Classical modulation procedures - Signals, Processes, and Systems - page 251

Frequency domain

4,0
3,5
3,0
2,5
2,0
1,5
1,0
0,5
0,0
3,5
3,0
2,5
2,0
1,5
1,0
0,5
0,0
2,50
2,25
2,00
1,75
1,50
1,25
1,00
0,75
0,50
0,25
0,00
1,75
1,50
1,25
1,00
0,75
0,50
0,25
0,00
1,50
1,25
1,00
0,75
0,50
0,25
0,00

Center Fr equency 512 H z Fr equency swing 256 Hz

32
Hz

Bandwidth of the FM - signal

250 500 750 1000

Hz

Illustration 174: Formula for estimating the bandwidth of an FM signal

Here are once again the spectra of Illustration 171 and Illustration 172. The interval between the lines
corresponds to the frequency of the sinusoidal source signal (here 32 Hz). In the bottommost representa-
tion the quantities for the determination of the “essential FM bandwidth. A frequency swing of 320 - see
Illustration 170 bottom left - results in one half of a spectrum of (320 + 2 <

32)Hz. The total bandwidth
results accordingly at 2(320 + 2 < 32) Hz. For all other cases the following holds: B FM = 2( Δ f C + 2f S ).

The investigation of the influence of the frequency swing f C , Signal f S and mid-

frequency f C on the bandwidth B of the FM signal in the Illustration 171 and Illustration
172 gives an unambiguous result. Only the frequency swing

Δ

Δ f C and signal frequency f s

determine the bandwidth B FM of the FM signal.

Illustration 174 leads finally to the formula for the bandw idth of an FM signal.

B FM = 2( Δ f C + 2f S )