Patent Publication Number: US-7212580-B2

Title: Multi-level signal clock recovery technique

Description:
PRIORITY AND RELATED APPLICATIONS 
     The present application claims priority to provisional patent application entitled, “MULTI-LEVEL SIGNAL CLOCK RECOVERY TECHNIQUE,” filed on Feb. 15, 2002 and assigned U.S. application Ser. No. 60/357,362. The entire contents of this provisional application are hereby incorporated by reference. 
    
    
     TECHNICAL FIELD 
     The present invention relates to high speed communications. More particularly, the present invention relates to a system and method for recovering clock signals from multi-level signals in high speed optical and electrical communications. 
     BACKGROUND OF THE INVENTION 
     In order to obtain increase spectral efficiency and therefore increased data throughput for both optical and electrical data transport systems, complex modulation schemes, such as multilevel (ML) signaling, are desired by the communications industry for both electrical and optical domain applications. Clock recovery of the resulting complex waveforms can be difficult, but is critical for data recovery. 
     Conventional telecommunication clock-recovery (CR) integrated circuits (IC&#39;s) are generally only designed for use with binary non-return-to-zero (NRZ) (or equivalently On-Off-Keyed, OOK, waveforms). Conventional CR IC&#39;s may employ comparators to determine the clock signal from the multi-level signal. Such an approach usually does not detect a high percentage of the transitions of a multilevel signal that are important to determine the clock signal. 
     Other conventional clock recovery units directly process multilevel signals to recover the clock signals. However, such units are not useful in the high speed communications environment because of the processing time needed by these conventional units to extract the clock signals from the multi-level signals. 
     In yet another conventional approach, processing of the multi-level signal is focused on the middle of the multi-level signal and not the edges of the signal. More precisely, the slopes and amplitudes at the temporal decision points of the multilevel signals are examined to align the recovered clock so as to minimize an estimated sampling error. Such an approach focuses on minute signal amplitude variations, where the signal is expected to be flat, rather than major signal transitions, where the signal amplitude should generally experience major changes. The latter property is more indicative of the underlying clock. Also, usually in this conventional approach, the method involves decoding signal values prior to clock recovery. Such decoding is subject to decoding errors. 
     In view of the foregoing, there is a need in the art for efficiently detecting clock signals in a multilevel signal. There is a further need in the art for a system and method to determine clock signals from a multilevel signal in high speed communication applications. 
     SUMMARY OF THE INVENTION 
     This invention offers an efficient method for recovering the clock or equivalently the symbol timing information of very high-speed ML waveforms. It can be particularly applicable to the clock recovery of ML signals within the receivers of high-speed telecommunication systems. 
     An ideal clock recovery approach usually synchronizes the rising (or falling) edge of the clock to the transitions of the ML signal. Signal transitions are usually defined as the process of the signal changing from one symbol (or level) to another. 
     Clock recovery of a multi-level signal can be performed in a two-step process. First, the transitions within the ML signal can be detected by a novel transition detector (TD). And second, the output of the TD circuit can comprise a pseudo-non-return-to-zero (pNRZ) signal that can drive a conventional OOK clock recovery (CR) IC. The NRZ signal is referred to as pNRZ because it can lack meaningful data content. 
     One objective of the TD circuit is to convert the edges of the signal into the pseudo-NRZ (pNRZ) signal for subsequent processing by a standard NRZ OOK clock recovery IC. It is desired to capture as many transitions as possible to allow the conventional NRZ clock recovery (CR) chip to optimally perform. In practice, NRZ clock recovery chips can lock to OOK NRZ data streams with reasonably diminished transition density (such as on the order of 1/10 to 1/100), but their locking performance can sometimes suffer. 
     An ideal transition detector can produce an output that inverts on every transition of the ML data stream. Since the pNRZ signal is generated in order to recover the clock, it is reasonable to assume that the clock does not exist for the TD function and therefore, the TD circuit is probably an analog and/or asynchronous function. 
     Another important feature of the present invention is that a ML signal Vin can be differentiated. This differentiated signal can be zero when the signal is flat (e.g. in the middle of the data symbol or when two adjacent symbols are the same) and large in magnitude when a transition occurs. Whether the derivative is positive or negative (corresponding to upward or downward transitions) can be immaterial since one objective of the present invention is simply to detect the transition and not its direction. 
