A math problem over my head...

http://www.analog-innovations.com/MathProblem.png

Would some math whiz solve this for me?

Thanks!

...Jim Thompson
--
| James E.Thompson | mens |
| Analog Innovations | et |
| Analog/Mixed-Signal ASIC's and Discrete Systems | manus |
| San Tan Valley, AZ 85142 Skype: skypeanalog | |
| Voice480)460-2350 Fax: Available upon request | Brass Rat |
| E-mail Icon at http://www.analog-innovations.com | 1962 |

I love to cook with wine. Sometimes I even put it in the food.

On 6/28/2015 5:41 PM, Jim Thompson wrote:
A math problem over my head...

http://www.analog-innovations.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

On 6/28/2015 5:41 PM, Jim Thompson wrote:
A math problem over my head...

http://www.analog-innovations.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 non-negative when F and W are
non-negative. 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

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.analog-innovations.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/Mixed-Signal ASIC's and Discrete Systems | manus |
| San Tan Valley, AZ 85142 Skype: skypeanalog | |
| Voice480)460-2350 Fax: Available upon request | Brass Rat |
| E-mail Icon at http://www.analog-innovations.com | 1962 |

I love to cook with wine. Sometimes I even put it in the food.

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[n-1]
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 Fermi-Dirac 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.analog-innovations.com/MathProblem.png

Would some math whiz solve this for me?

Thanks!

...Jim Thompson
--
| James E.Thompson | mens |
| Analog Innovations | et |
| Analog/Mixed-Signal ASIC's and Discrete Systems | manus |
| San Tan Valley, AZ 85142 Skype: skypeanalog | |
| Voice480)460-2350 Fax: Available upon request | Brass Rat |
| E-mail Icon at http://www.analog-innovations.com | 1962 |

I love to cook with wine. Sometimes I even put it in the food.

On Sun, 28 Jun 2015 14:41:00 -0700, Jim Thompson
wrote:

A math problem over my head...

http://www.analog-innovations.com/MathProblem.png

Would some math whiz solve this for me?

Thanks!

...Jim Thompson

My bad... in my curve-fitting 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/Mixed-Signal ASIC's and Discrete Systems | manus |
| San Tan Valley, AZ 85142 Skype: skypeanalog | |
| Voice480)460-2350 Fax: Available upon request | Brass Rat |
| E-mail Icon at http://www.analog-innovations.com | 1962 |

I love to cook with wine. Sometimes I even put it in the food.