Aufgaben:Exercise 2.2Z: Non-Linearities - Revision history

Guenter at 11:24, 14 April 2021

2021-04-14T11:24:51Z

Guenter at 15:02, 12 April 2021

2021-04-12T15:02:05Z

Guenter at 15:00, 12 April 2021

2021-04-12T15:00:25Z

Guenter: Guenter moved page Aufgaben:Exercise 2.2Z: Nonlinearities to Aufgaben:Exercise 2.2Z: Non-Linearities

2021-04-12T14:57:19Z

Guenter moved page Exercise 2.2Z: Nonlinearities to Exercise 2.2Z: Non-Linearities

Guenter at 14:37, 12 April 2021

2021-04-12T14:37:19Z

Noah at 09:18, 26 March 2021

2021-03-26T09:18:18Z

Javier: Text replacement - "Category:Exercises for Signal Representation" to "Category:Signal Representation: Exercises"

2021-03-23T12:39:08Z

Text replacement - "Category:Exercises for Signal Representation" to "Category:Signal Representation: Exercises"

Noah at 02:14, 4 January 2021

2021-01-04T02:14:27Z

Oezdemir: Oezdemir moved page Aufgaben:Aufgabe 2.2Z: Nichtlinearitäten to Aufgaben:Exercise 2.2Z: Nonlinearities

2020-11-01T16:09:16Z

Oezdemir moved page Aufgabe 2.2Z: Nichtlinearitäten to Exercise 2.2Z: Nonlinearities

Oezdemir at 16:09, 1 November 2020

2020-11-01T16:09:03Z

@@ Line 55: / Line 55: @@
 '''(3)'''&nbsp;  Due to the periodicity and symmetry, averaging in the range from&nbsp; $0$&nbsp; bis&nbsp; $T_0/2$ is sufficient.
-* With the corresponding characteristic curve, the following then applies::
+* With the corresponding characteristic curve, the following then applies:
 :$$z_0=\frac{1}{T_0/2}\int^{T_0/2}_0 x^2(t)\,{\rm d}t=\frac{4\rm V^2}{T_0/2}\int^{T_0/2}_0 ({2t}/{T_0})^2\, {\rm d}t={4}/{3}\rm \;V^2
 \hspace{0.15cm}\underline{\approx1.333\rm \;V^2}.$$

@@ Line 45: / Line 45: @@
 ===Solution===
 {{ML-Kopf}}
-'''(1)'''&nbsp;  The DC signal&nbsp; $x_0$&nbsp; is the mean value of the signal&nbsp; ${x(t)}$. Averaging over a period duration&nbsp; $T_0 = 1 \, \text{ms}$ is sufficient. One obtains:
+'''(1)'''&nbsp;  The DC signal&nbsp; $x_0$&nbsp; is the mean of signal&nbsp; ${x(t)}$.&nbsp; Averaging over a period duration&nbsp; $T_0 = 1 \, \text{ms}$ is sufficient.&nbsp; One obtains:
 :$$x_0=\frac{1}{T_0}\int^{T_0}_0 x(t)\,{\rm d} t \hspace{0.15cm}\underline{=1\,\rm V}.$$
-'''(2)'''&nbsp;  In half the time&nbsp; ${y(t)} = 1\, \text{V}$, in the other half is is between&nbsp; $0$&nbsp; and&nbsp; $1\, \text{V}$&nbsp; with the mean value at&nbsp; $0.5 \,\text{V}$&nbsp; &rArr; &nbsp;  $y_0 \hspace{0.15cm}\underline{= 0.75 \,\text{V}}$.
+'''(2)'''&nbsp;  In half the time&nbsp; ${y(t)} = 1\, \text{V}$, in the other half is is between&nbsp; $0$&nbsp; and&nbsp; $1\, \text{V}$&nbsp; with the mean at&nbsp; $0.5 \,\text{V}$&nbsp; &rArr; &nbsp;  $y_0 \hspace{0.15cm}\underline{= 0.75 \,\text{V}}$.

