EE3008_Lecture4 - 1 Lecture 4 Analog Communications Part II...

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1 Lecture 4. Analog Communications Part II. Frequency Modulation (FM) • Angle Modulation (FM and PM) • Spectral Characteristics of FM signals • FM Modulator and Demodulator Department of Electronic Engineering EE3008 Principles of Communications Lecture 4
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2 Angle Modulation 1 ( ) ( ) 2 d t f t dt Ψ π = ( ) cos( ( )) AnM s t A t Ψ = An angle-modulated signal can be written as : Instantaneous Phase : Instantaneous Frequency ( ) t Ψ ( ) f t For a typical carrier signal: ( ) 2 ( ) c t f t t Ψ π θ = + Phase Modulation (PM): ( ) ( ) t s t θ α = ( ) cos(2 ( )) PM c s t A f t s t π α = + Frequency Modulation (FM): 1 2 π d θ ( t ) dt = ks ( t ) ( ) cos(2 ( ( ) )) t FM c s t A f t k s d π τ τ −∞ = + Department of Electronic Engineering EE3008 Principles of Communications Lecture 4 f ( t ) = f c + 1 2 π d θ ( t ) dt
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3 Phase Deviation and Frequency Deviation Phase Modulation (PM) signal Frequency Modulation (FM) signal ( ) cos(2 ( )) PM c s t A f t s t π α = + ( ) cos(2 ( ( ) )) t FM c s t A f t k s d π τ τ −∞ = + ( ) 2 ( ) c t f t s t Ψ π α = + Instantaneous Frequency max | ( ) | ks t Instantaneous Phase max | ( ) | s t α is called the maximum (peak) phase deviation is called the maximum (peak) frequency deviation 1 ( ) ( ) ( ) Hz 2 c d t f t f ks t dt Ψ π = = + Peak phase deviation represents the maximum phase difference between the transmitted signal and the carrier signal. Peak frequency deviation represents the maximum departure of the instantaneous frequency from the carrier frequency. Department of Electronic Engineering EE3008 Principles of Communications Lecture 4
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4 Relationship between PM and FM ( ) cos(2 ( )) PM c s t A f t s t π α = + ( ) cos(2 ( ( ) )) t FM c s t A f t k s d π τ τ −∞ = + PM Modulator s ( t ) FM Modulator Phase modulation of the carrier with a message signal is equivalent to frequency modulation of the carrier with the derivative of the message signal. We will only focus on FM in the following. ds ( t ) dt A cos(2 π f c t + s ( t )) Department of Electronic Engineering EE3008 Principles of Communications Lecture 4
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5 FM Signal s FM ( t ) s ( t ) Department of Electronic Engineering EE3008 Principles of Communications Lecture 4
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