JP2018060516A - Method of constructing equivalent circuit of capacitor, and simulation method and apparatus thereof - Google Patents

Abstract

PROBLEM TO BE SOLVED: To satisfactorily approximate characteristics to those obtained when a DC voltage is superposed, with a simple arrangement, and to improve practicability and operability.SOLUTION: An equivalent circuit obtained when a DC voltage is not applied is used as a reference for a capacitor equivalent circuit model obtained when a DC voltage is superposed on a signal. A portion indicating capacity is converted into a voltage control current source or a voltage source used to adjust a signal in response to a superposed DC current voltage. The voltage control current source or the voltage source is described by approximation expression of a current or a voltage indicating change of a signal corresponding to change in capacitor characteristics caused by application of the DC current voltage superposition. An element indicating capacity in the equivalent circuit by the superposition of the DC current voltage is operated as if it was a variable element. This approximation expression does not provide any calculation load to a simulator and prevents divergence.SELECTED DRAWING: Figure 1

Description

  The present invention relates to a capacitor equivalent circuit construction method, simulation method, and apparatus therefor, and more particularly to a capacitor equivalent circuit construction method and simulation method suitable when a DC voltage (DC bias voltage) is superimposed on a signal voltage. And an apparatus for the same.

  Generally, a capacitor has frequency characteristics due to its material and structure, and deviates from the characteristics of an ideal capacitive element. For this reason, when calculating the capacitor characteristics with a simulator or the like, an equivalent circuit model that matches the actually measured frequency characteristics of the capacitor is required and provided by each capacitor vendor.

  However, in recent years, especially in multilayer ceramic capacitors, a model that expresses the characteristics when DC voltage is superimposed has become necessary, and simulation models that only match frequency characteristics with only actual measurements for signals without DC voltage cannot be used. It is coming.

  For example, there is a “capacitor circuit simulation model and its construction method, circuit simulation method and circuit simulator” disclosed in Patent Document 1 below, which uses a voltage-controlled current source to When a voltage is applied to a capacitor, an equivalent circuit model that automatically flows a current corresponding to a characteristic corresponding to the applied DC voltage is presented. Thereby, the characteristic at the time of DC voltage superposition at the time of measurement can be reproduced with high accuracy.

JP 2012-150579 A

  However, in the background art described above, as shown in FIG. 1 of the same publication, the circuit configuration includes an element for performing a differential operation, and further, as shown in FIG. In such cases, problems such as divergence may occur. Further, the fact that the approximation formula of the DC superimposition characteristic is a polynomial approximation can also cause a problem of divergence. In addition, since there are many complicated calculation formulas, the calculation load on the calculation software or the like actually used increases, and as a result, the calculation takes time.

  In addition, since the structure of the equivalent circuit model is complicated, it takes a lot of man-hours and time to build a simulation model of one capacitor, and it is possible to build a simulation model without technical knowledge. In addition, there is a disadvantage that it is difficult to secure engineers.

  The present invention focuses on the above points, solves various practical problems caused by the complexity of the equivalent circuit model, and approximates the DC voltage superposition characteristics satisfactorily with a simple configuration. It is an object of the present invention to provide a capacitor equivalent circuit construction method, simulation method, and apparatus that are excellent in practicality and workability.

  The method for constructing an equivalent circuit for a capacitor according to the present invention is a method for constructing an equivalent circuit for a capacitor in which a DC voltage may be superimposed on a signal, and only a signal is applied with no DC voltage applied. In a state where a value of each circuit element included in the equivalent circuit is obtained by actual measurement to obtain a reference equivalent circuit, and a circuit element included in the reference equivalent circuit, the value being obtained by superimposing a DC voltage. Replacing a circuit element that changes with a voltage-controlled current source or a voltage-controlled voltage source; adding a closed circuit representing a state in which only a signal is applied to the replaced circuit element; And outputting from the voltage controlled current source or the voltage controlled voltage source a current or voltage having a value obtained by multiplying the current or voltage generated in the element by a coefficient.

  One of the main forms is to compare the frequency characteristic of the circuit element measured in a state where a DC voltage is superimposed on the signal and the frequency characteristic of the circuit element measured in a state where only the signal is applied, A step of obtaining a change in the value of the circuit element due to the DC voltage superimposition, and a voltage or current in the voltage controlled current source or the voltage controlled voltage source based on the change in the value of the circuit element due to the DC voltage superposition obtained in the step And a step of outputting a coefficient multiple of the value of.

  In another embodiment, in the closed circuit, a voltage source or a current source is connected in series with the circuit element replaced with the voltage controlled current source or the voltage controlled voltage source. The output of the voltage controlled current source or the voltage controlled voltage source is controlled based on the voltage or current applied to the closed circuit. Alternatively, when there are a plurality of circuit elements included in the reference equivalent circuit, a voltage control current source or a voltage control voltage source in which each circuit element is replaced, or a closed circuit is integrated in common for the plurality of circuit elements. It is characterized by that. Furthermore, the capacitor is a multilayer ceramic capacitor.

  The simulation method of the present invention is characterized in that characteristics of an electronic circuit including a capacitor of the equivalent circuit are obtained by using an equivalent circuit of the capacitor constructed by any one of the construction methods.

