Superminaren/50ohm-contents-dl
1
0
Fork 0
Code Issues Pull Requests Actions Packages Projects Releases Wiki Activity

fix, slides: replace aligned-environment by split-environment

Browse Source 
This is not relevant in our case as it just influences equation
numbering. But to be consistent we change it though.
This commit is contained in:
Mario Haustein
2026-02-06 18:22:58 +01:00
parent fca3de5b57
commit 9a58094239
13 changed files with 84 additions and 84 deletions
Download Patch File Download Diff File Expand all files Collapse all files
contents/slides/frequenzgenauigkeit.md
+10 -10
View File
@@ -31,7 +31,7 @@ $435MHz \cdot \frac{1}{10^6} = \frac{435\cdot \cancel{10^6}Hz}{\cancel{10^6}} =
* gesucht: $f_{min}, f_{max}$
<fragment>
$\begin{aligned}f_{min} &= f\,-\,f \cdot \frac{10}{10^6}\\ &= 14,2MHz\,-\,\frac{14,2\cdot \cancel{10^6}Hz\cdot 10}{\cancel{10^6}}\\ &= 14,2MHz\,-\,142Hz\\ &= 14,199858MHz\end{aligned}$
$\begin{split}f_{min} &= f\,-\,f \cdot \frac{10}{10^6}\\ &= 14,2MHz\,-\,\frac{14,2\cdot \cancel{10^6}Hz\cdot 10}{\cancel{10^6}}\\ &= 14,2MHz\,-\,142Hz\\ &= 14,199858MHz\end{split}$
</fragment>
---
#### Lösungsweg Teil 2
@@ -40,7 +40,7 @@ $\begin{aligned}f_{min} &= f\,-\,f \cdot \frac{10}{10^6}\\ &= 14,2MHz\,-\,\frac{
* gesucht: $f_{min}, f_{max}$
<fragment>
$\begin{aligned}f_{max} &= f\,+\,f \cdot \frac{10}{10^6}\\ &= 14,2MHz\,+\,\frac{14,2\cdot \cancel{10^6}Hz\cdot 10}{\cancel{10^6}}\\ &= 14,2MHz\,+\,142Hz\\ &= 14,200142MHz\end{aligned}$
$\begin{split}f_{max} &= f\,+\,f \cdot \frac{10}{10^6}\\ &= 14,2MHz\,+\,\frac{14,2\cdot \cancel{10^6}Hz\cdot 10}{\cancel{10^6}}\\ &= 14,2MHz\,+\,142Hz\\ &= 14,200142MHz\end{split}$
</fragment>
---
[question:AI506]
@@ -51,7 +51,7 @@ $\begin{aligned}f_{max} &= f\,+\,f \cdot \frac{10}{10^6}\\ &= 14,2MHz\,+\,\frac{
* gesucht: $\Delta f$
<fragment>
$\begin{aligned}\Delta f &= 29MHz \cdot 0,01\%\\ &= 29\cdot \cancel{10^6}Hz \cdot 100\cdot \cancel{10^{-6}}\\ &= 2900Hz\end{aligned}$
$\begin{split}\Delta f &= 29MHz \cdot 0,01\%\\ &= 29\cdot \cancel{10^6}Hz \cdot 100\cdot \cancel{10^{-6}}\\ &= 2900Hz\end{split}$
</fragment>
---
[question:AI507]
@@ -62,7 +62,7 @@ $\begin{aligned}\Delta f &= 29MHz \cdot 0,01\%\\ &= 29\cdot \cancel{10^6}Hz \cdo
* gesucht: $\Delta f$
<fragment>
$\begin{aligned}\Delta f &= 14100kHz \cdot 0,00001\%\\ &= 14,1\cdot \cancel{10^6}Hz \cdot 0,1\cdot \cancel{10^{-6}}\\ &= 1,41Hz\end{aligned}$
$\begin{split}\Delta f &= 14100kHz \cdot 0,00001\%\\ &= 14,1\cdot \cancel{10^6}Hz \cdot 0,1\cdot \cancel{10^{-6}}\\ &= 1,41Hz\end{split}$
</fragment>
---
[question:AI508]
@@ -73,7 +73,7 @@ $\begin{aligned}\Delta f &= 14100kHz \cdot 0,00001\%\\ &= 14,1\cdot \cancel{10^6
* gesucht: $\Delta f$
<fragment>
$\begin{aligned}\Delta f &= 100MHz \cdot \frac{1}{10^6}\\ &= \frac{100\cdot \cancel{10^6}Hz}{\cancel{10^6}}\\ &= 100Hz\end{aligned}$
$\begin{split}\Delta f &= 100MHz \cdot \frac{1}{10^6}\\ &= \frac{100\cdot \cancel{10^6}Hz}{\cancel{10^6}}\\ &= 100Hz\end{split}$
</fragment>
---
[question:AI509]
@@ -84,14 +84,14 @@ $\begin{aligned}\Delta f &= 100MHz \cdot \frac{1}{10^6}\\ &= \frac{100\cdot \can
* gesucht: $f_{min},f_{max}$
<fragment>
$\begin{aligned}\Delta f &= 145MHz \cdot \frac{10}{10^6}\\ &= \frac{145\cdot \cancel{10^6}Hz \cdot 10}{\cancel{10^6}}\\ &= 1450Hz\end{aligned}$
$\begin{split}\Delta f &= 145MHz \cdot \frac{10}{10^6}\\ &= \frac{145\cdot \cancel{10^6}Hz \cdot 10}{\cancel{10^6}}\\ &= 1450Hz\end{split}$
</fragment>
<fragment>
<left>
$\begin{aligned}f_{min} &= f\,-\,\Delta f\\ &= 145MHz\,-\,1450Hz\\ &= 144,99855MHz\end{aligned}$
$\begin{split}f_{min} &= f\,-\,\Delta f\\ &= 145MHz\,-\,1450Hz\\ &= 144,99855MHz\end{split}$
</left>
<right>
$\begin{aligned}f_{max} &= f\,+\,\Delta f\\ &= 145MHz\,+\,1450Hz\\ &= 145,00145MHz\end{aligned}$
$\begin{split}f_{max} &= f\,+\,\Delta f\\ &= 145MHz\,+\,1450Hz\\ &= 145,00145MHz\end{split}$
</right>
</fragment>
---
@@ -105,11 +105,11 @@ $\begin{aligned}f_{max} &= f\,+\,\Delta f\\ &= 145MHz\,+\,1450Hz\\ &= 145,00145M
<fragment>
<left>
$\begin{aligned}\Delta f &= 144,4MHz \cdot \frac{1}{10^6}\\ &= \frac{144,4\cdot \cancel{10^6}Hz}{\cancel{10^6}}\\ &= 144,4Hz\end{aligned}$
$\begin{split}\Delta f &= 144,4MHz \cdot \frac{1}{10^6}\\ &= \frac{144,4\cdot \cancel{10^6}Hz}{\cancel{10^6}}\\ &= 144,4Hz\end{split}$
</left>
</fragment>
<fragment>
