On 03/09/2015 05:44 AM, dakupoto@gmail.com wrote:> On Friday, March 6, 2015 at 7:53:48 AM UTC-5, Robert Macy wrote: >> On Fri, 06 Mar 2015 00:37:19 -0700, <dakupoto@gmail.com> wrote: >> >>>> ....snip.... >>> The basic scheme the author has followed is to >>> use the frequency plane(s = jw) expressions for >>> conductance, impedance, inductance, resistance >>> and propagation constant and then take the >>> inverse transform of these quantities in the >>> SPICE code. This is perfectly fine in theory, >>> because any complex expression may be split up >>> in a partial fractions expansion, and then the >>> inverse Laplace transform of each of these can >>> parts may be obtained. >>> The problem starts when one considers the s=plane >>> expressions for impedance and propagation >>> constant -- BOTH have square roots. And as far >>> as I could see from my trusty copy of Abramovich >>> and Stegun, BOTH forward and backward Laplace >>> transforms for expressions with positive >>> fractional exponents do not exist !!! >>> For example, the s-plane expression for the >>> frequency dependent resistance is: >>> R(w) = Rdc(1 + (w/Wr)^2))^0.25 >>> So how is the LTSpice engine going to evaluate >>> the inverse transform for this expression ? >>> In my humble opinion, a frequency plane solution >>> with a simple C/C++ module with the input signal >>> frequency being increased incrementally would provide a lot better >>> solution -- I await each of >>> your comments on this. >>> >> >> The last time I used a SPICE model with a 'frequency' term and tried to do >> a really useful analysis, like try to observe the expected change to the >> digital square wave, or obtain a useful set of 'eye patterns' for Error >> Rate Detection values; the analysis went from step, step, ..step.., >> ....step....., to predicting it might not finish in my lifetime, Stopping >> the analysis before anywhere nearly completed, it added insult to injury, >> the results had wild variations of error. so... >> >> I now make my OWN transmission line models using lumped models in small >> enough sections the error at maximum frequency [as caused by minimum >> risetime] PLUS, and this has been illuminating in understanding EMC >> emanations off a cable, it is possible to include 'free space' and >> actually estimate radiation from circuitry in a system that is not >> properly done. >> >> How to do Skin effect? I found that around 5 sets of elements, configured >> like eddy current models, inductor parallel with resistor feeding parallel >> inductor, etc can be made to pretty accurately 'curve fit' the resistance >> vs frequency, and a few more terms will even yield fairly accurate 'phase' >> shift from skin effects. [Note technique pretty accurately models those >> lossy RF Beads, somewhere I have a set of models for commercially >> available parts that are good to 1GHz, some beyond.] The advanatage of >> keeping the model frequency independent is that the model can be used for >> either .ac or .tran analyses. And, not take several days to RUN. >> >> Now, applied to transission lines, the model has conductor inductance and >> loss, return path inductance and loss [usually left out of lossy models], >> capacitance between conductor and return path, dielectric loss, AND the >> coupling [also left out of most models] which makes coax and twisted pair >> so desirable to use. At least with such a model you KNOW what's inside it. >> >> Also, you can really get to 'see' the dispersion in a cable. put in a step >> and watch the value step then 'slide' up to where it's supposed to go. >> >> The FREE PC Tools to create these models: femm 4.2; octave [Matlab clone]; >> and LTspice. [Of note, Mike Engelhardt, creator of LTspice, placed inside >> LTspice an 'array' function, which Alex Bordodynov has used to create >> incredible transmission line models. The array function makes it easy to >> have a very simple schematic containing a LOT of sections, 250 to more >> than 1000 sections with the schematic showing only a single little >> transmission line symbol. And, again since the model has NO frequency term >> it is easy to do either .ac or .tran analyses. > > I am wholly in favor of the infinitesimal > lumped element model, but have some questions > about actual the values of these lumped capacitors/conductors/inductors. > Specifically, so far I have found that the > published values for resistance per unit > length, capacitance per unit length etc., > use the unit of length as either kilo-foot > or kilometer. Resistance is directly > proportional to length, so the resistance > of e.g., a 0.5 centimeter unit length > transmission line can be easily computed. > But what about shunt conductance per unit > length and more importantly inductance per > unit length ? > In addition, each of these parameters have > frequency dependencies, but they can be > tackled. > Any hints/suggestions would be very helpful. >Some years ago we had reasonable success modelling lossy and dispersive transmission lines. The base was modeling the two-port with some controlled sources plus some equivalent lumped networks. One of them was