Chapter 5 Phase Pre-emphasis Techniques 103
5.4 Phase Pre-emphasis
previous bits are shown. For the kth previous transition, the transition between the -k and -k-1 bit, we denote the timing deviation as , the conditioned mean described in (3.9). For instance, the first transition describes the transition between the previous and the penultimate bit. Figure 5.5 illustrates that the magnitude of the DDJ due to the kth transition tapers off quickly. After the third transition, the magnitude is small compared to the period. Phase pre-emphasis manipulates the data transitions to neutralize DDJ.
The relationship between different data sequences and the threshold crossing time is illustrated in Figure 5.6. A few data sequences are plotted to demonstrate the associated timing deviation and to illustrate the operation of the pre-emphasis scheme. Detection of each previous transition is used to compensate the current transition time. The detection of kth previous transition is denoted for the current bit, , and is calculated from , where is the XOR operator. The compensated transmit time is calculated through the following algorithm.
. (5.13)
For example, the 0010 sequence results in the fastest threshold crossing time for a first-order system. For this sequence, X[1] and X[2] are both one, implying that we will introduce the largest delay to compensate the fast transition for this sequence. On the other
Figure 5.5 Data eye showning the contribution to data-dependent jitter of previous transitions.
tc DDJ( ),k
X k[ ] D n[ ]
X k[ ] = D n[ –1]⊕D n[ –1–k] ⊕
tcomp[ ]n = X[ ]t1 c DDJ( )1, +X[ ]t2 c DDJ( )2, +X[ ]t3 c DDJ( ),3
hand, the 1110 sequence results in the slowest threshold crossing time. For this sequence X[1] and X[2] will both be zero and the transmitter will introduce not introduce delay in the transmitted bit timing. In this example, we illustrate two 1110 curves corresponding to whether the initial condition, the unshown previous bit, is zero or one. Ideally, compensa- tion is introduced for each previous transition until the DDJ contributed by these two curves is negligible.
In Figure 5.7, we demonstrate how phase pre-emphasis, along with amplitude pre-emphasis, introduces DDJ and ISI to the signal that is removed by the loss mechanisms in the serial link. The combination of both approaches can provide more signal integrity. In essence, the feed-forward amplitude pre-emphasis is a symbol-spaced FIR filter. The addition of phase compensation is to introduce an approximation for a half symbol-spaced FIR filter. While the use of amplitude pre-emphasis alone can provide some improvement in the DDJ, the symbol-spaced FIR filter cannot generally adjust the DDJ and the ISI to be simultaneously zero. Consequently, the use of half symbol-spaced FIR filters can minimize both the DDJ and ISI.
Figure 5.6 Phase pre-emphasis operation and truth table for compensating DDJ.
For the purposes of this work the coefficients of the equalizer are assumed to be adjusted ad hoc. The DDJ in simple LTI systems can be solved exactly to calculate the necessary timing compensation but generally some pulse response characterization or equalizer adaptation is required to adjust both phase and amplitude pre-emphasis coefficients. The coefficients for the phase pre-emphasis could be compensated by sampling the timing deviation at the receiver for particular transmitted data sequences. For instance, in Figure 5.6 the 0110 sequence introduces the delay while the 0101 sequence introduces the delay . At the receiver, these particular sequences could be detected and a timing interval could be calculated from the mean transition timing. The coefficients would be transmitted back to the transmitter in a back-channel scheme.
Additionally, phase pre-emphasis improves the voltage margins. By aligning the transition deviations of the DDJ, the pulse response rises farther before the sampling time.
This is illustrated in Figure 5.5, where the compensation of first transition brings the two separate groups of rising and falling edges together to a common edge. Consequently, the voltage margins between the slowest rising and falling edges increases.
The power-to-bit rate ratio (PBRR) is compared for a feed-forward transmitter with and without phase pre-emphasis. PBRR measures the marginal improvement between power consumption of the serial link and the equalization needed to achieve higher rates.
Minimizing this ratio is important in environments where thousands of serial links operate simultaneously. First, we calculate the timing and voltage margins for each possible value
tc DDJ( ),2 tc DDJ( ),1
Figure 5.7 Operation of phase and amplitude pre-emphasis.
of G and Ibias and determine whether these parameters meet a minimum receiver differential swing of 200mV and timing margin of ∆T=0.75T. For all the G and Ibias that meet the margins, we choose the values that achieve the lowest power consumption according to (5.7), as in Figure 5.4. The phase pre-emphasis is assumed to consume no power, which is not the case, but the difference in power with and without phase pre-emphasis indicates the power target that must be met to make phase pre-emphasis worthwhile. The calculation is performed over numerous bit rates to observe the trend in power consumption with and without phase pre-emphasis for several different channel bandwidths.
The result of this calculation is shown for three different channel cutoff frequencies in Figure 5.8. For fc=2GHz, the power consumption with phase pre-emphasis is improved by about 0.1mW/Gb/s. For fc=1GHz, the difference between the minimum power consumption with and without phase pre-emphasis increases to 0.25mW/Gb/s.
Additionally, it is clear that the power-to-bit rate ratio decreases slowly with higher bit rates. For fc=500MHz, the difference in the PBRR is around 0.5mW/Gb/s and changes slightly over the range of achievable bit rates. Clearly, phase pre-emphasis extends the achievable bit rate by 1Gb/s. This illustrates that the use of phase pre-emphasis can
Figure 5.8 Power consumption as a function of bit rate for various channel cutoff frequencies with and without the use of phase pre-emphasis.
provide some power savings for each serial link given that the power consumption for phase pre-emphasis does not overwhelm the power consumption savings.