WO2018217786A1

WO2018217786A1 - Multi-stage sampler with increased gain

Info

Publication number: WO2018217786A1
Application number: PCT/US2018/033935
Authority: WO
Inventors: Armin TAJALLI
Original assignee: Kandou Labs, S.A.; Invention Mine, Llc
Priority date: 2017-05-22
Filing date: 2018-05-22
Publication date: 2018-11-29
Also published as: DE112018002645T5; CN111034137A; CN115643137A; CN111034137B

Abstract

Methods and systems are described for obtaining, at an input stage of a sampler, a continuous-time analog differential voltage, and responsively generating an integrated analog differential voltage by discharging a pair of pre-charged output nodes in an integration period according to the continuous-time analog differential voltage, the integration period initiated by a sampling clock, and providing the integrated analog differential voltage to a plurality of slicing circuits having inputs connected to the pair of output nodes, each slicing circuit of the plurality of slicing circuits generating a respective sliced output signal based on a respective slicing threshold of a set of slicing thresholds.

Description

MULTI-STAGE SAMPLER WITH INCREASED GAIN

CROSS-REFERENCE TO RELATED APPLICATIONS

[0001] This application claims the benefit of U. S. Provisional Application No. 62/509,713, filed May 22, 2017, naming Armin Tajalli, entitled "Multi-Stage Sampler with Increased Gain", the contents of which are hereby incorporated herein by reference in its entirety for all purposes.

REFERENCES

[0002] The following prior applications are herein incorporated by reference in their entirety for all purposes:

[0003] U.S. Patent Publication 2011/0268225 of Application 12/784,414, filed May 20, 2010, naming Harm Cronie and Amin Shokrollahi, entitled "Orthogonal Differential Vector Signaling" (hereinafter "Cronie I").

[0004] U.S. Patent Publication 2011/0302478 of Application 12/982,777, filed December 30, 2010, naming Harm Cronie and Amin Shokrollahi, entitled "Power and Pin Efficient Chip-to- Chip Communications with Common-Mode Resilience and SSO Resilience" (hereinafter "Cronie II").

[0005] US Patent Application No. 13/542599, filed July 5, 2012, naming Armin Tajalli, Harm Cronie, and Amin Shokrollahi entitled "Methods and Circuits for Efficient Processing and Detection of Balanced Codes" (hereafter called "Tajalli I".)

[0006] U.S. Patent Application No. 13/842,740, filed March 15, 2013, naming Brian Holden, Amin Shokrollahi and Anant Singh, entitled "Methods and Systems for Skew Tolerance in and Advanced Detectors for Vector Signaling Codes for Chip-to-Chip Communication", hereinafter identified as [Holden I];

[0007] U.S. Provisional Patent Application No. 61/946,574, filed February 28, 2014, naming Amin Shokrollahi, Brian Holden, and Richard Simpson, entitled "Clock Embedded Vector Signaling Codes", hereinafter identified as [Shokrollahi I]. [0008] U.S. Patent Application No. 14/612,241, filed August 4, 2015, naming Amin Shokrollahi, Ali Hormati, and Roger Ulrich, entitled "Method and Apparatus for Low Power Chip-to-Chip Communications with Constrained ISI Ratio", hereinafter identified as [Shokrollahi II].

[0009] U.S. Patent Application No. 13/895,206, filed May 15, 2013, naming Roger Ulrich and Peter Hunt, entitled "Circuits for Efficient Detection of Vector Signaling Codes for Chip-to- Chip Communications using Sums of Differences", hereinafter identified as [Ulrich I].

[0010] U.S. Patent Application No. 14/816,896, filed August 3, 2015, naming Brian Holden and Amin Shokrollahi, entitled "Orthogonal Differential Vector Signaling Codes with Embedded Clock", hereinafter identified as [Holden II].

[0011] U.S. Patent Application No. 14/926,958, filed October 29, 2015, naming Richard Simpson, Andrew Stewart, and Ali Hormati, entitled "Clock Data Alignment System for Vector Signaling Code Communications Link", hereinafter identified as [Stewart I].

[0012] U.S. Patent Application No. 14/925,686, filed October 28, 2015, naming Armin Tajalli, entitled "Advanced Phase Interpolator", hereinafter identified as [Tajalli II].

[0013] U.S. Provisional Patent Application No. 62/286,717, filed January 25, 2016, naming Armin Tajalli, entitled "Voltage Sampler Driver with Enhanced High-Frequency Gain", hereinafter identified as [Tajalli III].

[0014] U.S. Provisional Patent Application No. 62/326,593, filed April 22, 2016, naming Armin Tajalli, entitled "Sampler with Increased Wideband Gain and Extended Evaluation Time", hereinafter identified as [Tajalli IV].

[0015] U.S. Provisional Patent Application No. 62/326,591, filed April 22, 2016, naming Armin Tajalli, entitled "High Performance Phase Locked Loop", hereinafter identified as [Tajalli V].

[0016] U.S. Provisional Patent Application No. 62/411 ,920, filed October 22, 2016, naming Armin Tajalli, entitled "Multi-Stage Sampler with Increased Gain", hereinafter identified as [Tajalli VI]. FIELD OF THE INVENTION

[0017] The present embodiments relate to communications systems circuits generally, and more particularly to obtaining an instantaneous measurement and filtering of a received signal voltage relative to a provided clock signal, as one component of detecting received communications signals from a high-speed multi-wire interface used for chip-to-chip communication.

BACKGROUND

[0018] In modern digital systems, digital information has to be processed in a reliable and efficient way. In this context, digital information is to be understood as information available in discrete, i.e., discontinuous values. Bits, collection of bits, but also numbers from a finite set can be used to represent digital information.

[0019] In most chip-to-chip, or device-to-device communication systems, communication takes place over a plurality of wires to increase the aggregate bandwidth. A single or pair of these wires may be referred to as a channel or link and multiple channels create a communication bus between the electronic components. At the physical circuitry level, in chip- to-chip communication systems, buses are typically made of electrical conductors in the package between chips and motherboards, on printed circuit boards ("PCBs") boards or in cables and connectors between PCBs. In high frequency applications, micro strip or stripline PCB traces may be used.

