Practical 2: Carson’s Rule and Bessel Function Null
Perform Practical
Use the Make Connections diagram to show the required connections on the
hardware.
In this Practical you are going to measure the deviation using a dc voltage to
drive the modulator and then use the Bessel null method to confirm the value
using ac modulation. The first measurement is the amplitude of the ac
modulation source.
Open the oscilloscope, spectrum analyser, frequency counter and voltmeter.
Set the Function Generator to Fast and select a sine wave.
Adjust the Frequency control on the Function Generator block and use the
frequency counter to set the modulation frequency to approximately 10 kHz.
Set the voltmeter to ac p-p and measure the peak to peak amplitude of the
sine wave. The peak value is half of this value.
Refer to the Make Connections diagram and remove connection 2 and add
connection 5, so that the modulation source is now the dc Source.
Set the voltmeter to dc and adjust the dc Source voltage to minus half the ac
peak to peak value that you measured. This should set the carrier to the
frequency corresponding to when the modulation is at its most negative. Move
the frequency counter probe (yellow) to the carrier output (monitor point 1),
measure the frequency and note the value.
Now set the dc Source voltage to plus half the ac peak to peak value and
measure the carrier frequency. Note the value. You can also see the
frequency change on the oscilloscope and the spectrum analyser.
The difference between these two carrier frequencies is the peak to peak
frequency change, i.e. twice the deviation. Calculate the deviation and note it
down.
Remove connection 5 and replace connection 2 so the modulation source is
again the Function Generator.
Move the frequency counter probe (yellow) back to the modulation (monitor
point 2).
Slowly increase the modulation frequency, while observing the spectrum
analyser display. You should be able to see the individual sidebands and the
carrier. Note that the carrier amplitude starts to decrease. There should be a
frequency between 15 kHz and 20 kHz where the carrier disappears. Adjust
the modulation frequency carefully so that the carrier is as near to zero
amplitude as you can. Note the frequency of the modulation.
Remembering that the first Bessel null occurs when beta is 2.405, the
deviation can be calculated using
f  2.405 f m
Where Δf is the deviation and fm is the 1st Bessel null frequency.
Compare the value you measured from the dc measurement and that from
using the Bessel null method. Due to the design of the modulator, the
deviation at high frequency will be slightly different than at low frequency,
such that the results will not be exactly the same for both methods.
Now use Carson’s rule to calculate the bandwidth for this combination of
modulation frequency and deviation.
Use the spectrum analyser and cursors to see how this compares with the
occupied bandwidth. Remember, bandwidth is measured at the points each
side of the peak and –3 db below it.
You can also calculate the control sensitivity for the VCO thus:
s
2 f
V p p
Where S is the sensitivity, Δf is the deviation and Vp-p is the peak to peak
magnitude of the ac modulation.