<right>
$\begin{aligned}f_{B,max,Abw} &= f_{B,max} + \Delta f\\ &= 2,7kHz + 144,4Hz\\ &= 2,8444kHz\end{aligned}$
$\begin{split}f_{B,max,Abw} &= f_{B,max} + \Delta f\\ &= 2,7kHz + 144,4Hz\\ &= 2,8444kHz\end{split}$
</right>
</fragment>
contents/slides/impedanztransformation.md
+2 -2
View File
@@ -45,7 +45,7 @@
* gesucht: $Z$
<fragment>
$\begin{aligned}Z &= \sqrt{Z_E \cdot Z_A}\\ &= \sqrt{240Ω \cdot 60Ω}\\ &= 120Ω\end{aligned}$
$\begin{split}Z &= \sqrt{Z_E \cdot Z_A}\\ &= \sqrt{240Ω \cdot 60Ω}\\ &= 120Ω\end{split}$
</fragment>
---
[question:AG418]
@@ -56,7 +56,7 @@ $\begin{aligned}Z &= \sqrt{Z_E \cdot Z_A}\\ &= \sqrt{240Ω \cdot 60Ω}\\ &= 120
* gesucht: $Z$
<fragment>
$\begin{aligned}Z &= \sqrt{Z_E \cdot Z_A}\\ &= \sqrt{600Ω \cdot 240Ω}\\ &= 380Ω\end{aligned}$
$\begin{split}Z &= \sqrt{Z_E \cdot Z_A}\\ &= \sqrt{600Ω \cdot 240Ω}\\ &= 380Ω\end{split}$
</fragment>
---
contents/slides/leistungsvertaerker.md
+4 -4
View File
@@ -176,12 +176,12 @@
<left>
<fragment>
$\begin{aligned}R_E &= \frac{(R_3+R_6) \cdot R_4}{(R_3 + R_6) + R_4}\\ &= \frac{220Ω + 150Ω) \cdot 6,8kΩ}{220Ω + 150Ω + 6,8kΩ}\\ &= \frac{2,516MΩ^2}{7170Ω}\\ &= 351Ω\end{aligned}$
$\begin{split}R_E &= \frac{(R_3+R_6) \cdot R_4}{(R_3 + R_6) + R_4}\\ &= \frac{220Ω + 150Ω) \cdot 6,8kΩ}{220Ω + 150Ω + 6,8kΩ}\\ &= \frac{2,516MΩ^2}{7170Ω}\\ &= 351Ω\end{split}$
</fragment>
</left>
<right>
<fragment>
$\begin{aligned}\frac{U_Z}{U_{GS}} &= \frac{R_2 + R_E}{R_E}\\ \Rightarrow \frac{6,2V}{U_{GS}} &= \frac{270Ω+351Ω}{351Ω}\\ &= 1,77\\ \Rightarrow U_{GS} &= \frac{6,2V}{1,77}\\ &= 3,50V\end{aligned}$
$\begin{split}\frac{U_Z}{U_{GS}} &= \frac{R_2 + R_E}{R_E}\\ \Rightarrow \frac{6,2V}{U_{GS}} &= \frac{270Ω+351Ω}{351Ω}\\ &= 1,77\\ \Rightarrow U_{GS} &= \frac{6,2V}{1,77}\\ &= 3,50V\end{split}$
</fragment>
</right>
@@ -243,11 +243,11 @@ $\begin{aligned}\frac{U_Z}{U_{GS}} &= \frac{R_2 + R_E}{R_E}\\ \Rightarrow \frac{
<left>
<fragment>
$\begin{aligned}g &= P_2 - P_1\\ &= 43dBm - (-5dBm)\\ &= 43dBm + 5dBm\\ &= 48dB\end{aligned}$
$\begin{split}g &= P_2 - P_1\\ &= 43dBm - (-5dBm)\\ &= 43dBm + 5dBm\\ &= 48dB\end{split}$
</fragment>
</left>
<right>
<fragment>
$\begin{aligned}g &= 10 \cdot \log_{10}{(\frac{P_2}{P_1})}dB\\ &= 10 \cdot \log_{10}{(\frac{20W}{0,3mW})}dB \\ &\approx 48dB\end{aligned}$
$\begin{split}g &= 10 \cdot \log_{10}{(\frac{P_2}{P_1})}dB\\ &= 10 \cdot \log_{10}{(\frac{20W}{0,3mW})}dB \\ &\approx 48dB\end{split}$
</fragment>
</right>
contents/slides/modulatoren.md
+1 -1
View File
@@ -137,7 +137,7 @@
* gesucht: $f_{USB}$
<fragment>
$\begin{aligned}f_{USB} &= f_Q - (f_{LSB} - f_Q)\\ &= 9MHz - (9,0015MHz - 9MHz)\\ &= 9MHz - 0,0015MHz\\ &=8,9985MHz\end{aligned}$
$\begin{split}f_{USB} &= f_Q - (f_{LSB} - f_Q)\\ &= 9MHz - (9,0015MHz - 9MHz)\\ &= 9MHz - 0,0015MHz\\ &=8,9985MHz\end{split}$
</fragment>
---
contents/slides/naeherungsformel_2.md
+11 -11
View File
@@ -34,7 +34,7 @@ DIN EN 50413, für Amateurfunk relevant nur ATV mit 0,38 und SATV mit 0,54
</right>
<fragment>
$\begin{aligned}E &= \frac{\sqrt{30Ω \cdot P_A \cdot G_i}}{d}\\ \Rightarrow d &= \frac{\sqrt{30Ω \cdot P_A \cdot G_i}}{E}\\ &= \frac{\sqrt{30Ω \cdot 100W \cdot 1,64}}{28\frac{V}{m}}\\ &= 2,5m\end{aligned}$
$\begin{split}E &= \frac{\sqrt{30Ω \cdot P_A \cdot G_i}}{d}\\ \Rightarrow d &= \frac{\sqrt{30Ω \cdot P_A \cdot G_i}}{E}\\ &= \frac{\sqrt{30Ω \cdot 100W \cdot 1,64}}{28\frac{V}{m}}\\ &= 2,5m\end{split}$
</fragment>
---
@@ -63,12 +63,12 @@ $P_\text{EIRP} = P_S\cdot10^{\frac{g_d - a + 2,15}{10}}$
<fragment>
<left>
$\begin{aligned}P_{EIRP} &= P_S \cdot 10^{\frac{g_d -a + 2,15dB}{10dB}}\\ &= 300W \cdot 10^{\frac{0dBd - 0,5dB + 2,15dB}{10dB}}\\ &= 438,7W\end{aligned}$
$\begin{split}P_{EIRP} &= P_S \cdot 10^{\frac{g_d -a + 2,15dB}{10dB}}\\ &= 300W \cdot 10^{\frac{0dBd - 0,5dB + 2,15dB}{10dB}}\\ &= 438,7W\end{split}$
</left>
</fragment>
<fragment>
<right>
$\begin{aligned}E &= \frac{\sqrt{30Ω \cdot P_{EIRP}}}{d}\\ \Rightarrow d &= \frac{\sqrt{30Ω \cdot P_{EIRP}}}{E}\\ &= \frac{\sqrt{30Ω \cdot 438,7W}}{28\frac{V}{m}}\\ &= 4,10m\end{aligned}$
$\begin{split}E &= \frac{\sqrt{30Ω \cdot P_{EIRP}}}{d}\\ \Rightarrow d &= \frac{\sqrt{30Ω \cdot P_{EIRP}}}{E}\\ &= \frac{\sqrt{30Ω \cdot 438,7W}}{28\frac{V}{m}}\\ &= 4,10m\end{split}$
</right>
</fragment>
@@ -90,12 +90,12 @@ $\begin{aligned}E &= \frac{\sqrt{30Ω \cdot P_{EIRP}}}{d}\\ \Rightarrow d &= \fr
