1 / 26

CPET 355

CPET 355. 2. The Physical Layer Data Communications and Networking Paul I-Hai Lin, Professor Electrical and Computer Engineering Technology Purdue University, Fort Wayne Campus. 2. The Physical Layer. Introduction Data Communications – Theoretical Basics Guided Transmission Media

maisie-nicholson
Download Presentation

CPET 355

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. CPET 355 2. The Physical Layer Data Communications and Networking Paul I-Hai Lin, Professor Electrical and Computer Engineering Technology Purdue University, Fort Wayne Campus Prof. Paul Lin

  2. 2. The Physical Layer • Introduction • Data Communications – Theoretical Basics • Guided Transmission Media • Wireless Transmission • Communication Satellites • The Public Switched Telephone Networks • The Mobile Telephone Systems • Cable Television Prof. Paul Lin

  3. Related Technologies • 10 Top Bell Labs Inventions that change the world - http://www.bell-labs.com/about/history/changedworld.html • Transistor - 1947 • Laser - 1958 • Optical Communications – backbone of the Internet • Data Networking – 80s-90s, Digital Subscriber Lines (DSL) • Digital Transmission and Switching - 1962 • Cellular Telephone Technology – 1940s • Communications Satellites - 1962 • Digital Signal Processors - 1979 • Touch-Tome Telephone - 1963 • Unix Operating System and C Language – 1969 to 1972 Prof. Paul Lin

  4. Data Communications – Theoretical Basics • Fourier Analysis • Periodic functions • Fourier series • Bandwidth-Limited Signals • Filters • Bandwidth • The Maximum Data Rate of a Channel • Nyquist theorem • Shannon Theorem, http://www.bell-labs.com/news/2001/february/26/1.html Prof. Paul Lin

  5. Fourier Analysis • Periodic functions • A periodic function can be defined as any function for which g(t) = g(t + T) for all t. • Examples e1 = sin(2ft + ); f = 60Hz e = sin(230t) + sin(260t); Prof. Paul Lin

  6. Periodic Function Examples • MATLAB Example 1: e1 = sin(2ft + ); f = 60Hz,  =0 %Program: sin60hz.m t = 0:0.001:1; % Time vector e = sin(2*pi*60*t); figure(1), stem(e(1:30)); figure(2), stem(e(1:30)), grid on; figure(3), plot(t,e), grid on, figure(4), plot(t(1:50),e(1:50)), grid on; figure(5), plot(t(1:100),e(1:100)), grid on; Prof. Paul Lin

  7. Figure 1- Stem output of e1 = sin(2ft + ); f = 60Hz,  =0 Prof. Paul Lin

  8. Figure 5: e1 = sin(2ft + ); f = 60Hz,  =0 Prof. Paul Lin

  9. Periodic Function Examples • MATLAB Example 2: % Program: sin30_60hz.m t = 0:0.001:1; % Time vector f1 = 30; f2 = 60; e = sin(2*pi*f1*t)+ sin(2*pi*f2*t); figure 1, stem(e(1:30)); figure 2, plot(e(1:100)), grid on; Prof. Paul Lin

  10. Stem Plot of e = sin(2*pi*f1*t)+ sin(2*pi*f2*t); Prof. Paul Lin

  11. Signal Plot of e = sin(2*pi*f1*t)+ sin(2*pi*f2*t); Prof. Paul Lin

  12. MATLAB Example 3 - e = 5sin(23000t); %sin3000hz.m f = 3000; % Signal frequency T = 1/f; % Signal Period A1 = 5; % Signal Amplitude fs = 100*f; % Sampling frequency ts = 1/fs; % Sampling time t = 0:ts:2*T; % Time vector e1 = A1*sin(2*pi*f*t); plot(t,e1), grid on; Prof. Paul Lin

  13. Signal Plot of e = 5sin(23000t); Prof. Paul Lin

  14. Band-Limited Signals • The bit pattern of ASCII character ‘b’ 0110 0010 • The output voltage 0 1 1 0 0 0 1 0 Time Prof. Paul Lin

  15. Band-Limited Signals – MATLAB Example 4 • Equations on Page 86 - 88 an = (1/(pi*n))[cos(pi*n/4)-cos(3*pi*n/4)+cos(6*pi*n/4)-cos(7*pi*n/4)] bn = (1/(pi*n))[sin(3*pi*n/4)-sin(pi*n/4)+sin(7*pi*n/4)-sin(6*pi*n/4)] c = ¾ rms_n = (an^2 + bn^2)^1/2 Prof. Paul Lin

