Department of Electronic and Information Engineering Communication Laboratory. Sampling and Time Division Multiplexing

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1 Department of Electronic and Information Engineering Communication Laboratory Sampling and Time Division Multiplexing Objective To investigate sampling and time division multiplexing techniques. Background Knowledge (1) Sampling Concept The sampling of an analog signal consists of checking signal amplitude at regular sampling interval (T). Shannon/Nyquist shows that the sampling frequency, F s = 1/T, must be at least twice the maximum baseband frequency F s >2F max. Otherwise, the baseband and harmonics would overlap and cause distortion. It would not be possible to recover the original signal. This overlapping of the spectra is called aliasing. In practice, a sampling frequency quite well above 2F max is normally used. Pulse Amplitude Modulation (PAM) Pulse Amplitude Modulation (PAM) is considered the first step in analog-to-digital conversion. PAM samples an analog signal before generating a series of pulses based on the results of sampling. A PAM signal is a signal that has had a proportion of its waveform removed at regular intervals leaving behind a series of pulses whose amplitudes describe the original waveform. It is a foundation of pulse code modulation (PCM), another analog to digital conversion method. Figure 1: General waveform of PAM. Sample and Hold A waveform can be represented by a sequence of pulses, snapshots of the waveform at equally spaced intervals. These pulses are known as samples. Provided that there are enough samples, i.e. that the sample frequency is high enough, the original signal can be completely recovered from its sampled equivalent. To restore a Pulse Amplitude Modulation (PAM), it is only necessary to sample the PAM waveform when it is non-zero, and then filter the sampled waveform to re-produce the original signal. To make the recovered signal less vulnerable to noise, it is useful to hold the last sample until the next one is taken. This is known as sample and hold. Figure 2: Sample and hold. 1

2 A signal is sampled by connecting it quickly to a capacitor via a switch. While the signal is connected, the capacitor is charged until it soon reaches the level of the signal. The time constant of the charging circuit is made as small as possible so that the time taken to reach the signal level is minimal. When the switch disconnects the signal from the capacitor, the level that the capacitor had reached at that point is held due to the high impedance input of the buffer amplifier, which aims to prevent the capacitor discharging. The waveform that is seen at the output of the buffer amplifier resembles a series of steps, the leading edges of which are rounded off due to the capacitor being charged to the next level at this point. (2) Aliasing A waveform can be represented by a sampled waveform made up of samples of the original signal taken at equally spaced intervals. To ensure that the sampled signal contains enough information to enable the original signal to be regenerated without distortion, the Nyquist frequency at which samples are taken needs to be at least twice that of the highest frequency component in the original signal. Otherwise, the original waveform cannot be recovered because aliasing occurs. The result of this is that the recovered signal appears to be one of much lower frequency, as shown in Figure 3. Figure 3:Aliasing (3) Multiplexing Multiplexing is the term given to describe the transmission of two or more signals down a common channel. The reason for multiplexing signals is to economise on channel or link usage and to be able to covey the maximum amount of information down any given link. If two, or more, signals can use the same cable, at the same time, then the link will be running more efficiently and the cost of the service to each will be lower. There are two common forms of multiplexing used in communications: Time Division Multiplexing (TDM) and Frequency Division Multiplexing (FDM). Time Division Multiplexing TDM is the process of switching between two, or more, signals serially in time. When a signal is sampled by narrow pulses there are large intervals between the samples in which no signal exists. It is possible to transmit and interleave the samples of other signals in the periods between those of the first one and to continue them in one waveform. TDM allows simultaneous transmission of several signals over a single wideband link. The switches at transmitter and receiver are synchronised and perform the sampling and interlacing. Consider a set of N independent messages: m1(t), m2(t),...mn(t), each strictly bandlimited to f < W. If these are sampled at F s = 1/T = 2W, each results in a PAM signal with F s samples per second. With the sampling for each message offset by a time 2