  The simulation apparatus of the present invention is characterized in that the equivalent circuit of the capacitor constructed by any one of the construction methods is connected instead of the capacitor included in the circuit to be simulated, and the characteristics of the circuit to be simulated are calculated. To do. The above and other objects, features and advantages of the present invention will become apparent from the following detailed description and the accompanying drawings.

  According to the present invention, the circuit showing the characteristic change due to the DC voltage superposition is added to the circuit elements included in the equivalent circuit with reference to the equivalent circuit when no DC voltage is applied. Calculation load is reduced, and calculation problems due to divergence and the like are also reduced. In addition, the characteristic change of the passive component when the DC voltage is superimposed can be expressed with relatively simple and high accuracy.

It is explanatory drawing which shows the fundamental view of Example 1 with respect to a capacitive element. It is explanatory drawing which shows the fundamental view of Example 1 with respect to a resistive element. It is explanatory drawing which shows the other view of Example 1 with respect to a capacitive element. It is a circuit diagram which shows an example of the equivalent circuit at the time of DC voltage no application. It is a graph which shows the frequency characteristic at the time of DC voltage no application and superimposition. It is a graph which shows the change of the minimum capacity | capacitance value of an equivalent circuit element when changing the superimposed DC voltage, and a capacity | capacitance change rate. FIG. 5 is a circuit diagram showing a circuit configuration when the equivalent circuit of FIGS. 1 and 2 is applied to the equivalent circuit section of FIG. 4. FIG. 5 is a circuit diagram showing an overall circuit configuration when the equivalent circuit of FIGS. 1 and 2 is applied to the reference equivalent circuit of FIG. 4. It is explanatory drawing which shows the fundamental view of Example 2 of this invention. FIG. 10 is an explanatory diagram illustrating a method for grouping a plurality of voltage control voltage sources connected to an equivalent circuit in the second embodiment. 6 is a circuit diagram showing an equivalent circuit when a DC voltage is superimposed and applied in Embodiment 2. FIG. It is a block diagram which shows the Example of the simulation apparatus of this invention.

  Hereinafter, the best mode for carrying out the present invention will be described in detail based on examples.

First, Embodiment 1 of the present invention will be described with reference to FIG. As shown in FIG. 1A, when the signal voltage Vac is applied between the terminals of the capacitor C10 of the capacitor C, the signal current Iac expressed by Equation 1 flows.

On the other hand, as shown in FIG. 5B, the capacitive element C10 in FIG. 5A is replaced with a voltage-controlled current source E10, and the signal voltage Vac is copied to the voltage source E12. A capacitive element C10 and a monitor voltage source Vm for current monitoring are connected in series to the voltage source E12 to form a closed circuit. Since the monitor voltage source Vm does not affect the current characteristics of the closed circuit, the closed circuit is equivalent to the circuit shown in FIG. 5A, and the signal current Iac shown in the equation (2) flows through the capacitive element C10. .

This signal current Iac is monitored by the monitor voltage source Vm and fed back to the voltage control current source E10. The voltage control current source E10 multiplies the signal current Iac by the coefficient C ^* and outputs it. By performing the operation as described above, the current I (E10) flowing between the terminals is expressed by the equation (3). As is apparent from Equation (3), the equivalent circuit of FIG. 1B is equivalent to a circuit in which a capacitive element obtained by multiplying the capacitance C of the capacitive element C10 by C ^* is connected. In this way, by using the voltage controlled current source E10, the characteristics at the time of superimposing the DC voltage can be expressed.

As in the case of the capacitive element, an equivalent circuit obtained by multiplying the resistance by R ^* can be obtained for the resistive element by substantially the same procedure. That is, as shown in FIG. 2A, when the signal voltage Vac is applied between the terminals of the resistance element R10 having the resistance value R, the signal current Iac expressed by the equation (4) flows.

On the other hand, as shown in FIG. 5B, the resistance element R10 in FIG. 6A is replaced with a voltage-controlled current source E10, and the signal voltage Vac is copied to the voltage source E12. A resistor R10 and a monitor voltage source Vm for current monitoring are connected in series to the voltage source E12 to form a closed circuit. Since the monitor voltage source Vm does not affect the current characteristics of the closed circuit, the closed circuit is equivalent to the circuit shown in FIG. 5A, and the signal current Iac shown in the equation (5) flows through the resistance element R10. .

This signal current Iac is monitored by the monitor voltage source Vm and fed back to the voltage control current source E10. The voltage control current source E10 multiplies the signal current Iac by a coefficient R ^* ("divides") and outputs the signal. By performing the operation as described above, the current I (E10) flowing between the terminals is expressed by Equation 6. As is apparent from Equation (6), the equivalent circuit of FIG. 2B is equivalent to a circuit in which a resistance element R ^* times the resistance value R of the resistance element R10 is connected (current is 1 / R ^* times). Become.

Furthermore, it is possible to configure an equivalent circuit in which the capacitance of the capacitive element C10 is multiplied by C ^* with a voltage control voltage source. As shown in FIG. 3A, the signal voltage Vac between the terminals of the capacitor C10 of the capacitor C is expressed by the equation 7 with respect to the signal current Iac.

