Basic Concepts

2.2.1 NRZ Data

“Non-return to zero” (NRZ) data is a data format used in many high-speed communication systems. As shown in Fig. 2.4, Each logical bit of NRZ data specifies

Chapter 2 Overview of Equalizer for Serial Link System

one of two signal levels. This type of waveform is called NRZ to distinguish it from

“return to zero” (RZ) data. Each bit of RZ data consists of two sections: the first section represents the bit value, and the second section is always equal to a logical zero. In other words, every two bits are separated by a redundant zero symbol.

Because the property of RZ data, it needs about twice as much bandwidth as NRZ data does. This is the reason why NRZ data is much suitable for high-speed applications.

Figure 2.4 NRZ and RZ data.

2.2.2 Pseudo-Random Binary Sequence

Most wire-line communication systems employ binary amplitude modulation. A random binary sequence (RBS) comprises logical ONEs and ZEROs that usually occur with equal probabilities. In Fig. 2.5, if each bit period is Tb seconds, then the bit rate, Rb, is equal to 1/Tb bits per second. Fig. 2.5 also reveals that the ONEs and ZEROs assume equal and opposite values, thereby yielding a zero average.

Figure 2.5 Random binary sequence.

Logical data

NRZ RZ

Chapter 2 Overview of Equalizer for Serial Link System

In simulation and chip measurement, it is difficult to generate absolutely RBS.

Hence it is common to utilize “pseudo-random” binary sequence (PRBS). Each PRBS is a repetition of a pattern, containing a RBS of a number of bits (Fig. 2.6).

Figure 2.6 Pseudo-random binary sequence.

A PRBS of length 2^m－1 means the pattern repeats every 2^m－1 bits, where m is a positive integer. For example, if there is a PRBS of length 2³－1, the sequence will repeat every 7 bits, and the maximum run length is 3. Maximum run length is the maximum number of consecutive ONEs or ZEROs in a pattern. The random nature of data implies that a binary sequence may contain arbitrarily long maximum run length.

The long runs produce difficulties in the design of receiver circuits. For instance, in CDR design, the low data transitions during a long run may cause the oscillator to drift and hence generate jitter. Therefore, random data may be encoded to limit the maximum run length. 8-bit/10-bit (8B/10B) coding [13] is a coding algorithm that converts a sequence of 8 bits to a 10-bit word to guarantee a maximum run length of 5 bits. Although the data rate increases by 25%, many aspects of transceiver design can be relaxed.

2.2.3 Intersymbol Interference

Intersymbol Interference (ISI) has been a serious limitation on data rates that can be sent through a communication channel. ISI generally refers to the interference that occurs between the current received bit and other previously received bits. The

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interference indicates that the portions of previously received bits add to the bit that is being received. This phenomenon can be seen by the following example.

(a) (b)

Figure 2.7 (a) A low-pass filter. (b) Effect of low-pass filtering on random data.

Fig. 2.7(a) is a RC low-pass filter, when a random binary sequence passes through it, the high-frequency components are attenuated, as illustrated in Fig. 2.7(b).

For a single ONE followed by a ZERO, the output does not reach the peak, but for two consecutive ONEs, it does. The output voltage levels corresponding to ONEs and ZEROs vary with time, making it difficult to define a decision threshold voltage. For example, if the threshold is set at Va/2, the voltages at t=t1, and t=t2 are very susceptible to noise and the decision circuit may make a wrong decision of bit. Such undesirable phenomenon is called “intersymbol interference” (ISI). ISI produces degradation in system performance and is the major source of bit errors.

In fact, there are two factors that ISI is occurred by the low-pass nature of communication channel. One is the bandwidth of channel, and the other is the density of transitions in the data stream. For the factor of bandwidth, we can see Fig. 2.7 again. The rising edge of output voltage before t=t1 can be expressed as

-t/R C

V (t)=V (1-e ).

out a (2.1)

Therefore, the larger the RC, i.e. narrower bandwidth, the lower output voltage level can reach. For the factor of the transition density of input pattern, Fig. 2.8 is an example to show the problem.

Chapter 2 Overview of Equalizer for Serial Link System

Figure 2.8 Response of long run passes a moderate limited bandwidth channel.

In Fig. 2.8 assume the bandwidth of channel is moderate limited, when more consecutive ONEs are followed by a single ZERO, the output voltage which is supposed to be a ZERO may be far from logical ZERO. It is obvious that the longer the identical series of ONEs before a ZERO, the worse the effect of ISI on the amplitude of the ZERO bit and vice versa. Since the longer the input stays at constant amplitude, the more the channel charges to the amplitude which will make it more difficult to discharge when the input switches.

