Frequency modulation
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Frequency Modulation. Analog and Digital Communications Autumn 2005-2006. 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

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Frequency Modulation

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Frequency modulation

Frequency Modulation

Analog and Digital Communications

Autumn 2005-2006

CS477: Analog and Digital Communications


Spectral analysis of fm

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

NBFM and NBPM

Consider the bandpass transmitted signal:

For narrowband approximation:

CS477: Analog and Digital Communications


Nbfm and nbpm1

NBFM and NBPM

Thus, for NBFM and NBPM:

CS477: Analog and Digital Communications


Tone modulation

Tone Modulation

Thus, for NBFM and NBPM:

CS477: Analog and Digital Communications


Tone modulation with nb

Tone Modulation with NB

CS477: Analog and Digital Communications


Tone modulation with nb1

Tone Modulation with NB

CS477: Analog and Digital Communications


Tone modulation with wb

NOTE:

and

are periodic

Tone Modulation with WB

Try to write their Fourier series expansion!

CS477: Analog and Digital Communications


Tone modulation with wb1

where

and

Tone Modulation with WB

CS477: Analog and Digital Communications


Tone modulation with wb2

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


Fm bandwidth

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


Fm bandwidth single tone

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


Fm bandwidth generic signal

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

Transmission BW: Summary

CS477: Analog and Digital Communications


Generating nbfm signals

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


Generating nbfm signals1

(NBPM)

900

NBPM Modulator

NBFM Output

Input

Generating NBFM Signals

Indirect method:

(NBPM/NBFM)

CS477: Analog and Digital Communications


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