Applets:Attenuation of Copper Cables - Revision history

Guenter at 14:25, 8 April 2023

2023-04-08T14:25:52Z

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Noah at 21:04, 25 March 2023

2023-03-25T21:04:29Z

Noah at 21:00, 25 March 2023

2023-03-25T21:00:20Z

Hwang at 16:08, 23 January 2023

2023-01-23T16:08:34Z

Guenter at 17:54, 11 January 2023

2023-01-11T17:54:47Z

Javier: Text replacement - "”" to """

2021-05-28T14:41:12Z

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2021-05-28T14:39:47Z

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Tasnad at 15:33, 24 February 2021

2021-02-24T15:33:12Z

Tasnad at 15:32, 24 February 2021

2021-02-24T15:32:52Z

Tasnad at 15:32, 24 February 2021

2021-02-24T15:32:29Z

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 In this applet
 *we neglect the influence of the transmitted pulse form &nbsp; &rArr; &nbsp; $H_{\rm S}(f) \equiv 1$ &nbsp; &rArr; &nbsp; dirac shaped transmission signal $s(t)$, and
-*presuppose a binary Nyquist system with cosine&ndash;roll&ndash;off around the Nyquist frequency $f_{\rm Nyq} = [f_1 + f_2]/2 =1(2T)$ :
+*presuppose a binary Nyquist system with raised cosine around the Nyquist frequency $f_{\rm Nyq} = [f_1 + f_2]/2 =1(2T)$ :
 :$$H_{\rm K}(f) · H_{\rm E}(f) = H_{\rm CRO}(f).$$
-[[File:Applet_Kabeldaempfung_2_version2.png|right|frame|Frequency Response with cosine&ndash;roll&ndash;off|class=fit]]
+[[File:Applet_Kabeldaempfung_2_version2.png|right|frame|Frequency Response with raised cosine|class=fit]]
 This means: The [[Digital_Signal_Transmission/Properties_of_Nyquist_Systems#First_Nyquist_criterion_in_the_frequency_domain|"first Nyquist criterion"]] is met<br> &rArr; &nbsp; Timely successive impulses do not disturb each other<br>⇒  &nbsp; there are no [[Digital_Signal_Transmission/Causes_and_Effects_of_Intersymbol_Interference|"Intersymbol Interferences"]].