used to model the desired Zo(s)=sqrt((R+Ls)/(G+Cs)). The other, the propagation function F(s)=exp(-theta(s)), with theta(s)=l*sqrt((R+Ls)(G+Cs)) was modeled with an ideal transmission line together with a shaping network. The procedure to find the lumped equivalent used multipoint Pad� approximation. The usual Pad� approximants try to fit the first terms of the Taylor series at s=0. In our approach, we took a bilinear transformation from s to z plane s=so*(1-z)/(1+z) with so = sqrt(RG/LC) and then made a multipoint Pad� approximation, fitting some terms around z=0, and fixing the first series term at z=1 and z=-1 (lastly this corresponds to fitting to f=inf and f=0 and the intermediate frequency so). This performed much better than the previous techniques without having to do any kind of optimization, i.e. the procedure was explicit. You may google the title "An explicit method for modeling lossy and dispersive transmission lines" Pere Pere
Ideal vs. lossy transmission line model question
Started by ●February 27, 2015
Reply by ●March 12, 20152015-03-12
Reply by ●March 12, 20152015-03-12
On Thu, 12 Mar 2015 02:36:45 -0700, o pere o <me@somewhere.net> wrote:>> ...snip.... > > Some years ago we had reasonable success modelling lossy and dispersive > transmission lines. The base was modeling the two-port with some > controlled sources plus some equivalent lumped networks. One of them was > used to model the desired Zo(s)=sqrt((R+Ls)/(G+Cs)). The other, the > propagation function F(s)=exp(-theta(s)), with > theta(s)=l*sqrt((R+Ls)(G+Cs)) was modeled with an ideal transmission > line together with a shaping network. > > The procedure to find the lumped equivalent used multipoint Pad� > approximation. The usual Pad� approximants try to fit the first terms of > the Taylor series at s=0. In our approach, we took a bilinear > transformation from s to z plane > > s=so*(1-z)/(1+z) with so = sqrt(RG/LC) > > and then made a multipoint Pad� approximation, fitting some terms around > z=0, and fixing the first series term at z=1 and z=-1 (lastly this > corresponds to fitting to f=inf and f=0 and the intermediate frequency > so). > > This performed much better than the previous techniques without having > to do any kind of optimization, i.e. the procedure was explicit. > > You may google the title "An explicit method for modeling lossy and > dispersive transmission lines" > > PereFascinating approach! As many of you know, google is no longer my friend in searches, in between yielding high quantity of rubbish; it now deems me inappropriate to work with and either bogs down, or worse, hangs our PC's! This translates into the PC is completely locked up while doing a search so NOTHING else can be done!!! arrrrrgggg! It often takes an hour and a half to get a 20kB paper! Pere, is it possible for you to directly send me a copy of your paper to the above email address? Robert
Reply by ●March 12, 20152015-03-12
On 03/12/2015 03:04 PM, RobertMacy wrote:> On Thu, 12 Mar 2015 02:36:45 -0700, o pere o <me@somewhere.net> wrote: > >>> ...snip.... >> >> Some years ago we had reasonable success modelling lossy and >> dispersive transmission lines. The base was modeling the two-port with >> some controlled sources plus some equivalent lumped networks. One of >> them was used to model the desired Zo(s)=sqrt((R+Ls)/(G+Cs)). The >> other, the propagation function F(s)=exp(-theta(s)), with >> theta(s)=l*sqrt((R+Ls)(G+Cs)) was modeled with an ideal transmission >> line together with a shaping network. >> >> The procedure to find the lumped equivalent used multipoint Pad� >> approximation. The usual Pad� approximants try to fit the first terms >> of the Taylor series at s=0. In our approach, we took a bilinear >> transformation from s to z plane >> >> s=so*(1-z)/(1+z) with so = sqrt(RG/LC) >> >> and then made a multipoint Pad� approximation, fitting some terms >> around z=0, and fixing the first series term at z=1 and z=-1 (lastly >> this corresponds to fitting to f=inf and f=0 and the intermediate >> frequency so). >> >> This performed much better than the previous techniques without having >> to do any kind of optimization, i.e. the procedure was explicit. >> >> You may google the title "An explicit method for modeling lossy and >> dispersive transmission lines" >> >> Pere > > Fascinating approach! > > As many of you know, google is no longer my friend in searches, in > between yielding high quantity of rubbish; it now deems me inappropriate > to work with and either bogs down, or worse, hangs our PC's! This > translates into the PC is completely locked up while doing a search so > NOTHING else can be done!!! arrrrrgggg! It often takes an hour and a > half to get a 20kB paper! > > Pere, is it possible for you to directly send me a copy of your paper to > the above email address? > > RobertI have posted it here (in case anyone else is interested) http://circuit.epsem.upc.edu/public/sed/an-explicit-method-for-modeling-lossy-and-dispersive-transmission-lines/at_download/file An e-mail copy should also reach you... Pere
Reply by ●March 12, 20152015-03-12
