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]>
105 lines
3.4 KiB
Markdown
105 lines
3.4 KiB
Markdown
--- style="font-size: 0.7em;"
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## Antennkarakteristik och riktverkan
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<left>
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[picture:264:a_strahlungscharakteristik_dipol_richt:Strålningskarakteristik för en riktantenn jämfört med en dipol]
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* *Fram/bak-förhållandet* beskriver hur mycket bättre det sänds och tas emot i huvudstrålriktningen.
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</left>
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<right>
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* Riktantenner sänder och tar emot även bakåt – en oönskad effekt.
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* Antennförstärkningen avser bara huvudstrålriktningen (jämfört med en dipol eller en isotrop strålare).
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</right>
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---
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### Fram/bak-förhållande i decibel
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<left>
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[picture:263:a_strahlungscharakteristik_richt:Strålningskarakteristik för en riktantenn]
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</left>
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<right>
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* Fram/bak-förhållandet anges ofta i decibel.
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</right>
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---
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#### Räkneexempel 1
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* given: $P_R = \qty{0,6}{\watt}$
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* given: $P_V = \qty{15}{\watt}$
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* sökt: $\frac{\text{Fram}}{\text{Bak}}$
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<fragment>
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$\begin{split}\frac{\text{Fram}}{\text{Bak}} &= 10 \cdot \log_{10}{\left(\frac{P_V}{P_R}\right)} \unit{\dB}\\ &= 10 \cdot \log_{10}{\left(\frac{\qty{15}{\watt}}{\qty{0,6}{\watt}}\right)} \unit{\dB}\\ &= \qty{14}{\dB}\end{split}$
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</fragment>
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---
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--- style="font-size: smaller;"
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#### Räkneexempel 2
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<left>
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* given: $g_D= \qty{10}{\dB}$
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* given: $\frac{\text{Fram}}{\text{Bak}} = \qty{20}{\dB}$
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</left>
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<right>
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* given: $P_S = \qty{100}{\watt}$
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* sökt: $P_R$
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</right>
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<left>
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<fragment>
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$\begin{split}P_V &= P_{ERP}\\ &= P_S \cdot 10^{\frac{g_d}{\qty{10}{\dB}}}\\ &= \qty{100}{\watt} \cdot 10^{\frac{\qty{10}{\dB}}{\qty{10}{\dB}}}\\ &= \qty{1000}{\watt}\end{split}$
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</fragment>
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</left>
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<right>
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<fragment>
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$\begin{split}\qty{20}{\dB} &= 10 \cdot \log_{10}{\left(\frac{P_V}{P_R}\right)} \unit{\dB}\\ \Rightarrow \frac{P_V}{P_R} &= 10^{\frac{\qty{20}{\dB}}{\qty{10}{\dB}}}\\ &= 100\\ \Rightarrow P_R &= \frac{P_V}{100}\\ &= \frac{\qty{1000}{\watt}}{100}\\ &= \qty{10}{\watt}\end{split}$
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</fragment>
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</right>
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---
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--- style="font-size: smaller;"
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#### Räkneexempel 3
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<left>
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* given: $g_D= \qty{15}{\dB}$
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* given: $\frac{\text{Fram}}{\text{Bak}} = \qty{25}{\dB}$
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</left>
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<right>
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* given: $P_S = \qty{6}{\watt}$
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* sökt: $P_R$
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</right>
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<left>
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<fragment>
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$\begin{split}P_V &= P_{ERP}\\ &= P_S \cdot 10^{\frac{g_d}{\qty{10}{\dB}}}\\ &= \qty{6}{\watt} \cdot 10^{\frac{\qty{15}{\dB}}{\qty{10}{\dB}}}\\ &= \qty{189,7}{\watt}\end{split}$
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</fragment>
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</left>
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<right>
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<fragment>
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$\begin{split}\qty{25}{\dB} &= 10 \cdot \log_{10}{\left(\frac{P_V}{P_R}\right)} \unit{\dB}\\ \Rightarrow \frac{P_V}{P_R} &= 10^{\frac{\qty{25}{\dB}}{\qty{10}{\dB}}}\\ &= 316,2\\ \Rightarrow P_R &= \frac{P_V}{316,2}\\ &= \frac{\qty{189,7}{\watt}}{316,2}\\ &= \qty{0,6}{\watt}\end{split}$
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</fragment>
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</right>
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---
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--- style="font-size: smaller;"
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#### Räkneexempel 4
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<left>
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* given: $U_V = \qty{300}{\micro\volt\per\meter}$
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* given: $U_R = \qty{20}{\micro\volt\per\meter}$
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</left>
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<right>
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* given: $U_D = \qty{128}{\micro\volt\per\meter}$
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* sökt: $g_D$, $\frac{\text{Fram}}{\text{Bak}}$
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</right>
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<left>
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<fragment>
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$\begin{split}g_D &= 20 \cdot \log_{10}{\left(\frac{U_V}{U_D}\right)} \unit{\dB}\\ &= 20 \cdot \log_{10}{\left(\frac{\qty{300}{\micro\volt\per\meter}}{\qty{128}{\micro\volt\per\meter}}\right)}\\ &= \qty{7,4}{\dB}\end{split}$
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</fragment>
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</left>
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<right>
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<fragment>
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$\begin{split}\frac{\text{Fram}}{\text{Bak}} &= 20 \cdot \log_{10}{\left(\frac{U_V}{U_R}\right)} \unit{\dB}\\ &= 20 \cdot \log_{10}{\left(\frac{\qty{300}{\micro\volt\per\meter}}{\qty{20}{\micro\volt\per\meter}}\right)}\\ &= \qty{23,5}{\dB}\end{split}$
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</fragment>
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</right>
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