Applets:Attenuation of Copper Cables - Revision history

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	The same applies to the  »'''small coaxial cable'''«   ⇒  short '''Coax (1.2/4.4 mm)''':		The same applies to the  »'''small coaxial cable'''«   ⇒  short '''Coax (1.2/4.4 mm)''':
	:$$\alpha_0 = 0.068\, \frac{ {\rm dB} }{ {\rm km} }\hspace{0.05cm}, \hspace{0.2cm}		:$$\alpha_0 = 0.068\, \frac{ {\rm dB} }{ {\rm km} }\hspace{0.05cm}, \hspace{0.2cm}\alpha_1 = 0.0039\, \frac{ {\rm dB} }{ {\rm km \cdot MHz} }\hspace{0.05cm}, \hspace{0.2cm} \alpha_2 =5.2\, \frac{ {\rm dB} }{ {\rm km \cdot \sqrt{MHz} } }\hspace{0.05cm}.$$
	\alpha_1 = 0.0039\, \frac{ {\rm dB} }{ {\rm km \cdot MHz} }\hspace{0.05cm}, \hspace{0.2cm} \alpha_2 =5.2\, \frac{ {\rm dB} }{ {\rm km \cdot \sqrt{MHz} } }\hspace{0.05cm}.$$

	*These values can be calculated from the cables' geometric dimensions and have been confirmed by measurements at the FTZ in Darmstadt – see [Wel77]<ref name ='Wel77'>Wellhausen, H. W.: Dämpfung, Phase und Laufzeiten bei Weitverkehrs–Koaxialpaaren. Frequenz 31, S. 23-28, 1977.</ref>.		*These values can be calculated from the cables' geometric dimensions and have been confirmed by measurements at the FTZ in Darmstadt – see [Wel77]<ref name ='Wel77'>Wellhausen, H. W.: Dämpfung, Phase und Laufzeiten bei Weitverkehrs–Koaxialpaaren. Frequenz 31, S. 23-28, 1977.</ref>.
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	==About the Authors==		==About the Authors==
	This interactive calculation was designed and realized at the  [http://www.lnt.ei.tum.de/startseite Lehrstuhl für Nachrichtentechnik]  of the  [https://www.tum.de/ Technische Universität München].		This interactive calculation was designed and realized at the  [http://www.lnt.ei.tum.de/startseite Lehrstuhl für Nachrichtentechnik]  of the  [https://www.tum.de/ Technische Universität München].
	*The original version was created in 2009 by  [[Biographies_and_Bibliographies/~~An_LNTwww_beteiligte_Studierende~~#Sebastian_Seitz_.28Diplomarbeit_LB_2009.29\|Sebastian Seitz]]  as part of his Diploma thesis using "FlashMX–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]] ).		*The original version was created in 2009 by  [[Biographies_and_Bibliographies/Students_involved_in_LNTwww#Sebastian_Seitz_.28Diplomarbeit_LB_2009.29\|Sebastian Seitz]]  as part of his Diploma thesis using "FlashMX–Actionscript" (Supervisor: [[Biographies_and_Bibliographies/LNTwww_members_from_LNT#Prof._Dr.-Ing._habil._Günter_Söder_(at_LNT_from_1974-2024)\|Günter Söder]] ).
	*In 2018 this Applet was redesigned and updated to "HTML5" by  [[Biographies_and_Bibliographies/~~An_LNTwww_beteiligte_Studierende~~#Jimmy_He_.28Bachelorarbeit_2018.29\|Jimmy He]]  as part of his Bachelor's thesis (Supervisor:  [[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  [[Biographies_and_Bibliographies/Students_involved_in_LNTwww#Jimmy_He_.28Bachelorarbeit_2018.29\|Jimmy He]]  as part of his Bachelor's thesis (Supervisor:  [[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]]) .

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	{{LntAppletLinkEn\|attenuationCopperCables_en}}		{{LntAppletLinkEn\|attenuationCopperCables_en}}
			[[de:Applets:Attenuation_of_Copper_Cables]]

Maintenance script: Update domain links: en.lntwww.de → en.lntwww.lnt.ei.tum.de, www.lntwww.de → lntwww.lnt.ei.tum.de

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Update domain links: en.lntwww.de → en.lntwww.lnt.ei.tum.de, www.lntwww.de → lntwww.lnt.ei.tum.de

← Older revision		Revision as of 13:09, 16 March 2026
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	{{LntAppletLinkEn\|attenuationCopperCables_en}}         [https://~~www~~.~~lntwww~~.de/Applets:Dämpfung_von_Kupferkabeln '''English Applet with German WIKI description''']		{{LntAppletLinkEn\|attenuationCopperCables_en}}         [https://lntwww.lnt.ei.tum.de/Applets:Dämpfung_von_Kupferkabeln '''English Applet with German WIKI description''']