[0020] Common methods for transmitting signals over bus wires include single-ended and differential signaling methods. In applications requiring high speed communications, those methods can be further optimized in terms of power consumption and pin-efficiency, especially in high-speed communications. More recently, vector signaling methods have been proposed to further optimize the trade-offs between power consumption, pin efficiency and noise robustness of chip-to-chip communication systems. In those vector signaling systems, digital information at the transmitter is transformed into a different representation space in the form of a vector codeword that is chosen in order to optimize the power consumption, pin-efficiency and speed trade-offs based on the transmission channel properties and communication system design constraints. Herein, this process is referred to as "encoding". The encoded codeword is communicated as a group of signals from the transmitter to one or more receivers. At a receiver, the received signals corresponding to the codeword are transformed back into the original digital information representation space. Herein, this process is referred to as "decoding".

[0021] Regardless of the encoding method used, the received signals presented to the receiving device are sampled (or their signal value otherwise recorded) at intervals best representing the original transmitted values, regardless of transmission channel delays, interference, and noise. The timing of this sampling or slicing operation is controlled by an associated Clock and Data Recovery (CDR) timing system, which determines the appropriate sample timing. [Stewart I] and [Tajalli V] provide examples of such CDR systems.

BRIEF DESCRIPTION

[0022] To reliably detect the data values transmitted over a communications system, a receiver accurately measures the received signal value amplitudes at carefully selected times. In some embodiments, the value of the received signal is first captured at the selected time using a known sample-and-hold or track-and-hold circuit (or known variants such as amplify-and-hold or integrate-and-hold), and then the resulting value is measured against one or more reference values using a known voltage comparator circuit. Other embodiments first use a comparator to "slice" the analog signal and obtain a digital result, then digitally sample the resulting binary value using a clocked digital latch.

[0023] Other embodiments utilize circuits capable of applying both the time- and amplitude- domain constraints, producing a result that represents the input value at a particular time and relative to a provided reference level. [Tajalli III] provides examples of such embodiments, in which the high frequency gain of the sampling circuit may be advantageously boosted over a narrow frequency range, in a so-called high frequency peaking action as graphically illustrated by the gain vs. frequency chart of FIG. 6A.

[0024] It is also possible to provide enhanced signal gain over a wide frequency range, as shown by the gain vs. frequency chart of FIG. 6B and described in the embodiments herein. Additional embodiments are described in which the clocked sampling action is further enhanced by reliance on dynamic circuit operation rather than the static mode of operation used in [Tajalli III]. BRIEF DESCRIPTION OF FIGURES

[0025] FIG. 1 is a schematic diagram of a voltage sampler with high frequency peaking and offset compensation.

[0026] FIG. 2 is a schematic diagram of a voltage sampler embodiment with increased signal gain over a wide frequency range and offset compensation.

[0027] FIG. 3 is a schematic diagram of one embodiment of a dynamic mode CMOS sampling circuit allowing an extended input signal evaluation time.

[0028] FIG. 4 is a block diagram showing a cascade of sampling integrator/amplifiers acting upon a single input signals and producing four results suitable for processing in four phases.

[0029] FIG. 5 is a schematic showing one embodiment of a dynamic mode CMOS self retimed integrator suitable for use as the samplers/integrators of FIG. 4.

[0030] FIG. 6A is a gain vs. frequency plot showing high frequency "peaking" gain enhancement as provided by the circuit of FIG. 1.

[0031] FIG. 6B is a gain vs. frequency plot showing wideband gain enhancement as provided by the circuit of FIG. 2.

[0032] FIG. 7 illustrates one embodiment of a cascaded series of discrete time domain samplers providing increased wideband and high frequency gain with offset compensation.

[0033] FIG. 8 illustrates a second embodiment of a cascaded series of discrete time domain samplers providing increased wideband and high frequency gain while supporting DC signal correction wherein each sampler stage has differential inputs and outputs.

[0034] FIG. 9 is a frequency vs. gain plot for one cascaded sampler embodiment.

[0035] FIG. 10 is a schematic diagram of one embodiment of a sampler stage with increased high frequency gain and controllable-polarity offset compensation.

[0036] FIG. 11 A is a block diagram of a cascaded system utilizing the sampler stages of FIG. 10. [0037] FIG. 11B is a block diagram of a clock delay circuit, in accordance with some embodiments.

[0038] FIG. l l C is a block diagram of a local oscillator generating various phases of a clock circuit, in accordance with some embodiments.

[0039] FIG. 12 is a flowchart of a method 1200, in accordance with some embodiments.

[0040] FIGs. 13 A and 13B illustrate multi-stage sampling clock relationships, in accordance with some embodiments.

[0041] FIG. 14 is a flowchart of a method 1400, in accordance with some embodiments.

[0042] FIG. 15 illustrates a sampler/integrator stage driving multiple samplers, in accordance with some embodiments.

[0043] FIG. 16 illustrates a sampler/integrator stage acting as an integrate-and-hold stage, in accordance with some embodiments.

[0044] FIG. 17 illustrates pre-cursor receiver compensation, in accordance with some embodiments.

[0045] FIG. 18 is a block diagram of a single integrator driving multiple latches, in accordance with some embodiments.

[0046] FIG. 19 is a flowchart of a method 1900, in accordance with some embodiments.

DETAILED DESCRIPTION

[0047] To reliably detect the data values transmitted over a communications system, a communications receiver accurately measures its received signal value amplitudes at carefully selected times, typically at or near the center of that received signal's period of stability between transitions. This point is commonly described as the "center of eye", (referring to the well-known "eye diagram" of signal amplitude vs. clock intervals) and is typically determined by use of a local "receive clock" which is configured to occur at that desirable sampling time. Generation and ongoing control of such receive clock timing is well understood in the art, as Clock and Data Recovery (CDR) systems measure and incrementally adjust sample timing versus receive signal stability time to optimize sample timing. [0048] In some embodiments, the value of the received signal is first captured at the selected time using a sample-and-hold or track-and-hold circuit, and then the resulting value is measured against one or more reference values using a known voltage comparator circuit.

[0049] Other embodiments utilize circuits capable of applying both the time- and amplitude- domain constraints, producing a result that represents the input value at a particular time and relative to a provided reference level. [Tajalli III] provides examples of such voltage sampler embodiments, in which the high frequency gain of the sampling circuit may be advantageously boosted over a narrow frequency range, in a so-called high frequency peaking action as graphically illustrated by the gain vs. frequency chart of FIG. 6A. Such high frequency peaking is particularly useful in receiver frequency compensation of communications channel characteristics. A further embodiment is described herein, in which the clocked sampling action is further enhanced by reliance on dynamic circuit operation rather than the static mode of operation used in [Tajalli III].

[0050] Dynamic circuit operation may also be applied to wideband amplification to provide enhanced signal gain over a wide frequency range, as shown by the gain vs. frequency chart of FIG. 6B and described in embodiments herein.

