The receiver comprises a continuous time linear equalizer with 6 dB of equalization, and half rate slicers. 2-4 data deserializer and BERT are also needed to measure BER and characterize data quality. Quadrature outputs of the CMU are applied to a phase interpolator to set the clock phases for timing recovery at receiver. Absolute Jitter is measured at each clock repeater output using the real-time oscilloscope TDS6154C TIE measurement. Different clock forwarding configurations are examined. Namely, all-reference, all-PLL, MDLL with FIR, and configurable PLL/MDLL clock forwarding. The results are depicted in Fig. 5.5. The plot shows absolute jitter accumulation from one clock repeater to the next across the link. As obvious from the plot, reference clock forwarding and PLL clock forwarding results in 16.5ps and 6.6ps of RMS jitter at the link output, respectively. Those are excessive amounts of jitter that cannot be tracked by a practical receiver at the end of the link. Although all-PLL forwarding shows less jitter accumulation than all-reference forwarding, yet the clock exhibits excessive jitter peaking due to cascaded stages of PLLs and high ring oscillator jitter. The 4th repeater in the all-PLL forwarding also has excessive jitter transfer peaking due to process variation. The other lines in the graph show the benefit of CMU configurability and FIR technique in lowering the link jitter. The FIR filtering technique with MDLL divided output results in 2.2ps RMS jitter. The configurable PLL/MDLL yields 2.7ps RMS jitter. Note that with an FIR a PLL setting is not needed since the input noise is kept low. The settings for the FIR coefficients and the CMU input mux are overlaid in the figure. As discussed in section 3.5, all-MDLL and mostly-MDLL setting is needed early on the link to favor forwarding of the clean clock. Later on the link, PLL or semi-PLL setting is used to benefit from PLL filtering. Also repeater 4 CMU shows excessive jitter in PLL mode and is bypassed altogether from clock forwarding by setting .
While absolute jitter is a crucial metric for asynchronous data reception by a CDR module at the end of the cable,drying room uncorrelated jitter is important for synchronously clocked systems to determine tracking between the data and clock paths. Fig. 5.6 portrays the untracked jitter accumulation across the link for a delay of 1 forward clock period. For an All-PLL system, the untracked jitter is 3.4ps rms at the output of the under-damped 4th repeater, and 2.8ps rms at the last repeater. The jitter tracking for the FIR filtered technique outperforms the all-PLL design. It shows 31% reduction in untracked jitter with respect to the all-PLL at the 4th repeater, and 18% reduction at the last repeater. The result suggests the link can be extended even further with good jitter tracking capability. The plot also shows the allreference forwarding has excessive untracked jitter across one period that renders it unusable for clock forwarding. Data path characterization is performed at the last 2 repeaters where clock jitter is the maximum. Fig. 5.7 shows the bathtub curves for the link at 12Gbps. At the Tx output, the bathtub plot is obtained by sweeping the clean source clock phase with respect to the data. The Tx eye is completely closed for all-reference and all-PLL clocking forwarding. For the configuration using the MDLL with FIR filtering, 0.55UI open eye is measured at the Tx output. At the receiver input the eye opening is 0.27UI at BER of 10−12 for a PRBS31 pattern. Data eye diagrams are shown in Fig. 5.8. The eye diagram is completely closed in case of all-reference forwarding whether it’s triggered by an asynchronous clean clock as in Fig. 5.8, or triggered by the same forward clock as in Fig. 5.8. In case of allPLL forwarding, eye is completely closed with asynchronous triggering in Fig. 5.8, which suggests inoperability of an asynchronous CDR at the Rx side. However, all-PLL clock forwarding shows good tracking with data, Fig. 5.8, and 4.9ps RMS jitter. On the other hand, MDLL and FIR filtering outperforms all-PLL clock forwarding whether it is triggered asynchronously or synchronously. In Fig. 5.8 and , the eyes show 4.4ps and 3.9 RMS jitter at the end of the link with asynchronous and synchronous triggering, respectively.
The pattern used is PRBS-31 pattern. Table 5.2 summarizes the link performance. The CMU section consumes a total of 9.6mW. The transmitter driver and pre-driver dissipate the majority of power at 24.4mA due to the voltage swing and the pre-emphasis. The receiver front end consumes 1.2mA. The clock driver consumes 5mA. Total chip power is 48mW including high-speed pattern generators and error detectors. Reliable reception is demonstrated at the end of a 115m CAT7 cable at 12Gbps. Total repeater chip area is 1mm2 . With such a small area and power, it is feasible to embed such a repeater within a cable for extending the reach of copper cables. The chip micrograph in Fig. 5.9 shows the design with each building block marked individually. This work demonstrates the potential use of source synchronous repeaters as means of extending multi-Gbps cable links for distances exceeding 100 meters. A 115 meter CAT7 cable is used to demonstrate reliable data transmission at 12Gbps. Longer reach can potentially be achieved since the total jitter at the end of the cable is only 4.4ps RMS. The work describes and validates an area-efficient phase filtering technique using a phase-based FIR to filter jitter across cascaded repeaters. To achieve both the clock multiplication and the phase delay of the FIR, an MDLL is used that can produce a 6GHz clock output. While challenges such as mechanical attachment, robustness to strain, tracking of environmental variations, etc., clearly exist for a repeater based copper link that embeds the repeater within the cable, this work indicates that the power and area requirements for the electronic circuits is feasible. The work also provides a fast semi-analytical method for modeling linear time variant noise accumulation across clock forwarded repeaters. The analysis provides accurate correlation with transient noise analysis and measured accumulated jitter for low and moderate levels of jitter accumulation. Because the analysis is based on a linear noise analysis, it tends to overestimate jitter when noise level increases and perturbs the DC operating point of the repeater. The work also demonstrates the fastest multiplying delay locked loop implemented in literature.