On the other hand, as shown in FIG. 5B, the capacitive element C10 in FIG. 6A is replaced with a voltage control voltage source E20, and a monitor power source Vm is connected in series. The signal current Iac monitored by the monitor power source Vm is copied to the current source E22. A capacitive element C10 is connected in series to the current source E22 to form a closed circuit. This closed circuit is equivalent to the circuit shown in FIG. 5A, and the signal current Iac shown by the equation 8 flows through the capacitive element C10.

When the signal voltage Vac applied to the capacitive element C10 is fed back to the voltage control voltage source E20 and the voltage fed back by the voltage control voltage source E20 is multiplied by 1 / C ^* and output, the voltage across the terminals of the current source E22 is output. Since V (3,4) does not affect the monitor voltage source Vm, the inter-terminal voltage V (1, 2) shown in Equation 9 is obtained, and as a result, the capacitance C of the capacitive element C10 is represented by C ^*. A doubled equivalent circuit is obtained.

In the case of a resistor element, the equivalent procedure is obtained by multiplying the output of the voltage control voltage source by R ^{* in} the same procedure, and multiplying the resistance value of the resistor element by R ^* .

By utilizing such a relationship, the DC voltage Vdc of the capacitive element and the resistive element of an equivalent circuit (hereinafter referred to as “reference equivalent circuit”) to which only the signal voltage Vac is applied when no DC voltage Vdc is applied (no superposition). The reference equivalent is obtained by previously measuring the capacitance change rate and resistance change rate due to superposition, and connecting a voltage controlled current source (voltage controlled voltage source in FIG. 3) in series to each element as described above. The DC voltage superposition characteristics of the capacitor represented by the circuit can be expressed. That is,
a. The circuit constants of the capacitive element and the resistive element included in the reference equivalent circuit are obtained in advance by actual measurement.
b, Next, the values of the capacitive element and the resistive element in a state in which the DC voltage Vdc is superimposed and applied to the signal voltage Vac are obtained by actual measurement.
c, Capacitance change rate and resistance change rate due to DC voltage superposition are obtained from the value of each element when DC voltage Vdc of a is 0 and the value of each element when DC voltage superimposition is applied (bac + Vdc). .
d, The current I (E ₁₀ ) is obtained from the obtained change rates by the above formulas 3 and 6.
e. By connecting a voltage-controlled current source E10 (voltage-controlled voltage source E20 in FIG. 3) of the obtained current I (E ₁₀ ) instead of the capacitive element and the resistive element in the reference equivalent circuit, the DC voltage Vdc is An equivalent circuit can be obtained when applied in a superimposed manner on the signal voltage Vac.

  FIG. 4A shows an example of a reference equivalent circuit to which the DC voltage Vdc is not applied. This reference equivalent circuit is known as FIG. 17 of JP 2013-228997 A. In the figure, capacitances Cm and C1 to C3 are connected in series, and resistances RC1 to RC3 are connected in parallel to the capacitances C1 to C3, respectively. Further, a capacitance C0 is connected in parallel to the entire circuit. The equivalent circuit portion QA described above is a capacitive portion, and by connecting a voltage control current source reflecting the rate of change due to DC voltage superimposition to each element included in this, an equivalent circuit of DC voltage superimposition characteristics. It can be.

  The equivalent circuit portion QA is further connected with a resistance R0 in parallel and an inductance L0 in series. Further, an inductance Lm, and three series circuits in which the inductances L1 to L3 and the resistances RL1 to RL3 are connected in series are further connected in parallel, which are connected in series to the inductance L0. Resistance Rdc is also connected in series. A series circuit of a capacitance Ct and a resistance Rt is connected in parallel to the above circuit.

  Here, in the above-described equivalent circuit portion QA, there are eight circuit elements, and the capacitance change rate and the resistance change rate at the time of superimposing the DC voltage of each element may be examined, but the work efficiency is not necessarily good. I can't say that. Therefore, in this embodiment, frequency characteristics of several samples of the multilayer ceramic capacitor are used.

  FIG. 5 shows frequency characteristics when a small amplitude signal is applied to a multilayer ceramic capacitor sample using a typical material. For example, frequency characteristics when a small amplitude signal is applied are measured using several types of samples of 22 μF multilayer ceramic capacitors manufactured by the applicant. (A) shows the characteristics when no DC voltage is applied, and (B) shows the characteristics when DC voltage is superimposed. The horizontal axis of the graph indicates frequency (logarithm), and the vertical axis indicates capacity.

  As shown in these solid line graphs GFa and GFb, it has been found that the capacitance of the capacitor linearly decreases with respect to the logarithm of the frequency and finally converges to a certain capacitance value as a lower limit value. The chain line graphs GLa and GLb are straight lines indicating a decrease in capacity, and the lower limit values are GPa and GPb. As is apparent from the comparison of these graphs, it can be seen that the slopes of the graphs GLa and GLb and the lower limit values GPa and GPb change between when the DC voltage Vdc is not applied and when it is superimposed. As described above, the change in the frequency characteristic of the capacitance due to the presence or absence of the DC voltage superposition of the multilayer ceramic capacitor is the change in the two parameters of the capacitance change rates ΔGLa and ΔGLb and the lower limit capacitance values GPa and GPb indicated by the slopes of the graphs GLa and GLb. It is characterized by.

