Abstract:
Embodiments of the present disclosure provide methods, systems, and apparatuses related to dynamic element matching for time-to-digital converters. Other embodiments may be described and claimed.

Description:
FIELD 
     Embodiments of the present disclosure relate to the field of circuits and, more particularly, to dynamic element matching for time-to-digital converters. 
     BACKGROUND 
     Phase-locked loops (PLLs) are common building blocks in wireless transceivers. They provide a reference signal used to modulate/demodulate data between baseband and radio frequencies. In a digital PLL (DPLL), the phase of a voltage-controlled oscillator (VCO) is measured by a time-to-digital converter (TDC) and compared with a high-purity, low-frequency reference inside a phase detector. The phase detector produces a digital word being equal to the error phase, which is digitally filtered and then sent to digital-to-analog converter (DAC) in order to set the control voltage of the VCO. The VCO phase is measured and filtered in the digital domain rather than in analog PLL, thus both an analog-to-digital converter (ADC) and a DAC are used. The TDC acts as an ADC inside the DPLL by measuring the VCO phase and quantizing it to produce a digital word. 
     Typical implementations of the TDC use a delay line or a delay-locked loop (DLL). A DLL produces an integer number of equally spaced phases by dividing the input signal period into an integer number (equal to the number of delay elements used). The phase of the input signal is measured by sampling each phase of the DLL with a reference clock, with the sampled sequence (zeros and ones) containing the information on the phase to be measured. The time resolution (e.g., the least significant bit (LSB)) of the TDC is equal to the time delay introduced by each delay element in the DLL. The finite TDC resolution introduces quantization error which, under certain conditions, can be considered as a white noise. The coarser the time resolution, the higher the quantization noise. Since the TDC noise is added in the PLL feedback path, the noise is low pass filtered by the PLL and it appears as PLL in-band noise. 
     Typical implementations of the TDC exhibit some mismatch between the amplitude of each LSB. As a consequence the VCO measured phase shows an error, which inherits the same periodicity of the VCO phase itself. This periodic error appears in the DPLL output signal spectrum as spurious sidebands around the carrier. These spurs limit the application of a DPLL as a frequency generator where high spectral purity is desired as the spurs are impractical to be filtered since a low-bandwidth DPLL would be needed. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       Embodiments will be readily understood by the following detailed description in conjunction with the accompanying drawings. To facilitate this description, like reference numerals designate like structural elements. Embodiments are illustrated by way of example and not by way of limitation in the figures of the accompanying drawings. 
         FIG. 1  illustrates a digital phase-locked loop in accordance with some embodiments. 
         FIG. 2  shows various waveforms depicting operation of a digital phase-locked loop in accordance with some embodiments. 
         FIG. 3  illustrates a phase shifter in accordance with some embodiments. 
         FIGS. 4   a - 4   b  show waveforms illustrating respective phase switching windows in accordance with some embodiments. 
         FIG. 5  is a flowchart showing an operation of a digital phase-locked loop in accordance with some embodiments. 
         FIG. 6  is a chart depicting phase noise as a function of frequency associated with a prior art digital phase-locked loop. 
         FIG. 7  is a chart depicting phase noise as a function of frequency associated with a digital phase-locked loop in accordance with some embodiments. 
     
    
    
     DETAILED DESCRIPTION 
     In the following detailed description, reference is made to the accompanying drawings which form a part hereof wherein like numerals designate like parts throughout, and in which is shown by way of illustration embodiments in which the disclosure may be practiced. It is to be understood that other embodiments may be utilized and structural or logical changes may be made without departing from the scope of the present disclosure. Therefore, the following detailed description is not to be taken in a limiting sense, and the scope of embodiments in accordance with the present disclosure is defined by the appended claims and their equivalents. 
     Various operations may be described as multiple discrete operations in turn, in a manner that may be helpful in understanding embodiments of the present disclosure; however, the order of description should not be construed to imply that these operations are order dependent. 
     For the purposes of the present disclosure, the phrase “A and/or B” means (A), (B), or (A and B). For the purposes of the present disclosure, the phrase “A, B, and/or C” means (A), (B), (C), (A and B), (A and C), (B and C), or (A, B and C). 
