, no one has presented selecting which N? xtals from a set of P xtals will best match a specified N pole response. All the treatments I've found use the N xtals which most closely match the idealized design values.
A VNA makes measuring the phase and amplitude response of xtals very simple.? And the nanoVNA has made it cheap.? This suggests simply multiplying the transfer functions of each possible? section and using linear programming to solve for the set of N of P xtals which most closely give the desired response.? The general term for this is "basis pursuit".
Though NP hard on the surface, in fact, the optimal (L0) choice can be computed in L1 time using linear programming.? David Donoho of Stanford proved this in 2004. L0 is combinatorially intractable. L1 is more easily handled,? even very large problems which would be combinatorially impossible.
Does anyone know of prior work on selecting which of a set of measured xtals will most closely match the required amplitude and phase response?
Have Fun!
Reg
|
Yes, I am talking about linear programming as developed by Dantzig in the late 40's for solving logistical problems for USAF. Lots of linear algebra, but quite a lot more. It is Traveling Salesman and family territory.
I consider the work by Donoho and Candes in 2004-2008 the biggest advance in applied mathematics since Wiener, Shannon et al.
The paper linked below is the best description I know of. Unfortunately, this paper moves around a *lot*! The Introduction is all you need to read to grasp what it's about. The mathematics are the gnarliest stuff I ever read. In all I spent 3 years reading 3000 pages. But it is absolutely amazing what you can do.
https://stacks.stanford.edu/file/druid:qg769wc9289/2004-09.pdf
Have Fun!
Reg
On Saturday, June 12, 2021, 02:38:17 PM CDT, ebrucehunter via groups.io <brucekareen@...> wrote:
Reg,
I apologize for this being off topic.?
I am afraid I cannot be of any help with the design of crystal filters as my only experience with them has been to use a resistance-loaded 100 MHz crystal to clean up sub-harmonics from a multiplier.? However, when you mentioned "linear programming," a long standing question came to mind.? By linear programming are you referring to the methods utilized for business computations such as finding approximations to the Traveling Salesman problem?? Or you talking about linear algebra.
I was an engineer in an earlier life and later went back to school for a business degree.? There we learned to use linear programming methods -? first computational and graphical, then a computer program, to solve various business problems and to perform optimizations.? I never really understood the underlying theory behind these business methods as they did not involve matrices, yet the school I attended required competence in linear algebra and calculus for entry.
Regards,
Bruce, KG6OJI?
-----Original Message----- From: Reginald Beardsley via groups.io <pulaskite@...> To: [email protected]; [email protected]Sent: Sat, Jun 12, 2021 11:41 am Subject: [qex] Optimal Crystal Filter Design There is quite a lot of literature and software for designing filters using idealized xtals, but so far as I can find, no one has presented selecting which N? xtals from a set of P xtals will best match a specified N pole response. All the treatments I've found use the N xtals which most closely match the idealized design values.
A VNA makes measuring the phase and amplitude response of xtals very simple.? And the nanoVNA has made it cheap.? This suggests simply multiplying the transfer functions of each possible? section and using linear programming to solve for the set of N of P xtals which most closely give the desired response.? The general term for this is "basis pursuit".
Though NP hard on the surface, in fact, the optimal (L0) choice can be computed in L1 time using linear programming.? David Donoho of Stanford proved this in 2004. L0 is combinatorially intractable. L1 is more easily handled,? even very large problems which would be combinatorially impossible.
Does anyone know of prior work on selecting which of a set of measured xtals will most closely match the required amplitude and phase response?
Have Fun!
Reg
|
Thanks Reg,
Perhaps the link you furnished will provide more insight.? I always felt there was a big gap between linear algebra,? and the linear programming used in business applications.? Because of complexity, the mathematical underpinnings of linear programming might not be covered in business courses.? I sense some professors teaching its use might not thoroughly understand what is going on either.
Regards,
Bruce, KG6OJI
-----Original Message-----
From: Reginald Beardsley via groups.io <pulaskite@...>
To: [email protected]
Sent: Sat, Jun 12, 2021 12:52 pm
Subject: Re: [qex] Optimal Crystal Filter Design
Yes, I am talking about linear programming as developed by Dantzig in the late 40's for solving logistical problems for USAF. Lots of linear algebra, but quite a lot more. It is Traveling Salesman and family territory.
I consider the work by Donoho and Candes in 2004-2008 the biggest advance in applied mathematics since Wiener, Shannon et al.
