Frequency Modulation

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## Frequency Modulation

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**Frequency Modulation**Analog and Digital Communications Autumn 2005-2006 CS477: Analog and Digital Communications**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: CS477: Analog and Digital Communications**NBFM and NBPM**Consider the bandpass transmitted signal: For narrowband approximation: CS477: Analog and Digital Communications**NBFM and NBPM**Thus, for NBFM and NBPM: CS477: Analog and Digital Communications**Tone Modulation**Thus, for NBFM and NBPM: CS477: Analog and Digital Communications**Tone Modulation with NB**CS477: Analog and Digital Communications**Tone Modulation with NB**CS477: Analog and Digital Communications**NOTE:**and are periodic Tone Modulation with WB Try to write their Fourier series expansion! CS477: Analog and Digital Communications**where**and Tone Modulation with WB CS477: Analog and Digital Communications**All values in the line spectrum are scaled by**Tone Modulation with WB (Do Example 5.1-2 and Exercise 5.1-3 in text) CS477: Analog and Digital Communications**Observation for**falls off quickly for Consider components only for Significant frequency components lie within Observation for is insignificant for Consider components only for Significant frequency components lie within FM Bandwidth Consider Tone Modulation CS477: Analog and Digital Communications**depends upon the allowable distortion level**Usually approximated by For worst case, use: What is the corresponding value of NO! A smaller may result in larger FM Bandwidth: Single Tone Is this the maximum value? CS477: Analog and Digital Communications**Use**For practical systems : FM Bandwidth: Generic Signal Estimate BW using worst case tone modulation! Define Deviation ratio: Approximations: Carson’s rule: Carson’s rule is applied for extreme values of deviation ratio. It underestimates the BW for practical systems. (Do Example 5.2-1 and Exercise 5.2-1 in text) CS477: Analog and Digital Communications**Transmission BW: Summary**CS477: Analog and Digital Communications**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 CS477: Analog and Digital Communications**(NBPM)**900 NBPM Modulator NBFM Output Input Generating NBFM Signals Indirect method: (NBPM/NBFM) CS477: Analog and Digital Communications