Abstract:
Methods and apparatuses for time to digital conversion (TDC) are disclosed. A timing circuit comprises a TDC circuit, a calibration module, and a correction module. The TDC circuit is configured to provide a timing signal indicative of a timing difference between edges of a periodic reference clock signal and a variable feedback signal. The TDC circuit is also configured to provide a delay signal that is variably delayed relative to the reference clock signal. The calibration module is configured to provide a calibration signal to increase and decrease a total delay of the TDC circuit based on a time delay of the calibration signal plus a time delay of a correction signal. The correction module, which is configured to receive the timing signal and provide the correction signal, minimizes harmonic spurs in a frequency response of the timing signal by operating at a frequency of the reference clock signal.

Description:
BACKGROUND 
       [0001]    A time to digital converter (TDC) is a circuit known in the art to detect phase offset (such as jitter) between two signals, e.g., a control signal of a phase locked loop and a reference clock signal. 
         [0002]      FIG. 1  is a block diagram of a known TDC in a configuration known as a Vernier delay line. The principles of this TDC  100  are described in U.S. Pat. Pub. No. 2009/0225631 by Shimizu et al., “Time-To-Digital Converter,” which is hereby incorporated by reference herein in its entirety. The TDC  100  has a first delay line in which a sequence of delay cells  114  are arranged to sequentially delay an original clock CK. Each delay cell  114  delays its input by a predetermined delay amount τ 1 , and a plurality of delay taps CK 1 , CK 2 , CK 3 , . . . are provided to the data (D) inputs of corresponding D-type flip flops  116 . A signal SC to be measured is provided to a second delay line in which each delay cell in a sequence of delay cells  115  delays its input by a predetermined delay amount τ 2 , where τ 1  is typically greater than τ 2 . The first and second delay lines may be implemented using pairs of inverters, for example. Successive taps from the second delay line are provided as clock inputs SC 1 , SC 2 , SC 3 , . . . to corresponding flip flops  116 . 
         [0003]    Because τ 1 &gt;τ 2 , signals in the sequence SC 1 , SC 2 , SC 3 , . . . are advanced relative to signals in the sequence CK 1 , CK 2 , CK 3 , . . . . In other words, if a rising clock edge of CK 1  occurs before a rising clock edge of SC 1 , there will be a point along the first and second delay lines at which a delay tap from the second sequence  115  “catches up” to a corresponding delay tap from the first sequence  114 . In this example, the Q outputs from flip flops  116  are ‘1’ up to this point and ‘0’ thereafter. An encoder circuit  117  receives the Q outputs and encodes a position at which such crossover occurs, and the encoded result represents the jitter of the signal SC to be measured with respect to the reference clock CK. For example, if 2 N  flip flops are employed, encoder  117  provides an N-bit encoded value representing a jitter of signal SC. 
         [0004]    Conventional TDC  100  has certain deficiencies. Due to variations in process, voltage, and temperature, the total delay of a delay line may be different than the desired value, resulting in certain disadvantageous effects. For example, a variation in the total delay of delay cells  115  may result in undesirable phase noise in the encoded signal indicating jitter. Furthermore, mismatch between individual delay cells may result in other disadvantageous effects. For example, variations in the delays of delay cells  115  may result in harmonic “spurs” (spurious noise components) in a frequency response of the encoded jitter signal. Both these disadvantageous effects impair the ability to accurately measure jitter. 
         [0005]      FIG. 2  is a block diagram of a known timing circuit  200  that seeks to address the phase noise and spur problems discussed above. Timing circuit  200  is fully described in Temporiti et al., “A 3 GHz Fractional All-Digital PLL With a 1.8 MHz Bandwidth Implementing Spur Reduction Techniques,” IEEE Journal of Solid-State Circuits, Vol. 44, No. 3, pp. 824-34, March 2009, and only a brief description of the principles of that circuit follows. Circuit  200  includes a TDC  230  as well as feedback to control delay cells in the TDC  230 . A signal CK DCO  to be measured, provided by a digitally controlled oscillator, is provided to D inputs of D-type flip flops  240 - 1 ,  240 - 2 , . . . ,  240 -N (generally  240 ). A reference clock signal CK REF  is provided to a clock doubler  210  that also receives input from a pseudorandom number generator (PRNG)  220 . The reason for the presence of the clock doubler  210  and the PRNG  220  will be apparent shortly. Much as in TDC  100 , the output from the clock doubler  210  is provided to delay cells  250 - 1 ,  250 - 2 , . . . ,  250 -N (generally  250 ), and successive delay taps are provided to clock inputs of corresponding D flip flops  240 . The output from TDC  230  is an encoded signal representing a jitter between CK DCO  and CK REF , and this output is shown in  FIG. 2  as emanating from the last flip flop  240 -N for convenience, although it is understood that an encoder (not shown) provides encoding much as in  FIG. 1 . 
