Amplitude Modulation Transmitter question (graphs needed)

[orla22]

This is not a HW question but an activity i am working on. The attachment is a symbolic AM transmitter.

The carrier is 15MHz and message frequency is 2Mhz.

I want to sketch the waveforms labelling them in as much detail as possible.
Also sketch the output waveform in both time and frequency domains and calculate its bandwidth (a paint rough drawing would be helpful)
If the signal was alternated with a 2kHz tone every 0.25s, sketch output waveform in both time and frequency domain and calulate its bandwidth. Repeating this with commercial speech replacing the message tone.

 

[orla22]

Amplitude Modulation Transmitter question

This is not a HW question but an activity i am working on. The attachment is a symbolic AM transmitter.
https://www.physicsforums.com/attachment.php?attachmentid=18736&d=1241306119

The carrier is 15MHz and message frequency is 2Mhz.

I want to sketch the waveforms labelling them in as much detail as possible.
Also sketch the output waveform in both time and frequency domains and calculate its bandwidth (a paint rough drawing would be helpful)
If the signal was alternated with a 2kHz tone every 0.25s, sketch output waveform in both time and frequency domain and calulate its bandwidth. Repeating this with commercial speech replacing the message tone.

 

[vk6kro]

Have a look at this page which describes amplitude modulation.
The diagrams are good.
Scroll down and look at the spectral diagrams too.

http://en.wikipedia.org/wiki/Amplitude_modulation

Amplitude modulation is just a mixing process where the original frequencies plus and minus their difference are the outputs. So, you can work them out easily.

You might have that 2 MHz frequency wrong. Should it be 2 KHz?

 

[Defennder]

Ok, but I assume you've put in some of your effort. What have you done so far? It looks like the AM scheme you're using is the simple envelope AM. So to start off, what do you know about how to sketch the waveform in time domain after you've added a DC signal?

 

[orla22]

yea sorry its 567 Hz. can you possibly post a drawing of the graphs?

 

[orla22]

i am stuck, which is why i posted the problem...

 

[Defennder]

You appear to have double posted the problem here:
https://www.physicsforums.com/showthread.php?t=311324

I'll try to see how I can help. First you need to understand how the conventional AM envelope method works. Basically firstly a DC signal is added to the message signal to ensure that the signal varies over the positive values only (think of it as the message signal being elevated above the axis). Then this signal is next mutiplied by a carrier of much higher frequency in this case 15MHz. The message signal as you've clarified in the other thread has frequency of 567Hz.

The diagram you provided is missing an arrow from the carrier to the multiplication operation. Once this is done, the resulting waveform wil display on its envelope a shape which is similar to that of the original message signal.

Now for sketching it in the frequency domain. Suppose the carrier is $$\cos (2\pi 15 \cdot 10^6t)$$.

Then the message signal after adding the DC signal and multiplying by carrier is:
$$(\alpha + x(t))\cos (2\pi 15 \cdot 10^6t)$$.

Now to sketch this in the frequency domain you have to first Fourier transform the above. How do you do transform the cosine carrier wave? Firstly express it in terms of complex sinusoids, then F.T. the complex sinusoids using the table of Fourier transform. When you're done with this, remember next that multiplication in the time domain corresponds to convolution in the frequency domain. What is the result of convoluting a X(f) (the FT of the messge signal) with the FT of the cosine carrier wave? There's a special result you might need here.

When you're done with that, you're ready to sketch the diagram. Remember that for all real signals, the corresponding magnitude spectrum has to be symmetric. Once you've got the diagram you should be able to deduce the bandwidth of the resulting signal.

As for the additional problem, I don't know what does it mean for the message signal to alternate with a 2khz tone. Maybe someone else can help you here.

Good luck. Hope this helps.

 

[vk6kro]

Yes, have a look here:

http://education.tm.agilent.com/index.cgi?CONTENT_ID=9

Choose the 100 % option and press fast forward.
It is a much better diagram than I could draw.

You can do a screen grab of it if you like.

 

[orla22]

ahh yes v good. what question does that answer in my post?

 

[vk6kro]

It was clear from your question that you don't know what Amplitude Modulation is, so I sent you two links to places you could find out about it.

As you may know, there are rules about answering specific problems. Here is one of them:

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[Defennder]

This thread is a duplicate of the one posted here:
https://www.physicsforums.com/showthread.php?t=311325

 

[orla22]

It was clear from my post that it is not a HW question

 

[vk6kro]

Don't worry about it. No problem.

If we answer a question like that, that may be homework, the reply might get deleted.

Any and all assistance given to homework assignments or textbook style exercises should be given only after the questioner has shown some effort in solving the problem. If no attempt is made then the questioner should be asked to provide one before any assistance is given. Under no circumstances should complete solutions be provided to a questioner, whether or not an attempt has been made.

I have had a couple of replies deleted.

I know it seems odd that we reply to oddball stuff (how to generate a million volts !) and yet a serious topic like yours is off limits. I don't know the history of that, but we have to be aware of the rules.
I contribute to another site where we sometimes get people put an entire assignment on as a question and hope someone will do it all for them. Nobody learns anything if that is successful.

Just go and read up on it if you are interested and if you have any specific questions about something you don't understand, come back and ask about it. It is easy stuff, so you should be able to get a grip on it yourself.

 

[orla22]

Amplitude Modulation transmitter

if carrier wave is 20MHz and message frequency 1kHz.

what does a sketch of both waveforms in detail look like?

 

[orla22]

the process is shown as product why can't we just add the signals?
and what's requirements for constant input which is added to message?

 

[vk6kro]

Without even trying to draw it, the 20 MHz signal looks like a sinewave.
When the 1 KHz signal is added, the 20 MHz sinewave is still a sinewave, but it varies in amplitude at a 1 KHz sinusoidal rate.

If you looked at it on a CRO you would see a sinewave along the top of the 20 MHz signal (which would look like a blur if you could see the 1 KHz signal) and another sinewave along the bottom of the 20 MHz signal. The one at the bottom would appear upside down compared to the one at the top, so they tended to meet in the middle on negative going half cycles.


It may make it clearer if I explain how AM can be produced :-

In the olden days... you would have an oscillator and then an RF amplifier, making a transmitter.
The output of this went to an antenna.

The supply voltage for the RF amplifier went through a transformer winding before it got to the RF amplifier.
On the other side of this transformer (called a modulation transformer ) was a fairly powerful audio amplifier.
This would vary the power supply voltage getting to the RF amplifier if there was audio coming out of it.
It could vary from zero volts to twice the supply voltage on really loud audio.

When it did this, the RF amplifier output also varied in the same way so that the signal had audio on it. It would normally be speech, too, not sinewaves.

 

[TurtleMeister]

On a spectrum analyzer it would look like three vertical lines, or very sharp cones with the point at the top, with the center line being the tallest and located at 20Mhz. The two lines on the side would be shorter depending on the modulation percentage. The left one would be centered at 19.999 Mhz and the right one centered at 20.001 Mhz. The center line is the carrier and the left and right are the sidebands (where the message is located).

http://www.microwaves101.com/encyclopedia/spectrumanalyzer.cfm
Scroll down to Modulation measurements

 

[berkeman]

It was clear from my post that it is not a HW question

I've merged your 3 threads on this topic into this one here in Homework Help. Your SINGLE thread belongs here.

You MUST show your work on these questions. We do not give out answers to homework/coursework/self-study questions. Please re-read the PF Rules link at the top of the page before posting anything further.

You must do the bulk of the work on answering your questions. You do the sketches. You do the research.