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Frequency Modulation

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Frequency Modulation

Analog and Digital Communications

Autumn 2005-2006

CS477: Analog and Digital Communications

- 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

Consider the bandpass transmitted signal:

For narrowband approximation:

CS477: Analog and Digital Communications

Thus, for NBFM and NBPM:

CS477: Analog and Digital Communications

Thus, for NBFM and NBPM:

CS477: Analog and Digital Communications

CS477: Analog and Digital Communications

CS477: Analog and Digital Communications

NOTE:

and

are periodic

Try to write their Fourier series expansion!

CS477: Analog and Digital Communications

where

and

CS477: Analog and Digital Communications

All values in the line spectrum are scaled by

(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

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

Is this the maximum value?

CS477: Analog and Digital Communications

Use

For practical systems :

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

CS477: Analog and Digital Communications

- 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

- Use a voltage-controlled oscillator

CS477: Analog and Digital Communications

(NBPM)

900

NBPM Modulator

NBFM Output

Input

Indirect method:

(NBPM/NBFM)

CS477: Analog and Digital Communications