3 interval T/N the various sampled signals can be added together to produce a composite TDM signal. Interleaved Sampling of Two waveforms Multiplexed Samples Figure 4: Two signals are multiplexed to produce a composite TDM signal. Often, instead of each sample being momentary, the sampled values are held until the next sample comes along. This is called sample and hold, which is described before. An example of a time-division multiplexed, sample and hold waveform is shown in Figure 5. Figure 5: Analogue TDM, sample and hold waveform. (4) Analogue-to-Digital Converter Before an analogue signal can be transmitted down a digital link, it must be converted to digital form. This may be done by an analogue-to-digital (A/D) converter. Each sampled value of the analogue waveform is applied to the input of the A/D converter in sequence and a digital value is obtained for each. This process is known as digitising or encoding. A simple code often used when analogue waveforms are digitised in the Binary Coded Decimal (BCD) code. The number of bits in the digital output of an A/D converter is fixed by the circuit design of the converter. Typical converters have 8, 12, or 16-bit output codes. Any given A/D converter can only cope with analogue input voltages over a limited range. This means that this finite input range is converted to a digital output which has a limited number of bits. An 8-bit converter can give an output of one of 256(2 8 ) digital words. 3

4 (5) Digital TDM In a similar way that analogue waveforms may be interleaved in time to give analogue TDM, digital words may be multiplexed to give digital TDM. For example: if two digital data streams are: Word Stream A Stream B these may be multiplexed as the digitally multiplexed data stream in the sequence: A1 B1 A2 B2 A3 B3 A4 B4 A5 B If the bit rate of each of the multiplexed signals is maintained, it will take a longer time to transmit the multiplexed data than it would for each individual stream alone. In the case of the example above, it would take twice as long. Therefore, a faster bit rate would be of advantage. However, the maximum bit rate that can be accommodated on any practical link is limited by the bandwidth of that link. Maximum bit rate = 2 x (bandwidth) If the bandwidth used is not sufficient, not only may information be lost, but also data from one of the channels may interfere with that from another. This interference can be reduced by increasing the bandwidth of the channel, however this may be wasteful of bandwidth and consequently expensive. An alternate method of reducing the intersymbol interference is by shaping the pulses so that they contain less high frequency components. (6) Digital-to-Analogue Conversion D/A Conversion is the reverse procedure to A/D Conversion. It converts the digital data corresponding to an analogue sample into analogue form. The converted output, stepped analogue waveform is normally filtered to remove the steps and produce a smooth waveform. The quantisation thus produces some distortion. The higher the number of bits in the digital word, the lower will be the quantisation noise and the lower will be the distortion in the output waveform. However, the higher the number of bits for the converters, the more expensive the system usually is. (7) Demultiplexing The multiplexed waveform, whether it is analogue or digitally multiplexed, has to be demultiplexed to retrieve the original constituent waveforms or data. The demultiplexing process is the opposite of multiplexing and the switching between channels must be synchronised with the multiplexing. If there is not synchronisation, the wrong information may be sent to the wrong destination, or corrupted data or waveforms may result. To achieve synchronisation, multiplexed data is normally grouped into Frames comprising one sample of the data from each of the required number of multiplexed channels plus synchronisation bit(s). 4

5 Reference 1. Ferrel G. Stremler, Introduction to Communication Systems 3 rd, Addison Wesley 2. Time Division Multiplexing 3. Multiplexing x/multiplex.html Equipment 1. PC Interface Box (RAT ) 2. Interface Card (serial No /1/72) 3. Digital Data Formatting Board PCM & Link Analysis Board Oscilloscope (only be used in part 2 experiment) 6. Feedback Power Supply PC with Discovery Software Preliminary Preparation 1. Connect the equipment as the following diagram and DO NOT turn on any power at this moment. Monitor Oscilloscope Computer Keyboard Interface RAT Interface Card Digital Data Formatting Board Figure 6: Setting. Power Supply 2. Switch on the Oscilloscope and set it as follows: Vert. Amp 0.5V/Div Hori. Amp 0.5ms/Div 3. Turn on the Computer first and connect the Digital Data Formatting Board to the Interface before switching on the FEEDBACK Power Supply Note: Connect the voltages of the Board to that of the Interface carefully, otherwise, the Board will be burnt! 4. In DOS Prompt mode, type <CD\FBTP> and then <START>. 5. Turn on the power. 6. Use the Mouse to click at the <System> in the Menu Bar and then select <Index>. 7. Click <30> in the list for Assignment 30 and then select <Yes> for this experiment. 8. Click at the <Practicals> in the Menu Bar, and select <Practical 2> for Part 1 experiment. 9. Use Channel 1 of the Oscilloscope to monitor any point on the Boards. 5

