Digital logic circuits often rely on clock signals for synchronization, derivation of reference signals, measuring phase differences, and other functions. The circuits may be segregated into different integrated circuits or different subsystems of a larger electronic device.
One approach for getting the clock signal to components is to distribute the clock signal from a centralized clock to every component requiring the clock signal. One disadvantage of this approach is that clock signals tend to have constraints that are difficult to maintain when the distribution is over a relatively large area or used to drive a relatively large number of components.
Another technique for distributing a clock signal entails distributing a reference clock signal to different components or even different regions within an integrated circuit. Each component or region has a local phase locked loop (PLL) or local delay locked loop (DLL) buffer to derive one or more local clock signals from the reference clock signal. Such designs are sometimes referred to as a “clock tree”. The use of a tree structure allows clocked buffers to be configured for the specifics of the loads they are driving as well as limiting the load to be driven by any clock signal.
A PLL is “locked” when the PLL output clock frequency (FOUT_CLK) matches and tracks the frequency of the reference clock (FREF_CLK) and the PLL output clock is maintaining a predetermined phase angle relative to that of the reference clock (typically zero). Depending upon the type of PLL, calibration is typically accomplished by searching through frequency bands until a frequency band is found that includes the frequency of the reference clock signal. Searching for the calibration band takes a finite amount of time. The calibration time impacts the overall time to initialize the system relying on the PLL. Calibration time for finding the calibration frequency band for the PLL is an important attribute of a PLL.
One prior art method of calibration uses a binary search algorithm to identify the calibration band. The prior art calibration process iteratively selects a candidate band for PLL operation. Each iteration typically eliminates half of the remaining bands as candidates for the calibration band. Given B frequency bands to search, a binary search algorithm can identify the calibration band with a worst case number of guesses on the order of log2(B) guesses, i.e., O(log2(B)). Due to the number of reference clock cycles required to accumulate a meaningful difference between the frequency of the reference clock signal and the frequency of the output clock signal this amount of time may be too long for some applications.
An integrated circuit apparatus for calibrating a phase locked loop (PLL) circuit that includes a phase comparator configured to receive a reference clock signal and a feedback clock signal and generate a phase error signal, a variable frequency oscillator configured for receiving the phase error signal and generating a corresponding fast clock signal at an output of the variable frequency oscillator, and a divider that is configured to divide the fast clock signal by a divisor (N) so as to generate the feedback clock signal, includes a calibration circuit. The calibration circuit is coupled to receive the reference clock signal and the fast clock signal and to provide a frequency band selection signal to the variable frequency oscillator. The calibration circuit includes a counting circuit operable for counting a number of cycles of the fast clock signal over a period of time defined by a number of cycles (M) of the reference clock signal. The calibration circuit also includes a selection block operable for performing a convergence test using the counted number of fast clock cycles, N, and M, wherein the selection block generates the frequency band selection signal in accordance with the results of the convergence test to select a next candidate calibrated frequency band.
By using a convergence test based upon the count of cycles of the fast clock signal and N, the calibration circuitry can converge on the calibrated frequency band in fewer reference clock cycles per iteration than required with a convergence test based upon the count of cycles of the output clock or feedback signal.
Other features and advantages of the present invention will be apparent from the accompanying drawings and from the detailed description that follows below.
The present invention is illustrated by way of example and not limitation in the figures of the accompanying drawings, in which like references indicate similar elements and in which:
Calibration circuitry 170 is used to identify the calibration band for the PLL. In one embodiment, the calibration circuitry may be electrically de-coupled from the PLL via switches 162, 134 when the PLL is not being calibrated. While in a calibration mode, however, the calibration circuitry receives REF_CLK 160 and FST_CLK 132 as inputs and provides a control signal 174 to the VFO.
