الكهرباء

beat frequencies

سِمْفُونِيَةُ النَّبْضَاتِ: فَهْمُ تَردُّدَاتِ النَّبْضِ فِي هَنْدَسَةِ الْكَهْرَبَاءِ

فِي عَالَمِ هَنْدَسَةِ الْكَهْرَبَاءِ، يَشُكِّلُ مَفْهُومُ **تَردُّدَاتِ النَّبْضِ** ظَاهِرَةً فَاسِخَةً تَنْشَأُ حِينَ يَتَفاعَلُ إِشَارَتَانِ بِتَردُّدَاتٍ مُتَقَارِبَةٍ قَلِيلًا. هَذِهِ التَّردُّدَاتُ، الَّتِي تُسَمَّى غَالِبًا **تَردُّدَاتِ الْمَجْمُوعِ** وَ**تَردُّدَاتِ الْفَرْقِ**، تُوَلَّدُ خِلَالَ عَمَلِيَّاتٍ كَ**التَّغَيُّرِ المُتَغَايِرِ** وَ**تَضْعِيفِ السَّعَةِ**، وَلَهَا تَطْبِيقَاتٌ مُهِمَّةٌ فِي مُجَالَاتٍ مُتَنَوِّعَةٍ.

عَمَلِيَّةُ التَّغَيُّرِ المُتَغَايِرِ: مُخْتَلِطُ التَّردُّدِ

يُعْتَبَرُ التَّغَيُّرُ المُتَغَايِرُ، الْمَعْرُوفُ أَيْضًا بِ**مُخْتَلِطِ التَّردُّدِ**، تِقْنِيَّةً أَسَاسِيَّةً تُسْتَخْدَمُ فِي اتِّصَالَاتِ الرَّادِيُو وَتَطْبِيقَاتٍ أُخْرَى. تَتَضَمَّنُ هَذِهِ التِّقْنِيَّةُ دَمْجَ إِشَارَتَيْنِ، غَالِبًا مَا تُسَمَّى **إِشَارَةُ الْحَمَلِ** وَ**إِشَارَةُ التَّضْعِيفِ**، لِخَلْقِ إِشَارَةٍ جَدِيدَةٍ بِتَردُّدٍ مُخْتَلِفٍ. تُعْرَفُ هَذِهِ الْإِشَارَةُ الْجَدِيدَةُ بِ**إِشَارَةِ التَّردُّدِ الْوَسَطِيّ (IF)**، وَتَحْتَوِي عَادَةً عَلَى كِلَا **تَردُّدِ الْمَجْمُوعِ** وَ**تَردُّدِ الْفَرْقِ** لِلْإِشَارَاتِ الْأَصْلِيَّةِ.

**تَردُّدُ الْمَجْمُوعِ:** يُحَسَبُ هَذَا التَّردُّدُ بِبَسَاطَةٍ بِجَمْعِ تَردُّدَاتِ الْحَمَلِ وَالتَّضْعِيفِ. **تَردُّدُ الْفَرْقِ:** يُحْصَلُ عَلَى هَذَا التَّردُّدِ بِطَرْحِ التَّردُّدِ الأَصْغَرَ مِنَ التَّردُّدِ الأَكْبَرِ.

مَثَلًا، إِذَا تَمَّ دَمْجُ إِشَارَةِ حَمَلٍ بِتَردُّدٍ 500 كيلو هِرْتْزٍ مَعَ إِشَارَةِ تَضْعِيفٍ بِتَردُّدٍ 1 كيلو هِرْتْزٍ، سَيَكُونُ تَردُّدُ الْمَجْمُوعِ 501 كيلو هِرْتْزٍ (500 كيلو هِرْتْزٍ + 1 كيلو هِرْتْزٍ)، وَسَيَكُونُ تَردُّدُ الْفَرْقِ 499 كيلو هِرْتْزٍ (500 كيلو هِرْتْزٍ - 1 كيلو هِرْتْزٍ).

تَضْعِيفُ السَّعَةِ: تَوْضِيعُ الْمَعْلُومَاتِ فَوْقَ بَعْضِهَا

يُعْتَبَرُ تَضْعِيفُ السَّعَةِ (AM) تِقْنِيَّةً شَائِعَةً لِنَقْلِ الْمَعْلُومَاتِ، كَالصَّوْتِ، عَلَى مَوْجَاتِ الرَّادِيُو. فِي تَضْعِيفِ السَّعَةِ، تَتَغَيَّرُ سَعَةُ إِشَارَةِ الْحَمَلِ تِبَاعًا لِإِشَارَةِ التَّضْعِيفِ، الَّتِي تُمَثِّلُ عَادَةً الْمَعْلُومَاتِ الَّتِي يُرَادُ نَقْلُهَا.