         [0006]    A calibration module  260 , comprising a grouper  262  to process groups of bits, an adder  264 , a low pass filter  266 , and a quantizer  268 , provides a calibration signal based on the encoded output from TDC  230 . A correction module  270  provides N correction signals that are added to the calibration signal at adders  280 - 1 ,  280 - 2 , . . . ,  280 -N and used to control delay cells, e.g., via principles of variable capacitance. Thus, calibration and correction loops are present in a feedback configuration. The effects of the calibration and correction modules are to reduce phase noise and spurs, respectively. The clock doubler  210  is needed because 50% of available cycles are set aside for calibration. The PRNG  220  is used to inject pseudorandom jitter to improve performance, including by reducing unwanted periodicities. 
         [0007]    The calibration loop in circuit  200  collects many input signals (groups of five signals for integration), resulting in a relatively long calibration time. Circuit  200  needs multipliers in correction module  270 , requiring large silicon area in a practical embodiment. Clock doubler  210  and PRNG  220  area also needed, resulting in high power consumption, which decreases performance in terms of noise. Because of the clock doubler  210  and the use of 50% of samples for calibration, the operation speed of circuit  200  is twice the input frequency. 
         [0008]      FIG. 3  is a block diagram of another known timing circuit. Circuit  300  is described in Chang et al., “A fractional spur free all-digital PLL with loop gain calibration and phase noise cancellation for GSM/GPRS/EDGE,” IEEE Int. Solid-State Circuits Conf. (ISSCC) Dig. Tech. Papers, pp. 222-23, 598, February 2008. Circuit  300  includes a phase frequency detector and cyclic TDC  310  that receives a reference clock CK REF  and a feedback signal CK FB . As part of a phase locked loop, circuit  300  provides a digital loop filter  330 , a digitally controlled oscillator  332 , and a divider  234  that provides the feedback signal CK FB . A sigma-delta modulator  340  is used to randomly change a frequency division value of the divider  234  to reduce spurious noise. Sigma-delta modulators are known in the art and are described at, e.g., U.S. Pat. No. 7,279,990, by Hasegawa, “Sigma-Delta Modulator for PLL Circuits,” which is hereby incorporated by reference herein in its entirety. Sigma-delta modulator  340  receives a numerator value F that is accumulated in a manner that causes the frequency division ratio of divider  234  to vary. A scale factor  370 , which is the ratio of an output clock period to the delay time of a delay cell, is used to update the phase locked loop. The scale factor replaces the calibration loop of circuit  200  for phase noise mitigation. Circuit  300  does not contain a correction loop, resulting in phase noise performance of circuit  300  being worse than that of circuit  200 . With adders  320 ,  342  and  350 , delay element  360 , scale factor  370 , and multiplier  380 , the input to the digital loop filter  330  is controlled in a manner that provides some phase noise cancellation. The use of a cyclic TDC, in which the output of a last delay cell feeds back to an input of a first delay cell, reduces the number of delay cells but induces in-band phase noise. The use of a multiplier  380  increases silicon area. The performance of circuit  300  in terms of spurs and phase noise is worse than that of circuit  200 . 
         [0009]    It is desirable to employ TDC timing techniques that reduce phase noise and spurs with reduced circuit complexity and increased efficiency. 
       SUMMARY 