The calibration circuitry relies on a search algorithm to locate a range or band of frequencies to which the PLL should be set to initially operate within. This band is referred to as the calibration band. Once the correct range of frequencies is located, the remainder of the PLL circuit should be able to lock to and follow the reference clock. The calibration circuitry incorporates a selection block 172 that performs a convergence test to facilitate identifying the calibration band out of a plurality of possible bands. In one embodiment, the convergence test is iteratively applied to a candidate band of the remaining untested bands to eliminate approximately one-half of the remaining bands with each iteration.
An initial candidate calibrated frequency band is selected in step 212 from a set (plurality) of B frequency bands as the band to test. In step 220 an iteration test is performed to determine if the halt condition for the calibration process has been reached, i.e. whether the calibration process is completed. If no further iterations are to take place, the process ends with step 290. Otherwise the process starts an iteration of the selection process.
In step 230, the number of reference clock cycles (REF_CLK_COUNT) and fast clock cycles (FST_CLK_COUNT) are counted until the count of REF_CLK cycles reaches a pre-determined value, M.
A convergence test is performed in step 240. The convergence test determines which of the candidate bands out of the remaining bands being considered should be discarded from consideration for the next round of iteration testing. Each iteration eliminates approximately one half of the remaining bands from consideration. The process is a binary search process which is also known as a half-interval search.
The process relies on a convergence test using the number of reference clock cycles (REF_CLK_COUNT) and the number of fast clock cycles (FST_CLK_COUNT) for each iteration. In other words, the test used for convergence to a final calibration band is a function of FST_CLK_COUNT and REF_CLK_COUNT. The nomenclature used to denote this test is as follows:
The REF_CLK_COUNT may be set to a pre-determined value, M, such that the test function can be expressed as ƒ(FST_CLK_COUNT, M) where M corresponds to the number of reference clock cycles used for a given binary search algorithm test iteration. In one embodiment, the convergence test is a function ƒ(FST_CLK_COUNT, N·M), where N is the divider ratio and N·M is the product of N and M. For a constant M and N, a convergence test expressed as ƒ(FST_CLK_COUNT) inherently includes formulaic expressions involving constants as part of the formulation.
In various embodiments, the convergence test is expressed as an inequality between FST_CLK_COUNT and N·M, a difference between FST_CLK_COUNT and N·M, or an inequality between a difference between FST_CLK_COUNT and N·M with another value such as zero.
Step 242 selects the next candidate calibrated frequency band based upon the results of the convergence test. The process then returns to step 220 to determine whether the calibration process is complete. The last candidate calibrated frequency band becomes the calibrated frequency band.
A plurality (M) of D flip-flops determines the number of reference clock cycles used for each decision cycle of the search block 370. A state change from low to high of REF_CLK 360 will trigger a change in the output of D flip-flop 310 which will cause counter 320 to begin counting the number of cycles of FST_CLK. The change in the output of D-flip flop 310 will synchronously (with REF_CLK) cascade to D flip-flop 312 and to each successive D flip-flop. A change in the state of the Mth D flip-flop 314 stops counter 320. The counter and flip-flops co-operate to collect the count of FST_CLK cycles (i.e., FST_CLK_COUNT) which occurs within a pre-determined number (M) of REF_CLK cycles (i.e., REF_CLK_COUNT). In one embodiment, M is selected to be an integer power of 2.
In one embodiment, M is selectable. A multiplexer may be used, for example, to select from a plurality of pre-determined index of D flip-flops as the stop input to counter 320. For example, a multiplexer may be used to select the output of the 256th, 512th, 1024th, or 2048th D flip-flop as the stop input to counter 320.
The counter output (i.e., FST_CLK_COUNT) is provided to a summer 350. The summer also receives a value corresponding to the product 346 of REF_CLK_COUNT (i.e., M) 344 and N 342 where N corresponds to the divide ratio from the divider 140. The product 346 of M and N is provided by multiplier 340. In one embodiment N is an integer power of 2. In one embodiment at least one of N and M is a integer power of 2. The use of an integer power of 2 for one of N or M enables the use of a shift register as a multiplier. In one embodiment multiplier 340 is a shift register.
