Patent Publication Number: US-11031926-B2

Title: Digital clock circuit for generating high-ratio frequency multiplication clock signal

Description:
CROSS-REFERENCE TO RELATED APPLICATION 
     This application is a national stage application under 35 U.S.C. § 371 of International Application No. PCT/CN2019/112164, filed Oct. 21, 2019, the contents of which are incorporated by reference in the entirety. 
     TECHNICAL FIELD 
     The present invention relates to data transmission technology, more particularly, to a digital clock circuit for generating clock signal with free-running high-ratio frequency multiplication over an input frequency. 
     BACKGROUND 
     For clock generation circuit, a difficult task is how to form a phase locked loop (PLL) with ultra-large multiplier factor to generate high-frequency clock signal. In conventional clock circuit with PLL designs, the frequency multiplier/divide factor is basically set at 16/32164/128. Very few designs are based on complex cascading algorithms to set the frequency multiplier factor to be about 1000. Basically, as the frequency multiplier/divide factor is increased, jitter in the output of the PLL of the conventional clock circuit becomes larger and larger, quickly degrading the quality of the clock signal. In general, the jitter in a clock signal cannot exceed 5% of the clock period, substantially limiting options of obtaining an ultra-large frequency multiplier/divider factor through the PLL design. Therefore, improved digital clock circuit is desired. 
     SUMMARY 
     In an aspect, the present disclosure provides a digital clock circuit for generating high-ratio frequency multiplication clock signal. The digital clock circuit includes a first sub-circuit including a first digitally-controlled oscillator configured to be driven by a frequency control word F to control a first output frequency of a first periodic signal synthesized from multiple first pulses. The first sub-circuit also includes a first frequency divider to generate a trigger signal having a frequency equal to 1/M of the first output frequency. Additionally, the digital clock circuit includes a second sub-circuit having a loop of feedback. The loop of feedback includes a frequency detector to compare an input frequency with a feedback frequency, a controller to adjust the frequency control word F based on an output of the frequency detector, and a second digitally-controlled oscillator configured to be driven by the frequency control word F plus a constant C to control a second output frequency of a second periodic signal synthesized from multiple second pulses induced by the trigger signal. The second sub-circuit also includes a second frequency divider to set the feedback frequency equal to 1/N of the second output frequency in the loop of feedback. The first output frequency is substantially higher than the input frequency by a multiplier factor of a few orders of magnitudes. 
     Optionally, the first sub-circuit further includes a free-running oscillator configured to generate oscillations based on noise and output the multiple first pulses having a first frequency with equally spaced phase shift. 
     Optionally, the free-running oscillator includes multi-stages of NAND-gate circuits cascaded in K b /2 number of stages with a pair of NAND-gate-based flip-flop structures in each stage to generate K h  number of first pulses with equally spaced phase shift of 1/K h  of a first period given by inverse of the first frequency. 
     Optionally, the first digitally-controlled oscillator includes a direct period synthesizer including a first K h -to-1 multiplexer coupled to an accumulation-register controlled by a fractional part of the frequency control word F via an accumulator to input K h  first pulses through a lower path for generating a low level of the first periodic signal, a second K h -to-1 multiplexer coupled to an adder-register controlled by a half of an integer part of the frequency control word F via an adder to input the K h  first pulses through an upper path for generating a high level of the first periodic signal, and a 2-to-1 multiplexer plus a D-type flip-flop to control transition between the upper path and the lower path to output the first periodic signal with the first output frequency proportional to the first frequency with a factor of K h  over the frequency control word F. 
     Optionally, the first frequency divider includes L-stage-cascaded high-frequency toggle flip flops configured to produce an output frequency at an output of each stage equal to ½ of an input frequency at an input of each stage. The L-stage-cascaded high-frequency toggle flip flops outputs the trigger signal at an output of a last L-th stage with 1/M of the first output frequency, where M=2 L . 
     Optionally, the first sub-circuit further includes a trigger oscillator driven by the trigger signal to generate multiple second pulses of a second frequency with equally spaced phase shift. 
     Optionally, the trigger oscillator includes a K 1 /2-stage Johnson counter configured to output K 1  number of second pulses with equally spaced phase shift of 1/K 1  of a second period given by inverse of 1/M of the first output frequency. 