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

Guenter at 14:25, 8 April 2023

2023-04-08T14:25:52Z

Show changes

Noah at 21:04, 25 March 2023

2023-03-25T21:04:29Z

← Older revision		Revision as of 23:04, 25 March 2023
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	In this applet		In this applet
	*we neglect the influence of the transmitted pulse form   ⇒   $H_{\rm S}(f) \equiv 1$   ⇒   dirac shaped transmission signal $s(t)$, and		*we neglect the influence of the transmitted pulse form   ⇒   $H_{\rm S}(f) \equiv 1$   ⇒   dirac shaped transmission signal $s(t)$, and
	*presuppose a binary Nyquist system with cosine~~–roll–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 $f_{\rm Nyq} = [f_1 + f_2]/2 =1(2T)$ :
	:$$H_{\rm K}(f) · H_{\rm E}(f) = H_{\rm CRO}(f).$$		:$$H_{\rm K}(f) · H_{\rm E}(f) = H_{\rm CRO}(f).$$

	[[File:Applet_Kabeldaempfung_2_version2.png\|right\|frame\|Frequency Response with cosine~~–roll–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> ⇒   Timely successive impulses do not disturb each other<br>⇒   there are no [[Digital_Signal_Transmission/Causes_and_Effects_of_Intersymbol_Interference\|"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> ⇒   Timely successive impulses do not disturb each other<br>⇒   there are no [[Digital_Signal_Transmission/Causes_and_Effects_of_Intersymbol_Interference\|"Intersymbol Interferences"]].

Noah at 21:00, 25 March 2023

2023-03-25T21:00:20Z

Hwang at 16:08, 23 January 2023

2023-01-23T16:08:34Z

← Older revision		Revision as of 18:08, 23 January 2023
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	Number "0" is a "Reset" button:		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.		*Displays a "Reset text" to further describe the applet.

Guenter at 17:54, 11 January 2023

2023-01-11T17:54:47Z

← Older revision		Revision as of 19:54, 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==

Javier: Text replacement - "”" to """

2021-05-28T14:41:12Z

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Javier: Text replacement - "„" to """

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← Older revision		Revision as of 23:00, 25 March 2023
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	Aside from the attenuation function $a_{\rm K}(f)$ the applet can display:		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 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''  $\eta_\text{K+E}$ 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''  $\eta_\text{K+E}$ 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''  $ \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''  $ \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==		==Theoretical Background==
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	:$$\left \| H_{\rm K}(f)\right \|=10^{-a_\text{K}(f)/20} = {\rm e}^{-a_\text{K, Np}(f)}.$$		:$$\left \| H_{\rm K}(f)\right \|=10^{-a_\text{K}(f)/20} = {\rm e}^{-a_\text{K, Np}(f)}.$$
	*The index "K" makes it clear, that the considered LTI system is a cable (German : '''K'''abel).		*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 $\rm 1 \ Np = 20 \cdot \lg (e) \ dB= 8.6859 \ dB$.		* 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.		* This applet exclusively uses dB values.
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	*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 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-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.


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	{{GraueBox\|TEXT=		{{GraueBox\|TEXT=
	$\text{Example 1:}$		$\text{Example 1:}$
	*For $k_3 = 1$ (frequency proportional attenuation factor) we get   $\alpha_0 = k_0\hspace{0.05cm} ,\hspace{0.2cm} \alpha_1 = {k_2}/{ {f_0} }\hspace{0.05cm} ,\hspace{0.2cm} \alpha_2 = 0\hspace{0.05cm} .$		*For $k_3 = 1$ (frequency-proportional attenuation factor) we get   $\alpha_0 = k_0\hspace{0.05cm} ,\hspace{0.2cm} \alpha_1 = {k_2}/{ {f_0} }\hspace{0.05cm} ,\hspace{0.2cm} \alpha_2 = 0\hspace{0.05cm} .$
	*For $k_3 = 0.5$ (Skin effect) we get the coefficients:   $\alpha_0 = k_0\hspace{0.05cm} ,\hspace{0.2cm}\alpha_1 = 0\hspace{0.05cm} ,\hspace{0.2cm} \alpha_2 = {k_2}/{\sqrt{f_0} }\hspace{0.05cm}.$		*For $k_3 = 0.5$ (Skin effect) we get the coefficients:   $\alpha_0 = k_0\hspace{0.05cm} ,\hspace{0.2cm}\alpha_1 = 0\hspace{0.05cm} ,\hspace{0.2cm} \alpha_2 = {k_2}/{\sqrt{f_0} }\hspace{0.05cm}.$
	*For $k_3 < 0.5$ we get a negative $\alpha_1$. Conversion is only possible for $0.5 \le k_3 \le 1$.		*For $k_3 < 0.5$ we get a negative $\alpha_1$. Conversion is only possible for $0.5 \le k_3 \le 1$.
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	[[File:Applet_Kabeldaempfung_2_version2.png\|right\|frame\|Frequency Response with cosine–roll–off\|class=fit]]		[[File:Applet_Kabeldaempfung_2_version2.png\|right\|frame\|Frequency Response with cosine–roll–off\|class=fit]]