       [0010]    An embodiment discloses a timing circuit comprising a time to digital conversion (TDC) circuit, a calibration module, and a correction module. The TDC circuit is configured to provide a timing signal indicative of a timing difference between edges of a periodic reference clock signal and a variable feedback signal. The TDC circuit also is configured to provide a delay signal that is variably delayed relative to the reference clock signal. The calibration module is configured to receive the delay signal and a second feedback signal and provide a calibration signal to increase and decrease a total delay of the TDC circuit. The total delay of the TDC circuit is based on a time delay of the calibration signal plus a time delay of a correction signal. The correction module is configured to receive the timing signal and provide the correction signal. The correction module minimizes harmonic spurs in a frequency response of the timing signal by operating at a frequency of the reference clock signal. 
         [0011]    The timing circuit may also include a digital loop filter (DLF), a digitally controlled oscillator (DCO), a divider, and a counter. The DLF is configured to provide a digital control signal based on the timing signal. The DCO is configured to tune a frequency of an output clock signal based on the digital control signal. The divider is configured to divide the output clock signal in frequency by an integer M or an integer M+1 and provide a divided signal that feeds back to the TDC circuit as the first feedback signal and that feeds back to the calibration module as the second feedback signal. The counter is configured to accumulate the first feedback signal and provide an increment signal. The increment signal causes the divider to divide by M+1 instead of M in an event that an accumulated sum of the first feedback signal exceeds a predetermined threshold. 
         [0012]    Another embodiment discloses a method of controlling timing signals. A reference clock signal and first and second feedback signals are received. The reference clock signal is delayed via N delay cells to provide a delay signal. A timing signal is generated at a frequency of the reference clock signal. The timing signal is indicative of a timing difference between edges of the reference clock signal and of the first feedback signal. Delay cells are adjusted based on the delay signal, the second feedback signal, and the timing signal to calibrate a total delay of the delay cells and to reduce mismatch among delay cells. 
         [0013]    The method may also include generating a digital control signal based on the timing signal via a low pass filtering operation. A frequency of an output clock signal is tuned based on the digital control signal. The output clock signal is divided in frequency by an integer M or an integer M+1 to provide a divided signal, which is fed back as the first and second feedback signals. The first feedback signal is accumulated, and the output clock signal is divided in frequency by M+1 in an event the accumulated first feedback signal exceeds a predetermined threshold. 
         [0014]    The construction and method of operation of various embodiments, however, together with additional advantages thereof will be best understood from the following descriptions of specific embodiments when read in connection with the accompanying figures. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0015]    The following will be apparent from elements of the figures, which are provided for illustrative purposes and are not necessarily to scale. 
           [0016]      FIG. 1  is a block diagram of a known TDC in a Vernier delay line configuration. 
           [0017]      FIG. 2  is a block diagram of a known timing circuit. 
           [0018]      FIG. 3  is a block diagram of another known timing circuit. 
           [0019]      FIG. 4  is a block diagram of a timing circuit in accordance with an exemplary embodiment. 
           [0020]      FIG. 4A  is a block diagram of a delay cell using tri-state buffers. 
           [0021]      FIG. 5  is a block diagram of a calibration module in accordance with an embodiment. 
           [0022]      FIG. 6  is a block diagram of a correction module in accordance with an exemplary embodiment. 
           [0023]      FIG. 7  is a block diagram of an accumulator in accordance with an exemplary embodiment. 
           [0024]      FIG. 8  is a block diagram of a comparator and a register in accordance with an exemplary embodiment. 
           [0025]      FIG. 9  is a block diagram of a phase locked loop in accordance with an exemplary embodiment. 
           [0026]      FIG. 9A  is a block diagram of a counter used with a divider for fractional variation in accordance with an exemplary embodiment. 
           [0027]      FIG. 10  is a block diagram of a digital loop filter in accordance with a phase locked loop embodiment. 
           [0028]      FIG. 11  is a flow diagram in accordance with an exemplary embodiment. 
       