     Consequently, the invention can threshold the absolute value of the derivative instead of the signed derivative, unlike many conventional clock recovery techniques known in the art that use the sign, positive or negative, of the slope around a nominal sampling point to determine whether a clock should be advanced or delayed. 
     The present invention evaluates the edges of the multi-level signals rather than flat regions in the center of the decision timing of the multi-level signals. And unlike conventional clock recovery techniques that require decoding of the multilevel signals prior to recovering the clock signal, the present invention can operate without decoding any of the multi-level signals prior to clock recovery. In other words, the present invention recovers clock signals with an analog process that is unlike many conventional clock recovery techniques that digitize multilevel signals prior to recovering any clock signals. 
     The present invention can use the derivative of the ML signal for detection of the ML signal&#39;s transitions. The ML input signal, Vin, can be differentiated in order to produce a waveform that can be labeled dVin/dt. The differentiated signal can drive two comparators with thresholds set to Vref+ and Vref−. The comparators can produce two outputs that can be labeled “Up” and “Down”, which will become true as the signal, Vin, moves up or down, respectively. 
     When the signal rises, a positive derivative is present. The upper comparator with threshold set to Vref+ can assert an “Up” output. Similarly, when the input signal falls, a negative derivative is present and the lower comparator can assert a “Down” output. These two outputs labeled “Up” and “Down” are then combined to produce the necessary pNRZ output. 
     The rising edges of the “Up” and “Down” signals can be “captured” with two toggle flip-flops (T-FF&#39;s). The T-FF&#39;s can simply invert their outputs on every rising edge from the comparators. The output of the T-FF&#39;s can be exclusive OR&#39;ed (XOR&#39;ed) together to produce the desired pNRZ signal. An XOR function will usually invert its output, if the state of either input changes provided the other input remains constant. Since Vin cannot move both up and down simultaneously, a rising edge occurring from either “Up” or “Down” will usually result in an inversion of the TD output. This can represent the ideal pNRZ signal generation as discussed above. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a block diagram of an exemplary multilevel clock recovery system according to an exemplary embodiment of the present invention. 
         FIG. 2  is a block diagram illustrating some key functions of the transition detector circuit according to one exemplary embodiment of the present invention. 
         FIG. 3  is a block diagram illustrating exemplary elements of the transition detector circuit according to one exemplary embodiment of the present invention. 
         FIG. 4  is a series of graphs illustrating idealized waveforms for the operation of the exemplary transition detector circuit illustrated in  FIG. 3 . 
         FIG. 5  is a top-level schematic for an exemplary transition detector circuit shown in  FIG. 3 . 
         FIG. 6  is a block diagram of a series-C based differentiator circuit according to one exemplary embodiment of the present invention. 
         FIG. 7  is a schematic of an exemplary differentiator circuit according one preferred exemplary embodiment of the present invention. 
         FIG. 8  is a schematic diagram of an exemplary differential differentiator (DIFFDIFF) circuit according to one exemplary embodiment of the present invention. 
         FIG. 9  is a schematic diagram of an exemplary current reference circuit according to one exemplary embodiment of the present invention. 
         FIG. 10  is a series of graphs illustrating a simulation of the frequency response of the exemplary differentiator circuit illustrated in  FIG. 8 . 
         FIG. 11  a series of graphs illustrating simulated waveforms for the operation of an exemplary transition detector circuit according to one exemplary embodiment of the present invention. 
         FIG. 12  is a diagram illustrating a waveform for the derivative threshold point in an exemplary transition detector circuit according to exemplary embodiment of the present invention. 
         FIG. 13  is an illustration of a simulated eye-diagram and output diagram for an exemplary transition detector circuit according to one exemplary embodiment of the present invention. 
         FIG. 14  is a series of graphs illustrating the deterministic jitter that can be introduced by the transition detection method illustrated  FIG. 3 . 
         FIG. 15  is a block diagram of illustrating a detection method to remove deterministic jitter according to one exemplary embodiment of the present invention. 
         FIG. 16  is a block diagram illustrating a more detailed version of the detection method illustrated in  FIG. 15 . 
         FIG. 17  is a block diagram illustrating a more detailed and exemplary implementation of the modules illustrated in  FIG. 16 . 
     
