Exercise 3-1 PAM Signals Demodulation EXERCISE OBJECTIVE When you have completed this exercise you will be able to demonstrate the recovery of the original message signal from a PAM signal using the PAM Receiver. DISCUSSION OUTLINE The Discussion of this exercise covers the following points: Filtering Aperture distortion DISCUSSION Filtering The technique most commonly used for demodulating PAM signals is low-pass filtering. A low-pass filter has the effect of averaging or "smoothing out" the PAM signal. The result is a reconstruction of the original message signal from the samples in the PAM signal. Figure 3-2 shows the sampling of a sine wave message signal. Figure 3-2. Reconstruction of original message signal using a low-pass filter. Festo Didactic 39862-00 99
Ex. 3-1 PAM Signals Demodulation Discussion The sampling rate is greater than the Nyquist rate (greater than twice the frequency of the sine wave). The PAM signal follows the waveform of the message signal. When the PAM signal is "smoothed out" using a low-pass filter, the resulting signal is a faithful reproduction of the original message signal. Observations in the frequency domain help to illustrate the demodulation of PAM signals. The PAM signal spectrum contains the message signal as well as replicas of the message signal. The low-pass filter in the PAM Receiver removes the replicas from the PAM signal spectrum, leaving only the message signal. Proper demodulation of the PAM signal results in accurate reconstruction of the original message signal. This is only possible when the following conditions are met: the message signal is band-limited, the sampling rate is sufficiently high and the filter characteristics are correctly chosen. Figure 3-3 shows the PAM spectrum of a band-limited message signal sampled at the Nyquist rate. An ideal filter, which passes all frequencies up to fmax equally well, but completely eliminates all those above fmax, could be used to reconstruct the message signal. Figure 3-3. f s = 2f max (Nyquist rate), Ideal filter. Such an ideal low-pass filter, however, is impossible to build. Practical low-pass filters have a gradual rolloff, although the rolloff can be quite sharp. For this reason, the sampling rate must be somewhat greater than the Nyquist rate. In Figure 3-4, the sampling rate used is greater than the Nyquist rate. A practical low-pass filter could be used to remove the replicas, leaving the message signal. The cutoff frequency of the filter must be carefully chosen. If the cutoff frequency is too high, part of the first replica will appear in the reconstructed signal. If it is too low, some of the frequency components of the message signal may be severely attenuated. A cutoff frequency of 3.4 khz for the filter in a PAM receiver allows good reception of the ITU (International Telecommunications Union) standard bandwidth signals. Figure 3-4. f s > 2f max High-order filter. 100 Festo Didactic 39862-00
Ex. 3-1 PAM Signals Demodulation Discussion In Figure 3-5, the sampling rate and the cutoff frequency of the low-pass filter are the same as in Figure 3-4. The response of the filter, however, is different. In Figure 3-5, the rolloff is not sufficiently sharp. As a result, the filter passes part of the first replica. Reducing the cutoff frequency of the filter would prevent it from passing part of the first replica, but this would attenuate part of the message signal. Increasing the order of the filter to produce a sharper rolloff, or increasing the sampling rate to spread out the spectral groupings would allow proper demodulation. Figure 3-5. f s > 2f max Low-order filter. The order of the filter affects how well it operates as a PAM receiver. High-order filters, usually fifth order or greater, are used in PAM receivers. Such filters have sharp rolloff characteristics which allow them to remove the unwanted frequency components without affecting the message signal. Because of the averaging effect of a low-pass filter, the power, and therefore the amplitude of the reconstructed signal varies with the power of the PAM signal. Increasing the pulse duty cycle or the peak-to-peak amplitude of the PAM signal causes the amplitude of the reconstructed signal to increase. Aperture distortion When the pulses of the sampling signal are narrow, the sampling method used (natural or flat-top) has little effect on the PAM signal. When the pulses are wide, and the sampling rate is only slightly greater than the Nyquist rate, the sampling method used does affect the PAM signal. With natural sampling, the attenuation of the frequency components is uniform within each element in the spectrum, as in Figure 3-6. Figure 3-6. PAM signal spectrum, natural sampling. With flat-top sampling, however, the degree of attenuation follows the envelope of the spectrum, as in Figure 3-7. Festo Didactic 39862-00 101
