SYSC3501 HW Lab 3

# SYSC3501 HW Lab 3 - Hardware Laboratory#3 Frequency...

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Hardware Laboratory #3 Frequency Modulation by Geoffrey C. Green and Adrian D. C. Chan SYSC 3501 Communication Theory Department of Systems and Computer Engineering Faculty of Engineering Carleton University © March 10, 2008

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Department of Systems and Computer Engineering Page 2 of 13 SYSC3501 – Communication Theory Hardware Laboratory #3 1 Purpose In Hardware Lab #2, we examined the time and spectral characteristics of amplitude modulated signals (using the AM-DSB-SC and AM-DSB-C modulation schemes). The purpose of this laboratory is to do a similar analysis for frequency-modulated (FM) signals. In doing so, the student will gain experience with FM modulators and receivers. In addition, an oscilloscope/ spectrum analyzer will be used to measure time-domain characteristics and spectral characteristics of various FM signals. 2 Prelaboratory Theory Recall that a frequency-modulated signal ) ( t s FM is given by the equation: + = t f c c FM d m k t f A t s 0 ) ( 2 2 cos ) ( τ π where: c A is the carrier amplitude, c f is the carrier frequency, ) ( t m is the message signal, f k is the frequency sensitivity factor. Note that f k is a fixed parameter of the FM modulator used in this laboratory and can not be adjusted; however, amplifying m(t) by a constant value would result in an equivalent effect. For a specific message signal (a sinusoid with amplitude m A and frequency m f ) we have: ) 2 cos( ) ( t f A t m m m = When we plug this ) ( t m into the relation above, we get the following FM wave: + = t m m f c c FM d f A k t f A t s 0 ) 2 cos( 2 2 cos ) ( which can be simplified to:
Department of Systems and Computer Engineering Page 3 of 13 SYSC3501 – Communication Theory Hardware Laboratory #3 [ ] ) 2 sin( 2 cos ) ( τ π β m c c FM f t f A t s + = Note that: m f A k f = Δ is called the frequency deviation – it depends on the amplitude of the message signal and represents the maximum amount that the instantaneous frequency of the FM wave deviates from the carrier frequency, and m f f Δ = , the FM modulation index , represents the maximum amount that the phase of the FM wave deviates from the unmodulated carrier. It varies linearly with the amplitude of ) ( t m and inversely with the frequency of ) ( t m . Either of these quantities can be adjusted to vary . There are two cases of interest: 1. Narrowband FM (NBFM) In this case, . 1 << With the use of trigonometric identities (see text section 4.4 for derivation), the FM-modulated signal ) ( t s NBFM can be approximated as: ) 2 sin( ) 2 sin( 2 cos ) ( t f t f A t f A t s c m c c c NBFM 2. Wideband FM (WBFM) In this more general case, assumes an arbitrary value (i.e. not necessarily 1 << ), and the FM-modulated signal ) ( t s WBFM is given by (can be shown): −∞ = + = n m c n c WBFM t nf f J A t s ] ) ( 2 cos[ ) ( ) ( where ) ( n J is n

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SYSC3501 HW Lab 3 - Hardware Laboratory#3 Frequency...

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