@@ Line 6: / Line 6: @@
 We start from the triangular signal&nbsp; ${x(t)}$&nbsp; according to the figure above.
-If we apply this signal to an amplitude limiter, we get the signal
+*If we apply this signal to an amplitude limiter, we get the signal
 :$$y(t)=\left\{ {x(t)\atop \rm 1V}{\hspace{0.5cm} {\rm for}\quad x(t)\le \rm 1V \atop {\rm else}}\right..$$
-A second non-linearity provides the signal
+*Another non-linearity provides the signal
 :$$z(t)=x^2(t).$$
 The DC signal components are designated&nbsp; $x_0$,&nbsp; $y_0$&nbsp; and&nbsp; $z_0$&nbsp; in the following.
@@ Line 20: / Line 18: @@
 ''Hint:''
-*This exercise belongs to the chapter&nbsp; [[Signal_Representation/Direct_Current_Signal_-_Limit_Case_of_a_Periodic_Signal|Direct Current Signal - Limit Case of a Periodic Signal]].
+*This task belongs to chapter&nbsp; [[Signal_Representation/Direct_Current_Signal_-_Limit_Case_of_a_Periodic_Signal|Direct Current Signal - Limit Case of a Periodic Signal]].

← Older revision		Revision as of 14:37, 12 April 2021
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−	[[Category:Signal Representation: Exercises\|^2.2 Direct Current ~~Signal - Limit Case of a Periodic~~ Signal^]]	+	[[Category:Signal Representation: Exercises\|^2.2 Direct Current Signal^]]

@@ Line 3: / Line 3: @@
 }}
-[[File:P_ID322__Sig_Z_2_2.png|right|frame|Gleichanteil nach Nichtlinearitäten]]
+[[File:P_ID322__Sig_Z_2_2.png|right|frame|DC component after non-linearities]]
 We start from the triangular signal&nbsp; ${x(t)}$&nbsp; according to the figure above.
 If we apply this signal to an amplitude limiter, we get the signal
-:$$y(t)=\left\{ {x(t)\atop \rm 1V}{\hspace{0.5cm} {\rm f\ddot{u}r}\quad x(t)\le \rm 1V \atop {\rm sonst}}\right..$$
+:$$y(t)=\left\{ {x(t)\atop \rm 1V}{\hspace{0.5cm} {\rm for}\quad x(t)\le \rm 1V \atop {\rm else}}\right..$$
 A second non-linearity provides the signal
 :$$z(t)=x^2(t).$$
@@ Line 20: / Line 20: @@
 ''Hint:''
-*This exercise belongs to the chapter&nbsp; [[Signal_Representation/Direct_Current_Signal_-_Limit_Case_of_a_Periodic_Signal|Direct Current Signal - Limit Case of a Periodic Signal.]].
+*This exercise belongs to the chapter&nbsp; [[Signal_Representation/Direct_Current_Signal_-_Limit_Case_of_a_Periodic_Signal|Direct Current Signal - Limit Case of a Periodic Signal]].

← Older revision		Revision as of 12:39, 23 March 2021
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−	[[Category:~~Exercises for~~ Signal Representation\|^2.2 Direct Current Signal - Limit Case of a Periodic Signal^]]	+	[[Category:Signal Representation: Exercises\|^2.2 Direct Current Signal - Limit Case of a Periodic Signal^]]