@@ Line 11: / Line 11: @@
 Aside from the attenuation function $a_{\rm K}(f)$  the applet can display:
 *the associated magnitude frequency response $\left | H_{\rm K}(f)\right |=10^{-a_\text{K}(f)/20},$
-*the equalizer frequency response $\left | H_{\rm E}(f)\right | = \left | H_{\rm CRO}(f)   /  H_{\rm K}(f)\right | $, that leads to a nyquist total frequency response $ H_{\rm CRO}(f) $,
+*the equalizer frequency response $\left | H_{\rm E}(f)\right | = \left | H_{\rm CRO}(f)   /  H_{\rm K}(f)\right | $, that leads to a Nyquist total frequency response $ H_{\rm CRO}(f) $,
-*the corresponding magnitude square frequency response $\left | H_{\rm E}(f)\right |^2 $.
+*the corresponding squared magnitude frequency response $\left | H_{\rm E}(f)\right |^2 $.
-The integral over $\left | H_{\rm E}(f)\right |^2 $ is a measure of the noise exaggeration of the selected Nyquist total frequency response and thus also for the expected error probability.From this, the ''total efficiency'' &nbsp;$\eta_\text{K+E}$ for channel (ger.:'''K'''anal) and equalizer (ger.:'''E'''ntzerrer) is calculated, which is output in the applet in $\rm dB$.
+The integral over $\left | H_{\rm E}(f)\right |^2 $ is a measure of the noise exaggeration of the selected Nyquist total frequency response and thus also for the expected error probability. From this, the ''total efficiency'' &nbsp;$\eta_\text{K+E}$ for channel (ger.:'''K'''anal) and equalizer (ger.:'''E'''ntzerrer) is calculated, which is output in the applet in $\rm dB$.
-Through optimization of the roll-off-factor $r$ of the cosine roll-off frequency response $ H_{\rm CRO}(f) $ one gets the ''Channel efficiency'' &nbsp;$ \eta_\text{K}$. This therefore indicates the deterioration of the overall system due to the attenuation function $ a _ {\ rm K} (f) $ of the transmission medium.
+Through optimization of the roll-off factor $r$ of the raised cosine frequency response $ H_{\rm CRO}(f) $ one gets the ''channel efficiency'' &nbsp;$ \eta_\text{K}$. This therefore indicates the deterioration of the overall system due to the attenuation function $ a _ {\ rm K} (f) $ of the transmission medium.
 ==Theoretical Background==
@@ Line 26: / Line 26: @@
 :$$\left | H_{\rm K}(f)\right |=10^{-a_\text{K}(f)/20} = {\rm e}^{-a_\text{K, Np}(f)}.$$
 *The index "K" makes it clear, that the considered LTI system is a cable (German : '''K'''abel).
-*For the first calculation rule, the damping function $a_\text{K}(f)$ must be used in $\rm dB$ (decibel).
+*For the first calculation rule, the attenuation function $a_\text{K}(f)$ must be used in $\rm dB$ (decibel).
-*For the second calculation rule, the damping function $a_\text{K, Np}(f)$ must be used in $\rm Np$ (Neper).
+*For the second calculation rule, the attenuation function $a_\text{K, Np}(f)$ must be used in $\rm Np$ (Neper).
 * The following conversions apply:  $\rm 1 \ dB = 0.05 \cdot \ln (10) \ Np= 0.1151 \ Np$ or $\rm 1 \ Np = 20 \cdot \lg (e) \ dB= 8.6859 \ dB$.
 * This applet exclusively uses dB values.
@@ Line 37: / Line 37: @@
 *The attenuation function $a_{\rm K}(f)$ is directly proportional to the cable length $l$; $\alpha_{\rm K}(f)= a_{\rm K}(f)/l$ is referred to as the "attenuation factor" or "kilometric attenuation".
 *The frequency-independent component $α_0$ of the attenuation factor takes into account the Ohmic losses.
-*The frequency proportional portion $α_1 · f$ of the attenuation factor is due to the derivation losses ("crosswise loss") .
+*The frequency-proportional portion $α_1 · f$ of the attenuation factor is due to the derivation losses ("crosswise loss") .