[0051] The source of the input signal to the embodiments described herein may be derived from a single wire signal, or may be derived from a weighted linear combination of multiple wire signals, such as provided by a Multi Input Comparator or mixer (MIC) used to detect vector signaling codes.

Sampler with High Frequency peaking

[0052] It is common for communications links to be operated at data transfer rates at or near the declining portion of the link's response vs. frequency curve. Thus, it is desirable for receivers to be configurable to provide additional high frequency gain, as compensation for the reduced response of the communications link.

[0053] [Tajalli III] provided one example of a sampler circuit capable of providing additional narrowband high frequency gain through use of a secondary gain path enabled by a frequency- selective RC network. The circuit of FIG. 1 provides another embodiment of this type with lower quiescent current draw, due to its reliance on dynamic switching mode in all transistors. Positive cycles of CK turn on transistors 110 and 111 pre-charging nodes Vout+ and Vout-, with the complementary or inverse phase of CK enables transistors 150 and 160, allowing those charges to flow through the differential transistor pairs 120/121 and 140/141 to ground, those momentary current flows being controlled by the voltage levels presented by inputs Vin+ and Vin-. Because of the non-overlap between charge sources and discharge sinks being on, this circuit draws essentially no quiescent current, and effectively samples input signals at the falling edge of CK.

[0054] As with the circuit of [Tajalli III], the parallel differential transistor pair 140/141 provides additional high-frequency peaking in this embodiment and optional offset voltage compensation, as the differential pair inputs are driven by Vin+ and Vin- with a frequency response shaped by high-pass RC filters 170/180, and 171/ 181 having a corner frequency of f_z w . Incremental adjustment of offset correction voltages Voc+ and Voc- may be made

2nRC

as necessary to adjust the balance of differential outputs Vout.

[0055] As is common practice, f_z will typically be chosen to be at or near the natural high frequency falloff of the received signal amplitude vs. frequency curve to provide the desired peaking characteristic, as illustrated in FIG. 6A.

Sampler with increased wideband gain

[0056] The same dynamic mode operation may be used in a sampling circuit with wideband gain, as shown in the schematic of FIG. 2.

[0057] Although a similar incremental-linear analysis may be applied here as in the previous example, an alternative interpretation may be of more descriptive value, especially in operational configurations where the clock frequency is significantly higher than corner frequency f_z . In this alternative analysis, first stage 210 effectively acts as a high frequency mixer, producing differential output signals Vm+ and Vm- which are effectively the carrier CK mixed with or modulated by differential input Vin. Second stage 220 then effectively acts as a synchronous demodulator, mixing Vm with CK to produce differential outputs Vout again. As the modulated carrier frequencies involved are higher than corner frequency f_z, the modulated signals effectively pass unaffected through capacitors C, allowing both differential pairs in 220 to provide gain at all signal frequencies. In one embodiment, the resulting transfer function was seen to be effectively flat over a wide frequency range, as illustrated in FIG. 6B, with approximately 6 dB of additional gain. As in the previous example, incremental adjustment of offset correction voltages Voc+ and Voc- may be made as necessary to adjust the balance of differential outputs Vout.

Sampler with extended evaluation time

[0058] In switched dynamic circuits such as that of FIG. 2, the static voltage of internal nodes such as Vm+ and Vm- are dependent not only on the transistor action of the differential pair, but also on the integrating action of the distributed node capacitance on the charge transferred on CK transitions. This integrating behavior can become significant, especially when multiple dynamically clocked stages are cascaded as in this example.

[0059] FIG. 3 shows the schematic diagram of a modified version of the previous sampler, in which two partially overlapping clocks CK and CK' are used to obtain extended input evaluation time. For descriptive purposes without implying a limitation, CK and CK' in this explanation are assumed to have an approximate quadrature relationship, as shown in the timing diagram of FIG. 3. In practice, both clocks may be generated by a multiphase clock generator, or one clock may be synthesized from the other using a delay element. During the first 90 degrees of the clock cycle, the sampler is reset by turning on the tope three PMOS FETS that charge the Vs nodes to the supply voltage. On the rising edge of CK (during the second 90 degrees of the clock cycle) the Vs outputs take on differential output levels proportionate to the voltage levels seen at Vin- and Vin+, where one side is discharged to ground and the other remains charged at the supply voltage. Those levels remain unchanged while either CK or CK' is high. Specifically, in the third 90 degree portion, the addition of the top PMOS FET driven by the quadrature (or otherwise delayed) clock CK' prevents the recharge/reset action that would have otherwise occurred when CK returns low (turning off the tail current at the bottom and turning on the middle PMOS FETs to recharge Vs). Only after CK' goes low in conjunction with CK during the final 90 degrees do the output nodes Vs+ and Vs- get precharged to high levels during a reset interval Thus, the voltage sample occurs at the rising edge of CK, and is maintained through the falling edge of CK' (rather than merely the falling edge of CK). This extended output duration provides increased set-up time for a subsequent integrator/sampler or latch element. Clock signals utilized in the further examples described herein may be similarly modified, including but not limited to clock duty cycles and relative clock phase overlap or non-overlap, to provide comparable extended output duration in those embodiments. Cascades of clocked samplers

[0060] Clocked samplers with the described functionality are amenable to cascaded operation, as in the embodiment shown in the block diagram of FIG. 4. Input signal Vin is sampled at 410 and 415 by samplers operating on complementary phases of a two-phase sampling clock at frequency Fck/2. The resulting sampled results are each themselves sampled twice, by samplers operating on complementary phases of sampling clocks at frequency Fck/4. That is, each sampled result provided by 410 is alternately sampled by 420 or by 425 (as their sampling clock operates at one half the rate of the previous sample clock). Similarly, each sampled result provided by 415 is alternately sampled by 430 or by 435. The four results thus obtained are again sampled at 440, 445, 450, and 455, and those ultimate sampled results are digitally latched at 460, 465, 470, 475 to produce digital outputs Voutl, Vout2, Vout3, and Vout4.

[0061] In practical embodiments, splitting data processing between two phase operation with its simple clocking regime, and four- (or greater) phase operation with its relaxed latency provides a useful tradeoff between power, speed, and complexity. Such cascaded samplers may be designed for any arbitrary number of resultant phases using known art clock division and/or clock steering logic, thus neither "two phase" nor "four phase" should be considered limiting in this description.