  As a result, the equivalent circuit to which the DC voltage Vdc is applied in a superimposed manner also needs to have element components corresponding to the capacitance change rates ΔGLa and ΔGLb and the lower limit capacitance values GPa and GPb, as shown in FIG. For each of the eight circuit elements included in the equivalent circuit portion QA shown in FIG. 6, it is not necessary to examine the rate of change of the capacitance or resistance due to the DC voltage superposition. Actually, the capacitance frequency characteristics of the multilayer ceramic capacitor when no DC voltage is applied are matched with the reference equivalent circuit, and the circuit constant at that time is used as a reference. Next, the equivalent circuit shown in FIG. When the common rate of change corresponding to the applied voltage is applied to the constants of the respective elements in the parts QA1 and QA2, the equivalent circuit constant when the DC voltage superimposed application is applied can be determined.

  FIG. 5C shows the state. In the figure, the solid line graph GFA shows the measured capacitance frequency characteristics of the 22 μF multilayer ceramic capacitor manufactured by the applicant when no DC voltage is applied, and the solid line graph GFB shows the measured capacitance when the DC voltage of the capacitor is superimposed. Shows frequency characteristics. The superimposed DC voltage Vdc is 1 [V]. As shown in these graphs, the capacity change rate and the lower limit capacity value are reduced by superimposing the DC voltage Vdc, and the graph GFA becomes the graph GFB.

On the other hand, the dotted line graph GSA is obtained by combining the measured capacitance frequency characteristics when no DC voltage is applied with the reference equivalent circuit shown in FIG. Specific numerical examples of each circuit element are as follows.
Cm = 1.5718uF
C1 = 1uF
C2 = 0.52638uF
C3 = 0.001uF
RC1 = 36.345Ω
RC2 = 7.9335Ω
RC3 = 6.5488Ω

  With respect to such a circuit constant when no DC voltage is applied, the capacitance value of the capacitance C0 of the equivalent circuit portion QA1 is about 0.698 times, and the capacitance values of the capacitances Cm and C1 to C3 of the equivalent circuit portion QA2 are about 0.48 times. The capacitance frequency characteristic obtained from the equivalent circuit when the resistance values of the resistances RC1 to RC3 are about 1 / 0.48 times is shown as a dotted line graph GSB. When this is compared with the graph GFB of actual measurement values, it can be seen that the values agree very well. Further, when the capacitance value of the capacitance C0 of the equivalent circuit portion QA1 is changed, the lower limit capacitance value of the graph GSB (corresponding to the GPa and GPb) changes, and the capacitance values of the capacitances Cm and C1 to C3 of the equivalent circuit portion QA2 change. If the resistance values of the resistances RC1 to RC3 are changed, the capacity change rate of the graph GSB (corresponding to the slopes of the graphs GLa and GLb) changes. As described above, the characteristic of the equivalent circuit portion QA1 of the reference equivalent circuit of FIG. 4 substantially corresponds to the lower limit capacitance value, and the characteristic of the equivalent circuit portion QA2 substantially corresponds to the capacitance change rate.

  FIG. 5 described above is a case where the superimposed DC voltage Vdc is 1 [V]. However, if the same processing is repeated while changing the value of the DC voltage Vdc, the DC voltage Vdc and the equivalent circuit unit QA1, The relationship with the change rate of each circuit constant of each element included in QA2 can be obtained. In FIG. 6 (A), the calculated value obtained by combining the measured value of the lower limit capacity value with respect to the DC voltage Vdc is indicated by a circle, and in FIG. 6 (B), the measured capacity change rate with respect to the DC voltage Vdc. The calculated value that combines the values is indicated by a circle. 4A corresponds to the rate of change of the capacitance C0 of the equivalent circuit portion QA1 (rate of change relative to the value when no DC voltage is applied), and FIG. 3B shows the capacitances Cm, C1 to C1 of the equivalent circuit portion QA2. This corresponds to the rate of change of the capacitance value of C3 (change rate with respect to the value when no DC voltage is applied) and the reciprocal of the rate of change of resistance values of the resistances RC1 to RC3.

The measured value graph of FIG. 6 is expressed by the following mathematical formula 10. In the equation, Vpk, ζk, αk, βk are fitting coefficients.

  Looking at the equation (10), the function is an even function with respect to the DC voltage Vdc and symmetrical with respect to the reverse voltage, and there is no fear of divergence such as a power series. For this reason, contradiction of calculation results on the simulator and load during calculation are unlikely to occur. In this way, by connecting the voltage controlled current source in which the change rate of the circuit constant due to the DC voltage superimposition application is described using the above equation 10 to each element of the equivalent circuit portions QA1 and QA2, in series, The rate of change in capacitance and the rate of change in resistance caused by the superposition of Vdc can be expressed.

  Next, an application example of the equivalent circuit shown in FIGS. 1 and 2 will be described with respect to the equivalent circuit portion QA shown in FIG. 4 described above. For example, focusing on the equivalent circuit portion QA2 shown in FIGS. 4B to 7A, the capacitance values of the capacitances Cm and C1 to C3 are C * times, and the resistance values of the resistances RC1 to RC3 are 1 / C * times. Replace with the equivalent circuits of FIG. 1 (B) and FIG. 2 (B). For the parallel connection of the capacitance C1 and the resistance RC1, normally, the voltage controlled current sources corresponding to the respective rates of change should be connected to each other. The set of the capacitance C2 and the resistance RC2, the set of the capacitance C3 and the resistance RC3 are summarized in the same manner, and the entire equivalent circuit portion QA2 is replaced with the voltage controlled current source E10.