The paper linked below is the best description I know of. Unfortunately, this paper moves around a *lot*! The Introduction is all you need to read to grasp what it's about. The mathematics are the gnarliest stuff I ever read. In all I spent 3 years reading 3000 pages. But it is absolutely amazing what you can do.
https://stacks.stanford.edu/file/druid:qg769wc9289/2004-09.pdf
Have Fun!
Reg
On Saturday, June 12, 2021, 02:38:17 PM CDT, ebrucehunter via groups.io <brucekareen@...> wrote:
Reg,
I apologize for this being off topic.?
I am afraid I cannot be of any help with the design of crystal filters as my only experience with them has been to use a resistance-loaded 100 MHz crystal to clean up sub-harmonics from a multiplier.? However, when you mentioned "linear programming," a long standing question came to mind.? By linear programming are you referring to the methods utilized for business computations such as finding approximations to the Traveling Salesman problem?? Or you talking about linear algebra.
I was an engineer in an earlier life and later went back to school for a business degree.? There we learned to use linear programming methods -? first computational and graphical, then a computer program, to solve various business problems and to perform optimizations.? I never really understood the underlying theory behind these business methods as they did not involve matrices, yet the school I attended required competence in linear algebra and calculus for entry.
Regards,
Bruce, KG6OJI?
-----Original Message----- From: Reginald Beardsley via groups.io <pulaskite@...> To: [email protected]; [email protected]Sent: Sat, Jun 12, 2021 11:41 am Subject: [qex] Optimal Crystal Filter Design
There is quite a lot of literature and software for designing filters using idealized xtals, but so far as I can find, no one has presented selecting which N? xtals from a set of P xtals will best match a specified N pole response. All the treatments I've found use the N xtals which most closely match the idealized design values.
A VNA makes measuring the phase and amplitude response of xtals very simple.? And the nanoVNA has made it cheap.? This suggests simply multiplying the transfer functions of each possible? section and using linear programming to solve for the set of N of P xtals which most closely give the desired response.? The general term for this is "basis pursuit".
Though NP hard on the surface, in fact, the optimal (L0) choice can be computed in L1 time using linear programming.? David Donoho of Stanford proved this in 2004. L0 is combinatorially intractable. L1 is more easily handled,? even very large problems which would be combinatorially impossible.
Does anyone know of prior work on selecting which of a set of measured xtals will most closely match the required amplitude and phase response?
Have Fun!
Reg
|
I use the simplex solver in GLPK, the Gnu Linear Programming Kit with arbitrary precision arithmetic. I cannot recommend it more highly. Linear algebra is the means. The difference just is the problem formulation. GLPK is incredibly robust and reliable.
I stumbled into this inverting, with spectacular results, the heat equation via basis pursuit to analyze fluid flow in porous media. Then one day I realized I'd been taught this was impossible. I *had* to understand how this was possible. Boy, was I in trouble!
I understand how to do this. I'm asking because I don't want to reinvent the wheel. Before I do it, I want to investigate if it's been done. If it has, I'll evaluate that to see what else might be needed. I'm used to working on other people's code. If not, I'll write a program to generate the GMPL input files with equations and the xtal data. It's been several years, but if I figured it out once, I can do it again. GMPL is a variant of AMPL. Similar, but not exactly the same.
The basic problem is an iterated multiplication, aka Shah function. That can be treated via linear programming as the sum of logarithms.
I'd like to point out that selecting sets of N xtals from P xtals to make a set of M filters that gives the best average performance is not a big step. The cost is really just machine time, which is very cheap. This has value far beyond xtal filters. If incoming test is necessary, this is a general solution to optimizing small batch production where tolerances matter.
Have Fun!
Reg
On Saturday, June 12, 2021, 05:11:12 PM CDT, ebrucehunter via groups.io <brucekareen@...> wrote:
Thanks Reg,
Perhaps the link you furnished will provide more insight.? I always felt there was a big gap between linear algebra,? and the linear programming used in business applications.? Because of complexity, the mathematical underpinnings of linear programming might not be covered in business courses.? I sense some professors teaching its use might not thoroughly understand what is going on either.
Regards,
Bruce, KG6OJI
-----Original Message----- From: Reginald Beardsley via groups.io <pulaskite@...> To: [email protected]Sent: Sat, Jun 12, 2021 12:52 pm Subject: Re: [qex] Optimal Crystal Filter Design Yes, I am talking about linear programming as developed by Dantzig in the late 40's for solving logistical problems for USAF. Lots of linear algebra, but quite a lot more. It is Traveling Salesman and family territory.