    
    
     DETAILED DESCRIPTION 
       [0029]      FIG. 4  is a block diagram of a timing circuit in accordance with an exemplary embodiment. Circuit  400  includes a time to digital conversion (TDC) circuit  410 , a calibration module  420  for phase noise reduction, and a correction module  430  for spur reduction. Calibration module  420  and correction module  430  are arranged in feedback configuration to provide calibration and correction loops that can be implemented with simpler circuits than those found in prior art systems. As a result, silicon area and power are saved, and performance in terms of phase noise and spurs is increased relative to the prior art. 
         [0030]    TDC circuit  410  includes a plurality of latches  412  configured to switch values of a feedback signal CK DIV  based on a reference clock signal CK REF . Specifically, in an example where the latches are D-type flip flops, CK REF  is provided to a delay line comprising delay cells  414 - 1 ,  414 - 2 ,  414 - 3 , . . . ,  414 -N (generally  414 ), each of which may be a pair of inverters or composed of other suitable delay elements as known in the art. In an embodiment, N is 16, although other values may be used as well. Delay taps from delay cells  414  are provided to clock edges of the flip flops  412 . An output of delay cell  414 -N, referred to as DCDL OUT  because it is the variably delayed output of a digitally controlled delay line, corresponds to CK REF  delayed by one period of CK REF  when calibration is achieved as described further below. Delay cells  414  are adjusted (increased or decreased in delay) based on signals from calibration module  420  and correction module  430  that are summed at adders  460 - 1 ,  460 - 2 ,  460 - 3 , . . . ,  460 -N (generally  460 ), which may be implemented as multiple adders or as a single adder  460 . CK DIV  may be coupled to a delay line, e.g., in a Vernier delay line configuration (not shown) as known in the art. TDC circuit also includes an encoder (not shown) that encodes a timing signal  415  indicative of a jitter of CK DIV  relative to CK REF . Timing signal  415  may be a P-bit signal, where N=2 P . Delay cells  414  may be implemented using tri-state buffers known in the art, e.g., as described in Park et al., “All-Digital Synthesizable UWB Transmitter Architectures,” Proc. of the 2008 IEEE Int. Conf. on Ultra-Wideband (ICUWB2008), Vol. 2, p30, 2008.  FIG. 4A  is a block diagram of a delay cell using tri-state buffers. Delay cell  414 - i  may be any of the delay cells  414  in  FIG. 4 . Delay cell  414 - i  includes a buffer  416  and P tri-state buffers  418 - 0 , . . . ,  418 -P ( 418  generally) coupled in parallel. The tri-state buffers  418  receive respective enable inputs from respective bits of the timing signal  415 . When turned off, the output of each tri-state buffer  418  is high-impedance (‘Z’), thereby switching to increased delay. Conversely, when a tri-state inverter  418  is turned on, delay time is decreased. Thus, delay between nodes IN and OUT may be tuned by P bits of the timing signal  415 . Calibration module  420  receives DCDL OUT  and CK DIV1 , which is CK DIV  shifted in time. CK DIV  is a variable feedback signal provided by a phase locked loop, and the feedback signal arrives at different times at different portions of circuit  400 . Therefore, it is convenient to refer to CK DIV  as a first feedback signal and CK DIV1  as a second feedback signal, as these are the same signal arriving at different times at different locations. 
         [0031]    Calibration module  420  includes a phase detector  422  and a counter  424 , and the resulting calibration signal  425  is provided to each of the adders  460 . Correction module  430  receives the timing signal  415 . An array of accumulators  432  processes the timing signal to provide accumulation signals  433  to an array of comparators  434 . Comparators  434  provide comparison signals  435  to an array of registers  436 , which store the comparison signals and provide N correction signals  437 . Accumulation signals  433 , comparison signals  435 , and correction signals  437  may respectively be provided as multiple signals (as shown in  FIG. 4 ) or as single signals, as is known in the art. The N correction signals  437  are provided to corresponding adders  460  to adjust different delay cells  414  differently so as to reduce delay mismatch among the delay cells  414 . 