The output of summer 350 is provided to selection block 372. Selection block 372 relies upon a convergence test which is a function of FST_CLK_COUNT and REF_CLK_COUNT, i.e., ƒ(FST_CLK_COUNT, REF_CLK_COUNT). The convergence test may apply an inequality test between FST_CLK_COUNT and REF_CLK_COUNT, for example. In this case, given that REF_CLK_COUNT=M, the value FST_CLK_COUNT−N·M is computed and provided to selection block 372. For an inequality test, the value indicates which of FST_CLK_COUNT and N·M is larger than the other (or equal). The selection block can thus determine which bands to eliminate or alternatively which band to select for the next iteration of the selection process. Selection block 372 outputs a frequency band selection signal 374 to the VFO to select the next candidate calibration frequency band based on the results of the convergence test. In one embodiment, signal 374 includes a digital code for selecting the frequency band. The digital code value is latched into the VFO. This process repeats until the selection block has selected a frequency band or determined no band qualifies for selection. If one of the frequency bands qualifies for selection as the calibration frequency band, the last candidate calibration frequency band becomes the calibration frequency band.
A feedback loop 482 couples the PLL clock output to a feedback input 414 of the phase comparator 410. The phase comparator generates a signal corresponding to a phase error signal which is filtered by loop filter 420. The filtered phase error signal controls the frequency of VFO 430. The frequency and phase of the VFO vary in response to the filtered phase error signal. The VFO is driven to cause the PLL clock output (OUT_CLK 480) to match the phase and frequency of the reference clock REF_CLK 460. Although only the monitored output 480 is shown, the PLL may drive multiple outputs.
In one embodiment, the calibration circuitry 470 is selectively coupled to the remainder of the PLL circuitry via switches 462, 434. The switch positions illustrated are the positions effective during the calibration process. Outside of the calibration mode the switches may be toggled open to electrically de-couple the calibration circuitry from the remainder of the PLL circuitry.
The selection block 472 of the calibration circuitry performs a convergence test that is a function of FST_CLK_COUNT and REF_CLK_COUNT. In particular, the convergence test compares FST_CLK_COUNT with N·M, where N is the divider ratio for divider 440 and M is the number of reference clock cycles used in an iteration of the search process. Based upon the result of this comparison, the selection block provides a frequency band selection signal 474 which is latched into the VFO. The frequency band selection signal selects a candidate calibrated frequency band for each iteration of the search process. At the conclusion of the search the last candidate calibrated frequency band becomes the calibrated frequency band.
In one embodiment, the phase locked loop circuitry with calibration circuitry is fabricated on a semiconductor substrate 402 for incorporation into an integrated circuit package. In one embodiment, the integrated circuit package includes a microcontroller 490 and memory 492 to facilitate programmatic control of the calibration. Circuitry connecting the microcontroller to other elements is not expressly illustrated.
“Programmable” or “programmatic control” means that the variables such as number of frequency bands, divider ratio, and other variables can be programmatically set and varied and that the values are not permanently fixed at the time of manufacture. This may be accomplished by storing the values in a register, memory, or other storage location from which the values can be retrieved. In one embodiment, the values are stored in volatile memory. In an alternative embodiment, the values are stored in a non-volatile memory in order to preserve the values across power-down cycles of the apparatus.
A feedback loop 582 couples the PLL clock output to a feedback input 514 of the time-to-digital converter 510. The time-to-digital converter generates a signal corresponding to a phase error signal which is filtered by digital loop filter 520. The filtered phase error signal controls the frequency of DCO 530. The frequency and phase of the DCO vary in response to the filtered phase error signal. The DCO is driven to cause the PLL clock output (OUT_CLK 580) to match the phase and frequency of the reference clock REF_CLK 560. Although only the monitored output 580 is shown, the PLL may drive multiple outputs.