6 Experimental Procedures & Questions Part 1: Sample and Hold You will examine a PAM signal which is sampled by a sample and hold circuit. This circuit is driven by a periodic sample pulse at the sample frequency. The sampling frequency is matched automatically to the frequency of the PAM signal s pulses. The PAM signal can be changed in frequency, and the length of the sample pulse can be varied. Figure 7: Hardware configuration of part 1 experiment. 1. Select <Practical 2> in the Assignment Click at <Conditions> in the Menu Bar and select <oscilloscope>. 3. Observe the PAM signal <18> by changing the <signal frequency> control and the <signal level> control. 4. Observe the sample pulses at <3> and investigate the effect of altering the <sample time> control, which adjusts the length of the sample pulses. 5. Examine the sample and held signal <19> by varying the <sample time> control. Question 1: What happens to the signal <19> when the sample pulses at <3> are made very short? Explain briefly by considering the circuit in Figure Adjust the <sample time> control until the sample pulses at <3> are long. 7. Adjust the <signal frequency> control until the frequency of the PAM signal at <18> is large. 8. Observe the result of the signal and held signal <19>. Question 2: What happens to the signal <19> when the sample pulse is made long and the frequency of the PAM signal is made large? Explain briefly. Question 3: Why is there a buffer amplifier at the output of the sample and hold circuit? Question 4: What are the ideal requirements for the sample and hold circuit in terms of its sample time and its charging time constant? 6

7 Part 2: Aliasing A PAM signal of variable frequency is sampled at 4kHz, resulting in a sample and held signal. By adjusting the PAM signal s frequency over its full range, you will observe the effects of sampling at a rate which is below the Nyquist rate. Oscilloscope Figure 8: Hardware configuration of part 2 experiment. 1. Select <Practical 3> in the Assignment Click at <Conditions> in the Menu Bar and select <oscilloscope> to observe source signal <16> and the kilohertz value on the screen. 3. Connect the sampled and help signal <19> to the oscilloscope at the same time. 4. Adjust the <signal frequency> control over its whole range (from minimum/left to maximum/right) slowly and examined the resulting sampled signal <19>. Question 5: Describe what happens to the output signal <19> from the waveforms when the kilohertz value displayed is above 4kHz. 5. Re-adjust the <signal frequency> control until the sampled and held output signal <19> appears to become a square wave of constant amplitude at a certain frequency. 6. Connect <16> to the <oscilloscope> and then record the kilohertz value displayed. Question 6: What is the frequency of the PAM signal when this occurs? Why? Note: You have to follow the instructions below before starting the experiments left. 1. Turn off the power. 2. Replace the Digital Data Formatting (53-150) by the PCM & Link Analysis (53-170). 3. Turn on the power. 4. Use the Mouse to click at the <System> in the Menu Bar and then select <Index>. 5. Click <21> in the list for Assignment 21 and then select <Yes> for this experiment. 6. Click at the <Practicals> in the Menu Bar, and select <Practical 1> for Part 3 experiment. 7

8 Part 3: Analogue TDM Given that two analogue signals:1 and 2 may be switched manually, or automatically multiplexed. Signal 1 Signal 2 Multiplexer 23 MUX Sig. 1 Sig MUX Clock Figure 9: Hardware configuration of part 3 experiment. 1. Select <Practical 1> in the Assignment Set the <PCM bandwidth> control to maximum (turn the control to the right end). 3. Set the <noise level> control to minimum (turn the control to the left end). 4. Set all other controls to their mid positions. 5. Click the <MUX> button to switch to Signal 2. Question 7: What is the form of Signal 2 observed? 6. Adjust the <DC chan 0> control and observe the result. Question 8: What happens to Signal 2 after adjust the <DC chan 0> control? 7. Click the <MUX> button to switch to Signal 1. Question 9: What is the form of Signal 1 observed? 8. Reset the <DC chan 0> to its mid position. 9. Click at <Conditions> in the Menu Bar and select <Change MUX> to observe signal <23> from the oscilloscope. Question 10: Draw the waveform and explain the shape of the output signal <23>. 10. Adjust the <DC chan 0> control and observe the result. Question 11: Explain your observation. 8

