Influence of load on bus characteristics - Page 1
Forum section: electronics / projects

author: lowpy
author_rank: Newbie
timestamp: December 21, 2019, 04:45:46 pm
content: I an trying to find (or figure out) the relationship between the load introduced by nodes added to a bus and the changes in the characteristics of the transmission line. By characteristics here I refer to elements such as: characteristic impedance, propagation delay/velocity... etc. I am using the lossless line model in my work.These can be easily calculated for a transmission line without loads by using the distributed circuit parameter representation of the transmission line.For example the characteristic impedance is Z0=sqrt(L0/C0), if we consider the lossless line model, with L0and C0being the distributed inductance and capacitance per unit length,.However, for each added node on the bus, these characteristics change given the added load capacitance. For loads evenly distributed along the line the distributed load capacitance introduced by the nodes is added to calculations, e.g.: the line impedance now becomes: Z'=sqrt(L0/(C0+Cd)), where Cdis calculated as the sum of the evenly distributed load capacitances divided by the length of the line over which they are distributed.My question is what happens if these loads are not equally distributed along the bus? How should the load capacitance be considered for calculating line characteristics? Should an equivalent distributed load be calculated like in the case of even node distribution or should separate calculations be made for each bus interval between 2 nodes?Thanks in advance!

author: T3sl4co1l
author_rank: Super Contributor
timestamp: December 21, 2019, 08:45:18 pm
content: The general effect, for periodic loading, is to make a photonic crystal, which has a bandgap, i.e., a bandstop characteristic. Transmission is unreliable (with respect to frequency or pulse width or dispersion, say) above the bandgap, and approximates normal transmission line behavior below.Consider a wave approaching a node: some is reflected back, and somewhat less is transmitted onward. Then at the next node the same, and so on, and all the reflections between them. (The part reflected back to the source gives the apparent change in impedance. Which is only applicable at low frequencies, where the lumped loading looks continuous, which is to say, there is a small phase angle between nodes.)For a random distribution of some PDF, I wonder if you can solve the same relations, to find the expected value and variance of bandgap center, width (or band edges), attenuation, and Zo. That would be the setup, but I don't know how to proceed from here; it's been a long time since I did statistics, or ensemble transmission lines...I've certainly not done it with transmission lines, but I'm familiar with the approach used to solve the resistance of non-adjacent points on an infinite resistor mesh: you use the Fourier transform, because you only have to write the indices of the probed locations, and their Kirchhoff equations. Perhaps a similar thing would apply here, but I'm not sure how to bring aperiodic statistics into it; perhaps it would be similar to modeling RF noise.In general, you will still have the same LF approximation, but it will only be applicable for frequencies less than the largest electrical length between any pair of nodes. Above there, expect peaks and dips as random pairs or groups of nodes act as resonators -- bandpass networks.Hah, I wonder if you could model single errors as doping in the photonic crystal -- that is, introducing an allowed level within the prohibited band. This wouldn't be so effective for a high density of errors though.The width of any given "accidental passband", within the stopband, will depend on the ratio of its impedance to the line as usual (either Zo or Z'), and I suppose its insertion loss too.At some point of refinement, loss will inevitably have to be considered, as insertion losses will be higher than the ideal case, and bands (stop and pass) will be wider.Oh, there's also the matter of where stopped signals go -- they could transmit all the way through to the far terminator, but be suppressed from any number of intermediate nodes; or they could be reflected to the source. And for the lossy case, they can be absorbed by the network and reach few (or even none?) of the above.Tim

author: lowpy
author_rank: Newbie
timestamp: December 23, 2019, 10:05:47 am
content: Thank you for your detailed analysis of the problem. I really appreciate you taking time to go into the different aspects that should be considered when analyzing transmission line characteristics in the presence of loads.It is now clear to me that this is not a trivial a problem and I cannon hope to tackle it on my own (given my limited background in electronics). Also it kind of explains why I wasn't able to find an answer to my question in books or papers covering transmission line modeling.I will have to settle with simulating the behavior for my use cases in LTspice.Thanks again Tim!Stefan

author: MagicSmoker
author_rank: Super Contributor
timestamp: December 23, 2019, 11:08:53 am
content: I highly recommend this book if you don't have it:https://smile.amazon.com/High-Speed-Digital-Design-Handbook/dp/0133957241/ref=sr_1_1?keywords=high+speed+digital+design&qid=1577098311&sr=8-1.Lots of examples with governing equations and all of which are clearly explained.

author: lowpy
author_rank: Newbie
timestamp: December 23, 2019, 11:30:20 am
content: Thanks for the recommendation. I'll give it a look.