From dbb7c8f33bd79f62f00a6b8b1fcc04e1565faac6 Mon Sep 17 00:00:00 2001 From: Klagarge Date: Sat, 16 Mar 2024 18:54:01 +0100 Subject: [PATCH] add RF --- infotro/Eln/RF.md | 79 ++++++++++++++++++++++++++++ infotro/Eln/medias/rf-capacitor.png | Bin 0 -> 23721 bytes infotro/Eln/medias/rf-inductor.png | Bin 0 -> 94632 bytes infotro/Eln/medias/rf-resistor.png | Bin 0 -> 21598 bytes infotro/README.md | 1 + infotro/_navbar.md | 1 + 6 files changed, 81 insertions(+) create mode 100644 infotro/Eln/RF.md create mode 100644 infotro/Eln/medias/rf-capacitor.png create mode 100644 infotro/Eln/medias/rf-inductor.png create mode 100644 infotro/Eln/medias/rf-resistor.png diff --git a/infotro/Eln/RF.md b/infotro/Eln/RF.md new file mode 100644 index 0000000..ef3264c --- /dev/null +++ b/infotro/Eln/RF.md @@ -0,0 +1,79 @@ +

+Radio Fréquence +

+ +---------- + +# Skin effect +Le courant électrique circule principalement à la surface des conducteurs. + +Pour un fil de cuivre rond, la résistance en continue est donnée par la formule suivante: +$$R_{DC} = \rho\frac{l}{\pi r²}$$ +avec: +- $R_{DC}$: résistance en continue +- $\rho$: résistivité du cuivre +- $l$: longueur du fil +- $r$: rayon du fil + +La résistance en courant alternatif est donnée par la formule suivante: +$$R_{AC} = R_{DC} \frac{r}{2\delta}$$ +avec: +- $R_{AC}$: résistance en courant alternatif +- $R_{DC}$: résistance en continue +- $r$: rayon du fil +- $\delta$: profondeur de pénétration du courant + +La profondeur de pénétration du courant est donnée par la formule suivante: +$$\delta = \sqrt{\frac{\rho}{\pi f \mu_0}}$$ +avec: +- $\delta$: profondeur de pénétration du courant +- $\rho$: résistivité du cuivre +- $f$: fréquence +- $\mu_0$: perméabilité magnétique du vide $= 4\pi 10^{-7} H/m$ + +On peut en déduire la résistance en courant alternatif: +$$R_{AC} = \frac{l\sqrt{\rho\pi\mu_0}}{2\pi r} \sqrt{f}$$ + +Pour calculer l'inductance et la capacité d'un fil, on peut utiliser les formules suivantes: +$$\begin{align} +L&=\frac{\mu_{0}l}{\pi}acosh\left( \frac{d}{2r} \right) \\ +C&=\frac{\pi\epsilon_{0}l}{acosh\left( \frac{d}{2r} \right)} +\end{align}$$ +avec: +- $\mu_{0}$: perméabilité magnétique du vide $=4\pi\cdot 10^{-7}\left[ \frac{H}{m} \right]$ +- $\epsilon_{0}$: permittivité du vide $=8.854\cdot 10^{-12}\left[ \frac{F}{m} \right]$ + +# Model à haute fréquence + +## Inductance +![rf-inductor.png](medias%2Frf-inductor.png ':size=50%') + +Facteur de qualité : +$$Q(f) = \frac{X_{L}(f)}{R(f)} \qquad \qquad R_{AC}(f)= \frac{l\sqrt{ \rho \pi \mu_{0} }}{2\pi r}\sqrt{ f}$$ + +Réactance & Impédance: +$$X_{L}=\omega L=2\pi fL \qquad \qquad Z_{L}=jX_{L}=j\omega L$$ + +Résonance : $\omega_{r} ≃\omega_{0}=\frac{1}{\sqrt{ LC }}$
+SRF: Self Resonant Frequency = $\frac{\omega_{r}}{2\pi}$ + +$$Z_{L,tot} = (j\omega L+R) \mid \mid \frac{1}{j\omega C} =\frac{sL+R}{1+sRC+s^{2}LC}$$ + +[image] + +# Capacité +![rf-capacitor.png](medias%2Frf-capacitor.png ':size=50%') + +Facteur de qualité : +$$Q(f) = \frac{X_{C}(f)}{R} \qquad \qquad \omega_{r} ≃\omega_{0}=\frac{1}{\sqrt{ LC }}$$ + +Réactance & Impédance: +$$X_{C}=\frac{1}{\omega C} \qquad \qquad Z_{C}=\frac{1}{j\omega C}$$ + +[image] + +# Résistance +![rf-resistor.png](medias%2Frf-resistor.png ':size=35%') + + + diff --git a/infotro/Eln/medias/rf-capacitor.png b/infotro/Eln/medias/rf-capacitor.png new file mode 100644 index 0000000000000000000000000000000000000000..f8b8fa36cb0f83fe4360fc8c8c11f5109da856f5 GIT binary patch literal 23721 zcmbTecRZGV|36GBtL%`y$xbC(*()TQ>{&M1qq4I}NH)oK+FLeBb~cHO>`ln;b##5N z`~LlLKOVow{p<4S`h0qv=h<-_@AvEVdam~ws;Vq|9ftx34GrzOyquI88rmf<`1d-j ztML1G+OQHdH1t4gNl8_CNl7{fCwmKP8*?-?wiurnQMtAUR2_zTISgDlt^|(Vs#jWG 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Programmation en langage assembleur](/infotro/SEm/PLA.md) diff --git a/infotro/_navbar.md b/infotro/_navbar.md index 9ff236a..cb0978e 100644 --- a/infotro/_navbar.md +++ b/infotro/_navbar.md @@ -11,6 +11,7 @@ * [AD/DA](/infotro/Eln/ADDA) * [Signaux et échantillonnage](/infotro/Eln/SignauxEtEchantillonnage) * [Filtres](/infotro/Eln/Filtres) + * [RF](/infotro/Eln/RF) * [SEm - Systèmes Embarqués](/infotro/SEm/) * [PLA - Programmation en langage assembleur](/infotro/SEm/PLA) * [ASM - Assembleur ARM](/infotro/SEm/ASM)