I consider the work by Donoho and Candes in 2004-2008 the biggest advance in applied mathematics since Wiener, Shannon et al.
The paper linked below is the best description I know of. Unfortunately, this paper moves around a *lot*! The Introduction is all you need to read to grasp what it's about. The mathematics are the gnarliest stuff I ever read. In all I spent 3 years reading 3000 pages. But it is absolutely amazing what you can do.
https://stacks.stanford.edu/file/druid:qg769wc9289/2004-09.pdf
Have Fun!
Reg
On Saturday, June 12, 2021, 02:38:17 PM CDT, ebrucehunter via groups.io <brucekareen@...> wrote:
Reg,
I apologize for this being off topic.?
I am afraid I cannot be of any help with the design of crystal filters as my only experience with them has been to use a resistance-loaded 100 MHz crystal to clean up sub-harmonics from a multiplier.? However, when you mentioned "linear programming," a long standing question came to mind.? By linear programming are you referring to the methods utilized for business computations such as finding approximations to the Traveling Salesman problem?? Or you talking about linear algebra.
I was an engineer in an earlier life and later went back to school for a business degree.? There we learned to use linear programming methods -? first computational and graphical, then a computer program, to solve various business problems and to perform optimizations.? I never really understood the underlying theory behind these business methods as they did not involve matrices, yet the school I attended required competence in linear algebra and calculus for entry.
Regards,
Bruce, KG6OJI?
-----Original Message----- From: Reginald Beardsley via groups.io <pulaskite@...> To: [email protected]; [email protected]Sent: Sat, Jun 12, 2021 11:41 am Subject: [qex] Optimal Crystal Filter Design There is quite a lot of literature and software for designing filters using idealized xtals, but so far as I can find, no one has presented selecting which N? xtals from a set of P xtals will best match a specified N pole response. All the treatments I've found use the N xtals which most closely match the idealized design values.
A VNA makes measuring the phase and amplitude response of xtals very simple.? And the nanoVNA has made it cheap.? This suggests simply multiplying the transfer functions of each possible? section and using linear programming to solve for the set of N of P xtals which most closely give the desired response.? The general term for this is "basis pursuit".
Though NP hard on the surface, in fact, the optimal (L0) choice can be computed in L1 time using linear programming.? David Donoho of Stanford proved this in 2004. L0 is combinatorially intractable. L1 is more easily handled,? even very large problems which would be combinatorially impossible.
Does anyone know of prior work on selecting which of a set of measured xtals will most closely match the required amplitude and phase response?
Have Fun!
Reg
|
Reg,
Your certainly right about the value of Donoho's introduction.? I can now think of Linear Programming as a method of dealing with problems where you have fewer equations than unknowns.
Thanks again,
Bruce
-----Original Message-----
From: Reginald Beardsley via groups.io <pulaskite@...>
To: [email protected]
Sent: Sat, Jun 12, 2021 12:52 pm
Subject: Re: [qex] Optimal Crystal Filter Design
Yes, I am talking about linear programming as developed by Dantzig in the late 40's for solving logistical problems for USAF. Lots of linear algebra, but quite a lot more. It is Traveling Salesman and family territory.
I consider the work by Donoho and Candes in 2004-2008 the biggest advance in applied mathematics since Wiener, Shannon et al.
The paper linked below is the best description I know of. Unfortunately, this paper moves around a *lot*! The Introduction is all you need to read to grasp what it's about. The mathematics are the gnarliest stuff I ever read. In all I spent 3 years reading 3000 pages. But it is absolutely amazing what you can do.
https://stacks.stanford.edu/file/druid:qg769wc9289/2004-09.pdf
Have Fun!
Reg
On Saturday, June 12, 2021, 02:38:17 PM CDT, ebrucehunter via groups.io <brucekareen@...> wrote:
Reg,
I apologize for this being off topic.?
I am afraid I cannot be of any help with the design of crystal filters as my only experience with them has been to use a resistance-loaded 100 MHz crystal to clean up sub-harmonics from a multiplier.? However, when you mentioned "linear programming," a long standing question came to mind.? By linear programming are you referring to the methods utilized for business computations such as finding approximations to the Traveling Salesman problem?? Or you talking about linear algebra.
I was an engineer in an earlier life and later went back to school for a business degree.? There we learned to use linear programming methods -? first computational and graphical, then a computer program, to solve various business problems and to perform optimizations.? I never really understood the underlying theory behind these business methods as they did not involve matrices, yet the school I attended required competence in linear algebra and calculus for entry.
