MULTIPLEXING definition , techniques , Frequency , time Division Multiplexing (FDM) ,
DIGITAL MULTIPLEXERS
Inside this Chapter

• Introduction
• multiplexing
• A PAM/TDM System
• Introduction to Digital Multiplexers
• Classification of Digital Multiplexers
• Multiplexing Hierarchy for Digital Communication
• North American Hierarchy
• T Lines
• A PCM-TDM System (T1 Carrier System)
• E Lines

5.1       INTRODUCTION
In last two chapters, we have discussed the pulse analog modulation and pulse digital modulation methods. In this chapter, we shall discuss an important process in communication system known as multiplexing. In the articles to follow, we shall discuss what is multiplexing and what are the types of multiplexing and then proceed for a detailed aspects of multiplexing.
5.2       MULTIPLEXING
Multiplexing may be defined as a technique which allows many users to share a common communication channel simultaneously. There are two major types of multiplexing techniques. They are as under:
(i)         Frequency division multiplexing (FDM),
(ii)        Time division multiplexing (TDM).
5.2.1. Frequency Division Multiplexing (FDM)
(i)         Definition
This technique permits a fixed frequency band to every user in the complete channel bandwidth. Such frequency slot is allotted continuously to that user. As an example consider that the channel bandwidth is 1 MHz. Let there be ten users, each requiring upto 100 kHz bandwidth. Then the complete channel bandwidth of 1 MHz can be divided into ten frequency bands, i.e. each of 100 kHz and every user can be allotted one independent frequency band. This technique is known as Frequency Division Multiplexing (FDM).
(ii) Main Application Area

 DO YOU KNOW? The number of simultaneous conversations that can be transmitted using FDM depends on the total bandwidth available which in turn, varies with the medium.

