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# The power dissipated load the modulated wave thus

856

Chapter 19

P (
)
2
⎢⎢⎣
(
) 2 (

J V 2 c

) 2 (

J V 3 c

) 2
R R R R
(19.18)
P V c 2 [ J 2 0 2 ( J 1 2 J 2 2 J 2 3 …)]
R
J 2 0 ( J 1 2 J 2 2 J 2 3 … >

Example 19.7
An FM transmitter transmits with a rated system deviation of 60 kHz and a maximum modulating frequency of 15 kHz. If the carrier amplitude is 25 V, determine the number of side frequencies required to ensure that 98% of the power is contained in the carrier and side frequencies. Sketch the spectrum diagram.

Solution
The frequency deviation is given by:

δ �
J 0
J 1

� �0 0660

J 2

0 3641

J 3
J 4
J 5
J 6
J 7

0 0152

It will be seen that only J2 , J3 , J4 , J5 and J0 are required:

J 2 0 2 ( J 2 2 J 2 3 J 2 4 J 2 5 J 2 7 )
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Communications Systems
J1 0.3641

J3

J2

J5

–0.0660

J0
–0.3971

BW ( 6 15 2

180 kHz

This is a considerable saving in bandwidth and hence a reduction in noise in the modulator circuits.

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