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Electrical Communications Systems ECE.09.433

Electrical Communications Systems ECE.09.433. Frequency Modulation II. Dr. Shreek Mandayam Electrical & Computer Engineering Rowan University. Plan. Angle Modulation Systems Analyzing FM Signals - Battle Plan!!!! Single-tone FM Wideband FM Bessel Functions. ECOMMS: Topics.

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Electrical Communications Systems ECE.09.433

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  1. Electrical Communications SystemsECE.09.433 Frequency Modulation II Dr. Shreek Mandayam Electrical & Computer Engineering Rowan University

  2. Plan • Angle Modulation Systems • Analyzing FM Signals - Battle Plan!!!! • Single-tone FM • Wideband FM • Bessel Functions

  3. ECOMMS: Topics

  4. Signals Systems • Time Domain • Complex Envelope • Spectrum • Single-tone FM • Narrowband FM • Wideband FM • Bessel Functions • Power Performance Transmitters Receivers Standards Modulation Index Efficiency Bandwidth Noise Analyzing FM Signals - Battle Plan!!! Instrument Demo

  5. Bessel’s Differential Equation • German mathematician and astronomer Friedrich Wilhelm Bessel (1784 - 1846) • Discovered this equation while investigating planetary motion • 2nd order ODE, Nonlinear, Variable Coefficients, Homogeneous • Very important in applied mathematics and engineering • Governing equation for problems with cylindrical geometries, e.g. waveguides, vibrating strings, and …………!!!!!!!

  6. Bessel Functions Matlab Demo » help besselj BESSELJ Bessel function of the first kind. J = BESSELJ(NU,Z) is the Bessel function of the first kind, J_nu(Z).The order NU need not be an integer, but must be real.The argument Z can be complex. The result is real where Z is positive. » » » » x=0:0.1:10; » plot(x,besselj(0,x)); » title('Bessel Function of Order Zero, J_0(x)'); » xlabel('x'); »

  7. Bessel Functions Matlab Demo %ECOMMS Spring 19 Classroom Demo %S. Mandayam, ECE, Rowan University clear;close all; n=0:6; beta=0:0.1:10; Jn=besselj(n,beta'); plot(beta',Jn); grid on; xlabel('Frequency Modulation Index: \beta'); ylabel('J_n(\beta)'); legend('J_0(\beta)','J_1(\beta)','J_2(\beta)', 'J_3(\beta)','J_4(\beta)','J_5(\beta)','J_6(\beta)'); title('J_n(\beta): Spectral Amplitudes of an FM signal at f_c \pm nf_m'); http://engineering.rowan.edu/~shreek/fall19/ecomms/demos/besselfun.m Instrument Demo

  8. J1(b) |S(f)| / (Ac/2) J2(b) J3(b) J0(b) 0fc-3fm fc-2fm fc-fm fc fc+fm fc+2fm fc+3fm f FM Signal & Spectrum Single-tone FM Signal Single-tone FM Spectrum

  9. Summary

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