From: Jack Smith
Subject: Re: Armstrong FM Calculations
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Date: Mon, 02 Sep 2002 11:31:09 GMT
NNTP-Posting-Date: Mon, 02 Sep 2002 07:31:09 EDT
Organization: Cox Communications
The solution I developed is:
200 KHz --> multiply by 80 = 16.000 MHz
6.92 MHz injection osc multiplied by 2 = 13.840 MHz
Mix 16.000 MHz and 13.840 MHz and take the difference output = 2.160
2.160 MHz mixer output --> multiply by 50 = 108.000 MHz.
Deviation is multiplied by 80 * 50 = 4000.
This gives you the exact required answer.
JackOn Mon, 2 Sep 2002 10:22:53 +0100, John Woodgate
>I read in sci.electronics.design that Mark Dunne
> wrote (in igo.ie>) about 'Armstrong FM Calculations', on Sat, 31 Aug 2002:
>>I was wondering if anyone could help me with a problem i'm having in working
>>out the calculations for an Armstrong FM transmitter, I have a 200kHz
>>carrier and a frequency deviation of 20hz at the lowest modulation frequency
>>of 40Hz, this gives me a multiplication factor of 4000 or 4096 when using 2
>>64X multiplier blocks. I require a 108Mhz carrier with an 80kHz deviation
>>using a 6.92Mhz oscillator. when using the two multiplier blocks on the
>>frequency deviation i get 81.92kHz which is acceptable but the carrier
>>frequency when mixed with the 6.92Mhz oscillator is 376.32Mhz which is way
>>off! What am i doing wrong? Any help with this would be much appreciated.
>It seems to me that this is more of a mathematical puzzle than an
>To get 80 kHz deviation from 20 Hz, there must be a *deviation*
>multiplication process with factor M = 80 000/20 = 4000.
>To get a 108 MHz carrier, there must be a *frequency* multiplication
>process with a factor N = 108/0.2 = 540.
>Since N is less than M, there must be a heterodyne process that reduces
>the carrier frequency while retaining the deviation. This process must,
>according to the terms of the problem, use an oscillator at 6.92 MHz or
>a multiple thereof.
>We can write an equation for the heterodyne process and all possible
>intermediate (x, y) and final (n) frequency multiplications:
>108 = n(6.92x - 0.2y)
>We can write an equation for the deviation multiplication:
>ny = M = 4000
>We cannot solve for n and x separately, but nx = 908/6.92.
>I would have expected that to be a whole number, but it isn't; nx =
>131.21, and 131 is a prime number, so nx is difficult to achieve! Short
>of using fractional frequency division, the problem appears insoluble
>with the numbers given. nx = 131 gives a final carrier frequency of
>106.52 MHz, while nx = 132, which is maybe easier to achieve, gives a
>final carrier frequency of 113.44 MHz.
>If, as is likely in practice, the carrier frequency requirement needs to
>be met with much greater precision than the deviation, we could take nx
>= 132 and thus get ny = 4027 (maybe that is a prime number!), giving a
>deviation of 80.54 kHz and a final carrier frequency of 108.04 MHz.
>The possibility of obtaining a closer solution by tweaking the 200 kHz
>or 6.92 MHz frequencies is left as an exercise for the student!
>Apologies in advance if there are arithmetical errors.