     Optionally, the frequency detector includes a first input port receiving an input signal with the input frequency, a second input port receiving a feedback signal from the loop of feedback with the feedback frequency, a trigger sub-circuit, and a combined logic sub-circuit. The trigger sub-circuit includes four D-type flip-flops coupled to the first input port via a ½-frequency-divider and to the second input port partially via an inverter and configured to determine the input frequency to be greater or smaller than the feedback frequency. The combined logic sub-circuit includes two XOR gates, two inverters, and two AND gates coupled to the trigger sub-circuit. The combined logic sub-circuit is configured to output a first control signal to a first control port in a first timeframe if the input frequency is determined to be greater than the feedback frequency and output a second control signal to a second control port in a second timeframe if the input frequency is determined to be smaller than the feedback frequency. 
     Optionally, the controller is configured to reduce the frequency control word F by one in each loop of feedback in the first timeframe in response to the first control signal and to increase the frequency control word F by one in each loop of feedback in the second timeframe in response to the second control signal, or to keep the frequency control word F unchanged in response to no reception of the first control signal and the second control signal. 
     Optionally, the second digitally-controlled oscillator includes a direct period synthesizer including a first K 1 -to-1 multiplexer coupled to an accumulation-register controlled by a fractional part of the frequency control word F via an accumulator to input K second pulses through a lower path for generating a low level of the second periodic signal. The second digitally-controlled oscillator also includes a second K 1 -to-1 multiplexer coupled to an adder-register controlled by a half of an integer part of the frequency control word F via an adder to input the K 1  second pulses through an upper path for generating a high level of the second periodic signal. The second digitally-controlled oscillator further includes a 2-to-1 multiplexer plus a D-type flip-flop to control transition between the upper path and the lower path to output the second periodic signal with the second output frequency proportional to the second frequency with a factor of K 1  over a sum of the frequency control word F and the constant C. 
     Optionally, the second output frequency is set to a time-average frequency with the frequency control word F being switched between an integer I and I+1 in the loop of feedback. 
     Optionally, the loop of feedback is in a dynamic equilibrium to make the feedback frequency locked to the input frequency and make the first output frequency to be substantially linearly dependent on the input frequency with a multiplier factor of M·N multiplying the sum of the frequency control word F and the constant C. 
     Optionally, the first periodic signal with the first output frequency is outputted as a high-frequency clock signal with enhanced accuracy by selecting the constant as an integer substantially larger than the integer I. 
     Optionally, the second frequency divider is configured to be a low-frequency programmable counter with N being set to be smaller than M. 
     In another aspect, the present disclosure provides a digital clock generator for generating a high-ratio frequency multiplication clock signal. The digital clock generator includes a frequency detector configured to compare an input signal of an input frequency received from an input port with a feedback signal of a feedback frequency from a loop of feedback to generate control signals. The digital clock generator further includes a controller coupled to the frequency detector to adjust a frequency control word F in the loop of feedback based on the control signals. Additionally, the digital clock generator includes a first digitally-controlled oscillator coupled to the controller and a first oscillation generator to receive multiple first pulses of a first frequency with equally spaced phase shift, and configured to generate a first synthesized signal to an output port with a first output frequency controlled by the frequency control word F. The digital clock generator further includes a first frequency divider coupled to the output port to generate a trigger signal with 1/M of the first output frequency. Furthermore, the digital clock generator includes a second oscillation generator induced by the trigger signal to generate multiple second pulses of a second frequency with equally spaced phase shift. The digital clock generator further includes a second digitally-controlled oscillator coupled to the controller and the second oscillation generator, and configured to generate a second synthesized signal to the loop of feedback with a second output frequency controlled by the frequency control word F plus a constant C. Moreover, the digital clock generator includes a second frequency divider in the loop of feedback to generate the feedback signal with the feedback frequency being 1/N of the second output frequency. The loop of feedback makes the feedback frequency locked to the input frequency so as to make the first output frequency substantially linearly dependent on the input frequency multiplied by M·N·(F+C). 
     In yet another aspect, the present disclosure provides a chip for generating high-ratio frequency multiplication clock signal including a digital clock circuit described herein. The chip is implemented in a digital integrated circuit in either FPGA or ASIC format. 
     In still another aspect, the present disclosure provides a method for generating high-ratio frequency multiplication clock signal from a low-frequency input signal. The method includes a step of comparing a low-frequency input signal with a feedback signal in a loop of feedback to generate control signals. The method further includes a step of generating a frequency control word F based on the control signals. Additionally, the method includes a step of using at least a least significant bit of the frequency control word F to drive a first digitally-controlled oscillator to generate a first synthesized signal of a first output frequency based on multiple first periodic pulses with equally spaced phase shift. The method further includes a step of dividing the first output frequency by M to obtain a trigger signal with 1/M of the first output frequency. Furthermore, the method includes a step of using the frequency control word F plus a constant C to drive a second digitally-controlled oscillator to generate a second synthesized signal of a second output frequency based on multiple second periodic pulses with equally spaced phase shift induced by the trigger signal. The method further includes dividing the second output frequency by N to obtain a feedback frequency with 1/N of the second output frequency to the loop of feedback. Moreover, the method includes outputting the first synthesized signal as a clock signal with the first output frequency being substantially linearly dependent on an input frequency of the low-frequency input signal multiplied by M·N·(F+C). 