	This means: The [[Digital_Signal_Transmission/~~Eigenschaften_von_Nyquistsystemen~~#~~Erstes_Nyquistkriterium_im_Frequenzbereich~~\|first Nyquist criterion]] is met<br> ⇒   Timely successive impulses do not disturb each other<br>⇒   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> ⇒   Timely successive impulses do not disturb each other<br>⇒   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:		In the case of white Gaussian noise, the transmission quality is thus determined solely by the noise power in front of the receiver:
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	This quality criterion is specified in the applet for both parameter sets in logarithm form:   $10 \cdot \lg \ \eta_\text{K+E} \le 0 \ \rm dB$.		This quality criterion is specified in the applet for both parameter sets in logarithm form:   $10 \cdot \lg \ \eta_\text{K+E} \le 0 \ \rm dB$.

	*Through variation and optimization of the receiver   ⇒   roll-off factor $r$ we get the '''~~Channel~~ efficiency''':		*Through variation and optimization of the receiver   ⇒   roll-off factor $r$ we get the '''channel efficiency''':

	:$$\eta_\text{K} = \min_{0 \le r \le 1} \ \eta_\text{K+E} .$$}}		:$$\eta_\text{K} = \min_{0 \le r \le 1} \ \eta_\text{K+E} .$$}}
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	This results in the following consequences:		This results in the following consequences:
	*In the area up to $f_{1} = 10 \ \text{MHz: }$ $H_{\rm CRO}(f) = 1$   ⇒   $\left \vert H_{\rm E}(f)\right \vert ^2 = \left \vert H_{\rm K}(f)\right \vert ^{-2}$ (see yellow ~~deposit~~).		*In the area up to $f_{1} = 10 \ \text{MHz: }$ $H_{\rm CRO}(f) = 1$   ⇒   $\left \vert H_{\rm E}(f)\right \vert ^2 = \left \vert H_{\rm K}(f)\right \vert ^{-2}$ (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 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 $\left \vert H_{\rm E}(f = 0)\right \vert ^2 = 1$.		*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 $\left \vert H_{\rm E}(f = 0)\right \vert ^2 = 1$.

← Older revision		Revision as of 16:41, 28 May 2021
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	Following relationship exists between the magnitude frequency response and the attenuation function:		Following relationship exists between the magnitude frequency response and the attenuation function:
	:$$\left \| H_{\rm K}(f)\right \|=10^{-a_\text{K}(f)/20} = {\rm e}^{-a_\text{K, Np}(f)}.$$		:$$\left \| H_{\rm K}(f)\right \|=10^{-a_\text{K}(f)/20} = {\rm e}^{-a_\text{K, Np}(f)}.$$
	*The index "K~~”~~ makes it clear, that the considered LTI system is a cable (German : '''K'''abel).		*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 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).		*For the second calculation rule, the damping function $a_\text{K, Np}(f)$ must be used in $\rm Np$ (Neper).
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	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:		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:
	:$$a_{\rm K}(f)=(\alpha_0+\alpha_1\cdot f+\alpha_2\cdot \sqrt{f}) \cdot l.$$		:$$a_{\rm K}(f)=(\alpha_0+\alpha_1\cdot f+\alpha_2\cdot \sqrt{f}) \cdot l.$$
	*It is important to note the difference between $a_{\rm K}(f)$ in $\rm dB$ and the "alpha~~”~~ coefficient with other pseudo–units.		*It is important to note the difference between $a_{\rm K}(f)$ in $\rm dB$ and the "alpha" coefficient with other pseudo–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~~”~~ or "kilometric attenuation~~”~~.		*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-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/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.

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	*An exercise description is displayed.		*An exercise description is displayed.
	*Parameter values are adjusted to the respective exercises.		*Parameter values are adjusted to the respective exercises.
	*Click "Show solution~~”~~ to display the solution.		*Click "Show solution" to display the solution.
	*Exercise description and solution are in English.		*Exercise description and solution are in English.