[0062] FIG. 5 is a schematic diagram of one embodiment of a CMOS sampler/integrator particularly well suited to cascaded operation as in FIG. 4. Input clock CK and its compliment CK control first sampler stage 510 and second sampler stage 520 respectively. In practice, this alternation of complementary stages provides an advantageous self-retiming behavior that simplifies clocking where there are two or more consecutive stages of such sampler/integrators, also described herein as integrate-and-hold stages, because of the extended valid output duration obtained in this configuration. Such cascaded sampler architectures also allow significant gain to be obtained; in one embodiment, 27 dB of gain was obtained from a series of such stages with only 0.5 mV of RMS noise.

[0063] FIG. 16 shows a further embodiment of the sampler/integrator 510 of FIG. 5, in which additional series pass transistors 1611 and 1612 are added to the discharge path in the first sampler stage 1610, which corresponds to stage 510 of FIG. 5. When clock CK goes high, precharged outputs Vo+ and Vo- quickly resolve to a valid output result, but in the unmodified embodiment of FIG. 5 would continue to discharge to Vss. In this further embodiment, pass transistors 161 1 and 1612 terminate this discharge as soon as the common mode output voltage of outputs Vo+ and Vo- decays below their threshold voltage, providing this embodiment with an extended evaluation time. Comparable action may be seen in second sampler stage 1620, where pass transistors 1621 and 1622 similarly terminate discharge to Vdd as soon as the common mode output voltage of Vout+ and Vout- decays below their threshold voltage. Either stage 1610 or stage 1620 individually, or the cascaded sequence of stages 1610 and 1620 together demonstrates the desirable extended valid output duration associated with integrate- and-hold behavior.

Decision Feedback Equalization

[0064] Decision Feedback Equalization or DFE is a well-known technique used to improve signal detection capabilities in serial communication systems. It presumes that the transmission line characteristics of the communications channel between transmitter and receiver is imperfect, thus energy associated with previously transmitted bits may remain in the channel (for example, as reflections from impedance perturbations) to negatively impact reception of subsequent bits. A receiver's DFE system processes each bit detected in a past unit interval (UI) through a simulation of the communications channel to produce an estimate of that bit's influence on a subsequent unit interval. That estimate, herein called the "DFE correction", may be subtracted from the received signal to compensate for the predicted inter-symbol interference. Practical DFE systems produce DFE corrections derived from multiple previous unit intervals.

[0065] At very high data rates, there may not be sufficient time to detect a received bit, calculate its associated DFE correction, and apply that correction to the next received unit interval in time to detect the next bit. Thus, some embodiments utilize so-called "unrolled DFE", where correction values are determined for some or all possible combinations of previous data values, those speculative corrections are applied to multiple copies of the received signal, and speculative detections made of the resulting corrected signal instances. When the earlier data values are finally resolved, the correct speculatively detected output may be chosen as the received data value for that unit interval.

[0066] As may be readily apparent, "unrolling" of DFE for even a modest number of historical unit intervals in this way maintains a significant number of speculative results effectively in parallel, introducing significant circuit complexity and associated power consumption. Cascaded samplers with DFE

[0067] The cascaded sampler embodiment of FIG. 7 provides an interesting alternative to unrolled DFE. As with previous examples, each primary Discrete Time Integration element (for example 710) is associated with a secondary Discrete Time Integration element (decision- feedback offset generator 715) providing offset compensation (DFE correction value VDC1) and boosted high frequency gain (determined by the time constant of RC.)

[0068] As the first stage composed of 710/715 is cascaded with the second stage of 720/725 and third stage of 730/735, significant signal gain is produced between input Vin and the ultimate data result sampled at Latch 740. The gain vs. frequency plot of one such embodiment is shown as FIG. 9, where "G" is the typical gain of a single stage composed of two Discrete Time Integration elements, each typically contributing a gain of approximately 0.5G.

[0069] Each Discrete Time Integration element 710, 715, 720, 725, 730, 735 in FIG. 7 may be as previously described as 210 of FIG. 2. In an alternative embodiment, alternating instances of FIG. 5's 510 and 520 may be used for consecutive stages of FIG. 7.

[0070] As is well understood in the art, differential inputs as in the example Discrete Time Integration elements may be utilized as single-ended inputs by tying the unused second input to an appropriate source of DC bias and AC virtual ground. Alternatively, the fully differential embodiment of FIG. 8 may be used with either the elements of FIG. 2 or FIG. 5, all such variations being considered equivalent herein.

[0071] The DFE voltage magnitudes VDC1, VDC2, VDC3 of FIG. 7 (and for FIG. 8, their differential signal equivalents) may be used to correct fixed offset voltage errors or as inputs for DFE correction signals.

[0072] It should be noted that as the cascaded series of Discrete Time Integrators passes along sampled voltage output values in consecutive clock intervals, it constitutes a form of analog signal memory or analog delay line. Thus, in the case where the voltage inputs are used for DFE correction, those inputs may take on the appropriate DFE correction value (i.e. associated with the proper historical data value) at or before the sampling time, that association being relative to the sampled signal being processed by that stage at that time. For the embodiment shown in FIG. 8 where the correction voltage inputs are differential, it was observed that DFE correction values may be expressed as differential voltage pair {VDCa, VDCb} if the historical bit was a Ί ', and by the swapped pair {VDCb, VDCa} if the historical bit was a 'Ο'. Thus, the equivalent of a dual pole dual throw switch could be used to modify a single DFE voltage magnitude value VDC, directing either the original value or the swapped (reverse polarity) value into that stage of the system, controlled by the historic data bit associated with that previous time unit interval.

[0073] In one embodiment, the DFE magnitude values of {VDCa, VDCb} are chosen such that the resulting voltages (both directly and with the described differential swapping) satisfy both the necessary DFE correction criterion and normalize undesirable DC offset in the Discrete Time Integrator cascade. In some embodiments, the DFE magnitude values VDC may include a DC voltage offset component.

[0074] A further embodiment incorporates a modified Discrete Time Integrator embodiment as illustrated in FIG. 10. As with FIG. 8, all signals are differential. For avoidance of confusion, it should be noted that the schematic of FIG. 10 corresponds to one complete stage 801 , 802, 803 of FIG. 8, comprising both Discrete Time Integrators, RC filter, etc., and adding a switching element to selectively swap a polarity of the DFE correction magnitude value under the control of a historical data input.

[0075] In this embodiment, the received analog input voltage Vin is sampled by transistors 1001, 1002, 1003, 1004, 1005 and augmented by high frequency peaking provided by filter networks RC and one of differential pairs 1011/1012 or 1021/1022 in the DFE offset generator and transistor 1040. The particular differential pair is selected by transistors 1031/1032 using historical data DH[N]+ and DH[N]-, the high frequency peaking result augmenting sampled analog voltage outputs Vout+ and Vout- with either a direct analog of the VDC+ and VDC- voltages, or their differentially swapped equivalent.

