PULSE MODULATION

1. PULSE MODULATION CHAPTER 4 Part 1 EKT343 –Principle of Communication Engineering

2. Chapter Outline PART 1: • Basic sampling technique • Generation and recovery • Pulse Amplitude Modulation (PAM) • Pulse Duration Modulation (PDM) • Pulse Position Modulation (PPM) • Advantages & Disadvantages EKT343 –Principle of Communication Engineering

3. Sampling • To convert a signal from continuous time to discrete time, a process called sampling is used.  The value of the signal is measured at certain intervals in time. Each measurement is referred to as a sample.  • When the continuous analog signal is sampled at a frequency F, the resulting discrete signal has more frequency components than did the analog signal.  To be precise, the frequency components of the analog signal are repeated at the sample rate.  EKT343 –Principle of Communication Engineering

4. Sampling • Sampling a signal: Analog → Digital conversion by reading the value at discrete points • A process of taking samples of information signal at a rate of Nyquist’s sampling frequency. EKT343 –Principle of Communication Engineering

5. Nyquist’s Sampling Theorem : The original information signal can be reconstructed at the receiver with minimal distortion if the sampling rate in the pulse modulation system equal to or greater than twice the maximum information signal frequency. fs >= 2fm (max) EKT343 –Principle of Communication Engineering

6. infinite bandwidth cannot be sampled. • the sampling rate must be at least 2 times the highest frequency, not the bandwidth. EKT343 –Principle of Communication Engineering

7. Example 1 A complex low-pass signal has a bandwidth of 200 kHz. What is the minimum sampling rate for this signal? Solution: The bandwidth of a low-pass signal is between 0 and f, where f is the maximum frequency in the signal. Therefore, we can sample this signal at 2 times the highest frequency (200 kHz). The sampling rate is therefore 400,000 samples per second. EKT343 –Principle of Communication Engineering

8. Example 2 A complex bandpass signal has a bandwidth of 200 kHz. What is the minimum sampling rate for this signal? Solution : We cannot find the minimum sampling rate in this case because we do not know where the bandwidth starts or ends. We do not know the maximum frequency in the signal. EKT343 –Principle of Communication Engineering

9. Undersampling & Oversampling • Undersampling is essentially sampling too slowly, or sampling at a rate below the Nyquist frequencyfor a particular signal of interest. Undersampling leads to aliasing and the original signal cannot be properly reconstructed • Oversampling is sampling at a rate beyond twice the highest frequencycomponent of interest in the signal and is usually desired. EKT343 –Principle of Communication Engineering

10. Aliasing effect • If the required condition of the sampling theorem that fs >= 2fmmax is not met, then errors will occur in the reconstruction. • When such errors arise due to undersampling, aliasing is said to occur • Undersampling: Sampling rate is too low to capture high-frequency variation EKT343 –Principle of Communication Engineering

11. Aliasing effect EKT343 –Principle of Communication Engineering

12. Example 3 For an intuitive example of the Nyquist theorem, let us sample a simple sine wave at three sampling rates: a) fs = 2f (Nyquist rate) b) fs = 4f (2 times the Nyquist rate), c) fs = f (one-half the Nyquist rate). Figure shows the sampling and the subsequent recovery of the signal. SOLUTION: It can be seen that sampling at the Nyquist rate can create a good approximation of the original sine wave (part a). Oversampling in part b can also create the same approximation, but it is redundant and unnecessary. Sampling below the Nyquist rate (part c) does not produce a signal that looks like the original sine wave.

13. Recovery of a sampled sine wave for different sampling rates EKT343 –Principle of Communication Engineering

14. Natural Sampling • Tops of the sample pulses retain their natural shape during the sample interval. • Frequency spectrum of the sampled output is different from an ideal sample. • Amplitude of frequency components produced from narrow, finite-width sample pulses decreases for the higher harmonics • Requiring the use of frequency equalizers EKT343 –Principle of Communication Engineering

15. Natural Sampling EKT343 –Principle of Communication Engineering

16. Flat-top Sampling • Common used in PCM systems. • Accomplish in a sample-and-hold circuit • To periodically sample the continually changing analog input voltage & convert to a series of constant-amplitude PAM voltage levels. • The input voltage is sampled with a narrow pulse and then held relatively constant until the next sample is taken. EKT343 –Principle of Communication Engineering

17. Cont’d… • Sampling process alters the frequency spectrum & introduces aperture error. • The amplitude of the sampled signal changes during the sample pulse time. • Advantages: • Introduces less aperture distortion • Can operate with a slower ADC EKT343 –Principle of Communication Engineering

18. Flat-top Sampling EKT343 –Principle of Communication Engineering

19. ANALOG PULSE MODULATION (PM) • Sampling analog information signal • Converting samples into discrete pulses • used to represent an analog signal with digital data • among the first of the pulse techniques to be utilized • Carrier signal is pulse waveform and the modulated signal is where one of the carrier signal’s characteristic (either amplitude, width or position) is changed according to information signal. EKT343 –Principle of Communication Engineering

