Patent Publication Number: US-2022239293-A1

Title: Pulse generator for generating fluctuated voltage-spike trains

Description:
CROSS REFERENCE TO RELATED APPLICATIONS AND INCORPORATION BY REFERENCE 
     This application claims benefit of priority under 35 USC 119 based on Japanese Patent Application No. P2021-012464 filed Jan. 28, 2021, the entire contents of which are incorporated by reference herein. 
     BACKGROUND OF THE INVENTION 
     Field of the Invention 
     The present invention relates to a pulse generator that can generate fluctuated voltage-spike trains, which are suitable for neural network devices, quantum computers and others. 
     Description of the Related Art 
     In recent years, as to the computer architectures for artificial intelligence (AI), there are some reports such that brain-inspired information-processing scheme referred as “spiking neuron” is a promising candidate as a high capability scheme to be used in AI computer architectures (for example, please refer to “NIKKEI ELECTRONICS”, 2020.07, pp. 56-62). A model that faithfully mimics the mechanism of the human-brain&#39;s nerve cells or neurons of a living body more and more is called “spiking neural network (SNN)”. In the SNN, information is transmitted by frequencies and timings of voltage-spikes and not by magnitudes or amplitudes of the voltage-spikes, inspired by the system of information transmission in the living body. 
     Also, in brain networks in human-brains, the greater the number of synapses—joints between the neurons—for a single neuron, or for a piece of information, denser the brain network. Therefore, higher and higher the density of the brain network, better and better the efficiency of information transmission, and then, a higher-level human-brain is realized. However, in order to realize a brain system comparable to brains of mammals, together with tens of millions to hundreds of millions, and even more neurons, it is necessary to connect tens of millions to tens of thousands of synapses to a single neuron. Such large scale of tens of millions of synapses means that an enormous amount of pulse generators, each of which generates a huge number of voltage spikes, must be merged in a single integrated circuit for realizing an advanced processing scheme with the SNN, which mimics the operations and functions in living body. 
     For example, G. Indiveri et al. have reviewed an electronic circuit, which mimics an axon-hillock of neurons as the electronic circuitry for generating the voltage spikes (please refer to G. Indiveri et al., “Neuromorphic Silicon Neuron Circuits”, Front. Neurosci., vol. 5, No. 73, 2011). However, in the neuromorphic silicon neuron circuits, when the frequency and timings of the voltage spikes are controlled, a circuit scale becomes very large. Thus, it is impossible to realize integrated circuits (chips) for realizing the AI computer architecture compatible to the brain of the mammals, as mentioned above. That is, in future, in order to further improve the information-processing capability of the AI computer architecture, and to install the integrated circuits in a mobile system such as a robot, it is desired to develop compact pulse generators having fewer elements than known technologies so that a great many pulse generators can be assembled in a computer system. 
     SUMMARY OF THE INVENTION 
     An aspect of the present invention inheres in a pulse generator encompassing (a) an output circuit connected between a higher-potential power-supply and a lower-potential power-supply, the output circuit is implemented by a resistor-connected complementary transistor-circuit including a CMOS inverter, and a resistive element connected in series to the CMOS inverter, and (b) a voltage source for supplying an input voltage to the CMOS inverter, the input voltage swings in a span including at least a simultaneous-conduction regime of the CMOS inverter, with respect to a swing-center potential set to an inverter threshold as a reference. In the pulse generator pertaining to the aspect of the present invention, shoot-through currents flowing in the CMOS inverter is represented as a triangle in a current versus voltage characteristic diagram of the CMOS inverter, in which values of the input voltage to the CMOS inverter is indicated on a voltage axis of the current versus voltage characteristic diagram, a maximum value of the shoot-through current is defined as a height of the triangle, the inverter threshold is defined as a voltage providing the maximum of the shoot-through current, and the simultaneous-conduction regime is defined as a length of a bottom side of the triangle. And furthermore, in the pulse generator pertaining to the aspect of the present invention, a resistance value of the resistive element is selected such that a potential drop by the shoot-through current when the maximum value of the shoot-through current flows through the resistive element provide a deviation of the input voltage from the simultaneous-conduction regime, and a train of spike-shaped pulses is delivered from the output circuit, by repeating process of conductions and interruptions of the shoot-through current. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a block diagram illustrating a pulse generator pertaining to a first embodiment of the present invention; 
         FIG. 2  is a circuit diagram illustrating an outline of a CMOS inverter as an example of an output circuit in the pulse generator pertaining to the first embodiment; 
         FIG. 3  is a timing table illustrating each of time-series states of the resistor-connected complementary transistor-circuit, configured to explain a part of mechanisms for providing spike-train signals by the resistor-connected complementary transistor-circuit recited in  FIG. 2 ; 
         FIG. 4  is a circuit diagram of a resistor-connected complementary transistor-circuit as the output circuit of the pulse generator according to an experimental example; 
         FIG. 5A  is a view illustrating measured waveforms in the resistor-connected complementary transistor-circuit recited in  FIG. 4 ; 
         FIG. 5B  is an enlarged view of  FIG. 5A  illustrating an enlarged portion of the measured oscillation waveforms; 
         FIG. 6A  is a circuit diagram illustrating a resistor-connected complementary transistor-circuit implemented by a double-stage CMOS inverter pertaining to a second embodiment of the present invention; 
         FIG. 6B  is a circuit diagram illustrating an example of a complementary circuit implemented by a NAND gate; 
         FIG. 6C  is a circuit diagram illustrating an example of a complementary circuit implemented by an AND gate; 
         FIG. 7  illustrates experimental results for explaining that a reproducibility (controllability) of the spike-train signals is improved by the output circuit recited in  FIG. 6A ; 
         FIG. 8  is a view illustrating simulation results of transmission characteristics and current characteristics of the CMOS inverter; 
         FIG. 9  illustrates measured data of the transmission characteristics and current characteristics of the CMOS inverters; 
         FIG. 10  is a diagram illustrating power-supply voltage vs. shoot-through current characteristics of the resistor-connected complementary transistor-circuit, which implements the output circuit; 
         FIG. 11  is a diagram illustrating relationships between resistive values and input voltages of resistive elements, according to the pulse generator pertaining to the second embodiment; 
         FIG. 12  is a block diagram illustrating a part of a neural network, as an application example of the pulse generator pertaining to the first embodiment; 
         FIG. 13  is a flowchart illustrating an example of basic operations of a first neuron circuit recited in  FIG. 12 ; and. 
         FIG. 14  is a schematic circuit diagram illustrating an outline of an amoeba computer embracing octuple pseudopodia-units, to which the pulse generators pertaining to the first and second embodiment are applied, configured to generate the fluctuations by the mechanism of the amoeba computer. 
     
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     In general, when a voltage at levels of intermediate values (hereafter, referred as “intermediate-level potential”) of an inter-terminal voltage of a CMOS inverter, or a voltage near the intermediate-level potential is applied to an input terminal of the CMOS inverter, because a pMOS transistor and an nMOS transistor are turned on simultaneously, a phenomenon that a shoot-through current flows in the CMOS inverter occurs. As recited in Texas Instruments, output voltages are uncertain and become unstable when the shoot-through current flows (refer to White Paper of Texas Instruments Inc., SLLA364a, April 2017-May 2017 Revision). However, the present inventors have studied carefully the behaviors of simultaneous-conductive states very hard, and finally, have found that the oscillations caused by the simultaneous-conductive state, which were previously avoided as unstable oscillations, can be used and exploited as “a controlled spontaneous spike-train signal”. 
     Hereafter, first and second embodiments are exemplified as a technology in which the oscillations caused by the simultaneous-conductive state that were conventionally considered to be unstable can be utilized and leveraged as the controlled spike-train signal. In the description of the drawings, the identical or similar parts are denoted by the identical or similar reference numerals, and redundant descriptions thereof will be omitted. However, the drawings are schematic, and the relationship between the thickness and the plane dimensions, the ratio of the thickness of each layer, etc., may be different from the actual one. In addition, dimensional relations and ratios may also differ between the drawings. 
     Further, the first and second embodiments illustrated below exemplify the apparatus and methods for embodying the technical idea of the present invention, and the technical idea of the present invention does not specify the material, shape, structure, arrangement, or the like of the components as follows. 
     First Embodiment 
     As illustrated in  FIG. 1 , a pulse generator  10  pertaining to a first embodiment of the present invention encompasses an output circuit  11 , which can provide spike-train signals as output voltages V out , and a voltage source  12  for supplying specific input voltages V in  to the output circuit  11 . The output circuit  11  embraces “a resistor-connected complementary transistor-circuit” illustrated in  FIG. 2 . The resistor-connected complementary transistor-circuit includes a CMOS inverter, which is a complementary circuit whose lower voltage side terminal is connected to a lower-potential power-supply V SS , and a resistive element R C  connected between a higher-potential power-supply V DD  and a higher voltage side terminal of the complementary circuit. The complementary circuit in the pulse generator pertaining to the first embodiment is implemented by a single-stage CMOS inverter, and the single-stage CMOS inverter is implemented by a pMOS transistor Q P  whose source terminal (source electrode), which serves as the higher voltage side terminal of the CMOS inverter, is connected to the resistive element R C , and an nMOS transistor Q N , of which a drain terminal (drain electrode) is connected to a drain terminal of the pMOS transistor Q P . A source terminal of the nMOS transistor Q N , which serves as the lower voltage side terminal of the CMOS inverter, is connected to the lower-potential power-supply V SS . 
     According to the pulse generator pertaining to the first embodiment, a connection node between the resistive element R C  and the source terminal of the pMOS transistor Q P  is defined as “a higher-potential side node V C ”, in the configuration of the resistor-connected complementary transistor-circuit illustrated in  FIG. 2 . An electric connection node between a gate terminal (gate electrode) of the pMOS transistor Q P  and a gate terminal (gate electrode) of the nMOS transistor Q N  implements an input terminal of the CMOS inverter. The higher-potential power-supply V DD  is, for example, the power supply of a positive potential V DD , and the lower-potential power-supply V SS  is, for example, a ground potential (=0 volt). In a normal using method of a CMOS inverter, pulses having an amplitude of a rated inter-terminal voltage of the CMOS inverter, or pulsating waves having amplitude voltage (peak value)=input voltage V in , are entered to the input terminal of the CMOS inverter, and the CMOS inverter is accordingly made to act as an inverter, or NOT gate. 
     That is, the pulse generator pertaining to the first embodiment does use very consciously an intermediate-level potential (≈a simultaneous-conduction voltage) V 1/2  of the CMOS inverter, which is typically inhibited when the CMOS inverter is used, and conversely ventures to use “potentials lying in a specific limited latitude” as the input voltage V in  of the CMOS inverter at predetermined timings. As a result, it is possible to establish the pulse generator that can control a spike train frequency with simple and compact circuit topology, and therefore, a great number of the pulse generators can be easily installed in a complex computer system. In order to control operations caused by the inflows of the shoot-through currents that were conventionally considered to induce unstable oscillations, the voltage source  12  in the pulse generator  10  pertaining to the first embodiment has speculated various voltage drops caused by the resistive element R C , and defines “a swing-center potential V th_c ” as represented by following Eq. (1): 
         V   in   =V   th_c +½(Δ V   th0   +ΔV   non-os ) cos (ω t )  (1).
 
     Defining the swing-center potential V th_c  in Eq. (1) at a middle of voltage swings, and by feeding the input voltage V in , which swings with minute amplitudes within a range between an upper limit value (V th_c +ΔV th0/2 ) and a low limit value (V th_c −ΔV th0/2 ) of a simultaneous-conduction regime ΔV th0 , to the resistor-connected complementary transistor-circuit pertaining to the first embodiment, it is possible to generate the spike-train signals of which a pulse width and a frequency are controlled. 
     As well known, an inverter threshold V th  of a CMOS inverter can be represented by following Eq. (2): 
     
       
         
           
             
               
                 
                   
                     V 
                     th 
                   
                   = 
                   
                     
                       
                         V 
                         C 
                       
                       - 
                       
                         
                           ❘ 
                           &#34;\[LeftBracketingBar]&#34; 
                         
                         
                           V 
                           th_p 
                         
                         
                           ❘ 
                           &#34;\[RightBracketingBar]&#34; 
                         
                       
                       + 
                       
                         
                           V 
                           th_n 
                         
                         ⁢ 
                         
                           
                             
                               β 
                               n 
                             
                             / 
                             
                               β 
                               p 
                             
                           
                         
                       
                     
                     
                       1 
                       + 
                       
                         
                           
                             β 
                             n 
                           
                           / 
                           
                             β 
                             p 
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   2 
                   ) 
                 
               
             
           
         
       
     
     In a case of the usual CMOS inverter, the inverter threshold V th  is defined on an I-V characteristics diagram illustrated  FIG. 8 , which will be referred later. Namely, delineating a triangle as represented by a solid line in  FIG. 8 , the inverter threshold V th  is defined on a voltage axis of the I-V characteristics diagram, such that the inverter threshold V th  is a voltage at which a vertical line passing through an apex of the triangle crosses the voltage axis. In Eq. (2), V th_p  is a gate threshold voltage of the pMOS transistor Q P , and V th_n  is a gate threshold voltage of the nMOS transistor Q n . Also, ß p  is a coefficient that determines drain current versus drain voltage characteristics in a saturation region of the pMOS transistor Q P  as represented by Eq. (9b), which will be explained later. Similarly, ß n  is a coefficient that determines drain current versus drain voltage characteristics in a saturation region of the nMOS transistor Q N  as represented by Eq. (9a), which will be explained later. Each of ß p  and ß n  is a parameter based on element structures, such as a thickness of a gate insulating film, a gate length and others. In a case of silicon (Si), the electron mobility μ n  is about three times the hole mobility μ h . Thus, when the pMOS transistor Q P  and the nMOS transistor Q N  are assumed to be perfectly equal in various element structures such as the thickness of the gate insulating film and others, (ß n /ß p ) 1/2 =1.73 in Eq. (2). 
     The input voltages V in , for which the pMOS transistor Q P  and the nMOS transistor Q N  are scheduled to be turned on simultaneously, has a span corresponding to a width defined by a specific limited latitude, as illustrated in the triangle delineated by the solid line in  FIG. 8 . And therefore, the input voltages V in  for simultaneous conduction is not a voltage value at a point given by the inverter threshold V th . The swing-center potential V th_c  represented in the first term on the right side of Eq. (1) is a direct current (DC) component. Although the swing-center potential V th_c  in the first term on the right side of Eq. (1) may be determined by a voltage based upon the inverter threshold V th , when the shoot-through current flows through the usual CMOS inverter, the swing-center potential V th_c  is a voltage that shall be corrected and adjusted, as represented by Eq. (7a), which will be explained later. As can be understood from Eq. (2), the inverter threshold V th  is not based on the resistor value of the resistive element R C . To the contrary, the swing-center potential V th_c  in the first term on the right side of Eq. (1) is a value based on the resistor values of the resistive elements R C , although the swing-center potential V th_c  is defined as a value when the shoot-through current does not flow through the resistive element R C . 
     The simultaneous-conduction regime ΔV th0  implements a part of an amplitude of an alternating current (AC) component cos (ωt) represented in the second term on the right side in Eq. (1). The simultaneous-conduction regime ΔV th0  is a voltage span corresponding to a length of a bottom side of the triangle delineated by the solid line in  FIG. 8 , and a voltage represented by Eq. (25a), which will be explained later. An additional wingspan ΔV non-os  implements extended another part of the amplitude of the AC component cos (ωt) of the second term on the right side in Eq. (1). The additional wingspan ΔV non-os  is a voltage span corresponding to a width of a supplemental region collateral to both sides of the bottom side in the triangle delineated by the solid line in  FIG. 8 . The actual additional wingspan ΔV non-os  is divided into two. Then, ΔV non-os /2 is extended toward a higher-potential power-supply side of the simultaneous-conduction regime ΔV th0 , and ΔV non-os /2 is extended toward a lower-potential power-supply side of the simultaneous-conduction regime ΔV th0 . The additional wingspan ΔV non-os  that becomes the total width of the two halved ΔV non-os /2+ΔV non-os /2 may be selected as about ⅓ to two times of the simultaneous-conduction regime ΔV th0 , preferably about ½ to ⅚ times. The meaning of the AC component of the second item on the right side in Eq. (1) lies in a condition such that the amplitude of the input voltage V in  shall swing in between a maximum value and a minimum value, the maximum value and the minimum value are defined as the upper and lower edges of the additional wingspan ΔV non-os , as the amplitude of the input voltage V in  swings to extend over the span of the simultaneous-conduction regime ΔV th0  toward regions in the span of the additional wingspan ΔV non-os  in the output circuit  11  pertaining to the first embodiment. 
     A shoot-through current will flow through the CMOS inverter, as input voltages V in  represented by Eq. (1) are applied to the gate terminal of the pMOS transistor Q P  and the gate terminal of the nMOS transistor Q N , and when the potential of the input voltage V in  is plunged into “an oscillation-drive active (ODA) range” defined in the span of the simultaneous-conduction regime ΔV th0 , according to the circuit topology of the resistor-connected complementary transistor-circuit illustrated in  FIG. 2 . When the shoot-through current flows through the CMOS inverter, the potential of the higher-potential side node V C  is decreased owing to a resistance value of the resistive element R C . Thus, the resistive element R C  is an important component for the operation of the pulse generator pertaining to the first embodiment. For carry out the operations of the pulse generator to generate the voltage-spike trains, the alternating speeds in the AC component cos (ωt) of the second term on the right side in Eq. (1) are required to be sufficiently slower than the switching speeds of each of the pMOS transistor Q P  and the nMOS transistor Q N . Moreover, the alternating speed in the shoot-through current of the resistor-connected complementary transistor-circuit illustrated in  FIG. 2  and the alternating speed in the potential at the higher-potential side node V C  associated with the change of the shoot-through current is required to be approximately equal to the switching speeds of each of the pMOS transistor Q P  and the nMOS transistor Q N , or faster than the switching speeds of each of the pMOS transistor Q P  and the nMOS transistor Q N . 
     With regard to the resistance values of the resistive elements R C , together with the conditions of the switching speeds, the potential drops of the higher-potential side node V C , which are caused by the inflow of the shoot-through current, are required to comply with predetermined conditions. The values of the swing-center potentials V th_c  represented in the first term on the right side in Eq. (1) may be the fixed values that are predetermined by the resistance values of the resistive elements R C  or may be the variable values that can be set in view of the resistance values of the resistive elements R C . For determining the swing-center potentials V th_c  as the variable values based on the resistance values of the resistive elements R C , the voltage source  12  will prepare a lookup table (LUT), which indicates a relationship between the resistance values of the resistive elements R C  and the simultaneous-conduction voltages of the CMOS inverters from pre-performed experiments, and the values of the swing-center potentials V th_c , can be determined depending on the LUT. 
     In actuality, situations that voltages at both ends of the bottom side in the triangle exhibited in  FIG. 8 , which indicates the simultaneous-conduction regime ΔV th0  in Eq. (1), are insufficient to turn on the pMOS transistor Q P  and the nMOS transistor Q N  simultaneously, occur in many cases. Especially, the role of the potential drops in the higher-potential side node V C , which are caused by the inflows of the shoot-through currents to the resistive element R C , is important in the pulse generator pertaining to the first embodiment. Therefore, amount of the shoot-through current is required to be larger values close to the peak value (maximum value) ΔI C , which flows through the resistive element R C . The peak value (maximum value) ΔI C  of the shoot-through current is indicated as the height of the apex of the triangle exhibited in  FIG. 8 . So, “an effective drive span ΔV osc ” serving as the ODA range, in which the CMOS inverters effectively turn on simultaneously so that the potential of the higher-potential side node V C  can oscillate, is limited to a span narrower than the length of the bottom side in the triangle exhibited in FIG.  8 , in the circuit topology of the resistor-connected complementary transistor-circuit. The effective drive span ΔV osc  is defined as a narrower specific length of a bottom side in a format of Eq. (19a), which will be explained later, by using “an effective-drive-span setting (EDSS) coefficient A” that is a coefficient experimentally defined. Thus, Eq. (1) defining the input voltage V in , which is used in the pulse generator pertaining to the first embodiment, is represented by Eq. (3), by using the effective drive span ΔV osc . 
         V   in   =V   th_c +(½)(Δ V   osc   +ΔV   non-os ) cos (ω t )  (3)
 
     The swing-center potential V th_c  in Eq. (3) is the voltage determined in view of the inverter threshold V th0 , and the swing-center potential V th_c  typically differs from the inverter threshold V th0  as explained in Eq. (1). In Eq. (1), although the input voltage V in  is explained as the voltage that swings at least within the simultaneous-conduction regime ΔV th0  with respect to the swing-center potential V th_c , the input voltage V in  demonstrated in Eq. (3) swings in such a way that the effective drive span ΔV osc  serves as the ODA range of the CMOS inverter. According to the pulse generator pertaining to the first embodiment, the input voltage V in  being swinging in the ODA range is supplied to the input terminal of the CMOS inverter. The sum of the effective drive span ΔV osc  and the additional wingspan ΔV non-os  is assumed to be smaller than ½ of a voltage V C0  of an original higher-potential side node V C  in which the shoot-through current does not flow through the resistive element R C , as represented by Eq. (4a): 
       Δ V   osc   +ΔV   non-os   &lt;V   C0 /2  (4a).
 
     In many cases, because the experimentally defined EDSS coefficient A is about seven to fifteen, the following Eq. (4b) is approximated: 
       Δ V   osc   &lt;&lt;V   C0 /2  (4b).
 
     Also, the pulse trains may be steadily generated by setting the additional wingspan ΔV non-os =0, if the pulse generator pertaining to the first embodiment is not supposed to be in an intermittent mode, in which pulse trains are intermittently generated as wavelets after inverter intermission periods as illustrated in  FIG. 5A , which will be explained later. In a case that the intermittent pulse trains of the wavelet shape are not generated, if the effective drive span ΔV th0  is replaced to the effective drive span ΔV osc  serving as the ODA range, Eq. (3) can be represented by following Eq. (5a): 
         V   in   =V   th_c +(½)(Δ V   osc ) cos (ω t )  (5a)
 
       Δ V   osc   ≤ΔV   th0   (5b).
 
     The value of the effective drive span ΔV osc  in Eq.s (5a) and (5b) belongs to the ODA range in which the CMOS inverter is driven in such a way that spike-shaped pulse voltage trains are delivered from the output circuit  11  by turning on and off the shoot-through currents, and the ODA range may be indicated as a value sufficiently smaller than the simultaneous-conduction regime ΔV th0 . 
       Δ V   osc   &lt;&lt;ΔV   th0   (5c)
 
     Eq. (5c) means that, the voltage source  12  can transmit the input voltage V in  in such a way that an amplitude of an AC component, superimposed on a DC component of the input voltage V in , swings in a span sufficiently smaller than the simultaneous-conduction regime ΔV th0 , when the intermittent mode as illustrated in  FIG. 5A  is not targeted. As can be understood from later-described explanations, as well as Eqs. (5b) and (5c), by setting an amplitude variation ΔV osc /2 in the ODA range implemented by the AC component superimposed on the DC component of the input voltage V in  to a minute amplitude variation of the ODA range in a span smaller than the simultaneous-conduction regime ΔV th0 /2, it is possible to carry out a control such that a pulse width of a spike pulse swings in a narrower range. Moreover, as a limit in which the values of the effective drive spans ΔV osc  in Eq. (5a) is minimized, a constant voltage supply of DC voltage, in which the voltage source  12  supplies only the DC voltage of the swing-center potential V th_c  as a fixed value, can be provided. In a case that the voltage source  12  supplies the DC voltage, the pulse generator pertaining to the first embodiment becomes an oscillator. In a case that the voltage source  12  supplies the DC voltage on which the AC voltage is superimposed, the pulse generator pertaining to the first embodiment becomes an AD converter of pulse width modulation (PWM) scheme. In addition, in a case that the voltage source  12  is used as the constant voltage supply of DC voltage, if the DC voltage delivered from the constant voltage supply is made to have ripple components, the spike-train signals delivered by the output circuit  11  can have fluctuating components. Even if variation caused by thermal noise is superimposed on the DC voltage delivered from the constant voltage supply, the spike-train signals delivered by the output circuit  11  can be made to have the fluctuating components. The fluctuating component includes variation at a rising timing of the spike pulse—which is hereafter referred to as “a pulse-firing timing”—. 
     V C  represented in the first term of the component on the right side in Eq. (2) corresponds to a power-supply voltage of a usual CMOS inverter and is a fixed value. However, in the circuit topology of the resistor-connected complementary transistor-circuit illustrated in  FIG. 2 , V C  can be values of swinging values, correspondingly to the potentials V C  of the higher-potential side node V C . That is, in the pulse generator pertaining to the first embodiment, since the inverter threshold V t h is based on the voltage V C  of the higher-potential side node V C  illustrated in  FIG. 2 , Eq. (2) can be represented as a function of the voltage V C , as represented by following Eq. (6): 
         V   th   =f ( V   C )  (6).
 
     As can be understood from the technical content on the right side in Eq. (2), attention should be paid to a subject matter that the inverter threshold V th  is not always equal to an intermediate value V C /2 of the higher-potential side node V C . For example, if (ß n /ß p ) 1/2 =1.73 and |V th_p |=V th_n =1.5 volts are assumed, at a condition of V C =5 volts, the inverter threshold becomes V th =2.23 volts from Eq. (2). Thus, the inverter threshold V th  is a value lower than V C /2=2.5 volts. Only in a case of ß n =ß p  and |V th_p |=V th_n , the inverter threshold becomes V th =V C /2. Moreover, in the configuration of the resistor-connected complementary transistor-circuit illustrated in  FIG. 2 , the voltages of the higher-potential side node V C  are variables that induce potential drops caused by the resistive element R C , depending on the conductive states of the pMOS transistor Q P  and the nMOS transistor Q N . According to the pulse generator pertaining to the first embodiment, the inverter threshold V th  is known to be not a constant value, as illustrated by Eq. (6). 
     In light of Eq. (6), in the explanation of the pulse generator pertaining to the first embodiment, the inverter threshold V th  corresponding to the voltage V C0  on the original higher-potential side node V C  when the shoot-through current does not flow through the resistive element R C  is defined as “no-load inverter-threshold V th0 ”. That is, as a constant value necessary for the explanation of the input voltage V in  of the pulse generator pertaining to the first embodiment, the initial value of the inverter threshold V th  is defined as a reference value, because the first terms on the right sides in each of Eqs. (1) and (3) must be fixed values, respectively, as the first terms mean DC components, respectively. According to the pulse generator pertaining to the first embodiment, the no-load inverter-threshold V th0 =f(V C0 ) is used as the reference value, and the swing-center potential V th_c  represented in the first terms on the right sides in each of Eqs. (1) and (3) are represented by following Eq. (7a): 
         V   th_c   =V   th0   −ΔV   mod_H   (7a).
 
     ΔV mod_H  on the right side in Eq. (7a) is “a voltage-adjustment parameter” that is experimentally determined, in order to adjust the values of the swing-center potentials V th_c  represented in the first terms on the right sides in each of Eqs. (1) and (3) to reasonable values with respect to the no-load inverter-threshold V th0 . If the voltage-adjustment parameter is ΔV mod_H =0, V th_c =V th0  is established from Eq. (7a). However, adjustments based on experimental data are required, which will be explained later. The reason why “o” is appended to the end of the subscripts of the effective drive spans ΔV th0  of the second terms on the right sides in each of Eqs. (1) and (3) lies in the definition in  FIG. 8 . The effective drive span ΔV th0  is defined as a length of a bottom side of the triangle, setting the no-load inverter-threshold V th0  as a center of the bottom side, as can be understood from  FIG. 8 . The voltage-adjustment parameters ΔV mod_H  are the values depending on the resistance values of the resistive elements R C , as can be understood from  FIG. 11  described later. 
       Δ V   mod_H =η( R   C )  (7b)
 
     Then, the voltage-adjustment parameters ΔV mod_H  can be represented as a function η(R C ) of the resistance values of the resistive elements R C , as represented by the Eq. (7b). If the resistance value of the resistive element R C  is determined by a method of the present Specification, the method will be described later, the values of the voltage-adjustment parameters ΔV mod_H  are elected as the fixed values, from Eq. (7b). Thus, the first terms on the right sides in each of Eqs. (1) and (3) become fixed values. 
     In addition, in the configuration of the pulse generator  10  pertaining to the first embodiment illustrated in  FIG. 1 , it is allowed that a waveform-observing unit (output observation circuit) for measuring variations with respect to the output voltages V out  is installed on an output side of the output circuit  11 . And furthermore, when a voltage-generator controller is further installed on an input side of the voltage source  12 , data of the output voltages V out  can be fed back to the voltage-generator controller from the waveform-observing unit. That is, it is allowed that by the feedback data from the waveform-observing unit, the voltage-generator controller can control the voltage source  12 , and the voltage source  12  carries out a feedback control. In the feedback control, the values of the swing-center potential V th_c , the effective drive span ΔV osc  and the additional wingspan ΔV non-os  can be adjusted to optimal values, respectively, in view of the variations of the resistance values of the resistive element R C . According to the mechanism of the pulse generator  10  pertaining to the first embodiment, the phases of the input and the output are not always required to be inverted, differently from a case of a ring oscillator. Also, as explained with regard to Eq. (12), a function Φ(t) may be periodic signals such as a saw-tooth wave or a rectangular wave, or alternatively, may be non-periodic signals. Thus, various waveforms generators, such as a sinusoidal wave generator, a saw-tooth wave generator, a rectangular wave generator and others, may be employed as the voltage source  12 . Furthermore, the voltage-generator controller may control the voltage source  12  to provide the sinusoidal wave, the saw-tooth wave, the rectangular wave, or others, after controlling the voltage source  12  to select any one of various waveforms of the generating pulses, such as the sinusoidal wave, the saw-tooth wave, the rectangular wave, or others. 
     In  FIG. 8 , although the no-load inverter-threshold V th0 , serving as the reference of the swing-center potential V th_c  in Eqs. (1) and (3), is defined as the voltage at which the vertical line, passing through the apex of the triangle delineated by the solid line, crosses the voltage axis in I-V characteristic diagram, the no-load inverter-threshold V th0  corresponds to a central value of voltages at which shoot-through currents flow in usual CMOS inverters having no resistive load. As explained already, the voltages in the range spanning the length of the bottom side in the triangle delineated by the solid line in  FIG. 8  is the effective drive span ΔV th0  of the pulse generator pertaining to the first embodiment. The additional wingspan ΔV non-os  implementing a part of the amplitude of the AC component of the second terms on the right sides in Eqs. (1) and (3) is the total value of the widths of the voltage spans, each of which is expanded and defined by the width of ΔV non-os /2 in the shapes of wings on each of both sides of the bottom side in the triangle delineated by the solid line in  FIG. 8 . According to the pulse generator pertaining to the first embodiment, because the voltage V C0  of the original higher-potential side node V C  to which the shoot-through current does not flow is a fixed value (=V DD ), the no-load inverter-threshold V th0  is the fixed value. Therefore, the first terms on the right sides in each of Eqs. (1) and (3), based upon the no-load inverter-threshold V th0  as the reference, becomes the fixed values corresponding to the DC component. In the following, as the input voltage V in , the sinusoidal wave is assumed to be superimposed on the DC components prescribed by Eqs. (1) and (3). And, referring to a timing table illustrated in  FIG. 3 , the voltage source  12  will be explained such that the assumed input voltage V in  is fed to the output circuit  11 . 
     Pulse Generation Principle 
     In the timing table illustrated in  FIG. 3 , an input voltage V in  in which a sinusoidal wave, whose oscillation span is limited by an effective drive span ΔV osc , is superimposed on the DC component prescribed by Eq. (3) is assumed to be supplied to the output circuit  11  by the voltage source  12 . The uppermost row of the timing table illustrated in  FIG. 3  indicates an initial state in which the spike-train signal is not generated, at a timing of time T 0 . At time T 0 , with regard to the voltage source  12 , the input voltage V in  prescribed by Eq. (3) is assumed to be located on “H (high)” level higher than the swing-center potential V th_c  and exhibit a gradually decreasing trend in a sinusoidal wave cos (ωt) of a frequency ω toward the swing-center potential V th_c . At this time, the pMOS transistor Q P  is kept in cut-off state, and the nMOS transistor Q N  is also kept in conductive state. Thus, the output voltage V out  of the resistor-connected complementary transistor-circuit illustrated in  FIG. 2  becomes “L (Low)=0 V”. However, since the shoot-through current does not flow, the higher-potential side node V C  at the connection node between the resistive element R C  and the pMOS transistor Q P  is kept in the power-supply voltage V DD . 
     Although the timing table illustrated in  FIG. 3  exemplifies a case in which in the pulse generator pertaining to the first embodiment, the input voltage V in  in the initial state (time T 0 ) is located on the “H (high)” level higher than the swing-center potential V th_c , a case may be assumed in which the input voltage V in  is located on the “L” level lower than the swing-center potential V th_c  and exhibits a gradually increasing trend in the sinusoidal wave cos (ωt) of the second term on the right side in Eq. (3) toward the swing-center potential V th_c . Next, at time T 1 , the voltage source  12  gradually decreases the input voltage V in  toward the swing-center potential V th_c  from the voltage on the “H” level, in the sinusoidal wave of cos (ωt) represented at the second term on the right side. 
     When the input voltage V in  is gradually decreased in the sinusoidal wave of cos (ωt) represented at the second term on the right side and becomes lower than the upper limit value (V th_c +ΔV osc /2) of the effective drive span ΔV osc  and is plunged toward the swing-center potential V th_c  at a speed slower than a time constant of the CMOS inverter, a voltage V GS  between gate and source is biased in such a way that the pMOS transistor Q P  is turned on, while conductive state of the nMOS transistor Q N  is kept. When a potential with respect to holes just under the gate electrode of the pMOS transistor Q P  begins to drop in such a way that the pMOS transistor Q P  transits to conductive state, a displacement current is generated which is caused by gate capacitance such as a capacitance C GS  between gate and source in the pMOS transistor Q P . The displacement current induces a spike voltage capacitively generated in the pMOS transistor Q P  due to the instantaneous pseudo-short-circuit, the output voltage V out  is sharply risen from “L=0 V” to a value close to the voltage V C0  of the original higher-potential side node V C , which will be explained later with reference to  FIG. 5A . Since the value of the spike voltage is slightly smaller than the power-supply voltage V DD , the output voltage V out  is not perfectly increased to the height of the power-supply voltage V DD . Due to the variation of the potential just under the gate electrode of the pMOS transistor Q P , when a channel begins to be formed just under the gate electrode of the pMOS transistor Q P , the pMOS transistor Q P  enters a transient conductive state, and a conduction current begins to flow in a saturation region near a linear region of the pMOS transistor Q P . That is, since both pMOS transistor Q P  and nMOS transistor Q N  turn into conductive state, a shoot-through current I C  (&gt;0) as a DC current (conduction current) begins to flow through the CMOS inverter. 
     After the capacitive spike voltage is generated at time T 1 , the shoot-through current I C  begins to flow as the conduction current. Thus, at time T 2 , the potential of the higher-potential side node V C  is decreased from the power-supply voltage V DD =V C0  to a value represented by following Eq. (8): 
         V   C1   =V   DD   −R   C   I   (8).
 
     Here, R C  of Eq. (8) is the resistance value of the resistive element R C , and I is a current value of the shoot-through current I C , as a result that both of the pMOS transistor Q P  and the nMOS transistor Q N  turn into conductive state. As the potential of the higher-potential side node V C  is decreased from V C0  to V C1 , at time T 3 , the reference voltage necessary for the simultaneous-conductive state of the CMOS inverters is decreased from the original no-load inverter-threshold V th0  to an under-load inverter-threshold V th =f (V C1 )&lt;V th0 . 
     The current value I of the shoot-through current I C  in Eq. (8) depends on a current I DS_nMOS  between drain and source in the nMOS transistor Q N  and a current I DS_pMOS  between drain and source electrode of the pMOS transistor Q P . The current I DS_nMOS  between drain and source in the nMOS transistor Q N  is represented by following Eq. (9a), and the current I DS_pMOS  between drain and source electrode of the pMOS transistor Q P  is represented by following Eq. (9b): 
         I   DS_nMOS =(½)β n ( V   in   −V   th_n ) 2   (9a)
 
         I   DS_pMOS =(½)β p ( V   in   −V   th_p |) 2   (9b)
 
     The frequency ω of the sinusoidal wave of cos (ωt) represented at the second term on the right side in Eq. (3) is selected as a frequency that is sufficiently slower than each of the turn-on time and the turn-off time of the pMOS transistor Q P . And, at time T 4 , when the change of the input voltage V in  becomes faster than the variation of the frequency ω, and the reference voltage necessary for the simultaneous-conductive state of the CMOS inverters has decreased to an under-load inverter-threshold V th1 =f(V C1 ), the input voltage V in  becomes relatively larger than the under-load inverter-threshold V th1 , and therefore, the input voltage V in  becomes a potential at a level being deviated from the under-load conductive-spans ΔV th1 , which are defined on both sides of the under-load inverter-threshold V th1  at a center. 
         V   in   &gt;V   th1 +(½)Δ V   th1   (10)
 
     As represented in Eq. (10), when the input voltage V in  becomes relatively larger than the voltage of the upper edge of the under-load conductive-span ΔV th1 , whose reference is the under-load inverter-threshold V th1 , the pMOS transistor Q P  transits to cut-off state, and the nMOS transistor Q N  is kept in conductive state. When the pMOS transistor Q P  enters cut-off state, charges begin to be accumulated in the gate capacitance such as the capacitance C GS  between gate and source in the pMOS transistor Q P . Thus, at time T 5 , the output voltage V out  will decrease toward “L≈0 V”, and the shoot-through current I C  also decreases toward zero. Also, since the shoot-through current I C  does not flow as the conduction current, the higher-potential side node V C  is recovered from V C1 =(V DD −R C I) to the power-supply voltage V DD =V C0 . Since the shoot-through current I C  does not flow, the inverter threshold V th  necessary for the simultaneous-conductive state of the CMOS inverters is increased at time T 6 , and recovered from the under-load inverter-threshold V th1  at time T 4  to the original no-load inverter-threshold (initial value) V th0 =f(V C0 ). 
     At time T 7  at which the inverter threshold V th  necessary for the simultaneous-conductive state is recovered to the initial value V th0 , the input voltage V in  again approaches the swing-center potential V th_c  that is set with the original no-load inverter-threshold V th0 =f(V C0 ). 
         V   in   ≤V   th_c +(½)Δ V   th0   (11)
 
     When Eq. (11) is hold, the input voltage V in  becomes the state equal to the time T 1 . That is, as long as the input voltage V in , which swings according to the sinusoidal wave of cos (ωt) prescribed by Eq. (3), alters at a speed slower than a repetitive frequency of the spike-train signal, or slower than the time constant of the CMOS inverter, the states of the timings T 1  to T 7  are repeated, and therefore, the spike-train signals are delivered from the output circuit  11 . 
     When the reduction of the input voltage V in , caused by the sinusoidal wave of cos (ωt) at the second term on the right side in Eq. (3), brings to levels belonging to the range between the upper limit value (V th_c +ΔV osc /2) and the lower limit value (V th_c −ΔV osc /2) of the effective drive span ΔV osc  with the swing-center potential V th_c  at a center, the states of the timings T 1  to T 7  are repeated, and therefore, the output voltage V out  fluctuates. When the reduction of the input voltage V in , caused by the sinusoidal wave of cos (ωt) at the second term on the right side in Eq. (3), brings to levels exceeding the lower limit value (V th_c −ΔV osc /2) of the effective drive span ΔV non-os , and is further decreased to a level in a range at the additional wingspan ΔV non-os , the nMOS transistor Q N  transits to cut-off state, and the spike-train signal is not generated, and the signal of “H” level is delivered as the output signal from the output circuit  11 . 
     As more time elapses, after the variation of the sinusoidal wave of cos (ωt) at the second term on the right side in Eq. (3) has passed through the minimum value, the input voltage V in  begins to gradually re-rise obeying the sinusoidal wave of cos (ωt) to the swing-center potential V th_c  from the “L” side. When the variation of the input voltage V in  is increased to a value exceeding the lower limit value (V th_c −ΔV osc /2) of the effective drive span ΔV osc , the nMOS transistor Q N  transits to conductive state. Accordingly, the input voltage V in  arrives at the levels in which both of the pMOS transistor Q P  and the nMOS transistor Q N  can be turned on. When the input voltage V in  is slowly increased in the effective drive span ΔV osc , the operation states similar to the timings T 1  to T 7  are repeated, similarly to the timing table illustrated in  FIG. 3 . Since the operation states similar to the timings T 1  to T 7  are repeated, the output voltage V out  is fluctuated, and the spike-train signals are delivered from the output circuit  11 . As more time elapses, the sinusoidal wave of cos (ωt) at the second term on the right side in Eq. (3) becomes large. Then, when the input voltage V in  is increased to the “H” level up to a value exceeding the upper limit value (V th_c +ΔV osc /2) of the effective drive span ΔV osc , the spike-train signal is not generated, and the output signal from the output circuit  11  remains at “L≈0 V”. 
     On the basis of the pulse generation principle exemplified in the timing table illustrated in  FIG. 3 , in order to verify the operations in which the pulse generator represented in  FIGS. 1 and 2  generates the spike-train signal, the inventors of the present invention have trial manufactured the output circuit  11  of the resistor-connected complementary transistor-circuit as illustrated in  FIG. 4 . Although  FIG. 5B  is a view in which a time axis in  FIG. 5A  is extended,  FIGS. 5A and 5B  illustrate measured waveforms provided by the resistor-connected complementary transistor-circuit illustrated in  FIG. 4 . The power-supply voltage of the resistor-connected complementary transistor-circuit illustrated in  FIG. 4  is assigned to V DD =5 volts, and the resistance value of the resistive element R C  is set to be 200 ohms. Also, for the input voltage V in  when the spike-train signal is generated, 2.2 volts is applied as the swing-center potential V th_c  necessary for the simultaneous-conductive state. The value of V th_c =2.2 volts is low by 0.3 volt, as compared with the central value (V DD /2=2.5 volts) of the voltage between the higher-potential power-supply V DD  and the lower-potential power-supply (ground potential=0 volt). 
     If the variation of the sinusoidal wave of cos (ωt) at the second term on the right side in Eq. (3) provides levels belongs to the range between the upper limit value (V th_c +ΔV osc /2) and the lower limit value (V th_c −ΔV osc /2) of the effective drive span ΔV osc , the spike-train signals can be delivered. Thus,  FIG. 5A  intermittently illustrates quadruple groups of spike trains in all. That is,  FIG. 5A  illustrates a way the spike-train signals can be generated when the variation of the amplitude of the sinusoidal wave of cos (ωt) provides levels belongs to the range between the upper limit value (V th_c +ΔV osc /2) and the lower limit value (V th_c −ΔV osc /2) of the effective drive span ΔV osc . And  FIG. 5A  further illustrates a way the spike-train signal is not generated, when the amplitude of the sinusoidal wave of cos (ωt) is increased up to the levels exceeding the upper limit value (V th_c +ΔV osc /2) of the effective drive span ΔV osc  and increased. One group of spike trains on the left end side in  FIG. 5A  indicates a case in which the input voltage V in  prescribed by Eq. (3) is increased with the elapse of time, from a small amplitude on the “L” side and increased up to a value exceeding (V th_c −ΔV osc /2) and plunged into the effective drive span ΔV osc . At the moment of starting the operation in which both of the pMOS transistor Q P  and the nMOS transistor Q N  try to turn into conductive states, due to the generation of the displacement current caused by the gate capacitance of the pMOS transistor Q P , the output voltage V out  induces the spike voltages that are sharply risen up to the values close to the voltage V C0 =V DD  of the original higher-potential side node V C . 
     As can be understood from  FIG. 5A , a value of the spike voltage is about 4.2 volts slightly smaller than the power-supply voltage V DD =5 volts. Although the potential of holes just under the gate electrode of the pMOS transistor Q P  begins to be dropped, the pMOS transistor Q P  does not enters the perfect conductive state, and an on-resistance R ON_P  of the pMOS transistor Q P  is relatively high. When the potential of holes just under the gate electrode of the pMOS transistor Q P  begins to drop, the potential of electrons just under the gate electrode of the nMOS transistor Q N  rises and begins to move in a direction in which the potential is shifted from a saturation region to a linear region side. And, since the shoot-through current I C  is made to flow ascribable to the condition that both the pMOS transistor Q P  and the nMOS transistor Q N  enter an intermediate (insufficient) conductive state, the potential of the higher-potential side node V C  is decreased, which causes the pMOS transistor Q P  to enter cut-off state. Even if the pMOS transistor Q P  enters cut-off state, as illustrated in  FIG. 5A , the output voltage V out  does not become perfect zero-volt and has decreased to “L≈0 V” close to zero-volt. This is because at a stage at which the pMOS transistor Q P  enters cut-off state, the nMOS transistor Q N  is still kept in the transient conductive state close to the boundary between the linear region and the saturation region, and even an on-resistance R ON_N  of the nMOS transistor Q N  still is kept in the relatively high state. In light of the condition of the later-described Eq. (20), in the case of ß n &gt;ß p  prescribed by Eqs. (9a) and (9b), it is difficult for the current in the perfect saturation region to flow through the nMOS transistor Q N , and even the on-resistance R ON_N  is relatively high. As a result, a voltage drop caused by the on-resistance R ON_N  of the nMOS transistor Q N  is generated at a non-negligible magnitude. Thus, the output voltage V out  is not reached to a perfect zero-volt level. When the pMOS transistor Q P  enters cut-off state, the potential of the higher-potential side node V C  is recovered, which starts an operation for the pMOS transistor Q P  to try to enter again the transient conductive state. Such operations for alternating the conductive states and the cut-off states of the pMOS transistor Q P  generate the spike pulses, and the spike-train signals are delivered as the output voltage V out . 
     In this way, operations are repeated in which, when the input voltage V in  illustrated in  FIG. 3  is increased up to the levels exceeding the (V th_c −ΔV osc /2) in the time period of the left end in  FIG. 5A  and plunged into the effective drive span ΔV osc  at the speed slower than the time constant of the CMOS inverter, both pMOS transistor Q P  and nMOS transistor Q N  turn into conductive states. An operation in which the variation of the input voltage V in  is slower than the time constant of the CMOS inverter and both pMOS transistor Q P  and nMOS transistor Q N  try to enter the intermediate (partial) conductive state is repeated, thereby generating the spike-train signals. As can be understand from  FIG. 5A , the potential at the higher-potential side node V C  is also oscillated together with the voltage oscillation of the output voltage V out  as illustrated at the left end of  FIG. 5A . Also, even the shoot-through current I C  is oscillated together with the voltage oscillation of the output voltage V out  as illustrated at the left end of  FIG. 5A . 
     With the further elapse of time, the amplitude of the sinusoidal wave of cos (ωt) at the second term on the right side in Eq. (3) becomes large and is increased to the levels exceeding (V th_c +ΔV osc /2), and therefore, the levels of the sinusoidal wave of cos (ωt) are deviated from the effective drive span ΔV osc , then the generation of the spike-train signals is stopped. When the amplitude of the sinusoidal wave of cos (ωt) is increased to the “H” level exceeding (V th_c +ΔV osc /2), even in a case that the potential of the higher-potential side node V C  has decreased to V C1  by the shoot-through current I C , the pMOS transistor Q P  is kept in cut-off state because the input voltage V in  deviated from the effective drive span ΔV osc  of the CMOS inverter. If the pMOS transistor Q P  is kept in cut-off state, the accumulation of the charges in the gate capacitance of the pMOS transistor Q P  is kept. That is, focusing to the spike-train signals in the leftmost time period illustrated in  FIG. 5A , when the pMOS transistor Q P  enters cut-off state at the completion timing at the right edge in the leftmost time period (oscillation period), the pMOS transistor Q P  is kept in cut-off state, and the nMOS transistor Q N  is kept in conductive state after the right edge completion timing. That is, as illustrated in  FIG. 5A , in the time period after the completion of the generation of one group (cluster) of the leftmost spike trains, the output voltage V out  from the output circuit  11  is still “L≈0 V”. 
     As can be understood from Eq. (3), when the sinusoidal wave of cos (ωt) at the second term on the right side in Eq. (3) continues to be increased with the elapse of time, the input voltage V in  begins to decrease again and slowly after passing through the maximum value. When the input voltage V in  has decreased to a value smaller than (V th_c +ΔV osc /2), the input voltage V in  is plunged into the effective drive span ΔV osc  in the second oscillation period from the left in  FIG. 5A . Both pMOS transistor Q P  and nMOS transistor Q N  turn into conductive state, in the effective drive span ΔV osc  in the second oscillation period from the left in  FIG. 5A . And, a second cluster (one group) of spike trains in the second oscillation period from the left is generated because an operation for the pMOS transistor Q P  to repeat conductive state and cut-off state is repeated in the second oscillation period from the left in  FIG. 5A . The second cluster of spike trains in the second oscillation period from the left continues to be generated in the time period in which the peak value of the input voltage V in  belongs to the second effective drive span ΔV osc  in the second oscillation period from the left in  FIG. 5A . As illustrated in  FIG. 5A , even the potential at the higher-potential side node V C  is oscillated together with the voltage oscillation of the output voltage V out  in the second oscillation period from the left, which is located at the right of the timing of the output voltage V out =L in  FIG. 5A . Also, the shoot-through current I C  is oscillated together with the voltage oscillation of the output voltage V out  in the second oscillation period from the left in  FIG. 5A . 
     With the elapse of time, when the reduction of the sinusoidal wave of cos (ωt) at the second term on the right side in Eq. (3) is proceeded and the input voltage V in  is decreased beyond (V th_c −ΔV osc /2), the input voltage V in  is deviated from the effective drive span ΔV in  When the input voltage V in  has decreased to a potential deviated from the effective drive span ΔV osc , the nMOS transistor Q N  transits to cut-off state. That is, at the timing at which the potential of the higher-potential side node V C  is recovered to the voltage V C0  of the original higher-potential side node V C , after the potential of the higher-potential side node V C  has decreased to V C1  by the shoot-through current I C , the nMOS transistor Q N  enters cut-off state because the input voltage V in  is deviated from the effective drive span ΔV osc . When the pMOS transistor Q P  is kept in conductive state and the nMOS transistor Q N  is kept in cut-off state, the potential of the output voltage V out  is kept at a value close to the voltage V C0 =V DD  of the original higher-potential side node V C . In this way, if the nMOS transistor Q N  is kept in cut-off state, the spike-train signal is not delivered, and the signal of the “H” level is delivered as the output signal from the output circuit  11 . That is, in the time period after the completion of the generation of the second cluster of spike trains in the second oscillation period from the left in  FIG. 5A , although the output voltage V out  from the output circuit  11  is close to the power-supply voltage V DD , the output voltage V out  is located at the “H” level smaller than the power-supply voltage V DD . 
     With the further elapse of time, the amplitude of the sinusoidal wave of cos (ωt) at the second term on the right side in Eq. (3) becomes the minimum value. After that, the amplitude begins to be slowly increased from the minimum value. When the amplitude of the sinusoidal wave of cos (ωt) at the second term on the right side in Eq. (3) is gradually increased from the minimum value and exceeds (V th_c −ΔV osc /2), the input voltage V in  is plunged into the effective drive span ΔV osc  in the third oscillation period from the left in  FIG. 5A . When the variation of the input voltage V in  is increased to a value at which the input voltage V in  is plunged into the effective drive span ΔV osc , both pMOS transistor Q P  and nMOS transistor Q N  turn into conductive state. And, in the third oscillation period from the left, an oscillation in which an alternating operation for the pMOS transistor Q P  to repeat conductive state and cut-off state is repeated is generated, thereby generating a third cluster of spike trains in the third oscillation period from the left in  FIG. 5A . As illustrated in  FIG. 5A , the potential at the higher-potential side node V C  is oscillated together with the voltage oscillation of the output voltage V out  in the third oscillation period from the left in  FIG. 5A . Also, even the shoot-through current I C  is oscillated together with the voltage oscillation of the output voltage V out  in the third oscillation period from the left in  FIG. 5A . 
     With the further elapse of time, when the sinusoidal wave of cos (ωt) at the second term on the right side in Eq. (3) becomes large and the input voltage V in  is increased to the levels exceeding (V th_c +ΔV osc /2) and deviated from the effective drive span ΔV in  the generation of the spike-train signals is stopped. That is, in association with the increase of the amplitude of the sinusoidal wave of cos (ωt), when the input voltage V in  is increased to the “H” level exceeding (V th_c +ΔV osc /2), the input voltage V in  is deviated from the effective drive span ΔV osc . Thus, the pMOS transistor Q P  is kept in cut-off state. That is, when the pMOS transistor Q P  enters cut-off state at the timing at which it is located at the right edge of the spike-train signal in the third oscillation period from the left in  FIG. 5A , after the third oscillation period, the pMOS transistor Q P  is kept in cut-off state, and the nMOS transistor Q N  is kept in conductive state. That is, at the final timing of the third spike-train signal in the third oscillation period from the left in  FIG. 5A , when the input voltage V in  is increased to the “H” level exceeding (V th_c +ΔV osc /2), the pMOS transistor Q P  is kept in cut-off state, and the nMOS transistor Q N  is kept in conductive state. That is, as illustrated in  FIG. 5A , in the time period after the completion of the generation of the third cluster of the spike trains in the third oscillation period from the left in  FIG. 5A , the output signal from the output circuit  11  is still “L≈0 V”. 
     As represented by Eq. (3), the input voltage V in  continues to be increased in association with the variation of the sinusoidal wave of cos (ωt) at the second term on the right side, and after passing through the maximum value, the input voltage V in  begins to decrease again and slowly. When the input voltage V in  has decreased to the value smaller than (V th_c +ΔV osc /2), the input voltage V in  is plunged into the effective drive span ΔV osc  in the fourth oscillation period from the left in  FIG. 5A . As long as the input voltage V in  belongs to a level in the effective drive span ΔV osc  and the variation of the input voltage V in  is slower than the time constant of the CMOS inverter, the operation for both of the pMOS transistor Q P  and the nMOS transistor Q N  to try to be turned on is repeated, thereby generating the spike-train signals. As long as the variation of the input voltage V in  prescribed by Eq. (3) belongs to the level in the effective drive span ΔV osc  in the fourth oscillation period from the left in  FIG. 5A , it is a time period in which a fourth (namely, rightmost) cluster of the spike trains in the fourth oscillation period from the left continues to be generated. As illustrated in  FIG. 5A , the potential at the higher-potential side node V C  is oscillated together with the voltage oscillation of the output voltage V out  in the fourth oscillation period from the left in  FIG. 5A . Also, even the shoot-through current I C  is oscillated together with the voltage oscillation of the output voltage V out  in the fourth oscillation period from the left in  FIG. 5A . 
     With the further elapse of time, when the reduction of the sinusoidal wave of cos (ωt) at the second term on the right side in Eq. (3) is proceeded and the potential is decreased beyond (V th_c −ΔV osc /2), the potential of the input voltage V in  is deviated from the effective drive span ΔV osc . When the input voltage V in  has decreased to the potential deviated from the effective drive span ΔV in  the nMOS transistor Q N  transits to cut-off state and kept in cut-off state. Due to the deviation from the effective drive span ΔV osc  of the CMOS inverter, the nMOS transistor Q N  is kept in cut-off state. However, since the pMOS transistor Q P  is kept in conductive state, the potential of the output voltage V out  is kept at a value close to the voltage V C0 =V DD  of the original higher-potential side node V C . In the time period in which the pMOS transistor Q P  is kept in conductive state and the nMOS transistor Q N  is kept in cut-off state, the spike-train signal is not delivered, and the signal of the “H” level is delivered as the output signal from the output circuit  11 . That is, in the time period after the completion of the generation of the fourth cluster of the spike trains in the fourth oscillation period from the left in  FIG. 5A , the output signal from the output circuit  11  is at the “H” level, as illustrated at the right-hand side in  FIG. 5A . 
     The pulse generator represented in  FIGS. 1 and 2  can be considered to have an AD conversion function of pulse width modulation (PWM), which converts analog values of the swinging input voltages (input values) V in , on which the sinusoidal wave of cos (ωt) is superimposed, into digital values as pike-shaped pulses, although minute variations of the input voltage V in  cannot be read from the diagram illustrated in  FIG. 5A .  FIG. 5B  illustrates the fourth cluster of the spike trains in the fourth oscillation period from the left in  FIG. 5A  in which the time axis is extended, and generation of nonuple spike trains is demonstrated between 4.4 milliseconds and 6.1 milliseconds. 
       FIGS. 5A and 5B  illustrate that spontaneous spike-train signals are generated near 2.2 volts of the input voltage V in . In the illustration in  FIG. 5B  in which the time axis is extended, “fluctuation” is illustrated in which the slight variation of the input voltage V in  leads to the variations of pulse widths of spike-shaped pulses and pulse intervals, and pulse widths on the trailing side of the pulse trains are extended. That is,  FIG. 5A  illustrates macro “fluctuation” in which cluster (one group) of spike-train signals are generated intermittently and periodically, similarly to the AD conversion function of PWM scheme. On the other hand,  FIG. 5B  illustrates the generation of micro “fluctuation” in which the slight reduction of the input voltage V in  causes the increase of the pulse width of the spike-shaped pulses. Micro “fluctuation” can be also generated in the firing timings of the spike-shaped pulses by the slight variation of the input voltage V in , although the minute changes of the firing timings may be difficult to understand in  FIG. 5B . That is, since gain is high near the inverter threshold V th , the generations of the spike-shaped pulses are very sensitive to the fluctuations in the input potentials, and the pulse-firing timings are accordingly fluctuated. However, the fluctuations are not perfectly random fluctuations, and the variations of the pulse widths, pulse intervals and pulse-firing timings of the spike-shaped pulses can be somewhat controlled in a specific limited latitude, because the fluctuations are ascribable to the potentials of the input voltages V in . 
     That is, according to the pulse generator pertaining to the first embodiment, by slightly swinging the values of the input voltages V in  entered to the output circuit  11  to values near the swing-center potential V th_c  of the resistor-connected complementary transistor-circuit, the pulse widths and pulse intervals, which are delivered from the output circuit  11 , can be controlled as “the fluctuating signal controlled within a desirable latitude”. For example, the micro signals to be superimposed on the input voltage V in  fed from the voltage source  12  are not limited to the sinusoidal waves of cos (ωt) exemplified in Eq. (3) and may be a saw-tooth wave, a rectangular wave, and others. More generally, by using a function Φ(t) that varies depending on time t, which includes the saw-tooth wave, the rectangular wave, and others, Eq. (3) can be represented by following Eq. (12): 
         V   in   =V   th_c +(½)(Δ V   osc   +ΔV   non-os )Φ( t )  (12)
 
     That is, the function Φ(t) may be a periodically-varying signal or a non-periodically-varying signal. For example, as described already, in the case that the DC voltage is supplied from the voltage source  12  built in the pulse generator  10  in  FIG. 1 , without using the voltage source  12  as a constant voltage supply of a higher precision, even if the input voltage V in  on which minute ripple components are superimposed is designed to be delivered, the output circuit  11  can provide “a fluctuating signal” in which the fluctuations of the pulse widths, the pulse intervals, the pulse-firing timings, and others are controlled in a specific limited latitude. Even in a case that thermal noise is superimposed, since there is a limit to the wave height value (maximum voltage) of the thermal noise, it is possible to generate “the fluctuating signal controlled in a specific limited latitude”. Similarly, irregular signal waveforms such as thermal noise may be superimposed on a regular signal such as the sinusoidal wave, the saw-tooth wave, the rectangular wave, and others as the function Φ(t) represented at the second term on the right side in Eq. (12). 
     Pulse Generation Condition 
     As the pulse generation conditions of the output circuit  11  in the pulse generator pertaining to the first embodiment illustrated in  FIG. 2 , there are the following two requirements: 
     First Requirement 
     A first requirement is a capability of the inflow of the shoot-through current I C . That is, the first requirement needs a presence of an input voltage V in  for enabling the pMOS transistor Q P  and the nMOS transistor Q N , which implement the resistor-connected complementary transistor-circuit, to enter into a simultaneous-conductive state (ΔI C &gt;0), as represented by solid line in  FIG. 8 . And, by the operation for driving the pMOS transistor Q P  and the nMOS transistor Q N  transistors into the simultaneous-conductive state, the shoot-through current I C  is transiently increased by ΔI C  as the peak value. From an I C  curve illustrated in  FIG. 8 , it is possible to get an information of a gate threshold V th_p  of the pMOS transistor Q P  and an information of a gate threshold V th_n  of the nMOS transistor Q N . 
     Second Requirement 
     A second requirement requires a behavior such that the potential at the higher-potential side node V C  in the circuit topology illustrated in  FIG. 2  shall decrease by the generation of the shoot-through current I C  flowing through the resistive element R C , and the inverter threshold V th  necessary for the simultaneous-conductive state of the CMOS inverters shall be decreased. 
     In light of the first and second requirements, the conditions for determining the resistance values of the resistive elements R C  can be written as followings. 
         R   C   I   C0   &lt;V   DD   +V   th_p   −V   th_n   (13)
 
         R   C ( A′ΔI   C   +I   C0 )&gt; V   DD   +V   th_p   −V   th_n   (14)
 
         A′=Aβ   p   1/2 /(β n   1/2 +β p   1/2 )  (15)
 
     However, I C0  written on the left sides in Eqs. (13) and (14) is the value of unintentional (non-intended) shoot-through current I C  associated with sub-threshold currents in an initial state (V in =“H” or “L”) and leakage currents (leakage current between V DD  and V SS ), and I C0  is mainly composed of DC components. In the unintentional shoot-through current I C0 , components caused by non-ideal factors such as manufacturing processes and others are main, and the unintentional shoot-through current I C0  contains variability and dispersion. Coefficient A on the right side defining a resistance-value setting-coefficient A′ in Eq. (15) corresponds to “the EDSS coefficient”, which will be explained in Eq. (19a). The effective drive span ΔV osc  to achieve the voltage-oscillation of the higher-potential side node V C  can be determined in the span of the simultaneous-conduction regime ΔV th0  with the EDSS coefficient A, by making the CMOS inverter to operate in the simultaneous-conductive state effectively and sufficiently, and furthermore, by flowing the necessary shoot-through current. The EDSS coefficient A=1 corresponds to a condition that the pMOS transistor Q P  is strictly turned off due to the variation ΔV th0  of the inverter threshold V th0  necessary for the simultaneous-conductive state. Experimentally, in the range of the EDSS coefficient A≈7 to 15, for example, at A≈10, the spike-shaped pulses ares generated as illustrated in  FIGS. 5A and 5B . 
     Also, the resistance-value setting-coefficient A′ prescribed by Eqs. (14) and (15) is a value that is experimentally calculated from ß n  and ß p  with the EDSS coefficient A as a parameter. Usually, the resistance-value setting-coefficients are values of A′≈5 to 20, preferably, A′≈8 to 15. For example, the resistance-value setting-coefficient can be set as A′≈10. As explained already in Eq. (12), ß p  is the coefficient for determining drain currents in saturation region of the pMOS transistor Q P , and ß n  is the coefficient for determining drain currents in saturation region of the nMOS transistor Q N . Also, experimentally, the range of the resistive elements R C  that enables the pulses to be generated by the pulse generator pertaining to the first embodiment is a region slightly wider than a scope determined by inequality expressions in Eqs. (13) and (14). Moreover, the unintentional shoot-through current I C0  has the variations due to the non-ideal factors. Thus, the upper limits of the resistance values of the resistive elements R C  tend to be fluctuated. 
     Eq. (13) can be rewritten as in Eq. (16), by using the relation of the following Eq. (17). 
         V   th_n   &lt;V   C0   +V   th_p   (16)
 
     V C0  prescribed by Eq. (16) is the potential at the higher-potential side node V C  in the initial state in the circuit topology illustrated in  FIG. 2 , and can be represented, similarly to the already-explained Eq. (8), as follows: 
         V   C0   =V   DD   −R   C   I   C0   (17).
 
     Here, R C  of Eq. (17) is the resistance value of the resistive element R C . 
     In light of Eq. (16), in a case of a situation that the following Eq. (18) holds, the pMOS transistor Q P  and the nMOS transistor Q N  cannot be turned on simultaneously, for any input value (input voltage V in ). Thus, the shoot-through current cannot flow through the resistor-connected complementary transistor-circuit. 
         V   th_n   &gt;V   C0   +V   th_p   (18)
 
     In addition, when the transient shoot-through current I C  begins to flow, a potential at the higher-potential side node V C  is decreased, which leads to a possibility the potential at that the higher-potential side node V C  cannot comply with Eq. (16). However, even in the foregoing case, because the reduction of the potential at the higher-potential side node V C  causes one of the pMOS transistor Q P  and the nMOS transistor Q N  to transit to cut-off state, the shoot-through current I C  is stopped, and the potential at the higher-potential side node V C  is again increased. Hence, the potential at the higher-potential side node V C  is spontaneously returned to comply with Eq. (16). 
     The second requirement can be represented by following Eqs. (19a) to (19c). 
       Δ V   osc &gt;( V   C   +V   th_p   −V   th-n )/ A   (19a)
 
         V   C   =V   DD   −R   C   I   C   (19b)
 
         I   C   =I   C0   +ΔI   C   (19c)
 
     As explained in Eq. (15), “A” of a denominator on a right side in Eq. (19a) is the EDSS coefficient. The EDSS coefficient defines the effective drive span ΔV osc  required to make the CMOS inverters enter the effective simultaneous-conductive state, by which the valid shoot-through current can flow. Furthermore, the EDSS coefficient defines the effective drive span ΔV osc  required to achieve the voltage-oscillation of the higher-potential side node V C  in the span of the simultaneous-conduction regime ΔV th0 . Experimentally, the EDSS coefficient A is approximately equal to about seven to fifteen, and typically, A is approximately equal to about ten. 
     That is, if the input voltage V in  is set to the voltage within the effective drive span ΔV osc  with the swing-center potential V th_c  of the CMOS inverter at a center, the pMOS transistor Q P  and the nMOS transistor Q N  enter the simultaneous-conductive state that is effectively available, and the transient shoot-through current I C  is generated. At this time, since the voltage drop in the resistive element R C  causes the potential at the higher-potential side node V C  to be decreased, the inverter threshold V th  necessary for the simultaneous-conductive state of the CMOS inverters is decreased, and the input voltage V in  is relatively increased with respect to the swing-center potential V th_c . Because the simultaneous-conduction regime ΔV th0 , which is the amount of change in the inverter threshold V th0 , is finite as illustrated by the length of the bottom side in the triangle exhibited in  FIG. 8 , the pMOS transistor Q P  transits from conductive state to cut-off state, and the shoot-through current I C  is spontaneously decreased. 
     In principle, as prescribed by Eq. (3), in the initial state, the swing-center potential V th_c  of the input voltage V in  does not have to exactly coincide with the inverter threshold V th0  of the CMOS inverter, and allowable to have values close to the inverter threshold V th0 . In a state when the shoot-through current is flowing, the drain currents of the pMOS transistor Q P  and the nMOS transistor Q N  are required to coincide with each other. Thus, the condition of the following Eq. (20) is required. 
         I   DS_nMOS   =I   DS_pMOS   (20)
 
     The drain current I DS-nMOS  of the nMOS transistor Q N  prescribed by Eq. (20) is given by Eq. (9a) as explained already. Also, the drain current I DS_pMOS  of the pMOS transistor Q P  is obtained by Eq. (9b). 
     By substituting the right side of each of Eq.s (9a) and (9b) into Eq. (20), it is possible to derive the following Eqs. (21) and (22). 
     
       
         
           
             
               
                 
                   
                     V 
                     th 
                   
                   = 
                   
                     
                       
                         
                           
                             β 
                             n 
                           
                         
                         · 
                         
                           V 
                           
                             th 
                             . 
                             n 
                           
                         
                       
                       + 
                       
                         
                           
                             β 
                             p 
                           
                         
                         · 
                         
                           ( 
                           
                             
                               V 
                               C 
                             
                             + 
                             
                               V 
                               th_p 
                             
                           
                         
                       
                     
                     
                       
                         
                           β 
                           n 
                         
                       
                       + 
                       
                         
                           β 
                           p 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   21 
                   ) 
                 
               
             
           
         
       
       
         
           
             
               
                 
                   
                     Δ 
                     ⁢ 
                     
                       I 
                       C 
                     
                   
                   = 
                   
                     
                       1 
                       2 
                     
                     ⁢ 
                     
                       
                         
                           β 
                           n 
                         
                         ⁢ 
                         
                           β 
                           p 
                         
                       
                       
                         
                           β 
                           n 
                         
                         + 
                         
                           β 
                           p 
                         
                         + 
                         
                           2 
                           ⁢ 
                           
                             
                               
                                 β 
                                 n 
                               
                               ⁢ 
                               
                                 β 
                                 p 
                               
                             
                           
                         
                       
                     
                     ⁢ 
                     
                       
                         ( 
                         
                           
                             V 
                             C 
                           
                           + 
                           
                             V 
                             th_p 
                           
                           - 
                           
                             V 
                             th_n 
                           
                         
                         ) 
                       
                       2 
                     
                   
                 
               
               
                 
                   ( 
                   22 
                   ) 
                 
               
             
           
         
       
     
     If both numerator and denominator of Eq. (21) are divided by ß p   1/2 , and furthermore, V th_p  is defined as an absolute value to be expressed as a positive value, the result becomes the same as the already explained expression of Eq. (2). 
     For the sake of simplicity, the unintentional shoot-through current I C0  such as leakage current is assumed to be ignorable, because the unintentional shoot-through current I C0  can be regarded as being fully small compared with the peak value ΔI C  of the transient current variation illustrated in  FIG. 8 . If I C0 &lt;&lt;ΔI C , Eq. (22) can be represented as the following Eq. (23) by using Eqs (19b) and (19c). 
     
       
         
           
             
               
                 
                   
                     Δ 
                     ⁢ 
                     
                       I 
                       C 
                     
                   
                   = 
                   
                     
                       1 
                       2 
                     
                     ⁢ 
                     
                       
                         
                           β 
                           n 
                         
                         ⁢ 
                         
                           β 
                           p 
                         
                       
                       
                         
                           β 
                           n 
                         
                         + 
                         
                           β 
                           p 
                         
                         + 
                         
                           2 
                           ⁢ 
                           
                             
                               
                                 β 
                                 n 
                               
                               ⁢ 
                               
                                 β 
                                 p 
                               
                             
                           
                         
                       
                     
                     ⁢ 
                     
                       
                         ( 
                         
                           
                             V 
                             DD 
                           
                           - 
                           
                             
                               R 
                               C 
                             
                             ⁢ 
                             Δ 
                             ⁢ 
                             
                               I 
                               C 
                             
                           
                           + 
                           
                             V 
                             th_p 
                           
                           - 
                           
                             V 
                             th_n 
                           
                         
                         ) 
                       
                       2 
                     
                   
                 
               
               
                 
                   ( 
                   23 
                   ) 
                 
               
             
           
         
       
     
     Also, by solving a quadratic equation of the peak value ΔI C  in the transient current derived from Eq. (23), the following Eq. (24) is obtained as the solution of the peak value ΔI C  of the transient current variation illustrated in  FIG. 8 . 
     
       
         
           
             
               
                 
                   
                     Δ 
                     ⁢ 
                     
                       I 
                       C 
                     
                   
                   = 
                   
                     
                       
                         
                           1 
                           
                             R 
                             C 
                           
                         
                         [ 
                         
                           
                             
                               
                                 
                                   β 
                                   n 
                                 
                                 + 
                                 
                                   β 
                                   p 
                                 
                                 + 
                                 
                                   2 
                                   ⁢ 
                                   
                                     
                                       
                                         β 
                                         n 
                                       
                                       ⁢ 
                                       
                                         β 
                                         p 
                                       
                                     
                                   
                                 
                               
                               
                                 
                                   β 
                                   n 
                                 
                                 ⁢ 
                                 
                                   β 
                                   p 
                                 
                               
                             
                             ⁢ 
                             
                               1 
                               
                                 R 
                                 C 
                               
                             
                           
                           + 
                           
                             ( 
                             
                               
                                 V 
                                 DD 
                               
                               + 
                               
                                 V 
                                 
                                   th 
                                   
                                     - 
                                     p 
                                   
                                 
                               
                               - 
                               
                                 V 
                                 
                                   th 
                                   
                                     - 
                                     n 
                                   
                                 
                               
                             
                             ) 
                           
                         
                         ] 
                       
                       ⁢ 
                       ↵ 
                     
                     ± 
                     
                       
                         1 
                         
                           R 
                           C 
                         
                       
                       ⁢ 
                       
                         
                           
                             
                               
                                 
                                   
                                     [ 
                                     
                                       
                                         
                                           
                                             
                                               B 
                                               n 
                                             
                                             + 
                                             
                                               β 
                                               p 
                                             
                                             + 
                                             
                                               2 
                                               ⁢ 
                                               
                                                 
                                                   
                                                     β 
                                                     n 
                                                   
                                                   ⁢ 
                                                   
                                                     β 
                                                     p 
                                                   
                                                 
                                               
                                             
                                           
                                           
                                             
                                               β 
                                               n 
                                             
                                             ⁢ 
                                             
                                               β 
                                               p 
                                             
                                           
                                         
                                         ⁢ 
                                         
                                           1 
                                           
                                             R 
                                             C 
                                           
                                         
                                       
                                       + 
                                       
                                         ( 
                                         
                                           
                                             V 
                                             DD 
                                           
                                           + 
                                           
                                             V 
                                             th_p 
                                           
                                           - 
                                           
                                             V 
                                             th_n 
                                           
                                         
                                         ) 
                                       
                                     
                                     ] 
                                   
                                   2 
                                 
                                 - 
                               
                             
                           
                           
                             
                               
                                 
                                   ( 
                                   
                                     
                                       V 
                                       DD 
                                     
                                     + 
                                     
                                       V 
                                       th_p 
                                     
                                     - 
                                     
                                       V 
                                       th_n 
                                     
                                   
                                   ) 
                                 
                                 2 
                               
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   24 
                   ) 
                 
               
             
           
         
       
     
     As already explained in Eq. (3), the simultaneous-conduction regime ΔV th0  defines the voltages lying in the range spanning the length of the bottom side in the triangle by the solid line in  FIG. 8 . However, If we set V C =V DD  in  FIG. 8 , the simultaneous-conduction regime ΔV th0  will correspond to a length of a bottom side in a triangle represented by a solid line in  FIG. 9 . 
       Δ V   th0   =V   DD   +V   th_p   −V   th_n   (25a)
 
     So, under the assumption of Eq. (25a), by using a conductance G C  of the resistive element R C  and an element-structure parameter γ, the following Eqs. (25b) and (25c) will be held. 
         G   C =1/ R   C   (25b)
 
       γ=[β n +β p +2(β n β p ) 1/2 ]/(β n β p )  (25c)
 
     Then, Eq. (24) can be simplified and represented as the following Eq. (26): 
       Δ I   C   =G   C (γ G   C   +ΔV   th0 )± G   C [ G   C (γ G   C   +ΔV   th0 ) 2   −ΔV   th0 ) 2 ] 1/2   (26).
 
     In view of Eq. (25a), Eq. (26) can be represented as the following Eq. (27) in a format of a function F(R C , V DD ) of R C  and V DD , by using the resistance value R C  of the resistive element R C , such 
       Δ I   C   =F ( R   C   ,V   DD )  (27)
 
     Practically, the resistance value of the resistive element R C  is recursively determined by linking the peak value ΔI C  of the transient current variation, the resistance value of the resistive element R C  and the power-supply voltage V DD  with each other as represented by Eq. (27), and using the experimental data. A curve X running on the lower side in  FIG. 10  illustrates a relationship between the power-supply voltage V DD  and the unintentional shoot-through current I C0  when the input voltage is zero-volt. Also, a curve Y rising at the center in  FIG. 10  is a graph illustrating a relationship between the power-supply voltages V DD  and shoot-through currents (I C0 +ΔI C ), when the shoot-through currents are flowing in the CMOS inverter, by setting the input voltages to flow the shoot-through currents. 
     The resistance values of the resistive elements R C  will be determined, by using a load curve indicated by a dashed line in the power-supply voltage versus shoot-through current characteristics exhibited in  FIG. 10 . The load curve will be expressed by following Eq. (28): 
         I =(1/ R   C ) V   (28).
 
     An upper oblique line delineated on the upper side, which passes through a point (voltage: 2 volts; current: 3 milliamperes) and a point (voltage: 5 volts; current: 3 milliamperes) in  FIG. 10  is a load curve intersecting a current axis at 3 milliamperes and a voltage axis at 5 volts in I-V characteristic diagram. And, the upper oblique line as the load curve assumes: V DD =5 volts, R C =1 kilo-ohms and a resistance-value setting-coefficient A′=10. In  FIG. 10 , a lower oblique line delineated on the lower side, which passes through a point (voltage 2 volts; current: 0.3 milliampere) and a point (voltage 5 volts; current: 0 milliampere) is a load curve of R C =10 kilo-ohms, which intersects the current axis at 0.5 milliampere and the voltage axis at 5 volts in the I-V characteristic diagram. 
     Concretely, the curve X, which connects data points each of which is marked with open circles in  FIG. 10 , is a V DD −I C0  curve that indicates a case of R C =0, namely, a situation in which there is no resistive element R C  in  FIG. 2 . By the curve X, V DD −I C0  curve is obtained which indicates the relationship between V DD  and I C0  at a condition of V in =0 volt. The curve Y, which connects filled circles (indicated by dots) in  FIG. 10  is a curve in which measured data at a condition when the shoot-through current flows through the CMOS inverter are plotted, when the levels of V in  belong to the effective drive span ΔV osc , namely, the levels of V in  lie in the range between the upper limit value (V th_c +ΔV osc /2) and the lower limit value (V th_c −ΔV osc /2). By the curve Y, which connects the filled circles in  FIG. 10 , the V DD  vs. (I C0 +ΔI C ) curve is obtained which indicates the relationship between V DD  and the (I C0 +ΔI C ). With V DD −I C0  curve indicated by the curve X in  FIG. 10  and the V DD  vs. (I C0 +ΔI C ) curve indicated by the curve Y as a base, when ΔI C  is multiplied by the A′, V DD  vs. (I C0 +A′ΔI C ) curve is calculated which indicates a relationship between V DD  and the (I C0 +A′ΔI C ). 
     And, as illustrated in  FIG. 10 , a load curve of the resistive element R C  is illustrated with respect to V DD −I C0  curve and the V DD  vs. (I C0 +A′ΔI C ) curve. The resistance value of the resistive element R C  can be determined by selecting a resistance value of the resistive element R C , which satisfies the conditions indicated by following Eqs. (29) and (30). Namely, the selection of the resistance value of the resistive element R C  shall be determined by a position of the intersection of V DD −I C0  curve and the load curve, and by a position of the intersection of the V DD  vs. (I C0 +A′ΔI C ) curve and the load curve: 
         V   DD   −R   C   I   C0   &gt;V   th_n   −V   th_p   (29)
 
         V   DD   −R   C ( I   C0   +A′ΔI   C )&lt; V   th_n   −V   th_p   (30)
 
       FIG. 10  illustrates a case of V th_n −V th_p =2.94 volts. 
     In addition, in the resistor-connected complementary transistor-circuit, the gate threshold V th_p  of the pMOS transistor Q P  and the gate threshold V th_n  of the nMOS transistor Q N  can be estimated from I C −V in  characteristics under a condition when the resistive element R C  is not inserted. For example, the gate threshold V th_p  and the gate threshold V th , can be estimated by the simulation result in  FIG. 8  and the measured data in  FIG. 9 . Also, since ΔI C &gt;&gt;I C0 , V DD  vs. A′(I C0 +ΔI C ) curve can be used in place of the V DD  vs. (I C0 +A′ΔI C ) curve. Under the condition when ΔI C &gt;&gt;I C0 , the desirable resistance value of the resistive element R C  can be obtained by multiplying the resistance value acquired from the load curve by A′, even if not multiplying ordinate of the V DD  vs. (I C0 +ΔI C ) curve by A′. The subject matter in the technical idea of the pulse generator pertaining to the first embodiment lies in the reduction in the potential levels of the higher-potential side node V C  of the CMOS inverter when the shoot-through current flows. Thus, the resistive element R C  is not always limited to the concrete circuit arrangement that is physically designed as the real circuit elements exemplified in  FIG. 2 , and it is natural that the resistive element R C  can be replaced with a mechanism or stray elements whose function is equivalent to the resistive element R C . Thus, when the term of “the resistive element R C ” is referred in the explanation of the pulse generator pertaining to the first embodiment, the term of the resistive element R C  can include the various mechanisms each of which has an action, a behavior, and a performance equivalent to the resistive element R C . As an example of the mechanism or stray elements whose action, behavior, or performance is equivalent to the resistive element R C , there is a case in which inner stray resistance exists in a power supply, and there is a case of tracking delay caused by load fluctuation when an output impedance of a power-supply apparatus is not sufficiently larger than the load impedance. For example, even the fluctuation of the power-supply voltage in a step-up and step-down circuit of an AC adaptor can serve as the action, behavior, or performance equivalent to the resistive element R C . 
     As mentioned above, according to the pulse generator pertaining to the first embodiment, the output circuit  11  for delivering the spike-train signals is implemented by the single-stage CMOS inverter, and to the CMOS inverter, the resistive element R C  is connected in series between the higher-potential power-supply V DD  and the pMOS transistor Q P , and the resistor-connected complementary transistor-circuit is constructed. And, in light of the voltage drop caused by the resistive element R C , with the swing-center potential V th_c  as represented by Eq. (12) as the reference potential, by applying the input voltage V in , which is minutely variated in the range between the upper limit value (V th_c +ΔV osc /2) and the lower limit value (V th_c −ΔV osc /2) of the effective drive span ΔV osc , to the resistor-connected complementary transistor-circuit, it is possible to deliver the spike-train signals of which the pulse width and the frequency are controlled. Thus, according to the pulse generator pertaining to the first embodiment, since the circuit topology is simple and compact configuration, it is easy to install many pulse generators in the complex computer system, and it is possible to provide the pulse generator that can perform the control in which the fluctuations of the pulse width, the frequency and others are moderate, being controlled in a limited latitude. 
     Neural Network 
     An example will be explained in which the pulse generator pertaining to the first embodiment is applied to a neuron circuit of a neural network. That is, hereafter, a neural network is explained in which the pulse generator pertaining to the first embodiment is used in a neuron circuit for transmitting and receiving information through voltage spike. 
     As a part of the structure is schematically illustrated in  FIG. 12 , a first neuron circuit  1 A and a second neuron circuit  1 B transmit and receive the information through a first output voltage V out1  and a second output voltage V out2  in a neural network such as SNN. Since the first neuron circuit  1 A and the second neuron circuit  1 B are equal in the configuration, here, the configuration of the first neuron circuit  1 A is explained as an example. 
     As illustrated on the left side in  FIG. 12 , the first neuron circuit  1 A includes a pulse generator  2  for transmitting voltage spikes, a detector  3  for detecting an input-information I, and a controller  4  for controlling the frequency and timings of the voltage spikes by the input-information I. The pulse generator  2  includes, for example, the pulse generator recited in the first embodiment, as explained in  FIGS. 1 and 2 . 
     And, when detecting the specific input-information I, the detector  3  notifies the detection of the specific input-information I to the controller  4 . As illustrated in Step S 1  in  FIG. 13 , when receiving a notification (excitability) indicating the detection of the specific input-information I from the detector  3 , the controller  4  checks a second voltage spikes (feedback information: inhibitory) from the second neuron circuit  1 B, in Step S 2 . And, in Step S 3 , the controller  4  determines the frequency and timings of the voltage spikes (firing) as the first output voltage V out1 , by the specific input-information I and a second feedback information V out2 . 
     For transmitting the voltage spikes having the determined frequency and timings, the controller  4  applies an input voltage V in  to the pulse generator  2  at a predetermined timing. In a period while receiving the input voltage V in , the pulse generator  2  supplies the voltage spikes as the first output voltage V out1  to the second neuron circuit  1 B. 
     In this way, although the controller  4  tries to deliver the voltage spikes ascribable to the specific input-information (excitability), the frequency and firing timing of the voltage spikes are adjusted by the feedback information (inhibitory). With the repetition of the operations, the output voltage V out1  of the first neuron circuit  1 A is converged in a direction in which the voltage spikes are delivered, or a direction in which the voltage spikes are not delivered. In recent years, attention is paid to the research of firing timings of spike pulses in the neuron circuit. However, by using the pulse generator recited in the first embodiment, it is possible to control the fluctuation of the frequency and timings of the firing of the spike pulses within a specific limited latitude and generate the spike pulses. 
     As mentioned above, according to the neural network pertaining to the application example of the first embodiment, it is possible to achieve AI computer architecture having a performance compatible to mammal-like brain, by using the compact pulse generator explained in  FIGS. 1 and 2  to the first neuron circuit  1 A and the second neuron circuit  1 B. That is, even in a case that the huge number of pulse generators  2  are required such as the AI computer architecture, performance of which is addressing to a level compatible to the mammal-like brain, the large number of pulse generators can be monolithically integrated in a single chip, because the pulse generator  2  pertaining to the first embodiment is compactly structured. Thus, according to the pulse generator  2  pertaining to the first embodiment, it is possible to achieve robots, moving vehicles, mobile objects and others each of which has AI computer architecture whose information processing capability is improved more and more due to the neural network such as SNN where the huge number of pulse generators  2  are integrated. 
     Second Embodiment 
     As “a complementary circuit”, an output circuit  11  pertaining to a second embodiment of the present invention encompasses a first CMOS inverter  11   a  and a second CMOS inverter  11   b  connected in parallel configured to implement a ladder-shaped two-stage structure, as illustrated in  FIG. 6A . Similarly to the circuit diagram illustrated in  FIG. 2 , each of the first CMOS inverter  11   a  at the first stage (initial stage) and the second CMOS inverter  11   b  at the second stage includes a pMOS transistor Q P  and an nMOS transistor Q N . However, in the pulse generator pertaining to the second embodiment, “the resistor-connected complementary transistor-circuit” is constructed, in which one resistive element R C =20 kilo-ohms is commonly connected in series to a parallel circuit of the first CMOS inverter  11   a  and second CMOS inverter  11   b , to implement the complementary circuit composed of double CMOS inverters. Both first CMOS inverter  11   a  and second CMOS inverter  11   b , which implement the complementary circuit, share the resistive element R C  as a series-connected element, and realize the resistor-connected complementary transistor-circuit. And, as illustrated in  FIG. 6A , both of the inverter  11   a  and the inverter  11   b  are connected between the higher-potential power-supply V DD  (V DD =7 volts) and the ground potential (lower-potential power-supply), and thereby, implementing the output circuit  11  in the pulse generator pertaining to the second embodiment. 
     The operation of the first CMOS inverter  11   a  at the first stage (initial stage) in the pulse generator pertaining to the second embodiment can be described along the timing table illustrated in  FIG. 3  used in the explanation of the pulse generator pertaining to the first embodiment as already explained. At first, in the voltage source  12  installed in the pulse generator pertaining to the second embodiment, a signal of sinusoidal wave with cos (ωt) is supposed to be superimposed on the DC component prescribed by Eq. (3) as the input voltage V in  at time T 0  in an initial condition, similarly to the timing table illustrated in  FIG. 3 . At time T 0 , a level of the sinusoidal wave of cos (ωt) of the input voltage V in  prescribed by Eq. (3) is assumed to be a “H” level, which is higher than a swing-center potential V th_c  of the first CMOS inverter  11   a  at the first stage. 
     At time T 0 , the pMOS transistor in the first CMOS inverter  11   a  at the first stage is kept in cut-off state, while the nMOS transistor in the first CMOS inverter  11   a  is kept in conductive state. Thus, the output voltage V out  of the first CMOS inverter  11   a  illustrated in  FIG. 6A  is “L≈0 V”. When the output voltage V out  of the first CMOS inverter  11   a  becomes the voltage of the “L” level, the pMOS transistor in the second CMOS inverter  11   b  at the second stage transits to conductive state, while the nMOS transistor in the second CMOS inverter  11   b  is kept in cut-off state. Although the output voltage V out  of the second CMOS inverter  11   b  becomes the “H” level, the higher-potential side node V C  defined as a connection node between the resistive element R C  and a common node of the first CMOS inverter  11   a  and the second CMOS inverter  11   b  is kept in the power-supply voltage V DD =7 volts. 
     According to Eqs. (2) and (6), the inverter threshold V th  of each of the first CMOS inverter  11   a  and the second CMOS inverter  11   b  depends on the power-supply voltage V C  of each of the first CMOS inverter  11   a  and the second CMOS inverter  11   b . That is, in the pulse generator pertaining to the second embodiment, the inverter threshold V th  of the first CMOS inverter  11   a  depends on the voltage V C  of the higher-potential side node V C  illustrated in  FIG. 6A , and the swing-center potential V th_c  is also depending on the voltage V C  of the higher-potential side node V C . Similarly to the behavior in the timing table illustrated in  FIG. 3 , when the input voltage V in  fed from the voltage source  12  at time T 1  has decreased to the value smaller than (V th_c +ΔV osc /2), in accordance with the sinusoidal wave of cos (ωt) prescribed by Eq. (3), the first CMOS inverter  11   a  is plunged into the operation region in the effective drive span ΔV osc . 
     When the AC component of the input voltage V in  swings at a speed slower than a time constant of the first CMOS inverter  11   a , and the potential of the input voltage V in  arrives to a level in the effective drive span ΔV in  an operation is started in which both pMOS and nMOS transistors in the first CMOS inverter  11   a  try to turn on. When the operation is started in which both pMOS and nMOS transistors in the first CMOS inverter  11   a  try to turn on is started, a displacement current is generated which is caused by gate capacitance such as a capacitance C GS  between gate and source in the pMOS transistor. Then, the displacement current induces a spike voltage by which the output voltage V out  of the first CMOS inverter  11   a  is sharply risen to a value close to the voltage V C0 =V DD  of the original higher-potential side node V C . In  FIG. 6A , when the power-supply voltage is assumed to be V DD =7 volts, similarly to the diagram illustrated in  FIG. 5A , a value of the spike voltage is the similar level of the “H” level, which is slightly smaller than the power-supply voltage V DD =7 volts. When the output voltage V out  of the first CMOS inverter  11   a  arrives at the “H” level, the pMOS transistor of the second CMOS inverter  11   b  transits to cut-off state, and the nMOS transistor of the second CMOS inverter  11   b  transits to conductive state. Thus, the output voltage V out  of the second CMOS inverter  11   b  illustrated in  FIG. 6A  becomes “L”. 
     Also, since the shoot-through current I C  flows through the first CMOS inverter  11   a , at time T 2 , the potential of the higher-potential side node V C  begins to decrease similarly to the indication in Eq. (8). However, R C  of Eq. (8) is the resistance value of the resistive element R C , and I is a current value of the shoot-through current I C  in the first CMOS inverter  11   a . Then, when the potential of the higher-potential side node V C  decreases to V C1  at time T 3 , the inverter threshold V th  serving as the reference potential of the swing-center potential V th_c  in the first CMOS inverter  11   a  is reduced from the no-load inverter-threshold V th0 , which is an initial value, to the under-load inverter-threshold V th1 =f(V C1 )&lt;V th_c . 
     At time T 4 , when a reference voltage necessary for the simultaneous-conductive state of the first CMOS inverter  11   a  has decreased to the under-load inverter-threshold V th1 =f(V C1 ), the input voltage V in  becomes relatively larger than the under-load inverter-threshold V th1  of the first CMOS inverter  11   a . As a result, the pMOS transistor in the first CMOS inverter  11   a  transits to cut-off state, and the nMOS transistor in the first CMOS inverter  11   a  is kept in conductive state. Thus, at time T 5 , the output voltage V out  of the first CMOS inverter  11   a  will decrease toward “L”, and the shoot-through current I C  also decreases to zero. 
     When the output voltage V out  of the first CMOS inverter  11   a  becomes the voltage of the “L” level, the pMOS transistor in the second CMOS inverter  11   b  transits to conductive state, and the nMOS transistor in the second CMOS inverter  11   b  transits to cut-off state, and the output voltage V out  of the second CMOS inverter  11   b  becomes “H”. Since the shoot-through current I C  does not flow through the first CMOS inverter  11   a , the higher-potential side node V C  is recovered from V c1 =(V DD −R C I) to the power-supply voltage V DD =V C0 . Due to the recovery of the potential of the higher-potential side node V C , at time T 6 , the inverter threshold V th  serving as the reference potential of the swing-center potential V th_c  of the first CMOS inverter  11   a  is risen and recovered from the under-load inverter-threshold V th1  at the timing of the T 4  to the original no-load inverter-threshold V th0 =f(V C0 ). 
     At time T 7  at which the inverter threshold V th  serving as the reference potential of the swing-center potential V th_c  of the first CMOS inverter  11   a  is returned to the original no-load inverter-threshold V th0 , the input voltage V in  again approaches the swing-center potential V th_c  of the first CMOS inverter  11   a  and becomes the same situation as the time T 1 . That is, since the situations at the timings T 1  to T 7  are repeated, the output voltage V out  of the first CMOS inverter  11   a  is fluctuated, thereby transmitting the spike-train signals from the first CMOS inverter  11   a . Thus, the spike-train signals transmitted from the first CMOS inverter  11   a  are inverted, and the inverted signals are delivered from an output terminal of the second CMOS inverter  11   b . In the operation of the output circuit  11  in the pulse generator pertaining to the second embodiment, the inverter in which both pMOS and nMOS transistors become conductive states is only the first CMOS inverter  11   a . Thus, without any inflow of the shoot-through current to the second CMOS inverter  11   b , the operation similar to the usual CMOS inverter can be performed. 
     With the elapse of time, when the reduction of the sinusoidal wave of cos (ωt) at the second term on the right side in Eq. (3) is proceeded and the input voltage V in  is decreased beyond (V th_c −ΔV osc /2), the input voltage V in  is deviated from the effective drive span ΔV osc . When the input voltage V in  has decreased to a potential deviated from the effective drive span ΔV in  the nMOS transistor Q N  transits to cut-off state. That is, even at the timing, at which he potential of the higher-potential side node V C  is recovered to the voltage V C0  of the original higher-potential side node V C  after the potential of the higher-potential side node V C  has decreased to V C1  by the shoot-through current I C , because the potential of the higher-potential side node V C  is deviated from the effective drive span ΔV osc  of the first CMOS inverter  11   a , the nMOS transistor Q N  of the first CMOS inverter  11   a  is kept in cut-off state. When the pMOS transistor Q P  is kept in conductive state and the nMOS transistor Q N  is kept in cut-off state, the potential of the output voltage V out  is kept at the values of the “H” level close to the voltage V C0 =V DD  of the original higher-potential side node V C . 
     If the nMOS transistor Q N  of the first CMOS inverter  11   a  is kept in cut-off state, the spike-train signals are not delivered from the first CMOS inverter  11   a , and the signal of the “H” level is delivered as the output signal from the first CMOS inverter  11   a . That is, similarly to the time periods after the completions of the generations of the spike trains in the second and fourth oscillation periods from the left in  FIG. 5A , although the output voltages V out  from the first CMOS inverter  11   a  are close to the power-supply voltage V DD , the output voltages V out  re located at the “H” level smaller than the power-supply voltage V DD . 
     When the output voltage V out  of the first CMOS inverter  11   a  arrives at the voltage of the “H” level, the pMOS transistor in the second CMOS inverter  11   b  transits to cut-off state, the nMOS transistor in the second CMOS inverter  11   b  transits to conductive state, and the output voltage V out  of the second CMOS inverter  11   b  becomes “L=0 V”. Since the shoot-through current I C  does not flow through the first CMOS inverter  11   a , the higher-potential side node V C  is recovered from V C1 =(V DD −R C I) to the power-supply voltage V DD =V C0 . 
     With the further elapse of time, the amplitude of the sinusoidal wave of cos (ωt) at the second term on the right side in Eq. (3) becomes the minimum value. After the timing of the minimum value, the amplitude begins to be slowly increased from the minimum value. When the amplitude of the sinusoidal wave of cos (ωt) represented at the second term on the right side in Eq. (3) is gradually increased from the minimum value and the input voltage V in  exceeds (V th_c −ΔV osc /2), the input voltage V in  is plunged into the levels in the effective drive span ΔV osc  of the first CMOS inverter  11   a . When the variation of the input voltage V in  is increased to a value at which the input voltage V in  is plunged into the levels in the effective drive span ΔV osc  of the first CMOS inverter  11   a , both of the pMOS transistor Q P  and the nMOS transistor Q N  in the first CMOS inverter  11   a  become conductive states. And, similarly to the situations in the first and third oscillation periods from the left in  FIG. 5A , the oscillations by the repeated operations of the pMOS transistor Q P  in the conductive states is generated, thereby generating clusters of spike trains in each of the first and third oscillation periods. 
     That is, since the output voltage V out  of the first CMOS inverter  11   a  is fluctuated and the spike-train signals are delivered from the first CMOS inverter  11   a , the spike-train signals transmitted from the first CMOS inverter  11   a  are inverted are delivered from the output terminal of the second CMOS inverter  11   b . With the further elapse of time, the sinusoidal wave of cos (ωt) represented at the second term on the right side in Eq. (3) become large and the input voltage V in  is increased to a value exceeding (V th_c +ΔV osc /2) and deviated from the effective drive span ΔV in  the generation of the spike-train signals from the first CMOS inverter  11   a  is stopped. That is, in a case that in association with the increase of the sinusoidal wave of cos (ωt) so that the input voltage V in  becomes the “H” level exceeding (V th_c +ΔV osc /2), the pMOS transistor Q P  is kept in cut-off state even when the potential of the higher-potential side node V C  has decreased to V C1  by the shoot-through current I C , because the input voltage V in  is higher than the voltage of the effective drive span ΔV osc  of the first CMOS inverter  11   a.    
     That is, similarly to the timings at the right edges of spike-trains in the first and third oscillation periods from the left in  FIG. 5A , when the pMOS transistor Q P  in the first CMOS inverter  11   a  enters cut-off state, after the first and third oscillation periods, the pMOS transistor Q P  in the first CMOS inverter  11   a  is kept in cut-off state, and the nMOS transistor Q N  is kept in conductive state. That is, in a case that the input voltage V in  is increased to the “H” level exceeding (V th_c +ΔV osc /2), the pMOS transistor Q P  in the first CMOS inverter  11   a  is kept in cut-off state, and the nMOS transistor Q N  is kept in conductive state. That is, similarly to the time period after the completion of the generation of the spike trains in the first and third oscillation periods from the left in  FIG. 5A , the output signals from the first CMOS inverter  11   a  is still “L≈0 V”. In the first and third oscillation periods, in which the output signals from the first CMOS inverter  11   a  is kept in “L≈0 V”, the output signals from the second CMOS inverter  11   b  is kept in the “H” level. 
     With the further elapse of time, as represented by Eq. (3), with regard to the input voltage V in , after passing through the maximum value, the variation of the sinusoidal wave of cos (ωt) begins to decrease again and slowly. Then, when the input voltage V in  has decreased to the value smaller than (V th_c +ΔV osc /2), the input voltage V in  is plunged into the levels in the effective drive span ΔV osc  of the first CMOS inverter  11   a . Since the following operations are the same explanation as the already-described operations in the first embodiment, the duplicate explanation is omitted. In the pulse generator recited by the first embodiment, the technical feature that “the fluctuating signals”, which are controlled by the minute variations of the input voltage V in , can be obtained has been already explained, as exemplified in  FIG. 5B . The fluctuations such as the pulse widths, the pulse intervals, the pulse-firing timings, and others, which are generated in the first CMOS inverter  11   a  are delivered to the input terminal of the second CMOS inverter  11   b , and the inverted spike-train signals of the first CMOS inverter  11   a  are delivered from the output terminal of the second CMOS inverter  11   b.    
     Thus, according to the pulse generator pertaining to the second embodiment, the variations of the pulse widths, the pulse intervals, the pulse-firing timings, and others are controlled as the fluctuations, which are somewhat limited in a specific latitude, and the fluctuations are delivered from the second CMOS inverter  11   b  as output signals, similarly to the pulse generator of the first embodiment. Because the variations are confined in the specific latitude, the variations are distinguishable from the perfectly random fluctuations, and therefore, the output signals having a feature being distinguishable from the perfectly random fluctuations are delivered from the second CMOS inverter  11   b . Even in the pulse generator pertaining to the second embodiment, the macro “fluctuations”, in which clusters of the spike-train signals are generated intermittently and periodically, are generated similarly to the waveforms illustrated in  FIG. 5A . And furthermore, according to the pulse generator pertaining to the second embodiment, the micro “fluctuations”, in which the pulse widths are altered by the minute variations in the input voltage V in , are generated as illustrated in  FIG. 5B . That is, according to the pulse generator pertaining to the second embodiment, when the values of the input voltage V in  entering to the first CMOS inverter  11   a  minutely swing near the swing-center potential V th_c  of the first CMOS inverter  11   a  as represented by Eq. (12), the fluctuating signals, in which the pulse width and the pulse interval are controlled within a desirable latitude, can be provided from the second CMOS inverter  11   b.    
     According to the pulse generator pertaining to the second embodiment, the first CMOS inverter  11   a  and the second CMOS inverter  11   b  are connected in tandem (connected in parallel) in double stages, and the resistor-connected complementary transistor-circuit is accordingly implemented, which can improve the reproducibility of the pulse characteristics of the spike-train signals. That is, according to the pulse generator pertaining to the second embodiment, it is possible to stably generate the spike-shaped pulsed signals that has the fluctuations of the predetermined pulse width, pulse interval, pulse-firing timing, and others. The subject matter means that the pulse generator pertaining to the second embodiment can provide “the fluctuating signals in which the pulse width, the pulse interval and others are controlled within a desirable latitude” as the fluctuations, of which reproducibility is improved. For example, as illustrated in  FIG. 7 , a relationship between the swing-center potentials V th_c  of the input voltages V in  exhibited in abscissa and spike train frequencies of the output voltages V out  exhibited in ordinate can be made approximately equal, independently of the event numbers of spike-train signals occurrences—a first occurrence, a second occurrence and a third occurrence—. 
     In  FIG. 6A , the power-supply voltage of V DD =7 volts and the resistance value R C =20 kilo-ohms assigned to the resistive element R C  are assumed for the resistor-connected complementary transistor-circuit in the pulse generator pertaining to the second embodiment. As represented by Eq. 7(b), for determining the swing-center potential V th_c  of the input voltage V in , which enables the spike-train signals composed of spike-shaped pulses to be generated, it is necessary to consider the dependency of the voltage-adjustment parameter ΔV mod_H  on the resistance values of the resistive element R C . That is, the input voltages V in  for generating the spike-train signals depends on the resistance values of the resistive element R C , which will be explained later with reference to  FIG. 11 . For example, a range of the input voltages V in =1.403 volts to 1.430 volts illustrated in  FIG. 7  is lower than the central value (V DD /2=3.5 volts) in between the higher-potential power-supply V DD  and the lower-potential power-supply (ground potential=0 volt) illustrated in  FIG. 6A , by 2 volts (≈57 percent) or more for a case of the resistance value R C =20 kilo-ohms. Data indicating the input voltage V in  dependency of the repetition frequency (spike train frequency) of the spike trains illustrated in  FIG. 7  indicates that the frequencies can be controlled in a range of 320 kHz to 740 kHz, by swinging the values of the second terms on the right sides in Eq. (3) or (12) in the range of 1.403 volts to 1.430 volts, under a condition that the swing-center potential V th_c  necessary for the simultaneous-conductive state is set as a fixed value. 
     As mentioned above, the inverter in which both pMOS and nMOS transistors of the output circuit  11  in the pulse generator pertaining to the second embodiment turn into the simultaneous-conductive state is only the first CMOS inverter  11   a . Thus, the shoot-through current does not flow through the second CMOS inverter  11   b , except for an initial state. For example, I C01  is defined as a value of a shoot-through current I C1  at the time of the initial state (for example, V in =0 volt) of the first CMOS inverter  11   a , and I C02  is defined as a value of a shoot-through current I C2  at the time of the initial state (for example, V in =0 volt). And, if the initial state is assumed to be I C01 =I C02 =I C0 , it is possible to apply all of theories, which are explained with Eqs. (13) to (28) for the oscillation conditions of the pulse generator of the first embodiment, to the pulse generator pertaining to the second embodiment, because it is enough to focus to only the shoot-through current of the first CMOS inverter  11   a.    
     Thus, by using the method similar to  FIG. 10  used in the explanation of the pulse generator of the first embodiment, and focusing to only the characteristics and operation of the first CMOS inverter  11   a , it is possible to experimentally determine the range of the resistance values of the resistive elements R C  that enables the pulses in the pulse generator pertaining to the second embodiment. As the output circuit  11 , although a double-stage CMOS inverter is illustrated in an insertion view on the upper right portion in  FIG. 11 , the insertion view on the upper right portion in  FIG. 11  differs from the circuit topology of the power-supply voltage V DD =7 volts illustrated in  FIG. 6A  in that the power-supply voltage of the higher-potential power-supply V DD  is V DD =5 volts in the insertion view. In  FIG. 11 , ordinate indicates the values of the swing-center potentials V th_c  of the input voltages V in  when the spike-train signals composed of spike-shaped pulses can be generated. However, as the experimental results illustrated in  FIG. 11 , the spike-train signals can be obtained in a region between 300 ohms and 100 kilo-ohms as the resistance values R C_osc  of the resistive element R C . The experimental results illustrated in  FIG. 11  indicate that proper values of the swing-center potentials V th_c  of the input voltages V in  illustrated on ordinate are decreased with the increase of the resistance values of the resistive elements R C  illustrated on abscissa. Thus, depending on the variation of the resistance values of the resistive elements R C , it is necessary to alter the preset values of swing-center potential V th_c , which is represented at the first term on the right side in Eq. (3). It is necessary to pay careful attention to a situation that a range of input voltages V in =1.91 volts to 1.11 volts, exhibited on ordinate in  FIG. 11 , indicates a resistance value dependency of the input voltages V in . As illustrated in  FIG. 11 , the range indicating the resistance value dependency of the input voltages V in  lies in a zone lower by 20 percent or more compared with the central value (V DD /2=2.5 volts) in between the higher-potential power-supply V DD  and the lower-potential power-supply (ground potential=0 volt), and the potential levels of the zone is 2 volts or less. Characteristics that the appropriate values of the input voltages V in  illustrated in  FIG. 11  are decreasing together with the resistance values of the resistive elements R C  indicate the dependency on the resistance values of the resistive elements R C  of the voltage-adjustment parameter ΔV mod_H  represented by Eq. (7b). 
     In addition, if we define the appropriate resistance values of the resistive elements R C  that enables the pulse generation in the pulse generator pertaining to the second embodiment as R C_osc_mes , the theoretical value R C_osc_mes  will be estimated from  FIG. 10  base upon the theoretical equations used in the explanation of the pulse generator of the first embodiment, and the theoretical values of R C_osc_mes =750 ohms to 30 kilo-ohms can be obtained. In the examples indicated in the pulse generator pertaining to the second embodiment, the values of R C_osc =300 ohms to 100 kilo-ohms are acquired from the experimental results illustrated in  FIG. 11 . Then the range of experimentally determined values is larger than the range of theoretical values of R C_osc_mes =750 ohms to 30 kilo-ohms, which is estimated from  FIG. 10  and the above-mentioned theoretical equations. That is, not only the theoretical value but also the experimental confirmation is required for the dependency on the resistance values of the resistive elements R C  of the voltage-adjustment parameter ΔV mod_H  represented by Eq. (7b). 
     As mentioned above, the output circuit  11  pertaining to the second embodiment has the configuration of the resistor-connected complementary transistor-circuit in which the complementary circuit encompasses the first CMOS inverter  11   a  and the second CMOS inverter  11   b , which are connected in parallel in the shape of ladder. Furthermore, the resistive element R C  is connected in series between the higher-potential power-supply V DD  and the pMOS transistor Q P  in each of the complementary circuits. And, by applying the input voltage V in , which has the potential levels lying in the effective drive span ΔV osc  with the swing-center potential V th_c  at a center, to the first CMOS inverter  11   a  at the first stage (initial stage), the spike-train signals, of which the pulse widths and the frequencies are controlled, can be delivered from the second CMOS inverter  11   b  at the second stage. Because the circuit topology represents a simple and compact configuration as illustrated in  FIG. 6A , it is possible to assemble a huge number of pulse generators to be easily installed in the complex computer system. Furthermore, it is possible to control the fluctuations of the pulse widths, the frequencies, and others to be moderate such that the fluctuations are confined in a specific limited latitude. In addition, the stage number of the CMOS inverters implementing the complementary circuit, in a topology of the ladder-shaped parallel connection, building up the output circuit  11  in the pulse generator pertaining to the second embodiment is not limited to double stages, and triple stages or more stages can be used. 
     Also, the circuit topology of the complementary circuit implementing the output circuit  11  is not limited to the tandem connection of the simple CMOS inverters as illustrated in  FIG. 6A . The technical idea of the pulse generators pertaining to the second embodiment can be applied to various logic gates if a complementary circuit has a circuit topology including a CMOS inverter in some way. For example, with regard to the complementary circuit implemented by a double-input negated logical-conjunction (NAND) gate, in which double-inputs are commonly connected as illustrated in  FIG. 6B , by connecting a resistive element in series to a power supply side of a complementary circuit, it is confirmed to be able to generate pulsed signals having the fluctuations and improve the reproducibility of the fluctuations, similarly to the experimental results illustrated in  FIG. 7 . The complementary circuit implemented by a double-input NAND circuit illustrated in  FIG. 6B  is constructed in which one nMOS transistor and one pMOS transistor are added to a negation (NOT) circuit as is well known. That is, double pMOS transistors are arranged in parallel on a higher-potential power-supply side, and double nMOS transistors are connected in series to a connection node of the double pMOS transistors. Thus, the CMOS structures are constructed so that the series-connected nMOS transistors and one of the pMOS transistors are paired one by one to implement corresponding input terminals, although the double input terminals are short-circuited to implement a single input terminal. The resistive element is connected between a connection node of source electrodes of each of the double pMOS transistors and the higher-potential power-supply, and a connection node of drain electrodes of each of the double pMOS transistors and a drain electrode of an upper nMOS transistor are connected to each other to serve as an output terminal. Because the double input terminals of the series-connected nMOS transistors are short-circuited to implement a single input terminal, the double nMOS transistors serves as a single nMOS transistor. Hence, similarly to the complementary circuit illustrated in  FIG. 6A , since the shoot-through current flows through the CMOS circuit, the spike pulses is repeatedly generated. 
     Moreover, the technical idea of the pulse generator pertaining to the second embodiment can be similarly applied to another complementary circuit implemented by a double-input logical-conjunction (AND) gate in which double-inputs are commonly connected as illustrated in  FIG. 6C . That is, regarding the complementary circuit illustrated in  FIG. 6C , the inventors of the present invention have confirmed that by connecting a resistive element in series to a power supply side of the complementary circuit, it is possible to generate the pulsed signals having the fluctuation and generate the pulsed signals having the “fluctuation” in which reproducibility is excellent, similarly to the experimental result illustrated in  FIG. 7 . The complementary circuit illustrated in  FIG. 6C  corresponds to the structure in which an input terminal of the CMOS inverter is connected to the output terminal of the double-input NAND circuit illustrated in  FIG. 6B . Thus, sine the shoot-through current flows through the CMOS circuit on the NAND circuit side located on the input side, it is possible to generate the spike pulses having the “fluctuation” in which reproducibility is excellent, by the complementary circuit illustrated in  FIG. 6C . Also, similarly to the complementary circuit which encompasses the tandem connection of the CMOS inverters illustrated in  FIG. 6A , it may be easily understand the effectiveness of the reproducibility improvement caused by the additional tandem connection of the CMOS inverter to the NAND to implement the AND gate illustrated in  FIG. 6C . 
     Also, a subject matter in the technical idea pertaining to the pulse generator of the second embodiment lies in the reduction of the potential levels at the higher-potential side node V C  of the complementary circuit, when the shoot-through current flows, similarly to the pulse generator of the first embodiment. Thus, the resistive element R C  is not always limited to the concrete circuit arrangement that is physically designed as the real circuit elements exemplified in  FIG. 6A , and it is natural that the resistive element R C  can be replaced by unintentional mechanism or stray elements whose action, behavior, or performance is equivalent to the resistive element R C . Thus, in the explanation of the pulse generator pertaining to the second embodiment, the resistive element R C  shall include the mechanism or the stray elements having the action, behavior, and performance equivalent to the resistive element R C . And therefore, as to the fluctuations of the power-supply voltage will serve as a contrastive circuit element equivalent to the resistive element R C . 
     Similarly to the application of the pulse generator of the first embodiment, the pulse generator pertaining to the second embodiment can be also applied to the neural network in which information is transmitted and received through the voltage spikes. That is, similarly to the circuit diagram illustrated in  FIG. 12 , the first and second neuron circuits transmit and receive the information through the corresponding first and second output voltages, in the neural network. The first and second neuron circuits have the same configuration as each other. However, the first neuron circuit includes voltage-spike generator for generating voltage spikes, a detector for detecting input-information, and a controller for controlling the frequency and timings of the voltage spikes by the input-information, similarly to the illustration on the left side in  FIG. 12 . 
     The voltage-spike generator includes the pulse generator pertaining to the second embodiment, for example, which has the double-stage CMOS inverter as explained in  FIG. 6A . And, when detecting the specific input-information, the detector in the neural network pertaining to the second embodiment notifies the specific input-information to the controller. Similarly to the process flows illustrated in Steps S 1  to S 3  in  FIG. 13 , the controller applies an input voltage to the voltage-spike generator at a predetermined timing, configured to deliver the voltage spikes having the determined frequency and timings. While receiving the input voltage, the voltage-spike generator supplies the voltage spikes as the output voltage to the second neuron circuit. That is, although the controller tries to deliver the voltage spikes ascribable to the specific input-information (excitability), the frequency and firing timing of the voltage spikes are adjusted by the feedback information (inhibitory). With the repetitions of the above operations, the output voltages of the first neuron circuit are converged in directions in which the voltage spikes are delivered, or directions in which the voltage spikes are not delivered. 
     As mentioned above, according to the neural network pertaining to the application example of the second embodiment, by using the compact pulse generators as exemplified in  FIGS. 6A, 6B and 6C  as the first and second neuron circuits, each of which implements a part of the pulse generator, a very many voltage-spike generators can be integrated in a single chip, because the size of voltage-spike generators pertaining to the second embodiment is compact, even under a requirement that a huge number of voltage-spike generators are required. Thus, according to the voltage-spike generator pertaining to the second embodiment, by implementing the neural network such as the SNN in which the huge number of voltage-spike generators are integrated, it is possible to achieve the robots, moving vehicles, mobile objects, and others each of which includes AI computer architecture whose information-processing capability is improved more and more. 
     OTHER EMBODIMENT 
     As described above, the first and second embodiments of the present invention have been described, but because Specifications and Drawings implement a mere part of the disclosure of the present invention, and it should not be understood that Specifications and Drawings are intended to limit the scope of the present invention. Various alternative embodiments, examples and operational techniques will become apparent to those skilled in the art from the above disclosure. For example, in the pulse generators pertaining to the first and second embodiments, the situations are explained in which the resistor-connected complementary transistor-circuit is implemented by the complementary circuit whose lower voltage side terminal is connected to the lower-potential power-supply, and the resistive element connected between the higher-potential power-supply and the higher voltage side terminal of the complementary circuit. However, the connection topology illustrated in  FIG. 2  is merely exemplification. In reverse, the resistor-connected complementary transistor-circuit may be implemented by the complementary circuit whose higher voltage side terminal is connected to the higher-potential power-supply, and the resistive element is connected between the lower-potential power-supply and the lower voltage side terminal of the complementary circuit. In this case, instead of the higher-potential side node in the pulse generators pertaining to the first and second embodiments, “a lower-potential power-supply side node” is defined by a connection node between the lower voltage side terminal of the complementary circuit and the resistive element. 
     In the pulse generator pertaining to other embodiment in which the resistive element is connected between the lower-potential power-supply and the lower voltage side terminal of the complementary circuit, the right side in Eq. (7a) is rewritten as the following Eq. (31). 
         V   th_c   =V   th0   +ΔV   mod_L   (31)
 
     ΔV mod_L  represented at the second term on the right side in Eq. (31) is the voltage-adjustment parameter, which is experimentally determined in order to set the swing-center potential V th_c , is similar to ΔV mod_H  represented at the second term on the right side in Eq. (7a). Similarly to the relation represented by Eq. (7b), the voltage-adjustment parameter ΔV mod_L  prescribed by Eq. (31) varies in view of the resistance value of the resistive element R C . Therefore, even in the pulse generator pertaining to the other embodiment, similarly to the pulse generators pertaining to the first and second embodiments, there is a case that in view of the resistance value of the resistive element R C , the swing-center potential V th_c  is set to a considerably high value equal to or more than 20 percent of V DD /2, as compared with the central value (V DD /2) of the voltage between the higher-potential power-supply and the lower-potential power-supply. If the swing-center potential V th_c  is set to the considerably high value, even in the pulse generator pertaining to the other embodiment, the input voltage V in , required to deliver the spike-train signals, becomes a considerably high value, as compared with the central value (V DD /2) of the voltage between the higher-potential power-supply and the lower-potential power-supply. 
     In the description of the pulse generators pertaining to the first and second embodiments in the explanation of  FIG. 5B  and the like, it has been explained that “the fluctuating signals”, in which the variations of the pulse widths, pulse intervals, pulse-firing timings, and others are somewhat controlled in a specific limited latitude, are generated by the minute variation of the input voltage V in . The “fluctuating signals” can be applied to “an amoeba computer” as described in JP Application No. 2020-184993 in which one of the present inventors is included as a co-inventor. 
     In the amoeba computer, it is possible to search for the solutions of a problem that searches for the optimal solution of various scheduling and combinations quickly and efficiently, by utilizing the probabilistic behaviors derived from “the fluctuation of a device” whose hint is received from the fluctuating behaviors of living organism or animate beings. For example, in the “amoeba-inspired electronic computer” mimicking behaviors of a single-celled amoeba as illustrated in  FIG. 14 , it is possible to provide a method that gets a suitable pattern quickly and surely, as compared with a conventional Neumann-computer, by utilizing the probabilistic operation obtained from the fluctuation of the pulse generator pertaining to the first or second embodiment, as “the fluctuation of a device”. 
     The amoeba core as the living organism wants to stretch as many legs as possible to outer wards in order to maximize the absorption amount of nutrients. On the other hand, the single-celled amoeba shrinks the legs when light is irradiated to the single-celled amoeba. If adopting a feedback rule, in which the on/off of light irradiations are updated by the shapes of the single-celled amoeba—the states of expansions and contractions of the legs—, the amoeba core illustrated in  FIG. 14  searches for an optimal solution or sub-optimal solutions of the combinatorial optimization problem, in a process in which the single-celled amoeba is deformed by carrying out trial-and-errors configured to extend only a combination of legs that can minimize the risks of the light irradiations. In “amoeba-based computer”, a plurality of freely deforming legs in the single-celled amoeba, and a portion serving as the hub (center) of the plurality of legs memorize the experiences of the light irradiations. That is, the deformations of legs and the portion serving as the hub of the legs generate suitable “probabilistic fluctuations”, responding to optical stimuli, through the complex spatiotemporal oscillation dynamics of large free degrees in the plurality of legs. And the probabilistic fluctuations in the amoeba-based computer achieve the effectiveness similar to the quantum annealing of a quantum computer. 
       FIG. 14  exemplifies a structure of an amoeba core  101  embracing octuple pseudopodia-units, each of which has a series circuit implemented by a resistor and a diode, corresponding to a structure of a single-celled amoeba having octuple legs. In amoeba core  101 , the octuple pseudopodia-units are radially arrayed. Input terminals of a double-input NOR gate  301  are connected between a pair of an output terminal X 1.0  and an output terminal X 1.1  which correspond to double legs of the single-celled amoeba responsible for determining a value of a variable x 1 . Similarly, input terminals of double-input NOR gates  302 ,  303  and  304  are connected between a pair of an output terminal X 2.0  and an output terminal X 2.1  which are responsible for determining a value of a variable x 2 , between a pair of an output terminal X 3.0  and an output terminal X 3.1  which are responsible for determining a value of a variable x 3 , and between a pair of an output terminal X 4.0  and an output terminal X 4.1  which are responsible for determining a value of a variable x 4 , respectively. When inhibition signals referred to as output-adjusting signals (bounce-back signals) are applied, the octuple pseudopodia-units illustrated in  FIG. 14  are electrically shrunk, and the output voltages are decreased. And when the inhibition signals are not applied, the octuple pseudopodia-units are electrically extended, and the output voltages are increased. However, similarly to the single-celled amoeba that is the living organism, even when the pseudopodia-units are electrically extended and the output voltages are increased, the “fluctuating actions” that are not extended are generated at a constant fluctuating probability. In the amoeba-inspired electronic computer, by mimicking the behavior of the single-celled amoeba, “the fluctuating probability” is provided non-uniformly from the outside. 
     The amoeba core  101  searches for the solution while repeating the trial-and-errors, in which all the legs are extended and shrunk in simultaneous parallel scheme, under an environment in which undesirable state-transitions are prohibited by bounce-back rules delivered by a bounce-back control logic-circuit  201 . And, the solution is discovered when all of the legs to which inverted signals of bounce-back signals L 1.0 , L 1.1 , . . . , L 4.0 , L 4.1  from the bounce-back control logic-circuit  201  are not applied arrives at a stable state in which all of the legs are kept in an extending state. In order to solve a problem of N variables, 2N amoeba legs are required. However, in  FIG. 14 , each of terminals at tip sides of octuple legs of the amoeba core connected to the bounce-back control logic-circuit  201  is grounded through input/output-rule circuits  510 ,  511 ;  520 ,  521 ;  530 ,  531 ;  540 ,  541 , and a value of an output of each of output terminals X 1.0 , X 1.1 , . . . , X 4.0 , X 4.1  of the octuple pseudopodia-units is determined. 
     Since the pulse generator pertaining to the first or second embodiment is built in each of the input/output-rule circuits  510 ,  511 ;  520 ,  521 ;  530 ,  531 ;  540 ,  541  illustrated in  FIG. 14 , it is possible to generate the fluctuation necessary for the amoeba-inspired electronic computer. The necessary fluctuation means that, although fluctuation is required to be obtained to the generation of the spike-train signals used in an electronic amoeba circuit, the fluctuation is controlled within a desirable latitude. The pulse generators pertaining to the first and second embodiments can provide “the necessary fluctuation” because the fluctuation of the spike-train signals can be controlled within the desirable range. Especially, a feature that the pulse generator pertaining to the first or second embodiments embraces the fluctuations in the pulse-firing timing is important for the circuit operation of the amoeba core  101  illustrated in  FIG. 14 . That is, in a circuit in each of the input/output-rule circuits  510 ,  511 ;  520 ,  521 ;  530 ,  531 ;  540 ,  541  used in the amoeba core  101  illustrated in  FIG. 14 , since start timings are different even if pulse periods are equal, the fluctuations in the pulse-firing timing serve as functions that work positively for solution search in a computer system using the amoeba core  101 . Also, since the pulse generators pertaining to the first and second embodiments is compact configuration in structure, the huge number of fluctuation generation devices corresponding to various variables can be assembled as integrated circuits. Thus, the pulse generators pertaining to the first and second embodiments are preferable for the applications to solution searching systems by the electronic amoeba circuits. 
     For example, the output terminal of the double-input NOR gate  301  placed between the output terminal X 1.0  and output terminal X 1.1  of the pseudopodia-unit responsible for determining the value of the variable x 1  is entered to a second input terminal of the input/output-rule circuit  510  placed between the output terminal X 1.0  and the ground potential, and also entered to a second input terminal of the input/output-rule circuit  511  of the output terminal X 1.1  simultaneously. And, as illustrated in  FIG. 14 , an inverted signals of the bounce-back signals (output-adjustment signals) L 1.0  is entered through an inverter  410  to a first input terminal of the input/output-rule circuit  510  of the output terminal X 1.0  of the pseudopodia-unit, and the necessary fluctuation is generated. Also, an inverted signals of the bounce-back signals L 1.1  is entered through an inverter  411  to a first input terminal of the input/output-rule circuit  511  of the output terminal X 1.1  of the pseudopodia-unit, and the necessary fluctuation is generated. And, respective output signals from the output terminal X 1.0  and the output terminal X 1.1  of the pseudopodia-unit are entered to the bounce-back control logic-circuit  201 . 
     Similarly, the output terminal of the double-input NOR gate  302  connected between the output terminal X 2.0  and the output the terminal X 2.1  which are responsible for determining the value of the variable x 2  is entered to both of a second input terminal of the input/output-rule circuit  520  of the output terminal X 2.0  and a second input terminal of the input/output-rule circuit  521  of the output terminal X 2.1 , and the necessary fluctuation is generated. Moreover, inverted signals of the bounce-back signals L 2.0  and the bounce-back signals L 2.1  are fed through an inverter  420  and an inverter  421  to first input terminals of the input/output-rule circuit  520  of the output terminal X 2.0  and the input/output-rule circuit  521  of the output terminal X 2.1  of the pseudopodia-unit, respectively and independently of each other, and the necessary fluctuations are generated. And, respective output signals from the output terminal X 2.0  and the output terminal X 2.1  of the pseudopodia-unit are entered to the bounce-back control logic-circuit  201 . 
     Similarly, through an inverter  430  and an inverter  431 , an output terminal of the double-input NOR gate between the output terminal X 3.0  and the output terminal X 3.1  which are responsible for determining the value of the variable x 3  is entered to both of a second input terminal of the input/output-rule circuit  530  of the output terminal X 3.0  and a second input terminal of the input/output-rule circuit  531  of the output terminal X 3.1 , and inverted signals of the bounce-back signals L 3.0  and the bounce-back signals L 3.1  are entered to first input terminals of the input/output-rule circuit  530  of the output terminal X 3.0  and the input/output-rule circuit  531  of the output terminal X 3.1 , respectively and independently of each other, and the respective necessary fluctuations are generated. And, respective output signals from the output terminal X 3.0  and the output terminal X 3.1  of the pseudopodia-unit are entered to the bounce-back control logic-circuit  201 . 
     Even similarly, an output terminal of the double-input NOR gate between the output terminal X 4.0  and the output terminal X 4.1  which are responsible for determining the value of the variable x 4  is entered to both of a second input terminal of the input/output-rule circuit  540  of the output terminal X 4.0  and a second input terminal of the input/output-rule circuit  541  of the output terminal X 4.1 , and through an inverter  440  and an inverter  441 , inverted signals of the bounce-back signals L 4.0  and the bounce-back signals L 4.1  are entered to first input terminals of the input/output-rule circuit  540  of the output terminal X 4.0  and the input/output-rule circuit  541  of the output terminal X 4.1 , respectively and independently of each other, and the necessary fluctuations are generated. And, respective output signals from the output terminal X 4.0  and the output terminal X 4.1  of the pseudopodia-unit are entered to the bounce-back control logic-circuit  201 . In this way, the independent inverted signals of the bounce-back signals L 1.0 , L 1.1 , . . . , L 4.0 , L 4.1  are entered to the first input terminals of the input/output-rule circuits of the octuple pseudopodia-units, respectively and independently of each other, and the necessary fluctuations are generated, thereby changing the circuit states of each of the corresponding input/output-rule circuits. And, similarly to phenomenon in which the single-celled amoeba, surviving in the natural world, changes the length of legs configured to adapt to environment, the output signals from of the output terminals X 1.0 , X 1.1 , . . . , X 4.0 , X 4.1  of the pseudopodia-unit, which implement the electronic circuit mimicking the amoeba, are changed by the bounce-back signals L 1.0 , L 1.1 , . . . , L 4.0 , L 4.1 . Thus, the optimization problem of complex combination can be solved at high speed by an algorithm of a bio-inspired computer. 
     In addition, as a matter of course, the present invention shall include various subject matters in which the respective features explained in the first and second embodiments are arbitrarily applied, or alternatively, the present invention shall include various embodiments which are not described here. Therefore, the technical scope of the present invention is determined only by the “technical features specifying the invention” construed from the scope of claims, if the determined technical feature that can be interpreted and construed from the claims is appropriate from the contents of description.