    
    
     DETAILED DESCRIPTION OF EXEMPLARY EMBODIMENTS 
     Clock recovery of a multi-level (ML) signal can be performed in a two-step process. First, the transitions within the ML signal can be detected by a novel transition detector (TD). And second, the output of the TD circuit can comprise a pseudo-non-return-to-zero (pNRZ) signal that can drive a conventional OOK clock recovery (CR) IC. The TD circuit can convert the edges of the ML signal into the pseudo-NRZ (pNRZ) signal. The TD circuit can capture as many transitions as possible to allow the conventional NRZ clock recovery (CR) chip to optimally perform. The TD circuit can differentiate the ML signal in order to detect the ML signal&#39;s transitions. 
     An exemplary transition detection circuit has been built by the inventors and simulated to operate at 2.7 Giga Symbols per second (Gsym/sec) in a Gallium Arsenide (GaAs) heterojunction bi-polar transistor (HBT) process. In other words, the inventors have fabricated a working model of the present invention. The present invention can also be readily adapted to a variety of other semiconductor processes such as Complimentary Metal Oxide Semiconductor (CMOS) or Silicon Germanium (SiGe) as is apparent to one of ordinary skill in the art. 
     Referring now to the drawings, in which like numerals represent like elements throughout the several Figures, aspects of the present invention and the illustrative operating environment will be described. 
     Referring to  FIG. 1 , this Figure is a block diagram of an exemplary multilevel clock recovery system  100  according to an exemplary embodiment of the present invention. The clock recovery system  100  can comprise a transition detector (TD)  105  and a conventional clock recovery unit (CR)  110  that can process OOK type signals. The output of the TD circuit  105  can comprise a pseudo-non-return-to-zero (pNRZ) signal that can drive the conventional OOK clock recovery (CR) IC  110 . The NRZ signal is referred to as pNRZ because it can lack meaningful data content. 
     Referring now to  FIG. 2 , this Figure is a block diagram illustrating some key functions of the transition detector circuit  105  according to one exemplary embodiment of the present invention. The transition detector circuit  105  can comprise three stages: a derivative stage  205 , an absolute value of the derivative stage  210 , and a threshold comparison stage  215 . 
     Referring now to  FIG. 3 , this Figure is a block diagram illustrating exemplary elements of the transition detector circuit  105  according to one exemplary embodiment of the present invention. The ML input signal, Vin, can be differentiated by a differentiator  305  in order to produce a waveform that can be labeled dVin/dt. The differentiated signal can drive two comparators  310 A,  310 B with thresholds set to Vref+ and Vref−. The comparators  310 A,  310 B can produce two outputs that can be labeled “Up” and “Down”, which will become true as the signal, Vin, moves up or down, respectively. 
     When the signal rises, a positive derivative is present. The upper comparator  310 A with threshold set to Vref+ can assert an “Up” output. Similarly, when the input signal falls, a negative derivative is present and the lower comparator  310 B can assert a “Down” output. These two outputs labeled “Up” and “Down” are then combined via an exclusive “OR” function  320  to produce the necessary pNRZ output. 
     The rising edges of the “Up” and “Down” signals can be “captured” with two toggle flip-flops (T-FF&#39;s)  315 A,  315 B. The T-FF&#39;s  315 A,  315 B simply invert their outputs on every rising edge from the comparators. The output of the T-FF&#39;s  315 A,  315 B can be exclusive OR&#39;ed (XOR&#39;ed) together at  320  to produce the desired pNRZ signal. An XOR function  320  will invert its output, if the state of either input changes provided the other input remains constant. Since Vin cannot move both up and down simultaneously, a rising edge occurring from either “Up” or “Down” will result in an inversion of the TD output. This can represent an ideal pNRZ signal generation. 
     Referring now to  FIG. 4 , this Figure is a series  400  of seven graphs  405 – 435  illustrating idealized waveforms for the operation of the exemplary transition detector circuit  105  illustrated in  FIG. 3 . The first graph  405  illustrates the multilevel signal input into the transition detector circuit  105 . 
     The second graph  410  illustrates a derivative of the multilevel signal from the first graph  405 . The third graph  415  illustrates an output of the first comparator  310 A. Meanwhile, the fourth graph  420  illustrates an output of the second comparator  310 B. The fifth graph  425  illustrates an output of the first toggle flip-flop  315 A. And the sixth graph  430  illustrates an output of the second toggle flip-flop  315 B. The seventh graph  435  illustrates the output of the exclusive “or” function  320 . 
       FIG. 5  illustrates the top-level schematic for the exemplary transition detector illustrated in  FIG. 3 . The circuit is a fully differential design and is functionally identical to the block diagram of  FIG. 3 . The differentiation function is performed by the circuit block labeled DIFFDIFF (X 13 ) (differential differentiator). The differentiated signal is amplified by a simple differential limiting amplifier, X 17 . 
     The differential output of the limiting amplifier is routed to two differential comparators that have thresholds set by the voltages at the input pins Vrdp, Vrdm, and the common reference pin Vr. The differential outputs from the comparators toggle two T-FF&#39;s that are made from two D-FF&#39;s (X 4  and X 11 ). The differential outputs of the FF&#39;s are XOR&#39;ed by a differential XOR gate, X 12 . Finally, the output of the XOR gate is buffered by an OUTBUF circuit, which provides appropriate drive for the OOK CR IC. 
     The differential differentiator circuit employs a novel approach as described below. Differentiation can be accomplished by a variety of methods. An exemplary differential differentiator  305 ′ is illustrated in  FIG. 6 . In this approach an amplifier, A 1 , with a low output impedance, drives a series-connected RC network. The resistor R combined with the output impedance of the amplifier must be low enough to force an accurate representation of the input signal across the capacitor. Then, the resulting current through the capacitor will be the derivative of the input voltage (with a possible gain/loss factor). That is, for an ideal capacitor: 
     
