**INTRODUCTION TO DISCRETE PAM SIGNALS (DIGITAL DATA FORMATS) , pulse amplitude modulation circuit , advantages of ?**

There are various techniques used to convert the analog signal to digital signal. But, the other way of obtaining digital data is from the source such as computers. The information from such a source is inherently discrete in nature. If such a discrete signal is transmitted over a bandlimited channel, then the signal gets dispersed. This causes the pulses to overlap and cause distortion. Such a distortion is called as intersymbol interference (ISI). In order to avoid this, we should not transmit the discrete signal as it is on the transmission medium. This data is first converted into a PAM suitable format and then transmitted over a communication channel. The various formats used are also called as **line codes.**

** **The use of an appropriate waveform for baseband representation of digital data is basic to its transmission from a source to a destination. This means that digital pulse modulation can be used for transmitting the output of a digital source.

We know that the signal symbols can amplitude modulate some carrier to generate amplitude modulated pulse train. Therefore, such signal may be represented as,

**EQUATION **…(6.1)

Here, a_{k} is the amplitude of k^{th} symbol in the message sequence.

p(t) is the pulsed carrier signal. i.e. is a basic pulse shape. It’s pulses are modulated by a_{k}.

*T* is the maximum duration (i.e., time period) allowed for the carrier pulse. The unmodulated carrier pulse p(t) is the rectangular pulse and it can take variable duty cycle. It can be represented as,

**EQUATION **…(6.2)

*x(t)* is the pulse waveform. To recover the original digital signal from *x(t)* we have to sample *x(t)* at some fixed intervals and check the signal in these intervals. This checking is the detection of the transmitted symbols. From equation (6.1), we observe that if *p(t)* is zero, then *x(t)* is also zero. Therefore, it is preferable to sample x(t) when p(t) is zero. This means that at this time [p(t)=0] no digital information is present/transmitted in the pulse waveform. Therefore, *x(t)* can be sampled periodically at t = kT where k = 0, ± 1, ± 2, …etc.

Also, p(t) is the rectangular pulse and may be written as,

p(t) = rect …(6.3)

Because, the pulse to pulse interval is “T”, therefore the width of the pulse should be less than or equal to T.

i.e., __<__ T

The signalling rate is given as,

r = …(6.4)

If ‘*T*‘ represents the duration of one bit, then T=T_{b} and signalling rate will be,

r = …(6.5)

**6.4 LINE CODING AND ITS PROPERTIES **

The digital data can be transmitted by various transmission or line codes such as on-off, polar, bipolar and so on. This is called **line-coding.** Each type of line-code has its advantages and disadvantages.

Thus, among other desirable properties, a line code must have the following properties:

**Transmission bandwidth**

For a line-code, the transmission bandwidth must be as small as possible.

**Power efficiency**

For a given bandwidth and a specified detection error probability, the transmitted power for a line code should be as small as possible.

**Error detection and correction capability**

It must be possible to detect and preferably correct detection errors. For example, in a bipolar case, a signal error will cause bipolar violation and thus can easily be detected.

**Favourable power spectral density**

** **It is desirable to have zero power spectral density (PSD) at *w* = 0 (i.e., dc) since ac coupling and transformers are used at the repeaters. Significant power in low-frequency components causes de wander in the pulse stream when ac coupling is used. The a.c. coupling is required since the de paths provided by the cable pairs between the repeater sites are used to transmit the power required to operate the repeaters.

**Adequate timing content**

** **It must be possible to extract timing or clock information from the signal.

**Transparency**

** **It must be possible to transmit a digital signal correctly regardles of the pattern of l’s and 0’s.

**6.5 VARIOUS PAM FORMATS OR LINE CODES**

Some of the important PAM formats or lien coding techniques are as under:

(i) Non-return to zero (NRZ) and return to zero (RZ) unipolar format.

(ii) NRZ and RZ polar format.

(iii) Non-return to zero bipolar format.

(iv) Manchester format.

(v) Polar quaternary NRZ format.

All the formats have been shown for a binary message 10110100. Figure 6.3 shows various PAM formats or line cords.

**DIAGRAM**

**FIGURE 6.3** *Various digital PAM signals formats (a) Unipolar RZ (b) Unipolar NRZ (c) Polar RZ (d) Polar NRZ (e) Bipolar NRZ (f) Split phase Manchester (g) Polar quaternary NRZ.*

**6.6 UNIPOLAR RZ AND NRZ **

**Definition**

** **In unipolar format, the waveform has a single polarity. The waveform can have +5 or +12 volts when high. The waveform is simple on-off.

**Unipolar RZ : Waveform and Expression**

In the unipolar RZ form, the waveform has zero value when symbol ‘0’ is transmitted and waveform has ‘A’ volts when ‘1’ is transmitted. In RZ form, the ‘A’ volts is present for T_{b}/2 period if symbol ‘1’ is transmitted and for remaining T_{b}/2, waveform returns to zero value, i.e., for unipolar RZ form, we have

**DIAGRAM**

**FIGURE 6.4*** Unipolar RZ format.*

If symbol ‘1’ is transmitted, then we have

**EQUATION** …(6.6)

and if symbol ‘0’ is transmitted, then

x(t) = 0 for 0 __<__ T < T_{b} (complete interval) …(6.7)

Hence, in unipolar RZ format, each pulse returns to a zero value. Figure 6.4 shows this signal format.

**Unipolar NRZ: Waveform and Expression**

A unipolar NRZ (i.e., not return to zero) format is shown in figure 6.5. When symbol ‘1’ is to be transmitted, the signal has *‘A’* volts for full duration. When symbol ‘0’ is to be transmitted, the signal has zero volts (i.e. no signal) for complete symbol duration.