<fragment>
<left>
$\begin{aligned}P_{EIRP} &= P_S \cdot 10^{\frac{g_d -a + 2,15dB}{10dB}}\\ &= 700W \cdot 10^{\frac{0dBd - 0,5dB + 2,15dB}{10dB}}\\ &= 1023,5W\end{aligned}$
$\begin{split}P_{EIRP} &= P_S \cdot 10^{\frac{g_d -a + 2,15dB}{10dB}}\\ &= 700W \cdot 10^{\frac{0dBd - 0,5dB + 2,15dB}{10dB}}\\ &= 1023,5W\end{split}$
</left>
</fragment>
<fragment>
<right>
$\begin{aligned}E &= \frac{\sqrt{30Ω \cdot P_{EIRP}}}{d}\\ \Rightarrow d &= \frac{\sqrt{30Ω \cdot P_{EIRP}}}{E}\\ &= \frac{\sqrt{30Ω \cdot 1023,5W}}{28\frac{V}{m}}\\ &= 6,26m\end{aligned}$
$\begin{split}E &= \frac{\sqrt{30Ω \cdot P_{EIRP}}}{d}\\ \Rightarrow d &= \frac{\sqrt{30Ω \cdot P_{EIRP}}}{E}\\ &= \frac{\sqrt{30Ω \cdot 1023,5W}}{28\frac{V}{m}}\\ &= 6,26m\end{split}$
</right>
</fragment>
@@ -117,12 +117,12 @@ $\begin{aligned}E &= \frac{\sqrt{30Ω \cdot P_{EIRP}}}{d}\\ \Rightarrow d &= \fr
<fragment>
<left>
$\begin{aligned}P_{EIRP} &= P_S \cdot 10^{\frac{g_d -a + 2,15dB}{10dB}}\\ &= 75W \cdot 10^{\frac{11,5dBd - 1,5dB + 2,15dB}{10dB}}\\ &= 1230,4W\end{aligned}$
$\begin{split}P_{EIRP} &= P_S \cdot 10^{\frac{g_d -a + 2,15dB}{10dB}}\\ &= 75W \cdot 10^{\frac{11,5dBd - 1,5dB + 2,15dB}{10dB}}\\ &= 1230,4W\end{split}$
</left>
</fragment>
<fragment>
<right>
$\begin{aligned}E &= \frac{\sqrt{30Ω \cdot P_{EIRP}}}{d}\\ \Rightarrow d &= \frac{\sqrt{30Ω \cdot P_{EIRP}}}{E}\\ &= \frac{\sqrt{30Ω \cdot 1230,4W}}{28\frac{V}{m}}\\ &= 6,86m\end{aligned}$
$\begin{split}E &= \frac{\sqrt{30Ω \cdot P_{EIRP}}}{d}\\ \Rightarrow d &= \frac{\sqrt{30Ω \cdot P_{EIRP}}}{E}\\ &= \frac{\sqrt{30Ω \cdot 1230,4W}}{28\frac{V}{m}}\\ &= 6,86m\end{split}$
</right>
</fragment>
@@ -144,12 +144,12 @@ $\begin{aligned}E &= \frac{\sqrt{30Ω \cdot P_{EIRP}}}{d}\\ \Rightarrow d &= \fr
<fragment>
<left>
$\begin{aligned}P_{EIRP} &= P_S \cdot 10^{\frac{g_d -a + 2,15dB}{10dB}}\\ &= 100W \cdot 10^{\frac{10,5dBd - 1,5dB + 2,15dB}{10dB}}\\ &= 1303,2W\end{aligned}$
$\begin{split}P_{EIRP} &= P_S \cdot 10^{\frac{g_d -a + 2,15dB}{10dB}}\\ &= 100W \cdot 10^{\frac{10,5dBd - 1,5dB + 2,15dB}{10dB}}\\ &= 1303,2W\end{split}$
</left>
</fragment>
<fragment>
<right>
$\begin{aligned}E &= \frac{\sqrt{30Ω \cdot P_{EIRP}}}{d}\\ \Rightarrow d &= \frac{\sqrt{30Ω \cdot P_{EIRP}}}{E}\\ &= \frac{\sqrt{30Ω \cdot 1303,2W}}{28\frac{V}{m}}\\ &= 7,1m\end{aligned}$
$\begin{split}E &= \frac{\sqrt{30Ω \cdot P_{EIRP}}}{d}\\ \Rightarrow d &= \frac{\sqrt{30Ω \cdot P_{EIRP}}}{E}\\ &= \frac{\sqrt{30Ω \cdot 1303,2W}}{28\frac{V}{m}}\\ &= 7,1m\end{split}$
</right>
</fragment>
@@ -171,11 +171,11 @@ $\begin{aligned}E &= \frac{\sqrt{30Ω \cdot P_{EIRP}}}{d}\\ \Rightarrow d &= \fr
<fragment>
<left>
$\begin{aligned}P_{EIRP} &= P_S \cdot 10^{\frac{g_d -a + 2,15dB}{10dB}}\\ &= 40W \cdot 10^{\frac{18dBd - 2dB + 2,15dB}{10dB}}\\ &= 2612,5W\end{aligned}$
$\begin{split}P_{EIRP} &= P_S \cdot 10^{\frac{g_d -a + 2,15dB}{10dB}}\\ &= 40W \cdot 10^{\frac{18dBd - 2dB + 2,15dB}{10dB}}\\ &= 2612,5W\end{split}$
</left>
</fragment>
<fragment>
<right>
$\begin{aligned}E &= \frac{\sqrt{30Ω \cdot P_{EIRP}}}{d}\\ \Rightarrow d &= \frac{\sqrt{30Ω \cdot P_{EIRP}}}{E}\\ &= \frac{\sqrt{30Ω \cdot 2612,5W}}{61\frac{V}{m}}\\ &= 4,6m\end{aligned}$
$\begin{split}E &= \frac{\sqrt{30Ω \cdot P_{EIRP}}}{d}\\ \Rightarrow d &= \frac{\sqrt{30Ω \cdot P_{EIRP}}}{E}\\ &= \frac{\sqrt{30Ω \cdot 2612,5W}}{61\frac{V}{m}}\\ &= 4,6m\end{split}$
</right>
</fragment>
contents/slides/nicht_sinus_signale.md
+1 -1
View File
@@ -110,5 +110,5 @@ $3 \cdot f = 3 \cdot 7,050MHz = 21,150MHz$
* gesucht: mehrere Harmonische
<fragment>
$\begin{aligned}2 \cdot 144,300MHz &= 288,600MHz\\ 3 \cdot 144,300MHz &= \bold{432,900MHz}\\ &\vdots\\ 9 \cdot 144,300MHz &= \bold{1298,700MHz}\end{aligned}$
$\begin{split}2 \cdot 144,300MHz &= 288,600MHz\\ 3 \cdot 144,300MHz &= \bold{432,900MHz}\\ &\vdots\\ 9 \cdot 144,300MHz &= \bold{1298,700MHz}\end{split}$
</fragment>
contents/slides/parbolspiegel_2.md
+4 -4
View File
@@ -51,7 +51,7 @@ $g_i = 10 \cdot \log_{10}{(\frac{\pi \cdot d}{\lambda})^2} \cdot \eta\,dB$
$\lambda = \frac{c}{f} = \frac{3\cdot 10^8\frac{m}{s}}{5,7GHz} = 0,053m$
</fragment>
<fragment>
$\begin{aligned}g_i &= 10 \cdot \log_{10}{(\frac{\pi \cdot d}{\lambda})^2} \cdot \eta\,dB\\ &= 10 \cdot \log_{10}{(\frac{\pi \cdot 0,3m}{0,053m})^2} \cdot 1dB\\ &= 25,1dBi\end{aligned}$
