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-   -   FM "deviation" (https://www.vintage-radio.net/forum/showthread.php?t=52203)

dominicbeesley 26th Mar 2010 12:24 pm

FM "deviation"
 
Hello all,

Following a few threads about radio and TV on here and my recent sig-gen project I've become more interested in FM.

One thing I'm not sure about is how the parameters for FM work. How does deviation relate to modulation. My guess reading between the lines is that deviation includes any sidbands and that the amount of modulation of carrier is effectively less - what I can't find out is what that should be...or am I missing the point?

Dom

Darren-UK 26th Mar 2010 12:37 pm

Re: FM "deviation"
 
Is this page on Wiki of any use?

dominicbeesley 26th Mar 2010 12:45 pm

Re: FM "deviation"
 
Thanks Darren,

I've read that one and the fuller one at http://en.wikipedia.org/wiki/Frequency_modulation but I'm still not clear on how much to modulate the carrier by for a normal FM signal.

In my cases I've got a digitally controlled oscillator and an A/D which can be used to program it.

I program the frequency out to be fc + x(t) * m for each sample.

Where x(t) is input signal 0..1 and m is the frequency modulation factor (not sure what that number is called).

But because x(t) is changing all the time this will produce lots and lots of sidebands going to infinity. These are normally cut off at the transmitter - now I suspect that that is what the peak deviation refers to the width of the filter. But what is the typical value of m?

When messing with modulating my siggen there is no filtering of sidebands but picking up on nearby radios values of m from 1kHz upto 100kHz tend to work but what should it be I don't know!

I may be getting all of the above wrong though!:blah:

Cheers

Dom

Ian - G4JQT 26th Mar 2010 1:00 pm

Re: FM "deviation"
 
Will this help? (From lectures 30 years ago...)

If you modulate the FM carrier with a 1 kHz square wave of maximum audio amplitude (VU meter 100% or PPM6 - OK with a square wave this won't be the same, but for the sake of argument...) on the positive half cycle the carrier will be the full 75 kHz above the centre frequency and on the negative 75 kHz below the centre frequency. This swing will happen at the modulating frequency, in this case 1000 times per second.

In practice programme content does not include square waves, but it serves as an illustration.

If you halve the modulating amplitude, the deviation will halve if you don't take pre-emphasis into account.

The bandwidth generated by the very complex sidebands is usually estimated at twice the deviation (75 + 75 = 150 kHz in this case) plus the (highest) modulating frequency.

I think this is the gist of FM transmission. Now if you *phase* modulate a carrier with a squarewave...

Regards,

Ian

GMB 26th Mar 2010 1:02 pm

Re: FM "deviation"
 
The deviation is exactly what it says, it's the instantaneous change in the carrier frequency made by the modulation.

The funny thing about FM is that the carrier is deviated in response to the amplitude of the input signal so the direct bandwidth requirement doesn't at first sight seem to depend on the input frequency like it does with AM.

So while it should be obvious that the bandwidth used must be at least twice the maximum deviation, it of course also depends on how fast the deviating is being done. The practical bandwith needed is about twice the sum of the maximum deviation and maximum frequency being encoded.

dominicbeesley 26th Mar 2010 1:45 pm

Re: FM "deviation"
 
Right, thanks both: I think I now understand - I was getting confused by f[sub]m[/sub] in the wikipedia article - but after re-reading (again) I realise that this is the maximum frequency of the baseband signal.

What's the effect on the sound of cutting off the sidebands above / below the maximum deviation?

So in my sig-gen example m should be 75kHz for mono....but how does this relate to the stereo signal. Or is the stereo stuff all done at "baseband" before frequency modulating....my brain hurts!

Cheers

Dom

kalee20 26th Mar 2010 2:14 pm

Re: FM "deviation"
 
I am sure that even with stereo, the transmitted frequency still deviates maximum 75kHz. But the stereo multiplexing, with the L-R difference frequency being double-sideband-suppressed-carrier amplitude modulated onto a 38kHz signal means the highest frequency applied to the transmitter's frequency modulator is now nearly 57kHz. So, the receiver bandwith needed is (2 x 75 + 57)kHz, or 207kHz.

