Difference between revisions of "Aufgaben:Exercise 1.1Z: VHF II Broadcasting"

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{{quiz-Header|Buchseite=Modulationsverfahren/Zielsetzung von Modulation und Demodulation
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{{quiz-Header|Buchseite=Modulation_Methods/Objectives_of_Modulation_and_Demodulation
 
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[[File:P_ID939__Mod_Z_1_1.png|right|]]
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[[File:P_ID939__Mod_Z_1_1.png|right|frame|Model of an FM radio transmitter]]
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Man bezeichnet elektromagnetische Wellen in einem Frequenzbereich von 30 bis 300 $MHz$ – entsprechend Wellenlängen zwischen zehn und einem Meter – als Ultrakurzwelle (UKW).
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Electromagnetic waves in a frequency range from  $\rm 30$  to  $\text{300 MHz}$  – corresponding to wavelengths between one and ten meters – are referred to as  "ultra-short waves".
  
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In common parlance, USW is also understood to mean the VHF II  ("Very High Frequency")  band, from   $\text{87.5}$  to  $\text{108 MHz}$,  which is still primarily used in Central Europe today for transmitting frequency-modulated radio programs using analog technology.
  
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Im allgemeinen Sprachgebrauch wird unter $\text{UKW}$ auch das Frequenzband $\text{VHF II}$ (''Very High Frequency'') von 87.5 bis 108 $MHz$ verstanden, das in Mitteleuropa vorwiegend zur Übertragung von frequenzmodulierten Hörfunkprogrammen in analoger Technik genutzt wird. Das gesamte Frequenzband ist in mehrere Kanäle mit einem Kanalraster von jeweils $300 kHz$ aufgeteilt.
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The entire frequency band is divided into several channels,  each with a channel spacing of   $\text{300 kHz}$.
  
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In der Grafik sehen Sie das Prinzipschaltbild. Insgesamt $K$ Quellensignale $q_k(t)$ werden mit unterschiedlichen Trägerfrequenzen $f_1, ... , f_K$ moduliert und addiert.
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The diagram displays the principle as a flow chart:
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*A total of  $K$  signals  $q_k(t)$  with different carrier frequencies  $f_1$, $f_2$,  ... , $f_k$, ... ,  $f_K$  are modulated and added together.
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*The summed signal is then beamed from a transmitter after power amplification. 
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*This outgoing signal is referred to as the transmission signal  $s(t)$.
  
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Das Summensignal wird dann nach Leistungsverstärkung von einem Sender abgestrahlt. Dieses abgehende Signal bezeichnen wir als das Sendesignal $s(t)$.
 
  
  
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'''Hinweis:''' Diese Aufgabe bezieht sich auf den Lehrstoff von [http://en.lntwww.de/Modulationsverfahren/Zielsetzung_von_Modulation_und_Demodulation Kapitel 1.1].  
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===Fragebogen===
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''Hints:''  
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*This exercise belongs to the chapter   [[Modulation_Methods/Objectives_of_Modulation_and_Demodulation|Objectives of modulation and demodulation]].
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*Particular reference is made to the page  [[Modulation_Methods/Objectives_of_Modulation_and_Demodulation#Channel_bundling_.E2.80.93_Frequency_Division_Multiplexing|Channel bundling – Frequency Division Multiplexing]].
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===Questions===
  
 
<quiz display=simple>
 
<quiz display=simple>
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{Welches Multiplexverfahren wird hier genutzt?
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{Which multiplexing method is used here?
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|type="[]"}
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|type="()"}
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+ Es handelt sich um $\text{FDM}$.
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+ Frequency Division Multiplexing.
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- Es handelt sich um $\text{TDM}$.
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- Time Division Multiplexing.
  