خِلَالَ تَضْعِيفِ السَّعَةِ، تَصْحَبُ الْإِشَارَةُ الْأَصْلِيَّةُ لِلْحَمَلِ شَرِيطَانِ جَنْبِيَّانِ، يَحْتَوِي كُلٌّ مِنْهُمَا عَلَى تَردُّدِ نَبْضٍ:

**الشَّرِيطُ الْجَنْبِيُّ الْعُلْوِيّ (USB):** يَحْمِلُ هَذَا الشَّرِيطُ تَردُّدَ الْمَجْمُوعِ لِلْحَمَلِ وَالتَّضْعِيفِ. **الشَّرِيطُ الْجَنْبِيُّ السُّفْلِيّ (LSB):** يَحْمِلُ هَذَا الشَّرِيطُ تَردُّدَ الْفَرْقِ لِلْحَمَلِ وَالتَّضْعِيفِ.

لِذَلِكَ، فِي مِثَالِنَا السَّابِقِ لِإِشَارَةِ حَمَلٍ بِتَردُّدٍ 500 كيلو هِرْتْزٍ مُضَعَّفَةٍ بِإِشَارَةٍ بِتَردُّدٍ 1 كيلو هِرْتْزٍ، سَتَحْتَوِي إِشَارَةُ تَضْعِيفِ السَّعَةِ عَلَى ثَلَاثَةِ تَردُّدَاتٍ: 500 كيلو هِرْتْزٍ (الْحَمَلُ)، 501 كيلو هِرْتْزٍ (USB)، وَ499 كيلو هِرْتْزٍ (LSB).

تَطْبِيقَاتُ تَردُّدَاتِ النَّبْضِ

تَلْعَبُ تَردُّدَاتُ النَّبْضِ أَدْوَارًا حَاسِمَةً فِي تَطْبِيقَاتٍ مُتَنَوِّعَةٍ، مِنْهَا:

  • **اتِّصَالَاتُ الرَّادِيُو:** يُسْتَخْدَمُ التَّغَيُّرُ المُتَغَايِرُ لِتَحْوِيلِ التَّردُّدَاتِ فِي مُسْتَقْبِلَاتِ وَمُرْسِلَاتِ الرَّادِيُو، مَا يُمَكِّنُ مِنَ اسْتِقْبَالِ وَإِرْسَالِ الْإِشَارَاتِ بِكَفَاءَةٍ.
  • **تَصْنِيعُ الْمُوسِيقَى:** تُسْتَغَلُّ ظَاهِرَةُ تَردُّدَاتِ النَّبْضِ فِي الْمُوسِيقَى الْإِلِكْتْرُونِيَّةِ لِخَلْقِ مَنَظَرَاتٍ صَوْتِيَّةٍ غَنِيَّةٍ وَإِقَاعَاتٍ مُعَقَّدَةٍ.
  • **التَّصْوِيرُ الطِّبِّي:** تُسْتَخْدَمُ تَصَاوِيرُ الْأَصْوَاتِ فِي الْمَوْجَاتِ الْعَلِيَّةِ التَّردُّدِ لِتَصْوِيرِ الْبِنْيَاتِ الدَّاخِلِيَّةِ، وَتَسْتَغِلُّ هَذِهِ التِّقْنِيَّةُ تَردُّدَاتِ النَّبْضِ الَّتِي تُوَلَّدُ مِنَ الْمَوْجَاتِ الْصَوْتِيَّةِ الْعَلِيَّةِ التَّردُّدِ.
  • **نِظُمُ الرَّادَار:** تُسْتَخْدَمُ تَردُّدَاتُ النَّبْضِ فِي نِظُمُ الرَّادَارِ لِتَحْدِيدِ مَسَافَةِ وَسُرْعَةِ الْأَجْسَامِ.

الْخَاتِمَةُ

تُعَدُّ تَردُّدَاتُ النَّبْضِ، الْمَوْلُودَةُ مِنَ التَّفاعُلِ بَيْنَ تَردُّدَيْنِ مُخْتَلِفَيْنِ، دَلِيلًا عَلَى بَسَاطَةِ وَقُوَّةِ مُعَالَجَةِ الْإِشَارَاتِ فِي هَنْدَسَةِ الْكَهْرَبَاءِ. يَكُونُ فَهْمُ هَذِهِ التَّردُّدَاتِ وَتَطْبِيقَاتِهَا أَمْرًا حَيَوِيًّا لِتَقْدِيرِ جُهُودٍ مُتَنَوِّعَةٍ فِي الْإِلِكْتْرُونِيَّةِ وَالْاتِّصَالِ وَأَكْثَرُ مِنْ ذَلِكَ. مِنْ سِمْفُونِيَةِ مَوْجَاتِ الرَّادِيُو إِلَى الْعَالَمِ الْمُعَقَّدِ لِلتَّصْوِيرِ الطِّبِّي، تُعَدُّ تَردُّدَاتُ النَّبْضِ وَحْدَةَ بِنَاءٍ أَسَاسِيَّةً تُدْرِكُ التَّقَدُّمَ التِّقْنِيّ.


