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Semester/SoSe 25/Mobilfunk/Conversion Table.md

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+---
+title: Conversion Table - Note
+timestamp: 15.08.2025 - 16:59
+tags:
+  - Note
+---
+![logo](logo.png)
+# Conversion Table
+
+>[!info] Logarithmic Conversion
+>Definition of Bell:
+>$1B = \log_{10}\frac{P_1}{P_2}$
+>Therefor a Dezibell:
+>$P_{dB} = 10\cdot\log_{10}\frac{P_1}{P_2} \longleftrightarrow \frac{P_1}{P_2} = 10^\frac{P_{dB}}{10}$ 
+
+
+Value Conversion according to:
+$$P_{dB} = 10 \cdot \log_{10} x$$
+
+| Value | DB  | Note          |
+| ----- | --- | ------------- |
+| 2     | 3   |               |
+| 4     | 6   |               |
+| 5     | 7   |               |
+| 10    | 10  |               |
+| 0.2   | -7  | $\frac{1}{5}$ |
+| 0.5   | -3  | $\frac{1}{2}$ |
+
+
+# Dezibel Units
+>[!info] $dBm$ & $dBW$
+>decibel millitwatt
+>measurement of Power level $P_{dBm}$
+>Ratio for Power $P$ compared to $1mW$
+>$$P_{dBm}=10\cdot\log_{10}\frac{P}{1mW}dBm$$
+>
+>decibel Watt
+>similar but for the reference $1W$
+>$$P_{dBW}=10\cdot\log_{10}\frac{P}{1W}dBW$$
+
+
+>[!warning] Conversion
+>$$P_{dBm}= P_{dBW} -30$$
+
+
+
+
+
+---
+
+# Cell Parameter Configurationen
+
+> [!info] SIR - Signal to Interference Ratio
+> $$SIR = \frac{1}{6} (3k)^{\frac{\gamma}{2}}$$
+> Cluster Size k:
+> $$k = \frac{1}{3}(\frac{D}{R})^2$$
+> with D:
+> $$D = R \cdot \sqrt{3k}$$
+> Testing k is done by:
+> $$k = i^2 + ij + j^2; \quad i,j\in\mathbb{N}$$
+
+
+