When the feedback current is multiplied by C ^* as in the case of a single element, the following equation (11) is obtained according to Kirchhoff's law. In the equation, Ici is the currents Icm, Ic1, Ic2, and Ic3 of the capacitances Cm, C1, C2, and C3, and IRci is the currents IRc1, IRc2, and IRc3 of the resistances RC1, RC2, and RC3. Since the voltage applied to each element Cm, C1 to C3, RC1 to RC3 does not change, as a result, the effect of multiplying the current flowing through each element constituting the equivalent circuit portion QA2 by C ^* is obtained. Therefore, the equivalent circuit of FIG. 7B has the capacitance values Cm and C1 to C3 of the equivalent circuit portion QA2 of FIG. 7A as C * times, and the resistance values of the resistances RC1 to RC3 as 1 / C * times. Thus, an equivalent circuit having a simple configuration in which the individual current sources are combined can be obtained without constructing an equivalent circuit using a current source for each element.

  Similarly, when the equivalent circuit of FIG. 1B is applied to the equivalent circuit portion QA1, the equivalent circuit shown in FIG. 4 becomes as shown in FIG.

Next, the overall operation of this embodiment will be described.
a. Each circuit constant of the circuit element included in the reference equivalent circuit of FIG. 4 is determined based on an actual measurement value of the frequency characteristic in a state where the DC voltage Vdc is not superimposed on the capacitor to be simulated.
b, Next, the frequency characteristic when the DC voltage Vdc is superimposed is measured, and the graph shown in FIG. 6 is obtained.
c, and the calculation of Equation 10 is performed from these graphs to determine the coefficients C ^* and R ^* of the voltage controlled current sources EC0 and ECm of FIG.
d. Next, when the DC voltage Vdc is superimposed, a change in circuit constant corresponding to the superimposed DC voltage Vdc is generated by the output of the current I (E ₁₀ ) from the voltage controlled current sources EC0 and ECm.
e, the equivalent circuit of FIG. 8 is described in a spice model format suitable for a typical spice simulator (LTspice, PSpice, etc.), for example, and simulation is performed on the simulator using the spice model. Alternatively, the circuit constant of each element of the equivalent circuit and the constant change rate information of the element of the capacitive part are described in the stand-alone or Web software, and the calculation method shown in the above embodiment is applied on the software. And presenting graphs and data of each frequency characteristic at an arbitrary DC voltage of the target multilayer ceramic capacitor, searching for a capacitor that satisfies a specified frequency characteristic at an arbitrary DC voltage, and frequency characteristics when applied to a simpler equivalent circuit Calculations may be performed.

  As described above, according to the present embodiment, the signal current corresponding to the superimposed DC voltage Vdc is superimposed on the portion QA expressing the capacitance with reference to the equivalent circuit shown in FIG. 4 when no DC voltage is applied. Voltage controlled current sources EC0 and ECm for adjusting Iac are connected in parallel, and the applied signal current change corresponding to the change in characteristics of the capacitor when DC voltage is superimposed is expressed by the voltage controlled current sources EC0 and ECm. . As a result, the element expressing the capacitance in the reference equivalent circuit behaves like a variable element when the DC voltage is superimposed. The approximate expression (Equation 10) of the coefficients (C *, R *) used for the currents (Equation 3 and Equation 6) of the voltage controlled current sources EC0 and ECm at that time reduces the calculation load during simulation. However, there is no calculation problem due to divergence within the operating voltage. As a result, the characteristics of the multilayer ceramic capacitor when an arbitrary DC voltage is superimposed can be accurately and quickly expressed on the equivalent circuit. In addition, the relatively simple equivalent circuit configuration facilitates operations such as alignment in creating an equivalent circuit, and improves the workability and efficiency of creating an equivalent circuit.

Next, Embodiment 2 of the present invention will be described with reference to FIGS. As shown in FIG. 9A, assuming that a voltage control voltage source is connected in series to the capacitive element and a voltage Vs expressed by the following equation (12) is applied by the voltage control voltage source, it is apparent that C It seems that the capacitance value of the capacitive element changes by the change rate of ^* .

Similarly, as shown in FIG. 9B, when a voltage control voltage source is connected in series to a resistance element and a voltage Vs expressed by the following equation (13) is applied by the voltage control voltage source, Apparently, it seems that the resistance value of the resistance element changes by the change rate of R ^* .

By utilizing such a relationship, the capacitance change rate and resistance change due to the superimposition of the DC voltage Vdc of the reference equivalent circuit to which only the signal voltage Vac is applied when no DC voltage Vdc is applied (no superimposition) and the DC voltage Vdc of the resistance element. By examining the rate in advance by actual measurement and connecting the voltage control voltage source in series to each element as described above, the DC voltage superposition characteristics of the capacitor represented by the reference equivalent circuit can be expressed. That is,
a. The circuit constants of the capacitive element and the resistive element included in the reference equivalent circuit are obtained in advance by actual measurement.
b, Next, the values of the capacitive element and the resistive element in a state in which the DC voltage Vdc is superimposed and applied to the signal voltage Vac are obtained by actual measurement.
c, Capacitance change rate and resistance change rate due to DC voltage superposition are obtained from the value of each element when DC voltage Vdc of a is 0 and the value of each element when DC voltage superimposition is applied (bac + Vdc). .
d, The voltage Vs is obtained from the obtained change rates according to the equations (12) and (13).
e. A DC control voltage source of the obtained voltage Vs is connected in series with the capacitive element and the resistive element in the reference equivalent circuit, thereby obtaining an equivalent circuit when the DC voltage Vdc is superimposed on the signal voltage Vac. be able to.