$\begin{split}g_i &= 10 \cdot \log_{10}{(\frac{\pi \cdot d}{\lambda})^2} \cdot \eta\,dB\\ &= 10 \cdot \log_{10}{(\frac{\pi \cdot 0,3m}{0,053m})^2} \cdot 1dB\\ &= 25,1dBi\end{split}$
</fragment>
---
[question:AG227]
@@ -70,7 +70,7 @@ $\begin{aligned}g_i &= 10 \cdot \log_{10}{(\frac{\pi \cdot d}{\lambda})^2} \cdot
$\lambda = \frac{c}{f} = \frac{3\cdot 10^8\frac{m}{s}}{5,7GHz} = 0,053m$
</fragment>
<fragment>
$\begin{aligned}g_i &= 10 \cdot \log_{10}{(\frac{\pi \cdot d}{\lambda})^2} \cdot \eta\,dB\\ &= 10 \cdot \log_{10}{(\frac{\pi \cdot 0,8m}{0,053m})^2} \cdot 1dB\\ &= 33,6dBi\end{aligned}$
$\begin{split}g_i &= 10 \cdot \log_{10}{(\frac{\pi \cdot d}{\lambda})^2} \cdot \eta\,dB\\ &= 10 \cdot \log_{10}{(\frac{\pi \cdot 0,8m}{0,053m})^2} \cdot 1dB\\ &= 33,6dBi\end{split}$
</fragment>
---
[question:AG228]
@@ -89,7 +89,7 @@ $\begin{aligned}g_i &= 10 \cdot \log_{10}{(\frac{\pi \cdot d}{\lambda})^2} \cdot
$\lambda = \frac{c}{f} = \frac{3\cdot 10^8\frac{m}{s}}{10,4GHz} = 0,029m$
</fragment>
<fragment>
$\begin{aligned}g_i &= 10 \cdot \log_{10}{(\frac{\pi \cdot d}{\lambda})^2} \cdot \eta\,dB\\ &= 10 \cdot \log_{10}{(\frac{\pi \cdot 0,8m}{0,029m})^2} \cdot 1dB\\ &= 38,8dBi\end{aligned}$
$\begin{split}g_i &= 10 \cdot \log_{10}{(\frac{\pi \cdot d}{\lambda})^2} \cdot \eta\,dB\\ &= 10 \cdot \log_{10}{(\frac{\pi \cdot 0,8m}{0,029m})^2} \cdot 1dB\\ &= 38,8dBi\end{split}$
</fragment>
---
[question:AG229]
@@ -108,5 +108,5 @@ $\begin{aligned}g_i &= 10 \cdot \log_{10}{(\frac{\pi \cdot d}{\lambda})^2} \cdot
$\lambda = \frac{c}{f} = \frac{3\cdot 10^8\frac{m}{s}}{10,4GHz} = 0,029m$
</fragment>
<fragment>
$\begin{aligned}g_i &= 10 \cdot \log_{10}{(\frac{\pi \cdot d}{\lambda})^2} \cdot \eta\,dB\\ &= 10 \cdot \log_{10}{(\frac{\pi \cdot 1,2m}{0,029m})^2} \cdot 1dB\\ &= 42,3dBi\end{aligned}$
$\begin{split}g_i &= 10 \cdot \log_{10}{(\frac{\pi \cdot d}{\lambda})^2} \cdot \eta\,dB\\ &= 10 \cdot \log_{10}{(\frac{\pi \cdot 1,2m}{0,029m})^2} \cdot 1dB\\ &= 42,3dBi\end{split}$
</fragment>
contents/slides/personenschutzabstand_3.md
+8 -8
View File
@@ -49,12 +49,12 @@ $d > \dfrac{\lambda}{2\pi}$
<fragment>
<left>
$\begin{aligned}E &= \frac{\sqrt{30Ω \cdot P_{EIRP}}}{d}\\ \Rightarrow P_{EIRP} &= \frac{(E \cdot d)^2}{30Ω}\\ &= \frac{(28\frac{V}{m} \cdot 5m)^2}{30Ω}\\ &= 653W\end{aligned}$
$\begin{split}E &= \frac{\sqrt{30Ω \cdot P_{EIRP}}}{d}\\ \Rightarrow P_{EIRP} &= \frac{(E \cdot d)^2}{30Ω}\\ &= \frac{(28\frac{V}{m} \cdot 5m)^2}{30Ω}\\ &= 653W\end{split}$
</left>
</fragment>
<fragment>
<right>
$\begin{aligned}P_{EIRP} &= P_S \cdot 10^{\frac{g_d - a + 2,15dB}{10dB}}\\ \Rightarrow P_S &= \frac{P_{EIRP}}{10^{\frac{g_d - a + 2,15dB}{10dB}}}\\ &= \frac{653W}{10^{\frac{6dBd - 0 + 2,15dB}{10dB}}}\\ &= \frac{653W}{6,53}\\ &\approx 100W\end{aligned}$
$\begin{split}P_{EIRP} &= P_S \cdot 10^{\frac{g_d - a + 2,15dB}{10dB}}\\ \Rightarrow P_S &= \frac{P_{EIRP}}{10^{\frac{g_d - a + 2,15dB}{10dB}}}\\ &= \frac{653W}{10^{\frac{6dBd - 0 + 2,15dB}{10dB}}}\\ &= \frac{653W}{6,53}\\ &\approx 100W\end{split}$
</right>
</fragment>
@@ -75,12 +75,12 @@ $\begin{aligned}P_{EIRP} &= P_S \cdot 10^{\frac{g_d - a + 2,15dB}{10dB}}\\ \Righ
<fragment>
<left>
$\begin{aligned}G_i &= 10^{\frac{g_i}{10dB}}\\ &= 10^{\frac{12,15dBi}{10dB}}\\ &= 16,4\end{aligned}$
$\begin{split}G_i &= 10^{\frac{g_i}{10dB}}\\ &= 10^{\frac{12,15dBi}{10dB}}\\ &= 16,4\end{split}$
</left>
</fragment>
<fragment>
<right>
$\begin{aligned}E &= \frac{\sqrt{30Ω \cdot P_A \cdot G_i}}{d}\\ &= \frac{\sqrt{30Ω \cdot 250W \cdot 16,4}}{30m}\\ &= \frac{350V}{30m}\\ &\approx 11,7\frac{V}{m}\end{aligned}$
$\begin{split}E &= \frac{\sqrt{30Ω \cdot P_A \cdot G_i}}{d}\\ &= \frac{\sqrt{30Ω \cdot 250W \cdot 16,4}}{30m}\\ &= \frac{350V}{30m}\\ &\approx 11,7\frac{V}{m}\end{split}$
</right>
</fragment>
@@ -96,12 +96,12 @@ $\begin{aligned}E &= \frac{\sqrt{30Ω \cdot P_A \cdot G_i}}{d}\\ &= \frac{\sqrt{
<fragment>
<left>
$\begin{aligned}P_{EIRP} &= P_{ERP} \cdot 1,64\\ &= 100W \cdot 1,64\\ &= 164W\end{aligned}$
$\begin{split}P_{EIRP} &= P_{ERP} \cdot 1,64\\ &= 100W \cdot 1,64\\ &= 164W\end{split}$
</left>
</fragment>
<fragment>
<right>
$\begin{aligned}E &= \frac{\sqrt{30Ω \cdot P_{EIRP}}}{d}\\ &= \frac{\sqrt{30Ω \cdot 164W}}{100m}\\ &= 0,7\frac{V}{m}\end{aligned}$
$\begin{split}E &= \frac{\sqrt{30Ω \cdot P_{EIRP}}}{d}\\ &= \frac{\sqrt{30Ω \cdot 164W}}{100m}\\ &= 0,7\frac{V}{m}\end{split}$