     Optionally, the method also includes a step of using a digital free-running oscillator to generate the multiple first periodic pulses of a first frequency from random noise without any external clock signal. 
     Optionally, the method still includes a step of using a Johnson counter to generate the multiple second periodic pulses of a second frequency equal to 1/M of the first output frequency induced by the trigger signal. 
     Optionally, the constant C is selected to be substantially larger than the frequency control word F as the loop of feedback reaches a dynamic equilibrium with the frequency control word F being switched between I and I+1. 
    
    
     
       BRIEF DESCRIPTION OF THE FIGURES 
       The following drawings are merely examples for illustrative purposes according to various disclosed embodiments and are not intended to limit the scope of the present invention. 
         FIG. 1  is a block diagram of a digital clock circuit for generating high-ratio frequency multiplication clock signal according to some embodiments of the present disclosure. 
         FIG. 2  is a circuit diagram of a free-running multi-stage cascaded NAND-Gate oscillator according to an embodiment of the present disclosure. 
         FIG. 3  is a schematic diagram illustrating K input pulses with equally spaced phase of a base time unit Δ to be loaded to a digitally-controlled oscillator according to an embodiment of the present disclosure. 
         FIG. 4  is a functional diagram of a logic circuit for time-average frequency direct period synthesis according to an embodiment of the present disclosure. 
         FIG. 5  is a circuit diagram of a high-frequency frequency divider with a divide factor M according to an embodiment of the present disclosure. 
         FIG. 6  is a circuit diagram of a K 1 /2-stage Johnson counter according to an embodiment of the present disclosure. 
         FIG. 7  is a schematic diagram of a logic circuit of the frequency detector according to an embodiment of the present disclosure. 
         FIG. 8  is a plot showing relationships between input/output frequencies and a frequency control word according to an embodiment of the present disclosure. 
     
    
    
     DETAILED DESCRIPTION 
     The disclosure will now be described more specifically with reference to the following embodiments. It is to be noted that the following descriptions of some embodiments are presented herein for purpose of illustration and description only. It is not intended to be exhaustive or to be limited to the precise form disclosed. 
     Conventional clock circuit based on phase locked loop (PLL) design has limitation in setting its frequency multiplier/divider factor no more than about 1000 due to large jitters in the clock signals. Most clock circuits relied on a crystal oscillator or the like to provide an input clock signal, which requires high power consumption and large chip area for generating high-ratio frequency multiplication clock signal, and is hard to be integrated in chips. 
     Accordingly, the present disclose provides, inter alia, a digital clock circuit for generating high-ratio frequency multiplication clock signal, an IC chip having the same, and a method thereof that substantially obviate one or more of the problems due to limitations and disadvantages of the related art. 
     In one aspect, the present disclosure provides a digital clock circuit based on free-running oscillation to generate high-ratio frequency multiplication clock signal.  FIG. 1  shows a block diagram of a digital clock circuit for generating high-ratio frequency multiplication clock signal according to some embodiments of the present disclosure. Referring to  FIG. 1 , the digital clock circuit is mainly formed with two parts. A first sub-circuit  10  contains a first digitally-controlled oscillator  100 . The first digitally-controlled oscillator  100  is configured to generate and output a high-frequency clock signal based on an oscillation signal from a free-running oscillation generator, and the first sub-circuit  10  is configured to supply a M-divided frequency signal to the second sub-circuit  20 . A second sub-circuit  20  includes a time-average-frequency frequency-locked loop (FLL) configured to receive a low-frequency input signal and use the loop of feedback to determine a frequency control word F to control a second digitally-controlled oscillator  200  to obtain a synthesized clock signal based on the M-divided frequency signal and to supply a N-divided frequency signal as a feedback signal in the FLL loop. The frequency control word F also is used to control the first digitally-controlled oscillator in the first sub-circuit  10 . 
     Referring to  FIG. 1 , in particular, the first sub-circuit  10  includes a free-running oscillator  50  to generate a free-running oscillation frequency. The first sub-circuit  10  also includes a first digitally-controlled oscillator  100  having a control port  101  for receiving a control signal, multiple input ports  102  for receiving multiple input pulses, an output port  103  for outputting a first output signal, and being configured to be a high-frequency direct period synthesizer. 
