studies on fir filter pre-emphasis for high-speed backplane data
TRANSCRIPT
Studies on FIR Filter Pre-Emphasis for High-Speed
Backplane Data Transmission
Abstract -- FIR filter-based transmitter pre-emphasis has been used to counteract inter-symbol interference (ISI) in high-speed backplane data transmission. In this paper, backplane channel characteristics are analyzed in both time and frequency domains. The analysis performed demonstrates that group delay distortion is a major ISI contributor in addition to amplitude attenuation. A Matlab program is then used to optimize FIR filter coefficients. Both symbol-spaced FIR (SSF) and fractionally-spaced FIR (FSF) techniques are compared at 3.125-, 6.5-, and 10-Gbps data rates. Finally, the results obtained from Matlab and ADS are compared. Keywords: FIR filter, ISI, Pre-emphasis, backplane, LMS
I. INTRODUCTION Inter-symbol-interference (ISI) is a major factor limiting the maximum distance and data rate of high-speed serial backplane data transmissions. ISI is caused by channel bandwidth limitations due to impairments of physical backplanes, such as skin-effect loss, dielectric losses, reflection, cross talk, etc. The overall effect of this distortion is that the receive eye at the far-end of a backplane can become too small to be recovered by the clock-data-recovery (CDR) block and bit errors start to appear. There are numerous techniques to increase the eye opening. Of these, pre-emphasis at the transmitter side has been proven to be one of the most effective techniques [1,2].
The FIR filter-based pre-emphasis function is used to boost the high-frequency content of the transmitted signal, thereby extending the bandwidth of the combined pre-emphasis and channel transfer functions. There are two types of FIR filters considered here: symbol-spaced and fractionally spaced. Due to the parametric variation of a physical backplane, an optimized FIR is required to obtain the best performance at the receive side. A Matlab coefficient estimator/simulator
program, therefore, has been developed to study the FIR filter pre-emphasis applied in backplane data transmission.
This paper starts with the channel characteristics analyzed in Section II. The Matlab program and flow-chart are described in Section III. Simulation results are presented and analyzed in Section IV. The results obtained with behavioral the Matlab and transistor-level ADS simulators are also compared in that section. Final conclusions are provided in Section V.
II. CHANNEL CHARACTERISTICS Figure 1 shows the configuration of a backplane transceiver link with FIR pre-emphasis. The entire backplane channel typically consists of a transmitter daughter card, connector, backplane, another connector, and another receiver daughter card.
Figure 1. FIR pre-emphasis for backplane channel
In this paper, a Tyco XAUI 34-inch FR4 backplane (referred to as 34-inch backplane) with two daughter cards is used as the channel model for FIR filter studies. The actual channel characteristics can be fully described by the measured differential S-parameters [3]. Figure 2(a) shows the amplitude attenuation and group delay of the backplane.
The bandwidth limitation effects on ISI and the group delay variation of a linear low-pass element are well understood. It should be noted, however, that additional group delay distortion, as observed in Figure 2(a), is also a major ISI contributor. This group delay distortion of a physical
Tad KwasniewskiDepartment of Electronics
Carleton University Ottawa, ON. K1S5B6, Canada
Tel: 613 5205762 Email:[email protected]
Yuming TaoOttawa IC Development
ALTERA Corp. Ottawa, ON. K2K3C9 Canada
Tel: 613 5916705 Email:[email protected]
Miao Li Department of Electronics
Carleton University Ottawa, ON. K1S5B6, Canada
Tel: 613 5205754 Email:[email protected]
Shoujun WangOttawa IC Development
ALTERA Corp. Ottawa, ON. K2K3C9 Canada
Tel: 613 5916767 Email:[email protected]
backplane can be attributed to the skin effect and undesired high-order modes existing within connectors and the transmission line. Figure 2(b) shows the channel impulse response with and without any group delay distortion (for clarity of the argument). For the no-group-delay case, the channel impulse response is attenuated, but dispersed symmetrically. The impulse response becomes asymmetrical when the channel impairments, in particular the group delay distortion, are fully included. Interestingly, the group delay is likely to speed up the leading edge of the impulse response, causing a long tail, as shown in Figure 2(b). For this 34-inch backplane, the pre-cursor ISI value seems to be negligible. As a consequence, the group delay distortion visibly degrades the eye opening as shown in Figure 3. The group delay distortion, therefore, should be taken into account for channel modeling and FIR filter design.
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Figure 3. Far-end eye diagrams at data rate of 3.125 Gbps: (a) without group delay distortion and (b) with group delay distortion
III. MATLAB PROGRAM
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Figure 4. FIR filter structure
The structure of the FIR filter is shown in Figure 4. For symbol-spaced FIR (SSF), the delay D is equal to one symbol period T. The transfer function of SSF in z- domain is given by:
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A Matlab program is developed to aid FIR-filter-based pre-emphasis design in backplane data communications applications. It consists of two parts: a tap-coefficients
calculator and a backplane link simulator, as shown in Figure 5Error! Reference source not found.Error! Reference source not found.(a) and (b), respectively.
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Figure 5. Error! Reference source not found.Matlab program flow chart: (a) Tap-coefficients calculator and (b) backplane link simulator
As shown Figure 5(a), the channel impulse response is first obtained by applying the inverse fast Fourier transform (IFFT) to the measured channel differential, S-parameter transfer function SDD21. Next, training data (from a pseudo- random source) is convolved with the impulse response to obtain the distorted data at the far end of the channel. The distorted data and the error signal, which is the difference between the delayed training data and FIR filter output, go into the least-mean-square (LMS) convergence engine. The LMS algorithm coefficient updating process follows the equation:
( ) ( ) eunCnC ⋅⋅+=+ μ1 (2) where C is the tap coefficient, is the step size, u is the distorted signal, and e is the error signal. As the algorithm convergences, the tap coefficients reach their optimum values.