On 03/12/2015 05:36 AM, o pere o wrote:> On 03/09/2015 05:44 AM, dakupoto@gmail.com wrote: >> On Friday, March 6, 2015 at 7:53:48 AM UTC-5, Robert Macy wrote: >>> On Fri, 06 Mar 2015 00:37:19 -0700, <dakupoto@gmail.com> wrote: >>> >>>>> ....snip.... >>>> The basic scheme the author has followed is to >>>> use the frequency plane(s = jw) expressions for >>>> conductance, impedance, inductance, resistance >>>> and propagation constant and then take the >>>> inverse transform of these quantities in the >>>> SPICE code. This is perfectly fine in theory, >>>> because any complex expression may be split up >>>> in a partial fractions expansion, and then the >>>> inverse Laplace transform of each of these can >>>> parts may be obtained. >>>> The problem starts when one considers the s=plane >>>> expressions for impedance and propagation >>>> constant -- BOTH have square roots. And as far >>>> as I could see from my trusty copy of Abramovich >>>> and Stegun, BOTH forward and backward Laplace >>>> transforms for expressions with positive >>>> fractional exponents do not exist !!! >>>> For example, the s-plane expression for the >>>> frequency dependent resistance is: >>>> R(w) = Rdc(1 + (w/Wr)^2))^0.25 >>>> So how is the LTSpice engine going to evaluate >>>> the inverse transform for this expression ? >>>> In my humble opinion, a frequency plane solution >>>> with a simple C/C++ module with the input signal >>>> frequency being increased incrementally would provide a lot better >>>> solution -- I await each of >>>> your comments on this. >>>> >>> >>> The last time I used a SPICE model with a 'frequency' term and tried >>> to do >>> a really useful analysis, like try to observe the expected change to the >>> digital square wave, or obtain a useful set of 'eye patterns' for Error >>> Rate Detection values; the analysis went from step, step, ..step.., >>> ....step....., to predicting it might not finish in my lifetime, >>> Stopping >>> the analysis before anywhere nearly completed, it added insult to >>> injury, >>> the results had wild variations of error. so... >>> >>> I now make my OWN transmission line models using lumped models in small >>> enough sections the error at maximum frequency [as caused by minimum >>> risetime] PLUS, and this has been illuminating in understanding EMC >>> emanations off a cable, it is possible to include 'free space' and >>> actually estimate radiation from circuitry in a system that is not >>> properly done. >>> >>> How to do Skin effect? I found that around 5 sets of elements, >>> configured >>> like eddy current models, inductor parallel with resistor feeding >>> parallel >>> inductor, etc can be made to pretty accurately 'curve fit' the >>> resistance >>> vs frequency, and a few more terms will even yield fairly accurate >>> 'phase' >>> shift from skin effects. [Note technique pretty accurately models those >>> lossy RF Beads, somewhere I have a set of models for commercially >>> available parts that are good to 1GHz, some beyond.] The advanatage of >>> keeping the model frequency independent is that the model can be used >>> for >>> either .ac or .tran analyses. And, not take several days to RUN. >>> >>> Now, applied to transission lines, the model has conductor inductance >>> and >>> loss, return path inductance and loss [usually left out of lossy >>> models], >>> capacitance between conductor and return path, dielectric loss, AND the >>> coupling [also left out of most models] which makes coax and twisted >>> pair >>> so desirable to use. At least with such a model you KNOW what's >>> inside it. >>> >>> Also, you can really get to 'see' the dispersion in a cable. put in a >>> step >>> and watch the value step then 'slide' up to where it's supposed to go. >>> >>> The FREE PC Tools to create these models: femm 4.2; octave [Matlab >>> clone]; >>> and LTspice. [Of note, Mike Engelhardt, creator of LTspice, placed >>> inside >>> LTspice an 'array' function, which Alex Bordodynov has used to create >>> incredible transmission line models. The array function makes it easy to >>> have a very simple schematic containing a LOT of sections, 250 to more >>> than 1000 sections with the schematic showing only a single little >>> transmission line symbol. And, again since the model has NO frequency >>> term >>> it is easy to do either .ac or .tran analyses. >> >> I am wholly in favor of the infinitesimal >> lumped element model, but have some questions >> about actual the values of these lumped capacitors/conductors/inductors. >> Specifically, so far I have found that the >> published values for resistance per unit >> length, capacitance per unit length etc., >> use the unit of length as either kilo-foot >> or kilometer. Resistance is directly >> proportional to length, so the resistance >> of e.g., a 0.5 centimeter unit length >> transmission line can be easily computed. >> But what about shunt conductance per unit >> length and more importantly inductance per >> unit length ? >> In addition, each of these parameters have >> frequency dependencies, but they can be >> tackled. >> Any hints/suggestions would be very helpful. >> > > Some years ago we had reasonable success