     The free-running oscillator  50 , in an embodiment, uses a logic circuit based on cascaded NAND-gate units to realize generation of the free-running oscillation frequency without using any voltage pulse source or crystal oscillator.  FIG. 2  shows a circuit diagram of a free-running multi-stage cascaded NAND-Gate oscillator according to an embodiment of the present disclosure. Referring to  FIG. 2 , the circuit is constructed, as an example, by cross cascading 8-stage of NAND-Gate units (P0, P1, . . . , through P15). Each stage includes a pair of NAND-Gate units. The whole oscillator circuit is configured to generate oscillations based on all noises and functional as a filter to gradually allow all oscillations to be stabilized at a fixed frequency value in a final equilibrium state. Additionally, each NAND-Gate unit (of all 16 units in  FIG. 2 ) is configured to output one periodic pulse with the same oscillation frequency but with a shifted phase that is equal to 1/16 of the period (of these pulses). 
     Assuming the phase shift is Δ for any two nearest neighboring NAND-Gate units of a K/2-stage cascaded structure in the free-running oscillator  50 , then K number of pulses with a first frequency f 1  is generated, as shown in an exemplary diagram of  FIG. 3 . The first frequency f 1  is mainly depended on manufacture process of the NAND-gate unit in the free-running oscillator  50 . Optionally, the first frequency f 1  is provided as an ultra-high frequency in a range as high as 1 MHz. In particular, each NAND-Gate unit introduces one phase delay of Δ. Referring to  FIG. 1 , in an example, K=K h , Δ=Δ h , the free-running oscillator  50  generates K h  number of first pulses of the first frequency f with equally spaced phase shift of Δ h . These K h  number of first pulses are provided to the input ports  102  of the first digitally-controlled oscillator  100 . 
     Referring to  FIG. 1  again, in an embodiment, the first digitally-controlled oscillator  100  is provided as a time-average-frequency direct period synthesizer configured to use a control signal received from the control port  101 , which is a frequency control word F h , to control a first output frequency of a synthesized periodic signal outputted to the output port  103  based on input of the K h  number of first pulses received via the input ports  102  from the free-running oscillator  50 .  FIG. 4  shows a functional diagram of a logic circuit of the time-average frequency direct period synthesizer. The K h  number of first pulses are generated by the free-running oscillator  50  having evenly-spaced phase shift Δ h  in a first frequency f 1 , an ultra-high frequency. 
     Starting from the K h  number of first pulses with evenly-spaced phase shift Δ h  and a frequency control word F h =I+r where I is an integer and r is a fraction of 0&lt;r&lt;1, the time-average frequency direct period synthesizer associated with the first digitally-controlled oscillator  100  creates two types of cycles TA=FΔ h  and TB=(I+1)·Δ h m in respective two timeframes. It then generates the output pulse train by using TA and TB in an interleaved fashion. The possibility of TA (and thus TB) occurrence is controlled by the value of r. The output frequency f TAF /period T TAF  can be calculated by 1/f TAF =T TAF =F h ·Δ h . Given enough resource (the number of bits used in r), almost any frequency can be generated. Further, the output signal waveform can be instantly changed since each individual first pulse is directly constructed. 
     The K h  first pulses are inputted respectively to two K-to-1 multiplexers. Here ( FIG. 4 ), K=K h . A first K-to-1 multiplexer (MUX_A) at a lower half of the figure is coupled to a 2-pipeline register controlled by the frequency control word F h  via an accumulator to allow the K h  first pulses to pass through a lower path to be a first output MUXOUT_A. Here ( FIG. 4 ), F=F h . 
     At a transition time t6, the accumulator associated with the lower path performs accumulation computation every rising edge of clock to handle that the frequency control word F h  is a real number including a fraction part r beyond an integer part I. The lower path K-to-1 multiplexer dominates the length of logic ‘0’ of output CLX1 at a low voltage level. At a first transition time t1, the SEL_LOW is fed into the first (or lower) K-to-1 multiplexer MUX_A at a rising edge of CLK2. So, it will choose one pulse of the K h  first pulses to be the first output MUXOUT_A. 
     A second K-to-1 multiplexer (MUX_B) is coupled to a 2-pipeline register controlled by the half frequency control word F h /2 via an adder to input the K h  first pulses through an upper path for generating a high level of a second output MUXOUT_B. The adder associated with the upper path only is driven by the integer part I of the frequency control word F h . The K-to-1 multiplexer MUX_B in the upper path dominates the length of logic ‘1’ of output CLK1 at a high voltage level. 
