# How to find modulation index for a multi tone modulation?

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#### magnetra

##### Full Member level 5 In case of DSB-AM, how to find the modulation index for a multi tone modulation?

s(t) = (A + sin(2*pi*fm1*t) + sin(2*pi*fm2*t))sin(2*pi*fc*t)

fm1 fm2 message freq
fc carrier freq

Magnetra modulation index of am + sinusoidal

First of all, multitone signal must be decomposed by Fourier series to a Fundamental and Harmonics, you can take the fundamental component and neglect the harmonics components. Thus, m=am/Ac

#### zorro am modulation modulation index less than 1 m>1

Hi magnetra,

The AM signal with two-tone modulation is in its general form:

s(t) = (A + a1*sin(2*pi*fm1*t+phi1) + a2*sin(2*pi*fm2*t+phi2)) * sin(2*pi*fc*t+phiC)

It is useful to define a modulation index for each modulating tone:
m1=|a1/A|
m2=|a2/A|

The condition that assures to don’t have overmodulation, regardless of the tone frequencies, is
m1+m2 <=1 .

The same can be generalized for more than 2 modulating tones.

Regards

Z

#### Bukitoo

##### Full Member level 2 role of modulation index in am

zorro is right.
I have a concept of modulation index, that maybe is wrong, but it includes the tipical definition.

When you modulate in AM you have to ensure that the phase of you modulated signal don`t change. That means that the |f(t)|MAX < A

so m= |f(t)|MAX / A . For the case that you have 2 tones, the worst case you have is |f(t)|MAX = a1 + a2 so m= (a1 + a1)/A (this is zorro result).

#### jeffttan

##### Member level 2 modulation index, definition

Good day!

i think the total modulation index of a multitone AM signal is M = sqrt (m1^2 +m2^2 +..... mn^2). M should be less than 1 to prevent overmodulation..

#### magnetra

##### Full Member level 5 modulation index definition am

I think the explanation given by zorro is valid. I verified it using Matlab.
But I've also heard the definition given by jeffttan. What is the logic behind that?

How is modulation index determined in a real world commercial AM broadcasting?

Magnetra

#### electronics_kumar modulation index multitone signal

i agree with view expressed by jeffttan

M = sqrt (m1^2 +m2^2 +..... mn^2). M should be less than 1 to prevent overmodulation..

#### magnetra

##### Full Member level 5 what is the meaning of modulation index for am

Well there seem to be two different views on the modulation index with multi tone message.
electronics_kumar please tell me why do u think the root of sum of squares of individual mod index is the resultant.
Thanks
Magnetra

#### zorro modulation index am

Hi friends,

Let’s consider a general AM signal with many sinusoidal modulating signals:

s(t) = {A + SUM[a_i*sin(2*pi*fm_i*t+phi_i)]} * sin(2*pi*fc*t+phiC)

The power of such a signal is

P = A^2/2 * {1 + SUM[m_i^2]}

where m_i = |a_i/A| .
In that sense, the multi-modulating-sinusoid AM signal has a power equivalent of a single-tone AM with modulation index

meff = sqrt(SUM[m_i^2]) .

For this reason can be helpful to define an “effective modulation index” meff. It can be used in signal-to-noise calculations, but not for overmodulation calculations.

The condition to prevent overmodulation in general is what I stated above, i.e.: SUM(m_i)<1 .

Here I say “in general”, and in my previous post I said “regardless of the tone frequencies”, because in the case that the modulating frequencies are harmonically related, then it is possible that the peak of the sum is less that the sum of the peaks.

In “real world”, overmodulation must me avoided because its transmission would cause spectral contamination and severe distortion in the received signal.

Regards

Z

#### abishek

##### Member level 1 modulation index calculation for am signal

as kumar says when m(t) is multi tone.....and µ1,µ2....µn are the individual indexes......the net index is sqrt(µ1^2 + µ2^2 ...............µn^2) as it is in like thd or any other case....

#### smith123

##### Member level 5 how to find modulation index

THAT IS GOOD I THINK .
M = sqrt (m1^2 +m2^2 +..... mn^2). M should be less than 1 to prevent overmodulation..

#### Alaa Mahmoud

##### Newbie level 3 I really enjoy with such dialogue .. thanks
but i would like to know two things:
1- what is the difference between
r.m.s modulation index (µ) = √ (m1^2)/2 +(m2^2)/2 +(m3^2)/2 .........+(mn^2)/2
and the total modulation index (mt) = √m1^2 +m2^2 +m3^2.........+(mn^2)
and from where the √ ?

2- how can i evaluate the multi-tone modulation with a single tone?

regards,
Alaa

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