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General: Frequency Deviation

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What is the frequency deviation for a 12.21 MHz reactance modulated oscillator in a 5 kHz deviation, 146.52MHz FM phone transmitter? [G8B07]

A. 101.75 Hz
B. 416.7 Hz
C. 5 kHz
D. 60 kHz

Whoa, what?  Guess what, dust off that calculator, because here’s where it starts to get mathy.  This question is also terribly worded.

What we’re looking for is the oscillator deviation.  The formula to calculate this is:

Oscillator Deviation = \frac{Transmitter Deviation}{(\frac{Output Frequency}{Oscillator Frequency})}

Simplified, it becomes this:

Oscillator Deviation = \frac{(Transmitter Deviation)(Oscillator Frequency)}{(Output Frequency)}

If we plug in our numbers, like so, don’t forget to use consistent units, so we must turn our 5kHz into .005MHz.

Oscillator Deviation = \frac{(.005)(12.21)}{(146.52)}

Solving…

Oscillator Deviation = .0004167 MHz, or 416.7 Hz, after we move the decimal six (mega!) places.

So our answer is B. 416.7 Hz

Now, mathematically you could think of this as a ratio between the oscillator and transmitter deviations and frequencies.  The equation for that looks like this, and winds up the same when you solve it….

\frac{Oscillator Deviation}{Oscillator Frequency} = \frac{Transmitter Deviation}{Transmitter Output Frequency}

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