     Referring to  FIG. 3 , additionally, a 2-to-1 multiplexer MUX_C controlled by CLK1 to control the transition of upper path and lower path. Now only one signal, from either upper path or lower path, arrives at a toggle flip-flop circuit which includes a D-type flip-flop and two inverters to toggle the output MUXOUT at every rising edge of clock, from ‘1’ to ‘0’ or from ‘0’ to ‘1’. 
     At a second transition time t2, the chosen signal passes the first K-to-1 multiplexer MUX_A and is fed into the 2-to-1 multiplexer MUX_C. 
     At a third transition time t3, which occurs simultaneously with t2, when CLK2 is at the state of logic ‘1’ after rising edge, the CLK1 is at the state of logic ‘0’. So, the 2-to-1 multiplexer MUX_C chooses the second output MUXOUT_B from the upper path as MUXOUT sent to the toggle flip-flop. 
     At a fourth transition time t4, the rising edge of the second output MUXOUT_B arrives at the toggle flip-flop which finishes the transition from 0 to 1. 
     At a fifth transition time t5, CLK1 now is transited to 1. So the 2-to-1 multiplexer MUX_C chooses the first output MUXOUT_A of the lower path to send to the toggle flip-flop. The whole process repeats itself. 
     Therefore, the frequency control word F h  is employed by the first digitally-controller oscillator  100  select one pulse from the K h  first pulses as a first periodic signal with a first output frequency f h =K h ·f 1 /F h =1/(F h ·Δ h ) at the output port  103 . 
     Referring back to  FIG. 1 , the first sub-circuit  10  also includes a first frequency divider  120  coupled to the output port  103  to receive the first periodic signal with the first output frequency f h . In an embodiment, the first frequency divider is a divider with a divide factor of M, M being an integer. Optionally, the first frequency divider  120  is a high-frequency divider and is configured to use L-stage cascaded Toggle Flip-Flop circuit to divide the frequency stage-by-stage digitally. This type of frequency divider introduces very low noise even it works in high-frequency range as high as 1 MHz.  FIG. 5  shows a schematic diagram of the L-stage Toggle Flip-Flop (TFF) circuit cascaded in series. Each TFF stage has an input port and an output port. A first TFF stage has an input receiving the first output frequency f h  from the output port  103  of the first digitally-controller oscillator  100 . When a signal passes a respective one stage, the frequency at its output port is reduced to a half of that at its input port. The last (L-th) TFF stage has an output port that outputs finally a M-divided signal having 1/M=½ L  of original input frequency. i.e., f h /M. 
     Optionally, the M-divided signal is served as a trigger signal for inducing additional oscillation pulses. In an embodiment, referring further to  FIG. 1 , the first sub-circuit  10  further includes a trigger oscillator  150  driven by the trigger signal to generate multiple second pulses of a second frequency with equally spaced phase shift.  FIG. 6  shows an example of the trigger oscillator configured as a K 1 /2-stage Johnson counter according to an embodiment of the present disclosure. The K 1 /2-stage Johnson counter includes K 1 /2-stage D-type flip-flops cascaded in series, each flip-flop stage has a clock input port receiving the trigger signal and a Q-output port outputting a pulse P i  and respectively a Qn-output port outputting a another pulse P K1/2+i . For the K 1 /2-stage Johnson counter, all Q output ports sequentially output K 1 /2 number of pulses P 1 , P 2 , P 3 , up to P K1/2 , all Qn-output ports sequentially output K 1 /2 number of pulses P K1/2+1 , P K1/2+2 , P K1/2+3 , up to P K1 . Functionally, the trigger oscillator  150  is substantially similar to the free-running oscillator  50  except that the trigger oscillator  150  needs the trigger signal inputted into the clock input port for generating K 1  number of second pulses of a second frequency f 2  with equally-spaced phase shift Δ where K 1 ·f 2 =1/Δ 1 . In an embodiment, K 1 f 2 =f h /M, these K 1  number of second pulses are ready to be loaded into a second digitally-controlled oscillator  200  in the second sub-circuit  20  configured as a frequency locked loop of feedback. 
     Referring to  FIG. 1  again, the second sub-circuit  20  includes a frequency detector (FD)  210  having a first input port receiving an input signal with an input frequency f i  and a second input port receiving a feedback signal with a feedback frequency f b . The frequency detector (FD)  210  serves as a first element in the FLL loop of feedback and is configured to compare the input frequency with the feedback frequency and output control signals based on comparison results about the input frequency f i  with the feedback frequency f b . 