         [0032]      FIG. 5  is a block diagram of a calibration module in accordance with an embodiment. Calibration module  420  includes a phase detector  422  and a counter  424  as shown in  FIG. 4 . The phase detector may be a latch, e.g., a D-type flip flop  422 . DCDL OUT  is coupled to a D input of the flip flop  422 , and CK DIV1  is coupled to a clock input. Phase detectors employing flip flops are known in the art and are described at, e.g., U.S. Pat. No. 4,593,253 by McCabe et al., “Flip-Flop Phase Detector Circuit for Phase Locked Loop,” and at U.S. Pat. Pub. No. 2009/0041172 by Kim et al., “Phase Detection Circuit,” both of which are hereby incorporated by reference herein in their entirety. Phase detector  422  compares the phase of inputs DCDL OUT  and CK DIV1 . If the phase of DCDL OUT  leads CK DIV1 , flip flop  422  provides a Q output at a high level. If the phase of DCDL OUT  lags CK DIV1 , flip flop  422  provides a Q output at a low level. The Q output from flip flop  422  is provided to an adder  526 , which provides a multi-bit output to a latch  527 , e.g., to a D input of a flip flop  527 . CK DIV1  is coupled to a corresponding clock input. A Q output of flip flop  527  is fed back to adder  526 , so that counter  424  accumulates the output of phase detector  422 . The accumulated multi-bit output is provided as calibration signal  425 , which is used to adjust a delay of each delay cell  414 . When the calibration loop is locked, the signals DCDL OUT  and CK DIV1  are in phase, and the total delay time is equal to the phase difference between CK DIV  and CK DIV1    
         [0033]      FIG. 6  is a block diagram of a correction module in accordance with an exemplary embodiment. Multi-bit timing signal  415  is provided to each accumulator  432 - 1 ,  432 - 2 , . . . ,  432 -N (generally  432 ) in the array of accumulators  432 . The i th  accumulator  432 - i , with i ranging between 1 and N, inclusive, also receives a constant value i−1. The output from each accumulator  432 - i  is provided to a corresponding comparator  434 - i  among comparators  434 - 1 ,  434 - 2 , . . . ,  434 -N (generally  434 ). The i th  comparator  434 - i , with i ranging between 1 and N, inclusive, also receives a constant value i−1, and compares the value received from accumulator  432 - i  with this constant value. Registers  436 - 1 ,  436 - 2 , . . . ,  436 -N (generally  436 ) store the comparison outputs from corresponding comparators  434 . Outputs from registers  436  are provided as corresponding correction signals  437 - 1 ,  437 - 2 , . . . ,  437 -N (generally  437 ). Details of accumulators  432 , comparators  434 , and registers  436  are provided below. 
         [0034]      FIG. 7  is a block diagram of an accumulator in accordance with an exemplary embodiment. Accumulator  432 - i  shown in  FIG. 7  may be any of the N accumulators  432 . Timing signal  415  and a constant value i−1 are added at adder  710 , with the result provided to a logic gate  720 . In an embodiment, each bit of the output of adder  710  is fed to an input of a gate  720  that effects a logical NOR operation. An output of gate  720  is coupled to an input of an adder  730 , an output of which is coupled to a data input of a latch  740 , e.g., to a D input of a flip flop  740 . CK DIV  is coupled to a clock input of flip flop  740 . A Q output of flip flop  740  is fed back to adder  730  and also provided as accumulation signal  433 - i , so that accumulator  432 - i  is configured to accumulate the outputs of the TDC circuit  410 . In an embodiment, adder  710  is a subtractor, i.e., one of the inputs is negated prior to addition. Accumulator  432 - i  increments an accumulated value if each input to gate  720  is at a low level (‘0’). When the value of the timing signal  415  is equal to the constant value i−1, the output of the adder  710  is zero, and the output of NOR gate  720  is at a high level. Thus, the accumulator  432 - i  is increased by 1. Therefore, the distribution of timing signal  415  is recorded in accumulator  432 - i , similar to a histogram. 
         [0035]      FIG. 8  is a block diagram of a comparator and a register in accordance with an exemplary embodiment. Comparator  434 - i  shown in  FIG. 8  may be any of the N comparators  434 . Accumulation signal  433 - i  is compared to constant value i−1 using conventional techniques, e.g., an adder  810  configured to subtract i−1 from accumulation signal  433 - i  and provide a resulting sign bit. The sign bit is coupled to an input of an adder  820 , a multi-bit output of which is coupled to a data input of a latch  830 , e.g., to a D input of a flip flop  830 . A clock input of flip flop  830  is not shown in  FIG. 8  for convenience but may be CK DIV . An output of flip flop  830  is fed back to adder  820  and is also provided as correction signal  437 - i . Thus, comparator  434 - i  compares the output from accumulator  432 - i  with a constant value i−1, and register  436 - i  records the output of the comparator. 