</right>
</fragment>
@@ -117,11 +117,11 @@ $\begin{aligned}E &= \frac{\sqrt{30Ω \cdot P_{EIRP}}}{d}\\ &= \frac{\sqrt{30Ω
<fragment>
<left>
$\begin{aligned}P_{EIRP} &= P_{ERP} \cdot 1,64\\ &= 100W \cdot 1,64\\ &= 164W\end{aligned}$
$\begin{split}P_{EIRP} &= P_{ERP} \cdot 1,64\\ &= 100W \cdot 1,64\\ &= 164W\end{split}$
</left>
</fragment>
<fragment>
<right>
$\begin{aligned}E &= \frac{\sqrt{30Ω \cdot P_{EIRP}}}{d}\\ &= \frac{\sqrt{30Ω \cdot 164W}}{100m}\\ &= 0,7\frac{V}{m}\end{aligned}$
$\begin{split}E &= \frac{\sqrt{30Ω \cdot P_{EIRP}}}{d}\\ &= \frac{\sqrt{30Ω \cdot 164W}}{100m}\\ &= 0,7\frac{V}{m}\end{split}$
</right>
</fragment>
contents/slides/sender_messungen.md
+15 -15
View File
@@ -93,7 +93,7 @@ Keine Berechnung notwendig, da es nur eine Antwort mit Dämpfungsglied gibt
<fragment>
$\begin{aligned}R &= (\frac{1}{R_T + R_T} + \frac{1}{R_V} + \frac{1}{R_V})^{-1}\\ &= (\frac{1}{330Ω + 330Ω} + \frac{1}{110Ω} + \frac{1}{110Ω})^{-1}\\ &= 50,77Ω\end{aligned}$
$\begin{split}R &= (\frac{1}{R_T + R_T} + \frac{1}{R_V} + \frac{1}{R_V})^{-1}\\ &= (\frac{1}{330Ω + 330Ω} + \frac{1}{110Ω} + \frac{1}{110Ω})^{-1}\\ &= 50,77Ω\end{split}$
</fragment>
--- style="font-size: smaller;"
@@ -103,7 +103,7 @@ $\begin{aligned}R &= (\frac{1}{R_T + R_T} + \frac{1}{R_V} + \frac{1}{R_V})^{-1}\
* gesucht: $U_A$
<fragment>
$\begin{aligned}P_E &= \frac{U_{E,eff}^2}{R}\\ \Rightarrow U_{E,eff} &= \sqrt{P_E \cdot R}\\ &= \sqrt{1W \cdot 50,77Ω}\\ &= 7,125V\end{aligned}$
$\begin{split}P_E &= \frac{U_{E,eff}^2}{R}\\ \Rightarrow U_{E,eff} &= \sqrt{P_E \cdot R}\\ &= \sqrt{1W \cdot 50,77Ω}\\ &= 7,125V\end{split}$
</fragment>
--- style="font-size: smaller;"
@@ -113,12 +113,12 @@ $\begin{aligned}P_E &= \frac{U_{E,eff}^2}{R}\\ \Rightarrow U_{E,eff} &= \sqrt{P_
<left>
<fragment>
$\begin{aligned}U_S &= U_{E,eff} \cdot \sqrt{2}\\ &= 7,071V \cdot 1,414\\ &= 10,07V\end{aligned}$
$\begin{split}U_S &= U_{E,eff} \cdot \sqrt{2}\\ &= 7,071V \cdot 1,414\\ &= 10,07V\end{split}$
</fragment>
</left>
<right>
<fragment>
$\begin{aligned}U_A &= \frac{U_S}{2}\,-\,U_F\\ &= \frac{10,07V}{2}\,-\,0,23V\\ &= 5,035V\,-\,0,23V\\ &= 4,805V \approx 4,8V\end{aligned}$
$\begin{split}U_A &= \frac{U_S}{2}\,-\,U_F\\ &= \frac{10,07V}{2}\,-\,0,23V\\ &= 5,035V\,-\,0,23V\\ &= 4,805V \approx 4,8V\end{split}$
</fragment>
</right>
@@ -146,12 +146,12 @@ $\begin{aligned}U_A &= \frac{U_S}{2}\,-\,U_F\\ &= \frac{10,07V}{2}\,-\,0,23V\\ &
<left>
<fragment>
$\begin{aligned}R &= (\frac{1}{R_T + R_T} + \frac{1}{R_1})^{-1}\\ &= (\frac{1}{330Ω + 330Ω} + \frac{1}{54,1Ω})^{-1}\\ &= 50Ω\end{aligned}$
$\begin{split}R &= (\frac{1}{R_T + R_T} + \frac{1}{R_1})^{-1}\\ &= (\frac{1}{330Ω + 330Ω} + \frac{1}{54,1Ω})^{-1}\\ &= 50Ω\end{split}$
</fragment>
</left>
<right>
<fragment>
$\begin{aligned}U_S &= (U_A + U_F) \cdot 2\\ &= (14,9V + 0,7V) \cdot 2\\ &= 31,2V\end{aligned}$
$\begin{split}U_S &= (U_A + U_F) \cdot 2\\ &= (14,9V + 0,7V) \cdot 2\\ &= 31,2V\end{split}$
</fragment>
</right>
@@ -162,12 +162,12 @@ $\begin{aligned}U_S &= (U_A + U_F) \cdot 2\\ &= (14,9V + 0,7V) \cdot 2\\ &= 31,2
* gesucht: $P_E$
<fragment>
$\begin{aligned}U_{E,eff}\\ &= \frac{U_S}{\sqrt{2}}\\ &= \frac{31,2V}{1,414}\\ &= 22,06V\end{aligned}$
$\begin{split}U_{E,eff}\\ &= \frac{U_S}{\sqrt{2}}\\ &= \frac{31,2V}{1,414}\\ &= 22,06V\end{split}$
</fragment>
</left>
<right>
<fragment>
$\begin{aligned}P_E &= \frac{U_{E,eff}^2}{R}\\ &= \frac{(22,06V)^2}{50Ω}\\ &\approx 9,7W\end{aligned}$
$\begin{split}P_E &= \frac{U_{E,eff}^2}{R}\\ &= \frac{(22,06V)^2}{50Ω}\\ &\approx 9,7W\end{split}$
</fragment>
</right>
@@ -196,12 +196,12 @@ $\begin{aligned}P_E &= \frac{U_{E,eff}^2}{R}\\ &= \frac{(22,06V)^2}{50Ω}\\ &\ap
<left>
<fragment>
$\begin{aligned}R &= (\frac{1}{R_{V1}} + \frac{1}{R_{V2}})^{-1}\\ &= (\frac{1}{R_{56Ω}} + \frac{1}{R_{470Ω}})^{-1}\\ &= 50,04Ω\end{aligned}$
$\begin{split}R &= (\frac{1}{R_{V1}} + \frac{1}{R_{V2}})^{-1}\\ &= (\frac{1}{R_{56Ω}} + \frac{1}{R_{470Ω}})^{-1}\\ &= 50,04Ω\end{split}$
</fragment>
</left>
<right>
<fragment>
$\begin{aligned}U_S &= \frac{U_A}{2} + U_F\\ &= \frac{15,3V}{2} + 0,23V\\ &= 7,88V\end{aligned}$
$\begin{split}U_S &= \frac{U_A}{2} + U_F\\ &= \frac{15,3V}{2} + 0,23V\\ &= 7,88V\end{split}$
</fragment>
</right>
@@ -212,12 +212,12 @@ $\begin{aligned}U_S &= \frac{U_A}{2} + U_F\\ &= \frac{15,3V}{2} + 0,23V\\ &= 7,8
