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 <noreply@anthropic.com>
134 lines
4.5 KiB
Markdown
134 lines
4.5 KiB
Markdown
## Skyddsavstånd: fjärrfältsberäkning (utan kabeldämpning)
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* För fasta amatörradioanläggningar bestäms skyddsavståndet med fjärrfältsformeln
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<fragment>
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$d=\dfrac{\sqrt{30\,\Omega\cdot P_A\cdot G_i}}{E}$
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</fragment>
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--- style="font-size: 0.7em;"
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#### Tilläggsinformation om moduleringsmetoder vid beräkning av skyddsavstånd
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* Spetseffekten (PEP) omvandlas till medeleffekt med en faktor beroende på moduleringsmetod; medeleffekten används i fjärrfältsformeln
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* De flesta moduleringsmetoder har här faktorn $\num{1}$
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* ATV: faktor $\num{0,38}$
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<note>
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EN 50413; för amatörradio är endast ATV med $\num{0,38}$ och SATV med $\num{0,54}$ relevanta
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</note>
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--- style="font-size: smaller;"
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#### Räkneexempel 1
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<left>
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* givet: $E = \qty{28}{\volt\per\meter}$
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* givet: $P_S = P_A = \qty{100}{\watt}$
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</left>
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<right>
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* givet: $G_i = 1,64$
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* sökt: $d$
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</right>
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<fragment>
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$\begin{split}E &= \frac{\sqrt{\qty{30}{\ohm} \cdot P_A \cdot G_i}}{d}\\ \Rightarrow d &= \frac{\sqrt{\qty{30}{\ohm} \cdot P_A \cdot G_i}}{E}\\ &= \frac{\sqrt{\qty{30}{\ohm} \cdot \qty{100}{\watt} \cdot 1,64}}{\qty{28}{\volt\per\meter}}\\ &\approx \qty{2,5}{\meter}\end{split}$
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</fragment>
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---
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## Skyddsavstånd: hänsyn till kabeldämpning
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* Först beräknas den ekvivalent isotropiskt utstrålade effekten (EIRP)
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<fragment>
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$P_\text{EIRP} = P_S\cdot10^{\frac{g_d - a + \qty{2,15}{\dB}}{\qty{10}{\dB}}}$
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</fragment>
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--- style="font-size: smaller;"
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#### Räkneexempel 2
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<left>
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* givet: $E = \qty{28}{\volt\per\meter}$
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* givet: $P_S = \qty{300}{\watt}$
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* givet: $a = \qty{0,5}{\dB}$
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</left>
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<right>
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* givet: $g_d = \qty{0}{\dBd}$
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* sökt: $d$
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</right>
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<fragment>
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<left>
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$\begin{split}P_{EIRP} &= P_S \cdot 10^{\frac{g_d -a + \qty{2,15}{\dB}}{\qty{10}{\dB}}}\\ &= \qty{300}{\watt} \cdot 10^{\frac{\qty{0}{\dBd} - \qty{0,5}{\dB} + \qty{2,15}{\dB}}{\qty{10}{\dB}}}\\ &\approx \qty{438,7}{\watt}\end{split}$
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</left>
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</fragment>
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<fragment>
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<right>
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$\begin{split}E &= \frac{\sqrt{\qty{30}{\ohm} \cdot P_{EIRP}}}{d}\\ \Rightarrow d &= \frac{\sqrt{\qty{30}{\ohm} \cdot P_{EIRP}}}{E}\\ &= \frac{\sqrt{\qty{30}{\ohm} \cdot \qty{438,7}{\watt}}}{\qty{28}{\volt\per\meter}}\\ &\approx \qty{4,10}{\meter}\end{split}$
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</right>
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</fragment>
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--- style="font-size: smaller;"
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#### Räkneexempel 3
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<left>
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* givet: $E = \qty{28}{\volt\per\meter}$
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* givet: $P_S = \qty{700}{\watt}$