         [0036]      FIG. 9  is a block diagram of a phase locked loop in accordance with an exemplary embodiment. Phase locked loop  900 , which may be used in frequency synthesizer applications and the like, comprises TDC circuit  410 , calibration module  420 , correction module  430 , and adder  460  described above, as well as additional elements described below. TDC circuit  410  receives an input clock signal CK IN , which may be the reference clock signal CK REF  of  FIG. 4 , and a feedback signal CK DIV . TDC provides a timing signal  415 , which is labeled TDC[3:0] in  FIG. 9  to indicate that the timing signal  415  may be 4 bits when N=16 delay cells are used as in  FIG. 4 . 
         [0037]    Timing signal  415  is provided to a digital loop filter  920  via an adder  910 , which enables the timing signal  415  to be modified by a cancellation loop as described further below. Digital loop filters (DLFs) are known in the art and perform analogous processing for digital phase locked loops (PLLs) as analog loop filters perform in analog PLLs. For example, a DLF is described in detail at U.S. Pat. Pub. No. 2009/0302958 by Sakurai et al., “Digitally Controlled Oscillator and Phase Locked Loop Circuit Using the Digitally Controlled Oscillator,” hereby incorporated by reference herein in its entirety. Functional details of a DLF in accordance with an embodiment are provided further below in the context of  FIG. 10 . DLF  920  provides control signals to tune a digitally controlled oscillator (DCO)  930 . 
         [0038]    DCOs are known in the art for providing analogous functionality for digital PLLs as voltage controlled oscillators provide for analog PLLs and are described at, e.g., U.S. Pat. No. 5,727,038 by May et al., “Phase Locked Loop Using Digital Loop Filter and Digitally Controlled Oscillator,” which is hereby incorporated by reference herein in its entirety. DCO  930  adjusts the frequency of an output signal CK OUT  so that clock frequencies may be matched (locked) by the phase locked loop  900 . DCO  930  may be implemented with nonlinear capacitors, active inverter stages, or other conventional DCO techniques as known in the art and described at, e.g., U.S. Pat. Pub. No. 2010/0013532 by Ainspan et al., “Phase-Locked Loop Circuits and Methods Implementing Multiplexer Circuit for Fine Tuning Control of Digitally Controlled Oscillators,” hereby incorporated by reference herein in its entirety. CK OUT  is divided in frequency by a divider  940 , which divides by an integer M or M+1. Such variable division is known in the art of fractional-type PLLs and is described at, e.g., U.S. Pat. Pub. No. 2004/0223576 by Albasini et al., “Fractional-Type Phase Locked Loop Circuit with Compensation of Phase Errors,” hereby incorporated by reference herein in its entirety. 
         [0039]    As is known in the art, providing fractional division enables greater accuracy and resolution for timing applications. A counter  960  provides an increment signal that is either 0 or 1 and that is added to constant integer value M at adder  950  to determine whether divider  940  divides by M or M+1. A counter  960  for fractional-type PLLs is known in the art and described at, e.g., U.S. Pat. No. 7,279,990 by Hasegawa.  FIG. 9A  is a block diagram of an example implementation of counter  960 . Referring to  FIG. 9A , a numerator value F is accumulated using an accumulator  962  comprising adder  964  and flip flop  966  based on clock signal CKDIV. The most significant bit of the Q output of flip flop  966  is provided to another flip flop  967  and to an inverter  968 . An output of an AND gate  969  coupled to inverter  968  and flip  967  at its inputs is provided to divider  940 . In other words, when the accumulated value exceeds a denominator value (modulo value) corresponding to a predetermined threshold, an overflow condition is met, and the divisor is incremented by one to M+1. In an embodiment, the output of counter  960  is provided to a cancellation loop, illustrated depicted in  FIG. 9  with a multiplier  970  corresponding to multiplier  380  of  FIG. 2 , to further reduce phase noise. 