       
         
           
             
               
                 
                   I 
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                     C 
                     ⁢ 
                     
                       
                         
                           ⅆ 
                           V 
                         
                         
                           ⅆ 
                           t 
                         
                       
                       . 
                     
                   
                 
               
               
                 
                   ( 
                   1 
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     The voltage across the resistor, R, will be directly proportional to this current (Ohm&#39;s law). Therefore, if the input amplifier has a gain G 1  and the output amplifier a gain G 2 , the circuit&#39;s transfer function will be: 
                     V   out     =     G1G2RC   ⁢       ⅆ     V   in         ⅆ   t                 (   2   )               
provided that the input voltage is appropriately impressed across the capacitor, C. In order for the input voltage to appear across the capacitor, the RC cutoff frequency must be much greater than the operating frequency:
 
                       f   op     ⁢     &lt;&lt;     1     2   ⁢   π   ⁢           ⁢     C   ⁡     (     R   +     R   out1       )               ,           (   3   )               
in which R out1  is the output impedance of amplifier A 1 ; and A 2  is assumed to have a high input impedance. Equation (3) indicates that the RC product must be small for high frequency operation (f op ).
 
     Therefore, the amplifier gains, G 1  and G 2 , must be large to offset the signal loss as per Equation (2). The approach illustrated in  FIG. 6  and described above is not a preferred exemplary embodiment because useful circuit function requires large gain and/or a low impedance amplifier to drive the RC network. 
     Referring now to  FIG. 7 , a preferred and exemplary embodiment of an exemplary differentiator  305 ″ is illustrated in  FIG. 7 . For this exemplary embodiment, a shunt capacitor C is directly connected to the output of a low impedance emitter follower  705 . The relevant RC time constant is simply the output resistance of the emitter follower  705  and the capacitance, C. Since the output impedance of an emitter follower can be designed to be very low, the RC bandwidth for impressing the voltage across the capacitor C can be very high. 
     The emitter follower  705  is further designed to have a collector resistance from which the output is derived. The capacitor, C, is charged through the transistor  710  and therefore the current through R out  is an identical representation (ignoring the transistor&#39;s finite β and an offset current) of the current in the capacitor C. By inspection, the output voltage, Vout, is as follows: 
                     V   out     ≅       -     RI   o       -       R   out     ⁢   C   ⁢       ⅆ     (       V   in     -     V   off       )         ⅆ   t                   (   4   )               
where I o  is the DC bias current and V off  is an input offset due primarily to V be . An important aspect of Equation (4) is that R out  can be set arbitrarily large (determined by the subsequent circuit load) so that the circuit can represent significant gain as compared to the basic conventional approach described earlier.
 