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* givet: $a = \qty{0,5}{\dB}$
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</left>
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<right>
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* givet: $g_d = \qty{0}{\dBd}$
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* sökt: $d$
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</right>
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<fragment>
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<left>
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$\begin{split}P_{EIRP} &= P_S \cdot 10^{\frac{g_d -a + \qty{2,15}{\dB}}{\qty{10}{\dB}}}\\ &= \qty{700}{\watt} \cdot 10^{\frac{\qty{0}{\dBd} - \qty{0,5}{\dB} + \qty{2,15}{\dB}}{\qty{10}{\dB}}}\\ &\approx \qty{1023,5}{\watt}\end{split}$
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</left>
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</fragment>
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<fragment>
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<right>
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$\begin{split}E &= \frac{\sqrt{\qty{30}{\ohm} \cdot P_{EIRP}}}{d}\\ \Rightarrow d &= \frac{\sqrt{\qty{30}{\ohm} \cdot P_{EIRP}}}{E}\\ &= \frac{\sqrt{\qty{30}{\ohm} \cdot \qty{1023,5}{\watt}}}{\qty{28}{\volt\per\meter}}\\ &\approx \qty{6,26}{\meter}\end{split}$
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</right>
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</fragment>
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--- style="font-size: smaller;"
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#### Räkneexempel 4
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<left>
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* givet: $E = \qty{28}{\volt\per\meter}$
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* givet: $P_S = \qty{75}{\watt}$
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* givet: $a = \qty{1,5}{\dB}$
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</left>
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<right>
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* givet: $g_d = \qty{11,5}{\dBd}$
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* sökt: $d$
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</right>
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<fragment>
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<left>
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$\begin{split}P_{EIRP} &= P_S \cdot 10^{\frac{g_d -a + \qty{2,15}{\dB}}{\qty{10}{\dB}}}\\ &= \qty{75}{\watt} \cdot 10^{\frac{\qty{11,5}{\dBd} - \qty{1,5}{\dB} + \qty{2,15}{\dB}}{\qty{10}{\dB}}}\\ &\approx \qty{1230,4}{\watt}\end{split}$
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</left>
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</fragment>
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<fragment>
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<right>
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$\begin{split}E &= \frac{\sqrt{\qty{30}{\ohm} \cdot P_{EIRP}}}{d}\\ \Rightarrow d &= \frac{\sqrt{\qty{30}{\ohm} \cdot P_{EIRP}}}{E}\\ &= \frac{\sqrt{\qty{30}{\ohm} \cdot \qty{1230,4}{\watt}}}{\qty{28}{\volt\per\meter}}\\ &\approx \qty{6,86}{\meter}\end{split}$
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</right>
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</fragment>
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--- style="font-size: smaller;"
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#### Räkneexempel 5
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<left>
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* givet: $E = \qty{61}{\volt\per\meter}$
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* givet: $P_S = \qty{40}{\watt}$
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* givet: $a = \qty{2}{\dB}$
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</left>
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<right>
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* givet: $g_d = \qty{18}{\dBd}$
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* sökt: $d$
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</right>
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<fragment>
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<left>
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$\begin{split}P_{EIRP} &= P_S \cdot 10^{\frac{g_d -a + \qty{2,15}{\dB}}{\qty{10}{\dB}}}\\ &= \qty{40}{\watt} \cdot 10^{\frac{\qty{18}{\dBd} - \qty{2}{\dB} + \qty{2,15}{\dB}}{\qty{10}{\dB}}}\\ &\approx \qty{2612,5}{\watt}\end{split}$
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</left>
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</fragment>
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<fragment>
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<right>
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$\begin{split}E &= \frac{\sqrt{\qty{30}{\ohm} \cdot P_{EIRP}}}{d}\\ \Rightarrow d &= \frac{\sqrt{\qty{30}{\ohm} \cdot P_{EIRP}}}{E}\\ &= \frac{\sqrt{\qty{30}{\ohm} \cdot \qty{2612,5}{\watt}}}{\qty{61}{\volt\per\meter}}\\ &\approx \qty{4,6}{\meter}\end{split}$
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</right>
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</fragment>
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