Minimum Frequency of FM Data / Catastrophic Error Scenario?

[Silly Questions]

I had a burning curiosity from the time I read the theory about what would happen if the receiver carrier drifted off the transmitter carrier, which seemed theoretically possible in certain edge cases. Then Tech99 explained it all, using the edgiest of all edge cases, a constant fed into the signal. He also suggested this is not desirable and described methods for not feeding a constant into your frequency-modulated signal.

If I'm getting something wrong I'm very interested in getting it right, otherwise I'm more-or-less satisfied I understand modulation index distortion. I am wondering though regarding "even-order non-linearity" what "even-order" means in this context?

My main interest is radio and radar in WWII, but that's a very long-term learning project. To understand the engineering iterations that brought radar from Tizzard's briefcase to Blackett Strait learning more radio theory couldn't hurt.

 

[sophiecentaur]

I still don't know where you got this "Mod Index distortion" from and what is of particular interest about it to you. There are all sorts of channel distortions that can affect the FM signal. Asymmetrical filtering can add phase distortion, multi path propagation can result in Amplitude modulation of the transmitted FM signal ( the basis of the first RADAR systems).
You need to understand that FM is effectively an 'AC coupled channel where the notional carrier frequency (corresponding to Zero Volts of the input modulating signal) is irrelevant. So much so that, when Analogue TV is sent on an FM link, the zero V DC video voltage is 'clamped' every line to follow any drift in the discriminator, modulator or IF mixing up and down to the link frequency on the way.
You really need to brush up on the formal basics of FM before exploring the more esoteric bits. It's too hard for an arm waving approach.

 

[Silly Questions]

I learned about modulation index distortion from Tech99. It's the very first conversation in this thread.

In the example he gave he demonstrates how constants in FM broadcasts need special encoding techniques. If you simply drop a constant onto an FM signal the receiver won't extract it; instead, the constant shifts the reference frequency and distorts the modulation index.

"The notional carrier frequency is irrelevant" is exactly the problem. In your example of clamping the video voltage at set intervals, what exactly is the transmitter sending around this time? If the transmitter sends an unmodulated carrier at that interval wouldn't that recalibrate the receivers? If you don't want distortion it seems like you'd have to contrive a way to make the notional carrier frequency relevant, as your example might suggest.

Why do I not know about other problems with FM? The peril of asymmetrical filtering isn't intuitively obvious to a beginner reading an FM theory book, sorting that question into the category of, "Didn't know to ask." The theory book I read didn't talk about how things might go wrong.

The only category of potential problems I could see for myself went mostly like this: If you had a monitor attached to the transmitter which perfectly subtracted the reference frequency and compared it to the output of an FM receiver of the on-air transmission, the difference in outputs between the two would be what, and under what circumstances would that difference be greatest?

 

[Averagesupernova]

@Silly Questions you seem to have a way to complicate your questions. Please take no offense but I find it difficult to 'decode' your questions. Sometimes I think that you are not grasping that there are standards set in transmitting systems. In the video example, there is never an unmodulated carrier. When there is no information sent, that is only part of the signal. Sync pulses and the color subcarrier reference are still sent. You can't just say I'm going to shut modulation off completely and then have an issue with: "Well NOW what the heck is the TV receiver going to do? The system is failing!"

 

[sophiecentaur]

what exactly is the transmitter sending around this time

This is a typical TV transmission problem. The transmitter just sends the normal TV signal. After demodulation, the TV circuit identifies a portion of the normal line waveform (the 'black level' ) and clamps the (AC coupled) demodulated signal to an internal voltage with a brief connection with a 'switch'. The time constant is long enough for the levels not to drift too far from line to line.
I really think you are cherry picking topics within FM. IMO this is not the best way to get a grasp of FM. Q and A just doesn't work in Engineering.

 

[Silly Questions]

I don't really know anything about analog electronics. FM as a data transmission medium was interesting to me because the "error correction" feedback, which in a normal clock would true the oscillator to the crystal, is where the data pops out. I speculated that might sometimes cause problems.

My original line of inquiry was how computer clocks work, then how PLL's work, then how the first PLL's (or PLL-equivalents) made FM radio possible. It's been an interesting ride.

 

[sophiecentaur]

Why do I not know about other problems with FM? The peril of asymmetrical filtering isn't intuitively obvious to a beginner reading an FM theory book, sorting that question into the category of, "Didn't know to ask." The theory book I read didn't talk about how things might go wrong.

I re-read this para and I see that you are not really aware of what Frequency Modulation is actually doing. Your question is definitely trying to run b before you can walk. (Very risky)

In an arm waving way we can liken FM to wobbling the frequency control knob on a lab oscillator in step with the voltage variations of the input signal. Not wrong - but it misses the essence of what's happening and the consequences of that form of modulation.

If you had a monitor attached to the transmitter which perfectly subtracted the reference frequency and compared it to the output of an FM receiver of the on-air transmission, the difference in outputs between the two would be what,

This passage is actually meaningless. What do you mean by "subtract the reference frequency"? In a wide deviation system, like FM radio the "reference frequency" is no more relevant to the transmitted signal than a frequency that's 1kHz above or below. If, by subtracting, you mean use a narrow filter at the nominal carrier frequency then all that would do is to reduce the transmitted power a bit, each time the carrier sweeps through that 'notch'. Basic FM is fairly tolerant to that sort of nasty. FM is very different from basic AM because in AM, the carrier is an essential part of the signal (a reference) and it's there all the time, carrying its Amplitude Envelope. As I have said before, often (for simple sinusoidal modulation at a particular frequency) there is no frequency component at the notional carrier at all.

It might help if you realize that Frequency Modulation is a sub-set of Phase Modulation that's not coherent - i.e. there is no reference carrier involved. However FM is demodulated, the demodulator output has no definite zero or origin.
OTOH, phase modulation can be demodulated coherently and there is an implied reference carrier frequency and phase from beginning to end.

Remember:
Phase is the Integral of Frequency (Imagine the angle of a wheel turning clockwise and anticlockwise along with a modulating signal.)
And Frequency is the time differential (rate of change) of Phase.

You can measure the Frequency without any knowledge of a reference phase and, as we know, when we do an indefinite Integration, the answer involves an arbitrary constant. For FM radio we don't care about that constant.

 

[sophiecentaur]

then how the first PLL's (or PLL-equivalents) made FM radio possible.

Nonsense, I'm afraid. The first FM demodulators used the slope of the frequency response of a simple tuned circuit to show the frequency received by the amplitude of what came out. PLLs came along decades after the first FM broadcasts. Iirc, actually the original FSK used two tuned filters to identify when the signal was at the higher frequency or the lower frequency. We're talking Valve circuits and hand wound inductors etc!

You must try to avoid being too fanciful about a topic that's very complicated and needs a very formal approach. Alternatively just work in terms of 'black boxes' with their functions marked on the side and leave it at that (a pragmatic approach).

 

[Silly Questions]

I'll take your advice. You've given me a lot to think about.