     The offsets involved in Equation (4) are undesirable, but they are both approximately constant. The variable I o  is set by a current source and V off  is approximately V be . Additionally, a fully differential design, as described below, eliminates these offsets. 
     Referring now to  FIG. 8 , a transistor level schematic diagram of an exemplary differentiator circuit (DIFFDIFF)  800  is illustrated. This circuit, though complex at first inspection, generally comprises two of the basic circuits shown in  FIG. 7  operated differentially. The input is first differentially buffered by the differential input amplifier comprising X 13  and X 14 . The differential outputs of this amplifier drive two emitter follower stages (each) comprising X 11 , X 16  and X 17 , X 9 . The low impedance output of the emitter followers accurately impresses the input voltage across capacitors C 3  and C 2 . These capacitors could be replaced by one differentially connected capacitor between the two emitter follower outputs. Such a connection assumes perfect symmetry of the amplifiers, and simulation suggests improved operation by using the equivalent split capacitor approach as shown. The resistors R 23  and R 24  were added to help stabilize the emitter follower amplifiers—it is well known that capacitive loads can cause instabilities with emitter follower amplifiers. The differential output is obtained from the collector resistors R 9  and R 1 . 
     Referring now to  FIG. 9 , this figure illustrates exemplary current reference circuit  900  used to control the bias of the differential differentiator circuit. This circuit can comprise a “Beta-helper”-type current reference source. In other words, this circuit  900  provides a current reference for all of the current sources at bottom of  FIG. 8 . 
     Specifically, the current reference source circuit  900  can provide current for the lowest row of transistors illustrated in  FIG. 8 . The present invention is not limited to this type of current reference source  900  illustrated in  FIG. 9 . Other current reference source circuits are known in the art and are not beyond the scope and spirit of the present invention. 
     Referring now to  FIG. 10 , a significant issue with the use of differentiators is that they have a frequency response that increases linearly with frequency. This has a tendency to amplify noise of the input signal. Therefore, a differentiator should ideally only operate over a bandwidth that matches the input signal.  FIG. 10  illustrates a simulation  1000  of the frequency response of the differentiator circuit. The ideal frequency response of a differentiator is simply j ω (The Fourier transform of dV/dt is j ω F(V)). The simulation in  Figure 10  shows a linear amplitude response up to approximately 2 GHz with a linear phase response starting at 90 degrees as expected at low frequencies. 
     The linear slope of the phase response is simply due to the delay through the circuit and has no consequence for normal operation (The Fourier transform of a time delay is a linear phase offset). The response is seen to peak at slightly over 3 GHz and was observed to roll off gracefully at higher frequencies. 
     Referring now to  FIG. 11 , this Figure illustrates a result of a simulation of the complete TD circuit driven  105  by an ML signal.  FIG. 11  includes a series of graphs  1100  that are similar to the graphs of  FIG. 4 . However,  FIG. 11  illustrates a simulated multi-level signal instead of an idealized multilevel signal that is illustrated in  FIG. 4 . 
       FIG. 11  also demonstrates that the transition circuit  105  catches almost all transitions as predicted. The first graph  1105  illustrates the multilevel signal input into the transition detector circuit  105 . 
     The second graph  1110  illustrates a derivative of the multilevel signal from the first graph  1105 . The third graph  1115  illustrates an output of the first comparator  310 A. Meanwhile, the fourth graph  1120  illustrates an output of the second comparator  310 B. The fifth graph  1125  illustrates an output of the first toggle flip-flop  315 A. And the sixth graph  1130  illustrates an output of the second toggle flip-flop  315 B. The seventh graph  1135  illustrates the output of the exclusive “or” function  320 . 
     Referring now to  FIG. 12 , this figure illustrates detail of the comparator process. In other words, this Figure illustrates a waveform  1200  and the derivative threshold points  1205 ,  1210  according to an exemplary transition detector circuit  105 . 
     Referring now to  FIG. 13 , this Figure is a series of graphs that summarizes the overall circuit performance of the transition detection circuit  105 . The first graph  1305  comprises an eye diagram of the TD output that will be fed to an OOK CR chip. Reasonable jitter width is observed and much of this jitter can be suppressed by the subsequent OOK CR IC&#39;s jitter rejection properties. The second graph  1310  illustrates the output of the transition detection circuit  105 . 
     From  FIG. 13 , one skilled in the art will recognize that the recovered signal, while giving a better result than without the use of the TD, exhibits what is known as deterministic jitter (DJ). DJ is temporal variability in the transition location due to patterns in the data sequence. 
       FIG. 14  illustrates the source of this DJ.  FIG. 14(   a ) illustrates an exemplary eye-diagram  1405  of a ML signal with 16 levels.  FIG. 14(   b ) illustrates exemplary corresponding absolute values  1410  of the derivatives of the signals illustrated in  FIG. 14(   a ). The only difference among the fifteen derivatives in  FIG. 14(   b ) is their amplitude, i.e. they are all scalings of a single function. The dashed horizontal line  1415  in  FIG. 14(   b ) illustrates the transition threshold Vref used. 
