"Mom, can we buy a picosecond electronics switch?" "No, we have a picosecond switch at home." The picosecond switch at home Mercury-wetted relay. https://w140.com/tekwiki/wiki/109#electronics
@chjara@akko.wtf It's the "new old" name. The "old old" name was Mikufans. It used to be a 100% niconico clone exclusively for anime fandom videos (it didn't even have file storage and relied on hotlinking to other mainstream video sites). For some inexplicable reason, later it managed to replace all the other per-existing video sites to become a huge general-purpose video site. I miss the early days when its homepage was filled by Vocaloid reposts.
What did I do tonight : searching for the real formula for calculating the capacitance of a rectangular parallel-plate capacitor online. Turned out that one needs a professional complex analyst to solve that, as it involves Schwarz–Christoffel mapping and incomplete elliptic integral of the second kind... :woozy_baa: #electronics
Exact solution of a 2D thin parallel-plate capacitor (A. E. H. Love, 1924): C = [\epsilon \cdot K(1-m) \cdot K(m)] \text{ F/m}in which: \epsilon is the material permittivity, m = k^2 is the argument of K(k) , and K(k) = \int_0^{\frac{\pi}{2}} \frac{{\rm{d}}\theta}{\sqrt{1-k^2 \sin^2\theta}} is the complete elliptic integral of the first kind. To determine the value m , first one needs to solve the following equation:\begin{align*} \dfrac{W}{S} = \dfrac{K(1-m)E[\phi,(1-m)]-E(1-m)\cdot F[\phi, (1-m)]}{[E(1-m)-K(1-m)]\cdot K(m)+K(1-m)E(m)} \end{align*}in which: W is the capacitor plate's cross section length, S is the plate spacing, m = k^2 is the argument of K(k) , \phi is the argument of E(\phi, k) , which is calculated according to \begin{align*} \sin^2 (\phi) &= \dfrac{K'(m)-E'(m)}{(1-m^2)K'(m)} \\ \phi &=\arcsin \left[\sqrt{\dfrac{(K(1-m)-E(1-m)}{(1-m)\cdot K(1-m)}} \right] \end{align*}Finally E(\varphi,k) = \int_0^\varphi \sqrt{1-k^2 \sin^2\theta}\, d\theta is the incomplete elliptic integral of the second kind, and E(k) = E(\frac{\pi}{2},k)=\int_0^{\frac{\pi}{2}}\sqrt {1-k^2 \sin^2\theta}\ {\rm{d}}\theta\! is the complete elliptic integral of the second kind.
To find the capacitance, first guess the value of m and calculate φ using a square root and an arcsin, then evaluate a bunch of elliptic integrals while varying m (and φ), until the second equation is equal to the aspect ratio of the capacitor. Finally plug the value of m into the first equation...
Conclusion: Physics is a mistake for anything other than spherical cows in a vacuum. #electronics
Previously: @niconiconi@cybre.space / Code monkey and sysadmin / No nations, no flags, no patriots. / Chaotic Neutral / Now Accelerationist / currently NEET + hikikomori / ? “Onii-chan is watching you!", use OpenPGP: FAD3EB05E88E8D6D / biologically male, self-identified as '; DROP TABLE genders;