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{Wieviele Programme könnte man maximal im $\text{VHF II}$–Band übertragen?
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{What is the maximum number of programs that could be transmitted in the VHF II band?
 
|type="{}"}
 
|type="{}"}
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$K$ = { 68 1% }
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$K \ = \ $ { 68 1% }
  
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{Welche der nachfolgenden Aussagen sind zutreffend?
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{Which of the following statements are true?
 
|type="[]"}
 
|type="[]"}
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+ Die $\text{UKW}$–Kanäle sind breitbandiger als diejenigen beim Lang–, Mittel– und Kurzwellenrundfunk.
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+ The VHF channels have higher bandwidth than those for long-wave, medium-wave and short-wave broadcasting.
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- Die Reichweite der $\text{UKW}$–Radiowellen ist größer als beim Lang–, Mittel– und Kurzwellenrundfunk.
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- The range of FM radio waves is greater than that of long-wave, medium-wave and short-wave broadcasting.
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- Das bei einem Empfänger ankommende Signal $r(t)$ unterscheidet sich fast nicht vom Sendesignal $s(t)$.
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- The signal arriving at the receiver &nbsp;$r(t)$&nbsp; is almost indistinguishable from the transmission signal  &nbsp;$s(t)$.
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- Die Funktionseinheit eines Radioempfängers zur Kanalseparierung („Einstellung der Sender”) ist der Tuner.
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+ The functional unit of a radio receiver for channel separation&nbsp; ("setting the radio station")&nbsp; is the&nbsp; "tuner".
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<br><br>
  
  
 
</quiz>
 
</quiz>
  
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===Musterlösung===
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===Solution===
 
{{ML-Kopf}}
 
{{ML-Kopf}}
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'''1.'''Es handelt sich um $\text{FDM}$ (''Frequency Division Multiplexing''). Das alternative Multiplexverfahren $\text{TDM}$ (''Time Division Multiplexing'') ist nur bei einem digitalen Übertragungssystem einsetzbar.
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'''(1)'''&nbsp; <u>Answer 1</u> is correct.  
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*'''FDM'''&nbsp; ("Frequency Division Multiplexing").  
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*The alternative multiplexing method, &nbsp; '''TDM'''&nbsp; ("Time Division Multiplexing")&nbsp; can only be implemented with a digital communications system.
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'''2.'''Aus der Gesamtbandbreite 20.5 $\text{MHz}$ und der Kanalbandbreite 0.3 $MHz$ erhält man $K = 68$.
 
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'''3.'''Das Kanalraster und damit die für einen Kanal zur Verfügung stehende Bandbreite ($300 kHz$) ist im $\text{UKW}$–Bereich deutlich größer als bei Lang–, Mittel– und Kurzwelle. Die im $\text{UKW}$–Rundfunk eingesetzte Frequenzmodulation ist zwar durch eine bessere Qualität gekennzeichnet, benötigt aber auch eine größere Bandbreite. Zum Vergleich wird im Mittelwellenbereich stets Amplitudenmodulation und (in Europa) ein Kanalraster von $9 kHz$ verwendet. Die $\text{NF}$-Bandbreite ist somit $4.5 kHz$.
 
  
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Die Reichweite ist bei $\text{UWK}$ geringer als in den anderen Frequenzbereichen, da $\text{UKW}$–Radiowellen nicht an der Ionosphäre reflektiert werden. Daher besteht ein $\text{UKW}$–Sendernetz meist aus recht vielen Sendern, die in geringen Abständen – meist auf Anhöhen – aufgebaut sind.
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'''(2)'''&nbsp; From the total bandwidth&nbsp; $\text{20.5 MHz}$&nbsp; and the channel bandwidth&nbsp; $\text{0.3 MHz}$&nbsp; we get $\underline{K = 68}$.
  
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Das am Empfänger ankommende Signal hat auf Grund der Freiraumdämpfung, die zumindest quadratisch mit der Entfernung zunimmt, einen sehr viel kleineren Pegel als das Sendesignal $s(t)$.
 