modelling lossy and dispersive > transmission lines. The base was modeling the two-port with some > controlled sources plus some equivalent lumped networks. One of them was > used to model the desired Zo(s)=sqrt((R+Ls)/(G+Cs)). The other, the > propagation function F(s)=exp(-theta(s)), with > theta(s)=l*sqrt((R+Ls)(G+Cs)) was modeled with an ideal transmission > line together with a shaping network. > > The procedure to find the lumped equivalent used multipoint Pad� > approximation. The usual Pad� approximants try to fit the first terms of > the Taylor series at s=0. In our approach, we took a bilinear > transformation from s to z plane > > s=so*(1-z)/(1+z) with so = sqrt(RG/LC) > > and then made a multipoint Pad� approximation, fitting some terms around > z=0, and fixing the first series term at z=1 and z=-1 (lastly this > corresponds to fitting to f=inf and f=0 and the intermediate frequency so). > > This performed much better than the previous techniques without having > to do any kind of optimization, i.e. the procedure was explicit. > > You may google the title "An explicit method for modeling lossy and > dispersive transmission lines" > > Pere > > PereI've often made nearly minimax (equiripple error) approximations using Chebyshev techniques. For a complicated function, you take a whole bunch of samples at Chebyshev abscissae (i.e. you warp the X axis by the derivative of the arcsin and then take equally spaced samples) and run an FFT, which gives you the Chebyshev polynomial expansion of the original function to whatever order you like. Then you make that into a ratio of two Chebyshev series by using the orthogonality relationship for Chebyshev polynomials, which gives a very cute and simple recursion formula that's easy to automate. With an M/N order rational function, you can match the Chebyshev coefficients up to order M+N. It's usually very close to the true minimax approximation, and no iteration is needed. This technique isn't at all original--I found it in a numerical analysis book from the '70s--but it's easy to do and it works like the bomb. Cheers Phil Hobbs -- Dr Philip C D Hobbs Principal Consultant ElectroOptical Innovations LLC Optics, Electro-optics, Photonics, Analog Electronics 160 North State Road #203 Briarcliff Manor NY 10510 hobbs at electrooptical dot net http://electrooptical.net
Reply by ●March 13, 20152015-03-13
On Thu, 12 Mar 2015 08:39:40 -0700, o pere o <me@somewhere.net> wrote:>> ...snip.... >> Robert > > I have posted it here (in case anyone else is interested) > http://circuit.epsem.upc.edu/public/sed/an-explicit-method-for-modeling-lossy-and-dispersive-transmission-lines/at_download/file > An e-mail copy should also reach you... > > PereThanks, got it! and sent confirmation reply.
Reply by ●March 19, 20152015-03-19
On Thursday, March 12, 2015 at 11:39:46 AM UTC-4, o pere o wrote:> On 03/12/2015 03:04 PM, RobertMacy wrote: > > On Thu, 12 Mar 2015 02:36:45 -0700, o pere o <me@somewhere.net> wrote: > > > >>> ...snip.... > >> > >> Some years ago we had reasonable success modelling lossy and > >> dispersive transmission lines. The base was modeling the two-port with > >> some controlled sources plus some equivalent lumped networks. One of > >> them was used to model the desired Zo(s)=sqrt((R+Ls)/(G+Cs)). The > >> other, the propagation function F(s)=exp(-theta(s)), with > >> theta(s)=l*sqrt((R+Ls)(G+Cs)) was modeled with an ideal transmission > >> line together with a shaping network. > >> > >> The procedure to find the lumped equivalent used multipoint Pad� > >> approximation. The usual Pad� approximants try to fit the first terms > >> of the Taylor series at s=0. In our approach, we took a bilinear > >> transformation from s to z plane > >> > >> s=so*(1-z)/(1+z) with so = sqrt(RG/LC) > >> > >> and then made a multipoint Pad� approximation, fitting some terms > >> around z=0, and fixing the first series term at z=1 and z=-1 (lastly > >> this corresponds to fitting to f=inf and f=0 and the intermediate > >> frequency so). > >> > >> This performed much better than the previous techniques without having > >> to do any kind of optimization, i.e. the procedure was explicit. > >> > >> You may google the title "An explicit method for modeling lossy and > >> dispersive transmission lines" > >> > >> Pere > > > > Fascinating approach! > > > > As many of you know, google is no longer my friend in searches, in > > between yielding high quantity of rubbish; it now deems me inappropriate > > to work with and either bogs down, or worse, hangs our PC's! This > > translates into the PC is completely locked up while doing a search so > > NOTHING else can be done!!! arrrrrgggg! It often takes an hour and a > > half to get a 20kB paper! > > > > Pere, is it possible for you to directly send me a copy of your paper to > > the above email address? > > > > Robert > > I have posted it here (in case anyone else is interested) > http://circuit.epsem.upc.edu/public/sed/an-explicit-method-for-modeling-lossy-and-dispersive-transmission-lines/at_download/file > > > An e-mail copy should also reach you... > > PereThanks a lot for the link.