     Various logic blocks may be introduced and described in terms of an operation provided by the blocks. These logic blocks may include hardware, software, and/or firmware elements in order to provide the described operations. While some of these logic blocks may be shown with a level of specificity, e.g., providing discrete elements in a set arrangement, other embodiments may employ various modifications of elements/arrangements in order to provide the associated operations within the constraints/objectives of a particular embodiment. 
     The description may use the phrases “in an embodiment,” or “in embodiments,” which may each refer to one or more of the same or different embodiments. Furthermore, the terms “comprising,” “including,” “having,” and the like, as used with respect to embodiments of the present disclosure, are synonymous. 
     Embodiments of the present disclosure describe a dynamic element matching (DEM) technique, which may also be referred to as a dithering technique, to suppress fractional spurs due to TDC mismatch in, e.g., a DPLL. In some embodiments, a randomized phase shift may be added before the TDC and then removed in the digital domain after the TDC. This dithering technique allows for the fractional spurs suppression without degrading the output spectrum since the introduction of the randomized phase shift breaks the periodicity of the VCO phase, thus the periodicity of the phase error due to the TDC mismatch, and the same phase shift is then removed in the digital phase domain after the TDC. 
       FIG. 1  illustrates a DPLL  100  in accordance with some embodiments. The DPLL  100  may include a phase detector  102  that receives a digital word  104 , from a feedback path  106 , representing a phase of an output signal  108  output by VCO  110 . The phase detector  102  may also receive a clock signal  112  and a reference digital word (Ref)  114 . The phase detector  102  may generate and output a digital phase error (DPE)  116  based on the differences between the digital word  104  and the reference digital word  114 . In the figures, the block arrows indicate a digital signal, while line arrows indicate an analog signal. 
     The digital phase error  116  may be filtered at filter  118  to generate a digital control signal (DCS)  120 . The digital control signal  120  may be converted to an analog control signal (ACS)  122  by a DAC  124 . The analog control signal  122  may be provided to the VCO  110  to adjust the phase of the output signal  108 . 
     The output signal  108  may be provided to a phase shifter (PS)  126  of the feedback path  106 . The phase shifter  126  may dither the output signal  108  by, e.g., providing a randomized phase shift to the output signal  108 , to provide a dithered, or delayed output signal (DOS)  128 . The amount of the randomized phase shift provided by the phase shifter  126  may be controlled by a digital phase shift control signal (PSCS)  130  that is provided to the phase shifter  126  by shift controller  132 . The shift controller  132  may include a pseudo-random number generator (PRNG)  134  and a summer  136 . 
     The phase shifter  126  may be coupled with, and provide the delayed output signal  128  to, a TDC  138 . The TDC  138  may include a DLL and may generate a digital word  140  that represents a phase of the delayed output signal  128 . The feedback path  106  may further include an adder  142  coupled with the TDC  138  and the shift controller  132 . The adder  142  may generate the digital word  104  based on the digital word  140  and the phase-shift control signal  130  and provide the digital word  104  to the phase detector  102 . By receiving the phase shift control signal  130  from the shift controller  132 , the adder  142  may have accurate knowledge of the amount of randomized phase shift provided by the phase shifter  126  to the delayed output signal  128 . Thus, the adder  142  may be able to accurately remove the amount of randomized phase shift such the digital word  104  represents the phase of the output signal  108 , rather than the phase of the delayed output signal  128 , which is represented by the digital word  140 . 
     How the above-described dithering technique breaks the periodicity of the VCO phase may be illustrated by reference to the waveforms depicted in  FIG. 2 .  FIG. 2  shows waveforms of a reference clock, a VCO signal (e.g., a digital representation of the output signal  108 ), and a VCO+φ signal (e.g., a digital representation of the delayed output signal  128 ) in accordance with various embodiments. T_VCO represents a period of the VCO signal. With the frequency of the VCO signal divided by the frequency of the reference clock being equal to 2.25, the phase of the VCO signal may repeat after four samples. The addition of randomized φ values as shown, causes the VCO+φ signal to lose its periodicity and, therefore, not repeat every four-sample period. The specific φ values that are shown do not restrict φ values in other embodiments. 
