Solved: solve 8 equations with 8 unknowns

mbadawy · ‎May 16, 2016

Hello, i'm new in using Mathcad, i just need to solve 8 equations with 8 unknowns(sound simple),but i don't know the right syntax to get the output, i tried several ones that i found in the help and tutorial but none is working, some syntax gives me my initial guess as the output and other syntax does nothing.

still the problem isn't only the syntax, i have no clue what should be the initial guess the solution is either very large or very small ( Pico or Giga maybe larger or smaller even), so is Mathcad able to solve such thing?

below is the attached worksheet. Thanks in advance.

LucMeekes · ‎May 16, 2016

O...K...

suppose your 6 resistors are equal. Then following the second equation, the reciprocal of their product must be approximately 10^72; that is, each of them should be about 10^-12 Ohm, that is pico-Ohm range.

Does that seem like a reasonable solution to you?

There is one error in your syntax: you use a boolean equals (shows as a boldface "=") in the Find() statement, where you should use an evaluation equals (shows as a regular "=").

The problem is not solvable, as you found out in Mathcad 15 and Prime. I tried a symbolic approach in Mathcad 11, with no solution found.

And I still question your equations because, even if they're a simplification, I think they should still make sense.

Finally: this does not look like a filter, because it lacks the frequency-dependent part. For a filter I would expect to see capacitors,

View solution in original post

LucMeekes · ‎May 16, 2016

1. Your constants are awefully high. While the equations appear to deal with some kind of electronic circuit, such high values for any of your constants can't be right.

2. Are you sure all your 8 equations are independent? And correct?

Example. Your 3rd equation says:

You add 3 terms, they must have the same dimensions. Now the last two terms are 1/Ohm^5, the first term should be too.Well, it does contain 5 R's in the denominator, but also a Gm in the numerator. And isn't the unit of Gm [1/R] ? That makes that term 1/Ohm^6, which you can't add to the other two.

Luc

mbadawy · ‎May 16, 2016

Thanks for your reply,

1- the constants are given so there is no way to adjust them nor can they be wrong, and yes it's a 6th order filter so the numbers are ok for that.
2- i checked the equations 4 times and i;m absolutely sure they are independent.
3- does that mean my syntax is correct? if yes, is there is any chance that Mathcad can't solve them because my initial guess is so far from the correct answer? i tried on prime but it only gave me the initial guess as an output so i suspected that it is the same problem on Mathcad 15 too.

yes the Gm unit is 1/ohm but that's only the simplified equations. it's a design problem so i had to assume some other Gms that existed in the equations, so the terms can be added no mistake in that. there was also caps in the original equations in case you still found the units not matching together.

LucMeekes · ‎May 16, 2016