Thus, for unipolar NRZ format,

If symbol T is transmitted, we have

x(t) = A for 0 __<__ t < T_{b} (complete interval) …(6.8)

If symbol ‘0’ is transmitted, we have

x(t) = 0 for 0 __<__ t < T_{b} (complete interval) …(6.9)

**DIAGRAM**

**FIGURE 6.5** *Unipolar NRZ format.*

**Impot tant Points**

** **(i) For NRZ format, it may be observed that the pulse does not return to zero on its own. If symbol ‘0’ is to be transmitted, then pulse becomes zero.

(ii) Internal computer waveforms are usually of unipolar NRZ type.

(iii) Because, there is no separation between the pulses, therefore, the receiver needs synchronization to detect unipolar NRZ pulse.

(iv) As compared to RZ format, NRZ pulse width (pulse to pulse interval is same) is more. Thus, energy of the pulse is more.

(v) However, unipolar format has some average DC value. This DC value does not carry any information.

**POLAR RZ AND NRZ**

**Polar RZ : Waveform and Expression**

** **In the polar RZ format, symbol ‘1’ is represented by positive voltage polarity whereas symbol `0′ is represented by negative voltage polarity. Because this is RZ format, the pulse is transmitted only for half duration. Thus, for polar RZ, if symbol ‘1’ is transmitted, then

**EQUATION **

and if symbol ‘0’ is transmitted, then

**EQUATION**

Polar RZ waveform has been shown in figure 6.6.

**DIAGRAM**

**FIGURE 6.6** *Polar RZ format.*

**Polar NRZ : Waveform and Expression**

** **The polar NRZ is shown in figure 6.7. In polar NRZ format, symbol ‘1’ is represented by positive polarity whereas symbol ‘0’ is represented by negative polarity. These polarities are maintained over the complete pulse duration i.e., for polar NRZ, we have

**DIAGRAM**

**FIGURE 6.7** *Polar NRZ format.*

If symbol ‘1’ is transmitted, then

x(t) = for 0 __<__ t < T_{b} …(6.12)

and if symbol ‘0’ is transmitted, then

x(t) = for 0 __<__ t < T_{b} …(6.13)

**Important Points**

** **(i) Since polar RZ and NRZ formats are bipolar, therefore, the average DC value is minimum in these waveforms.

(ii) If probabilities of occurrence of symbols ‘1’ and ‘0’ are same, then average DC components of the waveform would be zero.

**6.8 BIPOLAR NRZ [ALTERNATE MARK INVERSION (AMI)]**

**Definition**

DO YOU KNOW? |

The various line codes are also known by other names. For example, polar NRZ is also called NRZ-L, where L denotes the normal logical level assignment. Bipolar RZ is also called RZ-AMI, where AMI denotes alternate mark (binary 1) inversion. |

In this format, the successive Ts are represented by pulses with altenate polarity and ‘0’s are represented by no pulses.

**Waveform**

Figure 6.8 illustrates the Bipolar NRZ or AMI waveform. If there are even number of l’s, the DC component of the waveform would be zero. The advantage of this format is that the ambiguities due to transmission sign inversion are eliminated.

**DIAGRAM**

**FIGURE 6.8*** Bipolar NRZ format (AMI).*

**6.9 SPLIT PHASE MANCHESTER FORMAT **

**Definition and Waveform**

** **This type of waveform is shown in figure 6.9. In this case, if symbol ‘1’ is to be transmitted, then a positive half interval pulse is followed by a negative half interval pulse. If symbol ‘0’ is to be transmitted, then a negative half interval pulse is followed by a positive half interval pulse. Hence, for any symbol the pulse takes positive as well as negative value i.e.,

**Mathematical Expressions**

If symbol ‘1’ is to be transmitted, then

**equation **…(6.14)

and if symbol ‘0’ is to be transmitted, then

**EQUATION **…(6.15)

**FIGURE 6.9** *Split phase manchester format.*

**Important Points**

(i) The primary advantage of this format is that irrespective of the probability of occurrence of symbol ‘1’ and ‘0’ the waveform has zero average value. Therefore by this mode, the power saving is quite more.

(ii) However, the drawback of this format is that it requires absolute sense of polarity at the receiver end.

**6.10 POLAR QUATERNARY NRZ FORMAT **

**Definition and Waveform**

DO YOU KNOW? |

The Manchester NRZ line code has the advantage of always having a 0-dc value, regardless of the data sequency, but it has twice the bandwidth of the unipolar NRZ or polar NRZ code because the pulses are half the width. |

** **Figure 6.10 shows the waveform of this format. This format is derived to reduce the signalling rate `*r*‘. The message bits are grouped in the blocks of two. Therefore there are four possible combinations 00, 01, 10 and 11. To these four combinations, four amplitude levels are assigned. The Table 6.1 shows how this can be achieved.

**Table 6.1. Polar quaternary NRZ Format: Combinations of bits**

Message Combination |
x(t) = a_{n} |

00 01 10 11 |

In the waveform of figure 6.10, the first combination of two bits is 10. Thus, from Table 6.1, we may observe that the level should be . The second combination in figure 6.10 is 11, hence from Table 6.1, the level taken is

. Similarly other levels are selected. Hence, for two message bits only one pulse is transmitted with duration 2T_{b}, i.e.,

T_{s} = 2T_{b}

and signalling rate is given as,

…(6.16)

**DIAGRAM**

**FIGURE 6.10** *Polar Quaternary NRZ format*