[0076] In some embodiments, an apparatus includes a memory device 1 160 configured to store one or more historical data values, a Decision-Feedback Equalization (DFE) computation circuit 1150 configured to generate a DFE magnitude value, a decision-feedback offset generator (e.g., 1 110, 1120, 1 130) configured to receive the DFE magnitude value VDC and a historical data value DH[N] of the one or more historical data values, and to responsively generate an analog DFE correction value having a voltage magnitude equal to the DFE magnitude value and a polarity determined by the historical data value received from the memory device, and an analog sampler configured to receive an analog summation of the analog DFE correction value and an analog input signal Vin, and to generate a sampled voltage output Va according to a sampling clock Ckl . In the preceding embodiment, analog input signal Vin and sampled voltage output Va are with respect to decision-feedback offset generator 11 10.

[0077] In some embodiments, the analog input signal is a sampled voltage output received from a cascaded analog sampler. In alternative embodiments, the analog input signal corresponds to an analog output of a multi-input comparator.

[0078] In some embodiments, the decision-feedback offset generator includes a pair of decision feedback branches 101 1/1012 and 1021/1022, each decision feedback branch receiving the DFE magnitude value in respective inverse-polarity configurations, and a selection circuit 1031/1032 configured to receive the historical data value and to responsively enable one of the pair of decision feedback branches to determine the polarity of the DFE correction value. In some embodiments, the decision-feedback offset generator is further configured to receive a high-frequency injection of the analog input signal Vin. In some embodiments, the high-frequency injection of the analog input signal is received via a resistor- capacitor high-pass filter. In some embodiments, the decision-feedback offset generator is further configured to receive a voltage offset signal.

[0079] In some embodiments, the sampled voltage output has a propagation delay less than one unit-interval with respect to the received analog input signal. In alternative embodiments, the sampled voltage output has a propagation delay greater than one unit-interval with respect to the received analog input signal. In some embodiments, the memory device comprises a shift register.

[0080] The complete multistage embodiment shown in FIG. 11 A utilizes three instances of FIG. 10 shown as 11 10, 1 120, 1130, and takes advantage of the analog delay characteristic of cascaded Discrete Time Integrators by configuring differential input VDCl to be composed of the computed DFE correction for the [N-3] historical UI interval and DH[-3] the 3^rd previous data value, VDC2 to be composed of the computed DFE correction for the [N-2] historical UI interval and DH[-2] the 2^nd previous data value, and VDC3 to be composed of the computed DFE correction for the [N-l ] (i. e. immediately preceding) historical UI interval and DH[-1 ] the immediately preceding data value (all such timing descriptions being relative to the current signal input Vin.) This provides the full duration of three unit intervals for the detection of a given data value, before that data value is used by the DFE system. As a non-limiting example, digital shift register 1160 is illustrated storing and providing the previous data values to stages 1130, 1120, and 1110 (i.e. in this illustration 1160 shifts to the left), each data value being sampled and detected by latch 1 140 and also presented to data output Vout. DFE Computation 1150 is shown providing the previously-described DFE correction magnitude values VDC1, VDC2, VDC3, which represent the contribution of a given historical time unit interval to the observed perturbation of the current time unit interval's received signal. In some embodiments, VDC1, VDC2, and VDC3 may be represented as voltage magnitudes, whose polarity is determined by a historical data value. Each such voltage, combined with the polarity determined by selection information provided by the corresponding historical data bit for that historical time unit interval, produces a DFE correction value (also referred to herein as a DFE compensation value) appropriate to that processing stage's correction of the signal being sampled. As shown, each stage 1110-1130 receives a respective clock having respective delays. In some embodiments, the delay between any adjacent clock (CK1/CK2, CK2/CK3) may be on the order of 5-15psec. Alternatively, each clock may have a fixed phase relationship such as a quadrature phase relationship generated by a local oscillator in a PLL. Such oscillators may take the form of ring oscillators, such as the ring oscillator 1180 shown in FIG. 11 C.

[0081] For descriptive purposes the examples herein show the use of three cascaded processing stages with no limitation implied. Additional stages may be added, as examples to provide additional gain and/or provide additional corrective DC voltage magnitude inputs such as to support deeper DFE correction history, and fewer stages may be used, as examples if lower gain and/or fewer corrective DC voltage magnitude inputs suffice. Similarly, the various apparatus and methods disclosed herein may be combined with each other and with known art to, as one example, provide offset voltage adjustment and introduce a separate DFE correction voltage within a single stage, which may be an element of a multistage system.

[0082] For descriptive purposes, the examples herein describe cascaded stages of sampling elements being triggered by a single clock, introducing one clock cycle delay per stage. No limitation is implied, as triggering of individual stages may be initiated using multiple clock phases having any desired timing relationship, as long as the implementation-dependent setup and hold times for the particular embodiment are satisfied. Thus, given appropriately configured triggering clock phases, the overall delay through such a cascade may be a fraction of a clock cycle, or many clock cycles. [0083] In some embodiments, there may be a group delay ti from when outputs Va change according to input Vin, in the case of the first stage 1110. In such embodiments, CK2 may be delayed by an amount of at least ti in order to hold a charge of VDD at the output nodes of 1120 long enough for the inputs Va to stage 1120 to settle. In some embodiments, CK1 may be put through a delay element (not shown) in order to generate clocks CK2, CK3, and CK4, the delay element introducing a delay of at least t„ to each clock, where t„ is the group delay associated with a given stage. In some embodiments, this group delay value may be associated with capacitances in the transistors of each stage, as well as various other factors that are known to cause group delay. In most practical embodiments, t„ will be approximately the same. In some embodiments, t„ is approximately 5-15psec, however this should not be considered limiting. FIG. 11B illustrates a delay buffer for generating the clock signals CK2-CK4 based on CK1. As shown, a plurality of series-connected gates 1171-1173 are configured to provide clock signals CK2-CK4, respectively based on CK1. Each gate will introduce a delay corresponding to the group delay value t„ described above. FIG. 13A illustrates an exemplary relationship between clocks CK1 and CK2, in accordance with some embodiments. Alternatively, clocks CK1-CK4 may be various phases of a local oscillator clock, generated using, as a non-limiting example, a PLL. FIG. 11 C illustrates such an embodiment in which a local oscillator 1180 provides the four phases of the clock signals CK1 -CK4. In some embodiments, each adjacent clock signal may have a relative phase relationship of 45 degrees, such as in the example shown in FIG. 11 C. In alternative embodiments, each adjacent clock signal may have a relative phase relationship of 90 degrees (not shown). Such embodiments may be used as long as the analog-sampled voltages at the output nodes of a given stage do not begin to decay to VSS before the rising edge clock CK of the subsequent stage. FIG. 13B illustrates an example of clocks CK1 and CK2 having a phase offset of 45 degrees, however it should be noted that any phase offset relationship may be used as long as the phase offset relationship satisfies the above criteria.

