Ideal vs. lossy transmission line model question

dakupoto · 2015-02-28T03:54:30+00:00

Could some electronics guru please clarify a few subtle questions regarding lumped parameter model of transmission lines ? The simple loss-less lumped parameter model consists of an ideal capacitor-inductor pair per unit length. OTOH, the lossy model includes a series resistance with the ideal inductor and an dielectric conductance in parallel with the ideal capacitor. Similarly, the non-ideal capacitor model includes a series resistance and a series inductance with the ideal capacitor. The non-ideal inductor model includes parasitic capacitance and resistance values. So, the question is: if one were to replace the ideal capacitor/indcutor pair in the lossless transmission line model with a non-ideal capacitor/inductor pair, then would this new model effectively re-create the lossy transmission line model ? I have done some SPICE modelling on this idea, and the results look encouraging. What do you gurus feel ? Any hints/suggestions would be greatly appreciated. Thanks in advance.

Feb 28, 2015 25 Replies

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o pere o 11 years ago

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 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)

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

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RobertMacy 11 years ago

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

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o pere o 11 years ago

I have posted it here (in case anyone else is interested)

formatting link

An e-mail copy should also reach you...

Pere

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Phil Hobbs 11 years ago

I'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

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RobertMacy 11 years ago

Thanks, got it! and sent confirmation reply.

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dakupoto 11 years ago

stly

Thanks a lot for the link.

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