     The location where this horizontal line crosses a particular derivative is a respective declared transition point  1420 A,  1420 B. While only two declaration transition points  1420 A,  1420 B are labeled in  FIG. 14(   b ), those skilled in the art will appreciate that thirteen additional declarations transition points are not labeled but do exist and correspond to the remaining thirteen derivatives. 
     As is evident from  FIG. 14(   b ), this declaration point occurs earlier for larger level transitions. Due to this variability, jitter is introduced by the TD circuit and can degrade performance of subsequent circuitry making use of the recovered clock. While CR following the TD circuit will reduce this DJ, the CR may not be able to remove all the DJ. Furthermore, in the presence of additional random jitter and DJ from other sources, the CR may not be able to fully compensate for their aggregate effect. 
     The DJ illustrated in  FIG. 14  is due to sensitivity to data patterns. It is important to note that the DJ is not due to noise. Thus, it is theoretically possible to remove the DJ with appropriate methods.  FIG. 15  shows a block diagram extending the functionality in  FIG. 2  to remove DJ. The constant threshold transition detection (CTTD) of  FIG. 2  is actually included as a subset of  FIG. 15 . 
     The embodiment illustrated in  FIGS. 15 through 17  will be called the variable threshold transition detection (VTTD) circuit. The new function blocks are used to provide the CTTD with a variable threshold that scales with the size of the level change. This effectively normalizes the threshold thereby eliminating the inconsistency illustrated in  FIG. 14(   b ). 
     Referring now to  FIG. 15 , this Figure illustrates a variable threshold obtained by comparing a multi-level signal at different points in time. In particular, the signal Vin is delayed by an amount τ twice, splitting the signal off after each delay. This provides three instances of the signal: Vin(t+τ), Vin(t), and Vin(t−τ). If τ is chosen to be on the order of half a symbol period (note that exactness in the value of τ is not necessary), then Vin(t+τ) and Vin(t−τ) will correspond to the middle of the data symbols for the preceding and following symbols when Vin(t) is in the transition region. Thus, the difference Vin(t+τ)−Vin(t−τ) provides a good estimate of the size of the level change. Scaling this difference by an appropriate factor α (where α is nominally ½ in the absence of gain on circuit elements) provides the desired threshold on a continuous basis. 
     The difference Vin(t+τ)−Vin(t−τ) in  FIG. 15  is difficult to implement as illustrated. However, because the difference is only used by the threshold operation, which is implemented with comparators as in  FIG. 3 , this difference never need be explicitly performed. 
     Referring now to  FIGS. 16 and 17 , these Figures present an embodiment that functionally implements  FIG. 15  but without explicitly taking the difference Vin(t+τ)−Vin(t−τ). For clarity of exposition,  FIG. 16  presents the embodiment in higher-level function blocks whose specifics are given in  FIG. 17 . 
     As in  FIG. 15 , three instances of Vin are created by the use of a pair of τ delays. The middle tap Vin(t) is differentiated according to the embodiment previously described for the CTTD and scaled by 1/α. Note that Vin(t) is scaled by 1/α, in contrast to scaling Vin(t+τ) and Vin(t−τ) by α, to save on the number of amplifiers used. However, both approaches are inherently the same and are represented by the same embodiment. 
     The three signals Vin(t+τ), 1/α Vin(t), and Vin(t−τ) are then fed into three modules. The first module (i) tests if the derivative dVin(t)/dt of the ML signal is greater than the threshold α|Vin(t+τ)−Vin(t−τ)|. 
     The second module (ii) tests if the derivative dVin(t)/dt is less than the threshold −α|Vin(t+τ)−Vin(t−τ)|. The ‘OR’ing of these two events then corresponds to the absolute value of the derivative exceeding |α[Vin(t+τ)−Vin(t−τ)]| and thus conveys when the slope of the ML signal has exceeded the variable threshold. 
     The third module (iii) asserts a minimum value on the slope threshold. Note that when two adjacent symbols are the same, the variable threshold becomes zero, and modules (i) and (ii) will trigger. Module (iii) safeguards against such conditions causing a “false alarm” by additionally requiring the slope reach a minimum threshold in order to accept the results of modules (i) and (ii). While module (iii) asserts a slope on the derivative dVin(t)/dt, those skilled in the art will recognize that applying a threshold to the difference [Vin(t+τ)−Vin(t−τ)] is fundamentally the same embodiment. 
       FIG. 17  illustrates the details of each of the modules (i)–(iii) in  FIG. 16 . FIG.  17 (top) shows how module (i) can be implemented. As in  FIG. 16 , module (i) takes as its input Vin(t−τ), 1/α Vin(t), and Vin(t+τ). To implement the desired function, we note that the event
   d Vin( t ) /dt&gt;|α[ Vin( t+τ )−Vin( t−τ )]| 
is equivalent to the pair of events being true
 1/α d Vin( t ) /dt+ Vin( t−τ )&gt;Vin( t+τ ) 1/α d Vin( t ) /dt+ Vin( t+τ )&gt;Vin( t−τ ) 
as can be shown by those skilled in the art. The latter pair of conditions can be directly implemented as shown in FIG.  17 (top) to produce the desired functionality.
 