       FIG. 3  illustrates the phase shifter  126  in accordance with various embodiments. The phase shifter  126  may include a delay line  304  with a plurality of delay elements, e.g., delay elements  308 ,  312 ,  316 , and  320 , coupled with one another in series, through which the output signal  108  will be propagated. While  FIG. 3  shows four delay elements, it is understood that any number of delay elements may be used. The delay line  304  may be coupled with a phase detector (PD)/charge pump (CP)  324  that provides a control signal to each of the delay elements of the delay line  304  so that each of the delay elements provides an equal phase delay (or simply “delay”) of, e.g., 90 degrees. In general, the phase delay provided by each delay element of a DLL may be determined by dividing the total signal period, e.g., 360 degrees, by the number of delay elements. 
     Taps following each delay element may be coupled with a multiplexer (MUX)  328  as inputs that respectively represent the output signal delayed by a different number of delays. For example, the first tap may provide the MUX  328  with the output signal  108  delayed by one delay, the second tap may provide the MUX  328  with the output signal  108  delayed two delays, etc. The MUX  328  may select one of the inputs for output as the delayed output signal  128  based on the phase-shift control signal  130  received from the shift controller  132 . In this manner, a phase shift introduced to the output signal  108  may be randomized among a discrete set of known values, yet knowledge of the discrete set of values (and the selected input) may allow the adder  142  to accurately remove the introduced phase shift prior to providing the digital word  104  to the phase detector  102 . Removal of the introduced phase shift in the digital domain may facilitate accurate removal. In this manner, the dithering technique may break the periodicity without constituting an additional noise source for the DPLL  100 . 
     In some embodiments, it may be desirable for the whole dynamic range (as phase) of the TDC  138  to be exercised by the additional phase shift added by the MUX  328  in order to get an effective dynamic element matching over the TDC  138 . However, as shown in  FIGS. 4   a - b , it may also be desirable for a randomized phase shift to be limited in magnitude.  FIGS. 4   a - b  provide waveforms  404  and  408  respectively illustrating introductions of phase shifts of 120 degrees and 60 degrees in accordance with various embodiments. To avoid glitches, it may be desirable to switch from one phase to another when both signals have the same logic value. As can be seen from  FIGS. 4   a - b , switching from 0 degrees to 120 degrees provides a significantly smaller window in which the phase switch may be performed (phase-switching window), as compared to switching from 0 degrees to 60 degrees. 
     In order to exercise the whole dynamic range of the TDC  138 , while limiting the magnitude of the phase shift, the shift controller  132  may use the running sum of a PRNG sequence to drive the MUX  328  and thus provide a random walk through the entire range of possible phase shifts. 
     Consider, for example, an embodiment in which the MUX  328  had ten inputs, thus, enabling ten different phase shifts to be applied. In one embodiment, it may be desirable to limit the phase shift to 3 delay phases. That is, the first phase shift may include 0, 1, 2, or 3 delay phases; the second phase shift may have 0, 1, 2, or 3 delay phases added to the first phase shift; and so on. 
     The PRNG  134  and the summer  136  may cooperatively implement the above-described random walk as follows. The PRNG may generate a pseudo-random number (PRN) from a number of possible values that corresponds to the number of delay phases to which the phase shift may be limited. In some embodiments, the number of possible values may be one greater than the number of delay phases to which the phase shift may be limited to accommodate the possibility that no delay phase is added. The number of possible values will be less than the total number of inputs to the MUX  328 . In the above example, the PRNG  134  may be used to generate a sequence with a uniform randomized distribution from 0-3. The summer  136  may be a modulo-M adder that implements a modulo-M operation, where M is in the number of phases coming to the MUX  328 . The summer  136  may receive the PRN and add the PRN to the previous selection. Even if the PRNG  134  were to produce a sequence having low variance, the running sum will span all the possible M-levels and its variance will increase with time. Moreover, the consecutive phase shifts may be kept small, e.g., less than 90 degrees, due to the relatively small number of possible values of the PRNG output. 