     In an embodiment, the frequency detector  210  is configured to compare the input frequency f i  with the feedback frequency f b  to generate a first control signal fast and a second control signal slow alternately for determining a frequency control word F in the FLL loop of feedback.  FIG. 7  shows a schematic diagram of a logic circuit of the frequency detector according to an embodiment of the present disclosure. Referring to  FIG. 7 , the frequency detector  210  includes a first input port receiving a first signal of f 1 , which can be the input signal of f i  in  FIG. 1 , a second input port receiving a second signal of f 2 , which can be the feedback signal of f b  in  FIG. 1 . Additionally, the frequency detector  210  includes a trigger sub-circuit  2101  coupled to the first input port and the second input port and configured to detect a relationship between the first frequency f 1  and the second frequency f 2 . The frequency detector  210  further includes a combined logic sub-circuit  2102  coupled to the trigger sub-circuit  2101  to generate the first control signal fast to a first control port in a first timeframe and the second control signal slow to a second control port in a second timeframe. The first timeframe and second timeframe alternately appear one after other. 
     In an embodiment, the trigger sub-circuit  2101  includes four D-type flip-flops coupled to the first input port via a frequency-divider and to the second input port partially via an inverter. The trigger sub-circuit  2101  is configured to determine the first frequency f 1  being greater or smaller than the second frequency f 2 . The combined logic sub-circuit  2102  includes two XOR gates, two inverters, and two AND gates configured to output either the first control signal fast to the first control port in the first timeframe based on determination that the first frequency f 1  is greater than the second frequency f 1  or the second control signal slow to the second control port in the second timefiame based on determination that the first frequency f 1  is smaller than the second frequency f 2 . 
     Additionally, the second sub-circuit  20  includes a controller  220  coupled to the frequency detector  210  to receive the first/second control signals. In the embodiment, the first control signal fast drives the controller  220  to reduce a frequency control word F by one and the second control signal slow drives the controller  220  to increase the frequency control word F by one in each loop operation. In case, no control signal is received from the frequency detector  210 , the controller  220  is configured to maintain the frequency control word F without change. Eventually, the whole loop of feedback can reach a dynamic equilibrium as the first control signal fast and the second control signal slow are alternately generated and the frequency control word F is switched between I and I+1. In this equilibrium state, the second frequency f 2  is substantially locked to the first frequency f 1 . When input frequency changes, i.e., the locking target is changed, the frequency detector  210  is operated to determine the frequency control word F which is used to accomplish the frequency locking in the loop of feedback associated with the second sub-circuit  20  of the digital clock circuit and also is used to drive the first digitally-controlled oscillator. 
     Furthermore, referring to  FIG. 1 , the second sub-circuit  20  includes a second digitally-controlled oscillator  200  coupled to the controller  220  to receive a frequency control word F 1  to drive a pulse selection from the K 1  number of second pulses of a second frequency f 2  with equally spaced phase shift Δ 1  received from the trigger oscillator  150  of the first sub-circuit  10 . The second digitally-controlled oscillator  200  is configured also as a time-average frequency direct period synthesizer substantially similar to the first digitally-controlled oscillator  100 . It has been illustrated in  FIG. 4  and descriptions in associated paragraphs above. A difference is that the second digitally-controlled oscillator  200  is working at a relatively lower frequency as the second frequency f 2  is 1/M of the first output frequency f h  of the first digitally-controlled oscillator  100 . Here, M is selected as a large integer. For example, M=256. And, K 1  is different from K h  and Δ 1  is different from Δ h . Another difference is that the frequency control word F 1  of the second digitally-controlled oscillator  200  can be selected to be the frequency control word F (determined by the controller  220 ) plus a constant C, i.e., F 1 =F+C. Here the constant C is selected as a large integer, e.g., C=117. The second digitally-controlled oscillator  200  is configured to generate and output a second periodic signal with a second output frequency f 1 , substantially represented by f 1 =K 1 ·f 2 /F 1 , based on time-average frequency direct period synthesis (in the loop of feedback). 
     Moreover, the second sub-circuit  20  includes a second frequency divider  230  coupled to the second digitally-controlled oscillator  200  to receive the second periodic signal of the second output frequency f 1  and divide it to 1/N, where N is a divider factor. The second frequency divider  230  is configured to be substantially similar to the first frequency divider  120 . Optionally, it can be implemented with multi-stage digital counter or multiple delay-lines to generate the divider factor N. In order to make the time-average-frequency frequency-lock loop of the second sub-circuit  20  to lock the frequency faster, the divider factor N is selected to be an integer smaller than the integer M (the divider factor of the first frequency divider). For example, M=256, N=64. The output of the second frequency divider  230  is directly fed as the feedback frequency f b =f 1 /N back to the frequency detector  210  (see  FIG. 1 ). 