Next, connection of the voltage control voltage source to the reference equivalent circuit of FIG. 4 will be described. First, with respect to the equivalent circuit portion QA1, a voltage control voltage source DE1 having a voltage value obtained by applying the change rate shown in the graph of FIG. Next, paying attention to the equivalent circuit portion QA2, there are three sets of parallel connection of the capacitances C1 to C3 and the resistances RC1 to RC3. The change rate of each element of the equivalent circuit portion QA1 is common in capacitance, and the reciprocal of resistance is the change rate (see Equation 13). For this reason, when a voltage control voltage source describing the rate of change of the equation (10) is connected to each element connected in parallel, the admittance Y shown in the following equation (14) is obtained. In the equation, C is a value of capacitance connected in parallel, and R is a value of resistance connected in parallel.

  Referring to Equation 14, the admittance Y of the circuit in which the voltage control voltage source describing the rate of change of the capacitance is connected to the whole of the combination of the capacitance and the resistance connected in parallel. Therefore, the voltage control voltage source of each parallel connection set can be combined into one.

  FIG. 10A shows the state. For the parallel connection of the capacitance C1 and the resistance RC1, originally, the voltage control voltage sources DVC1 and DVRC1 corresponding to the rate of change should be connected to each other, but these are combined into the voltage control voltage source DV1. The same applies to the set of capacitance C2 and resistance RC2, and the set of capacitance C3 and resistance RC3.

Then, the voltage control voltage source of the above-described equivalent circuit portion QA2 becomes DVm and DV1 to DV3 shown in FIG. 4B, and is a circuit in which four impedances having the same capacitance change rate are connected in series. The impedance due to the series connection of the voltage control voltage sources DVm, DV1 to DV3 having the same rate of change is expressed by the following equation (15). Therefore, as shown in the figure, it is understood that this is equivalent to one in which all the elements other than the voltage control voltage source are connected and then one voltage control voltage source DE2 is connected in series.

  Next, when the voltage control voltage sources DE1 and DE2 detect the signal voltage Vac, it is necessary to remove the superposed DC voltage Vdc. For this reason, the input voltage (signal voltage Vac + superimposed DC voltage Vdc) of the reference equivalent circuit is supplied as a detection signal to the voltage control voltage sources DE1 and DE2 after the DC component is removed by a high-pass filter having a very low cutoff frequency. By adding such a filter circuit to the reference equivalent circuit of FIG. 4 together with the voltage control voltage sources DE1 and DE2, an equivalent circuit expressing the frequency characteristics when the DC voltage Vdc is superimposed can be obtained.

  An example is shown in FIG. In the equivalent circuit section QA1, the voltage control voltage source DE1 is connected in series, and in the equivalent circuit section QA2, the voltage control voltage source DE2 is connected in series. In the filter circuit GB, a high-pass filter is configured by the series capacitance CP and the parallel inductance LP, and the signal voltage Vac is detected by the load RP. Further, the input side and the output side of the equivalent circuit are connected to the voltage control voltage source DE3, and the input voltage Vin and the output voltage Vout are supplied. The voltage control voltage source DE3 outputs the difference between the input voltage Vin and the output voltage Vout. Then, the excess DC voltage Vdc is removed by the high-pass filter from the difference, and the signal voltage Vac is detected by the load RP and supplied to the voltage control voltage sources DE1 and DE2, respectively.

Next, the overall operation of this embodiment will be described.
a. Each circuit constant of the circuit element included in the reference equivalent circuit of FIG. 4 is determined based on an actual measurement value of the frequency characteristic in a state where the DC voltage Vdc is not superimposed on the capacitor to be simulated.
b, Next, the frequency characteristic when the DC voltage Vdc is superimposed is measured, and the graph shown in FIG. 6 is obtained.
c, and the calculation of Equation 10 is performed from these graphs to determine the coefficient C ^* of the voltage control voltage sources DE1 and DE2 in FIG. In this example, it is guaranteed that the voltage control voltage source DE2 summarizes the coefficients according to the equation (15). However, when the coefficients are determined individually (C ^* ≠ 1 / R ^* ), the voltage control voltage source DE2 Since the voltage sources cannot be combined like the source DE2, voltage control voltage sources remain connected in series to the individual elements.
d. Next, when the DC voltage Vdc is superimposed, the signal voltage Vac is detected by the filter circuit QB of FIG. 11, and thereby the circuit corresponding to the superimposed DC voltage Vdc by the output of the voltage Vs by the voltage control voltage sources DE1 and DE2. A constant change is generated.
e, the equivalent circuit of FIG. 11 is described in a spice model format suitable for a typical spice simulator (LTspice, PSpice, etc.), for example, and simulation is performed on the simulator using the spice model. Alternatively, the circuit constant of each element of the equivalent circuit and the constant change rate information of the element of the capacitive part are described in the stand-alone or Web software, and the calculation method shown in the above embodiment is applied on the software. And presenting graphs and data of each frequency characteristic at an arbitrary DC voltage of the target multilayer ceramic capacitor, searching for a capacitor that satisfies a specified frequency characteristic at an arbitrary DC voltage, and frequency characteristics when applied to a simpler equivalent circuit Calculations may be performed.