9 Part 4: Time and Frequency Domain This part aims to examine that a variable dc voltage is applied to the input of an Analogue-to-Digital Converter. Figure 10: Hardware configuration of part 4 experiment. 1. Select <Practical 2> in the Assignment Set the <PCM bandwidth> control to maximum (turn the control to the right end). 3. Set the <Noise level> control to minimum (turn the control to the left end). 4. Set the <DC chan 1> control to minimum (turn the control to the left end). 5. Set all other controls to their mid positions. 6. Observe A/D output <21> on the screen. Question 12: What is the waveform displayed? 7. Turn up the <DC chan 1> control and observe the result. Question 13: Does the A/D output waveform change? 8. Reset the <DC chan 1> control to minimum. 9. Turn it up extremely slowly until there is a change in state visible. You will observe several changes during turning the <DC chan 1> control. Question 14: Describe your observation briefly. Question 15: What happens when the input dc level is increased to its maximum limit? 9

10 Part 5: Digital Multiplexed Signal You will investigate the digital alternative method of TDM. Given that Signal 1 and 2 are dc levels. Figure 11: Hardware configuration of part 5 experiment. 1. Select <Practical 3> in the Assignment Set the <PCM bandwidth> control to maximum (turn the control to the right end). 3. Set the <DC chan 0>, <DC chan 1> and <Noise level> controls to minimum (turn the control to the left end). 4. Set all other controls to their mid positions. Question 16: What is the yellow trace monitoring? 5. Change to observe signal <23> now. 6. The <DC chan 0> control adjusts Signal 1 represented by zero state, while the <DC chan 1> control adjusts Signal 2 represented by one state. 7. Adjust the <DC chan 0> and <DC chan 1> controls alternatively. Question 17: Do each dc channel have the same state? Any relationship between them? 8. Turn both controls to minimum. 9. Change the monitor point <20>. 10. Increase the <DC chan 0> control and observe the <oscilloscope>. Question 18: Does the digitised value of the dc level appear in the correct time-slot of the A/D output waveform? 11. Trun the <DC chan 0> to minimum. 12. Increase the <DC chan 1> control and observe the oscilloscope. Question 19: Does the digitised value of the dc level appear in the correct time-slot of the A/D output waveform? 13. Vary both the dc level controls and observe the results on the <oscilloscope>. 10

11 Part 6: Digital-to-Analogue Conversion The Digital Signal is a multiplexed waveform produced from a triangle wave and a dc level. Figure 12: Hardware configuration of part 6 experiment. 1. Select <Practical 4> in the Assignment Set the <PCM bandwidth> control to maximum (turn the control to the right end). 3. Set the <DC chan 0>, <DC chan 1> and <Noise level> controls to minimum (turn the control to the left end). 4. Set all other controls to their mid positions. 5. Observe signal <8> on the screen. 6. Adjust the <Data 0> control for synchronism. 7. Turn the <DC chan 0> control slowly. Question 20: Does the digital waveform vary? 13. Change to monitor point <24> on the screen. 14. Re-adjust the <DC chan 0> control slowly. Question 21: Does the digital waveform vary? Question 22: What form of waveform is this? Question 23: What now has to be done to retrieve the constituent analogue signals from this waveform? 11

12 Part 7: Demultiplexing The TDM is an analogue, sample-and-hold, multiplexed waveform produced from a triangle wave and a dc level. Demultiplexing helps to recover two multiplexed signals to the original ones. Figure 13: Hardware configuration of part 7 experiment. 1. Select <Practical 5> in the Assignment Set the <PCM bandwidth> control to maximum (turn the control to the right end). 3. Set the <DC chan 0>, <DC chan 1> and <Noise level> controls to minimum (turn the control to the left end). 4. Set all other controls to their mid positions. 5. Adjust the <Data 0> control for synchronism. 6. Observe signal <24> on the screen. 7. Adjust the <DC chan 0> control and observe the result. Question 24: Does the waveform look familiar? 8. Now, change to monitor <27> on the <oscilloscope>. 9. Adjust the <DC chan 0> control and observe the result. Question 25: Draw the waveform. Does the demultiplexed wave at this point correspond with the originating dc level? 10. Change to monitor <28> and observe the result from the <oscilloscope>. Question 26: Does the demultiplexed wave at this point correspond with the originating triangle wave? Question 27: Why do you think that the triangle has been round off and steppes in the shape during the A/D, multiplexing, D/A and demultiplexing processes? 12