-*The dominant portion $α_2$ goes back to [[Digital_Signal_Transmission/Ursachen_und_Auswirkungen_von_Impulsinterferenzen#Frequenzgang_eines_Koaxialkabels|Skin effect]], which causes a lower current density inside the conductor compared to its surface. As a result, the resistance of an electric line increases with the square root of the frequency.
+*The dominant portion $α_2$ goes back to [[Digital_Signal_Transmission/Causes_and_Effects_of_Intersymbol_Interference#Frequency_response_of_a_coaxial_cable|"Skin effect"]], which causes a lower current density inside the conductor compared to its surface. As a result, the resistance of an electric line increases with the square root of the frequency.
@@ Line 89: / Line 89: @@
 {{GraueBox|TEXT=
 $\text{Example 1:}$&nbsp;
-*For $k_3 = 1$ (frequency proportional attenuation factor) we get &nbsp; $\alpha_0 = k_0\hspace{0.05cm} ,\hspace{0.2cm} \alpha_1 =  {k_2}/{ {f_0} }\hspace{0.05cm} ,\hspace{0.2cm} \alpha_2 = 0\hspace{0.05cm} .$
+*For $k_3 = 1$ (frequency-proportional attenuation factor) we get &nbsp; $\alpha_0 = k_0\hspace{0.05cm} ,\hspace{0.2cm} \alpha_1 =  {k_2}/{ {f_0} }\hspace{0.05cm} ,\hspace{0.2cm} \alpha_2 = 0\hspace{0.05cm} .$
 *For $k_3 = 0.5$  (Skin effect) we get the coefficients: &nbsp; $\alpha_0 = k_0\hspace{0.05cm} ,\hspace{0.2cm}\alpha_1 = 0\hspace{0.05cm} ,\hspace{0.2cm} \alpha_2 = {k_2}/{\sqrt{f_0} }\hspace{0.05cm}.$
 *For $k_3 < 0.5$ we get a negative $\alpha_1$. Conversion is only possible for $0.5 \le k_3 \le 1$.
@@ Line 106: / Line 106: @@
 [[File:Applet_Kabeldaempfung_2_version2.png|right|frame|Frequency Response with cosine&ndash;roll&ndash;off|class=fit]]
-This means: The [[Digital_Signal_Transmission/Eigenschaften_von_Nyquistsystemen#Erstes_Nyquistkriterium_im_Frequenzbereich|first Nyquist criterion]] is met<br> &rArr; &nbsp; Timely successive impulses do not disturb each other<br>⇒  &nbsp; there are no [[Digital_Signal_Transmission/Ursachen_und_Auswirkungen_von_Impulsinterferenzen|Intersymbol Interferences]].
+This means: The [[Digital_Signal_Transmission/Properties_of_Nyquist_Systems#First_Nyquist_criterion_in_the_frequency_domain|"first Nyquist criterion"]] is met<br> &rArr; &nbsp; Timely successive impulses do not disturb each other<br>⇒  &nbsp; there are no [[Digital_Signal_Transmission/Causes_and_Effects_of_Intersymbol_Interference|"Intersymbol Interferences"]].
 In the case of white Gaussian noise, the transmission quality is thus determined solely by the noise power in front of the receiver:
@@ Line 124: / Line 124: @@
 This quality criterion is specified in the applet for both parameter sets in logarithm form: &nbsp; $10 \cdot \lg \ \eta_\text{K+E} \le 0 \ \rm dB$.
-*Through variation and optimization of the receiver &nbsp; &rArr; &nbsp; roll-off factor $r$ we get the '''Channel efficiency''':
+*Through variation and optimization of the receiver &nbsp; &rArr; &nbsp; roll-off factor $r$ we get the '''channel efficiency''':
 :$$\eta_\text{K} = \min_{0 \le r \le 1} \ \eta_\text{K+E} .$$}}
@@ Line 138: / Line 138: @@
 This results in the following consequences:
-*In the area up to $f_{1} = 10 \ \text{MHz: }$ $H_{\rm CRO}(f)  = 1$ &nbsp; &rArr; &nbsp; $\left \vert H_{\rm E}(f)\right \vert ^2 = \left \vert H_{\rm K}(f)\right \vert ^{-2}$ (see yellow deposit).
+*In the area up to $f_{1} = 10 \ \text{MHz: }$ $H_{\rm CRO}(f)  = 1$ &nbsp; &rArr; &nbsp; $\left \vert H_{\rm E}(f)\right \vert ^2 = \left \vert H_{\rm K}(f)\right \vert ^{-2}$ (see yellow area).
 * The flank of $H_{\rm CRO}(f)$ is only effective from $f_{1}$ to $f_{2} = 30 \ {\rm MHz}$  and $\left \vert H_{\rm E}(f)\right \vert ^2$ decreases more and more.
 *The maximum of  $\left \vert H_{\rm E}(f_{\rm max})\right \vert ^2$ at $f_{\rm max} \approx 11.5 \ {\rm MHz}$  is twice the value of $\left \vert H_{\rm E}(f = 0)\right \vert ^2 = 1$.

