sm9_19

Prévia do material em texto

Problem 9.19. An FM system, operating at a pre-detection SNR of 14 dB, requires a 
post-detection SNR of 30 dB, and has a message power of 1 watt and bandwidth of 50 
kHz. Using Carson’s rule, estimate what the transmission bandwidth of the system must 
be. Suppose this system includes pre-emphasis and de-emphasis network with f3dB of 10 
kHz. What transmission bandwidth is required in this case? 
 
Solution 
We are given the pre-detection SNR of 14 dB (~25.1), so 
2
0
25.1
2
FM c
pre
T
ASNR
N B
= = 
 
and the post-detection SNR of 30 dB (~1000), so 
 
2 2
3
0
3
1000
2
c fFM
post
A k P
SNR
N W
= = 
 
Combining these two expressions, we obtain 
 
2
3
3
39.8
FM
post f T
FM
pre
SNR k PB
SNR W
= = 
 
Approximating the Carson’s rule for general modulation ( )1/ 2 1/ 22 2T f fB k P W k P= + ≈ , 
and if we replace with in this last equation, we obtain Pk f
2 4/2TB
 
3
3
3 39.8
4
FM
post T
FM
pre
SNR B
SNR W
≈ = 
 
Upon substituting W = 50 kHz, this last equation yields BT = 187.9 kHz. 
 
 
 
Excerpts from this work may be reproduced by instructors for distribution on a not-for-profit basis for testing or instructional purposes only 
to students enrolled in courses for which the textbook has been adopted. Any other reproduction or translation of this work beyond that 
permitted by Sections 107 or 108 of the 1976 United States Copyright Act without the permission of the copyright owner is unlawful.