@@ Line 4: / Line 4: @@
 [[File:P_ID322__Sig_Z_2_2.png|right|frame|Gleichanteil nach Nichtlinearitäten]]
-Wir gehen von dem dreieckförmigen Signal&nbsp; ${x(t)}$&nbsp; gemäß der oberen Abbildung aus.
+We start from the triangular signal&nbsp; ${x(t)}$&nbsp; according to the figure above.
-Gibt man dieses Signal auf einen Amplitudenbegrenzer, so entsteht das Signal
+If we apply this signal to an amplitude limiter, we get the signal
 :$$y(t)=\left\{ {x(t)\atop \rm 1V}{\hspace{0.5cm} {\rm f\ddot{u}r}\quad x(t)\le \rm 1V \atop {\rm sonst}}\right..$$
-Eine zweite Nichtlinearität liefert das Signal
+A second non-linearity provides the signal
 :$$z(t)=x^2(t).$$
-Die Gleichsignalanteile werden nachfolgend mit&nbsp; $x_0$,&nbsp; $y_0$&nbsp; bzw.&nbsp; $z_0$&nbsp; bezeichnet.
+The DC signal components are designated&nbsp; $x_0$,&nbsp; $y_0$&nbsp; and&nbsp; $z_0$&nbsp; in the following.
@@ Line 19: / Line 19: @@
-''Hinweis:''
+''Hint:''
-*Die Aufgabe gehört zum Kapitel&nbsp; [[Signal_Representation/Direct_Current_Signal_-_Limit_Case_of_a_Periodic_Signal|Gleichsignal - Grenzfall eines periodischen Signals]].
+*This exercise belongs to the chapter&nbsp; [[Signal_Representation/Direct_Current_Signal_-_Limit_Case_of_a_Periodic_Signal|Direct Current Signal - Limit Case of a Periodic Signal.]].
@@ Line 27: / Line 27: @@
-===Fragebogen===
+===Questions===
 <quiz display=simple>
-{Ermitteln Sie den Gleichsignalanteil&nbsp; $x_0$&nbsp; des Signals&nbsp; ${x(t)}$.
+{Determine the DC signal component&nbsp; $x_0$&nbsp; of the signal&nbsp; ${x(t)}$.
 |type="{}"}
 $x_0\ = \ $  { 1 3% } &nbsp; $\text{V}$
-{Ermitteln Sie den Gleichsignalanteil&nbsp; $y_0$&nbsp; des Signals&nbsp; ${y(t)}$.
+{Determine the DC signal component&nbsp; $y_0$&nbsp; of the signal&nbsp; ${y(t)}$.
 |type="{}"}
 $y_0\ = \ $ { 0.75 3% } &nbsp; $\text{V}$
-{Ermitteln Sie den Gleichsignalanteil&nbsp; $z_0$&nbsp; des Signals&nbsp; ${z(t)}$.
+{Determine the DC signal component&nbsp; $z_0$&nbsp; of the signal&nbsp; ${z(t)}$.
 |type="{}"}
 $z_0\ = \ $ { 1.333 3% }&nbsp;  $\text{V}^2$
@@ Line 48: / Line 48: @@
 </quiz>
-===Musterlösung===
+===Solution===
 {{ML-Kopf}}
-'''(1)'''&nbsp;  Der Gleichsignalanteil&nbsp; $x_0$&nbsp; ist der Mittelwert des Signals&nbsp; ${x(t)}$. Es genügt die Mittelung über eine Periodendauer&nbsp; $T_0 = 1 \, \text{ms}$, und man erhält:
+'''(1)'''&nbsp;  The DC signal&nbsp; $x_0$&nbsp; is the mean value of the signal&nbsp; ${x(t)}$. Averaging over a period duration&nbsp; $T_0 = 1 \, \text{ms}$ is sufficient. One obtains:
 :$$x_0=\frac{1}{T_0}\int^{T_0}_0 x(t)\,{\rm d} t \hspace{0.15cm}\underline{=1\,\rm V}.$$
-'''(2)'''&nbsp;  In der Hälfte der Zeit ist&nbsp; ${y(t)} = 1\, \text{V}$, in der anderen Hälfte liegt es zwischen&nbsp; $0$&nbsp; und&nbsp; $1\, \text{V}$&nbsp; mit dem Mittelwert bei&nbsp; $0.5 \,\text{V}$&nbsp; &rArr; &nbsp;  $y_0 \hspace{0.15cm}\underline{= 0.75 \,\text{V}}$.
+'''(2)'''&nbsp;  In half the time&nbsp; ${y(t)} = 1\, \text{V}$, in the other half is is between&nbsp; $0$&nbsp; and&nbsp; $1\, \text{V}$&nbsp; with the mean value at&nbsp; $0.5 \,\text{V}$&nbsp; &rArr; &nbsp;  $y_0 \hspace{0.15cm}\underline{= 0.75 \,\text{V}}$.
-'''(3)'''&nbsp; Aufgrund der Periodizität und der Symmetrie genügt die Mittelung im Bereich von&nbsp; $0$&nbsp; bis&nbsp; $T_0/2$.
+'''(3)'''&nbsp;  Due to the periodicity and symmetry, averaging in the range from&nbsp; $0$&nbsp; bis&nbsp; $T_0/2$ is sufficient.
-* Mit der entsprechenden Kennlinie gilt dann:
+* With the corresponding characteristic curve, the following then applies::
 :$$z_0=\frac{1}{T_0/2}\int^{T_0/2}_0 x^2(t)\,{\rm d}t=\frac{4\rm V^2}{T_0/2}\int^{T_0/2}_0 ({2t}/{T_0})^2\, {\rm d}t={4}/{3}\rm \;V^2
 \hspace{0.15cm}\underline{\approx1.333\rm \;V^2}.$$

← Older revision		Revision as of 16:09, 1 November 2020
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−	[[Category:Exercises for Signal Representation\|^2. ~~Periodische Signale~~^]]	+	[[Category:Exercises for Signal Representation\|^2.2 Direct Current Signal - Limit Case of a Periodic Signal^]]