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#1
Posted to sci.electronics.design,alt.binaries.schematics.electronic,sci.electronics.basics




Math Problem
A math problem over my head...
http://www.analoginnovations.com/MathProblem.png Would some math whiz solve this for me? Thanks! ...Jim Thompson   James E.Thompson  mens   Analog Innovations  et   Analog/MixedSignal ASIC's and Discrete Systems  manus   San Tan Valley, AZ 85142 Skype: skypeanalog    Voice480)4602350 Fax: Available upon request  Brass Rat   Email Icon at http://www.analoginnovations.com  1962  I love to cook with wine. Sometimes I even put it in the food. 
#2
Posted to sci.electronics.design,alt.binaries.schematics.electronic,sci.electronics.basics




Math Problem
On 6/28/2015 5:41 PM, Jim Thompson wrote:
A math problem over my head... http://www.analoginnovations.com/MathProblem.png Would some math whiz solve this for me? Thanks! ...Jim Thompson Using the multivariate second derivative test to classify the critical points of the function may help: https://en.wikipedia.org/wiki/Second...erivative_test 
#3
Posted to sci.electronics.design,alt.binaries.schematics.electronic,sci.electronics.basics




Math Problem
On 6/28/2015 5:41 PM, Jim Thompson wrote:
A math problem over my head... http://www.analoginnovations.com/MathProblem.png Would some math whiz solve this for me? Thanks! Are you looking for a closed solution or a "feel" for the domain? Just looking at it the first term will range over V. TANH() ranges over ±1, so the full term will range over 0 to 1 times V or at most V. The second term will always be nonnegative when F and W are nonnegative. The only time f(v) can be negative is if F is negative and the values of F and W (as well as V of course) are such that the magnitude of the second term is larger than the first. I can't pin that down in a closed form but I think this can help you intuitively map the domain a bit more.  Rick 
#4
Posted to sci.electronics.design,alt.binaries.schematics.electronic,sci.electronics.basics




Math Problem
On Sun, 28 Jun 2015 18:49:02 0400, bitrex
wrote: On 6/28/2015 5:41 PM, Jim Thompson wrote: A math problem over my head... http://www.analoginnovations.com/MathProblem.png Would some math whiz solve this for me? Thanks! ...Jim Thompson Using the multivariate second derivative test to classify the critical points of the function may help: https://en.wikipedia.org/wiki/Second...erivative_test Thanks! ...Jim Thompson   James E.Thompson  mens   Analog Innovations  et   Analog/MixedSignal ASIC's and Discrete Systems  manus   San Tan Valley, AZ 85142 Skype: skypeanalog    Voice480)4602350 Fax: Available upon request  Brass Rat   Email Icon at http://www.analoginnovations.com  1962  I love to cook with wine. Sometimes I even put it in the food. 
#5
Posted to sci.electronics.design,alt.binaries.schematics.electronic,sci.electronics.basics




Math Problem
Ah, I'd played with this a little bit before.
Ultimately, I believe Wescott's right. Intuitively, you're emulating a resistor and diode circuit  a system which SPICE solves iteratively, and a solution which is transcendental (you can only iterate the x[n] = e^x[n1] form to get an approximate result, there's no closed form analytical solution  see https://en.wikipedia.org/wiki/Lambert_W_Function for a way of writing it). Other sigmoid functions come to mind; you can use the FermiDirac statistic (aka Logistic function), 1 / (1 + exp(x)), to "turn on" the proportional part. But if you unwrap the tanh function, you'll see that's the same thing you're already doing (give or take some constants). In principle, there exists a function that exactly fills in that little remainder, that you're trying to patch with the Gaussian term. It's most likely transcendental as well... and may not even have a simple description other than to being the remainder to the function in question! Other sigmoids will have other shapes. Taking the integral of exp(x^2) might help (erf(x)). There are other kinds out there. Do consider that, since you're SPICEing, you can do some quite excellent numerical solutions, and may not be able to express your desired relation as an equation, but you might be able to with reasonable numerical stability and few additional nodes. Tim  Seven Transistor Labs Electrical Engineering Consultation Website: http://seventransistorlabs.com "Jim Thompson" wrote in message ... A math problem over my head... http://www.analoginnovations.com/MathProblem.png Would some math whiz solve this for me? Thanks! ...Jim Thompson   James E.Thompson  mens   Analog Innovations  et   Analog/MixedSignal ASIC's and Discrete Systems  manus   San Tan Valley, AZ 85142 Skype: skypeanalog    Voice480)4602350 Fax: Available upon request  Brass Rat   Email Icon at http://www.analoginnovations.com  1962  I love to cook with wine. Sometimes I even put it in the food. 
#6
Posted to sci.electronics.design,alt.binaries.schematics.electronic,sci.electronics.basics




Math Problem
On Sun, 28 Jun 2015 14:41:00 0700, Jim Thompson
wrote: A math problem over my head... http://www.analoginnovations.com/MathProblem.png Would some math whiz solve this for me? Thanks! ...Jim Thompson My bad... in my curvefitting the error looked like (Gaussian) exp(W*V^2) Looks the same but easier to deal with: 1[TANH(K*V)]^2 ...Jim Thompson   James E.Thompson  mens   Analog Innovations  et   Analog/MixedSignal ASIC's and Discrete Systems  manus   San Tan Valley, AZ 85142 Skype: skypeanalog    Voice480)4602350 Fax: Available upon request  Brass Rat   Email Icon at http://www.analoginnovations.com  1962  I love to cook with wine. Sometimes I even put it in the food. 
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