Increased drive capability

[0084] It may also be noted that the dynamic sampler/integrator and integrate-and-hold stages described herein produces results which are less influenced by output loading than, for example, the output of a Continuous Time Linear Equalizer (CTLE) circuit operating in a linear amplification mode. In a linear amplifier, additional load capacitance reduces the circuit's high frequency response, and compensation for this behavior typically results in a substantial increase in the linear circuit's power consumption. Conversely, additional sampler/integrator output capacitance will at most delay the time interval during which the output values are valid. A modest increase in output drive current (much less than for the equivalent continuous-time circuit) or a small adjustment of clock timing for latching or sampling of the result may be incorporated as correction of such a delay.

[0085] This increased immunity to output loading is particularly useful when a signal is fanned out to multiple subsequent stages, as in the transition from two-phase to four-phase clock domains illustrated in FIG. 4.

[0086] FIG. 15 shows another receiver embodiment, comprising a sampler 1510 including multiple cascaded integration stages, followed by a plurality of slicing circuits, wherein a data slicing circuit including a sampler/integrator 1520 and a respective latch 1550 is supplemented by a clock data recovery slicing circuit including sampler/integrator 1530 and corresponding latch 1560 and a statistical monitoring slicing circuit including sampler/integrator 1540 and corresponding latch 1570, the slicing circuits respectively producing received data results, timing information to enable Clock/Data recovery adjustment of the clock generator, and statistical receive "eye" information for a command/control/monitoring subsystem. If received signal 1515 were obtained directly from the output of a linear amplification stage such as a CTLE or MIC mixer as a continuous-time analog differential voltage, the combined capacitive loading of the multiple slicing circuits would introduce a significant frequency-domain pole impacting high-frequency response. Further, as the loading on the CTLE stage increases, the increase in current to sustain such loading increases in a non-linear fashion, significantly increasing power dissipation. However, introducing sampler 1510 (in this embodiment illustrated as a cascade of two consecutive integration stages without implying limitation) allows signal 1515 to be driven as an integrated analog differential voltage with relative immunity from the effects of such loading, improving overall receive signal quality while simultaneously utilizing less power than a continuous-time alternative design.

[0087] In some embodiments, a method includes obtaining, at an input stage of a sampler 1510, a continuous-time analog differential voltage Vin, and responsively generating an integrated analog differential voltage 1515 by discharging a pair of pre-charged output nodes in an integration period according to the continuous-time analog differential voltage. The integration period is initiated by a sampling clock. The integrated analog differential voltage is subsequently provided to a plurality of slicing circuits, e.g. , data slicing circuit comprising sampler/integrator 1520 and latch 1550 without implying limitation, each slicing circuit having inputs connected to the pair of output nodes and generating a respective sliced output signal based on a respective slicing threshold of a set of slicing thresholds. As shown in FIG. 15, the integrated analog differential voltage on nodes 1515 may correspond to a held voltage Vb that is generated by an integrate-and-hold stage, and the slicing circuits each include respective sampler/integrators 1520, 1530, and 1540 configured to apply respective slicing offsets and to generate respective localized differential voltages Vc Data, Vc_CDR, and Vc_Eye on nodes that fully discharge, the respective localized differential voltages being latched by latches 1550, 1560, and 1570, respectively.

[0088] Connecting the latches to a pair of output nodes undergoing a full discharge may be preferred as fully discharged nodes reduce prolonged current dissipation that may otherwise occur when holding a differential voltage at the input of the latch, increasing power dissipation. It should be noted, however, that some embodiments may provide a held integrated analog differential voltage generated by an integrate-and-hold stage directly to a latch. In some embodiments, it may be beneficial to utilize a multi-stage sampler composed of an odd number of cascaded integration stages prior to the latches generating the sliced outputs. In FIG. 15, each latch is preceded by three cascaded stages, ensuring that the nodes connected to the inputs of the latch will fully discharge. Specifically, analyzing FIG. 15, it may be observed that the nodes generating intermediate voltage Va will fully discharge, which will eventually cause the integration stage generating the voltage Vb to hold a differential voltage due to Va provided at the input of the second stage falling below the threshold voltage of the transistors. Subsequently, sampler/integrators 1520, 1530, and 1540 within the slicing circuits will all generate localized differential voltages provided to latches 1550, 1560, and 1570 on nodes that will fully discharge. In some embodiments, the cascaded stages of a multi-stage sampler alternate between (i) integration stages, where output nodes fully discharge, and (ii) integrate- and-hold stages, where the discharge of output nodes is terminated in response to the inputs connected to a preceding integration stage fall below the operating threshold of the input transistors. FIG. 18 described below describes an example using a single integration stage for providing an integrated analog differential voltage on nodes that full discharge to a plurality of slicing circuits composed of latches, and additionally analog adders for applying offset correction values to adjust the respective slicing threshold.

[0089] In the example of FIG. 15, the integration stages in samplers 1510, 1520, 1530, 1540 support an analog voltage offset input such as described with respect to the embodiment of FIG. 10. The offset inputs of the cascaded integration stages in sampler 1510 are shown accepting historical DFE correction values, while the slicing offset inputs of samplers 1520 and 1530 determine slicing threshold levels to detect data values and timing edges, respectively. Introduction of historical DFE correction values in the plurality of cascaded integration stages of 1510 allows the integrated analog differential voltage 1515 to be sampled for data, CDR, and eye, rather than known art approaches that would use the summation of multiple components of DFE correction to be added separately to each sampler's threshold input. This architectural flexibility may be utilized in multiple ways. In some embodiments, the data sampler 1520 and CDR sampler 1530 are configured to receive speculative DFE correction values that are inverted with respect to each other. In such embodiments, a first speculative DFE correction value for the data sampler 1520 may provide transition information by comparing the detected data result to a historical data result, and the second or inverted speculative DFE correction value for the CDR sampler 1530 may provide an early/late timing indication used by a CDR circuit to adjust a phase of the baud rate clock. Such embodiments may select one speculative DFE correction value as being used for the data slicing circuit and the other speculative DFE correction value as being used for the edge slicing circuit based on a previously-detected data value.