     In a similar fashion, module (ii) can be implemented as in FIG.  17 (middle) taking advantage of the equivalence of the event
 
 d Vin( t ) /dt&lt;−|α[ Vin( t+τ )−Vin( t−τ )]|
 
to the pair of events
 
1/α d Vin( t ) /dt+ Vin( t−τ )&lt;Vin( t+τ )
 
1/α d Vin( t ) /dt+ Vin( t+τ )&lt;Vin( t−τ )
 
being true. It should be evident to those skilled in the art that two of the four additions in modules (i) and (ii) are redundant and can be omitted. As previously stated, the separation of functionality into modules is for clarity of exposition and not an implementation constraint.
 
     Finally, for third module (iii), the minimum threshold requirement can be realized with the implementation shown in FIG.  17 (bottom) where the ML signal derivative is compared to the threshold Tmin. As in  FIG. 3 , a pair of thresholds is used to account for both when the derivative is positive and negative. The two comparators are then latched and ‘OR’ed to produce the desired output. 
     The present invention efficiently detects clock signals in a multilevel signal. The system and method of the present invention determine clock signals from a multilevel signal that can be used in high speed communication applications. Exemplary uses of the present invention include electrical backplane, Ethernet, and optical applications. 
     It should be understood that the foregoing relates only to illustrate the embodiments of the present invention, and that numerous changes may be made therein without departing from the scope and spirit of the invention as defined by the following claims.