* gesucht: $P_E$
<fragment>
$\begin{aligned}U_{E,eff} &= \frac{U_S}{\sqrt{2}}\\ &= \frac{7,88V}{1,414}\\ &= 5,57V\end{aligned}$
$\begin{split}U_{E,eff} &= \frac{U_S}{\sqrt{2}}\\ &= \frac{7,88V}{1,414}\\ &= 5,57V\end{split}$
</fragment>
</left>
<right>
<fragment>
$\begin{aligned}P_E &= \frac{U_{E,eff}^2}{R}\\ &= \frac{{5,57V}^2}{50,04Ω}\\ &\approx 600mW\end{aligned}$
$\begin{split}P_E &= \frac{U_{E,eff}^2}{R}\\ &= \frac{{5,57V}^2}{50,04Ω}\\ &\approx 600mW\end{split}$
</fragment>
</right>
@@ -234,12 +234,12 @@ $\begin{aligned}P_E &= \frac{U_{E,eff}^2}{R}\\ &= \frac{{5,57V}^2}{50,04Ω}\\ &\
<left>
<fragment>
$\begin{aligned}U_S &= \frac{U_A}{2} + U_F\\ &= \frac{15,3V}{2} + 0,23V\\ &= 7,88V\end{aligned}$
$\begin{split}U_S &= \frac{U_A}{2} + U_F\\ &= \frac{15,3V}{2} + 0,23V\\ &= 7,88V\end{split}$
</fragment>
</left>
<right>
<fragment>
$\begin{aligned}U_{E,eff} &= \frac{U_S}{\sqrt{2}}\\ &= \frac{7,88V}{1,414}\\ &= 5,57V\end{aligned}$
$\begin{split}U_{E,eff} &= \frac{U_S}{\sqrt{2}}\\ &= \frac{7,88V}{1,414}\\ &= 5,57V\end{split}$
</fragment>
</right>
@@ -249,7 +249,7 @@ $\begin{aligned}U_{E,eff} &= \frac{U_S}{\sqrt{2}}\\ &= \frac{7,88V}{1,414}\\ &=
* gesucht: $P_E$
<fragment>
$\begin{aligned}P_E &= \frac{(U_{E,eff} \cdot 10)^2}{R}\\ &= \frac{(5,57V \cdot 10)^2}{50Ω}\\ &\approx 60W\end{aligned}$
$\begin{split}P_E &= \frac{(U_{E,eff} \cdot 10)^2}{R}\\ &= \frac{(5,57V \cdot 10)^2}{50Ω}\\ &\approx 60W\end{split}$
</fragment>
--- style="font-size: smaller;"
contents/slides/spiegelfrequenzen.md
+4 -4
View File
@@ -58,7 +58,7 @@ Maßnahme für eine möglichst hohe Unterdrückung:
* gesucht: $f_S$
<fragment>
$\begin{aligned}f_S &= 2 \cdot f_{OSZ} - f_E\\ &= 2 \cdot 134,9MHz - 145,6MHz\\ &= 124,2MHz\end{aligned}$
$\begin{split}f_S &= 2 \cdot f_{OSZ} - f_E\\ &= 2 \cdot 134,9MHz - 145,6MHz\\ &= 124,2MHz\end{split}$
</fragment>
---
[question:AF203]
@@ -69,7 +69,7 @@ $\begin{aligned}f_S &= 2 \cdot f_{OSZ} - f_E\\ &= 2 \cdot 134,9MHz - 145,6MHz\\
* gesucht: $f_S$
<fragment>
$\begin{aligned}f_S &= 2 \cdot f_{OSZ} - f_E\\ &= 2 \cdot 39MHz - 28,3MHz\\ &= 49,7MHz\end{aligned}$
$\begin{split}f_S &= 2 \cdot f_{OSZ} - f_E\\ &= 2 \cdot 39MHz - 28,3MHz\\ &= 49,7MHz\end{split}$
</fragment>
---
[question:AF204]
@@ -84,7 +84,7 @@ $\begin{aligned}f_S &= 2 \cdot f_{OSZ} - f_E\\ &= 2 \cdot 39MHz - 28,3MHz\\ &= 4
* gesucht: $f_S$
<fragment>
$\begin{aligned}f_S &= 2 \cdot f_{OSZ} - f_E\\ &= 2 \cdot 24,94MHz - 14,24MHz\\ &= 35,64MHz\end{aligned}$
$\begin{split}f_S &= 2 \cdot f_{OSZ} - f_E\\ &= 2 \cdot 24,94MHz - 14,24MHz\\ &= 35,64MHz\end{split}$
</fragment>
---
[question:AF108]
@@ -96,7 +96,7 @@ $\begin{aligned}f_S &= 2 \cdot f_{OSZ} - f_E\\ &= 2 \cdot 24,94MHz - 14,24MHz\\
<fragment>
Bei $f_E &lt; f_{OSZ}$:
$\begin{aligned}f_S &= f_E + 2 \cdot f_{ZF}\\ &= 28,5MHz + 2 \cdot 10,7MHz\\ &= 49,9MHz\end{aligned}$
$\begin{split}f_S &= f_E + 2 \cdot f_{ZF}\\ &= 28,5MHz + 2 \cdot 10,7MHz\\ &= 49,9MHz\end{split}$
</fragment>
---
[question:AF109]
contents/slides/verkuerzungsfaktor_2.md
+14 -14
View File
@@ -22,12 +22,12 @@
<left>
<fragment>
$\begin{aligned}l_E &= \frac{1}{2} \cdot \frac{\lambda}{2}\\ &= \frac{1}{4} \cdot \frac{c}{f}\\ &= \frac{1}{4} \cdot \frac{3\cdot 10^8\frac{m}{s}}{14,2MHz}\\ &= \frac{1}{4} \cdot 21,13m\\ &= 5,28m\end{aligned}$
$\begin{split}l_E &= \frac{1}{2} \cdot \frac{\lambda}{2}\\ &= \frac{1}{4} \cdot \frac{c}{f}\\ &= \frac{1}{4} \cdot \frac{3\cdot 10^8\frac{m}{s}}{14,2MHz}\\ &= \frac{1}{4} \cdot 21,13m\\ &= 5,28m\end{split}$
</fragment>
</left>
<right>
<fragment>
$\begin{aligned}k_v &= \frac{l_G}{l_E}\\ \Rightarrow l_G &= k_v \cdot l_E\\ &= 0,95 \cdot 5,28m\\ &= 5,02m\end{aligned}$
$\begin{split}k_v &= \frac{l_G}{l_E}\\ \Rightarrow l_G &= k_v \cdot l_E\\ &= 0,95 \cdot 5,28m\\ &= 5,02m\end{split}$
</fragment>
</right>
@@ -49,12 +49,12 @@ $\begin{aligned}k_v &= \frac{l_G}{l_E}\\ \Rightarrow l_G &= k_v \cdot l_E\\ &= 0
<left>
<fragment>
$\begin{aligned}l_E &= \frac{1}{2} \cdot \frac{\lambda}{2}\\ &= \frac{1}{4} \cdot \frac{c}{f}\\ &= \frac{1}{4} \cdot \frac{3\cdot 10^8\frac{m}{s}}{7,1MHz}\\ &= \frac{1}{4} \cdot 42,25m\\ &= 10,56m\end{aligned}$
$\begin{split}l_E &= \frac{1}{2} \cdot \frac{\lambda}{2}\\ &= \frac{1}{4} \cdot \frac{c}{f}\\ &= \frac{1}{4} \cdot \frac{3\cdot 10^8\frac{m}{s}}{7,1MHz}\\ &= \frac{1}{4} \cdot 42,25m\\ &= 10,56m\end{split}$