GMB 26th Mar 2010 2:45 pm

Re: FM "deviation"
 
I think that should read 2x(75 + 57)kHz, or 264kHz.

kalee20 26th Mar 2010 3:18 pm

Re: FM "deviation"
 
I think it should, too.

Ian's post above gives twice deviation plus highest modulating frequency, but I have just convinced myself that I should have read it as twice (deviation plus highest modulating frequency) not as (twice deviation) plus highest modulating frequency.

I convinced myself by remembering that narrow-band FM has nearly the same spectral response as AM (the significant difference being that sidebands have a different phase relationship to the carrier). And AM has a total bandwidth of twice modulating frequency; the rule for FM gives exactly the same result for small deviation.

dominicbeesley 26th Mar 2010 4:25 pm

Re: FM "deviation"
 
No I am confused again...from Wikipedia article:

"Deviation and bandpass
Normally, each channel is 200 kHz (0.2 MHz) wide, and can pass audio and subcarrier frequencies up to 100 kHz. Deviation is typically limited to 150 kHz total (±75 kHz) in order to prevent interference to adjacent channels on the band. ...
"

Doesn't that give 2*(75 + 100) == 350MHz .... but all the ceramic filters I've played with are more like 200MHz wide so what gives! Or am I mixing things up again?

Dom

Jonster 26th Mar 2010 5:07 pm

Re: FM "deviation"
 
Carson's rule states the bandwidth used is

2x(f+d)

so the maximum bandwidth needed for stereo is 53kHz (15kHz higher than the 38kHz subcarrier) so 256kHz bandwidth. RDS at 57kHz gives us a little more. In some countries, other subcarriers at 76 and even 95kHz are used too.

kalee20 26th Mar 2010 5:27 pm

Re: FM "deviation"
 
Well, Carson's rule is what Ian's post above was on about, and I misused in my post above (corrected in my subsequent post).

Applying this does indeed give 2 x (75 + 100)kHz, if deviation is maximum 75kHz and the highest transmitted frequency is 100kHz. So bandwidth is 350kHz.

But channel width is 200kHz so what gives? Well, (and I'm just postulating now), I'd expect that anyone wanting to transmit 100kHz would reduce the amplitude, so that at 100kHz the maximum deviation is much, much less than 75kHz. Then, the total bandwidth approaches 200kHz. Lower modulating frequencies can have correspondingly greater amplitudes so that the deviation increases and the total bandwidth is used appropriately.

Something now niggles me that this might suffer with bad noise performance - it's the opposite of pre-emphasis - any comments folks?

G8HQP Dave 26th Mar 2010 5:41 pm

Re: FM "deviation"
 
Yes, to a first approximation FM bandwidth is 2x(f+d), but sidebands really do stretch out to infinity. Fortunately there is not much energy outside the above bandwidth, so filters can be used. A good stereo FM tuner will typically have 250-300kHz bandwidth, poorer or mono ones around 180-220kHz. A narrower bandwidth introduces distortion (unlike AM) as well as a frequency response limitation.

When stereo is transmitted the 19kHz pilot tone uses 10% of the deviation, so the L+R (mono) audio is limited to 67.5kHz deviation (90% of 75kHz).

Be careful with your 'm', which you defined as peak deviation and called frequency modulation factor. FM theory already has an 'm', called modulation index - it is equal to your 'm' divided by the highest baseband frequency. So mono FM has a peak m of 75/15=5. The larger m is, the more sidebands have to be included in order to avoid distortion. FM radio only works as well as it does because speech and music have very little high frequency content, even after preemphasis.

Going back to your original question: if your x(t) really does range over 0-1 then your m should be 150kHz. If x(t) is -1 to 1 then your m should be 75kHz. One question though: how often do you sample x(t)? How does this relate to the baseband Nyquist limit?

ppppenguin 26th Mar 2010 5:48 pm

Re: FM "deviation"
 
Quote:

Originally Posted by G8HQP Dave (Post 316720)
One question though: how often do you sample x(t)? How does this relate to the baseband Nyquist limit?