Ex. 3-1 PAM Signals Demodulation Procedure Outline Figure 3-7. PAM signal spectrum, flat-top sampling. This causes the higher frequencies in the message signal spectrum to be attenuated, as shown in Figure 3-8. This attenuation is called aperture distortion. In the reconstructed message signal, the higher frequencies will be slightly attenuated as compared to the original message signal. This distortion can be easily corrected by passing the reconstructed signal through a compensating network. When the duty cycle of the sampling signal is less than 10%, aperture distortion is negligible, and no compensation is required. Figure 3-8. Aperture distortion. PROCEDURE OUTLINE The Procedure is divided into the following sections: Set-up and connections PAM demodulation in the time domain PAM demodulation in the frequency domain PROCEDURE Set-up and connections 1. Turn on the RTM Power Supply and the RTM and make sure the RTM power LED is lit. File Restore Default Settings returns all settings to their default values, but does not deactivate activated faults. Double-click to select SWapp 2. Start the LVCT software. In the Application Selection box, choose PAM and click OK. This begins a new session with all settings set to their default values and with all faults deactivated. b If the software is already running, choose Exit in the File menu and restart LVCT to begin a new session with all faults deactivated. 102 Festo Didactic 39862-00
Ex. 3-1 PAM Signals Demodulation Procedure 3. Make the Default external connections shown on the System Diagram tab of the software. For details of connections to the Reconfigurable Training Module, refer to the RTM Connections tab of the software. b Click the Default button to show the required external connections. 4. As an option, connect a conventional oscilloscope or spectrum analyzer to the PAM Receiver OUTPUT using BNC T-connector. PAM demodulation in the time domain 5. Make the following Generator Settings: Function Generator A: Function... Sine Frequency (Hz)... 800 Function Generator B: Function... Pulse Frequency (Hz)... 8 000 Duty Cycle (%)... 50 Apply Duty Cycle to Clock... On 6. Click the PAM Generator tab in order to display the PAM Generator diagram. On the PAM Generator, ensure that Flat is selected for the Mode for flat-top sampling. Show the Probes bar (click in the toolbar or choose View Probes Bar). Connect Oscilloscope E probe to TP1 to observe the message signal. 7. Click the PAM Receiver tab in order to display the PAM Receiver diagram. On the PAM Receiver, select a 6 th order Low-Pass Filter and set the Cutoff Frequency of the filter to the maximum value of 8 khz. Ensure that the Gain is set to 1. Festo Didactic 39862-00 103
Ex. 3-1 PAM Signals Demodulation Procedure Connect the other oscilloscope probes as follows: Oscilloscope Probe Connect to Signal 1 TP1 PAM Receiver INPUT 2 TP3 PAM Receiver OUTPUT Oscilloscope Settings: Channel 1... 500 mv/div Channel 2... 500 mv/div Channel E... 1 V/div Time Base... 0.5 ms/div Trigger Slope... Rising Trigger Level... 0.5 V Trigger Source... Ext 8. Show the Oscilloscope (click in the toolbar or choose Instruments Oscilloscope). Figure 3-9 shows an example of settings and what you should observe. Figure 3-9. Message, PAM generated and PAM reconstructed signal; 8 khz receiver filter. In what way does the filtered PAM signal (PAM Receiver OUTPUT) resemble the original message signal? What is different about the two signals? 104 Festo Didactic 39862-00
Ex. 3-1 PAM Signals Demodulation Procedure Oscilloscope Settings: Channel 1... 500 mv/div Channel 2... 500 mv/div Channel E... 1 V/div Time Base... 0.5 ms/div Trigger Slope... Rising Trigger Level... 0.5 V Trigger Source... Ext 9. Slowly decrease the Receiver Low-Pass Filter Cutoff Frequency to 3.4 khz. At 3.4 khz, the output should resemble Figure 3-10. Figure 3-10. Message, PAM generated and PAM reconstructed signal; 3.4 khz receiver filter. What effect does reducing the Receiver Low-Pass Filter Cutoff Frequency have on the PAM Receiver OUTPUT? Does the PAM Receiver OUTPUT now resemble the original message signal? Explain. (Ignore the difference in phase between the two signals). 10. Turn Channel 1 Visible and Channel E Visible to Off on the oscilloscope in order to better observe the PAM Receiver OUTPUT. The output should resemble Figure 3-11. Festo Didactic 39862-00 105
Ex. 3-1 PAM Signals Demodulation Procedure Oscilloscope Settings: Channel 1... OFF Channel 2... 200 mv/div Channel E... OFF Time Base... 0.5 ms/div Trigger Slope... Rising Trigger Level... 0 V Trigger Source... Ch 2 Figure 3-11. PAM received signal with 6 th order receiver filter. Change the Order of the PAM Receiver Low-Pass Filter and observe the effects on the reconstructed signal. b The memory locations on the oscilloscope can be used to observe all resulting signals simultaneously. Click M1 or M2 in the instrument toolbar to store the current display in Memory 1 or Memory 2. Use the Memories setting to show the contents of Memory 1, Memory 2, or both. What impact does changing the Order of the PAM Receiver Low-Pass Filter have on the PAM Receiver OUTPUT? Explain. 11. Restore the settings so that the output again resembles Figure 3-11. On the PAM Generator, vary the Gain from the Min to the Max value. What effect does this have on the reconstructed signal? 106 Festo Didactic 39862-00