It is mainly used for modulated signal. This is due to the fact that a modulated signal can be placed in any frequency band by just changing the carrier frequency. However, at the receiver, these frequency multiplexed signals can be separated by the use of tuned circuits (i.e., bandpass filters) of their respective frequency band. And for every band, there are independent tuned circuits and demodulators.
5.2.2. Time Division Multiplexing (TDM)
(i)         Definition
As discussed earlier, in PAM, PPM and PDM, the pulse is present for a short duration and for most of the time between the two pulses, no signal is present. This free space between the pulses can be occupied by pulses from other channels. This is known as Time Division Multiplexing (TDM). Thus, time division multiplexing (TDM) makes maximum utilization of the transmission channel.
(ii)        Comparision with FMM
Hence, we can say that in FDM, all the signals are transmitted simultaneously over the same communication medium, and the signals occupy frequency slots. However, in TDM, the signals to be multiplexed are transmitted sequentially one after the other. Each signal occupies a short time slot as shown in figure 5.1. Thus, the signals are isolated from each other in the time domain, but all of them occupy the same slot in the frequency spectrum. Therefore, in TDM, the complete bandwidth of the communication channel is available to each signal being transmitted.
(iii)       Conceptual Diagram
Figure 5.1 shows the concept of TDM.
DIAGRAM
FIGURE 5.1 I0llustration of TDM concept
(iv)       Concep of Frame in TDM
At this stage, it may be noted that in context of TDM, we define one important term i.e., frame. One frame corresponds to the time period required to transmit all the signals once on the transmission channel. This has been shown in figure 5.1. Here, we have total four message signals to be transmitted. Hence, one frame will correspond to the time period required to transmit all the four signals once on the channel.
The TDM system can be used to multiplex analog or digital signals, however it is more suitable for the digital signal multiplexing.
5.3       A PAM/DM SYSTEM
(i)         Definition
Now, let us discuss a PAM/TDM system. Infact, this system combines the concepts of PAM and TDM both as shown in figure 5.2.
(ii)        Working Principle
Her e, the multiplexer is a single pole rotating switch or commutator. This switch can be a mechanical switch or an electronic switch and it rotates at fs rotations per second. As the switch arm rotates, it is going to make contact with the position 1, 2, 3 or N for a short time. There are N analog signals, to be multiplexed, which are connected to these contracts. Hence, the switch arm will connect these N input signals one by one to the communication channel.
T  he waveform of a TDM signal which is being transmitted has been shwon in figure 5.3. It shows that the rotary switch samples each message during each of its rotations.
Since, each rotation corresponds to one frame, therefore, one frame is completed in Ts seconds where Ts = 1/fs.
DIAGRAM
FIGURE 5.2 Block diagram of a PAM/TDM system
Hence, the function of the commutator is two fold as under:
(i)         To take narrow sample of each input message at a rate fs which is higher than 2fm.
(ii)        To sequentially interleave the N samples inside the interval Ts = 1/fs.
Now, the multiplexed signal at the output of the commutator is applied to a pulse amplitude modulator. It converts the PAM pulses into a form suitable for transmission over the communication channel. The input message signals are passed through low pass filters before applying them, to the commutator. These filters are actually the antialiasing filters which avoid the aliasing. The cutoff frequency of each low pass filter (LPF) is fm Hz.
DIAGRAM
FIGURE 5.3 (a) Sampling of the first input (b) Multiplexed PAM signal transmitted on the transmission channel
At the receiving end of PAM/TDM system, the received signal is applied to a pulse amplitude demodulator which performs the reverse operation of pulse amplitude modulator. At the receiver, there is one more rotating switch or decommutator used for demultiplexing. It will be interesting to know that this switch must rotate at the same speed as that of the commutator at the transmitter and its position must be synchronized with commutator in order to ensure proper demultiplexing. The low pass filters (LPFs) on the receiver side are used for the reconstruction of the original message signals.
5.3.1.   Signaling Rate and its Determination in a PAM/TDM System
(i)         Definition
As a matter of fact, the signaling rate of a TDM system is defined as the number of pulses transmitted per second. It is represented by r.
(ii)        Derivation of Expressiion
Let us now derive an expression for the signaling rate of the PAM/TDM system in the form of following few points:
(i)         Let fm = maximum frequency of all the input signals x1 to xN.
(ii)        Therefore, as per Nyquist criterion, the sampling frequency fs ≥ 2fm. Hence, the speed of rotation of commutators is fs rotations per second with fs ≥ 2 fm.
(iii)       As shown in figure 5.4, one revolution of commutators corresponding to one frame contains sample from each input signal.
Hence, 1 revolution = 1 frame N pulses
DIAGRAM
FIGURE 5.4 Evaluation of number of pulses per second for PAM/TDM system.
(iv)       One frame period is (1/fs) i.e., Ts, seconds. Therefore, in Ts seconds, N number of pukes are transmitted. Hence, the pulse to pulse spacing within the frame is given by,
Pulse to pulse spacing  =
(v)        As the period of one pulse (ON + OFF) is (1/Nfs) seconds, the number of pulses per second is given by,
Number of pulses per second = Nfs
This is nothing but the signaling rate.
Therefore, signaling rate of a TDM system = r = Nfs pulses/second.
But as fs ≥ 2fm, therefore,
signaling rate of a TDM system = r ≥ 2Nfm pulses per second.
NOTE:           Tt may be noted that TDM system is supposed to have its signaling rate as high as possible. It is evident from the expression above that the signaling rate can be increased by increasing the sampling rate fs, and /or the number of input signals N.
BW = (signaling rate)
5.3.2.   Transmission and its Significant in PAM/TDM System
As a matter of filet, the multiplexed PAM signals can be received properly if and only if the transmitter and receiver commutators are synchronized to each other in terms of the speed and the position. In order to ensure synchronization, a marker pulse is introduced at the end of each frame in the transmitted signals as shown in figure 5.5.
DIAGRAM
FIGURE 5.5 Illustration of frame synchronization and detection.
The amplitude of this pulse is kept higher than the maximum permissible amplitude of the multiplexed channels. At the receiver end, the received signal is compared with a DC reference level. The comparator responds to only the marker pulse to produce output. Thus, the marker pulse is separated from the remaining multiplexed channels. Due to the introduction of synchronizing pulse, only three signals instead of four can now be transmitted.
5.3.4. Concept of Crosstalk in a PAM/TDM System
(i)         Definition
Crosstalk basically means interference between the adjacent TDM channels. Infact, it is an unwanted coupling of information from one channel to the other. The guard time ‘Tg‘ is the time spacing introduced between the adjacent TDM channels.
(ii)        Important Points
Let us note few important points about crosstalk as under:
(i)         The communication channel over which the TDM signal is travelling should ideally have an infinite bandwidth in order to avoid the signal distortion. However, in practice, all the communication channels have a finite bandwidth. Such channels are known as the bandlimited channels.
(ii)        Whenever, a signal is passed over such bandlimited channel, the shape of the signal will change as shown in figure 5.6 (a).
(iii)       Whenever a PAM/TDM signal is transmitted over a bandlimited channel, the signal corresponding to x1 (t) will get mixed with x2(t) as shown in figure 5.6 (b) and this overlap will result into crosstalk.
DIAGRAM
FIGURE 5.6 (a) Transmission of signal over a bandlimited channel
DIAGRAM
FIGURE 5.6 (b) illustration of crosstalk in TDM
(iv)       One more reason for the crosstalk between the adjacent TDM signals is the use of bandlimiting filters. Because of these filters, the shapes of the TDM pulses are distorted and they get overlapped and crosstalk will take place.