1. Oct 06, 2005CS477: Analog and Digital Communications1 Frequency Modulation Analog and Digital Communications Autumn 2005-2006

2. Oct 06, 2005CS477: Analog and Digital Communications2 Spectral Analysis of FM Exponential modulation is non-linear Bandwidth of the transmitted signals depends upon the amplitude of the information signal Hard to analyze with Fourier transforms Narrowband approximation makes analysis a little easier  NBFM and NBPM For narrowband approximation to hold:

3. Oct 06, 2005CS477: Analog and Digital Communications3 NBFM and NBPM Consider the bandpass transmitted signal: For narrowband approximation:

4. Oct 06, 2005CS477: Analog and Digital Communications4 NBFM and NBPM Thus, for NBFM and NBPM:

5. Oct 06, 2005CS477: Analog and Digital Communications5 Tone Modulation Thus, for NBFM and NBPM:

6. Oct 06, 2005CS477: Analog and Digital Communications6 Tone Modulation with NB

7. Oct 06, 2005CS477: Analog and Digital Communications7 Tone Modulation with NB

8. Oct 06, 2005CS477: Analog and Digital Communications8 Tone Modulation with WB andare periodicNOTE: Try to write their Fourier series expansion!

9. Oct 06, 2005CS477: Analog and Digital Communications9 Tone Modulation with WB where and

10. Oct 06, 2005CS477: Analog and Digital Communications10 Tone Modulation with WB All values in the line spectrum are scaled by (Do Example 5.1-2 and Exercise 5.1-3 in text)

11. Oct 06, 2005CS477: Analog and Digital Communications11 FM Bandwidth falls off quickly for  Consider components only for Observation for is insignificant for  Consider components only for Observation for Consider Tone Modulation Significant frequency components lie within

12. Oct 06, 2005CS477: Analog and Digital Communications12 FM Bandwidth: Single Tone For worst case, use: depends upon the allowable distortion level Usually approximated by What is the corresponding value of Is this the maximum value? NO! A smaller may result in larger

13. Oct 06, 2005CS477: Analog and Digital Communications13 FM Bandwidth: Generic Signal Estimate BW using worst case tone modulation! Define Deviation ratio: Carson’s rule: Carson’s rule is applied for extreme values of deviation ratio. It underestimates the BW for practical systems. Use (Do Example 5.2-1 and Exercise 5.2-1 in text) Approximations: For practical systems :

14. Oct 06, 2005CS477: Analog and Digital Communications14 Transmission BW: Summary Condition(s)Single ToneGeneric Signal Carson’s Rule extreme Practical designs

15. Oct 06, 2005CS477: Analog and Digital Communications15 Generating NBFM Signals Direct method Use a voltage-controlled oscillator Output frequency is proportional to input voltage Use information signal as the input voltage Restricted to low power applications Most circuits unstable at carrier frequency Not suitable for commercial FM broadcast Require sophisticated feedback control

16. Oct 06, 2005CS477: Analog and Digital Communications16 Generating NBFM Signals Indirect method: (NBPM/NBFM) NBPM Modulator NBFM Output Input 90 0 (NBPM)