Regards,
Bruce, KG6OJI?
-----Original Message----- From: Reginald Beardsley via groups.io <pulaskite@...> To: [email protected]; [email protected]Sent: Sat, Jun 12, 2021 11:41 am Subject: [qex] Optimal Crystal Filter Design
There is quite a lot of literature and software for designing filters using idealized xtals, but so far as I can find, no one has presented selecting which N? xtals from a set of P xtals will best match a specified N pole response. All the treatments I've found use the N xtals which most closely match the idealized design values.
A VNA makes measuring the phase and amplitude response of xtals very simple.? And the nanoVNA has made it cheap.? This suggests simply multiplying the transfer functions of each possible? section and using linear programming to solve for the set of N of P xtals which most closely give the desired response.? The general term for this is "basis pursuit".
Though NP hard on the surface, in fact, the optimal (L0) choice can be computed in L1 time using linear programming.? David Donoho of Stanford proved this in 2004. L0 is combinatorially intractable. L1 is more easily handled,? even very large problems which would be combinatorially impossible.
Does anyone know of prior work on selecting which of a set of measured xtals will most closely match the required amplitude and phase response?
Have Fun!
Reg
|
I believe I had that in a course in Number Theory and as I recall it was called Diophantine equations. Regardless, crystal filters have been around long before linear programing or even ready to use computers for that matter. Yet, they were able to achieve excellent results. Even making filters for 455 KHz using military surplus crystals did a great job. While I appreciate the math and the use of it to optimize, is it necessary, or even needed? 73 ¨C Mike ? Mike B. Feher, N4FS 89 Arnold Blvd. Howell NJ 07731 848-245-9115 ?
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From: [email protected] < [email protected]> On Behalf Of ebrucehunter via groups.io Sent: Sunday, June 13, 2021 12:39 PM To: [email protected]Subject: Re: [qex] Optimal Crystal Filter Design ? Your certainly right about the value of Donoho's introduction.? I can now think of Linear Programming as a method of dealing with problems where you have fewer equations than unknowns. -----Original Message-----
From: Reginald Beardsley via groups.io <pulaskite@...>
To: [email protected]
Sent: Sat, Jun 12, 2021 12:52 pm
Subject: Re: [qex] Optimal Crystal Filter Design Yes, I am talking about linear programming as developed by Dantzig in the late 40's for solving logistical problems for USAF. Lots of linear algebra, but quite a lot more. It is Traveling Salesman and family territory.
I consider the work by Donoho and Candes in 2004-2008 the biggest advance in applied mathematics since Wiener, Shannon et al.
The paper linked below is the best description I know of. Unfortunately, this paper moves around a *lot*! The Introduction is all you need to read to grasp what it's about. The mathematics are the gnarliest stuff I ever read. In all I spent 3 years reading 3000 pages. But it is absolutely amazing what you can do.
Have Fun!
Reg On Saturday, June 12, 2021, 02:38:17 PM CDT, ebrucehunter via groups.io <brucekareen@...> wrote: I apologize for this being off topic.? I am afraid I cannot be of any help with the design of crystal filters as my only experience with them has been to use a resistance-loaded 100 MHz crystal to clean up sub-harmonics from a multiplier.? However, when you mentioned "linear programming," a long standing question came to mind.? By linear programming are you referring to the methods utilized for business computations such as finding approximations to the Traveling Salesman problem?? Or you talking about linear algebra. I was an engineer in an earlier life and later went back to school for a business degree.? There we learned to use linear programming methods -? first computational and graphical, then a computer program, to solve various business problems and to perform optimizations.? I never really understood the underlying theory behind these business methods as they did not involve matrices, yet the school I attended required competence in linear algebra and calculus for entry. -----Original Message-----
From: Reginald Beardsley via groups.io <pulaskite@...>
To: [email protected]; [email protected]
Sent: Sat, Jun 12, 2021 11:41 am
Subject: [qex] Optimal Crystal Filter Design There is quite a lot of literature and software for designing filters using idealized xtals, but so far as I can find, no one has presented selecting which N? xtals from a set of P xtals will best match a specified N pole response. All the treatments I've found use the N xtals which most closely match the idealized design values. A VNA makes measuring the phase and amplitude response of xtals very simple.? And the nanoVNA has made it cheap.? This suggests simply multiplying the transfer functions of each possible? section and using linear programming to solve for the set of N of P xtals which most closely give the desired response.? The general term for this is "basis pursuit". Though NP hard on the surface, in fact, the optimal (L0) choice can be computed in L1 time using linear programming.? David Donoho of Stanford proved this in 2004. L0 is combinatorially intractable. L1 is more easily handled,? even very large problems which would be combinatorially impossible. Does anyone know of prior work on selecting which of a set of measured xtals will most closely match the required amplitude and phase response?
