multi tone modulation using FM techniques

How to find modulation index for a multi tone FM signal ? Let us take our real case:

we have 8 KHz sub carrier ( use to modulate PSK data), apart from that we have 27.777KHz and 8Hz as tone signals , Is it possible to modulate all these tones using a single carrier? How the spectrum will look ? what will be the modulation index ? plz guide me.

Multi carrier modulation is very common on FM band 2 transmitters. All stereo transmissions modulate directly on the carrier left plus right signals, then there is a fixed subcarrier at 19 KHZ and the stereo difference signal is modulated on to a 38 KHZ carrier which is modulated on to the FM carrier. There are in addition, SCA channels that carry traffic data. So loads of carriers on a FM carrier.
Frank

In FM modulation, the modulation index is not important in itself but the bandwidth of the broadcasted FM signal is.

As you know, the FM modulation index for a sinusoidal modulating signal is defined as:
β = ΔFc/Fm
where:
ΔFc is the carrier deviation
Fm is the modulating frequency.

For EACH sinusoidal modulating signal of freqency Fm, the bandwith of the FM signal could be given as:
BW = 2 * ( ΔFc + Fm ) = 2 * ( β*Fm + Fm )
BW = 2 * Fm * ( β + 1 )

For multi tone FM broadcasting, the FM bandwidth should not exceed usually a limit (as 200 KHz for the radio FM Band, if I remember well).
Therefore for a constant BW, increasing Fm imposes on β to be lowered.

A generic N+tone modulated FM signal can be represented as:

y(t)=cos{ωc?t+K?[A1/ω1*sin(ω1?t)+A2/ω2*sin(ω2?t)+...+AN/ωN*sin(ωN?t)}

where K is the constant in Hz/V to convert from amplitude to frequency and Ai is the amplitude of the i-th tone.

each tone will have its own modulation index. they will be:

index1=K?A1/ω1
index2=K?A2/ω2
.
.
indexN=K?AN/ωN

(of course wi=2?Π?fi)

To estimate the occupated bandwidth you can use the Carson's rule:

first of all we need to calculate the maximum deviation frequency Δfmax=K?max(Ai)
then we will need the deviation rate: DR=Δfmax/max(fi)

BW≈2?Δfmax?(1+1/DR)

Finally the spectrum will be expressed in terms of products of Jn bessel functions.

Yes

There will be ( β + 1 ) significant sideband pairs for each sinusoidal modulating signal
Please note that the range of β in FM is:
0 ≦ β < infinity

The AM index for non-distorted envelope:
0 ≦ β ≦ 1

As you noticed, there is not a single modulation index for multi tone FM signal as in AM.