  As described above, according to the present embodiment, the signal voltage corresponding to the superimposed DC voltage Vdc is superimposed on the portion QA expressing the capacitance with reference to the equivalent circuit shown in FIG. 4 when no DC voltage is applied. Voltage control voltage sources DE1 and DE2 for adjusting Vac are connected in series, and the applied signal voltage change corresponding to the change in the characteristics of the capacitor when DC voltage is superimposed is expressed by voltage control voltage sources DE1 and DE2. . As a result, the element expressing the capacitance in the reference equivalent circuit behaves like a variable element when the DC voltage is superimposed. The approximate expression (Equation 10) of the coefficients (C *, R *) used for the voltages (Equation 12 and Equation 13) of the voltage control voltage sources DE1 and DE2 at that time reduces the calculation load during the simulation. However, there is no calculation problem due to divergence within the operating voltage. As a result, the characteristics of the multilayer ceramic capacitor when an arbitrary DC voltage is superimposed can be accurately and quickly expressed on the equivalent circuit. In addition, the relatively simple equivalent circuit configuration facilitates operations such as fitting in creating an equivalent circuit, and improves the workability and efficiency of creating an equivalent circuit.

  Next, an embodiment of the simulation apparatus will be described with reference to FIG. The simulation apparatus 100 according to the present embodiment is configured by a general computer system, and includes an arithmetic processing unit 110 mainly configured by a CPU, an input unit 122 such as a keyboard, an output unit 124 such as a liquid crystal display, and a program memory. 130 and the data memory 140 are connected. The program memory 130 stores a simulation program 132 (for example, a SPICE simulator). The data memory 140 stores a simulation target circuit 142 including a capacitor and a capacitor equivalent circuit 144 illustrated in FIGS. 8 to 11.

  The simulation target circuit 142 corresponds to a circuit in which the DC voltage Vdc is superimposed on the signal voltage Vac, for example, a power supply line of an arithmetic processing IC such as a CPU. The capacitor equivalent circuit 144 is prepared for each capacitor. For example, the equivalent circuit 144A, 144B,... When the simulation program 132 is a SPICE simulator, the capacitor equivalent circuit 144 is provided as a SPICE file.

  When it is instructed which capacitor of which model of which company is used as the capacitor included in the simulation target circuit 142, the equivalent circuit 144 of the corresponding capacitor is read from the data memory 140, and this is the simulation target circuit 142. Connected to the capacitor position. Based on the circuit, the simulation program 132 in the program memory 130 is executed by the arithmetic processing unit 110 to perform a desired simulation. By using the equivalent circuit at the time of applying the DC voltage superimposed shown in FIGS. 8 to 11, the time required for the simulation can be shortened and an efficient simulation can be performed efficiently.

As described above, according to the present embodiment, the following effects can be obtained.
(1) Electronic component manufacturers and their trading companies provide customers with equivalent circuits for the various capacitors they provide when DC voltage is superimposed, or publish them on the company's website to customers who adopt their products. On the other hand, convenience in circuit design can be achieved, and further, product sales opportunities can be created.
(2) Electronic device manufacturers and electronic circuit design companies can use the published equivalent circuit when DC voltage is superimposed to efficiently select the optimal electronic components for the design circuit and accurately select electronic products. Design is possible and the design time can be greatly reduced.

In addition, this invention is not limited to the Example mentioned above, A various change can be added in the range which does not deviate from the summary of this invention. For example, the following are also included.
(1) The reference equivalent circuit shown in the above embodiment is an example, and the present invention can be applied to reference equivalent circuits having various configurations.
(2) The numerical values and ratios of the circuit constants shown in the above embodiment are examples, and are not limited at all.
(3) In the above description, the case where the equivalent circuit using the voltage controlled current source E10 shown in FIGS. 1 and 2 is applied to the capacitive element and the resistive element included in the reference equivalent circuit has been mainly described. An equivalent circuit using the voltage control voltage source E20 shown in FIG. 3 may be used. In the above embodiment, the case of the capacitive element and the resistance element included in the reference equivalent circuit has been described, but the same applies to the case of the inductor element.
(4) The present invention is typically applied to a multilayer ceramic capacitor, but can be applied to equivalent circuits of various capacitors.

  According to the present invention, since a circuit showing a characteristic change due to a DC voltage superimposed on a signal is added on the basis of an equivalent circuit when no DC voltage is applied, a calculation load during simulation is reduced. In addition, calculation problems due to divergence and the like are reduced. In addition, since the characteristic change of the circuit element when the DC voltage is superimposed can be expressed relatively simply and with high accuracy, it is suitable for characteristic analysis of a multilayer ceramic capacitor or the like.