In one embodiment, the calibration circuitry 570 is selectively coupled to the remainder of the PLL circuitry via switches 562, 534. The switch positions illustrated are the positions effective during the calibration process. Outside of the calibration process the switches may be toggled open to electrically de-couple the calibration circuitry from the reference clock and the output clock of the PLL circuitry.
The selection block 572 of the calibration circuitry utilizes a convergence test that is a function of FST_CLK_COUNT and REF_CLK_COUNT. In particular, the convergence test compares FST_CLK_COUNT with the product of N and M (i.e., N·M), where N is the divider ratio for divider 540 and M is the number of reference clock cycles used in an iteration of the search process. Based upon the result of this comparison, the selection block provides a frequency band selection signal 574 that is latched into the DCO. The frequency band selection signal selects a candidate calibrated frequency band for each iteration of the search process. At the conclusion of the search the last candidate calibrated frequency band becomes the calibrated frequency band.
The embodiment of
A second divider 542 having a divide ratio K is coupled to provide a second output clock signal that is 1/K the frequency of the FST_CLK 532 signal. K may be selected such that K=N in some embodiments in order to provide a clock signal with the same frequency as REF_CLK 560 to a component 598. In alternative embodiments, K is selected such that K≠N. If K<N then the clock signal provided to component 598 will be higher in frequency than REF_CLK. If K>N then the clock signal provided to component 598 will be lower in frequency than REF_CLK. Generally, the frequency of the clock signal provided to component 598 may be expressed as N/K·FREF_CLK.
Thus through appropriate selection of N and K, the frequency of the clock signal to component 598 may be scaled as desired relative to FREF_CLK. For example, N and K may be chosen such that the clock signal to component 598 has a frequency that is: a multiple (e.g., 4), a fraction (e.g., ⅔), or other non-integer scale (e.g., 5/3) of FREF_CLK.
In one embodiment, the phase locked loop circuitry with calibration circuitry is fabricated on a semiconductor substrate for incorporation into an integrated circuit package. In one embodiment, the integrated circuit package includes a microcontroller 590 and memory 592 to facilitate programmatic control of the calibration. Circuitry connecting the microcontroller to other elements is not expressly illustrated.
After starting in step 610, the BAND_STEP, NEXT_BAND, and COUNT variables are initialized in block 612. The process of
This particular embodiment is one implementation of a binary search process. The maximum number of iterations is based upon the number of frequency bands. Thus if the iteration COUNT exceeds LOG2(NUM_BANDS) the process is terminated in step 690.
In step 622, the counters are initialized. In this case, REF_CLK_COUNT and FST_CLK_COUNT variables are initialized to zero. In step 630, the number of REF_CLK cycles and FST_CLK cycles are counted until the count of REF_CLK cycles reaches a pre-determined value, M. Step 622 need not be a separate step from 630. Typically, a “start counter” trigger may also be used to reset the counter. As indicated in
In step 640, a convergence test is performed. If N·REF_CLK_COUNT exceeds FST_CLK_COUNT, then a higher frequency band (i.e., faster frequencies) is selected for the next band. Accordingly, the process continues with step 642. Otherwise a lower frequency band is chosen and the process continues with step 644. Steps 642, 644 set NEXT_BAND accordingly. BAND_STEP is halved so long as the result is not less than one and the iteration count is incremented. The process then returns to step 620 to determine if the process should terminate or proceed with another iteration.
The process of
The convergence test is a function of FST_CLK_COUNT and REF_CLK_COUNT. In particular, the convergence test is a function of FST_CLK_COUNT and N·REF_CLK_COUNT. The REF_CLK_COUNT may be set to a pre-determined value, M, such that the test function may be expressed as ƒ(FST_CLK_COUNT, N·M) or more simply ƒ(FST_CLK_COUNT) given that N·M is a constant. By using a convergence test based upon the count of cycles of the fast clock signal and N, the calibration circuitry can converge on the calibration frequency band in fewer reference clock cycles per iteration than required with a convergence test based upon the count of cycles of the output clock. The use of FST_CLK_COUNT rather than OUT_CLK_COUNT enables the use of fewer reference clock cycles per iteration than required when using OUT_CLK_COUNT.