We're talking about analogue here. No sampling, no nyquist limit.

dominicbeesley 26th Mar 2010 6:39 pm

Re: FM "deviation"
 
Sorry Jeffrey but Daves right - read above I'm digitally controlling the oscillator.

At the moment I'm sampling only at just under 20kHz (so max frequency is only 10kHz)...

Sorry you were right m was a duff guess but I've got it that that == deviation. I think I'm starting to get the hang of what's going on...

Am I right in thinking that the size and number of side bands will be related not only to the frequency of the modulation signal but also its amplitude (as this will effectively alter the modulation index)?

Thanks to everyone for taking me through this it is beginning to make a lot more sense now....I think!

Cheers

Dom

G8HQP Dave 26th Mar 2010 10:43 pm

Re: FM "deviation"
 
Quote:

Am I right in thinking that the size and number of side bands will be related not only to the frequency of the modulation signal but also its amplitude (as this will effectively alter the modulation index)?
Yes. The number of significant sidebands depends on m=(peak deviation)/(baseband frequency), although I don't know the exact relationship as it depends on Bessel functions which always confuse me! Peak deviation depends on baseband amplitude.

Something to watch out for with your arrangement is that the baseband sampling at about 20kHz will mean that in addition to your wanted baseband signal you will have a set of baseband images too. These will be small for low baseband frequencies (due to the overall sinc baseband frequency response) but above a few kHz may produce their own sidebands. Strictly speaking you need to include a digital filter between your A-D and the digital oscillator, but you may get away without it.

dominicbeesley 27th Mar 2010 1:00 am

Re: FM "deviation"
 
Hi Dave, is that something other than Nyquist aliassing that you're referring to? I've got a 9kHz low pass filter at the analogue side of the A-D (it's not very good) and I add about 12dB of cut above 9kHz with the equaliser too...I'm still getting some quite hissy sibilants though.

What sort of digital filter...I'm pretty pushed for machine cycles in the FM interrupts routines but could probably manage a little FIR so long as it didn't need too many stages.

Dom

G8HQP Dave 27th Mar 2010 2:02 pm

Re: FM "deviation"
 
Its the other side of Nyquist aliassing. Assuming a normal sample-and-hold type sampling, if you compare your input analogue signal with the A-D output steps you can see that there is a difference - roughly a 20kHz triangular waveform. This will be small for low input frequencies, but gets bigger as you approach the Nyquist limit at 10kHz. This signal consists of images, the first of which is at 20kHz-f where f is your baseband frequency. In a normal digital system the images are removed by the reconstitution filter after the eventual D-A at the other end. In your case the signal stays digital as it frequency modulates the RF oscillator, so the sampling images will produce their own sidebands. These will go through the FM filters and the receiver, so a 2kHz tone will have an 18kHz image too.

The amplitude will follow a sinc law. I won't explain this, unless you ask, as if you understand digital filters you might know more about this than I do!

dominicbeesley 27th Mar 2010 8:30 pm

Re: FM "deviation"
 
Thanks Dave,

That makes some sense but not sure how I'd filter it out without introducing more samples and I don't get any time for that in the code on a 40MHz PIC I'm pushing the limits of what is possible in terms of both A/D speed and doing a 48bit multiply and bitbanging the DDS port....anyway for my simple FM receiver testing it will do for now. I intend to make something better later anyway.....this is all a bit off topic.

Thanks to everyone who has replied so far I think I'm now starting to more or less understand what's going on in an FM signal. I'm now quite intrigued that effectively the upper sideband of the L-R signal has a lower modulation index than the lower one. So far a better quality would it be better still to use both sidebands when recovering or best to filter out one band...I'm guessing its easy to detect as you have the pilot tone or is it sill best to use both sidebands?

Cheers

Dom

G8HQP Dave 27th Mar 2010 9:27 pm

Re: FM "deviation"
 
It will be fine for simple testing. Just be aware that the frequency response will droop above a few kHz due to the sinc.

I don't think anyone has ever tried an SSB stereo decoder! The filtering needed would ruin the close phase relationship with the L+R signal, so I don't think this is a runner.


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