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It's quite different from Diophantine equations which impose the constraint that only integer values are allowed. That would make no sense in the context of filter design.
The advantage is optimal use of the parts you have as opposed to requiring optimal parts which you do not have.
I've not yet built an 8-12 pole xtal filter, but everything I've read suggests they get "interesting" when you have that many poles. I bought 100 40 MHz 3rd overtone xtals for $10 long ago with the intent of using them for a high order xtal filter.
Have Fun!
Reg
On Sunday, June 13, 2021, 11:54:20 AM CDT, Mike Feher <n4fs@...> wrote:
I believe I had that in a course in Number Theory and as I recall it was called Diophantine equations. Regardless, crystal filters have been around long before linear programing or even ready to use computers for that matter. Yet, they were able to achieve excellent results. Even making filters for 455 KHz using military surplus crystals did a great job. While I appreciate the math and the use of it to optimize, is it necessary, or even needed? 73 ¨C Mike ? Mike B. Feher, N4FS 89 Arnold Blvd. Howell NJ 07731 848-245-9115 ?
From: [email protected] < [email protected]> On Behalf Of ebrucehunter via groups.io Sent: Sunday, June 13, 2021 12:39 PM To: [email protected]Subject: Re: [qex] Optimal Crystal Filter Design ? Your certainly right about the value of Donoho's introduction.? I can now think of Linear Programming as a method of dealing with problems where you have fewer equations than unknowns. -----Original Message-----
From: Reginald Beardsley via groups.io <pulaskite@...>
To: [email protected]
Sent: Sat, Jun 12, 2021 12:52 pm
Subject: Re: [qex] Optimal Crystal Filter Design Yes, I am talking about linear programming as developed by Dantzig in the late 40's for solving logistical problems for USAF. Lots of linear algebra, but quite a lot more. It is Traveling Salesman and family territory.
I consider the work by Donoho and Candes in 2004-2008 the biggest advance in applied mathematics since Wiener, Shannon et al.
The paper linked below is the best description I know of. Unfortunately, this paper moves around a *lot*! The Introduction is all you need to read to grasp what it's about. The mathematics are the gnarliest stuff I ever read. In all I spent 3 years reading 3000 pages. But it is absolutely amazing what you can do.
Have Fun!
Reg On Saturday, June 12, 2021, 02:38:17 PM CDT, ebrucehunter via groups.io <brucekareen@...> wrote: I apologize for this being off topic.? I am afraid I cannot be of any help with the design of crystal filters as my only experience with them has been to use a resistance-loaded 100 MHz crystal to clean up sub-harmonics from a multiplier.? However, when you mentioned "linear programming," a long standing question came to mind.? By linear programming are you referring to the methods utilized for business computations such as finding approximations to the Traveling Salesman problem?? Or you talking about linear algebra. I was an engineer in an earlier life and later went back to school for a business degree.? There we learned to use linear programming methods -? first computational and graphical, then a computer program, to solve various business problems and to perform optimizations.? I never really understood the underlying theory behind these business methods as they did not involve matrices, yet the school I attended required competence in linear algebra and calculus for entry. -----Original Message-----
From: Reginald Beardsley via groups.io <pulaskite@...>
To: [email protected]; [email protected]
Sent: Sat, Jun 12, 2021 11:41 am
Subject: [qex] Optimal Crystal Filter Design There is quite a lot of literature and software for designing filters using idealized xtals, but so far as I can find, no one has presented selecting which N? xtals from a set of P xtals will best match a specified N pole response. All the treatments I've found use the N xtals which most closely match the idealized design values. A VNA makes measuring the phase and amplitude response of xtals very simple.? And the nanoVNA has made it cheap.? This suggests simply multiplying the transfer functions of each possible? section and using linear programming to solve for the set of N of P xtals which most closely give the desired response.? The general term for this is "basis pursuit". Though NP hard on the surface, in fact, the optimal (L0) choice can be computed in L1 time using linear programming.? David Donoho of Stanford proved this in 2004. L0 is combinatorially intractable. L1 is more easily handled,? even very large problems which would be combinatorially impossible. Does anyone know of prior work on selecting which of a set of measured xtals will most closely match the required amplitude and phase response?
|
ebrucehunter