In summary an apparatus includes phase locked loop circuitry for generating an output clock corresponding to a reference clock. The phase locked loop circuitry includes a variable frequency oscillator generating a fast clock and a divider coupled to generate the output clock as 1/N of the fast clock. Calibration circuitry for selecting a calibrated frequency band for the variable frequency oscillator from a plurality (B) of candidate bands iteratively eliminates candidate bands as the calibrated band by performing a convergence test. The convergence test for a given iteration is a function of a count of cycles of the fast clock (FST_CLK_COUNT) occurring during a pre-determined number (M) of cycles of the reference clock.
In the preceding detailed description, the invention is described with reference to specific exemplary embodiments thereof. Various modifications and changes may be made thereto without departing from the broader scope of the invention as set forth in the claims. The specification and drawings are, accordingly, to be regarded in an illustrative rather than a restrictive sense.
Number | Name | Date | Kind |
---|---|---|---|
4684941 | Smith et al. | Aug 1987 | A |
4862485 | Guinea et al. | Aug 1989 | A |
5663105 | Sua et al. | Sep 1997 | A |
5748949 | Johnston et al. | May 1998 | A |
5757240 | Boerstler et al. | May 1998 | A |
5848355 | Rasor et al. | Dec 1998 | A |
5903195 | Lukes et al. | May 1999 | A |
6219797 | Liu et al. | Apr 2001 | B1 |
6259327 | Balistreri et al. | Jul 2001 | B1 |
6640311 | Knowles | Oct 2003 | B1 |
6643787 | Zerbe et al. | Nov 2003 | B1 |
6650193 | Endo et al. | Nov 2003 | B2 |
6683506 | Ye et al. | Jan 2004 | B2 |
6727767 | Takada | Apr 2004 | B2 |
6768387 | Masuda et al. | Jul 2004 | B1 |
6870411 | Shibahara | Mar 2005 | B2 |
6959066 | Wang et al. | Oct 2005 | B2 |
7012476 | Ogiso | Mar 2006 | B2 |
7323916 | Sidiropoulos et al. | Jan 2008 | B1 |
7405594 | Xu | Jul 2008 | B1 |
7434083 | Wilson | Oct 2008 | B1 |
7541848 | Masuda | Jun 2009 | B1 |
7545188 | Xu et al. | Jun 2009 | B1 |
7573303 | Chi et al. | Aug 2009 | B1 |
7586347 | Ren et al. | Sep 2009 | B1 |
7590163 | Miller et al. | Sep 2009 | B1 |
7671635 | Fan et al. | Mar 2010 | B2 |
7737739 | Bi | Jun 2010 | B1 |
7741981 | Wan et al. | Jun 2010 | B1 |
7750618 | Fang et al. | Jul 2010 | B1 |
7786763 | Bal et al. | Aug 2010 | B1 |
7800422 | Lee et al. | Sep 2010 | B2 |
7816959 | Isik | Oct 2010 | B1 |
7907625 | MacAdam | Mar 2011 | B1 |
7928880 | Tsukamoto | Apr 2011 | B2 |
7941723 | Lien et al. | May 2011 | B1 |
8010072 | Nathawad | Aug 2011 | B1 |
8018289 | Hu et al. | Sep 2011 | B1 |
8164367 | Bal et al. | Apr 2012 | B1 |