The obtained optimum tap coefficients are then applied to the transmitter FIR filter in the Matlab link simulator. The spectrum of data bit sequence, channel, and transfer functions of the FIR filter are first multiplied in the frequency domain, and then converted to the time domain using IFFT. Finally, the time domain response is used to obtain the far-end eye diagram.
IV. CASE STUDIES AND CORRELATION
The 34-inch FR4 backplane discussed above is used as the transmission channel. SSF and FSF are optimized through
the Matlab program at data rates of 3.125 Gbps, 6.25 Gbps and 10 Gbps. The tap number of SSF is varied to determine the optimum number. The performance of SSF and FSF is compared.
A. Symbol-spaced FIR Filter Figure 6 shows the pulse response of the channel at different data rates. The optimum tap coefficients of SSF are obtained at the above data rates for the post-tap number, varied from 1 to 10 (the total tap number is from 2 to 11). The far-end eye diagrams are drawn after applying the obtained SSF pre-emphasis to the link.
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Figure 5. Comparison of far-end eye diagrams without and with SSF pre-emphasis: (a) 3.125 Gbps; (b) 6.25 Gbps; and (c) 10 Gbps.
The selection of the optimum tap number is discussed separately [4]. In general, the optimum tap number is close to the least number of symbol-spaced points that cover the greatest part of the tail of the pulse response. For the 34-inch FR4 backplane used here, four post-taps were used for 3.125 Gbps and 6.25 Gbps, and five post-taps were used for 10 Gbps. SSF pre-emphasis, with the obtained optimum tap number and coefficients, is applied to the link at different data rates. Far-end eye diagrams, with and without SSF pre-emphasis, are compared in Figure 5. The effectiveness of SSF pre-emphasis can be clearly observed.
B. Fractionally-spaced FIR Filter The performance of SSF is limited by aliasing, as a result of sampling at 1/T. SSF cannot reliably compensate for channel impairments beyond the Nyquist frequency 1/2T. FSF samples at a fraction of T, and the pre-emphasis is defined beyond the 1/2T frequency point. It is expected that FSF pre-emphasis can perform better than SSF. Three cases are studied in the following example: 3-tap T-spaced FIR (2T span), 3-tap T/2-spaced FIR (1T span), and 5-tap T/2-spaced FIR (2T span). The performance comparison at different data rates is shown in Table 1.
The eye opening of the 3-tap FSF is worse than that of the 3-tap SSF because the 3-tap FSF only covers half the time span of the 3-tap SSF. FSF, however, always performs better than SSF if the same time span is covered. The 5-tap FSF shows larger horizontal eye openings than the 3-tap SSF for all three data rates. For the backplane channel studied here, the performance gain of T/2 FSF over SSF is not significant. Further improvement can be achieved with FSF pre-emphasis by reducing the delay D to a smaller fraction of T. The selection of FSF vs. SSF is channel-dependent and requires a trade-off between performance and implementation complexity.
Table 1. Horizontal (in unit intervals) and vertical (in volts) eye
openings for SSF vs. FSF pre-emphasis
3-tap SSF 3-tap FSF 5-tap FSF Data rate
[UI] [V] [UI] [V] [UI] [V]
3.125 Gbps 0.93 0.23 0.93 0.20 0.96 0.22
6.25 Gbps 0.86 0.11 0.83 0.11 0.89 0.12
10 Gbps 0.66 0.03 0.62 0.03 0.68 0.03
C. Simulation Correlation
A CML transmitter with 2-tap FIR pre-emphasis has been designed in 0.18-µm CMOS technology. This transmitter is then used to drive the 34-inch backplane with the optimized tap-coefficients obtained from the developed Matlab program. ADS is used as the transistor-level simulator due to its capability of simulating S-parameters in transient. The far-end eye-diagrams simulated using the Matlab program and ADS simulator are plotted in Figure 6(a) and (b), respectively. Comparing the horizontal and vertical eye-openings, a reasonably good correlation can be observed between these two link simulations.
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Figure 6. 6.5-Gbps data eye-diagrams at the far-end of 34-inch backplane without and with FIR pre-emphasis: (a) Matlab simulation and (b) ADS transistor-level simulation
V. CONCLUSION
One backplane channel has been thoroughly analyzed in the frequency and time domains. It was found that the group delay distortion is a major ISI contributor in addition to amplitude attenuation. Using the Matlab program, we studied the FIR filter pre-emphasis for backplane channel equalization and, as expected, FSF performs better than SSF, if the same time span is covered. Results from Matlab simulation are close to these obtained from the ADS simulation that included transistor-level FIR pre-emphasis. The Matlab program can be used to optimize FIR pre-emphasis and provide design guidelines for given backplane channels.
REFERENCES
[1] J. Zerbe, et al. “Equalization and clock recovery for a 2.5-10Gbs 2-PAM/4-PAM backplane transceiver cell,” ISSCC Digest of Technical Papers, paper 4.6, 2003.
[2] J.T. Stonick, Gu-Yeon Wei, J.L. Sonntag, D.K. Weinlader, “An adaptive PAM-4 5-Gb/s backplane transceiver in 0.25-um CMOS”, IEEE J. Solid-State Circuits, vol.38, pp. 436 –443, March 2003.
[3] OIF2003.104.03, “Common Electrical Interface (CEI) - electrical and jitter interoperability agreements for 6+ and 11+ Gbps I/O”, October 2003.
[4] M. Li, S. Wang, Y. Tao, and T. Kwasniewski, ‘FIR filter optimization as pre-emphasis of high-speed backplane data transmission’, International Conference of Communications, Circuits and Systems (ICCCAS), Chengdu, China, June 27-29, 2004.