</fragment>
</left>
<right>
<fragment>
$\begin{aligned}k_v &= \frac{l_G}{l_E}\\ \Rightarrow l_G &= k_v \cdot l_E\\ &= 0,95 \cdot 10,56m\\ &= 10,04m\end{aligned}$
$\begin{split}k_v &= \frac{l_G}{l_E}\\ \Rightarrow l_G &= k_v \cdot l_E\\ &= 0,95 \cdot 10,56m\\ &= 10,04m\end{split}$
</fragment>
</right>
@@ -75,12 +75,12 @@ $\begin{aligned}k_v &= \frac{l_G}{l_E}\\ \Rightarrow l_G &= k_v \cdot l_E\\ &= 0
<left>
<fragment>
$\begin{aligned}k_v &= \frac{l_G}{l_E}\\ \Rightarrow l_E &= \frac{l_G}{k_v}\\ &= \frac{20m}{0,95}\\ &= 21,05m\end{aligned}$
$\begin{split}k_v &= \frac{l_G}{l_E}\\ \Rightarrow l_E &= \frac{l_G}{k_v}\\ &= \frac{20m}{0,95}\\ &= 21,05m\end{split}$
</fragment>
</left>
<right>
<fragment>
$\begin{aligned}l_E &= \frac{\lambda}{2}\\ &= \frac{1}{2} \cdot \frac{c}{f}\\ \Rightarrow f &= \frac{1}{2} \cdot \frac{c}{l_E}\\ &= \frac{1}{2} \cdot \frac{3\cdot 10^8\frac{m}{s}}{21,05m}\\&= 7,125MHz\end{aligned}$
$\begin{split}l_E &= \frac{\lambda}{2}\\ &= \frac{1}{2} \cdot \frac{c}{f}\\ \Rightarrow f &= \frac{1}{2} \cdot \frac{c}{l_E}\\ &= \frac{1}{2} \cdot \frac{3\cdot 10^8\frac{m}{s}}{21,05m}\\&= 7,125MHz\end{split}$
</fragment>
</right>
@@ -102,12 +102,12 @@ $\begin{aligned}l_E &= \frac{\lambda}{2}\\ &= \frac{1}{2} \cdot \frac{c}{f}\\ \R
<left>
<fragment>
$\begin{aligned}l_E &= \frac{\lambda}{4}\\ &= \frac{1}{4} \cdot \frac{c}{f}\\ &= \frac{1}{4} \cdot \frac{3\cdot 10^8\frac{m}{s}}{7,1MHz}\\ &= \frac{1}{4} \cdot 42,25m\\ &= 10,56m\end{aligned}$
$\begin{split}l_E &= \frac{\lambda}{4}\\ &= \frac{1}{4} \cdot \frac{c}{f}\\ &= \frac{1}{4} \cdot \frac{3\cdot 10^8\frac{m}{s}}{7,1MHz}\\ &= \frac{1}{4} \cdot 42,25m\\ &= 10,56m\end{split}$
</fragment>
</left>
<right>
<fragment>
$\begin{aligned}k_v &= \frac{l_G}{l_E}\\ \Rightarrow l_G &= k_v \cdot l_E\\ &= 0,95 \cdot 10,56m\\ &= 10,04m\end{aligned}$
$\begin{split}k_v &= \frac{l_G}{l_E}\\ \Rightarrow l_G &= k_v \cdot l_E\\ &= 0,95 \cdot 10,56m\\ &= 10,04m\end{split}$
</fragment>
</right>
@@ -129,12 +129,12 @@ $\begin{aligned}k_v &= \frac{l_G}{l_E}\\ \Rightarrow l_G &= k_v \cdot l_E\\ &= 0
<left>
<fragment>
$\begin{aligned}l_E &= \frac{5}{8}\lambda\\ &= \frac{5}{8} \cdot \frac{c}{f}\\ &= \frac{5}{8} \cdot \frac{3\cdot 10^8\frac{m}{s}}{14,2MHz}\\ &= \frac{5}{8} \cdot 21,13\\ &= 13,20m\end{aligned}$
$\begin{split}l_E &= \frac{5}{8}\lambda\\ &= \frac{5}{8} \cdot \frac{c}{f}\\ &= \frac{5}{8} \cdot \frac{3\cdot 10^8\frac{m}{s}}{14,2MHz}\\ &= \frac{5}{8} \cdot 21,13\\ &= 13,20m\end{split}$
</fragment>
</left>
<right>
<fragment>
$\begin{aligned}k_v &= \frac{l_G}{l_E}\\ \Rightarrow l_G &= k_v \cdot l_E\\ &= 0,97 \cdot 13,20m\\ &= 12,80m\end{aligned}$
$\begin{split}k_v &= \frac{l_G}{l_E}\\ \Rightarrow l_G &= k_v \cdot l_E\\ &= 0,97 \cdot 13,20m\\ &= 12,80m\end{split}$
</fragment>
</right>
@@ -179,12 +179,12 @@ Ein Verlängerungsfaktor bedeutet <u>nicht</u>, dass sich die Welle mit *Überli
<left>
<fragment>
$\begin{aligned}l_E &= \lambda\\ &= \frac{c}{f}\\ &= \frac{3\cdot 10^8\frac{m}{s}}{7,1MHz}\\ &= 42,23m\end{aligned}$
$\begin{split}l_E &= \lambda\\ &= \frac{c}{f}\\ &= \frac{3\cdot 10^8\frac{m}{s}}{7,1MHz}\\ &= 42,23m\end{split}$
</fragment>
</left>
<right>
<fragment>
$\begin{aligned}k_v &= \frac{l_G}{l_E}\\ \Rightarrow l_G &= k_v \cdot l_E\\ &= 1,02 \cdot 42,23m\\ &= 43,10m\end{aligned}$
$\begin{split}k_v &= \frac{l_G}{l_E}\\ \Rightarrow l_G &= k_v \cdot l_E\\ &= 1,02 \cdot 42,23m\\ &= 43,10m\end{split}$
</fragment>
</right>
@@ -230,11 +230,11 @@ $v_\mathrm{k} = \dfrac{1}{\sqrt{\epsilon_\mathrm{r}}}$
<left>
<fragment>
$\begin{aligned}l_E &= \lambda\\ &= \frac{c}{f}\\ &= \frac{3\cdot 10^8\frac{m}{s}}{145MHz}\\ &= 2,07m\end{aligned}$
$\begin{split}l_E &= \lambda\\ &= \frac{c}{f}\\ &= \frac{3\cdot 10^8\frac{m}{s}}{145MHz}\\ &= 2,07m\end{split}$
</fragment>
</left>
<right>
<fragment>
$\begin{aligned}k_v &= \frac{l_G}{l_E}\\ \Rightarrow l_G &= k_v \cdot l_E\\ &= 0,66 \cdot 2,07m\\ &= 1,37m\end{aligned}$
$\begin{split}k_v &= \frac{l_G}{l_E}\\ \Rightarrow l_G &= k_v \cdot l_E\\ &= 0,66 \cdot 2,07m\\ &= 1,37m\end{split}$
</fragment>
</right>
contents/slides/vor_rueck_verhaeltnis.md
+7 -7
View File
@@ -41,7 +41,7 @@
* gesucht: $\frac{Vor}{Rück}$
<fragment>
$\begin{aligned}\frac{Vor}{Rück} &= 10 \cdot \log_{10}{(\frac{P_V}{P_R})} dB\\ &= 10 \cdot \log_{10}{(\frac{15W}{0,6W})} dB\\ &= 14dB\end{aligned}$