     When the loop of feedback through the time-average frequency direct period synthesizer associated with the second digitally-controlled oscillator  200  controlled by the control word F 1 =F+C reaches a dynamic equilibrium, the feedback frequency f b  is substantially locked with the input frequency f i . Because f b =f 1 /N, f 1 =f h /(M·F 1 ), therefore, a relationship of the first output frequency f h  and the input frequency f i  is obtained:
 
 f   h   =M·N·F   1   ·f   i   =R·f   i  
 
     R is a multiplication ratio of the output frequency over the input frequency and is comprised of a product of three multipliers, divider factor M, divider factor N. and F 1 . In particular, M&gt;N, and the frequency control word F 1  of the second digitally-controlled oscillator  200  is given by the control word F generated by the controller  220  plus a large constant C. For example, M=256, N=64, F 1 =128, the multiplication ratio R equals 2097152. In other words, the digital clock circuit of the present disclosure can turn an input pulse of a low frequency at 50 Hz to a clock signal of an ultra-high frequency at 104.8576 MHz. 
     In another embodiment of the present disclosure, referring to  FIG. 1 , the controller  220  is configured to supply the frequency control word F to both the first digitally-controlled oscillator  100  in the first sub-circuit  10  and the second digitally-controlled oscillator  200  in the second sub-circuit  20 . In other words, both the frequency control word F h  supplied to the first digitally-controlled oscillator  100  and the frequency control word F 1  supplied to the second digitally-controlled oscillator  200  can be drawn from the frequency control word F generated by the controller  220 . Optionally. F h =F, and F 1 =F+C, here C is an integer substantially larger than F. Optionally, F h  is selected to be the least significant bit of F 1 . For example, F 1  is an 8-bit control word, 1xxx-1101. F h  is a 4-bit control word, 1101. F 1  can be expressed as F h +127. 
     In the embodiment, the time-average-frequency locked loop (FLL) of feedback using the frequency control word F plus a substantially larger contact C to drive the second digitally-controlled oscillator  200  in the second sub-circuit is designed to enhance clock signal accuracy. In the FLL loop of feedback, the second output frequency f 1  is determined by a time-average frequency between two cycle frequencies f 11  and f 12  respectively associated with the frequency control word F at the dynamic equilibrium, i.e., f 1 =(1−r)·f 11 +r·f 12 , where r is a weight of f 11  and f 12 . For a nominal value F, f 11  and f 12  are very dissimilar. For example, f 11 =3000 and f 12 =3600. In the embodiment with F+C used for driving the second digitally-controlled oscillator  200  in the loop of feedback, e.g., F=11, C=96, then, f 11  and f 12  become less dissimilar to each other. For example, f 11 =3200 and f 12 =3400. Then the time-average frequency f has a reduced error in this case. The accuracy of the (first) output frequency f h  is relied on the accuracy of the (second) output frequency f 1  in the loop of feedback. Therefore, the outputted clock signal with the frequency f h  can achieve an enhanced accuracy. 
       FIG. 8  shows a plot showing relationships between input/output frequencies and a frequency control word according to an embodiment of the present disclosure. Referring to  FIG. 8 , it shows that a relationship between the input frequency and the output frequency versus the frequency control word F (with fixed divider factor M and N) is a monotonous relationship. When the frequency control word F has a large value, the relationship is substantially linear. Therefore, the output signal with the high-ratio multiplication frequency over the input frequency can be used as a high-frequency clock signal. In a specific experiment, an input signal of a frequency at 50 Hz is loaded into a clock circuit implemented in a FPGA chip on a circuit board and measured by Keysight 53230A Frequency Meter, the output frequency obtained is 124.148 MHz with a multiplication ratio R as large as 2482968. In general, depending on selection of the divider factor M, N, and the frequency control word F plus the constant C for designing the digital clock circuit, the multiplication ratio R of the digital clock circuit of the present disclosure is at least greater than 2000, or greater than 10000, or greater than 50000, or greater than 100000, or greater than 500000, or greater than 1000000, or greater than 2000000. 