C0, C1 to C3, Cm, Ct, CP: Capacitance C10: Capacitance element E10: Voltage controlled current source E12: Voltage source E20: Voltage controlled voltage source E22: Current source L0, L1 to L3, Lm, LP: Inductance R0, RC1 to RC3, RL1 to RL3, Rdc, Rt, RP: Resistance R10: Resistive elements DE1, DE2, DE3, DVC1, DVRC1, DVm, DV1 to DV3: Voltage control voltage sources QA, QA1, QA2: Equivalent circuit part QB: Filter circuit Vac: Signal voltage Vdc: DC voltage Vin: Input voltage Vout: Output voltage Vm: Monitor voltage source 100: Simulation device 110: Arithmetic processing unit 122: Input unit 124: Output unit 130: Program memory 132: Simulation program 140: Data memory 142: Simulation target circuit 144, 144A, 144B,...: Equivalent circuit of capacitor

FIG. 4A shows an example of a reference equivalent circuit to which the DC voltage Vdc is not applied. This reference equivalent circuit is known as FIG. 17 of JP 2013-228997 A. In the figure, capacitances Cm and C1 to C3 are connected in series, and resistances RC1 to RC3 are connected in parallel to the capacitances C1 to C3, respectively. Further, a capacitance C0 is connected in parallel to the entire circuit. More equivalent circuit QA is a moiety of the capacitive, the elements contained therein, by replacing the voltage controlled current source that reflects the rate of change by a DC voltage superimposed to an equivalent circuit of the DC voltage bias characteristics be able to.

Looking at the equation (10), the function is an even function with respect to the DC voltage Vdc and symmetrical with respect to the reverse voltage, and there is no fear of divergence such as a power series. For this reason, contradiction of calculation results on the simulator and load during calculation are unlikely to occur. In this manner, by substituting the equivalent circuit QA1, QA2 rate of change in circuit constant by a DC voltage superimposed application of the voltage controlled current source described using the number 10 formula, produced by superposition of DC voltage Vdc Capacitance change rate and resistance change rate can be expressed.

When the feedback current is multiplied by C ^* as in the case of a single element, the following equation (11) is obtained according to Kirchhoff's law. In the equation, Ici is the currents Icm, Ic1, Ic2, and Ic3 of the capacitances Cm, C1, C2, and C3, and IRci is the currents IRc1, IRc2, and IRc3 of the resistances RC1, RC2, and RC3. Since the voltage applied to each element Cm, C1 to C3, RC1 to RC3 does not change, as a result, the effect of multiplying the current flowing through each element constituting the equivalent circuit portion QA2 by C ^* is obtained. Therefore, the equivalent circuit of FIG. 7B has the capacitance values Cm and C1 to C3 of the equivalent circuit portion QA2 of FIG. 7A as C * times, and the resistance values of the resistances RC1 to RC3 as 1 / C * times. Thus, an equivalent circuit having a simple configuration in which the individual current sources are combined can be obtained without constructing an equivalent circuit using a current source for each element.

Claims (7)

A method for constructing an equivalent circuit of a capacitor in which a DC voltage may be applied in a superimposed manner on a signal,
In a state where no DC voltage is applied and only a signal is applied, obtaining a reference equivalent circuit by obtaining the value of each circuit element included in the equivalent circuit from actual measurement;
Replacing a circuit element included in the reference equivalent circuit, the value of which changes due to superposition of a DC voltage, with a voltage-controlled current source or a voltage-controlled voltage source;
Adding a closed circuit representing a state in which only the signal is applied to the replaced circuit element;
Outputting a current or voltage having a value obtained by multiplying a current or voltage generated in the circuit element by the closed circuit by a factor from the voltage controlled current source or the voltage controlled voltage source;
A method for constructing an equivalent circuit of a capacitor, comprising: The frequency characteristic of the circuit element measured in a state where a DC voltage is superimposed on the signal is compared with the frequency characteristic of the circuit element actually measured in a state where only the signal is applied, and Determining a change in value;
Based on the change in the value of the circuit element due to the DC voltage superposition obtained in the step, the step of outputting a coefficient multiple of the current or voltage value in the voltage controlled current source or voltage controlled voltage source;
The method for constructing an equivalent circuit for a capacitor according to claim 1, comprising: In the closed circuit, a voltage source or a current source is connected in series with the circuit element replaced with the voltage controlled current source or the voltage controlled voltage source,
3. The capacitor according to claim 1, wherein an output of the voltage controlled current source or the voltage controlled voltage source is controlled based on a voltage or current applied to the closed circuit by the voltage source or the current source. Equivalent circuit construction method.   When there are a plurality of circuit elements included in the reference equivalent circuit, a voltage controlled current source or a voltage controlled voltage source in which each circuit element is replaced or a closed circuit is grouped together for a plurality of circuit elements. The method for constructing an equivalent circuit for a capacitor according to any one of claims 1 to 3.   The said capacitor | condenser is a multilayer ceramic capacitor, The construction method of the equivalent circuit of the capacitor | condenser as described in any one of Claims 1-4 characterized by the above-mentioned.   An equivalent circuit of a capacitor characterized in that, by using the equivalent circuit of the capacitor constructed by the construction method according to any one of claims 1 to 5, characteristics of an electronic circuit including the capacitor of the equivalent circuit are obtained. Simulation method.   An equivalent circuit of the capacitor constructed by the construction method according to any one of claims 1 to 6 is connected instead of the capacitor included in the circuit to be simulated, and the characteristics of the circuit to be simulated are calculated. A device for simulating an equivalent circuit of a characteristic capacitor.

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