yes and i keep trying to NOT put 2 pages of explanation into the forum. lol.
I already know that i don’t need the det as a method to get the answer. i was trying it as a starting point.
i’ll try to provide the codensed version of what’s going on (put on your electrical engineering hat)
1 given a printed circuit board - discretize the board so that it can be expressed as per unit area lumped-element equivalents
2 take the lumped element equivalent and create what is called a “transmission matrix”.
3 the transmission matrix does exactly what you think it should, you chain N of them to represent the entirety of the board
4 take the resultant transmission matrix and use the determinant to calculate the impedance looking into the board at a particular unit cell.
as i said, i was using step 4 simply because that’s how the answer was represented. i KNOW it’s a terrible idea, and it’s a common problem in circuit theory because it’s very easy to represent the anwer to these sorts of problems as a calculation of the determinant (with row and column modifications).
the correct answer is to set-up solution vectors and cycle through them to get the answer but that is not a succinct way to put it in papers. comically, i thought using the det would be easier.
so the real problem is that i’m not 100% sure i’m generating the correct values ithe matrix. I know i’m generating the individual values for the matrix correctly, I know they are in the right locations.
however, the paper’s formulation may be wrong ( i went through the algebra this morning and i don’t think it is).
so my next task, is more correctness verification. the matrix values should absolutely not blow up. so i have a plan for a reduced set of values so i can explicitly test the value progression as i chain the matrices.
as to why i’m sure the values should not blow up - using a capacitor as a simple example. Chain N capacitors - you don’t get a value that is ~ C^n you get a value that is ~ C*n.
I need to look to look at a reduced problem space and make sure that’s what is happening.
safe to say, i’ve learned my lesson. stay away from determinants !