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Amplitude Modulation, Morse Code and the Fourier Series

There ain't no free lunch

Compromises and trade-offs must be made.

Amplitude Modulation, AM, was the first audio radio communications and broadcast method developed and is the easiest to understand.  Simply put, there is a continuous sine wave of a given assigned frequency and the amplitude of that wave is changed by a signal.  Usually the signal is an audio signal, but it can be other signals.  To keep things simple and understandable, the signal I talk about is a simple sine wave in the audio range of frequencies.  The frequency of the sine wave being modulated is called the carrier wave and is a much higher frequency.  In the case of AM radio in the United States this frequency is between 540 KHz and 1.6 MHz.  The carrier wave is the frequency you tune your dial to when you tune your radio.   Refer to the 2nd picture to visualize what is happening.

An Amplitude Modulated Waveform.

An Amplitude Modulated Waveform.

The interesting thing about this type of modulation is the same waveform can be created by adding three sine waves:  The carrier wave of the same frequency as before;  A Lower Sideband with a frequency of the carrier frequency – the modulation wave frequency; and An Upper Sideband with a frequency of the carrier frequency + the modulation frequency.   By limiting the bandwidth to the upper sideband – the lower sideband many stations can be put on the same radio dial without interfering with each other and all the other noise can be filtered out.

A very good detailed explanation can be found in this Wikipedia article.  I also have a spreadsheet available for download with all the calculations I talk about in the video.

So what does this have to do with the Fourier Series?  Imagine the gain of the modulation signal is increased to the point where it cuts off the peaks and distorts.  We have exactly the same situation I talked about with the overdrive distortion used to create “fuzz” on guitar amplifiers.   WE HAVE HARMONICS and now the bandwidth of the wave has increased to the point where this station is encroaching on neighboring stations frequencies.   This used to be a big problem on CB radios back in the 1970’s when the CB craze was popular.

Now think of a Morse Code signal.  It is basically a square wave turning the the carrier wave off and on as a key is pressed.  The amount of information being sent is very little and relatively slow, so we would expect a very small bandwidth.  On good transmitter circuits our expectation is correct, but those transmitters do not turn the carrier wave off and on in a square wave fashion.   Remember a square wave is actually an infinite number of harmonics and we were not able to create an ideal square wave with up to 1000 harmonics.  To prevent the excess harmonics, the good transmitters use about a 0.005 second ramp up and ramp down for the wave form.   Much better details about this is in this article: “An Intuitive Explanation of CW Bandwidth” by Mark Amos W8XR

Digital electronics depends upon signals quickly going from off to on.  In other words these are very near square waves and we are back into the harmonic problem and frequencies required a very high.  That creates more problems and digital designers have to be very careful to not kill too many of the higher harmonics.

In summary with fast moving signals not only do we have to think of them in the time domain, but also in the frequency domain.

The video associated with the post can be seen here:

I am getting closer and closer to being completed with the house remodelling job.and I hope to get back to doing more posts and some with actual construction soon.

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Amplitude Modulation, Morse Code and the Fourier Series” by Create-and-Make.com is licensed under a Creative Commons Attribution-ShareAlike 3.0 Unported License.

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Gary


 

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2 comments to Amplitude Modulation, Morse Code and the Fourier Series

  • Hi,
    I watched all your LibreCad tutorials. They are valuable and I thank you for your time and effort.

    Question: What is “mose” code? There are many references in your website. I looked on Google and can’t find what I consider a technical definition of “mose” code.

    Is it just a “spelling error” on your website? Did you really mean the telegraphy code created by SFB Morse?

    Thanks,
    Dan Morse

    • Gary

      Yes you are exactly correct. I will correct the spelling where I find it somewhere spell checker messed me up and I am not very good at proofreading. Also, if it happens to be personal because he is one of your ancestors I am very very sorry.

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