  16. Band-Limited Signals % bandlimit_p86 % Generating column vectors an = zeros(1,15); % Transpose operation to convert to row vector an = an'; bn = zeros(1,15)'; % Row vector rms_n = zeros(1,15)'; % Root mean square Prof. Paul Lin

  17. Band-Limited Signals for I = 1: 15 n = I; an(I) = (1/(pi*n))*(cos(pi*n/4)-cos(3*pi*n/4)+cos(6*pi*n/4)-cos(7*pi*n/4)); bn(I) = (1/(pi*n))*(sin(3*pi*n/4)-sin(pi*n/4)+sin(7*pi*n/4)-sin(6*pi*n/4)); rms_n(I) = sqrt(an(I)*an(I) + bn(I)*bn(I)); end Prof. Paul Lin

  18. Band-Limited Signals – Harmonic Number Prof. Paul Lin

  19. MATLAB Example 5 - Approximating a Square Wave % fourier.m - approximating a square wave f1 = 60; w1 = 2*pi*f1; Fs = 10E3; Ts = 1/Fs; A = 5; t_end = 40E-3; t = 0: Ts/10 : t_end; es = (4*A/pi)*(cos(w1*t) -1/3*cos(3*w1*t)) … +(1/5*cos(5*w1*t))-(1/7*cos(7*w1*t))… +1/9 *cos(9*w1*t) - 1/11 *cos(11*w1*t)); figure(1), plot(t, es), title('Square wave'), grid on, xlabel('time'),ylabel('Volts') Prof. Paul Lin

  20. Signal Plot of theApproximated Square Signal Prof. Paul Lin

  21. MATLAB Example 5 - Data Rate and Harmonics N = 8; % number of iteration B = 8; % no_bits = 8; bps = 300; fprintf('--------------------------------------------\n'); fprintf('Bps\t\tT(msec)\t\tFirst harmonics(Hz)\n'); for I = 1:N fn1 = bps/B; % First harmonic Tn1 = 1/fn1; % Period of each harmonic fprintf('%f | %f | %f\n', bps, Tn1, fn1); bps = bps + bps; end fprintf('--------------------------------------------\n'); Prof. Paul Lin

  22. MATLAB Example 5 - Data Rate and Harmonics ---------------------------------------------------- Bps T(msec) First harmonics(Hz) 300.000000 | 0.026667 | 37.500000 600.000000 | 0.013333 | 75.000000 1200.000000 | 0.006667 | 150.000000 2400.000000 | 0.003333 | 300.000000 4800.000000 | 0.001667 | 600.000000 9600.000000 | 0.000833 | 1200.000000 19200.000000 | 0.000417 | 2400.000000 38400.000000 | 0.000208 | 4800.000000 ---------------------------------------------------- Prof. Paul Lin

  23. The Maximum Data Rate of a Channel • Nyquist Theorem: If an arbitrary signal has been run through a low-pass filter of bandwidth H, the filtered signal can be completely reconstructed by making only 2H (exact) samples per second. Max data rate = 2*H*log2(V) bits/sec H – bandwidth V – discrete levels Prof. Paul Lin

  24. The Maximum Data Rate of a Channel • Nyquist Theorem: If signal consists of V discrete levels, the Max data rate = 2*H*log2(V) bits/sec • An Example: H = 3000 Hz, V = 2 (binary, 0 or 1) Max data rate = 2*3000*log2(2) = 6000 bps Prof. Paul Lin

  25. The Maximum Data Rate of a Channel • Shannon’s Theorem • Gives an upper bound to the capacity of a communication link, in bits per second (bps), as a function of the available bandwidth and the signal-to-noise ratio of the link. • Max number of bits per second = H*log2(S/N) H – bandwidth, S = signal power N – Noise power • S/N (dB) = 10 log10(1+S/N) Prof. Paul Lin

  26. The Maximum Data Rate of a Channel • Shannon’s Theorem • An Example: Find the max bps for a channel of H = 3000Hz, S/N (dB) = 30 dB. Solution: • Calculate S/N = 1000 from S/N (dB)= 10log10(S/N) • Compute H*log2(1 + S/N) = 2.99E+4 or < 30,000 bps Prof. Paul Lin

More Related