2.2.4 Eye Diagram

As discussed so far, ISI is a function of the bit patterns being sent across the channel. If the input pattern is very long and random, it becomes a very difficult task to find out the effect of ISI on both the amplitude and duration of the received bits. A common method for visualizing the nonidealities in random data is the “eye diagram.”

An eye diagram is created by capturing the output waveform which is divided into a short interval, e.g., two bits wide, and overlaid on top of each other. As an example, considering a 2-Gb/s random binary sequence is fed into a first-order low-pass filter having a －3-dB bandwidth of 500 MHz. As depicted in Fig. 2.9, we superimpose all 1-ns intervals to obtain the eye diagram. The two important parameters in an eye diagram are the vertical and horizontal openings of the eye. The vertical eye opening

Chapter 2 Overview of Equalizer for Serial Link System

(a)

(b)

Figure 2.9 An illustration of eye diagram construction. (a) input and output waveform.

(b) eye diagram.

represents the minimum amplitude the received bits can have. On the other hand, the horizontal eye opening defines the time interval over which the data can be sampled without error caused by ISI. In Fig. 2.9(b), we can also observe that the zero crossings experience some deviation from their ideal position. This is called “timing jitter.” As the amount of timing jitter increases, the horizontal eye opening decreases. Therefore, when data rates increase, timing jitter can become a significant problem and cause bit errors in data transmission systems.

Vin

Vout

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2.2.5 Bit Error Rate

The general definition of “bit error rate (BER)” is number of bit errors

BER= .

total number of bits received (2.2) In other words, the bit error rate (BER) is the percentages of bits that have errors relative to the total number of bits received in a transmission. It is unavoidable that the noise will exist in data transmission. The noise added to the signal degrades both the amplitude and the time resolution, closing the eye and increasing the BER.

Assume the noise amplitude n(t) has a Gaussian distribution with zero mean and a root mean square (rms) value of σn . Thus, we could write the PDF of n(t) as:

Next, if ONEs and ZEROs of the input sequence x(t) occur with equal probabilities, the PDF of x(t) contains two impulses at x＝－Va and x＝＋Va (assume the nominal values of ONEs and ZEROs are ＋Va and －Va, respectively), and each has a weight of 1/2. Having PDF of x(t) and n(t), we could obtain the amplitude distribution of x(t)＋n(t), as shown in Fig. 2.10.

As illustrated in Fig. 2.10, x(t)+n(t) shows a PDF consisting of two Gaussian distributions centered around ＋Va and －Va. The shaded area represents the error

Figure 2.10 PDF of signal plus noise.

Chapter 2 Overview of Equalizer for Serial Link System

samples and the BER can be expressed as:

0 1 1 0

BER=(P_−> +P_−> ), (2.4) where P_0->1 and P_1->0 represent the probability of “receiving a ONE while actually a ZERO is transmitted” and “receiving a ZERO while actually a ONE is transmitted”, respectively.

where the complementary error function erfc(t) is defined as:

2 - 2

Consequently, the BER is given by

a

Table 2.1 is the different BERs for different confidence intervals of root mean square value σn. For serial data transmission schemes, the required BER performance is generally less than about 10^-12, which according to this table translates to a necessary minimum margin of over ± 7σn.

In equalizer design, the timing jitter will affect the BER. The causes of jitter can be categorized into two types: deterministic jitter and random jitter. Deterministic jitter is often called a systematic jitter since it is generated by the system. Clock timing jitter and data signal jitter are deterministic jitter and they are predictable and bounded. We usually use peak-to-peak value to measure deterministic jitter. Random

Chapter 2 Overview of Equalizer for Serial Link System

jitter, also called Gaussian jitter, is an unpredictable electronic timing noise such as thermal noise. Root-mean-square value is often used to measure the random jitter.

Hence, if the random jitter is severe, the value of σn is large, and the BER is large according to EQ. 2.8.

Table 2.1 BERs for different confidence intervals.

interval BER

In previous sections, we have roughly introduced the effect of ISI on the quality of signal in data transmission. Since ISI arises from some imperfections of channels, in this section, we will discuss the characteristics of channel and build the channel model for our equalizer circuit design.

There are several types of channels utilized in high-speed interconnects, primarily based on the target application. These channels can be roughly classified into three categories. First, for chip-to-chip communication on a printed circuit board (PCB), short copper traces are used. Second, for systems such as local-area network requiring high-speed connection between two computers, coaxial cable or optical