On 6 November 2013 11:45, Andrew Simper <a...@cytomic.com> wrote: > Here is an updated version of the optimised trapezoidal integrated svf > which bundles up all previous state into equivalent currents for the > capacitors, which is how I solve non-linear circuits (although this > solution is just the linear one that I'm posting here). The only thing > to note that with trapezoidal integration you have gain terms of g = > tan(pi*cutoff/samplerate) which become very large with high cutoff, so > care needs to be taken if these "g" terms stand alone since the > scaling can get large and could impact numerical performance: > > http://www.cytomic.com/files/dsp/SvfLinearTrapOptimised2.pdf > > Here is a similar thing done for a Sallen Key low pass: > > http://www.cytomic.com/files/dsp/SkfLinearTrapOptimised2.pdf > > Please note there is absolutely nothing new here, this is all standard > circuit maths that has been around for ages, and all the maths behind > it was invented by people like Netwon, Leibnitz, and Euler, they > deserve all the credit and came up with ways of solving not just this > linear case but also the non-linear case. Depending on what you are > doing trapezoidal may not be the best integrator to use so most > systems of solving these equations support several types of > integrator. Here are some handy references: > > http://en.wikipedia.org/wiki/Capacitor > http://en.wikipedia.org/wiki/Nodal_analysis > http://qucs.sourceforge.net/tech/node26.html > http://www.ecircuitcenter.com/SPICEtopics.htm > > Please let me know if there are any mistakes. Enjoy! >
mostly ignoring the tangential properties of the thread, i like the implementation, and i value the choice of trapezoidal approximation here and how the "kirchhoff equality" calculations are explained. while i haven't played with this approach, the digital filters seems *quite* stable and accurate (particulary for the SVF case in comparison to other derivatives). also, i don't think that the linear interpolation for the integral approximation is that much of a bad trade off here and it will also not affect stability. perhaps, quadratic can be considered, but that will surely insert state variable changes tick wise. you may have given that a try already... actually trapezoidal is all over quantum mechanics because, say in comparison to midpoint you will get those control and state variable intermediates that mess calculation quite badly in cases that you can't really handle them in massively complicated models. in quantized signal DSP (which is also a widely approximating field in itself) we can play more with that because we get slightly more of the freedom and certainty. can't fault it on a larger scale and it has everything in the paper (+ source code), so... lubomir -- -- dupswapdrop -- the music-dsp mailing list and website: subscription info, FAQ, source code archive, list archive, book reviews, dsp links http://music.columbia.edu/cmc/music-dsp http://music.columbia.edu/mailman/listinfo/music-dsp