8179952 | Thurston et al. | May 2012 | B2 |
8188796 | Zhu et al. | May 2012 | B2 |
8259888 | Hua et al. | Sep 2012 | B2 |
8284816 | Clementi | Oct 2012 | B1 |
8305154 | Kubena et al. | Nov 2012 | B1 |
8416107 | Wan et al. | Apr 2013 | B1 |
8432231 | Nelson et al. | Apr 2013 | B2 |
8436677 | Kull et al. | May 2013 | B2 |
8456155 | Tamura et al. | Jun 2013 | B2 |
8471751 | Wang | Jun 2013 | B2 |
8537952 | Arora | Sep 2013 | B1 |
8693557 | Zhang et al. | Apr 2014 | B1 |
8704564 | Hasegawa et al. | Apr 2014 | B2 |
8723573 | Wang et al. | May 2014 | B1 |
8791763 | Taghivand | Jul 2014 | B2 |
8896476 | Harpe | Nov 2014 | B2 |
8933830 | Jeon | Jan 2015 | B1 |
8981858 | Grivna et al. | Mar 2015 | B1 |
9077386 | Holden et al. | Jul 2015 | B1 |
9100232 | Hormati et al. | Aug 2015 | B1 |
9455854 | Gao | Sep 2016 | B2 |
20020079937 | Xanthopoulos | Jun 2002 | A1 |
20020191727 | Staszewski et al. | Dec 2002 | A1 |
20030042985 | Shibahara et al. | Mar 2003 | A1 |
20030184350 | Wang et al. | Oct 2003 | A1 |
20040136440 | Miyata et al. | Jul 2004 | A1 |
20040165691 | Rana | Aug 2004 | A1 |
20050170787 | Yamamoto et al. | Aug 2005 | A1 |
20060103436 | Saitou et al. | May 2006 | A1 |
20060119402 | Thomsen et al. | Jun 2006 | A1 |
20060197614 | Roubadia et al. | Sep 2006 | A1 |
20060290391 | Leung et al. | Dec 2006 | A1 |
20070149144 | Beyer et al. | Jun 2007 | A1 |
20070247248 | Kobayashi et al. | Oct 2007 | A1 |
20080043893 | Nagaraj et al. | Feb 2008 | A1 |
20080104435 | Pernia et al. | May 2008 | A1 |
20080129351 | Chawla | Jun 2008 | A1 |
20080246546 | Ha et al. | Oct 2008 | A1 |
20090083567 | Kim et al. | Mar 2009 | A1 |
20090140896 | Adduci et al. | Jun 2009 | A1 |
20090153252 | Chen | Jun 2009 | A1 |
20090184857 | Furuta et al. | Jul 2009 | A1 |
20090231901 | Kim | Sep 2009 | A1 |
20090256601 | Zhang et al. | Oct 2009 | A1 |
20090262567 | Shin et al. | Oct 2009 | A1 |
20100007427 | Tomita et al. | Jan 2010 | A1 |
20100052798 | Hirai | Mar 2010 | A1 |
20100090731 | Casagrande | Apr 2010 | A1 |
20100109714 | Lindfors et al. | May 2010 | A1 |
20100164761 | Wan et al. | Jul 2010 | A1 |
20100194483 | Storaska et al. | Aug 2010 | A1 |
20100240323 | Qiao et al. | Sep 2010 | A1 |
20100323643 | Ridgers | Dec 2010 | A1 |
20110006936 | Lin et al. | Jan 2011 | A1 |
20110032013 | Nelson et al. | Feb 2011 | A1 |
20110095784 | Behel et al. | Apr 2011 | A1 |
20110234204 | Tamura et al. | Sep 2011 | A1 |
20110234433 | Aruga et al. | Sep 2011 | A1 |
20110285575 | Landez et al. | Nov 2011 | A1 |
20110304490 | Janakiraman | Dec 2011 | A1 |
20120013406 | Zhu et al. | Jan 2012 | A1 |
20120161829 | Fernald | Jun 2012 | A1 |