  
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Im Rundfunkempfänger hat tatsächlich der Tuner die Aufgabe der Kanalseparierung. Richtig sind somit die Lösungsvorschläge 1 und 4.
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'''(3)'''&nbsp; <u>Answers 1 and 4</u> are correct:
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*The channel spacing and thus the bandwidth&nbsp; $\text{300 kHz}$&nbsp; available for a channel is significantly larger in the VHF range than for long, medium and short wave broadcasting.&nbsp; Although the frequency modulation used in FM broadcasting is characterized by better quality,&nbsp; it also requires more bandwidth.
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*For comparison,&nbsp; in the medium wave range,&nbsp; amplitude modulation and a channel spacing of&nbsp; $\text{9 kHz}$&nbsp; is always used&nbsp; (in Europe) &nbsp; <br>&rArr; &nbsp; the source signal bandwidth is&nbsp; $B_{\rm LF} = \text{9 kHz/2 = 4.5 kHz}$.
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*The range of VHF is smaller than in the other frequency ranges because VHF radio waves are not reflected by the ionosphere.&nbsp;  Therefore,&nbsp; a VHF transmission network usually consists of quite a large number of transmitters,&nbsp; which are set up at small distances from each other – and mostly at an elevation &nbsp; &rArr; &nbsp; answer 2 is incorrect.
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*The signal arriving at the receiver has a much lower level than the transmission signal $s(t)$,&nbsp; due to atmospheric attenuation,&nbsp; which increases at least quadratically with distance&nbsp;  &rArr; &nbsp; answer 3 is incorrect.
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*In a radio receiver, the tuner indeed has the task of channel separation &nbsp; &rArr; &nbsp; answer 4 is correct.  
  
 
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[[Category:Aufgaben zu Modulationsverfahren|^1.1 Warum braucht man Modulation?^]]
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[[Category:Modulation Methods: Exercises|^1.1 Why do you need Modulation?^]]

Latest revision as of 18:18, 23 March 2022

Model of an FM radio transmitter

Electromagnetic waves in a frequency range from  $\rm 30$  to  $\text{300 MHz}$  – corresponding to wavelengths between one and ten meters – are referred to as  "ultra-short waves".

In common parlance, USW is also understood to mean the VHF II  ("Very High Frequency")  band, from  $\text{87.5}$  to  $\text{108 MHz}$,  which is still primarily used in Central Europe today for transmitting frequency-modulated radio programs using analog technology.

The entire frequency band is divided into several channels,  each with a channel spacing of   $\text{300 kHz}$.

The diagram displays the principle as a flow chart:

  • A total of  $K$  signals  $q_k(t)$  with different carrier frequencies  $f_1$, $f_2$, ... , $f_k$, ... ,  $f_K$  are modulated and added together.
  • The summed signal is then beamed from a transmitter after power amplification. 
  • This outgoing signal is referred to as the transmission signal  $s(t)$.





Hints:



Questions

1

Which multiplexing method is used here?

Frequency Division Multiplexing.
Time Division Multiplexing.

2

What is the maximum number of programs that could be transmitted in the VHF II band?

$K \ = \ $

3

Which of the following statements are true?

The VHF channels have higher bandwidth than those for long-wave, medium-wave and short-wave broadcasting.
The range of FM radio waves is greater than that of long-wave, medium-wave and short-wave broadcasting.
The signal arriving at the receiver  $r(t)$  is almost indistinguishable from the transmission signal  $s(t)$.
The functional unit of a radio receiver for channel separation  ("setting the radio station")  is the  "tuner".


Solution

Solution

(1)  Answer 1 is correct.

  • FDM  ("Frequency Division Multiplexing").
  • The alternative multiplexing method,   TDM  ("Time Division Multiplexing")  can only be implemented with a digital communications system.


(2)  From the total bandwidth  $\text{20.5 MHz}$  and the channel bandwidth  $\text{0.3 MHz}$  we get $\underline{K = 68}$.


(3)  Answers 1 and 4 are correct:

  • The channel spacing and thus the bandwidth  $\text{300 kHz}$  available for a channel is significantly larger in the VHF range than for long, medium and short wave broadcasting.  Although the frequency modulation used in FM broadcasting is characterized by better quality,  it also requires more bandwidth.
  • For comparison,  in the medium wave range,  amplitude modulation and a channel spacing of  $\text{9 kHz}$  is always used  (in Europe)  
    ⇒   the source signal bandwidth is  $B_{\rm LF} = \text{9 kHz/2 = 4.5 kHz}$.
  • The range of VHF is smaller than in the other frequency ranges because VHF radio waves are not reflected by the ionosphere.  Therefore,  a VHF transmission network usually consists of quite a large number of transmitters,  which are set up at small distances from each other – and mostly at an elevation   ⇒   answer 2 is incorrect.
  • The signal arriving at the receiver has a much lower level than the transmission signal $s(t)$,  due to atmospheric attenuation,  which increases at least quadratically with distance  ⇒   answer 3 is incorrect.
  • In a radio receiver, the tuner indeed has the task of channel separation   ⇒   answer 4 is correct.

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