	Number "0~~”~~ is a "Reset~~”~~ button:		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 page).
	*Displays a "Reset text~~”~~ to further describe the applet.		*Displays a "Reset text" to further describe the applet.


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	{{BlaueBox\|TEXT=		{{BlaueBox\|TEXT=
	'''(9)'''  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 $r= 0.7$.		'''(9)'''  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$\eta_\text{K}$.}}		:How does $\vert H_{\rm E}(f) \vert$ look like? Calculate the total efficiency $\eta_\text{K+E}$ and the channel efficiency$\eta_\text{K}$.}}

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	{{BlaueBox\|TEXT=		{{BlaueBox\|TEXT=
	'''(10)'''  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 $r= 0.7$.		'''(10)'''  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 $\eta_\text{K}$.}}		: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 $\eta_\text{K}$.}}

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	'''(N)'''     Exercise section		'''(N)'''     Exercise section

	'''(O)'''     Variation of the graphic display:$\hspace{0.5cm}$"$+$~~”~~ (Zoom in),		'''(O)'''     Variation of the graphic display:$\hspace{0.5cm}$"$+$" (Zoom in),

	$\hspace{0.5cm}$ "$-$~~”~~ (Zoom out)		$\hspace{0.5cm}$ "$-$" (Zoom out)

	$\hspace{0.5cm}$ "$\rm o$~~”~~ (Reset)		$\hspace{0.5cm}$ "$\rm o$" (Reset)

	$\hspace{0.5cm}$ "$\leftarrow$~~”~~ (Move left), etc.		$\hspace{0.5cm}$ "$\leftarrow$" (Move left), etc.

	'''Other options for graphic display''':		'''Other options for graphic display''':
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	==About the Authors==		==About the Authors==
	This interactive calculation was designed and realized at the  [http://www.lnt.ei.tum.de/startseite Lehrstuhl für Nachrichtentechnik]  of the  [https://www.tum.de/ Technische Universität München].		This interactive calculation was designed and realized at the  [http://www.lnt.ei.tum.de/startseite Lehrstuhl für Nachrichtentechnik]  of the  [https://www.tum.de/ Technische Universität München].
	*The original version was created in 2009 by  [[Biographies_and_Bibliographies/An_LNTwww_beteiligte_Studierende#Sebastian_Seitz_.28Diplomarbeit_LB_2009.29\|Sebastian Seitz]]  as part of his Diploma thesis using "FlashMX–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]] ).		*The original version was created in 2009 by  [[Biographies_and_Bibliographies/An_LNTwww_beteiligte_Studierende#Sebastian_Seitz_.28Diplomarbeit_LB_2009.29\|Sebastian Seitz]]  as part of his Diploma thesis using "FlashMX–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~~”~~ by  [[Biographies_and_Bibliographies/An_LNTwww_beteiligte_Studierende#Jimmy_He_.28Bachelorarbeit_2018.29\|Jimmy He]]  as part of his Bachelor's thesis (Supervisor:  [[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  [[Biographies_and_Bibliographies/An_LNTwww_beteiligte_Studierende#Jimmy_He_.28Bachelorarbeit_2018.29\|Jimmy He]]  as part of his Bachelor's thesis (Supervisor:  [[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 16:39, 28 May 2021
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	Following relationship exists between the magnitude frequency response and the attenuation function:		Following relationship exists between the magnitude frequency response and the attenuation function:
	:$$\left \| H_{\rm K}(f)\right \|=10^{-a_\text{K}(f)/20} = {\rm e}^{-a_\text{K, Np}(f)}.$$		:$$\left \| H_{\rm K}(f)\right \|=10^{-a_\text{K}(f)/20} = {\rm e}^{-a_\text{K, Np}(f)}.$$
	*The index ~~&bdquo;~~K” 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 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).		*For the second calculation rule, the damping function $a_\text{K, Np}(f)$ must be used in $\rm Np$ (Neper).
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	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:		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:
	:$$a_{\rm K}(f)=(\alpha_0+\alpha_1\cdot f+\alpha_2\cdot \sqrt{f}) \cdot l.$$		:$$a_{\rm K}(f)=(\alpha_0+\alpha_1\cdot f+\alpha_2\cdot \sqrt{f}) \cdot l.$$
	*It is important to note the difference between $a_{\rm K}(f)$ in $\rm dB$ and the ~~&bdquo;~~alpha” coefficient with other pseudo–units.		*It is important to note the difference between $a_{\rm K}(f)$ in $\rm dB$ and the "alpha” coefficient with other pseudo–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 ~~&bdquo;~~attenuation factor” or ~~&bdquo;~~kilometric attenuation”.		*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-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 (~~&bdquo;~~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/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.