$\begin{split}\frac{Vor}{Rück} &= 10 \cdot \log_{10}{(\frac{P_V}{P_R})} dB\\ &= 10 \cdot \log_{10}{(\frac{15W}{0,6W})} dB\\ &= 14dB\end{split}$
</fragment>
---
@@ -61,12 +61,12 @@ $\begin{aligned}\frac{Vor}{Rück} &= 10 \cdot \log_{10}{(\frac{P_V}{P_R})} dB\\
<left>
<fragment>
$\begin{aligned}P_V &= P_{ERP}\\ &= P_S \cdot 10^{\frac{g_d}{10dB}}\\ &= 100W \cdot 10^{\frac{10dB}{10dB}}\\ &= 1000W\end{aligned}$
$\begin{split}P_V &= P_{ERP}\\ &= P_S \cdot 10^{\frac{g_d}{10dB}}\\ &= 100W \cdot 10^{\frac{10dB}{10dB}}\\ &= 1000W\end{split}$
</fragment>
</left>
<right>
<fragment>
$\begin{aligned}20dB &= 10 \cdot \log_{10}{(\frac{P_V}{P_R})} dB\\ \Rightarrow \frac{P_V}{P_R} &= 10^{\frac{20dB}{10}}\\ &= 100\\ \Rightarrow P_R &= \frac{P_V}{100}\\ &= \frac{1000W}{100}\\ &= 10W\end{aligned}$
$\begin{split}20dB &= 10 \cdot \log_{10}{(\frac{P_V}{P_R})} dB\\ \Rightarrow \frac{P_V}{P_R} &= 10^{\frac{20dB}{10}}\\ &= 100\\ \Rightarrow P_R &= \frac{P_V}{100}\\ &= \frac{1000W}{100}\\ &= 10W\end{split}$
</fragment>
</right>
---
@@ -86,12 +86,12 @@ $\begin{aligned}20dB &= 10 \cdot \log_{10}{(\frac{P_V}{P_R})} dB\\ \Rightarrow \
<left>
<fragment>
$\begin{aligned}P_V &= P_{ERP}\\ &= P_S \cdot 10^{\frac{g_d}{10dB}}\\ &= 6W \cdot 10^{\frac{15dB}{10dB}}\\ &= 189,7W\end{aligned}$
$\begin{split}P_V &= P_{ERP}\\ &= P_S \cdot 10^{\frac{g_d}{10dB}}\\ &= 6W \cdot 10^{\frac{15dB}{10dB}}\\ &= 189,7W\end{split}$
</fragment>
</left>
<right>
<fragment>
$\begin{aligned}25dB &= 10 \cdot \log_{10}{(\frac{P_V}{P_R})} dB\\ \Rightarrow \frac{P_V}{P_R} &= 10^{\frac{25dB}{10}}\\ &= 316,2\\ \Rightarrow P_R &= \frac{P_V}{316,2}\\ &= \frac{189,7W}{316,2}\\ &= 0,6W\end{aligned}$
$\begin{split}25dB &= 10 \cdot \log_{10}{(\frac{P_V}{P_R})} dB\\ \Rightarrow \frac{P_V}{P_R} &= 10^{\frac{25dB}{10}}\\ &= 316,2\\ \Rightarrow P_R &= \frac{P_V}{316,2}\\ &= \frac{189,7W}{316,2}\\ &= 0,6W\end{split}$
</fragment>
</right>
@@ -112,11 +112,11 @@ $\begin{aligned}25dB &= 10 \cdot \log_{10}{(\frac{P_V}{P_R})} dB\\ \Rightarrow \
<left>
<fragment>
$\begin{aligned}g_D &= 20 \cdot \log_{10}{(\frac{U_V}{U_D})} dB\\ &= 20 \cdot \log_{10}{(\frac{300µV/m}{128µV/m})}\\ &= 7,4dB\end{aligned}$
$\begin{split}g_D &= 20 \cdot \log_{10}{(\frac{U_V}{U_D})} dB\\ &= 20 \cdot \log_{10}{(\frac{300µV/m}{128µV/m})}\\ &= 7,4dB\end{split}$
</fragment>
</left>
<right>
<fragment>
$\begin{aligned}\frac{Vor}{Rück} &= 20 \cdot \log_{10}{(\frac{U_V}{U_R})} dB\\ &= 20 \cdot \log_{10}{(\frac{300µV/m}{20µV/m})}\\ &= 23,5dB\end{aligned}$
$\begin{split}\frac{Vor}{Rück} &= 20 \cdot \log_{10}{(\frac{U_V}{U_R})} dB\\ &= 20 \cdot \log_{10}{(\frac{300µV/m}{20µV/m})}\\ &= 23,5dB\end{split}$
</fragment>
</right>
contents/slides/wellenwiderstand.md
+3 -3
View File
@@ -17,7 +17,7 @@ $Z = \dfrac{120Ω}{\sqrt{\epsilon_\mathrm{r}}} \cdot \ln{(\dfrac{2 \cdot a}{d})}
* gesucht: $Z$
<fragment>
$\begin{aligned}Z &= \dfrac{120Ω}{\sqrt{\epsilon_\mathrm{r}}} \cdot \ln{(\dfrac{2 \cdot a}{d})}\\ &= \dfrac{120Ω}{\sqrt{1}} \cdot \ln{(\dfrac{2 \cdot 200mm}{2mm})}\\ &\approx 635Ω\end{aligned}$
$\begin{split}Z &= \dfrac{120Ω}{\sqrt{\epsilon_\mathrm{r}}} \cdot \ln{(\dfrac{2 \cdot a}{d})}\\ &= \dfrac{120Ω}{\sqrt{1}} \cdot \ln{(\dfrac{2 \cdot 200mm}{2mm})}\\ &\approx 635Ω\end{split}$
</fragment>
---
## Wellenwiderstand einer Koaxialleitung
@@ -39,7 +39,7 @@ $Z = \dfrac{60Ω}{\sqrt{\epsilon_\mathrm{r}}} \cdot \ln{\dfrac{D}{d}}$
* gesucht: $Z$
<fragment>
$\begin{aligned}Z &= \dfrac{60Ω}{\sqrt{\epsilon_\mathrm{r}}} \cdot \ln{(\dfrac{D}{d})}\\ &= \dfrac{60Ω}{\sqrt{1}} \cdot \ln{(\dfrac{5mm}{1mm})}\\ &\approx 97Ω\end{aligned}$
$\begin{split}Z &= \dfrac{60Ω}{\sqrt{\epsilon_\mathrm{r}}} \cdot \ln{(\dfrac{D}{d})}\\ &= \dfrac{60Ω}{\sqrt{1}} \cdot \ln{(\dfrac{5mm}{1mm})}\\ &\approx 97Ω\end{split}$
</fragment>
---
[question:AG307]
@@ -51,7 +51,7 @@ $\begin{aligned}Z &= \dfrac{60Ω}{\sqrt{\epsilon_\mathrm{r}}} \cdot \ln{(\dfrac{
* gesucht: $Z$
<fragment>
$\begin{aligned}Z &= \dfrac{60Ω}{\sqrt{\epsilon_\mathrm{r}}} \cdot \ln{(\dfrac{D}{d})}\\ &= \dfrac{60Ω}{\sqrt{2,29}} \cdot \ln{(\dfrac{4,4mm}{0,7mm})}\\ &\approx 75Ω\end{aligned}$
$\begin{split}Z &= \dfrac{60Ω}{\sqrt{\epsilon_\mathrm{r}}} \cdot \ln{(\dfrac{D}{d})}\\ &= \dfrac{60Ω}{\sqrt{2,29}} \cdot \ln{(\dfrac{4,4mm}{0,7mm})}\\ &\approx 75Ω\end{split}$
</fragment>
---
### Anpassung von Koaxialleitungen