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School of Electrical, Electronics and Computer Engineering University of Newcastle-upon-Tyne

School of Electrical, Electronics and Computer Engineering University of Newcastle-upon-Tyne Baseband Digital Modulation Prof. Rolando Carrasco Lecture Notes University of Newcastle-upon-Tyne 2007. Baseband digital information. Bit-rate, Baud-rate and Bandwidth.

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School of Electrical, Electronics and Computer Engineering University of Newcastle-upon-Tyne

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  1. School of Electrical, Electronics and Computer Engineering University of Newcastle-upon-Tyne Baseband Digital Modulation Prof. Rolando Carrasco Lecture Notes University of Newcastle-upon-Tyne 2007

  2. Baseband digital information

  3. Bit-rate, Baud-rate and Bandwidth denotes the duration of the 1 bit Hence Bit rate = bits per second All the forms of the base band signalling shown transfer data at the same bit rate. denotes the duration of the shortest signalling element. Baud rate is defined as the reciprocal of the duration of the shortest signalling element. Baud Rate = baud In general Baud Rate ≠ Bit Rate For NRZ : Baud Rate = Bit Rate RZ : Baud Rate = 2 x Bit Rate Bi-Phase: Baud Rate = 2 x Bit Rate AMI: Baud Rate = Bit Rate

  4. Non Return to Zero (NRZ) The highest frequency occurs when the data is 1010101010……. i.e. This sequence produces a square wave with periodic time Fourier series for a square wave, If we pass this signal through a LPF then the maximum bandwidth would be 1/T Hz, i.e. to just allow the fundamental (1st harmonic) to pass.

  5. Non Return to Zero (NRZ) (Cont’d) The data sequence 1010…… could then be completely recovered Hence the minimum channel bandwidth

  6. Return to Zero (RZ) Considering RZ signals, the max frequency occurs when continuous 1’s are transmitted. . This produces a square wave with periodic time If the sequence was continuous 0’s, the signal would be –V continuously, hence

  7. Bi-Phase Maximum frequency occurs when continuous 1’s or 0’s transmitted. This is similar to RZ with Baud Rate = = 2 x Bit rate The minimum frequency occurs when the sequence is 10101010……. e.g. In this case = Baud Rate = Bit rate

  8. Digital Modulation and Noise The performance of Digital Data Systems is dependent on the bit error rate, BER, i.e. probability of a bit being in error. Prob. of Error or BER, Digital Modulation There are four basic ways of sending digital data • The BER (P) depends on several factors • the modulation type, ASK FSK or PSK • the demodulation method • the noise in the system • the signal to noise ratio

  9. Digital Modulation and Noise Amplitude Shift Keying ASK

  10. Digital Modulation and Noise Frequency Shift Keying FSK

  11. Digital Modulation and Noise Phase Shift Keying PSK

  12. System Block diagram for Analysis DEMODULATOR – DETECTOR – DECISION For ASK and PSK

  13. Demodulator-Detector-Decision FOR FSK

  14. Demodulator

  15. Demodulator Cont’d)

  16. Detector-Decision - is the voltage difference between a ‘1’ and ‘0’.

  17. Detector-Decision (Cont’d) ND is the noise at the Detector input. Probability of Error, Hence

  18. Probability density of binary signal

  19. Probability density function of noise (*) Using the change of variable

  20. This becomes (**) The incomplete integral cannot be evaluated analytically but can be recast as a complimentary error function, erfc(x), defined by Equations (*) and (**) become

  21. It is clear from the symmetry of this problem that Pe0 is identical to Pe1 and the probability of error Pe, irrespective of whether a ‘one’ or ‘zero’ was transmitted, can be rewritten in terms of v = v1 – v0 • for unipolar signalling (0 and v) • for polar signalling (symbol represented by voltage

  22. Detector-Decision (Cont’d)

  23. Detector-Decision (Cont’d)

  24. FM/ FSK Demodulation One form of FM/FSK demodulator is shown below In general VIN (t) will be Where is the input frequency (rad/sec)

  25. FM/ FSK Demodulation (Cont’d) i.e Thus there are two components Component (1) is at frequency 2 fIN Hz and component (2) is effectively a ‘DC’ voltage if is constant. The cut-off frequency for the LPF is designed so that component (1) is removed and component (2) is passed to the output.

  26. FM/ FSK Demodulation (Cont’d) The V/F characteristics and inputs are shown below Analogue FM Modulation Index

  27. FM/ FSK Demodulation (Cont’d) The spectrum of the analogue FM signal depends on and is given by

  28. Digital FSK Normalized frequency Deviation ratio The spectrum of FSK depends on h

  29. Digital FSK (Cont’d)

  30. FM/ FSK Demodulation (Cont’d) Consider again the output from the demodulator The delay is set to where and is the nominal carrier frequency Hence

  31. FM/ FSK Demodulation (Cont’d) The curve shows the demodulator F/V characteristics which in this case is non linear.

  32. Practical realization of F/V process The comparator is LIMITER – which is a zero crossing detector to give a ‘digital’ input to the first gate. This is form of ‘delay and multiply’ circuit where the delay is set by C and R with = CR

  33. Practical realization of F/V process (Cont’d)

  34. Practical realization of F/V process (Cont’d) Consider now ≠

  35. Practical realization of F/V process (Cont’d) Plotting Vout versus (Assuming A=1)

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