2.1.1 Pseudo-Random Binary Sequence (PRBS)
A random binary data are composed with logical ZEROs and ONEs. If the time of one-bit is Tb seconds means the data rate is 1/Tb bits per second. The real random binary data may occur with the long string of consecutive logical ZEROs or ONEs. We call this string as “a low transition density”, also mean low speed. Such low transition density would make the trouble for the schematic design, like offset cancellation. So, we usually will specify the longest string of consecutive logical
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7 bits (7 Tb)
(the longest consecutive string) 3 bits
Fig. 2.1. The example of 23-1 PRBS.
ZEROs or ONEs. For the above reason, the pseudo-random binary sequence (PRBS) is the commonly used data pattern [14]. It can be generated by linear feedback shift register (LFSR) [15] which would generate a maximum sequence, 2m-1 bits, and repeat the sequence again and again. Each sequence contains 2m-1-1 ZEROs and 2m-1 ONEs, and the longest consecutive logical ZEROs or ONEs would equal to m bits. An example is depicted in Fig. 2.1.
2.1.2 Bandwidth requirement
In high-speed schematics design, how to design bandwidth is an important issue.
The bandwidth trades with many other specifications, such as noise, power consumption and gain boost. For example, if we design a large bandwidth, the signal information can be preserved without distortion. But, in the meanwhile, the noise is also preserved which destroys the signal information. On the contrary, if we design a small bandwidth, although the noise could be decreased. But the signal is also distorted which is known as inter-symbol interface (ISI) [14] which due to insufficient bandwidth, insufficient
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t
1Fig. 2.2. Comparison between sufficient bandwidth and insufficient bandwidth.
phase linearity, and insufficient low-frequency cutoff, as depicted in Fig. 2.2. At t1, the signal have the error bit. This undesired phenomenon would corrupt the voltage level of ZEROs and ONEs, and result in the error bits. The rule of thumb for optimum bandwidth is 0.7 of data rate, Eq. (2.1) [14-15]. However, for modern high-speed data communication, this rule of thumb is no longer suitable. Because of the trade-off between bandwidth, power consumption and other specifications in high-speed application, the recently published paper usually setting bandwidth to be 0.5 of data rate[4, 9, 16], especially when the data rate is more than 10Gb/s. Furthermore, we call the 0.5 of data rate to be “Nyquist rate”. And we always pay attention to how much gain boost can be provided by equalizer at the Nyquist rate in adaptive equalizer design.
2.1.3 Eye-diagram
An eye-diagram is formed by folding all of signal into a particular time. The eye-diagram could provide us a lot of useful signal information, such as ISI, noise, Insufficient bandwidth
Sufficient bandwidth
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Vertical eye-opening Horizontal
eye-opening
Jitterp-p Jitterp-p
Fig. 2.3. Eye-opening.
signal slope and signal swing. And the eye-opening and jitter are the important specifications which can help us to judge the signal quality.
The eye-opening includes horizontal eye-opening and vertical eye-opening, as shown in Fig. 2.3. The horizontal eye-opening means the time interval which we successfully sample the signal’s logical level. The vertical eye-opening means the tolerant noise for the signal, this can be explained by signal-to-noise ratio (SNR).
2.1.4 Jitter
Jitter is defined as the deviation of a timing event from its ideal position. We usually measure it from eye-diagram, and the peak-to-peak measurement is often used to represent the amount of jitter (jitterp-p) which is shown in Fig. 2.3.
The jitter is composed with random jitter and deterministic jitter. The random jitter, as its name describing, is an unpredictable jitter. It’s resulted from noise, such as thermal noise and flicker noise, which occurring from semiconductors and components.
So, the random jitter can be well approximation by Gaussuan distribution, or called normal distribution. Because of that, we usually specify the random jitter by root-mean-square value which means the standard
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Fig. 2.4. Jitter classifications.
deviation of gaussian distribution. The deterministic jitter is a predictable jitter, and the peak-to-peak value is bounded. Furthermore, it can be divided into data-dependent jitter (DDJ), periodic jitter (PJ) and duty-cycle distortion jitter (DCDJ), as shown in Fig. 2.4.
The value of DDJ is affected by the surrouding bits, in other word that is the ISI effect.
The PJ is generated with the crosstalk. The DCDJ happens when the rising edges and falling edges of signal don’t cross each other at decision threshold voltage.
2.1.5 Noise, SNR and BER
For the high-speed data communication, bit-error-rate (BER) which is defined as the ratio of number of error bits occurring to the number of transferred bits is a key issue. The BER is defined as
the number of error bits
BER (2.1)
the number of transferred bits
For fitting in with a given BER. It can be designed by signal-to-noise ratio (SNR) [14], which is derived as
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And the Q function is defined as:
u2
( )
2 x
Q(x) 1 e du (2.3) 2
By the (2.2), for example, if we want the BER to be smaller than 10-12, the SNR need to be larger than 14. That is to say when our signal swing is only 100mVp-p, the value of noise has only 7mV of tolerant range. In high-speed and low-power design, noise would be a serious limitation in the modern data communication. Thus, the BER can help us to know how much noise can be tolerated on the trade-off between noise and bandwidth, and power consumption.
2.1.6 Channel Characteristic and Modeling
As the description in chapter 1, we need a channel to transferred serial data from transmitter to receiver. The channel loss would degrade the high-frequency power of signal. The cause of channel loss are skin effect and dielectric loss. The skin effect causes the current tend to flow at the surface of conductor. This phenomenon results in more and more effective resistance for signal, especially at high frequency. The dielectric loss is resulted from the heating effect on the dielectric material.
When we model the channel loss, we also bring these two effects into the channel model. The channel model is shown in Fig. 2.5 [16].
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Fig. 2.5 Channel model with skin effect and dielectric loss consideration
Channel Equalizer
Fig. 2.6 Diagram of equalizer operation
2.1.7 Priciple of Adaptive Equalizer Operation
In the receiver equalization, the linear equalizer (LEQ) is usually called equalizer (EQ) for short. As Fig. 2.6 showing, the channel degrades the high-frequency gain of signal. Thus, we use EQ to compensate the channel loss from moderate-frequency to Nyquist rate. Because of the various channel loss when the channel length is changing, there is in want of a detection schematic to judge whether the channel loss is compensated well or not. If not, the detection schematic would adjust the gain-boost of EQ until the channel loss is compensated well.
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