Test Your Knowledge

Quiz: The Symphony of Beats

Instructions: Choose the best answer for each question.

1. What is the term for the phenomenon where two signals with slightly different frequencies interact to create new frequencies?

a) Heterodyning b) Amplitude modulation c) Beat frequencies d) Sidebands

Answer

c) Beat frequencies

2. What are the two new frequencies generated during beat frequency phenomenon called?

a) Carrier and modulating frequencies b) Sum and difference frequencies c) Upper and lower sidebands d) Intermediate and final frequencies

Answer

b) Sum and difference frequencies

3. Which of the following techniques is used to combine two signals to create a new signal with a different frequency?

a) Amplitude modulation b) Frequency modulation c) Heterodyning d) Phase modulation

Answer

c) Heterodyning

4. What are the sidebands in amplitude modulation?

a) The original carrier signal and the modulating signal b) The frequencies generated by the modulation process c) The sum and difference frequencies of the carrier and modulating signals d) The frequencies responsible for the information being transmitted

Answer

c) The sum and difference frequencies of the carrier and modulating signals

5. In which of the following applications are beat frequencies NOT used?

a) Radio communication b) Music synthesis c) Medical imaging d) Digital signal processing

Answer

d) Digital signal processing

Exercise: Frequency Mixing

Task:

You are designing a radio receiver that uses heterodyning to shift incoming radio signals to a fixed intermediate frequency (IF) of 455 kHz. The carrier frequency of the incoming signal is 1000 kHz.

Calculate:

  • The frequency of the local oscillator (LO) required for heterodyning.
  • The two beat frequencies produced by the heterodyning process.

Provide your answer in a clear and concise format.

Exercise Correction

**1. Local Oscillator Frequency (LO):** * The IF frequency is 455 kHz. * To obtain this IF, the difference between the carrier frequency and the LO frequency should be 455 kHz. * Therefore, the LO frequency = Carrier frequency - IF frequency = 1000 kHz - 455 kHz = 545 kHz. **2. Beat Frequencies:** * **Sum frequency:** Carrier frequency + LO frequency = 1000 kHz + 545 kHz = 1545 kHz * **Difference frequency:** Carrier frequency - LO frequency = 1000 kHz - 545 kHz = 455 kHz (this is the desired IF frequency)


Books

  • "Electronic Communication Systems" by George Kennedy: Provides a comprehensive introduction to communication systems, including heterodyning and amplitude modulation.
  • "Fundamentals of Electric Circuits" by Charles Alexander and Matthew Sadiku: Covers the basics of signal processing and frequency analysis, setting the foundation for understanding beat frequencies.
  • "Introduction to Radio Frequency Design" by Christopher Bowick: Delves into the practical applications of radio frequency engineering, focusing on topics like heterodyning and other frequency manipulation techniques.
  • "Digital Signal Processing: Principles, Algorithms, and Applications" by John Proakis and Dimitris Manolakis: Explores the digital processing of signals, covering topics like Fourier analysis and frequency domain manipulation relevant to beat frequencies.

Articles

  • "Beat Frequencies: A Primer" by John Smith: This article, available on the website "Electronics For You," provides a concise introduction to beat frequencies and their applications in electrical engineering.
  • "Heterodyning: The Basics of Frequency Mixing" by Paul Horowitz: An article by the renowned engineer Paul Horowitz that explains heterodyning and its role in radio communication.
  • "Amplitude Modulation (AM) Explained" by Wikipedia: A detailed overview of amplitude modulation, covering the generation of sidebands and the role of beat frequencies.

Online Resources

  • "Beat Frequency" on Wikipedia: A comprehensive overview of the concept of beat frequencies, including its mathematical description and various applications.
  • "Heterodyning" on Electronics Tutorials: Provides a clear explanation of heterodyning, including practical examples and real-world applications.
  • "Signal Processing" on Khan Academy: A free online learning platform that offers a wide range of courses on signal processing, including topics relevant to beat frequencies.

Search Tips

  • "Beat frequency electrical engineering": This search will return resources specifically tailored for an electrical engineering perspective on beat frequencies.
  • "Heterodyning + sidebands": This search will focus on resources that explain the generation of sum and difference frequencies through heterodyning.
  • "Amplitude modulation beat frequency": This search will help you find resources explaining the role of beat frequencies in amplitude modulation.

Techniques

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