@@ Line 154: / Line 154: @@
 Number "0" is a "Reset" button:
-*Sets parameters to initial values (like after loading the page).
+*Sets parameters to initial values (like after loading the section).
 *Displays a "Reset text" to further describe the applet.

← Older revision		Revision as of 17:54, 11 January 2023
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−	{{LntAppletLinkEn\|attenuationCopperCables_en}}	+	{{LntAppletLinkEn\|attenuationCopperCables_en}}         [https://www.lntwww.de/Applets:Dämpfung_von_Kupferkabeln '''English Applet with German WIKI description''']

	==Applet Description==		==Applet Description==

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 Following relationship exists between the magnitude frequency response and the attenuation function:
 :$$\left | H_{\rm K}(f)\right |=10^{-a_\text{K}(f)/20} = {\rm e}^{-a_\text{K, Np}(f)}.$$
-*The index "K&rdquo; makes it clear, that the considered LTI system is a cable (German : '''K'''abel).
+*The index "K" makes it clear, that the considered LTI system is a cable (German : '''K'''abel).
 *For the first calculation rule, the damping function $a_\text{K}(f)$ must be used in $\rm dB$ (decibel).
 *For the second calculation rule, the damping function $a_\text{K, Np}(f)$ must be used in $\rm Np$ (Neper).
@@ Line 34: / Line 34: @@
 According to [Wel77]<ref name ='Wel77'>Wellhausen, H. W.: Dämpfung, Phase und Laufzeiten bei Weitverkehrs–Koaxialpaaren. Frequenz 31, S. 23-28, 1977.</ref> the Attenuation Function of a Coaxial Cable of length $l$ is given as follows:
 :$$a_{\rm K}(f)=(\alpha_0+\alpha_1\cdot f+\alpha_2\cdot \sqrt{f}) \cdot l.$$
-*It is important to note the difference between $a_{\rm K}(f)$ in $\rm dB$ and the "alpha&rdquo; coefficient with other pseudo&ndash;units.
+*It is important to note the difference between $a_{\rm K}(f)$ in $\rm dB$ and the "alpha" coefficient with other pseudo&ndash;units.
-*The attenuation function $a_{\rm K}(f)$ is directly proportional to the cable length $l$; $\alpha_{\rm K}(f)= a_{\rm K}(f)/l$ is referred to as the "attenuation factor&rdquo; or "kilometric attenuation&rdquo;.
+*The attenuation function $a_{\rm K}(f)$ is directly proportional to the cable length $l$; $\alpha_{\rm K}(f)= a_{\rm K}(f)/l$ is referred to as the "attenuation factor" or "kilometric attenuation".
 *The frequency-independent component $α_0$ of the attenuation factor takes into account the Ohmic losses.
-*The frequency proportional portion $α_1 · f$ of the attenuation factor is due to the derivation losses ("crosswise loss&rdquo;) .
+*The frequency proportional portion $α_1 · f$ of the attenuation factor is due to the derivation losses ("crosswise loss") .
 *The dominant portion $α_2$ goes back to [[Digital_Signal_Transmission/Ursachen_und_Auswirkungen_von_Impulsinterferenzen#Frequenzgang_eines_Koaxialkabels|Skin effect]], which causes a lower current density inside the conductor compared to its surface. As a result, the resistance of an electric line increases with the square root of the frequency.
@@ Line 149: / Line 149: @@
 *An exercise description is displayed.
 *Parameter values are adjusted to the respective exercises.
-*Click "Show solution&rdquo; to display the solution.
+*Click "Show solution" to display the solution.
 *Exercise description and solution are in English.
-Number "0&rdquo; is a "Reset&rdquo; button:
+Number "0" is a "Reset" button:
 *Sets parameters to initial values (like after loading the page).
-*Displays a "Reset text&rdquo; to further describe the applet.
+*Displays a "Reset text" to further describe the applet.
@@ Line 225: / Line 225: @@
 {{BlaueBox|TEXT=
-'''(9)'''&nbsp; Set '''Blue''' to ${\alpha_0}' = {\alpha_1}' = 0, \ {\alpha_2}' = 3, \ {l_{\rm blue} }' = 2$ and '''Red''' to "Inactive&rdquo;. Additionally set ${f_{\rm Nyq} }' =15$ and $r= 0.7$.
+'''(9)'''&nbsp; Set '''Blue''' to ${\alpha_0}' = {\alpha_1}' = 0, \ {\alpha_2}' = 3, \ {l_{\rm blue} }' = 2$ and '''Red''' to "Inactive". Additionally set ${f_{\rm Nyq} }' =15$ and $r= 0.7$.
 :How does $\vert H_{\rm E}(f) \vert$ look like? Calculate the total efficiency $\eta_\text{K+E}$ and the channel efficiency$\eta_\text{K}$.}}
@@ Line 234: / Line 234: @@
 {{BlaueBox|TEXT=