We were able to push the MDLL operation up to 6GHz by accurately placing the select aperture with respect to reference and VCO pulses. This MDLL exists at the core of the our clocking and filtering scheme. Its inputs can be configured to select the lowest of the input clock and the VCO clock for clock multiplication. Thus, it prevents jitter accumulation along the link. Outputs are also mixed to provide an effective FIR phase filter to filter the output clock. In the implemented prototype, a dedicated clock channel is used to forward the clock. In future work, the dedicated channel can be eliminated altogether and clock forwarding occurs on the common mode of the data channels or the power lines. Along that same line, a referenceless CDR could also be a viable alternative that needs to be investigated for repeater based copper cables. Finally,pruning cannabis to complete the experiment, multiple data channels could be added and the effect of cross talk on the entire link should be examined. Evaluating the health effects of social policies is critical to researchers, funders, and decision-makers seeking to promote healthful, evidence-based programs. Study designs such as differences-in-differences and panel fixed effects , which exploit variation in the timing and location of policy changes, have the potential to reveal causal inferences. Changes in health outcomes that are tied to the jurisdictions and times at which a particular policy is adopted can be used to isolate the causal effect of the policy . The amount of empirical health research on social policies using these methods has increased rapidly and yielded influential findings in recent years in epidemiology and other fields . One major concern with study designs that leverage variation in the timing and location of policy changes is that cooccurrence of policies can render it difficult to separately identify the causal effects of each policy. Isolating individual policy effects is crucial for delivering to decision makers evidence on whether to adopt a policy. Yet multiple related policies are often adopted or implemented in the same jurisdiction simultaneously or in quick succession, rendering it difficult to isolate the effect of 1 policy from the other. For example, a government that moves to overhaul its social safety net is likely to change multiple welfare-related policies in a single wave of legislative changes . Consequently, bundles of related policies, selected to address a particular set of health or social priorities and thus with similar potential health effects, are adopted concurrently, creating co-occurring policies. Co-occurring policies confound one another. Thus, if the co-occurring policies are relevant to the health outcome of interest, failing to account for co-occurring policies can severely bias estimated effects of specific social policies.
For example, if an effective policy A and an ineffective policy B are routinely adopted as a set, and their true effects are unknown, when researchers analyze effects of policy B without accounting for policy A, findings are likely to spuriously indicate that policy B is effective. Yet if jurisdictions typically adopt both policies together, adjustment for policy A to isolate the effect of policy B can lead to imprecise or unstable estimates and bias resulting from data sparsity . In extreme cases, estimates may be severely biased, undefined, or rely entirely on extrapolation because there is no independent variation in the policy of interest . Strong confounding and consequent data sparsity arising from co-occurring policies can be conceptualized as lack of common support in the data, also known as a violation of the “positivity assumption” . Lack of positivity implies that some confounder strata do not have variation in the exposure; for example, because places and times with the confounding policy always adopt the policy of primary interest . A rich literature exists on the problem of positivity and the use of propensity scores to assess and address it . However, several aspects of the policy co-occurrence problem make it important to consider separately from positivity issues that arise with other exposures. First, due to the nature of policy making , the levels of co-occurrence among policy variables may be far greater than those typically observed in non-policy studies . For example, governments adopt similar policies at similar times in part because they are responding to the desires and values of their constituents. Second, the most relevant analytic solutions may be distinct. For example, analytic solutions such as data-adaptive parameters that rely on large sample sizes may not be feasible for policy studies that are typically based on a small, fixed set of jurisdictions. Meanwhile, stronger theories or substantive knowledge about the mechanisms by which a particular social policy operates could guide analyses leveraging mediating variables for causal effect estimation . For example, how education policy affects educational attainment may be better understood than how educational attainment affects health. Furthermore, if some policies are always adopted together as a set, the most policy-relevant approach may be to modify the exposure definition to encompass both policies and then evaluate their combined effect, as opposed to attempting to disentangle their individual effects. Thus, the policy co-occurrence problem presents unique challenges and potential analytic solutions beyond typical confounding. Characterizing the extent and impact of policy cooccurrence is a crucial step for the development of rigorous evidence on social policy effects. Yet, to our knowledge, no epidemiologic research has directly addressed this issue. Authors of applied studies of social policies in fields including epidemiology, economics, and political science have acknowledged the issue by critiquing existing policy studies or, in some cases, applying solutions . Similar methodological challenges have arisen in environmental epidemiology when studying correlated and multi-pollutant exposures, but the emphasis of this research has been on identifying analytic solutions appropriate for pollutant measures, rather than on quantifying the extent of the problem .