modulation formula

[dr.power]

Hi guys,

Please take a look at this page:
https://www.electro-tech-online.com/custompdfs/2011/07/Expt5_Amplitude_Modulation.pdf

Is the formula for amplitude modulated signal is correct?
I mean the term of "VcVm/2", is that correct?

Thanks

 

[MrAl]

Hi,


That looks correct. What are you trying to do?

 

[dr.power]

Hi,


That looks correct. What are you trying to do?

Hi MrAl,

Thanks for your input,

Actually I am trying to learn about Amplitude modulation.
I came across a problem regarding the AM formula. As you know the term I talked about in the first post corresponds the magnitude of each sideband. I looked several references and noticed that one reference say that the above magnitude is "magnitude of the message/2" and one says it is "magnitude of carrier magnitude of the message/2".
Please compare the modulation final formula of my first post to this attached file (the last formula in page NO 2) to see what I mean (it really makes me confused):

I know that magnitude of the message is equal to modulation index times the magnitude of the carrier.

P.S I thank that the formula in the link of my first is wrong regarding the said terms...

 

[MrAl]

Hi,

That formula looks correct also. The only difference appears to be that the second one starts out with sin terms while the first one starts out with cos terms.

 

[dr.power]

Hi,

That formula looks correct also. The only difference appears to be that the second one starts out with sin terms while the first one starts out with cos terms.

Thanks MrAl.

Did you get what I was trying yo say?

Ok please take a look at the below pics so that notice what I am trying to say (my damn English knowledge)...
The first pic is taken from the link in my first post and the second one is taken from the second attached file in my other post:

 

[MrAl]

Hi,

No im not sure what you are trying to say. If both formulas work out correctly, then they work out correctly, so what are you saying one formula does not work or something?

 

[dr.power]

Hi,

No im not sure what you are trying to say. If both formulas work out correctly, then they work out correctly, so what are you saying one formula does not work or something?

Hi,

No im not sure what you are trying to say. If both formulas work out correctly, then they work out correctly, so what are you saying one formula does not work or something?

OK,

"Vc" is the peak amplitude of the carrier.
"Vm" is the peak amplitude of the message.
"m" is modulation index.
The modulation index or so called "m" is equal to Vm/Vc
Now take a look at the said terms in my above post (2 pics I mean).
Vm=m x Vc seems to be correct in the second pic and regarding some reference I took a look at, sohe term is m x Vc/2
But please take look at the first pic for the said term, It says "VcVm/2" which does not any relationship to the first pic's formula term. (VcVm/2 has nothing related to mVc/2... ""Vc"" for the said term in the first pic should not be written and then we can match both first and second formulas by saying that mVc is equal to Vm, hence the second formula (second pic has n extra VC for the said term (the said term is the magnitude of each side band of course ))

Makes sense now?

 

[MrAl]

Hi,

Yes, the two formulas are not exactly equivalent, just correct as they are originally written which is what i looked at.

To help make this more confusing, i found another formula that is even different than those two and leads to a multiplication of ALL three terms by Vc*Vm.

I think what might be happening is each formula is assuming a (perhaps different) normalized parameter such as Vc. With Vc=1 the second formula works the same as the first formula.

The formula i tested was:
Vc*cos(wc*t)*Vm*(1+cos(wa*t))
where
wc is the carrier frequency and wa is the message frequency.
This led to a signal that definitely had sum and different frequencies present at 1/2 amplitudes and carrier present too.

I guess they like to put Vm inside the parens like so:
Vc*cos(wc*t)*(1+k*Vm*cos(wa*t))
and then state some limits for k.

What you could do is simulate both of your original signals and vary m or Vm and see what you can find out. I have a feeling they are both right but with different assumptions applied. If you have to take a test on this, you should ask the instructor about this too.

 

[dr.power]

Hi,

Yes, the two formulas are not exactly equivalent, just correct as they are originally written which is what i looked at.

To help make this more confusing, i found another formula that is even different than those two and leads to a multiplication of ALL three terms by Vc*Vm.

I think what might be happening is each formula is assuming a (perhaps different) normalized parameter such as Vc. With Vc=1 the second formula works the same as the first formula.

The formula i tested was:
Vc*cos(wc*t)*Vm*(1+cos(wa*t))
where
wc is the carrier frequency and wa is the message frequency.
This led to a signal that definitely had sum and different frequencies present at 1/2 amplitudes and carrier present too.

I guess they like to put Vm inside the parens like so:
Vc*cos(wc*t)*(1+k*Vm*cos(wa*t))
and then state some limits for k.

What you could do is simulate both of your original signals and vary m or Vm and see what you can find out. I have a feeling they are both right but with different assumptions applied. If you have to take a test on this, you should ask the instructor about this too.

Thanks MrAl,

First please tell me what do you mean by ""normalized parameter "? I found another link about AM modulation talking about "normalized power" as well, I could not understand the meaning of it too.

I Will try it practically and make an AM modulator to see what is wrong as soon as I could get more time.

 

[MrAl]

Hi,

Normalizing in this context means you set one variable equal to 1 and then relate the other variables to that one.
For example, say we have variables a, b, and c, and they have the following values:
a=10
b=20
c=40

Now say we want to normalize 'a' in this set. We set a=1 and make the other values proportional so we end up with:
a=1
b=2
c=4

But say we want to normalize 'b' instead. We do the same but now we set b=1, so we now end up with:
a=0.5
b=1
c=2