SuperminarenandClaude Sonnet 5.5
f7fa8cfbc1
- Sections and slides rewritten in Swedish; German law and institutions replaced by Swedish/CEPT/ITU equivalents (PTS, SSA, PTSFS 2025:1, SSMFS 2008:18), unverified statements marked "% TODO VERIFY" - New toc: INSTEG, HAREC, UPPGRADERING; section idents are Swedish (see ident-map.tsv) - Exam-question tags, BNetzA question pool, solutions and the German SWL course removed - Static pages, snippets, applets, READMEs and image alt-texts translated - TikZ labels translated; SVG drawings regenerated (drawing 689 still fails to build upstream: it references a missing photo) - Changed from the original: not endorsed by DARC e.V., SSA or PTS Co-Authored-By: Claude Sonnet 5.5 <[email protected]>
49 lines
1.8 KiB
Markdown
49 lines
1.8 KiB
Markdown
## Noggrannhet hos frekvenser och mätområden
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* Noggrannhet anges i $\unit{\percent}$ (t.ex. ${1 \cdot \num{10^{-2}}}$) eller i parts per million ($\qty{1}{\ppm} = {1 \cdot \num{10^{-6}}}$)
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* Ibland anges den direkt i exponentialskrivsätt, t.ex. ${1 \cdot \num{10^{-7}}}$
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* Den angivna noggrannheten multipliceras med frekvensen för att beräkna möjlig avvikelse hos mätvärden eller visningar
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<note>
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Anmärkning om omräkning/skrivsätt för tiopotenser:
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$1 \cdot \num{10^{-2}} = \frac{1}{\num{10^2}}$
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$1 \cdot \num{10^{-6}} = \frac{1}{\num{10^6}}$
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osv.
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</note>
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---
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#### Exempel 1
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* given: $f = \qty{435}{\mega\hertz}$
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* sökt: $\qty{1}{\ppm}$ av $f$
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<fragment>
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$\qty{435}{\mega\hertz} \cdot \frac{1}{\num{10^6}} = \frac{435\cdot \qty{\cancel{10^6}}{\hertz}}{\cancel{\num{10^6}}} = \qty{435}{\hertz}$
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</fragment>
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---
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#### Exempel 2
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* given: $f = \qty{145}{\mega\hertz}$
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* given: avvikelse $= \qty{10}{\ppm}$
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* sökt: $f_{\mathrm{min}}, f_{\mathrm{max}}$
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<fragment>
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$\begin{split}\Delta f &= \qty{145}{\mega\hertz} \cdot \frac{10}{10^6}\\ &= \frac{145\cdot \qty{\cancel{10^6}}{\hertz} \cdot 10}{\cancel{10^6}}\\ &= \qty{1450}{\hertz}\end{split}$
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</fragment>
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<fragment>
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<left>
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$\begin{split}f_{\mathrm{min}} &= f\,-\,\Delta f\\ &= \qty{145}{\mega\hertz}\,-\,\qty{1450}{\hertz}\\ &= \qty{144,99855}{\mega\hertz}\end{split}$
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</left>
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<right>
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$\begin{split}f_{\mathrm{max}} &= f\,+\,\Delta f\\ &= \qty{145}{\mega\hertz}\,+\,\qty{1450}{\hertz}\\ &= \qty{145,00145}{\mega\hertz}\end{split}$
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</right>
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</fragment>
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---
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#### Exempel 3
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* given: $f = \qty{29}{\mega\hertz}$
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* given: avvikelse $= \qty{0,01}{\percent}$
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* sökt: $\Delta f$
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<fragment>
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$\begin{split}\Delta f &= \qty{29}{\mega\hertz} \cdot \qty{0,01}{\percent}\\ &= 29\cdot \qty{\cancel{10^6}}{\hertz} \cdot 100\cdot \cancel{\num{10^{-6}}}\\ &= \qty{2900}{\hertz}\end{split}$
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</fragment>
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