The power dissipated load the modulated wave thus

856	Chapter 19

	P	�	(				)			�	2	⎡ ⎢⎢⎣					) 2		�			J V 2 c			)	2	�	J V 3 c
∴				R			)			�	2	⎡ ⎢⎢⎣		R			) 2		�			R				2		R	(19.18)
∴	P	�	V c 2			�		[	J	2 0	�		2 (		J 1 2		�	J		2 2	�		J	2 3	�		…)]	R	(19.18)
			R			�		[	J	2 0	�		2 (		J 1 2		�	J		2 2	�			2 3	�		…)]
			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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