20. Pulse Amplitude Modulation (PAM) • The amplitude of pulses is varied in accordance with the information signal. • Width & position constant. • 2 types – • double polarity • single polarity EKT343 –Principle of Communication Engineering

21. Natural Sampling (PAM) • A PAM signal is generated by using a pulse train, called the sampling signal (or clock signal) to operate an electronic switch or "chopper". This produces samples of the analog message signal, as shown in Figure EKT343 –Principle of Communication Engineering

22. Flat Top Sampling (PAM) • a sample-and-hold circuit is used in conjunction with the chopper to hold the amplitude of each pulse at a constant level during the sampling time Flat-top sampling – generation of PAM signals. EKT343 –Principle of Communication Engineering

23. Cont’d • Pulse duration (τ) supposed to be very small compare to the period, Ts between 2 samples • Lets max frequency of the signal, W • If ON/OFF time of the pulse is same, frequency of the PAM pulse is Fs >= 2 W Ts =< 1/2W T « Ts =< 1/2W EKT343 –Principle of Communication Engineering

24. Transmission BW of PAM Signal • Bandwidth required for transmitter of PAM signal will be equal to maximum frequency EKT343 –Principle of Communication Engineering

25. Advantages & Disadvantages PAM • Advantage: • it allows multiplexing, i.e., the sharing of the same transmission media by different sources (or users). This is because a PAM signal only occurs in slots of time, leaving the idle time for the transmission of other PAM signals. • Disadvantage: • require a larger transmission bandwidth (very large compare to its maximum frequency) • Interference of noise is maximum • Needed for varies transmission power EKT343 –Principle of Communication Engineering

26. Pulse Density Modulation (PDM) • Sometimes called Pulse Duration Modulation/ Pulse Width Duration (PWM). • The width of pulses is varied in accordance to information signal • Amplitude & position constant. • PDM is used in a great number of applications Communications • The width of the transmitted pulse corresponds to the encoded data value EKT343 –Principle of Communication Engineering

27. PDM • Immune to noise • Power Delivery • Reduce the total amount of power delivered to a load • Applications: DC Motors, Light Dimmers, Anti-Lock Breaking System EKT343 –Principle of Communication Engineering

28. PWM signal output is generated by comparing summation result with reference level EKT343 –Principle of Communication Engineering

29. Cont’d... EKT343 –Principle of Communication Engineering

30. Advantages & Disadvantages PDM • Advantage: • Noise performance is better compare to PAM. • Disadvantages: • require a larger power transmission compare to PPM • Require very large bandwidth compare to PAM EKT343 –Principle of Communication Engineering

31. Pulse Position Modulation (PPM) • Modulation in which the temporal positions of the pulses are varied in accordance with some characteristic of the information signal. • Amplitude & width constant. • The higher the amplitude of the sample, the farther to the right the pulse is position within the prescribed time slot. EKT343 –Principle of Communication Engineering

32. Advantages & Disadvantages PPM • Advantage: • The amplitude is held constant thus less noise interference. • Signal and noise separation is very easy • Due to constant pulse widths and amplitudes, transmission power for each pulse is same. • Require less power compare to PAM and PDM because of short duration pulses. • Disadvantages: • Require very large bandwidth compare to PAM. EKT343 –Principle of Communication Engineering

33. Transmission BW of PDM/PPM Signal • PPM and PDM need a sharp rise time and fall time for pulses in order to preserve the message information. • Lets rise time, tr • From formula above, we know that transmission BW of PPM and PDM is higher than PAM tr« Ts EKT343 –Principle of Communication Engineering

34. Transmission BW of PAM Signal • Pulse duration (τ) supposed to be very small compare to the period, Ts between 2 samples • Lets max frequency of the signal, W • If ON/OFF time of the pulse is same, frequency of the PAM pulse is Fs >= 2 W Ts =< 1/2W T « Ts =< 1/2W EKT343 –Principle of Communication Engineering

35. Example 4 • For PAM transmission of voice signal with W = 3kHz. Calculate BT if fs = 8 kHz and τ= 0.1 Ts • SOLUTION EKT343 –Principle of Communication Engineering

36. Example 5 • For the same information as in example 1, find minimum transmission BW needed for PPM and PDM. Given tr= 1% of the width of the pulse. SOLUTION EKT343 –Principle of Communication Engineering

37. Pulse Modulation EKT343 –Principle of Communication Engineering

38. EKT343 –Principle of Communication Engineering

39. PAM, PWM, PPM EKT343 –Principle of Communication Engineering

40. Advantages & Drawbacks of Pulse Modulation • Noise immunity. • Relatively low cost digital circuitry. • Able to be time division multiplexed with other pulse modulated signal. • Storage of digital streams. • Error detection & correction • Requires greater BW to transmit & receive as compared to its analog counterpart. • Special encoding & decoding methods must be used to increased transmission rates & more difficult to be recovered. • Requires precise synchronization of clocks between Tx & Rx. EKT343 –Principle of Communication Engineering