Why does increasing the message bandwidth decrease the FM bandwidth?

[Tony Hau]

TL;DR

As the modulation index of FM is given by $m=\frac{\Delta}{f_{m}}$, if we increase $f_{m}$, why does the bandwidth of the FM decrease (as $m$ decreases, the bandwidth of FM, as given by Bessel equations, decreases accordingly)? We are trying to modulate more information into the carrier don't we need more bandwidth to achieve this, in common sense? Please help and thanks.

So I am trying to learning FM from textbooks and it says that the modulation index of FM is given by $m=\frac{\Delta}{f_{m}}$, where $f_{m}$ is the message signal bandwidth and $\Delta$ is the peak frequency deviation of the FM modulated signal. What I do not understand is that normally, if we want to transmit more information (e.g. by increasing the $f_{m}$), we will need more bandwidth to do this. Then, why the modulation index decreases by increasing the message signal bandwidth and hence the FM modulated signal bandwidth actually decreases (as indicated by Bessel equation)?

I have some ideas for this. For example, the Harley's theorem, which is given by $$C = B \log_2 (1+ \frac{S}{N})$$, states that even if we increase the bandwidth, if the signal-to-noise ratio of the modulated signal decreases, then the bits per second rate can actually stay the same. However, I don't know if it is possible too since decreasing the modulation index should not affect the SNR ratio.

Can anyone help? Please and many thanks.

 

[Baluncore]

The modulation index m tells you how many times the message bandwidth will fit in the maximum deviation.

If you double the message bandwidth, you must double the maximum deviation, to maintain the same modulation index m.

 

[Tony Hau]

The modulation index m tells you how many times the message bandwidth will fit in the maximum deviation.

If you double the message bandwidth, you must double the maximum deviation, to maintain the same modulation index m.

Hello thank you for your answer. However I just read about the topic at wikipedia (this) and here is the screenshot of this

It seems like frequency deviation can be held constant while increasing the message frequency as shown in the 2nd paragraph. But I have another idea after reading this.

If we increase the message signal bandwidth and hold the frequency deviation constant, the modulation index decreases. So the spectra component spacing increases. Consider the general formula for FM modulated signal $$ x(t)=A_{c}\Sigma_{n=-\infty}^{\infty}J_{n}(m)\cos[2\pi(f_{c}+nf_{m})t]$$, where $J_{n}(m)$ is the Bessel function of the first kind of order n and argument m, and m is the modulation index.

If $f_{m}$ increases, the spacing between the first spectral components away from the carrier frequency $f_{c}$ increases. This will increase the overall FM bandwidth. (although there are fewer effective spectral components now due to decreased modulation index m.)

Actually, as given by the Carson's rule $BW = 2(\Delta + f_{m})$, if we keep $\Delta$ constant while increasing $f_{m}$, the overall bandwidth increases.

So in conclusion, you actually need more FM bandwidth if you want to modulate more information (e.g. higher message signal frequency $f_{m}$).

What is your opinion?

 

[Baluncore]

What is your opinion?

For any particular modulation index, m;
the maximum deviation, Δ = f_m ⋅ m

 

[Tony Hau]

For any particular modulation index, m;
the maximum deviation, Δ = f_m ⋅ m

thank you for your answer and let me try to figure that out for a while...

 

[sophiecentaur]

So in conclusion, you actually need more FM bandwidth if you want to modulate more information (e.g. higher message signal frequency fm).

This is hardly surprising as a general principle for any modulation. The basic reason that FM is often "a good thing" is that the signal to noise ratio can be improved greatly by using high deviation, just by increasing the deviation. FM is basically a non-linear modulation system which has unexpected results. You are spreading the spectrum of the transmitted signal which increases the signal level that's demodulated by the discriminator but the effective noise power is limited by the receiver baseband low pass filter. This SNR increase is referred to as the FM Improvement (fewer channels available than for AM but increased quality).

There is, however, one big snag and that is that you need to increase the RF bandwidth of the transmitted signal. The peak noise amplitude (spikes) will be demodulated proportionally to the bandwidth so the 'noise threshold' is increased - meaning that the signal will break up earlier than for AM or narrow band FM. Great for high quality audio or video butnot so good for low grade comms where the receiver RF bandwidth can be low and so is the noise threshold. Narrow band FM 'dies gracefully' for low signals but high deviation FM 'crashes' sooner.

One great benefit of high deviation FM is the so-called FM Capture Effect. An interfering co-channel signal that's significantly lower level will be demodulated as a very low level baseband signal because the resultant of the added signal is a low level phase modulation, rather than a perturbation of the wanted frequency modulation. Wide band FM gives you better defined, interference free service areas - but, of course, disastrous interference outside the service area.