[0090] In one embodiment, DFE Correction 1 and DFE Correction 2 represent historical DFE correction values associated with the received data value during the third, and second-most recent unit intervals, respectively. The Data sampling slicing threshold is composed of a sampler calibration offset voltage, a sampler threshold voltage, and a computed DFE correction value associated with the received data value during the most recent preceding unit interval. The Edge sampling slicing threshold is composed of a sampler calibration offset voltage and a sampler threshold voltage; it is observed that baud-rate CDR sampling such as utilized here may be enhanced by omission of the most-recently-received component of CDR correction. The Eye sampling slicing threshold is composed of a sampler calibration offset voltage, an adjustable eye sampling threshold voltage, and optionally a computed DFE correction value associated with the received data value during the most recent preceding unit interval. In some embodiments, the integration periods of samplers 1520 and 1530 are triggered by a baud rate clock occurring at or near "center of eye".

[0091] In one particular embodiment, a single baud rate clock is used to trigger all samplers, with the offset input of sampler/integrator 1540 being adjustable by, as one example, a command/control/monitoring subsystem, so as to obtain statistical samples of received signal level as needed to generate a graph of statistical signal amplitude data. In a further embodiment, an optional phase-adjustable Eye sampling clock is used to trigger eye-scope sampler 1540 separately from the baud rate clock used to trigger, for example, data sampler 1520, allowing statistical signal samples to be gathered representing both amplitude and phase information.

[0092] DFE embodiments are known in which the computation of multiple unit interval compensation values are inherently summed or combined into a single result. A second embodiment applies such a combined correction at stage 1510, and optionally negates or applies the inverse correction specific to the most recent previous unit interval data to sampler 1530. Other combinations of individual DFE correction values, combined or summed DFE correction values, and fixed or adjustable offset voltages may be applied to 1510, 1520, 1530, and 1540 without limitation.

[0093] FIG. 18 is a block diagram of an alternative embodiment in which the slicing circuits are composed of latches 1820/1830/1840, one non-limiting example being a logical SR latch, and respective analog adders 1817/1827/1837. As shown in FIG. 18, a continuous-time analog differential voltage Vin is provided to input stage of sampler 1810, which generates the integrated analog differential voltage Va at differential output nodes 1815. The slicing thresholds have offsets applied via analog adders 1817/1827/1837, and the resulting corrected integrated differential voltages are provided to respective latches 1820, 1830, and 1840. When the integration period is initiated by the sampling clock, input stage 1810 begins integrating by discharging the pair of output nodes 1815 at different rates due to the continuous-time differential voltage Vin applied to the inputs. As the output nodes 1815 discharge, the latches generate a sliced output according to the corrected integrated analog differential voltage, and the sliced output is held despite the pair of output nodes fully discharging.

DFE pre-cursor correction

[0094] The previously described DFE correction values are applied at the receiver to correct the signals currently being detected for anomalies caused by signals in previously-received unit intervals. In the common terminology of the art, these may be described as "post-cursor" corrections. "Pre-cursor" corrections are also possible, and indeed are often applied within a transmitter (where both historical and forthcoming data values to be sent are readily available) as part of so-called Finite-Impulse-Response compensation or "pre-shaping" of the transmitted waveform. [0095] Applying pre-cursor corrections at the receiver may include passing the actual signal values to be detected through a delay, allowing "future" i.e. non-delayed received values to be applied as corrections to the delayed values, which are then sampled.

[0096] For a one Unit Interval pre-cursor correction, the received signals may be delayed by one UI. Using as a non-limiting example a receive signal stream of 25 Gbps/wire, a delay of 40 picoseconds would thus be introduced.

[0097] The received signal values may be delayed using a series of cascaded stages, which may include e.g., Sample-Integrate-Hold (SIH), Sample-Hold (SH) stages or a combination of both. The previously-described dynamic sampler embodiments of FIGs. 3, 5, and 16 may be readily applied to this usage, as may other known art SIH and SH embodiments. It may be noted that a single instance of the sampler of FIG. 5, (e.g. 510,) provides only a short effective hold time, as the integrated analog differential voltage decays from its pre-charged value through an active region, and then continues to decay to ground. However, in a sequential cascade of multiple integration stages 510 clocked essentially simultaneously or with a group delay as previously described, second instance decay towards ground will be cut off as soon as the first instance output drops low enough to cut off the second instance input transistors, effectively extending the second instance hold time.

[0098] The embodiment of FIG. 16 accentuates this effect by incorporating series transistors into each instance controlled by that instance's output; thus, as each output decays it cuts off that instance's discharge path, extending the effective hold time.

[0099] FIG. 17 shows a receiver embodiment incorporating pre-cursor compensation along with the post-cursor DFE correction of FIG. 15. Continuous-time analog differential voltage Vin passes through cascaded Sample-Integrate-Hold stages 1705, which collectively represent one Unit Interval of time delay. The non-delayed continuous-time analog differential voltage is scaled 1702 and added 1706 to the delayed signal, providing the desired pre-cursor compensation. Then, as previously described with respect to FIG. 15, subsequent Sample- Integrate-Hold stages 1710 allow addition of DFE correction values 1, 2, 3, and slicing circuits 1720, 1730, 1740 capture Data, Clock error, and Eye scope values. Receiving Methods

[0100] FIG. 12 is a flowchart of a method 1200, in accordance with some embodiments. As shown, method 1200 includes receiving, at step 1202, a historical data value from a memory device storing one or more historical data values and a DFE magnitude value from a Decision- Feedback Equalization (DFE) computation circuit. At step 1204, an analog DFE correction value is generated using a decision-feedback offset generator, the analog DFE correction value having a voltage magnitude equal to the DFE magnitude value and a polarity determined by the historical data value received from the memory device. At step 1206, an analog input signal is received and responsively an analog summation of the analog DFE correction value and the received analog input signal is generated at step 1208. At step 1210, a sampler generates a sampled voltage output by sampling the analog summation according to a sampling clock.

[0101] In some embodiments, the analog input signal is a sampled voltage output received from a cascaded analog sampler. In alternative embodiments, the analog input signal corresponds to an analog output of a multi-input comparator.

[0102] In some embodiments, generating the DFE correction value includes receiving, at a pair of decision feedback branches, the DFE magnitude value in respective inverse-polarity configurations, and selecting, using a selection circuit receiving the historical data value, one of the pair of decision feedback branches to determine the polarity of the DFE correction value.

[0103] In some embodiments, the DFE magnitude value includes a high-frequency injection of the analog input signal. In some embodiments, the high-frequency injection of the analog input signal is received via a resistor-capacitor high-pass filter. In some embodiments, the DFE magnitude value comprises a voltage offset signal.

