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Diffstat (limited to 'exercise03/exercise03.tex')
| -rw-r--r-- | exercise03/exercise03.tex | 24 |
1 files changed, 21 insertions, 3 deletions
diff --git a/exercise03/exercise03.tex b/exercise03/exercise03.tex index be192ce..ab95152 100644 --- a/exercise03/exercise03.tex +++ b/exercise03/exercise03.tex @@ -307,7 +307,7 @@ \item $\SI{20}{dBV} \cdot \log_{10} \left(\frac{\SI{2}{V}}{\SI{1}{V}}\right) = \SI{6}{dBV}$ (20 instead of 10 for voltages and currents) \item $\SI{10}{dB} \cdot \log_{10} \left(400000\right) = \SI{53}{dB}$ \item $\SI{10}{dBHz} \cdot \log_{10} \left(\frac{\SI{5}{GHz}}{\SI{1}{Hz}}\right) = \SI{97}{dbHz}$ - \item $\SI{10}{dBm/Hz} \cdot \log_{10} \left(\frac{\SI{8}{fW}}{\SI{1}{mW}}\right) = \SI{-111}{dB/Hz}$ + \item $\SI{10}{dBm/Hz} \cdot \log_{10} \left(\frac{\SI{8}{fW/MHz}}{\SI{1}{mW/Hz}}\right) = \SI{10}{dBm/Hz} \cdot \log_{10} \left(\frac{10^{-6} \cdot \SI{8}{fW/Hz}}{\SI{1}{mW/Hz}}\right) = \SI{-171}{dBm/Hz}$ \item $\SI{1}{\micro\volt} \cdot 10^{\SI{5}{dB\micro\volt} / 20} = \SI{1.8}{\micro\volt}$ \item $\SI{1}{mW} \cdot 10^{\SI{-10}{dBm} / 10} = \SI{100}{\micro.W}$ \end{enumerate} @@ -340,7 +340,7 @@ \begin{split} \SI{-73}{dBm} &\equiv \SI{50.1}{pW} \\ U = \sqrt{P \cdot R} &= \sqrt{\SI{50.1}{pW} \cdot \SI{50}{\ohm}} = \SI{50}{\micro\volt} \\ - \SI{50}{\micro\volt} &\equiv \SI{17}{dB\micro\volt} + \SI{50}{\micro\volt} &\equiv \underbrace{\SI{20}{dB\micro\volt}}_{\text{Attention!}} \cdot \log_{10}\left(\frac{\SI{50}{\micro\volt}}{\SI{1}{\micro\volt}}\right) = \SI{34}{dB\micro\volt} \end{split} \end{equation*} \item 2nd way: Convert everything to logarithmic scale. The multiplication of power and resistance must happen with ``pure'' SI units. @@ -350,10 +350,28 @@ \SI{-73}{dBm} \underbrace{- \SI{30}{dB}}_{\text{\si{mW} to \si{W}}} &= \SI{-103}{dBW} \quad \text{SI unit!} \\ \SI{-103}{dBW} + \SI{17}{dB\ohm} &= \SI{-86}{dBV} \quad \text{SI unit!} \\ \SI{-86}{dBV} \underbrace{+ \SI{120}{dB}}_{\text{\si{V} to \si{\micro\volt}}} &= \SI{34}{dB\micro\volt} \\ - \SI{34}{dB\micro\volt} &\equiv \SI{50}{\micro\volt} + \SI{34}{dB\micro\volt} &\equiv \SI{1}{\micro\volt} \cdot 10^{\frac{34}{20}} = \SI{50}{\micro\volt} \end{split} \end{equation*} \end{itemize} + + \textit{Remarks:} Conversion of different SI prefixes: + \begin{itemize} + \item From \si{mW} to \si{W}: + \begin{equation*} + \begin{split} + \SI{1}{mW} &= \SI{0.001}{W} \\ + \SI{10}{dB} \cdot \log_{10}\left(\frac{\SI{0.001}{W}}{\SI{1}{mW}}\right) &= \SI{-30}{dB} + \end{split} + \end{equation*} + \item From \si{V} to \si{\micro\volt}: + \begin{equation*} + \begin{split} + \SI{1}{V} &= \SI{1000000}{\micro\volt} \\ + \SI{20}{dB} \cdot \log_{10}\left(\frac{\SI{1000000}{\micro\volt}}{\SI{1}{V}}\right) &= \SI{120}{dB} + \end{split} + \end{equation*} + \end{itemize} \end{tasks} \end{solution} |