         [0040]    The cancellation loop reduces phase noise similar to the cancellation loop in timing circuit  200 . In the following discussion, reference is made to elements of timing circuit  200  in  FIG. 2 , although it should be understood that such elements are implemented in embodiments of the present subject matter as described below. The cancellation loop cancels the phase error between CK IN  and CK DIV  if the divisor is changed, which occurs during fractional variation for a fractional PLL. The counter  960 , which controls the divisor, can predict the phase error. For example, if an average divisor is 1.25 (fractional part=0.25), the divisor may be varied as follows: 1, 1, 1, 2 to achieve a cumulative effect of 5/4=1.25, i.e., the output of counter  960  over time (i.e., signal DSM as in  FIG. 3 ) may be 0, 0, 0, 1 (to increment the divisor). The numerator value F is 0.25, 0.25, 0.25, and 0.25 in comparison. Regarding phase error, CK IN  may develop a lag at each iteration, e.g., may be in phase with CK OUT  during a first iteration, may trail CK OUT  by 0.25 periods of CK OUT  after one iteration, may trail CK OUT  by 0.5 periods after another iteration, may trail CK OUT  by 0.75 periods after another iteration, and may be in-phase again after another iteration. Subtracting DSM from F as at adder  342  yields cancellation factors of 0.25, 0.25, 0.25, −0.75. Adding these cancellation factors to the phase error described above yields a sum term of 0.25, 0.5, 0.75, 0, i.e., the phase error is canceled. Thus, this sum term multiplied by a scale factor equals the phase error, where the scale factor is the ratio between output period and TDC resolution (which is the delay time of a delay cell). 
         [0041]      FIG. 10  is a block diagram of a digital loop filter (DLF) in accordance with a phase locked loop embodiment. DLF  920  provides a digital output that is used as a control signal to frequency tune DCO  930 , as is known in the art. Functionally, DLF  920  performs a low pass filtering operation as shown in  FIG. 10 , and DLF  920  may be implemented in various ways known to one of ordinary skill in the art to achieve such functionality. An input signal  1005  may be represented as x[n]. Multipliers  1010 ,  1020 , adders  1030 ,  1050 , and delay element  1040  may be configured as shown in  FIG. 10  to provide an output signal y[n]=βx[n]+α(x[n]+x[n−1]). Low pass filtering smooths the inputs to the DCO, which is beneficial due to digitization effects, as is known in the art. Thus, DLF  920  provides equivalent functionality as a series resistor-capacitor (RC) circuit for low pass filtering. 
         [0042]      FIG. 11  is a flow diagram in accordance with an exemplary embodiment. After process  1100  begins, a reference clock signal and first and second feedback signals are received ( 1110 ). The reference clock signal is delayed ( 1020 ) via N delay cells to provide a delay signal. A timing signal is generated ( 1030 ) at a frequency of the reference clock signal. The timing signal is indicative of a timing difference between edges of the reference clock signal and of the first feedback signal. Delay cells are adjusted ( 1040 ) based on the delay signal, the second feedback signal, and the timing signal to calibrate a total delay of the delay cells and to reduce mismatch among delay cells. Although process  1100  is shown as subsequently ending in  FIG. 11 , it should be understood that process  1100  may continue in iterative format in accordance with the principles of phase locked loops to provide continual timing adjustments. 
         [0043]    Various embodiments find wide application in communications systems, e.g., in Bluetooth and wireless LAN systems. Advantageously, various embodiments provide timing circuitry with reduced circuit complexity relative to the prior art. No multipliers are needed in the correction loop, saving circuit area and reducing power consumption. Similarly, pseudorandom number generators and clock doubling circuits are not needed, resulting in additional space and power savings. Calibration using only two inputs is faster than prior art calibration techniques that group greater than two (e.g., five) input signals together, and there are no input duty cycle restrictions unlike in prior art techniques that reserve, e.g., half of all samples exclusively for calibration. Various embodiments use simple circuit components, e.g., phase detectors, counters, accumulators, comparators, and registers, with underlying switching provided by latches, e.g., D-type flip flops. 
         [0044]    Various embodiments have been implemented with success. The total die area can be made at least as small as 1.4 mm in length by 0.8 mm in width, with the area of TDC and digital logic circuitry being about 0.025 mm 2  in accordance with a 65 nm CMOS process. Conventional techniques typically require an area of greater than 0.1 mm 2  for TDC and digital logic circuitry. Various embodiments accommodate fast calibration in about four input clock cycles, compared to greater than twenty input clock signals in prior art implementations that group multiple input signals. 
         [0045]    Table 1 lists performance results associated with noise performance of various embodiments. 
         [0000]    
       
