Oct 04, 2005CS477: Analog and Digital Communications1 Exponential Modulation Analog and Digital Communications Autumn

Oct 04, 2005CS477: Analog and Digital Communications2 Exponential Modulation Modulation in which information signal is encoded in carrier frequency or phase Amplitude of the transmitted signal is constant This modulation is robust to channel gain variations The modulation is non-linear Bandwidth of the transmitted signals depends upon the amplitude of the information signal

Oct 04, 2005CS477: Analog and Digital Communications3 Exponential Modulation Transmitted/Modulated signal: Total instantaneous angle: To obtain angle or exponential modulation: Make instantaneous phase dependent on the information signal

Oct 04, 2005CS477: Analog and Digital Communications4 Instantaneous Frequency Instantaneous frequency: For constant phase signals: For signals with time varying phase:

Oct 04, 2005CS477: Analog and Digital Communications5 Phase Modulation (PM) Make phase proportional to the information signal: Instantaneous frequency is dependent on the derivative of the information signal is called phase deviation

Oct 04, 2005CS477: Analog and Digital Communications6 Frequency Modulation (FM) Make instantaneous frequency dependent on the information signal is called frequency deviation What is the transmitted signal?

Oct 04, 2005CS477: Analog and Digital Communications7 PM to FM and Vice Versa (For FM) (For PM) PM Modulator FM OutputInput

Oct 04, 2005CS477: Analog and Digital Communications8 Peak and Average Powers Peak power is: Average power is: Peak to average power ratio is 2 Compare with DSB and AM Low peak to average power ratio is good for circuit designers

Oct 04, 2005CS477: Analog and Digital Communications9 AM, FM, and PM Comparison

Oct 04, 2005CS477: Analog and Digital Communications10 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:

Oct 04, 2005CS477: Analog and Digital Communications11 NBFM and NBPM Consider the bandpass transmitted signal: For narrowband approximation:

Oct 04, 2005CS477: Analog and Digital Communications12 NBFM and NBPM Thus, for NBFM and NBPM:

Oct 04, 2005CS477: Analog and Digital Communications13 Tone Modulation Thus, for NBFM and NBPM:

Oct 04, 2005CS477: Analog and Digital Communications14 Tone Modulation with NB

Oct 04, 2005CS477: Analog and Digital Communications15 Tone Modulation with NB

Oct 04, 2005CS477: Analog and Digital Communications16 Tone Modulation with WB andare periodicNOTE: