WO2004109916A1 - デジタルシステム、デジタルシステムのクロック信号調整方法および、その調整方法で実行する処理プログラムを記録した記録媒体 - Google Patents
デジタルシステム、デジタルシステムのクロック信号調整方法および、その調整方法で実行する処理プログラムを記録した記録媒体 Download PDFInfo
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- WO2004109916A1 WO2004109916A1 PCT/JP2004/007683 JP2004007683W WO2004109916A1 WO 2004109916 A1 WO2004109916 A1 WO 2004109916A1 JP 2004007683 W JP2004007683 W JP 2004007683W WO 2004109916 A1 WO2004109916 A1 WO 2004109916A1
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- digital system
- digital
- value
- power supply
- clock signal
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Classifications
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- G—PHYSICS
- G06—COMPUTING OR CALCULATING; COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F1/00—Details not covered by groups G06F3/00 - G06F13/00 and G06F21/00
- G06F1/04—Generating or distributing clock signals or signals derived directly therefrom
- G06F1/10—Distribution of clock signals, e.g. skew
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
- G01R31/00—Arrangements for testing electric properties; Arrangements for locating electric faults; Arrangements for electrical testing characterised by what is being tested not provided for elsewhere
- G01R31/28—Testing of electronic circuits, e.g. by signal tracer
- G01R31/317—Testing of digital circuits
- G01R31/31725—Timing aspects, e.g. clock distribution, skew, propagation delay
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
- G01R31/00—Arrangements for testing electric properties; Arrangements for locating electric faults; Arrangements for electrical testing characterised by what is being tested not provided for elsewhere
- G01R31/28—Testing of electronic circuits, e.g. by signal tracer
- G01R31/317—Testing of digital circuits
- G01R31/31725—Timing aspects, e.g. clock distribution, skew, propagation delay
- G01R31/31726—Synchronization, e.g. of test, clock or strobe signals; Signals in different clock domains; Generation of Vernier signals; Comparison and adjustment of the signals
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- H—ELECTRICITY
- H03—ELECTRONIC CIRCUITRY
- H03K—PULSE TECHNIQUE
- H03K5/00—Manipulating of pulses not covered by one of the other main groups of this subclass
- H03K2005/00013—Delay, i.e. output pulse is delayed after input pulse and pulse length of output pulse is dependent on pulse length of input pulse
- H03K2005/00019—Variable delay
- H03K2005/00058—Variable delay controlled by a digital setting
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- H—ELECTRICITY
- H03—ELECTRONIC CIRCUITRY
- H03K—PULSE TECHNIQUE
- H03K5/00—Manipulating of pulses not covered by one of the other main groups of this subclass
- H03K2005/00013—Delay, i.e. output pulse is delayed after input pulse and pulse length of output pulse is dependent on pulse length of input pulse
- H03K2005/0015—Layout of the delay element
- H03K2005/00156—Layout of the delay element using opamps, comparators, voltage multipliers or other analog building blocks
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- H—ELECTRICITY
- H03—ELECTRONIC CIRCUITRY
- H03K—PULSE TECHNIQUE
- H03K5/00—Manipulating of pulses not covered by one of the other main groups of this subclass
- H03K2005/00013—Delay, i.e. output pulse is delayed after input pulse and pulse length of output pulse is dependent on pulse length of input pulse
- H03K2005/0015—Layout of the delay element
- H03K2005/00234—Layout of the delay element using circuits having two logic levels
- H03K2005/0026—Layout of the delay element using circuits having two logic levels using memories or FIFO's
Definitions
- the present invention relates to a single or a plurality of digital systems operating in synchronization with a single or a plurality of clock signals, a clock signal timing adjustment method of a powerful digital system, and a processing program executed by the adjustment method It relates to a recording medium on which is recorded.
- the present invention is particularly effective when the number of digital circuit elements which are components of the digital system is large and the power supply voltage is lower than normal or the power supply voltage can be higher than normal.
- a digital system usually includes three types of logic elements, an AND element, an OR element, and a NOT element, and a storage element called a flip-flop that stores two states (1 bit) of true and false. You.
- the most basic flip-flop also has a three-terminal function of one input / output terminal and one clock terminal, and the digital signal of the input terminal is output to the output terminal at the rise of the digital signal called the clock signal applied to the clock terminal. It has the function of copying and holding its digital value until the next rising edge of the clock signal.
- a digital system that operates according to a finite number of clock signals is called a synchronization circuit, and in the synchronization circuit, the time difference between clock signals arriving at the clock terminals of each flip-flop affects the overall operation.
- the time difference between the clock signals is called clock skew.
- clock skew For example, for the same Ins time shift, if the clock frequency is 10 MHz, that is, if the clock cycle is 100 ns, the shift is 1%, whereas if the clock frequency is 100 MHz, that is, the clock cycle is 10 ns. In the case of, the deviation is 10%, and correction is required. In other words, a higher clock frequency requires a more precise timing adjustment technique.
- Conventional measures against clock skew in digital systems include: (1) A countermeasure method in which a designer manually adjusts the clock skew as much as possible when designing a digital system.
- the measure (1) does not solve the following problem. That is, electronic circuit elements such as transistors, resistors, and capacitors have variations in their characteristics, and the fluctuations of each element are not clear until an actual system is created. This is a characteristic that is particularly noticeable in devices in integrated circuits.
- the problem of the measure (2) is that it can be adjusted only in the direction in which the clock skew decreases.
- the countermeasure (2) is applied to a system designed to have such an exceptional timing. Can not ,.
- a digital system is a hardware design data library called IP, which is a target of intellectual property (Intellectual Property) and intended for use by a third party, or a normal hardware design data library.
- IP hardware design data library
- the functions and interface specifications are made public, but the internal structure may not disclose more information than the equivalent circuit.
- each digital signal is converted from ("0" to " When it changes to “1” or from “1” to “0”, a large power supply current flows.
- the timing of each signal that is, the timing of each flip-flop, is finely controlled within a range where the whole operates without error. This can be achieved by making adjustments, but for such precise timing adjustment, a new method such as the present invention described later is indispensable.
- EMI unnecessary electromagnetic radiation
- a digital system that operates at a low power supply voltage, such as a low power consumption system including a mobile phone
- the operation speed of each logic element included in the system is low, so that a failure due to a timing failure is likely to occur. . Therefore, in such a system, if the timing is adjusted so that it operates normally with a lower power supply voltage than normal, it will operate stably even at a low power supply voltage, and the power consumption of the digital system will be reduced. be able to.
- some digital systems do not operate at a normal power supply voltage due to large variations between elements, but may operate normally if the power supply voltage is raised above normal and the timing is adjusted. . Therefore, such a system can be used if the timing is adjusted so that it operates normally with a higher power supply voltage than usual, and the production yield of the digital system can be increased.
- a digital system performs digital processing according to a single or a plurality of clock signals to perform a predetermined basic function. , Each of which is inserted into a plurality of clock circuits for supplying the clock signal in the digital system, and is delayed according to a value indicated by the control signal.
- a plurality of delay elements each constituted by a circuit element for changing time; and a plurality of holding circuits for holding a plurality of control signals to be applied to the plurality of delay elements, wherein the plurality of holding circuits output an output voltage.
- the values of the plurality of control signals held by the holding circuits are changed by an external device by a probabilistic search method.
- the feature is that the function is changed so as to satisfy a predetermined specification.
- the clock signal adjusting method for a digital system according to the present invention performs digital processing according to one or more clock signals to perform a predetermined basic function of the clock signal of the digital system.
- a plurality of delay elements are respectively inserted in a plurality of clock circuits in the digital system that supply the clock signal, and the control signals are respectively transmitted to the plurality of delay elements.
- a plurality of control signals provided to the plurality of delay elements are held by a plurality of holding circuits provided in the digital system, and a variable output voltage power supply is configured. While the power is supplied to the digital system, the basic functions of the digital system are adjusted so as to satisfy predetermined specifications.
- the external device the value of said plurality of control signals in which a plurality of holding circuits holds, is characterized in that to change according to a probabilistic search technique.
- the control signal is inserted into a plurality of clock circuits in the digital system that supply a single or a plurality of clock signals, respectively.
- a plurality of control signals held by a plurality of holding circuits are given to a delay element configured by a circuit element that changes a delay time according to a value, and each delay element is provided according to a value indicated by the control signal.
- the clock signal is supplied to the basic circuit with an appropriate delay.
- delay in the present invention includes not only a positive delay, that is, a delay, but also a negative delay, that is, an advance. Therefore, according to the digital system of the present invention and the clock signal adjusting method of the digital system of the present invention, when the characteristics of the circuit element related to the above-mentioned predetermined basic function cannot be accurately grasped, or In addition, if errors occur in the characteristics of the circuit elements, or if there is uneven quality or design errors in the clock signal lines, or if the basic circuits in the digital system Even if it is boxed and its configuration is not clear, it can absorb the timing error of the clock signal and adjust the digital system to operate without error, so that it requires less design effort than the conventional technology. , Its basic functions are higher than those of the prior art. It is possible to obtain a digital system that is larger and faster than that required, and can also reduce the degradation of the function and performance of the digital system caused by
- the timing of the flip-flops of the entire digital system is precisely adjusted in a range where the entire digital system operates without error. Operation timing between flip-flops can be slightly shifted, thereby preventing the digital system from expanding due to increased power consumption and unnecessary electromagnetic radiation (EMI) due to simultaneous changes in digital signals. I can do it.
- EMI unnecessary electromagnetic radiation
- the plurality of holding circuits hold the digital system in a state where the power is supplied from the power supply device of variable output voltage. Since the values of the plurality of control signals are changed, as described in claims 5 and 18, the timing is adjusted so that the power supply voltage is lower than normal and operation is normal, so that the low power It can operate stably even with voltage, lowering the power consumption of the digital system, and since the variation of each element is large V, it does not operate at normal power supply voltage! By adjusting the timing so that the system operates normally with the power supply voltage higher than normal, the system can be used at a high power supply voltage and the digital system can be used. It is possible to increase the yield systems out of production.
- the degree of error-free operation of the digital system is determined by all adjustable It can be expressed by an evaluation function F using the delay value of the delay element as a parameter. That the digital system operates without error is equivalent to finding the solution of the above evaluation function F.
- the present inventor has paid attention to this point, and has found that a genetic algorithm can be applied to clock timing adjustment of a digital system.
- the genetic algorithm is one of the probabilistic search methods, (1) works effectively in a wide area search, and (2) does not require derivative information such as differential values other than the evaluation function F (3)
- the algorithm is easy to implement. Therefore, in the present invention, a genetic algorithm may be used for changing the plurality of control signals by the external device as described in claims 2 and 15.
- a genetic algorithm is also known in which a genetic algorithm is modified so that it can handle a tree-structured chromosome. Therefore, in the present invention, when the clock signal line has a tree structure, a genetic control is applied to the change of the plurality of control signals by the external device as described in claims 3 and 16. Programming may be used.
- the change of the control signal by the external device is performed by changing the output voltage of the power supply device in a stepwise manner, that is, by processing or increasing. In this way, the digital system can be operated with a lower power supply voltage or a minimum increased power supply voltage.
- the digital system according to the present invention described in claim 6 is characterized in that the digital system itself includes a setting device instead of using an external device.
- the digital system itself can be set instead of using an external device in accordance with the clock signal adjusting method for a digital system described in claim 14. It is characterized by having a device.
- the same operation and effect as those of the above digital system and the clock signal adjusting method of the digital system can be obtained, and moreover, external devices can be used.
- the setting means of the digital system itself is used, a further operation and effect can be obtained in that the adjustment can be performed at any time and in any place by the digital system alone except for the power supply device.
- a change of a plurality of control signals by the external device is performed by using a genetic algorithm. Is also good.
- the control signal is changed by the setting means and the output voltage of the power supply device is set to the digital system. It may be performed in a state lower than the designed power supply voltage value, or as described in claims 9 and 22, the control signal is changed by the setting means by changing the output voltage of the power supply stepwise. You may make it perform while doing it.
- the digital system in the digital system of the present invention and the clock signal adjusting method of the digital system of the present invention described above is a power supply device with a variable output voltage as described in claim 11 and claim 24. In this way, the digital system alone can make adjustments at any time and at any location except for external devices.
- the digital system of the digital system of the present invention and the clock signal adjusting method of the digital system of the present invention are configured as an integrated circuit as described in claims 12 and 25. In this way, it is possible to optimally adjust the clock signal for an integrated circuit in which variations in circuit elements are not apparent until actually created.
- the digital system of the digital system of the present invention and the clock signal adjusting method of the digital system of the present invention are configured as a circuit board as described in claims 13 and 26.
- the clock timing shift caused by unevenness in the process of the clock signal line in the digital circuit board manufacturing process or design error is absorbed, and the digital circuit board does not malfunction. Can be adjusted as follows.
- the digital system according to the present invention and the digital system according to the present invention are described above.
- the external device and the setting means in the clock signal adjusting method may be constituted by a computer such as a personal computer or a microcomputer as described in claim 27 and claim 28.
- the process of changing the values of the plurality of control signals held by the plurality of holding circuits in accordance with the stochastic search method so that the basic function of the digital system satisfies the predetermined specification can be easily and reliably performed in a short time.
- a plurality of holding circuits which are executed by a computer and held by a plurality of holding circuits, It is characterized by recording a processing program that changes the value of the control signal according to a stochastic search method so that the basic function of the digital system satisfies a predetermined specification.
- a processing program executed by a computer for the digital system of the present invention and the clock signal adjusting method of the digital system of the present invention can be recorded and stored at any location. Can adjust the clock signal.
- a recording medium in addition to a flexible disk, a data recording medium such as a hard disk, a CD-ROM, and an optical disk, and a storage element such as a ROM and a RAM can be used.
- FIG. 1 is a configuration diagram schematically showing a first embodiment of a digital system of the present invention applied to a general digital system.
- FIG. 2 is an explanatory diagram showing a relationship between a power supply voltage of a digital system and an operation delay.
- FIG. 3 is an explanatory diagram showing an effect of adjusting a delay set value of a delay element in a digital system.
- FIG. 4 is a configuration diagram showing a configuration example of an adjustment device in the embodiment.
- FIG. 5 is a configuration diagram showing a configuration example of a digital signal observation device in the embodiment.
- FIG. 6 is a configuration diagram showing a configuration example of a digital test signal generator in the embodiment.
- FIG. 7 is a configuration diagram showing a configuration example of a power supply device in the embodiment.
- FIG. 8 is a circuit diagram showing a configuration example of an adjustable delay element that can be used in the embodiment.
- FIG. 4 is an explanatory diagram showing waveforms of FIG.
- FIG. 10 is a circuit diagram showing another configuration example of the delay element that can be used in the embodiment.
- FIG. 11 is a circuit diagram showing still another configuration example of the delay element that can be used in the embodiment.
- FIG. 12 is a circuit diagram showing still another configuration example of the delay element that can be used in the embodiment.
- FIG. 13 is a circuit diagram showing still another configuration example of the delay element that can be used in the embodiment.
- FIG. 14 is a circuit diagram showing still another configuration example of the delay element that can be used in the embodiment.
- FIG. 15 is a configuration diagram showing a configuration example of an adjustable delay circuit that can be used in the above embodiment and generates positive and negative delays.
- FIG. 16 is a configuration diagram showing one configuration example of an adjustable delay element in the circuit shown in FIG. [17]
- FIG. 17 is a circuit diagram showing an example of a configuration including an adjustable delay element and a least significant bit of a register in the embodiment.
- FIG. 18 is a circuit diagram showing another example of the configuration including the adjustable delay element and the least significant bit of the register in the above embodiment.
- FIG. 19 is a flowchart showing an outline of a processing procedure of a first embodiment of a clock signal adjusting method for a digital system according to the present invention.
- FIG. 20 is a flowchart showing an outline of a procedure of a general genetic algorithm. [21] It is explanatory drawing which illustrates the chromosome used by a genetic algorithm.
- FIG. 22 is a flowchart showing a processing procedure of an adjustment device using a genetic algorithm in the method of the above embodiment.
- FIG. 23 is an explanatory diagram showing chromosomes used in the genetic algorithm in the method of the above embodiment, and register values and delay values that define the chromosomes.
- FIG. 24 is a flowchart showing a procedure of a selection process performed by a genetic algorithm in the method of the embodiment.
- FIG. 25 is an explanatory diagram showing a procedure of crossover processing performed by a genetic algorithm in the method of the embodiment.
- FIG. 26 is an explanatory diagram showing a procedure of a mutation process performed by a genetic algorithm in the method of the embodiment.
- FIG. 28 is a configuration diagram schematically showing a modification of the above embodiment.
- FIG. 29 is a configuration diagram schematically showing a memory test pattern generator circuit as a second embodiment of the digital system of the present invention.
- FIG. 30 is an explanatory diagram showing the relationship between the fitness and the number of generations during the experiment in the above example. [31] FIG. 31 is a configuration diagram schematically showing a modification of the above embodiment.
- FIG. 32 is a configuration diagram schematically showing a digital circuit board as a digital system according to a third embodiment of the present invention.
- FIG. 33 is a configuration diagram schematically showing a fourth embodiment of the digital system of the present invention.
- FIG. 34 is an explanatory diagram showing chromosomes used in genetic programming in the method of the above embodiment, and register values and delay values determined therefrom.
- FIG. 35 is an explanatory diagram showing a procedure of crossover processing performed by genetic programming in the method of the above embodiment.
- FIG. 36 is an explanatory diagram showing a procedure of a mutation process performed by genetic programming in the method of the above embodiment.
- the present invention is applicable to various digital systems that operate using a single or a plurality of clock signals. That is, by providing a plurality of timing adjustment portions in the clock circuit of the digital system to be adjusted, the clock signal can be adjusted according to the present invention.
- the present invention uses a power supply device whose output voltage is variable only during adjustment. In the following first embodiment, a case where the present invention is applied to a digital system generally operating using a single or a plurality of clock signals will be described.
- FIG. 1 is a configuration diagram schematically showing a first embodiment of the digital system of the present invention applied to a general digital system.
- the clock skew problem (failure due to poor clock signal timing) in a digital system prolongs the design process of the digital system, restricts the performance of elements constituting the digital system, and makes it impossible to use the digital system. It limits the performance of the system itself and is an obstacle to cost control.
- the operation speed of each logical element constituting the system is low, so that a failure due to a timing failure is likely to occur.
- the clock signal adjusting method of the present invention in which the timing adjustment of the clock signal is performed for each individual digital system under a low power supply voltage is indispensable, and particularly important for a low power consumption system.
- reference numeral 1 denotes a digital system that constitutes, for example, a microcomputer or the like, and performs predetermined basic functions such as data processing based on a given program
- 2 denotes a clock signal that requires timing adjustment
- Flip-flop 3 indicates a flip-flop that does not require timing adjustment.
- Reference numeral 4 denotes an adjustable delay element that can change the clock timing according to the value of the register.
- Reference numeral 5 denotes a register that holds the delay set value of the delay element 4. The delay element 4 is inserted between the clock terminal of the flip-flop 2 and a clock line for supplying the clock signal to the clock terminal.
- the register 5 is connected to the delay element 4 and changes the delay value of the delay element 4.
- the flip-flop 2 to be adjusted and the flip-flop 3 that does not need to be adjusted! (No adjustment is necessary) are components of the digital system 1.
- reference numeral 7 denotes an observation device for observing a digital output signal of the digital system 1 and an internal state of the digital system 1
- 8 denotes a test for adjusting the digital system 1 according to the method of the present invention.
- Reference numeral 6 is connected to the digital test signal generator 8 to cause the digital test signal generator 8 to start generating a signal for the digital system 1 and, at the same time, to be connected to the digital signal observation device 7 and An adjustment device for causing the observation device 7 to observe the output signal 11 of the digital system 1 and the digital system internal state signal 12 indicating the internal state of the digital system 1 as described later, and 14 is a power supply device.
- the adjustment device 6 calculates the delay time of the adjustable delay element 4 according to the adjustment method of the present invention, and writes the delay set value to the register 5.
- the adjusting device 6, the digital signal observing device 7, the digital test signal generating device 8, and the power supply device 14 are external devices.
- the power supply 14 supplies power to the digital system 1 through the power supply 99, and the output voltage of the power supply 14 can be controlled by the power supply control signal 98, and the adjusting device 6 Control.
- the digital system 1 in this embodiment may be configured as an integrated circuit or may be configured as a circuit board.
- the digital system 1 in this embodiment may be configured as a single system, or may be configured with a plurality of systems.
- the digital system 1 in this embodiment may include a plurality of system cards and include a communication path therein, and may be configured as a single system and internally include a bus. Including communication channels.
- the digital system 1 in this embodiment is a multi-chip It may be configured as a bridged integrated circuit.
- the power supply 14 may be built in the digital system 1. In that case, the output voltage of the built-in power supply 14 is made variable by the power control signal 98.
- the digital system 1 in this embodiment is an IP (Intellectual Property
- Property may be configured as hardware design data) or a hardware library intended for use by a third party.
- the adjusted flip-flop 2 and the not adjusted !, the flip-flop 3 are general D flip-flops, T flip-flops, SR flip-flops, JK flip-flops, Earl gate circuits, registers, and other clocks. It is a storage element that stores a state in accordance with a signal, or a storage circuit including a loop-shaped combinational circuit, and functions as a component of the digital system 1.
- the flip-flop 2 to be adjusted and the flip-flop 3 not adjusted in the digital system 1 are appropriately connected to a combinational circuit inside the digital system 1 to change the internal state according to the clock signal.
- the flip-flop 2 to be adjusted is a flip-flop adjusted by the method of the present invention
- the flip-flop 3 not adjusted is adjusted by the method of the present invention.
- This is a flip-flop that cannot be used.It is not possible to use other methods, such as timing adjustment based on simulation results at the time of designing the digital system 1, timing adjustment based on the results of trial production, and insertion of fixed-value delay elements into the data path or clock line. Adjustment by a conventional method, such as timing adjustment by, for example, is performed.
- the clock delay time of the flip-flop 2 to be adjusted is a delay time added by the adjustable delay element 4 inserted between the clock terminal of the flip-flop 2 and the clock line.
- the clock signal supplied to the clock terminal of the loop 2 has an adjustable delay element 4 inserted therein, and the timing is delayed by the delay time compared to the case where the clock signal is not provided.
- the digital system 1 to be adjusted includes the flip-flop 2 adjusted as described above and the flip-flop 3 not adjusted.
- the delay time of the adjusted flip-flop 2 That is, the clock terminal of the flip-flop 2 to be adjusted
- the digital system 1 can operate without error under a specific power supply voltage supplied.
- the operating speed of each logic element that composes the digital system becomes Low voltage slows down and often causes timing failures.
- the inverter IV which is one of the logic elements constituting the digital system, has a high power supply voltage (denoted as Vdd in the figure) as shown in Fig. 2 (b).
- Vdd high power supply voltage
- Fig. 2 (b) the higher the power supply voltage is, the earlier the output terminal appears (output 1), and the lower the power supply voltage is, the later the output appears (output 2). Therefore, by performing the above-described clock timing adjustment under the low power supply voltage, it is possible to operate even under the low power supply voltage. Furthermore, if a digital system that did not operate even at a high power supply voltage was caused by a slight timing defect, this clock timing adjustment at a low power supply voltage will reduce the power supply. It can be operated under voltage.
- each logic constituting the digital system can be operated.
- slightly increasing the operation speed of the device to increase the timing margin and adjusting the clock timing with the power supply voltage it is possible to achieve an improvement in the yield with only the minimum necessary increase in the power supply voltage.
- Digital system costs can be reduced.
- the delay set values of the adjustable delay element 4 affect each other. That is, as shown in FIG. 3, the effect of adjusting the delay set value of the adjustable delay element 4A connected to a certain flip-flop 2A is affected only by the input / output terminal of the flip-flop 2A and the combinational circuit 20. It extends to other tuned flip-flops 2 connected in-between.
- the adjustment method described below using the genetic algorithm based on the present invention is very effective.
- the delay set value of the adjustable delay element 4 connected to the clock terminal of the flip-flop 2 to be adjusted is adjusted so that the digital system 1 operates without error.
- FIG. 4 shows an example of the configuration of the adjusting device 6.
- reference numeral 6A denotes an adjustment algorithm execution device that executes an adjustment procedure according to the method of the present invention
- 6B denotes a delay setting device that writes a delay setting value to a register of the digital system 1.
- the delay setting device 6B sets the delay setting value calculated by the adjustment algorithm execution device 6A in the register 5 via the delay setting signal 93.
- the delay setting signal 93 is a digital value having the same bit width as that of the register 5 and controls the delay time generated by the adjustable delay element 4.
- the adjustment algorithm execution device 6A searches for an optimal value as the delay set value of the register 5 according to the genetic algorithm.
- the adjusting device 6 can be specifically constituted by an electronic computer such as a personal computer or a microcomputer. Further, the adjusting device 6 is a programmable LSI disclosed in Japanese Patent Application Laid-Open No. 9-294069, or Kajitani et al.
- GA "Realization of Structure Learning Circuit for Eural Network by GA” (Journal of the Neural Network Society of Japan vol.
- a program for realizing the function of the adjustment algorithm executor 6A includes a hard disk, a ROM (read only memory), a flash memory, an optical disk, a magneto-optical disk, a magnetic disk, and the like. Is stored in a recording medium.
- reference numeral 9 denotes a clock signal generated by the digital test signal generator 8
- 10 denotes a test signal generated by the digital test signal generator 8 and these signals are input to the digital system 1. .
- reference numeral 11 denotes a digital output signal output from the digital system 1
- reference numeral 12 denotes a digital system internal state signal obtained by extracting a part or all of the outputs of the flip-flops. Entered in 7.
- FIG. 5 shows a configuration example of the digital signal observation device 7. In the digital signal observation device 7, only the logic analyzer 7A is configured.
- a logic analyzer is a measurement device that generally observes digital signals in a digital system.
- the digital signal observation device 7 can be configured as a dedicated circuit and incorporated in the digital system 1.
- the logic analyzer 7A stores the values of the digital output signal 11 and the digital system internal state signal 12 when the digital system 1 operates without error, and stores the values of the output from the digital system 1 An evaluation value is calculated by comparison.
- the values of the digital output signal 11 and the digital system internal state signal 12 when the digital system 1 operates without error are stored in the adjusting device 6, and the digital output signal 11 from the digital system 1 is stored.
- the value of the digital system internal state signal 12 may be sent to the adjusting device 6 as it is, and the adjusting device 6 may calculate the evaluation value.
- FIG. 6 shows a configuration example of the digital test signal generator 8. In the digital test signal generator 8, only the digital signal generator 8A is configured.
- the digital signal generator 8A and the digital system 1 are connected by the probe of the digital signal generator 8A, and the digital signal generator 8A and the adjusting device 6 are connected by the GP-IP interface 8G.
- the digital signal generator 8A holds the data pattern of the output digital signal in its internal memory, and outputs it to the digital system 1 as a digital test signal 10 in synchronization with a clock signal 9 of a designated frequency.
- the digital test signal generator 8 can be configured as a dedicated circuit and built in the digital system 1.
- FIG. 7 shows a configuration example of the power supply device 14.
- the power supply 14 includes a plurality of variable output voltage power supplies 97 as necessary.
- the power supply unit 14 receives power supply from a commercial AC 100 V power supply or a battery from the outside, and distributes the power to the internal variable output voltage power supply 97. You.
- Each output voltage variable power supply 97 is a circuit for generating a single power supply voltage, and its output voltage can be changed by an external power supply control signal 98.
- a plurality of outputs of the variable voltage power supply 97 are output to the outside as a power supply 99.
- the output of the power supply 14 may have a fixed voltage, or the output voltage of the output voltage variable power supply 97 may be fixed and used.
- the total number of adjustment points of the flip-flop 2 to be adjusted is plural, and as illustrated in FIG. 2, in the adjustment point of the delay element 2, adjustment of one adjustment point 2A is performed by many other adjustment points.
- the present invention is particularly effective in the case where the adjustment result of the adjustment location is affected and a combination explosion of the adjustment search space occurs.
- the digital system 1 of this embodiment uses a plurality of adjustable flip-flops 2 each having a delay element 4 whose delay time can be adjusted according to a setting from an external device and connected to a clock terminal.
- the main feature is that the optimum delay value is searched using the probabilistic search algorithm to be executed, and the delay time itself is not directly measured.
- a method is used in which the timing of a clock signal supplied to each circuit block or flip-flop in a digital system is measured using a timing comparison circuit. That is, the timing comparison between the reference clock signal and the supplied clock signal or the timing comparison between the clock signals supplied to adjacent circuit blocks and flip-flops is performed, and the difference is used as a timing adjustment circuit. Feedback is used to make adjustments so that the measured difference is reduced.
- the first problem is the accuracy of the comparison.
- the clock skew of the reference clock itself becomes a problem.
- clock skew caused by wiring that leads a clock signal supplied to each circuit block or flip-flop to the comparison circuit becomes a problem.
- the second problem is the fact that even if clock skew can be ideally reduced to zero, this does not mean that the operating yield of the digital system is maximized.
- the clock system that supplies the clock signal is in an ideal state, the other logic circuits still have timing deviations in design specifications due to process variations and the like. Each logic element in the computer system operates at a timing different from the ideal state.
- FIG. 8 shows a configuration example in which the delay time (signal transmission timing) is changed by the adjustable delay element 4.
- This is a circuit in which Tr9 and TrlO as p-channel FETs and Trll and Trl2 as n-channel FETs are connected in series, and TrlO and Trll function as NOT elements.
- Tr9 and TrlO as p-channel FETs and Trll and Trl2 as n-channel FETs are connected in series, and TrlO and Trll function as NOT elements.
- Tr9 and TrlO as p-channel FETs and Trll and Trl2 as n-channel FETs are connected in series, and TrlO and Trll function as NOT elements.
- FIG. 9 shows waveforms of an input signal (input clock signal) to the NOT element and an output signal (output clock signal) of the NOT element power.
- the delay time of TA can be adjusted by the control signal voltage input to T27, and the delay time of TB can be adjusted by the control signal voltage input
- Tr9 and Trl2 can be omitted.
- FIGS. 10 to 13 show other configuration examples in which the delay time (signal transmission timing) is changed by the adjustable delay element 4.
- the NOT element D2 is configured using a transistor having a larger size, the parasitic capacitance of the transistor increases and a longer delay occurs, and as shown in FIG. 12, the number of elements does not increase. , The delay time can be changed.
- an integrating circuit is configured using the resistor R and the capacitor C, and the output is By shaping the waveform with a Schmitt trigger element s or the like, a delay circuit can be configured. With this configuration, it is possible to generate a delay proportional to the product of the value of the resistor R and the value of the capacitor C.
- the wiring LA having the length LLA shown in the upper part of the figure generates a delay LLA / LLB times the wiring LB having the same material and width and the length LLB shown in the lower part of the figure.
- the delay elements described above only have a function of delaying the clock signal with a deviation. However, if a PLL (phase locked loop) circuit or a DLL (delay locked loop) circuit is used, the clock signal is advanced. Negative delays can also occur.
- FIG. 15 shows a configuration example of an adjustable delay circuit that generates a delay in both positive and negative directions.
- reference numeral 94 denotes the above-described PLL circuit
- reference numeral 4 denotes an adjustable delay circuit (delay element) shown in FIG. If the PLL circuit 94 has a function to advance the clock by 8DT and the adjustable delay circuit 4 has a function to generate a delay from 0DT to 15DT, this circuit has a delay of 8DT to 7DT as a whole. Can be generated.
- the adjustable delay element 4 can be configured by combining the plurality of delay elements.
- FIG. 16 is a configuration diagram illustrating the configuration of the adjustable delay element 4.
- the adjustable delay element 4 in this example has a configuration in which the register 5 in FIG. 1 holds 4-bit data. Is supported.
- each bit 1S of the register value held in the register 5 is not shown in the drawing.
- Each switch circuit Swl-Sw4 corresponds to each switch circuit via a switch drive circuit, Each of the switch circuits Swl-Sw4 is configured to operate, and the resulting delayed clock signal is applied to the clock terminal of the flip-flop 2 to be adjusted.
- adjustable delay elements 4 shown in FIG. A delay element UD1-UD4 for generating the delay time and a switch circuit Swl-Sw4 for selectively using the delay elements UD1-UD4 are also configured.
- the delay elements UD1 to UD4 and the switch circuits Swl to Sw4 corresponding to the respective delay elements are alternately cascaded (
- the delay signal generated by the delay element is added to the clock signal, and the clock signal whose timing is delayed from the original clock signal by the generated delay time is adjusted. It is configured so that it can be supplied to the terminal.
- the delay element UD1 generates a delay time whose length is determined by design.
- the delay element UD2 generates a delay time twice as long as that of the delay element UD1, and similarly, the delay element UD3 has a delay time four times that of the delay element UD1, and the delay element UD4 has eight times the delay time of the delay element UD1.
- the switch circuit Swl-Sw4 corresponding to each of the delay elements UD1-UD4 is turned on / off based on the register value of the register 5, and when a certain bit out of the four bits of the register value is "1", the bit is set to "1".
- the switch circuit corresponding to (1) falls to the delay element side, and the delay time generated by the corresponding delay element is added to the clock signal.
- One of the four bits of the register value is “0”
- the switch circuit corresponding to the bit falls to the bypass side, the corresponding delay element is skipped, and the generated delay time is not added to the clock signal.
- the delay time of each of the delay elements UD1 to UD4 is set to 1DT, 2DT, 4DT, and 8DT so as to be added to the clock signal.
- the delay time applied to the clock signal can be adjusted in the range from the delay time 0 to the delay time 15DT by the combination of the switch circuit states.
- FIG. 17 shows a configuration example including the adjustable delay element 4 and the least significant bit 5 A of the register 5.
- D1 is a NOT element
- D11 is an AND element
- D12 is an OR element
- UD1 is a unit delay circuit
- 5A is the least significant bit (one bit) of register 5
- D15 is the clock input from the clock line. is there.
- Clock output D16 is applied to the clock terminal of the flip-flop to be adjusted.
- D17 is a delay setting value input to the register 5A
- D18 is a write signal to the register 5A.
- the switch here is a basic selector circuit using an AND element D11 and an OR element D12, and the output of one AND element D11 is provided with a delay element UD1 that generates a delay DT, and The output of one AND element D11 is directly connected to OR element D12, thereby skipping delay element UD1.
- the AND element D11 on the delay element UD1 side operates to generate a delay DT, and when the output of the register 5A is a logical value “0”, the delay element is output.
- the AND element D11 on the side that skips UD1 works, causing no delay! / ,.
- FIG. 18 shows another configuration example including the adjustable delay element 4 and one bit D 13 of the register 5.
- This configuration example includes a transfer gate element D20 and a buffer D19.
- the function of the transfer gate element D20 is the switch itself, and has the same function as the above-described combination of the AND element and the OR element.
- the digital system internal state signal 12 is composed of the output power of the adjusted flip-flop 2 and the unadjusted flip-flop 3 in part or all of the digital system 1, and is input to the digital signal observation device 7. .
- the outputs of those flip-flops should be prepared as output terminals of the digital system 1 and connected to the digital signal observation device 7.
- the outputs of the above-mentioned flip-flops are divided into a plurality of groups and input to the selector circuit.
- a method of repeatedly applying the test signal 10 may be used.
- the scan path circuit is built in the digital system 1, and the test signal 10 and the The stop signal 9 may be stopped halfway, the internal state of the digital system 1 at that time may be taken out using a scan path circuit, and passed to the digital signal observation device 7.
- the scan path circuit here is a circuit that realizes an operation mode in which a part or all of the flip-flops in the digital system 1 operate as a single or a plurality of shift registers. It is possible to observe the internal state on the way and to set the internal state with external force.
- one bit 5A of the register 5 has a setting input signal D17 and a setting (write) instruction signal D18, and the delay setting signal 93 is a signal of these two types for all registers. It is composed of The delay setting signal 93 is output from the delay setting device 6B and input to the digital system 1.
- the delay setting device 6B can be configured using a parallel interface board of a personal computer, and the number of bits is determined according to the bit width of the delay setting signal 93 described above.
- Delay setting device The signal 0 or 1 is given to the delay setting signal connected to the setting input terminal of a certain bit of a certain register 5 in the delay setting signal 93 output as the parallel interface output signal of the 6B, and the corresponding setting is performed. By giving a signal instructing the setting to the bit connected to the signal, writing to the register can be realized.
- the value written to the register is the value calculated by the adjustment algorithm execution device 6A.
- numbers may be assigned to all the registers 5 in the digital system 1, and the delay setting signal 93 may be constituted by this register number, a value to be written into the register, and a setting instruction signal.
- the delay setting signal 93 sent to the digital system 1 from the delay setting device 6B is distributed according to the register number using the multiplexer circuit in the digital system 1, and the register specified by the register number is used.
- a setting instruction signal as a setting instruction signal of a designated register.
- a parallel interface board can also be used for connection between the delay setting device 6B and the digital system 1.
- the set values for all registers are arranged in a line in the delay setting device 6B, and a serial signal (1 bit width signal) generated by parallel-to-serial conversion is used as the delay setting signal 93.
- the delay setting signal 93 is subjected to serial-parallel conversion inside the digital system 1 and each set value is written to each register. Since the delay setting signal 93 is a 1-bit signal, a serial interface circuit such as RS-232C can be used to connect the delay setting device 6B to the digital system 1.
- the adjustment device 6 After the digital system 1 is manufactured, in an adjustment step, as shown in FIG. 1, the adjustment device 6, the digital signal observation device 7, the digital test signal generation device 8, and the power supply device 14 are connected to the digital system 1
- the digital test signal generator 8 inputs the digital test signal 10 and the clock signal 9 to the digital system 1, and the adjuster 6 sets the register value of the register 5 according to the processing procedure shown in FIG. I do.
- step S1 the adjusting device 6 writes an initially set value that has been preliminarily determined into the register 5 and holds it as a register value.
- step S2 the digital test signal
- the generator 8 outputs a test signal, and in response to the test signal, the digital system 1 is operated under the input of the clock signal 9 having a constant frequency and the power supply 99 having a constant voltage.
- the digital signal observing device 9 observes the output of the digital system 1 and the internal state of the digital system, and sends the result to the adjusting device 6, and in the next step S4, the adjusting device 6 uses the sent observation value. Then, it is determined whether the digital system 1 operates without error.
- the voltage value of the power supply 99 can be lower than the design power supply voltage value of the digital system 1.
- step S5 If an erroneous operation is performed here, in step S5, the adjusting device 6 changes the register value held in the register 5, and in the next step S6, one time until the result of the change becomes stable. After waiting for a fixed time, in the next step S7, it is determined whether or not the force satisfies the end condition. If so, a series of processes of returning to step S2 if the end condition is not satisfied after performing the defective product process in step S8 are repeatedly executed. If it is determined in step S4 that the digital system 1 has operated without error, the non-defective processing is performed in step S9, and the processing ends.
- the first method is to switch the set values sequentially in an appropriate order for all combinations in the range of the expected register value
- the second method is to generate the set values randomly. It is a way to make it.
- the third method is a method in which a delay value obtained at the time of design is used as an initial setting value, and the setting value is slightly changed in the + direction and one direction from the initial setting value.
- the first and second methods can be used.
- the present embodiment uses the third method because a combination explosion is expected to occur in the adjustment search space of the register value where the number of adjustable delay elements 4 is large.
- a method called a genetic algorithm is used.
- an adjustment method of the digital system 1 using a genetic algorithm will be described.
- references to the genetic algorithm include, for example, the publisher ADDISON-WESLEY.
- the genetic algorithm referred to in the present invention refers to an evolutionary computation method (Evolutionary Computation).
- the degree of error-free operation of the digital system 1 can be represented by an evaluation function F with the delay values of all adjustable delay elements as arguments (input). That the digital system 1 operates without error is equivalent to finding a delay value that optimizes the evaluation function F. Focusing on this point, the present inventor has found that the genetic algorithm described above can be applied to the adjustment of the digital system 1.
- the adjusting device 6 changes the register value of the register 5 according to the genetic algorithm.
- the genetic algorithm first, a group of virtual organisms having genes is set, and the individual's ability to adapt to a predetermined environment survives according to the degree of the adaptation, and descendants descend. Increase the probability of leaving. Then, the child inherits the parent's gene by a procedure called genetic manipulation. By performing such generational changes and evolving genes and populations, individuals with high fitness will dominate the population. Genetic manipulations at this time include gene crossover and mutation that occur in the reproduction of actual organisms.
- FIG. 20 is a flowchart showing a schematic procedure of a powerful genetic algorithm.
- step S11 a chromosome of an individual is determined. That is, when the generations are changed, the parent's individual strength determines what kind of data is transmitted to the offspring individuals and in what format.
- FIG. 21 illustrates a chromosome.
- Each symbol Ai is a gene, and their possible values are alleles.
- Ch indicates a chromosome
- Gs indicates a locus
- the number M of the locus is 5.
- the allele a set of integers, a range of real values, and a simple sequence of symbols are determined according to the problem.
- the letters a—e are alleles.
- the set of genes thus encoded is the chromosome of an individual.
- step S11 a calculation method of a fitness indicating how much each individual has adapted to the environment is determined.
- the design is designed such that the higher the value of the evaluation function of the target optimization problem is, the higher the ⁇ variable or the lower the variable, the higher the fitness of the individual corresponding to the variable.
- individuals with higher fitness have a higher probability of surviving or producing offspring than individuals with lower fitness and higher individual fitness.
- individuals with low fitness are considered to be individuals that are not well adapted to the environment and are annihilated. This reflects the principle of natural selection in evolution. That is, fitness is a measure of the strength of each individual in view of the potential of survival.
- step S13 after the processing is started in step S12, the initial population of organisms is generated randomly using random numbers. If there is some prior knowledge about the search space, processing such as generating a population of organisms may be performed mainly on the parts that are considered to have high evaluation values.
- the total number of individuals to be generated is referred to as the number of individuals in a group.
- step S14 the fitness of each individual in the biological population is calculated based on the calculation method previously determined in step S11.
- step S15 individuals that are the basis of the next generation of individuals are selected from the population. However, performing only selection will only increase the proportion of individuals with the highest and highest fitness levels in the population, and will not generate new search points. Therefore, the following operations called crossover and mutation are performed.
- next step S16 a pair of two individuals is randomly selected at a predetermined frequency from the next generation individuals generated by the selection, and the chromosomes are rearranged to change the chromosomes of the offspring.
- the probability of occurrence of crossover is called a crossover rate.
- the offspring individuals generated by the crossover are individuals that have inherited the power traits of their parent individuals. This crossover process increases the chromosome diversity of the individual and causes evolution.
- the gene of the individual is changed with a certain probability (sudden mutation).
- the probability of occurrence of a mutation is called a mutation rate. If the content of a gene is rewritten with a low probability, the! / ⁇ ⁇ phenomenon is a phenomenon that can also be seen in the genes of real organisms. It should be noted, however, that if the mutation rate is set too high, the genetic characteristics of the parent trait will be lost due to crossover, which will be the same as searching randomly in the search space.
- next generation population is determined by the above processing.
- step S18 it is determined whether or not the generated next generation biological population satisfies the evaluation criteria for ending the search. Find out.
- the evaluation criteria depend on the problem, but typical ones are as follows.
- step S19 the process proceeds to step S19 to terminate the search, and obtain an individual with the highest fitness in the biological population at that time. The solution to the optimization problem. If the termination condition is not satisfied, the process returns to the process of calculating the fitness of each individual in step S14, and the search is continued. By repeating such generation alternation, the fitness of an individual can be improved while keeping the number of individuals in the group constant.
- the above is the outline of the genetic algorithm.
- the genetic algorithm framework described above is a loose one that does not specify actual programming details, and does not specify a detailed algorithm for each problem. Therefore, in order to use the genetic algorithm for adjusting the digital system of the present embodiment, the following items need to be realized for adjusting the digital system.
- FIG. 22 is a flowchart showing a processing procedure of the adjusting device 6 using the genetic algorithm in the present embodiment. Note that the process of FIG. 22 specifically shows the process of step S2 to step S6 of FIG.
- the major feature of this embodiment is that the register value of the register 5 is directly used as the chromosome of the genetic algorithm, which eliminates the need for processing for converting chromosome information into the register value. can do. That is, the chromosome in this example is composed of a plurality of register values of the register 5 as shown in FIG.
- a signal with a positive sign (no sign) delays the signal by that time, and a signal with a negative sign advances the signal by that time.
- a plurality of individuals are first created using uniform random numbers as an initial group of the genetic algorithm in step S1 of FIG.
- the value of each gene on each chromosome in the initial population takes a value of 1 at a probability of 0.5 and a value of 0 at a probability of 0.5.
- individuals that are considered to have higher fitness can be created as the initial population.
- Each individual in the initial population calculates the fitness from the observation value (step S3) sent from the digital signal observation device 7 by the adjustment device 6 using the above evaluation function. Thereafter, it is determined in step S4 whether or not the performance of the digital system 1 operates without error. If the digital system 1 operates without error, non-defective processing is performed in step S9, and the adjustment processing ends.
- step S9 In the case of all individuals in the initial population, if the non-defective processing in step S9 is not performed, the process proceeds to the genetic processing in steps S21 to S30. If it is determined that the performance of the digital system 1 has operated without error during the fitness calculation processing in step S26 or step S29, the non-defective processing is performed in step S9, and then the adjustment processing ends. If the chromosome (register value) that operates without error is not obtained even after performing the adjustment process by repeating steps S21 to S30 for a certain number of generations, the digital system 1 to be adjusted is determined to be defective, and In step S8 of step 19, processing as a defective product is performed.
- the selection process of the genetic algorithm is a process of selecting individuals to be left in the next generation from the population, and is performed in steps S21 to S30.
- two individuals 1 and 2 are selected at random in terms of collective power (step S21), and crossover and mutation are applied thereto, 24 (steps S22-S29), and then, as shown in the processing flow of FIG. 24, out of the four individuals of parent individuals 1, parent individuals 2, child individuals 1, and child individuals 2, Two individuals A and B are selected (step S31), and the individuals A and B are replaced with the parent individuals 1 and 2 in the population (step S32).
- This replacement process is generally
- a major feature is that the individuals in the entire population are not changed at the same time as in various genetic algorithms. Thereby, it is possible to perform a search with a small number of individuals in a group.
- step S22 the method shown in the explanatory diagram of Fig. 25 is used. This is an operation to partially replace chromosomes at random positions, a technique called one-point crossover.
- Chi and Ch2 are the chromosomes of the parents A and B that have survived as a result of the selection, and in the crossover process, these chromosomes are cut at the randomly selected crossover position CP.
- the intersection position is between the third gene and the fourth gene from the left.
- offspring A ′ and offspring B ′ having chromosomes Ch3 and Ch4, respectively are generated, and these are not replaced with the original individuals A and B.
- the mutation in step S23 which is executed following the crossover in step S22, is to change each bit of the gene of each chromosome from 0 to 1 or 1 to 0 with the occurrence probability of the mutation rate. It is.
- Figure 26 shows an example of mutation. In Fig. 26, mutations occur in the genes at the second bit from the left and the third bit from the right of the chromosome Ch5, each of which is changed to an allele on chromosome Ch6! .
- the delay element 4 having a variable delay value is used for the clock signal to the plurality of flip-flop elements in the digital system 1, and these delay elements are used.
- the delay value of 4 is searched so that the digital system 1 operates without error. Therefore, it absorbs clock timing errors caused by unevenness in clock signal line quality and design errors in the digital system manufacturing process, and compensates for lack of timing margins caused by lowering the power supply voltage.
- the digital system 1 can be tuned to operate without error, which means that a digital system that operates at a lower supply voltage than the prior art, with less V and design effort than the prior art, i.e. This means that a digital system with low power consumption can be obtained.
- some digital systems 1 that cannot be operated even when adjustments are made with the original power supply voltage can be adjusted to operate without error by slightly increasing the power supply voltage. This means that the operation yield can be improved with less labor and a minimum power supply voltage rise than in the conventional technology.
- the following adjustment method can be used. That is, in the adjustment method described above, the power supply voltage of the power supply 99 is assumed to be a constant value, but after the adjustment is completed, the power supply voltage of the power supply 99 is reduced, and the same adjustment is performed. Further adjustment can be made to reduce the operating voltage.
- FIG. 27 shows an adjustment method in the above case.
- step S61 the power supply voltage of the power supply 99 input to the digital system 1 is set to V0, and then in step S62, the adjusting device 6 performs the adjustment in steps S1 to S9 shown in FIG. I do.
- step S63 it is determined whether or not the digital system 1 has been adjusted to a non-defective product as a result of the adjustment in step S61. As a result of the adjustment, if the power becomes a non-defective product, the process is terminated. If the adjustment results in a non-defective product, the power supply voltage of the power supply 99 is set to a value VI smaller than V0 in step S64.
- step S65 the digital system 1 is adjusted as in step S62.
- step S66 the same determination as in step S63 is performed, and if the product is non-defective, the process of adjusting the power supply voltage of the power supply 99 to a smaller value is repeated. As a result of the repetition, when the power supply voltage of the power supply 99 is set to the lower limit value Vn in step S68, the adjustment is performed in step S69, and the process ends.
- the upper limit value V0 of the power supply voltage is determined by the design value of the digital system 1
- the lower limit value Vn is determined by the physically allowable power supply voltage.
- the value of n and the values of VI to Vn-1 are determined by the required accuracy of the adjustment. With this adjustment method, the value of the operating power supply voltage of the digital system 1 can be reduced according to the decrease in the timing margin.
- the stability of the digital system can be improved by operating the digital system determined to be good with the power supply voltage Vj at the frequency of Vi (i ⁇ j) when the system is used. it can.
- the clock timing is adjusted so that it operates at a lower power supply voltage than when it is used, and the clock timing is affected by fluctuations in the power supply voltage during operation, the digital system temperature, and the effects of external electromagnetic noise. This is because even if a subtle change occurs, malfunction may occur. If the power supply voltage is not adjusted to a good product in step S63 of the above adjustment method, the power supply voltage value is set to Vh
- the initial Vh is set slightly higher than the design value V0
- the adjustment from Step S1 to Step S9 can be performed again. If the timing adjustment is successful at this power supply voltage value Vh, it is possible to achieve an improvement in yield with only the minimum necessary increase in the power supply voltage. On the other hand, in the case of a force that cannot be adjusted to a good product even in this Vh, it is possible to further increase Vh in stages and continue the adjustment.
- This adjustment method can also be used in the mass production process of the digital system 1.
- the conventional mass production process in general, only operation tests were performed without adjusting the power supply voltage, and non-defective products were selected.
- the ratio of the digital system operating at a low power supply voltage value can be increased.
- the adjustment device 6, the digital signal observation device 7, the digital test signal generation device 8, and the power supply device 14 are detachably connected to the digital system 1 as external devices.
- a circuit corresponding to the external device may be incorporated in the digital system 1 as adjustment means.
- the power supply device 14 may be incorporated in the digital system 1 or connected as an external device independently of the adjustment device 6, the digital signal observation device 7, and the digital test signal generation device 8.
- FIG. 28 shows a modification configured as described above.
- a circuit corresponding to the external device is incorporated in the digital system 1 in addition to the digital system main body 1L.
- a switching switch 30 is provided between the input terminal and the output terminal of the digital system 1L and the external input terminal 32 and the external output terminal 33 of the digital system 1L, respectively. This The switching switch 30 may be provided inside the digital system 1L as shown in the drawing, and may be provided outside the digital system 1.
- the switching switch 30 When the switching switch 30 is operated, the output of the digital system main unit 1L is input to the digital signal observation circuit 7L, and the adjustment circuit 6L, the digital signal observation circuit 7L, and the digital test signal generation circuit 8L operate. And adjust the register value.
- the power supply unit 14L constantly supplies power to each unit in the digital system main unit 1L, and at the same time, changes the power supply voltage on the output side according to the power supply control signal 98 from the adjustment circuit 6L.
- the output of the digital system 1L is switched to the output terminal 33 by operating the switch 30.
- the light emitting element 31 that displays a warning when a register value at which the digital system main unit 1L operates without error is not obtained is provided.
- the switching switch 30 is not limited to a manual switch, and may be configured to switch automatically when the power is turned on.
- the clock signal 9 may be used as the clock signal 9.
- This embodiment is an example of a configuration in which the method of the present invention is applied to a memory test pattern generator circuit.
- FIG. 29 shows a digital system according to the present invention having the basic function of generating a memory test pattern.
- FIG. 2 is a configuration diagram showing a memory test pattern generator circuit 1G as a second embodiment of the system, corresponding to the digital system 1 in FIG. 1, and using the same other devices as those in FIG.
- adjustment device 6, digital signal observation device 7, digital test signal generation device 8, and power supply device 14 are external devices. Circuits similar to those shown in FIG. 1 are denoted by the same reference numerals.
- the adjusted flip-flop 2 is a normal D flip-flop
- the unadjusted flip-flop 3 is also a normal D flip-flop.
- the clock terminal of the unadjusted flip-flop 3 is connected directly to the clock line.
- An adjustable delay element 4 is inserted between the clock terminal of the adjusted flip-flop 2 and the clock line.
- a register 5 for controlling the delay time of the delay element 4 is connected to the adjustable delay element 4. If the register 5 has 4 bits, the adjustable delay element 4 can be configured as shown in FIG.
- the adjustable delay element 4 can generate a delay from Ops to 750 ps according to the value of the register 5.
- the register 5 can be composed of four ordinary D flip-flops.
- the register 5 receives a 4-bit delay value setting signal and a 4-bit common setting instruction signal.
- the delay setting signal (delay value setting line) 93 is obtained by collecting the delay value setting signal for 4 bits of the register 5 and the common setting signal for all registers.
- the digital system internal state signal 12 is a signal obtained by collecting all outputs of the flip-flop 2 to be adjusted.
- the decoder circuit 20A1 performs a decoding process on an input signal, and is configured as a thread matching circuit (not including a storage element such as a flip-flop).
- the ALU circuit 20A2 inputs a 4-bit input signal for each of the two systems and a 4-bit operation designation signal, performs an operation between the two input signals according to the operation designation signal, and outputs the operation result as a 4-bit output This is a combination circuit that outputs data.
- the inverter circuit 20A3 has a function of inverting or non-inverting an input signal according to an external force designation, and is configured as a combinational circuit.
- the PLL circuit 94 is connected between the input terminal of the clock signal 9 and the adjustable delay element 4 connected to the adjusted flip-flop 2, and supplies the same frequency to the adjusted flip-flop 2. And generates a clock signal advanced by the timing force S400ps.
- the adjustable delay element 4 can generate a delay from Ops to 750 ps, so the delay from -400 ps to 350 ps together, that is, from 400 ps advanced to 350 ps delayed A clock can be supplied to each adjusted flip-flop 2.
- the clock timing of the flip-flop 2 to be adjusted also varies from ⁇ 400 ps to 350 ps depending on the value set in the register 5. For example, when 1011 is set in the register 5, the clock timing of the corresponding adjusted flip-flop 2 is delayed by 150 ps with respect to the clock signal 9 supplied from the outside.
- the clock signal 9 is directly supplied to the clock terminal of the flip-flop 3 that is not adjusted, and the flip-flop 3 operates at the same timing as the clock signal 9 without being adjusted.
- one input of the ALU circuit 20A2 is fed back via the flip-flop 2 to be adjusted, and is not a simple pipeline structure.
- the flip-flops connected to the external terminals of the digital system 1 are all adjusted, and are not adjusted.
- the flip-flops 3 are adjusted and the other flip-flops are adjusted. It is not necessary.
- the method of the present invention is applicable and effective even if the characteristic value of each element appearing in the present example is not always accurate.
- the present embodiment is particularly suitable when applied to a memory test pattern generator circuit used for testing a high-speed memory element.
- the performance of the memory test pattern generator circuit 1G can be represented by an evaluation function F having the delay values of the plurality of adjustable delay elements 4A1-4A14 as arguments. Operating the memory test pattern generator circuit 1G without error is equivalent to obtaining a delay value that optimizes the evaluation function F.
- the adjusting device 6 sets the evaluation function F to Used to change the value in register 5 according to the genetic algorithm.
- Adjustment of delay element 4 is performed according to the flowcharts shown in FIGS. 19 and 22, as in the case of the first embodiment.
- This embodiment is characterized in that the value of the register 5 is directly used as the chromosome of the genetic algorithm. As a result, processing for converting chromosome information into register values becomes unnecessary.
- the chromosome in the present embodiment is also configured with the register values of the fourteen registers 5 corresponding to the fourteen delay elements.
- the memory test pattern generator circuit 1G was set with the register value represented by the chromosome of the individual. After that, a function indicating how close the output observed by the digital signal observation device 7 is to the expected value is used. Specifically, the value calculated by the following evaluation function F is used for fitness of the genetic algorithm.
- NT is the number of outputs of the memory test pattern generator circuit 1G for the sequence of the digital test signal 10
- NC is the number of times the digital value of the memory test pattern generator circuit output as expected was output. is there.
- the above evaluation function F takes a real value from 0 to 1, and when it takes a value of 1, the memory test pattern generator circuit 1G to be adjusted has operated without error. For example, assuming that NC is 253 and NT force is 500 in the output system of digital system 1 set by the register value represented by a certain chromosome, the value of evaluation function F in that case is 0.506.
- a plurality of individuals are first created using uniform random numbers as an initial group of the genetic algorithm in step S1 of FIG.
- the value of each gene on each chromosome in the initial population takes a value of 1 at a probability of 0.5 and a value of 0 at a probability of 0.5.
- the number of individuals in the population was 50.
- the memory test pattern generator circuit 1G is operated with the register value represented by each individual, and using the observation result of the observation device 5 in step S3, the adjustment device 6 in step S4 The fitness is calculated by the evaluation function. Then, in order, selection is performed in step S21, crossover is performed in step S22, and mutation processing is performed in step S23, thereby generating a population of individuals of the next generation (a population of solution candidates).
- the crossover rate which is the ratio of the number of individuals performing crossover to the total number of individuals, was 0.5, and the mutation rate was 0.0125.
- step S4 it is determined whether the memory test pattern generator circuit 1G operates without error, and when the memory test pattern generator circuit 1G operates without error, non-defective processing is performed, and the adjustment processing ends. If the chromosome (register value) satisfying the specification is not obtained even after performing the adjustment process repeatedly for a certain number of generations, the memory test pattern generator circuit 1G to be adjusted is determined to be defective, and the defective product is determined in step S8. Is performed. In this example, the number of generations at which repetition is stopped was set to 20. [0148] The following is an experimental result when the adjustment method using the genetic algorithm of the present embodiment is applied to the memory test pattern generator circuit 1G shown in FIG. 29. In this experiment, circuits were fabricated using LSI chips using CMOS technology.
- the memory test pattern generator circuit is mounted on a normal integrated circuit.
- the memory test pattern generator circuit can be mounted using a reconfigurable integrated circuit such as an FPGA or a CPLD.
- a reconfigurable integrated circuit such as an FPGA or CPLD with the delay adjustment element built in is developed and used. May be implemented.
- the delay elements 4A1-4A14 are inserted into the clock signal line to the flip-flop element, and the delay time of the delay elements 3 is measured by the memory test. Search so that the pattern generator circuit 1G operates without error even when the power supply voltage is lower than the specified (normal) voltage. Therefore, according to the present embodiment, clock signal errors due to unevenness in the quality of clock signal lines in the integrated circuit manufacturing process, errors in design, etc., and each logic element in the circuit based on a drop in power supply voltage
- the memory test pattern generator 1G can be adjusted to operate without errors by absorbing the decrease in operating speed of the memory, which requires less design effort than the conventional technology and is faster than the conventional technology. This means that a digital system with low power consumption can be obtained.
- the memory test pattern generator circuit 1G can be tuned to operate without errors by absorbing the rise in temperature, which requires less design effort than the conventional technology, and is faster and faster than the conventional technology. This means that a digital system with a high operating yield can be obtained.
- the current consumption and heat generation of the memory test pattern generator circuit 1G can also be observed and incorporated into the evaluation function.
- the amount of heat generated and the amount of current consumed by an LSI fluctuate depending on the clock timing input to the flip-flops inside the LSI, so that it is possible to meet various required specifications and improve the adjustment accuracy. .
- FIG. 31 shows a configuration example in the above case.
- reference numeral 13 is a thermometer
- 14 is a power supply.
- the thermometer 13 measures the temperature of the LSI of the memory test pattern generator circuit 1G, converts the value into an AZD, and transmits it to the adjusting device 6.
- the power supply device 14A is a device that supplies power to the memory test pattern generator circuit 1G 99.
- the power supply device 14A converts the current supply value into an AZD and transmits the converted value to the adjustment device 6.
- the adjusting device 6 monitors the temperature and the current consumption while the digital test signal generator 8 outputs the test signal 10, calculates the average temperature and the average current consumption during that, and further supplies the power control signal. 98 to the power supply 14A.
- fitness is the fitness in the genetic algorithm
- T is the measured average temperature
- I is the measured average current consumption
- Tm is the ideal average temperature
- Im is the ideal average current consumption
- wl , W2 are weighting factors.
- adjustment is performed until the memory test pattern generator circuit 1G does not malfunction, and after the malfunction does not occur, further adjustment is performed so that the average current consumption and the average temperature are closer to ideal values. . Then, as in the previous embodiment, adjustment is performed so that the power supply voltage is reduced within a range where the memory test pattern generator circuit 1G does not malfunction.
- the peak value during the observation of the current consumption may be incorporated into the above evaluation function.
- FIG. 32 shows the configuration of a digital circuit board according to the third embodiment.
- reference numeral 1B denotes a digital circuit board
- the system of this embodiment differs from the digital system 1 of the first embodiment in that It is configured using a digital circuit board 1B having the same basic functions as the digital system 1.
- the same components as those shown in FIG. 1 are denoted by the same reference numerals.
- a plurality of LSIs 1L1-1L10 to which the clock signal 9 is input and a plurality of electronic components 16 to which the clock signal is not input are mounted.
- the LSI and the electronic components are connected to each other by a data signal line (not shown).
- 4B1-4B10 are delay elements whose delay time can be adjusted, and their delay times are adjusted according to the values indicated by the registers 5B1-5B10, respectively.
- the adjustment points are 10 places.
- Reference numeral 15 denotes an electromagnetic wave measuring device as an external device.
- a digital signal current including a high frequency component and a harmonic component of the frequency flows on the board, so that the power of the radiated electromagnetic noise is large. Therefore, it affects the human body and other nearby electronic devices as EMI noise.
- the emission noise can reduce the peak value of the power by slightly shifting the input clock timing to each LSI. Therefore, by observing the radiation noise and adjusting the clock timing, the influence of the radiation noise on the outside can be reduced.
- Driving a digital circuit board with a low power supply voltage can reduce the total power of electromagnetic noise radiated from the board, which is effective as a measure against EMI.
- the electromagnetic wave measuring device 15 measures the power of the electromagnetic wave radiated from the substrate, converts the value into an AZD, and transmits it to the adjusting device 6.
- the adjusting device 6 monitors the electromagnetic wave power while the digital test signal generating device 8 is outputting the test signal, and calculates the peak value during the monitoring.
- the adjustment method of this embodiment is basically the same as the adjustment method of the first embodiment.
- the adjusting device 6, the digital signal observing device 7, the digital test signal generating device 8, the power supply device 14, and the electromagnetic wave measuring device 15 Are respectively connected to the digital circuit boards 1B.
- the power supply 14 supplies power to the digital circuit board 1B.
- the digital test signal generator 8 inputs the test signal 10 and the clock signal 9 to the digital circuit board 1B.
- the digital signal observing device 7 observes the output value of the digital circuit board 1B
- the electromagnetic wave measuring device 15 observes the radiation noise of the digital circuit board 1B, and supplies the same to the adjusting device 6, and the adjusting device 6 is, for example,
- the evaluation is performed using the evaluation function shown.
- the power supply 14 supplies the power supply voltage supplied to the digital circuit board 1B to the evaluation function to operate at the lowest power supply voltage as much as It is also possible to adjust so that the peak power p becomes low.
- the output of the power supply 14 is set to the lowest power supply voltage at which the digital circuit board 1B operates, and then, based on the evaluation function of [Equation 3],!
- the peak power P of the electromagnetic wave can be adjusted to be low, or the adjustment can be made by taking the weighted average of the peak power of the electromagnetic wave and each power supply voltage output by the power supply 14 as P
- the chromosomes and register values here are in one-to-one correspondence as in the case of the method of the first embodiment. That is, as shown in FIG. 23, the chromosome is composed of the register values of ten registers 5 corresponding to the ten adjustment points in the above embodiment. Then, each register 5 corresponding to each adjustment position is a 4-bit register here. Therefore, the chromosome length is 40 bits. Therefore, the size of the adjustment search space of the digital circuit board 1B of the above embodiment is 2 "40 10" 12 (10 to the 12th power), and it is needless to say that adjustment by full search is impossible.
- a plurality of adjustable delay elements 4B1-4B10 are used on the clock signal 9 in the digital circuit board 1B, and the delay values are output from the digital circuit board. Since adjustments are made to prevent malfunctions, the digital circuit board 1B does not malfunction by absorbing clock timing deviations caused by unevenness in the process of clock signal lines and design errors in the digital circuit board manufacturing process. , Can be adjusted as follows. Further, in the present embodiment, since the adjustment can be performed in consideration of the radiation noise radiated as an electromagnetic wave from the digital circuit board 1B, especially when a human body or other electronic devices exist around the digital circuit board 1B. It is suitable.
- the number of LSIs mounted on the substrate is set to ten. In the present invention, it goes without saying that the number of LSIs does not matter. In addition, when the magnitude of radiated noise power does not matter, such as when no human body or other electronic devices are present around the circuit board, it is not necessary to consider the value of P in the above evaluation function. But,.
- the method of this embodiment is particularly suitable when the clock frequency is high. This is because, when the clock frequency is high, the timing adjustment of the clock signal becomes more difficult, and the power of the high frequency component of the electromagnetic radiation noise becomes stronger.
- a genetic algorithm is used for the method of obtaining the initial setting value of the register 5 and the method of changing the register value from the initial setting value.
- an algorithm called genetic programming can be used instead of the genetic algorithm.
- the value of the register 5 is adjusted by the adjusting device 6 according to the genetic programming. change.
- This embodiment is particularly characterized in that the tree structure of the clock signal line is directly mapped to the chromosome structure of the genetic programming as the chromosome of the genetic programming. In this way, as in the first embodiment, a circuit for converting chromosome information into register values can be eliminated.
- the digital system 1T shown in Fig. 33 has the same basic function as the digital system 1; however, in this digital system 1T, a clock signal 9T is input to the digital system 1T, and the clock signal 9T is formed into a tree structure. The signal is branched and input to digital subsystems 1TS1 to 1TS6. Within these digital subsystems, the clock signal is provided to all flip-flops as a clock signal. A delay element 4T1 to 4T5 is inserted in each branch of the clock signal line, and each delay value can be changed according to the corresponding register value 5RT1-5RT5. The digital subsystems are connected by a data line (not shown).
- This adjustment method also follows the flowchart of FIG. 19 as in the first embodiment.
- the processing procedure of the genetic programming is the same as the flowchart shown in FIG. 22, except for the chromosome expression method and the crossover method.
- the tree structure shown in Fig. 34 is used as a chromosome for genetic programming. That is, using a tree structure that directly represents the connection state of the clock signal lines shown in FIG. 33, the bit strings of the chromosome nodes CS1 to CS5 correspond to the values of the registers 5RT1 to 5RT5.
- the adjustment method can be applied to any number of bits, needless to say that each register length is set to 3.
- the digital system 1T is set up with the register value represented by the chromosome of the individual, operated, and observed by the digital signal observation device 7. Use a function that indicates how close the digital output is to the expected value.
- a plurality of individuals are first created using uniform random numbers as an initial group for genetic programming in step S1 of FIG. That is, in this case, the value of each gene of each chromosome in the initial population takes a value of 1 at a probability of 0.5 and a value of 0 at a probability of 0.5.
- individuals that are considered to have higher fitness can be created as the initial population.
- the fitness value is calculated by the adjustment device 6 from the observation value (step S3) sent from the digital signal observation device 7 using the above evaluation function. At this time, it is determined in step S4 whether or not the performance of the digital system 1T operates without error. If the digital system 1T operates without error, the non-defective processing is performed in step S9, and then the adjustment processing ends.
- step S9 In all individuals in the initial population, if the non-defective processing in step S9 is not performed, the process proceeds to the genetic processing in steps S21 to S30. If it is determined that the performance of the digital system 1T has operated without error during the fitness calculation processing in step S26 or step S29, the non-defective processing is performed in step S9, and then the adjustment processing ends. If the chromosomes (register values) that operate without error cannot be obtained even after performing steps S21 and S30 repeatedly for a fixed number of generations, the digital system 1T to be adjusted is determined to be defective, and At step S8 in step 19, processing as a defective product is performed.
- step S22 the method shown in the explanatory diagram of FIG. 35 is used. This is an operation that partially replaces the chromosome tree structure at random positions. This is a unique operation.
- TR1 and TR2 are the chromosomes of the parents A and B selected as a result of the selection process in step S21, and in the crossover process, these chromosomes are cut at the randomly selected crossover position CP. Then, by exchanging the cut partial genotypes, a child A 'and a child B' having chromosomes TR3 and TR4, respectively, are generated. By using this method, crossover can be performed without destroying partial information of chromosomes effective for adjustment.
- the mutation in step S23 which is executed following the crossover in step S22, is to change each bit of the gene of each chromosome from 0 to 1 or 1 to 0 with the occurrence probability of the mutation rate. It is.
- Figure 36 shows an example of mutation. In FIG. 36, mutations occur in the genes enclosed in squares on chromosome TR5, each of which is changed to an allele on chromosome TR6.
- the above-described genetic programming enables efficient adjustment when the clock signal line has a tree structure.
- the present invention can be applied to all, a part, or a plurality of parts of a device using a digital system, regardless of the size of the digital system.
- the adjustment by the method of the present invention hardly hinders even if the accuracy of the delay value of the adjustable delay element 4 is low and monotonicity is not guaranteed. Therefore, the delay element used in the present invention can be manufactured on a semiconductor substrate with a smaller area than before.
- the present invention is not limited to the above-described examples.
- the present invention includes other configurations that can be easily modified by those skilled in the art within the scope of the claims. It is.
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| JP2005506771A JP4281015B2 (ja) | 2003-06-06 | 2004-06-03 | デジタルシステム、デジタルシステムのクロック信号調整方法および、その調整方法で実行する処理プログラムを記録した記録媒体 |
| US10/559,672 US20060236146A1 (en) | 2003-06-06 | 2004-06-03 | Digital system, clock signal adjusting method for digital system, recording medium recording processing program executed in the adjusting method |
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| JP2008217350A (ja) * | 2007-03-02 | 2008-09-18 | National Institute Of Advanced Industrial & Technology | ディジタルシステムの設計システムおよびディジタルシステムの製造方法 |
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| US20070240013A1 (en) * | 2006-01-27 | 2007-10-11 | Sony Computer Entertainment Inc. | Methods And Apparatus For Managing Defective Processors Through Clock Programming |
| US8677171B2 (en) * | 2008-04-14 | 2014-03-18 | Teklatech A/S | Method for controlling the dynamic power signature of a circuit |
Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| JPH0744519A (ja) * | 1993-08-03 | 1995-02-14 | Mitsubishi Electric Corp | 遺伝的アルゴリズム実装方法、およびそれを用いたネットワーク最適化方法 |
| JPH0981615A (ja) * | 1995-09-14 | 1997-03-28 | Sony Corp | 回路設計装置および方法 |
| JP2000207038A (ja) * | 1999-01-13 | 2000-07-28 | New Japan Radio Co Ltd | 定電圧出力回路の抵抗値決定方法 |
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| US5428764A (en) * | 1992-04-24 | 1995-06-27 | Digital Equipment Corporation | System for radial clock distribution and skew regulation for synchronous clocking of components of a computing system |
| US5475690A (en) * | 1994-11-10 | 1995-12-12 | Digital Equipment Corporation | Delay compensated signal propagation |
| US6192092B1 (en) * | 1998-06-15 | 2001-02-20 | Intel Corp. | Method and apparatus for clock skew compensation |
| US6658581B1 (en) * | 1999-03-29 | 2003-12-02 | Agency Of Industrial Science & Technology | Timing adjustment of clock signals in a digital circuit |
| US6539491B1 (en) * | 1999-11-08 | 2003-03-25 | International Business Machines Corporation | Method and apparatus for implementing IEEE 1149.1 compliant boundary scan |
| US6721892B1 (en) * | 2000-05-09 | 2004-04-13 | Palmone, Inc. | Dynamic performance adjustment of computation means |
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- 2004-06-03 US US10/559,672 patent/US20060236146A1/en not_active Abandoned
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| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| JPH0744519A (ja) * | 1993-08-03 | 1995-02-14 | Mitsubishi Electric Corp | 遺伝的アルゴリズム実装方法、およびそれを用いたネットワーク最適化方法 |
| JPH0981615A (ja) * | 1995-09-14 | 1997-03-28 | Sony Corp | 回路設計装置および方法 |
| JP2000207038A (ja) * | 1999-01-13 | 2000-07-28 | New Japan Radio Co Ltd | 定電圧出力回路の抵抗値決定方法 |
Cited By (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| JP2008217350A (ja) * | 2007-03-02 | 2008-09-18 | National Institute Of Advanced Industrial & Technology | ディジタルシステムの設計システムおよびディジタルシステムの製造方法 |
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| JPWO2004109916A1 (ja) | 2006-07-20 |
| JP4281015B2 (ja) | 2009-06-17 |
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