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Author Topic: A Modulation Math Problem  (Read 963 times)
TANAKASAN
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Posts: 933




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« on: April 21, 2013, 02:52:40 AM »

From the theory I already know that phase modulating a signal mathematically is the same as frequency modulating it, in fact some rig manufacturers use phase modulation in their transmit circuits. So, if I want to transmit the equivalent of 5 KHz deviation at 144 MHz how many degrees of phase modulation do I need to apply to the signal?

Note: I don't just need the answer here, I want to know how to work it out so that I can pass the information on.

Tanakasan

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M0HCN
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Posts: 473




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« Reply #1 on: April 21, 2013, 03:26:47 AM »

Alas it is not quite that simple....

Frequency is the rate of change of phase, so to increase the frequency by say 5Khz you have to cause the RATE OF CHANGE of phase to increase by 2 * pi * 5000 radians per second.

Just adding a fixed phase shift does not do it, you have to make the phase shift increase with time.

Fortunately if you simply place an integrator between the modulation input and the phase modulator you get exactly the required behavior, so it is not an insurmountable problem, but that integrator does mean that the response is dependent upon the modulating frequency.

HTH.

73 Dan.
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G8HQP
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« Reply #2 on: April 21, 2013, 02:03:14 PM »

The connection between frequency deviation and phase deviation involves the frequency of the baseband modulation, so your original question about 5kHz deviation does not give enough information to answer the question.
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TANAKASAN
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« Reply #3 on: April 21, 2013, 02:29:02 PM »

This is mainly due to a lack of maths ability on my part, for which I apologize. I've played around with FM modulators for the last couple of days and I'm beginning to understand the relationship between the carrier and the modulation frequency and how at certain modulation frequencies and depths the carrier nulls out (Bessel functions).

The thing is, I've been doing this empirically using an old FM handheld and an audio signal generator and now I need to understand the maths behind it. Is phase modulation the same, where certain audio frequencies and deviation settings will cause a carrier null?

Tanakasan
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VA7CPC
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« Reply #4 on: April 21, 2013, 05:27:22 PM »

A useful article here:

http://en.wikipedia.org/wiki/Frequency_modulation

and here:

http://en.wikipedia.org/wiki/Phase_modulation

.             Charles
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WB6BYU
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Posts: 13113




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« Reply #5 on: April 22, 2013, 07:16:05 AM »

Phase and frequency modulation are the same for a fixed frequency tone,
but, for the same input signal levels, not as the modulating frequency
changes.  To get PM to demodulate properly as FM over a range of
frequencies the modulating audio is shaped by (IIRC) 6dB / octave.
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