From f0784cfef658101c96519fe9eee042bdaaf4f6cb Mon Sep 17 00:00:00 2001 From: Klagarge Date: Wed, 20 Mar 2024 17:38:42 +0100 Subject: [PATCH] add transmission ligne & smith chart --- infotro/Eln/README.md | 3 +- infotro/Eln/RF.md | 31 ++++++++++++++++-- .../Eln/medias/add_line_on_smith_chart.png | Bin 0 -> 48418 bytes infotro/Eln/medias/rf-capacitor-graph.png | Bin 0 -> 63675 bytes infotro/Eln/medias/rf-inductor-graph.png | Bin 0 -> 76796 bytes 5 files changed, 30 insertions(+), 4 deletions(-) create mode 100644 infotro/Eln/medias/add_line_on_smith_chart.png create mode 100644 infotro/Eln/medias/rf-capacitor-graph.png create mode 100644 infotro/Eln/medias/rf-inductor-graph.png diff --git a/infotro/Eln/README.md b/infotro/Eln/README.md index 3a1bb68..3fbd37a 100644 --- a/infotro/Eln/README.md +++ b/infotro/Eln/README.md @@ -5,4 +5,5 @@ # Convertisseurs - [AD/DA](/infotro/Eln/ADDA) - [Signaux et échantillonnage](/infotro/Eln/SignauxEtEchantillonnage) -- [Filtres](/infotro/Eln/Filtres) \ No newline at end of file +- [Filtres](/infotro/Eln/Filtres) +- [RF](/infotro/Eln/RF) \ No newline at end of file diff --git a/infotro/Eln/RF.md b/infotro/Eln/RF.md index ef3264c..53b5643 100644 --- a/infotro/Eln/RF.md +++ b/infotro/Eln/RF.md @@ -32,7 +32,7 @@ avec: - $\mu_0$: perméabilité magnétique du vide $= 4\pi 10^{-7} H/m$ On peut en déduire la résistance en courant alternatif: -$$R_{AC} = \frac{l\sqrt{\rho\pi\mu_0}}{2\pi r} \sqrt{f}$$ +$$R_{AC} = \frac{l\sqrt{\rho\pi\mu_0}}{2\pi r} \sqrt{f} \qquad \qquad R_{AC(f_{2})} = R_{AC(f_{1})} \cdot \sqrt{ \frac{f_{2}}{f_{1}} }$$ Pour calculer l'inductance et la capacité d'un fil, on peut utiliser les formules suivantes: $$\begin{align} @@ -59,7 +59,7 @@ SRF: Self Resonant Frequency = $\frac{\omega_{r}}{2\pi}$ $$Z_{L,tot} = (j\omega L+R) \mid \mid \frac{1}{j\omega C} =\frac{sL+R}{1+sRC+s^{2}LC}$$ -[image] +![rf-inductor.png](medias/rf-inductor-graph.png) # Capacité ![rf-capacitor.png](medias%2Frf-capacitor.png ':size=50%') @@ -70,10 +70,35 @@ $$Q(f) = \frac{X_{C}(f)}{R} \qquad \qquad \omega_{r} ≃\omega_{0}=\frac{1}{\sqr Réactance & Impédance: $$X_{C}=\frac{1}{\omega C} \qquad \qquad Z_{C}=\frac{1}{j\omega C}$$ -[image] +![rf-capacitor-graph.png](medias/rf-capacitor-graph.png) # Résistance ![rf-resistor.png](medias%2Frf-resistor.png ':size=35%') +# Transmission line +$$ k = \frac{2\pi}{\lambda} \qquad \qquad \lambda = \frac{c_{mat}}{f} $$ + +$\Gamma$ (Gamma) : coefficient de réflexion + +# Smith Chart + + +## Ajouter une ligne de réflexion + + +1. Placer $Z1$ + 1. Normaliser ($\hat{Z_{1}}=\frac{Z_{1}}{Z_{0}}$) + 2. Placer le point au croisement de l'axe réel et imaginaire (Impédance = bleu) +2. Chercher $\Gamma$ (indice de reflexion) + 1. Tracer l'angle ("Angle of reflexion coefficient in degrees") + 2. Tracer le module (cercle au compas + rapport sur les échelles du bas) +3. Ajouter la ligne selon le sens + - $\circlearrowright$ : toward generator + - $\circlearrowleft$ : toward load +4. Lire les nouvelles valeures + 1. Tracer le nouvel angle $\to \angle(\Gamma_{2})$ + 2. 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