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| + | ===[http://www.roboternetz.de/phpBB2/viewtopic.php?t=19193 sin oder -sin in einer verrauschten Kurve finden]=== | ||
| + | [http://people.freenet.de/gjl/applets/fourierview-jar.html Applet] | ||
| + | ---- | ||
<math> | <math> | ||
S(a,b) = \sum_{i=1}^n (f(x_i)-m(x_i))^2 | S(a,b) = \sum_{i=1}^n (f(x_i)-m(x_i))^2 | ||
| Zeile 4: | Zeile 7: | ||
---- | ---- | ||
<math> | <math> | ||
| − | \int_0^{2 \pi b} |a\cdot\mathrm{sin}(b x) | \mathrm{d}x = 4 |a/b| | + | \int_0^{2 \pi/b} |a\cdot\mathrm{sin}(b x) | \mathrm{d}x = 4 |a/b| |
| + | </math> | ||
| + | ---- | ||
| + | <math> | ||
| + | (f\star g)(x) = \int_{-\infty}^\infty f(y)\,g(x-y) \,dy \qquad \mathrm{Faltung\ von\ }f\mathrm{\ und\ }g | ||
| + | </math> | ||
| + | ---- | ||
| + | <math> | ||
| + | (f\star t)_n = \sum_{i=-K}^K t_i \cdot f_{n+i} \qquad\mathrm{mit}\qquad 1 = \sum_{i=-K}^K t_i | ||
| + | </math> | ||
| + | ---- | ||
| + | <math> | ||
| + | F(x,y) = \int_{x-y}^{x+y} f(t)\,dt | ||
| + | </math> | ||
| + | ---- | ||
| + | === [http://www.roboternetz.de/phpBB2/viewtopic.php?p=232269 Transistor oder Mosfet]=== | ||
| + | <math> | ||
| + | dP = \frac{R_\mathrm{FET}}{(R_\mathrm{FET}+R)^2}U^2 \, dt \qquad\mathrm{mit}\qquad R_\mathrm{FET}=R_\mathrm{FET}(t) | ||
| + | </math> | ||
| + | |||
| + | <math> | ||
| + | \Delta P_\mathrm{FET} = U^2 \cdot \int_0^{\Delta t} \frac{R_\mathrm{FET}}{(R_\mathrm{FET}+R)^2} \, dt \sim \frac{U^2}{R} \Delta t \quad\Rightarrow\quad P_\mathrm{switch} \sim \frac{U^2}{R}\,f\,\Delta t \quad\mathrm{und}\quad P_\mathrm{on} \approx R_\mathrm{on}\frac{U^2}{R^2} \,\mathrm{duty} | ||
| + | </math> | ||
| + | |||
| + | <math> | ||
| + | P_\mathrm{FET} \approx P_R\cdot \left(\kappa\cdot f\cdot \Delta t + \frac{R_\mathrm{on}}{R}\,\mathrm{duty}\right) | ||
| + | </math> | ||
| + | |||
| + | === SMPS === | ||
| + | <math> | ||
| + | W_\mathrm{max} \cdot \mu_\mathrm{e} = \frac{\ell_\mathrm{e}} | ||
| + | {2 \cdot \mu_0\cdot A_\mathrm{e}} | ||
| + | \cdot (0.3T \cdot A_\mathrm{min})^2 | ||
| + | </math> | ||
| + | |||
| + | === C-Meter === | ||
| + | <math> | ||
| + | U_0 \,=\, V_\mathrm{CC} \, \frac{R_2}{R_2 + R_1} | ||
| + | </math> | ||
| + | |||
| + | <math> | ||
| + | U(t_=) \,=\, \frac{{}_1}{{}^2}\cdot V_\mathrm{CC} \,=\, U_0 \cdot e^{-\frac{t_=}{R_2\cdot C}} | ||
| + | </math> | ||
| + | |||
| + | <math> | ||
| + | C \,=\, \frac{t_=}{R_2 \cdot \operatorname{ln}\, \frac{2}{1+R_1/R_2}} | ||
</math> | </math> | ||
Aktuelle Version vom 13. Februar 2007, 16:50 Uhr
Inhaltsverzeichnis
sin oder -sin in einer verrauschten Kurve finden
[math] S(a,b) = \sum_{i=1}^n (f(x_i)-m(x_i))^2 [/math]
[math] \int_0^{2 \pi/b} |a\cdot\mathrm{sin}(b x) | \mathrm{d}x = 4 |a/b| [/math]
[math] (f\star g)(x) = \int_{-\infty}^\infty f(y)\,g(x-y) \,dy \qquad \mathrm{Faltung\ von\ }f\mathrm{\ und\ }g [/math]
[math] (f\star t)_n = \sum_{i=-K}^K t_i \cdot f_{n+i} \qquad\mathrm{mit}\qquad 1 = \sum_{i=-K}^K t_i [/math]
[math] F(x,y) = \int_{x-y}^{x+y} f(t)\,dt [/math]
Transistor oder Mosfet
[math] dP = \frac{R_\mathrm{FET}}{(R_\mathrm{FET}+R)^2}U^2 \, dt \qquad\mathrm{mit}\qquad R_\mathrm{FET}=R_\mathrm{FET}(t) [/math]
[math] \Delta P_\mathrm{FET} = U^2 \cdot \int_0^{\Delta t} \frac{R_\mathrm{FET}}{(R_\mathrm{FET}+R)^2} \, dt \sim \frac{U^2}{R} \Delta t \quad\Rightarrow\quad P_\mathrm{switch} \sim \frac{U^2}{R}\,f\,\Delta t \quad\mathrm{und}\quad P_\mathrm{on} \approx R_\mathrm{on}\frac{U^2}{R^2} \,\mathrm{duty} [/math]
[math] P_\mathrm{FET} \approx P_R\cdot \left(\kappa\cdot f\cdot \Delta t + \frac{R_\mathrm{on}}{R}\,\mathrm{duty}\right) [/math]
SMPS
[math] W_\mathrm{max} \cdot \mu_\mathrm{e} = \frac{\ell_\mathrm{e}} {2 \cdot \mu_0\cdot A_\mathrm{e}} \cdot (0.3T \cdot A_\mathrm{min})^2 [/math]
C-Meter
[math] U_0 \,=\, V_\mathrm{CC} \, \frac{R_2}{R_2 + R_1} [/math]
[math] U(t_=) \,=\, \frac{{}_1}{{}^2}\cdot V_\mathrm{CC} \,=\, U_0 \cdot e^{-\frac{t_=}{R_2\cdot C}} [/math]
[math] C \,=\, \frac{t_=}{R_2 \cdot \operatorname{ln}\, \frac{2}{1+R_1/R_2}} [/math]