20120200330 | Kawagoe et al. | Aug 2012 | A1 |
20120249207 | Natsume et al. | Oct 2012 | A1 |
20120262315 | Kapusta et al. | Oct 2012 | A1 |
20120293221 | Ma et al. | Nov 2012 | A1 |
20120297231 | Qawami et al. | Nov 2012 | A1 |
20120317365 | Elhamias | Dec 2012 | A1 |
20120328052 | Etemadi et al. | Dec 2012 | A1 |
20130002467 | Wang | Jan 2013 | A1 |
20130162454 | Lin | Jun 2013 | A1 |
20130194115 | Wu et al. | Aug 2013 | A1 |
20130211758 | Prathapan et al. | Aug 2013 | A1 |
20130300455 | Thirugnanam et al. | Nov 2013 | A1 |
20140021990 | Na et al. | Jan 2014 | A1 |
20140029646 | Foxcroft et al. | Jan 2014 | A1 |
20140210532 | Jenkins | Jul 2014 | A1 |
20140327478 | Horng et al. | Nov 2014 | A1 |
20140347941 | Jose et al. | Nov 2014 | A1 |
20150028960 | Yorita | Jan 2015 | A1 |
20150162921 | Chen et al. | Jun 2015 | A1 |
20150180594 | Chakraborty et al. | Jun 2015 | A1 |
20150200649 | Trager et al. | Jul 2015 | A1 |
20150213873 | Joo et al. | Jul 2015 | A1 |
20160013796 | Choi | Jan 2016 | A1 |
20160084895 | Imhof | Mar 2016 | A1 |
20160119118 | Shokrollahi | Apr 2016 | A1 |
20160162426 | Benjamin et al. | Jun 2016 | A1 |
20160211929 | Holden et al. | Jul 2016 | A1 |
Entry |
---|
“19-Output PCIE Gen 3 Buffer”, Si53019-A01A, Silicon Laboratories Inc., Rev. 1.1 May 2015, 34 Pages. |
“NB3W1200L: 3.3 V 100/133 MHz Differential 1:12 Push-Pull Clock ZDB/Fanout Buffer for PCIe”, ON Semiconductor, http://onsemi.com, Aug. 2013, Rev. 0, 26 Pages. |
Texas Instruments “CDCEx913 Programmable 1-PLL VCXO Clock Synthesizer With 1.8-V, 2.5-V, and 13-V Outputs”, Apr. 2015, pp. 1-36, pp. 11, 20-22. |
Avramov, et al., “1.5-GHz Voltage Controlled Oscillator with 3% Tuning Bandwidth Using a Two-Pole DSBAR Filter”, Ultrasonics, Ferroelectrics and Frequency Control. IEEE Transactions on. vol. 58., May 2011, pp. 916-923. |
Hwang, et al., “A Digitally Controlled Phase-Locked Loop with a Digital Ohase-Frequency Detector for Fast Acquisition”, IEEE Journal of Solid State Circuits, vol. 36, No. 10, Oct. 2001, pp. 1574-1581. |
Kratyuk, et al., “Frequency Detector for Fast Frequency Lock of Digital PLLs”, Electronic Letters, vol. 43, No. 1, Jan. 4, 2007, pp. 1-2. |
Mansuri, “Fast Frequency Acquisition Phase-Frequency Detectors for GSamples/s Phase-Locked Loops”, IEEE Journal of Solid-State Circuits, vol. 37 No. 10, Oct. 2002, pp. 1331-1334. |
Nagaraju, “A Low Noise 1.5GHz VCO with a 175% Tuning Range Using Coupled FBAR's”, IEEE International Ultrasonics Symposium (IUS), Oct. 2012, pp. 1-4. |
Natanabe, “An All-Digital PLL for Frequency Multilication by 4 to 1022 with Seven-Cycle Lock Time”, IEEE Journal of Solid-State Circuits, vol. 39 No. 2, Feb. 2003, pp. 198-204. |