-'''(10)'''&nbsp; Set '''Blue''' to ${\alpha_0}' = {\alpha_1}' = 0, \ {\alpha_2}' = 3, \ {l_{\rm blue} }' = 8$ and '''Red''' to "Inactive&rdquo;. Additionally, set ${f_{\rm Nyq} }' =15$ and $r= 0.7$.
+'''(10)'''&nbsp; Set '''Blue''' to ${\alpha_0}' = {\alpha_1}' = 0, \ {\alpha_2}' = 3, \ {l_{\rm blue} }' = 8$ and '''Red''' to "Inactive". Additionally, set ${f_{\rm Nyq} }' =15$ and $r= 0.7$.
 :How big is $\vert H_{\rm E}(f = 0) \vert$? What is the maximum value of $\vert H_{\rm E}(f) \vert$? Calculate the channel efficiency $\eta_\text{K}$.}}
@@ Line 281: / Line 281: @@
 &nbsp; &nbsp; '''(N)''' &nbsp; &nbsp; Exercise section
-&nbsp; &nbsp; '''(O)''' &nbsp; &nbsp; Variation of the graphic display:$\hspace{0.5cm}$"$+$&rdquo; (Zoom in),
+&nbsp; &nbsp; '''(O)''' &nbsp; &nbsp; Variation of the graphic display:$\hspace{0.5cm}$"$+$" (Zoom in),
-$\hspace{0.5cm}$ "$-$&rdquo; (Zoom out)
+$\hspace{0.5cm}$ "$-$" (Zoom out)
-$\hspace{0.5cm}$ "$\rm o$&rdquo; (Reset)
+$\hspace{0.5cm}$ "$\rm o$" (Reset)
-$\hspace{0.5cm}$ "$\leftarrow$&rdquo; (Move left),  etc.
+$\hspace{0.5cm}$ "$\leftarrow$" (Move left),  etc.
 '''Other options for graphic display''':
@@ Line 295: / Line 295: @@
 ==About the Authors==
 This interactive calculation was designed and realized at the&nbsp; [http://www.lnt.ei.tum.de/startseite Lehrstuhl für Nachrichtentechnik]&nbsp; of the&nbsp; [https://www.tum.de/ Technische Universität München].
-*The original version was created in 2009 by&nbsp; [[Biographies_and_Bibliographies/An_LNTwww_beteiligte_Studierende#Sebastian_Seitz_.28Diplomarbeit_LB_2009.29|Sebastian Seitz]]&nbsp; as part of his Diploma thesis using "FlashMX&ndash;Actionscript&rdquo; (Supervisor: [[Biographies_and_Bibliographies/An_LNTwww_beteiligte_Mitarbeiter_und_Dozenten#Prof._Dr.-Ing._habil._G.C3.BCnter_S.C3.B6der_.28am_LNT_seit_1974.29|Günter Söder]] ).
+*The original version was created in 2009 by&nbsp; [[Biographies_and_Bibliographies/An_LNTwww_beteiligte_Studierende#Sebastian_Seitz_.28Diplomarbeit_LB_2009.29|Sebastian Seitz]]&nbsp; as part of his Diploma thesis using "FlashMX&ndash;Actionscript" (Supervisor: [[Biographies_and_Bibliographies/An_LNTwww_beteiligte_Mitarbeiter_und_Dozenten#Prof._Dr.-Ing._habil._G.C3.BCnter_S.C3.B6der_.28am_LNT_seit_1974.29|Günter Söder]] ).
-*In 2018 this Applet was redesigned and updated to "HTML5&rdquo; by&nbsp; [[Biographies_and_Bibliographies/An_LNTwww_beteiligte_Studierende#Jimmy_He_.28Bachelorarbeit_2018.29|Jimmy He]]&nbsp; as part of his Bachelor's thesis (Supervisor:&nbsp; [[Biographies_and_Bibliographies/Beteiligte_der_Professur_Leitungsgebundene_%C3%9Cbertragungstechnik#Tasn.C3.A1d_Kernetzky.2C_M.Sc._.28bei_L.C3.9CT_seit_2014.29|Tasnád Kernetzky]]) .
+*In 2018 this Applet was redesigned and updated to "HTML5" by&nbsp; [[Biographies_and_Bibliographies/An_LNTwww_beteiligte_Studierende#Jimmy_He_.28Bachelorarbeit_2018.29|Jimmy He]]&nbsp; as part of his Bachelor's thesis (Supervisor:&nbsp; [[Biographies_and_Bibliographies/Beteiligte_der_Professur_Leitungsgebundene_%C3%9Cbertragungstechnik#Tasn.C3.A1d_Kernetzky.2C_M.Sc._.28bei_L.C3.9CT_seit_2014.29|Tasnád Kernetzky]]) .

← Older revision		Revision as of 15:33, 24 February 2021
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	==Once again:  Open Applet in new Tab==		==Once again:  Open Applet in new Tab==

−	{{~~LntAppletLinkEnDe~~\|attenuationCopperCables_en}}	+	{{LntAppletLinkEn\|attenuationCopperCables_en}}

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-{{LntAppletLinkEnDe|attenuationCopperCables_en|attenuationCopperCables}}
+{{LntAppletLinkEn|attenuationCopperCables_en}}
 ==Applet Description==
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 ==Once again:&nbsp; Open Applet in new Tab==
-{{LntAppletLinkEnDe|attenuationCopperCables_en|attenuationCopperCables}}
+{{LntAppletLinkEnDe|attenuationCopperCables_en}}

← Older revision		Revision as of 15:32, 24 February 2021
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	{{LntAppletLinkEnDe\|attenuationCopperCables_en\|attenuationCopperCables}}		{{LntAppletLinkEnDe\|attenuationCopperCables_en\|attenuationCopperCables}}
−	~~{{LntAppletLinkEnDe\|attenuationCopperCables\|attenuationCopperCables}}~~
−

	==Applet Description==		==Applet Description==