# Estimate the Audio Deviation on FM Subcarrier

## By J. R. Mathison, WB9OQM

### February 2013 A analog oscilloscope display has the property to multiply the audio deviation on a frequency modulated RF subcarrier without multiplying the RF frequency.

Feed the audio input of the subcarrier generator with an audio tone of fixed frequency, such as 1000 hz, and feed the RF output of the subcarrier generator into an oscilloscope.

Adjust the horizontal sweep to 'delayed' and 'expand' and adjust the period to easily see each individual cycle of sine wave. Adjust the 'horizontal position' to see the peaks as moving away from the trigger point. Use + trigger.

The 'marker' is the waveform, as shown in the drawing at above right, where the thickened trace causes the valleys between peaks, from both positive and negative directions, to just touch the 'zero' axis.

Commercial audio FM subcarriers using preemphasis usually have the deviation set at 75 Khz peak at 1000 hz of audio input, causing the 'marker' condition to appear approximately twenty-two peaks from the trigger point. As there are several cycles which approach this condition, the trick is to do an 'eyeball' interpolation to find the middle. By slowly adjusting the 'horizontal position' one can count the peaks back to the trigger point.

The 'marker' condition, as shown in the drawing, indicates where the multiplied peak deviation is 1/4 of the period of one cycle of the RF.
The derived formula for peak FM deviation of the subcarrier is:
Peak deviation in Khz = fsc / (4Nc - 1)
where fsc is the frequency of the subcarrier in Khz, and Nc is the number of waveform peaks minus one, counted back from the 'marker' to the trigger point on the oscilloscope. It is actually the number of periods between waveform peaks which is being counted.

For example: there are 27 waveform peaks counted back from the 'marker' on a subcarrier with an RF frequency of 5.76 Mhz.
Nc = 27 - 1 = 26, and peak deviation = 5760 / (4 * 26 - 1) = approximately 56 Khz peak deviation.

A 6.2 Mhz (6200 Khz) subcarrier with a peak deviation of 75 Khz will have 20.9 periods (22 waveform peaks approximately) from the 'marker' back to the trigger point. A wrong count by only one peak will result in approximately five percent error. It is best to practice this estimating method on a subcarrier which has been carefully calibrated using the Bessel null procedure, in order to get the feel of the oscilloscope, and counting a long line of waveform peaks while adjusting the horizontal position to allow their counting.

If the peak audio deviation on the RF subcarrier is low, one may not be able to get to the 'marker' waveform while obtaining an oscilloscope display which is readable. In this case, adjust the vertical gain so the peak to peak amplitude of the display is eight units on the graticule. Then move away from the trigger point until the valleys between peaks from positive and negative are 3/4 the total amplitude. For example, if the total peak to peak amplitude is four units positive and four units negative, the positive valleys should extend to the -2 graticule line, and the negative valleys should extend to the +2 graticule line. Do an 'eyeball' interpolation to find the middle of the group of valleys which seem to fulfill this condition.
Count the waveform peaks minus one, back to the trigger point and multiply the result by two for use in the formula above.

Disclaimer
I assume others have discovered and published the above procedure;
however, I have not been able to find their work.

Please send E-Mail to: mathison (aatt) sdf-eu.org
.
Last revision 2013-02-04