         
               
               
             
               
               
               
             
               
               
             
               
               
               
               
               
             
               
               
               
               
               
             
           
               
                   
                   
               
               
                   
                 Divisor 
               
             
          
           
               
                   
                 40 (integral) 
                 40 + 1/64 
               
             
          
           
               
                   
                 Case 
               
             
          
           
               
                   
                   
                   
                 Add 
                 Add 
               
               
                   
                   
                   
                 cancellation 
                 cancellation and 
               
               
                   
                 Conventional 
                 Conventional 
                 loop 
                 calibration loops 
               
               
                   
                   
               
             
          
           
               
                 DCO code 
                 6 
                 107 
                 9 
                 4 
               
               
                 variation 
               
               
                   
               
             
          
         
       
     
         [0046]    Table 1 shows DCO code variation for various cases, where less variation in the digital code is better, indicative of tighter timing control. Table 1 shows performance for integral clock division (with division by 40) and fractional division by 40+1/64. Conventionally, code variation of 107 is exhibited with fractional operation, which is worse than code variation of 6 with integral operation. With a cancellation loop alone, code variation is reduced to 9, and with cancellation and calibration loops in accordance with various embodiments, code variation is reduced to 4. Thus, phase noise is reduced by 20 log(107/4)=28.55 dBc/Hz by the various disclosed embodiments. Power consumption is less than 2 mW with the various embodiments. Additionally, the use of a correction loop in various embodiments mitigates undesirable spurs. Thus, various embodiments advantageously provide superior performance in terms of phase noise and spurs relative to the prior art, provide increased efficiency in terms of power, area, and speed, and provide reduced circuit complexity. 
         [0047]    The above illustrations provide many different embodiments for implementing different features. Specific embodiments of components and processes are described to help clarify the invention. These are, of course, merely embodiments and are not intended to serve as limitations beyond those described in the claims. 
         [0048]    Although embodiments are illustrated and described herein in one or more specific examples, embodiments are nevertheless not intended to be limited to the details shown, since various modifications and structural changes may be made therein without departing from the spirit of the embodiments and within the scope and range of equivalents of the claims.