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Registered Member #54278
Joined: Sat Jan 17 2015, 04:42AM
Location: Amite, La.
Posts: 367
Lately, I have been wondering about" The quadratic formal in GENERAL vs the quadratic formula for coilguns:
In standard high school algebra texts the quadratic formula is used to solve for x with the following general equation: If
A(x^2) +Bx +C = 0, It's solution for the two x's is:
-B +- [sqrt(B^2 - 4AC)] /2A. The tern INSIDE the square root symbol is called the DISCRIMINANT. (B^2)-(4AC), is thus the DISCRIMINATE of the x-solution equation. A lot of information can be obtained by just examining this discriminate. For example:
For (B^2)-(4AC): 1) If the discriminant is >0, then there are two solutions. 2) If the discriminant =0, then there is ONE solution. 3) If the discriminate <0, then the solutions are complex (no real solutions, but can be just as useful).
Now let's go to the quadratic solution for a coilgun (I guess this is a good way to describe it).
The 2nd order differential equation for a series (RLC) coilgun circuit can be approximated as: Li"(t) + Ri'(t) + (1/C) = 0 Where (i) is the current, i'(t) is the 1st derivative of current (i) with respect to t, and i(t) is the function of current (i) with respect to time.
For the coilgun form of the quadratic formula the discriminant is: (R^2)-(4L/C): From Barry's page, a lot of useful information lies in the "coilgun" discriminant also: So for the discriminant
(R^2)-(4L/C): (Let's call the coilgun solutions s1 and s2 (in places of the general x's above. (Ls"+Rs'+1/C=0)
1) If the discriminant is larger than zero, the two solutions (s1 and s2) are real numbers and the circuit is OVER-DAMPED. 2) If the discriminant is =0, each solution is 0 (s1=0 and s2=0), here, the circuit is CRITICALLY-DAMPED. 3) If the discriminant is <0, s1 and s2 are complex numbers and the circuit is UNDER-DAMPED (decaying oscillation).
HERE IS WHAT I AM WONDERING: In the general algebraic quadratic formula the constants: A, B, and, C, can be positive or negative. However, in the coilgun discriminant the circuit constants R, L, and, C can ONLY be positive since they represent actual circuit components. SO, are there any rules or laws that simplify or modify what the coilgun discriminant values can signify?
Registered Member #54278
Joined: Sat Jan 17 2015, 04:42AM
Location: Amite, La.
Posts: 367
...just noticed this: With the particular high voltage metal Aerovox energy pulse caps that I fixed and plan to use in in a couple of projects, there is likely to be slight negative undershoot--apps like high power laser tubes and special coilguns. Does anyone know if this is bad for the caps? I just noticed that -some- are polarity-marked--barely noticeable...can't be sensitive as 'lytics???
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