     In a specific embodiment, the present disclosure provides a digital clock generator for generating a high-ratio frequency multiplication clock signal. The digital clock generator includes a frequency detector configured to compare an input signal of an input frequency received from an input port with a feedback signal of a feedback frequency from a loop of feedback to generate control signals. The digital clock generator further includes a controller coupled to the frequency detector to adjust a frequency control word F in the loop of feedback based on the control signals. Additionally, the digital clock generator includes a first digitally-controlled oscillator coupled to the controller and a first oscillation generator to receive multiple first pulses of a first frequency with equally spaced phase shift, and configured to generate a first synthesized signal to an output port with a first output frequency controlled by the frequency control word F. The digital clock generator further includes a first frequency divider coupled to the output port to generate a trigger signal with 1/M of the first output frequency. Furthermore, the digital clock generator includes a second oscillation generator induced by the trigger signal to generate multiple second pulses of a second frequency with equally spaced phase shift. The digital clock generator further includes a second digitally-controlled oscillator coupled to the controller and the second oscillation generator, and configured to generate a second synthesized signal to the loop of feedback with a second output frequency controlled by the frequency control word F plus a constant C. Moreover, the digital clock generator includes a second frequency divider in the loop of feedback to generate the feedback signal with the feedback frequency being 1/N of the second output frequency. The loop of feedback makes the feedback frequency locked to the input frequency so as to make the first output frequency substantially linearly dependent on the input frequency multiplied by M·N·(F+C). The first synthesized signal is outputted as a clock signal with a high-ratio multiplication clock frequency over the input frequency. 
     In another aspect, the present disclosure provides a chip for generating high-ratio frequency multiplication clock signal comprising a digital clock circuit described herein. The digital clock circuit is based on pure digital circuitry design with high efficiency and free-running oscillation generation architecture to achieve high-ratio multiplication clock frequency. The chip can be implemented in a FPGA or ASIC digital integrated circuit for various electronic applications. 
     In yet another aspect, the present disclosure provides a method for generating high-ratio frequency multiplication clock signal from a low-frequency input signal. The method includes a step of comparing a low-frequency input signal with a feedback signal in a loop of feedback to generate control signals. The method further includes a step of generating a frequency control word based on the control signals. Additionally, the method includes a step of using at least a least significant bit of the frequency control word F to drive a first digitally-controlled oscillator to generate a first synthesized signal of a first output frequency based on multiple first periodic pulses with equally spaced phase shift. The method further includes a step of dividing the first output frequency by M to obtain a trigger signal with 1/M of the first output frequency. Furthermore, the method includes a step of using the frequency control word F plus a constant C to drive a second digitally-controlled oscillator to generate a second synthesized signal of a second output frequency based on multiple second periodic pulses with equally spaced phase shift induced by the trigger signal. The method further includes a step of dividing the second output frequency by N to obtain a feedback frequency with 1/N of the second output frequency in the loop of feedback. Moreover, the method includes a step of outputting the first synthesized signal as a clock signal with the first output frequency being substantially linearly dependent on an input frequency of the low-frequency input signal multiplied by M·N·(F+C). 
     Further in the embodiment, the method also includes a step of using a digital free-running oscillator to generate the multiple first periodic pulses of a first frequency from random noise without any external clock signal. 
     Additionally in the embodiment, the method includes a step of using a Johnson counter to generate the multiple second periodic pulses of a second frequency equal to IIM of the first output frequency induced by the trigger signal. 
     Moreover, in the embodiment of executing the method, the constant C is selected to be substantially larger than the frequency control word F as the loop of feedback reaches a dynamic equilibrium with the frequency control word F being switched between I and I+1. 
     The foregoing description of the embodiments of the invention has been presented for purposes of illustration and description. It is not intended to be exhaustive or to limit the invention to the precise form or to exemplary embodiments disclosed. Accordingly, the foregoing description should be regarded as illustrative rather than restrictive. Obviously, many modifications and variations will be apparent to practitioners skilled in this art. The embodiments are chosen and described in order to explain the principles of the invention and its best mode practical application, thereby to enable persons skilled in the art to understand the invention for various embodiments and with various modifications as are suited to the particular use or implementation contemplated. It is intended that the scope of the invention be defined by the claims appended hereto and their equivalents in which all terms are meant in their broadest reasonable sense unless otherwise indicated. Therefore, the term “the invention”, “the present invention” or the like does not necessarily limit the claim scope to a specific embodiment, and the reference to exemplary embodiments of the invention does not imply a limitation on the invention, and no such limitation is to be inferred. The invention is limited only by the spirit and scope of the appended claims. Moreover, these claims may refer to use “first”, “second”, etc. following with noun or element. Such terms should be understood as a nomenclature and should not be construed as giving the limitation on the number of the elements modified by such nomenclature unless specific number has been given. Any advantages and benefits described may not apply to all embodiments of the invention. It should be appreciated that variations may be made in the embodiments described by persons skilled in the art without departing from the scope of the present invention as defined by the following claims. Moreover, no element and component in the present disclosure is intended to be dedicated to the public regardless of whether the element or component is explicitly recited in the following claims.