modulation index & multi tone

[dr.power]

Hello guys,

Can somebody please tell me why in AM modulation the modulation index of a multi tone will be M = sqrt (m1^2 +m2^2 +..... mn^2)?
Where m1 & m2 & mn are the modulation index of every individual tone.
I am not able to understand the reason.
Why we have to take the sqrt of the summation of the individual modulation indexes to get the M?
By the way what is the "M" itself? I read a source saying that it is the total modulation index, and the other source which indicated that "M" is the effective modulation index.
What they mean by "effective" too? Is it RMS value or some thing like that?

Thanks

 

[MrAl]

Hi,

I've found different definitions too for various things in AM modulation theory. You have to read the paper and figure out what definitions they are using and go from there. You may have to work up the entire set of expressions to figure out what is going on, but it usually only involves sin or cos terms and using trig identities to get the expressions into the proper form.

 

[dr.power]

Hi,

I've found different definitions too for various things in AM modulation theory. You have to read the paper and figure out what definitions they are using and go from there. You may have to work up the entire set of expressions to figure out what is going on, but it usually only involves sin or cos terms and using trig identities to get the expressions into the proper form.

Thanks MrAl for your kindly input,

Actually I a, trying to see what Is happening through more than 4 different books, the best & easy understandable source I think is ""Principles of Electronic Communication Systems"" by Frenzel.

Any way I am agree with you.

The question of this thread is coming from this source:
**broken link removed**

take a look at the page #18 and 19 for "Amplitude modulation by multiple sine waves".

 

[MrAl]

Hi again,

From that paper without me going into detail i would think that like any other paper you should be able to trace the equations backwards and find out the origin of the expression as to how they arrived at that one. For your link example, starting with equation 1.2.34 you can see just above that they state, "Now from equation 1.2.32 we can obtain total modulation index m1", so you would go back and find equation 1.2.32 and figure out how they got 1.2.34 from that, then go back before 1.2.32 and find out how they got that, and keep going back and trying to understand how they got from one equation to the next and eventually you should get back to some more generally understood equation or concept. That process should show you how they got to that simpler equation.

 

[dr.power]

Hi again,

From that paper without me going into detail i would think that like any other paper you should be able to trace the equations backwards and find out the origin of the expression as to how they arrived at that one. For your link example, starting with equation 1.2.34 you can see just above that they state, "Now from equation 1.2.32 we can obtain total modulation index m1", so you would go back and find equation 1.2.32 and figure out how they got 1.2.34 from that, then go back before 1.2.32 and find out how they got that, and keep going back and trying to understand how they got from one equation to the next and eventually you should get back to some more generally understood equation or concept. That process should show you how they got to that simpler equation.

Thanks, MrAl,

Thats actually what I did, But did not find out the reason of my question in the post #1.
I came back to all equations there but Yet do not know why the Mt is equal to to SQRT of individual modulation indexes summed together..

 

[MrAl]

Hi again,

Didnt they start with a signal power equation or something?