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	*An exercise description is displayed.		*An exercise description is displayed.
	*Parameter values are adjusted to the respective exercises.		*Parameter values are adjusted to the respective exercises.
	*Click ~~&bdquo;~~Show solution” to display the solution.		*Click "Show solution” to display the solution.
	*Exercise description and solution are in English.		*Exercise description and solution are in English.


	Number ~~&bdquo;~~0” is a ~~&bdquo;~~Reset” button:		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 page).
	*Displays a ~~&bdquo;~~Reset text” to further describe the applet.		*Displays a "Reset text” to further describe the applet.


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	{{BlaueBox\|TEXT=		{{BlaueBox\|TEXT=
	'''(9)'''  Set '''Blue''' to ${\alpha_0}' = {\alpha_1}' = 0, \ {\alpha_2}' = 3, \ {l_{\rm blue} }' = 2$ and '''Red''' to ~~&bdquo;~~Inactive”. Additionally set ${f_{\rm Nyq} }' =15$ and $r= 0.7$.		'''(9)'''  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$\eta_\text{K}$.}}		:How does $\vert H_{\rm E}(f) \vert$ look like? Calculate the total efficiency $\eta_\text{K+E}$ and the channel efficiency$\eta_\text{K}$.}}

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	{{BlaueBox\|TEXT=		{{BlaueBox\|TEXT=
	'''(10)'''  Set '''Blue''' to ${\alpha_0}' = {\alpha_1}' = 0, \ {\alpha_2}' = 3, \ {l_{\rm blue} }' = 8$ and '''Red''' to ~~&bdquo;~~Inactive”. Additionally, set ${f_{\rm Nyq} }' =15$ and $r= 0.7$.		'''(10)'''  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 $\eta_\text{K}$.}}		: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 $\eta_\text{K}$.}}

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	'''(N)'''     Exercise section		'''(N)'''     Exercise section

	'''(O)'''     Variation of the graphic display:$\hspace{0.5cm}$~~&bdquo;~~$+$” (Zoom in),		'''(O)'''     Variation of the graphic display:$\hspace{0.5cm}$"$+$” (Zoom in),

	$\hspace{0.5cm}$ ~~&bdquo;~~$-$” (Zoom out)		$\hspace{0.5cm}$ "$-$” (Zoom out)

	$\hspace{0.5cm}$ ~~&bdquo;~~$\rm o$” (Reset)		$\hspace{0.5cm}$ "$\rm o$” (Reset)

	$\hspace{0.5cm}$ ~~&bdquo;~~$\leftarrow$” (Move left), etc.		$\hspace{0.5cm}$ "$\leftarrow$” (Move left), etc.

	'''Other options for graphic display''':		'''Other options for graphic display''':
Line 295:		Line 295:
	==About the Authors==		==About the Authors==
	This interactive calculation was designed and realized at the  [http://www.lnt.ei.tum.de/startseite Lehrstuhl für Nachrichtentechnik]  of the  [https://www.tum.de/ Technische Universität München].		This interactive calculation was designed and realized at the  [http://www.lnt.ei.tum.de/startseite Lehrstuhl für Nachrichtentechnik]  of the  [https://www.tum.de/ Technische Universität München].
	*The original version was created in 2009 by  [[Biographies_and_Bibliographies/An_LNTwww_beteiligte_Studierende#Sebastian_Seitz_.28Diplomarbeit_LB_2009.29\|Sebastian Seitz]]  as part of his Diploma thesis using ~~&bdquo;~~FlashMX–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]] ).		*The original version was created in 2009 by  [[Biographies_and_Bibliographies/An_LNTwww_beteiligte_Studierende#Sebastian_Seitz_.28Diplomarbeit_LB_2009.29\|Sebastian Seitz]]  as part of his Diploma thesis using "FlashMX–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 ~~&bdquo;~~HTML5” by  [[Biographies_and_Bibliographies/An_LNTwww_beteiligte_Studierende#Jimmy_He_.28Bachelorarbeit_2018.29\|Jimmy He]]  as part of his Bachelor's thesis (Supervisor:  [[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  [[Biographies_and_Bibliographies/An_LNTwww_beteiligte_Studierende#Jimmy_He_.28Bachelorarbeit_2018.29\|Jimmy He]]  as part of his Bachelor's thesis (Supervisor:  [[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]]) .