       FIG. 5  illustrates a flowchart  500  describing operation of the feedback path  106  of the DPLL  100  in accordance with some embodiments. At block  504 , the operation may include receiving, e.g., by the phase shifter  126 , the VCO output signal  108 . 
     At block  508 , the operation may include receiving, e.g., by the phase shifter  126 , the phase-shift control signal  130  from the shift controller  132 . The operation may then include, at block  512 , selecting and adding, e.g., by the phase shifter  126 , a phase shift from a discrete set of possible phase shifts based on the received phase-shift control signal. The phase-shifter  126  may provide the discrete set of possible phase shifts by inputting the VCO output signal  108  through a DLL as described above. A MUX  328  of the phase shifter  126  may output the delayed output signal  128 . 
     At block  516 , the operation may include generating, e.g., by the TDC  138 , a digital word  140  representing a phase of the delayed output signal  128 . The TDC  138  may include a DLL to facilitate generation of the digital word  140 . 
     At block  520 , the operation may include generating, e.g., by the adder  142 , a digital word representing a phase of the VCO output signal based on the phase-shift control signal  130  and the digital word  140 . As described above, the phase shift added by the phase shifter  126  may be removed by the adder  142 . 
       FIGS. 6 and 7  respectively illustrate charts  600  and  700  depicting phase noise as a function of frequency. Chart  600  is associated with a prior art DPLL, while chart  700  is associated with a DPLL in accordance with embodiments of the present invention. Values common to both charts include:
         DPLL reference frequency of 80 megaHertz (MHz) and a fractional number, N, of 60+1/1024, thus, the output frequency is 4800.078125 MHz, while spurs may appear at 78.125 kilohertz (kHz) and its multiples;   DPLL loop bandwidth of approximately 1 MHz;   delay of each delay cell of the DLL of the TDC generated using a Gaussian distribution with a variance of 1 picosecond; and   frequency bins of 76 Hz.       

     With respect to chart  700 , the number of inputs to a MUX of a phase shifter is 32 and a PRNG sequence generates a uniform distribution from 0-7, which may result in maximum phase shift of approximately 7/32*360=79 degrees. 
     Chart  600  shows that the output spectrum exhibits spurs as high as −39 decibels relative to the carrier (dBc). In chart  700 , on the other hand, the fractional spurs lower to −58 dBc. Moreover, the total phase noise integrated inside the transmission channel (100 Hz to 10 MHz) is −31.7 dBc in a prior art DPLL and −38.8 dBc with a DPLL, e.g., DPLL  100 , using the dithering techniques disclosed herein. Thus, the DPLL  100  may reduce fractional spurs by 18 dB and the integrated phase noise by 7 dB compared to a prior art DPLL. 
     The disclosed dynamic element matching technique works in the background to suppress fractional spurs. The disclosed embodiments do not require a modification to a TDC used in a feedback path of a DPLL and they do not have inherent bandwidth limitations since they do not attempt to compensate for mismatch of each TDC delay element. Still further, the disclosed embodiments provide insensitivity to process, voltage and temperature (PVT) variations since the DLL of the phase shifter automatically tracks any PVT variations associated with the DLL of the TDC. Embodiments of the present disclosure do not require calibrations when the DPLL frequency is adjusted; rather, the DLL of the phase shifter will automatically settle over a relatively short amount of time, e.g., within a few microseconds. 
     While disclosed embodiments discuss the DEM techniques with respect to specific circuits, e.g., DPLL  100  with DLL-based TDC  138 , other embodiments may use the disclosed DEM techniques with other circuits. For example, the disclosed DEM techniques may be used with non-DLL based TDCs; may be used with digitally controlled oscillator, rather than a VCO; etc. 
     Although certain embodiments have been illustrated and described herein for purposes of description of the preferred embodiment, it will be appreciated by those of ordinary skill in the art that a wide variety of alternate and/or equivalent embodiments or implementations calculated to achieve the same purposes may be substituted for the embodiments shown and described without departing from the scope of the present disclosure. Similarly, memory devices of the present disclosure may be employed in host devices having other architectures. This application is intended to cover any adaptations or variations of the embodiments discussed herein. Therefore, it is manifestly intended that embodiments in accordance with the present disclosure be limited only by the claims and the equivalents thereof.