This presentation is the property of its rightful owner.
1 / 16

# Frequency Modulation PowerPoint PPT Presentation

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

Frequency Modulation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

## 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