Ex. 3-1 PAM Signals Demodulation Procedure Vary the Duty Cycle of the sampling signal (Function Generator B). What effect does this have on the reconstructed signal? PAM demodulation in the frequency domain 12. Use the command File Restore Default Settings to return all of the settings to their default values. Make the following Generator Settings: Function Generator A: Function... Sine Frequency (Hz)... 1 000 Function Generator B: Function... Pulse Frequency (Hz)... 8 000 Duty Cycle (%)... 50 Apply Duty Cycle to Clock... On 13. Click the PAM Generator tab in order to display the PAM Generator diagram. Ensure that the Gain on the PAM Generator is set back to the maximum value of 1 and that the Mode is set to Nat. 14. Click the PAM Receiver tab in order to display the PAM Receiver diagram. Ensure that the PAM Receiver Low-Pass Filter is set to 6 th order and the Cutoff Frequency is at the maximum value of 8 khz. Show the Probes bar (click in the toolbar or choose View Probes Bar). Connect the Spectrum Analyzer probe to TP3 to observe the PAM Receiver OUTPUT. 15. Show the Spectrum Analyzer (click in the toolbar or choose Instruments Spectrum Analyzer). Figure 3-12 shows an example of settings and what you should observe. Festo Didactic 39862-00 107
Ex. 3-1 PAM Signals Demodulation Procedure Spectrum Analyzer Settings: Maximum Input... 0 dbv Scale Type... Logarithmic Scale... 5 dbv/div Averaging... 4 Time Window... Square Frequency Span... 2 khz/div Reference Frequency... 0 khz Figure 3-12. PAM reconstructed spectrum with 8 khz filter. Capture the output to the Spectrum Analyzer. Identify the message signal and the first replica on the capture. Spectrum Analyzer Settings: Maximum Input... 0 dbv Scale Type... Logarithmic Scale... 5 dbv/div Averaging... 4 Time Window... Square Frequency Span... 2 khz/div Reference Frequency... 0 khz 16. Slowly decrease the Receiver Low-Pass Filter Cutoff Frequency to 3.4 khz. At 3.4 khz, the output should resemble Figure 3-13. Figure 3-13. PAM reconstructed spectrum with 3.4 khz filter. What effect does reducing the Receiver Low-Pass Filter Cutoff Frequency have on the PAM Receiver OUTPUT spectrum? 108 Festo Didactic 39862-00
Ex. 3-1 PAM Signals Demodulation Conclusion Does the spectrum of the reconstructed signal resemble that of a sine wave signal? Explain. 17. Make the following Generator Settings: Function Generator A: Function... Sine Frequency (Hz)... 3 400 Function Generator B: Function... Pulse Frequency (Hz)... 8 000 Duty Cycle (%)... 95 Apply Duty Cycle to Clock... On 18. The duty cycle of the sampling signal is very large. The frequency of the message signal is relatively high (3.4 khz) compared to the Nyquist rate (fs / 2 = 4 khz). Under these conditions, what is the effect of changing the PAM Generator mode from natural to flat-top sampling on the PAM Receiver OUTPUT? What phenomenon is responsible for this effect? 19. When you have finished using the system, exit the LVCT software and turn off the equipment. CONCLUSION In this exercise, you demonstrated how a low pass filter can be used to reconstruct the original message signal by demodulating the PAM signal. You observed, in the time domain, that the filter averages or "smoothes out" the PAM signal, and that the order of the filter affects the quality of the reconstructed signal. You observed, in the frequency domain, that the filter removes the replicas from the PAM spectrum, leaving only the message signal. You demonstrated that increasing the pulse duty cycle, or the peak-to-peak amplitude of the PAM signal increases the amplitude of the reconstructed signal. You also observed the attenuation of higher frequencies in the reconstructed signal due to the aperture distortion when the pulse duty cycle of the sampling signal is large, and the sampling rate is low. Festo Didactic 39862-00 109
Ex. 3-1 PAM Signals Demodulation Review Questions REVIEW QUESTIONS 1. Explain the operation of a PAM receiver as seen in the time domain. 2. What effect does varying the duty cycle of the sampling signal have on the amplitude of the reconstructed signal? 3. Explain the operation of PAM receiver, as seen in the frequency domain. 4. Under what conditions are the higher frequencies in the message signal attenuated due to aperture distortion? 5. What would be the effect of insufficient filtering in a PAM receiver? 110 Festo Didactic 39862-00