EE 354
Modern Communication Systems
Frequency Modulation
Spring 2016
Instructor: C. R. Anderson
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Recall…
Amplitude modulation
u p  t   e  t  cos  2 f c t  

Frequency Modulation
u p  t   e  t  cos  2 f c t  

Phase Modulation
u p  t   e  t  cos  2 f c t  

FM and PM fall into a general category known as ________________.
Here, the message signal is used to modulate the
________________________________.
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New Concept: Instantaneous Frequency
Passband Signal:
u  t   e  t  cos  2 f c t    t 

Simplify As:
Question: If we have no modulation, what is the passband signal?
Question: What is the meaning of
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Instantaneous Frequency
Definition:
Instantaneous Frequency Offset from the Carrier: Given a signal of the
form e  t  cos  2 f c t    t   then the instantaneous frequency is given by:
Note:
Phase Modulation:
Phase mod. constant, units rad/V.
Frequency Modulation:
Freq. mod. constant, units Hz/V.
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FM / PM Examples
Given:

u  t   50 cos 2 1 MHz  t  0.1cos  2 500 Hz  t 

(a) Determine the instantaneous frequency.
(b) Determine the instantaneous frequency at t = 0.5 msec.
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What FM and PM Signals Look Like in Time
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Frequency spectrum of FM/PM
Frequency Modulation
Phase Modulation
Conceptually, what’s happening with an FM signal is that the
instantaneous frequency is sweeping around the carrier an amount of
f
Mathematically:
Matlab Spectrogram Demo
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FM Modulation Index
If the bandwidth (max frequency) of the message
signal is denoted by B then we can define:
Using the FM Modulation Index – for tone modulation –
we can write u p  t  in a more compact form:
Note:
For
For
we have narrowband FM
we have wideband FM
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Spectrum of an FM Signal
Question: What does the spectrum of an FM Signal look like? Note
that we have a problem here, because :
cos  A  B   cos  A   cos  B 
Thus, the analysis is much more complex, but can be broken down
into spectrum for Narrowband FM and spectrum for Wideband FM.
This requires some math:
See Provided Handout
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