[0104] In some embodiments, the sampled voltage output has a propagation delay less than one unit-interval with respect to the received analog input signal. In alternative embodiments, the sampled voltage output has a propagation delay greater than one unit-interval with respect to the received analog input signal. In some embodiments, the memory device comprises a shift register.

[0105] FIG. 14 is a flowchart of a method 1400, in accordance with some embodiments. As shown, a first amplifier stage receives, at step 1402, a first analog input signal and a first decision-feedback equalization (DFE) correction value, and responsively generates, at step 1404, a first analog output voltage responsive to a rising edge of a first sampling clock, the first output voltage having an associated group delay value with respect to the first input signal. At step 1406, a second amplifier stage receives the first analog output voltage and a second DFE correction value, and responsively generates, at step 1408, a second analog output voltage responsive to a rising edge of a second sampling clock, the rising edge of the second sampling clock having a delay with respect to the rising edge of the first sampling clock by an amount greater than the associated group delay value. At step 1410, a latch configured generates a sampled output data bit by sampling the second analog output voltage according to a rising edge of a third clock signal having a delay with respect to the rising edge of the second clock signal.

[0106] In some embodiments, the method includes generating the second and third clock signals using a delay element receiving the first clock signal as an input. In such embodiments, the respective delay values may be arbitrarily tuned by adjusting parameters (capacitive, etc.) of the delay element

[0107] In some embodiments, the first, second, and third clock signals have respective fixed phase-offsets. In such embodiments, a phase-locked loop (PLL) generates the clock signals having fixed phase offsets.

[0108] In some embodiment, each DFE correction value has (i) a magnitude associated with a calculated DFE magnitude value and (ii) a sign determined by a historical data bit.

[0109] In some embodiments, the first received analog input signal is an analog voltage output received from a third amplifier stage.

[0110] FIG. 19 is a flowchart of a method 1900, in accordance with some embodiments. In method 1900, a continuous-time analog differential voltage is obtained 1902 at an input stage of a sampler for responsively generating an integrated analog differential voltage by discharging a pair of pre-charged output nodes in an integration period according to the continuous-time analog differential voltage, the integration period initiated by a sampling clock. The integrated analog differential voltage is provided 1904 to a plurality of slicing circuits having inputs connected to the pair of output nodes, each slicing circuit of the plurality of slicing circuits generating a respective sliced output signal based on a respective slicing threshold of a set of slicing thresholds.

[0111] In some embodiments, the method further includes generating one or more intermediate signals e.g., Va in FIG. 15 using one or more cascaded stages connected to the input stage of the sampler, the one or more cascaded stages applying respective amplifications to the integrated analog differential voltage. In some such embodiments, the one or more intermediate signals comprises a held differential voltage Vb generated by an integrate-and-hold stage of the one or more cascaded stages. In a further embodiment, the method includes generating the integrated analog differential voltage by integrating the held differential voltage generated by the integrate-and-hold stage of the one or more cascaded stages.

[0112] In some embodiments, the slicing circuits comprise latches configured to generate the respective sliced output signal. In some embodiments, the set of slicing thresholds comprises a speculative DFE offset correction value. In some embodiments, the set of slicing thresholds comprises an edge sampling correction value. In some embodiments, the method further includes introducing a historical DFE correction values into the continuous-time analog differential voltage via the input stage.

Claims

1. A method comprising:

obtaining, at an input stage of a sampler, a continuous-time analog differential voltage, and responsively generating an integrated analog differential voltage by discharging a pair of pre-charged output nodes in an integration period according to the continuous-time analog differential voltage, the integration period initiated by a sampling clock; and

providing the integrated analog differential voltage to a plurality of slicing circuits having inputs connected to the pair of output nodes, each slicing circuit of the plurality of slicing circuits generating a respective sliced output signal based on a respective slicing threshold of a set of slicing thresholds.

2. The method of claim 1, further comprising generating one or more intermediate signals using a plurality of cascaded stages connected to the input stage of the sampler, the plurality of cascaded stages applying respective amplifications to the integrated analog differential voltage.

3. The method of claim 2, wherein the one or more intermediate signals comprises a held differential voltage generated by an integrate-and-hold stage of the plurality of cascaded stages.

4. The method of claim 3, wherein generating the integrated analog differential voltage further comprises integrating the held differential voltage generated by the integrate-and-hold stage of the plurality of cascaded stages.

5. The method of claim 1, wherein the slicing circuits comprise latches to generate the respective sliced output signal

6. The method of claim 1, wherein the set of slicing thresholds comprises a speculative DFE offset correction value.

7. The method of claim 1, wherein the set of slicing thresholds comprises an edge sampling correction value.

8. The method of claim 1, further comprising introducing a historical DFE correction values into the continuous-time analog differential voltage via the input stage.

9. An apparatus comprising:

an input stage of a sampler configured to obtain a continuous-time analog differential voltage, and to responsively generate an integrated analog differential voltage by discharging a pair of pre-charged output nodes in an integration period according to the continuous-time analog differential voltage, the integration period initiated by a sampling clock; and

a plurality of slicing circuits having inputs connected to the pair of output nodes, each slicing circuit of the plurality of slicing circuits configured to generate a respective sliced output signal based on the integrated analog differential voltage and a respective slicing threshold of a set of slicing thresholds.

10. The apparatus of claim 9, wherein the sampler comprises one or more cascaded stages connected to the input stage of the sampler, the one or more cascaded stages configured to generate respective intermediate signals, each cascaded stage of the one or more cascaded stages configured to apply a respective amplification to the integrated analog differential voltage.

11. The apparatus of claim 10, wherein the one or more cascaded stages comprises an integrate-and-hold stage configured to generate an intermediate signal

corresponding to a held differential voltage.

12. The apparatus of claim 11, wherein the one or more cascaded stages comprises an integration stage having an input connected to the integrate-and-hold stage and an output corresponding to the pair of output nodes, the integration stage configured to integrate the held differential voltage generated by the integrate-and-hold stage to generate the integrated analog differential voltage.

13. The apparatus of claim 9, wherein each slicing circuits of the plurality of slicing circuits comprises a latch to generate the respective sliced output signal

14. The apparatus of claim 9, wherein the set of slicing thresholds comprises a speculative DFE offset correction value, an edge sampling correction value, and an eye- scope sampling correction value.

15. The apparatus of claim 9, wherein the input stage is configured to introduce a historical DFE correction value into the continuous-time analog differential voltage.