- #1
Fisher92
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Homework Statement
An FM broadcast system has the following parameters:
*Deviation sensitivity 5 kHz/V.
*Information signal consists of 2 frequency components; 12sin(2π10000t), 10sin(2π15000t).
*Transmitter antenna impedance is 50Ω.
a) What are the modulating indexes for the 2 components?
b) Plot the power distribution of the transmitted signal. (Hint: Consider the
frequency components in the transmitted signal and the power of each
component.)
c) What percentage of transmitted power spills into the guard band and what
percentage of power spills to the adjacent channel?
d) Discuss methods that can be used to avoid transmitted power spilling outside the
allowed 150 kHz band.
Use Bessel function to calculate the BW
The Attempt at a Solution
a)
I am pretty sure that deviation sensitivity is not the same as deviation ratio but I don't think there is enough info not to treat them the same? - maybe a typo and its meant to be ratio?
for the first component:
The frequency is (by inspection) 10000=10kHz
[tex] m_f=\frac{\delta}{f_i} =\frac{5kHz}{10k} =0.5 [/tex] within the realms of plausibility at least/
for the second component:
The frequency is (by inspection) 15000=15kHz
[tex] m_f=\frac{\delta}{f_i} =\frac{5kHz}{15k} =0.33 [/tex]
These modulation indexes seem reasonable to me but the 'deviation sensitivity' label is annoying me .
b)
http://www.techpin.com/wp-content/uploads/2009/12/untitled-470x270.jpg
I am more thinking out loud here and looking for some pointers... could be way off base
From the Bessel Function frequency table above,
for the first component (mf=0.5),J0(carrier)=0.94,J1=0.24 and J2=0.03
If my understanding is correct, this means that I will get significant components at J0,J1&J2 and that the values in the tables are effectively a multiplier for the power seen at these frequencies? BUT, I don't have the carrier signal so I am stuck here...
UNLESS this is correct_doubt it but might as well check.
[tex]p=(0.94*\frac{12}{\sqrt(2)})^2/50=1.27W[/tex] This is for the carrier? J0? seems small
for J1=82.94mW
for J2=1.296mW
If this is correct, again not confident, I need the frequency that these powers occur at in order to plot the power distribution wouldn't I? How would I go about finding this?
I will need to hit up MATLAB to get this for the 33% mindex and repeat the above steps for the second frequency component given.
Getting long for a post anyway, all help/tips/pointers welcome & appreciated.