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I am currently practicing for my college exams and in this question, they are asking us to find the total multiplication needed in the system. But I am stuck because I have no idea of how to make use of this when both frequency deviation and oscillation frequency values are adjustable in a range.

Question:

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This is what I have done so far. Please be kind enough to take a look and give me a hint. Thank you!

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(Original Google Drive link for above image)

SamGibson
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leahnanno
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  • 9 to 10Hz frequency deviation is not very much : I would first be asking the source if there is a typo in the question. To answer it as given is a bit interesting... Your approach so far ignores the tight constraints on multiplier ratios. –  Jun 08 '21 at 12:27
  • @user_1818839 That is typical of Armstrong modulators, which are really phase modulators working in the I/Q domain. This is why nobody does it that way today, a PLL with slow loop filter working at the output frequency is so much less annoying. – Dan Mills Jun 08 '21 at 12:41

2 Answers2

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The key is that the mixer does not increase the deviation, only the multipliers do that, so the required multiplication is fixed by the required output deviation and deviation available from the modulator.

The generator has about 10Hz deviation (Armstrong modulators are basically phase modulators, and this is about right!), so it needs a multiplier chain totalling ~20k/10 = 2000, but we are restricted to doublers, which means powers of two.

Best we can do is 2^11 = 2048, which means input deviation will need to be 20kHz/(2^11) which is within the 9-10Hz control range, so that's sorted.

Question now is how to distribute that 2^11 to get an LO in the 9 - 10MHz range, remember the mixer has two output sidebands and you can pick whatever works.

200k * 2^11 = 409.5Mhz, so we are clearly going to be doing high side LO because we need the mixer output to be lower frequency then its input.

So now you just play with the multiplier distribution to find something where n1+n2 = 11, and the difference between mixer input frequency and output frequency lies in the 9 to 10MHz range.

Easy marks.

Dan Mills
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I will give you a start on the answer : the deviation is multiplied by M1*M2 and so is the NBFM carrier frequency in the absence of a mixing stage.

Thus you have no freedom to choose M1*M2 wrt the deviation, but the LO and mixing stage give you some freedom to choose M1 and M2 satisfying that constraint on M1*M2.

So divide the required deviation (20kHz) by the upper and lower NBFM deviation values (10 and 9Hz) to give upper and lower bounds on the overall multiplication ratio, and choose a (or the) power of 2 between them. If there isn't one, you know this approach has no solution.

Now that gives you a natural carrier frequency (200kHz * M1 * M2) for comparison with the desired carrier (96 MHz). That will tell you if you want to increase or decrease the frequency with the mixer stage, and by how much.

You can then work back by dividing the final carrier by various values of (M2 = 2^N) to find likely candidates which allow LO frequencies in the range given.