KR100593899B1 - Analysis method of high field nonlinear characteristics of capacitor - Google Patents

Abstract

The present invention relates to an equivalent circuit capable of expressing nonlinear characteristics of voltage and capacitance of a capacitor appearing in a high field. According to an aspect of the present invention, there is provided an equivalent circuit expressing a high field nonlinear characteristic of a capacitor having a predetermined capacity, comprising: two ideal capacitors connected in series with each other and having twice the capacity of the capacitor; And a dependent power supply connected in series between the two ideal capacitors. According to the present invention, since the nonlinear characteristics of the capacitor can be taken into account from the circuit design stage, by eliminating an additional tuning process according to the nonlinear characteristics after the actual circuit fabrication, productivity can be improved and manufacturing cost can be reduced. .

Dielectric Stacked Capacitors, MLCCs, Equivalent Circuits, Dependent Power Supplies, Circuit Design, Simulation

Description

ANALYSIS METHOD OF NON-LINEAR PROPERTY OF CONDENSER IN HIGH ELECTRIC FIELD

1 is an ideal voltage-charge relationship graph of a capacitor.

2 is an equivalent circuit diagram of a capacitor expressing a high field nonlinear characteristic according to the present invention.

3 is a configuration diagram of an experimental apparatus for measuring a high field nonlinear characteristic.

4A and 4B are graphs of a voltage-charge relationship comparing a non-linear characteristic of an actually measured capacitor and a characteristic simulated by an equivalent circuit according to the present invention.

* Description of the symbols for the main parts of the drawings *

1: condenser 2: frequency response analyzer

3: oscilloscope 4: power amplifier

5: current probe 6: computer

10: capacitor equivalent circuit 11, 12: ideal capacitor

13: subordinate power supply (V _c )

The present invention relates to a high field nonlinear characteristic analysis method of a capacitor capable of expressing nonlinear characteristics of a voltage and a capacitance in a high field. The present invention relates to a high-frequency nonlinear characteristic analysis method of a capacitor which can improve the accuracy of a circuit design by representing an equivalent circuit including a subordinate power supply connected in series.

In general, multilayer ceramic chip capacitors (MLCCs) are the most representative of Surface Mounting Device components, such as coupling, signal bypass, and time constant circuits in electronic devices. It is an important passive device that plays the role of forming a constant circuit, and it is a dielectric device that forms the basic circuit components of various electronic devices together with chip resistors. The dielectric multilayer capacitors are being used in basic circuit components such as electronic tuners, camcorders, HDTVs, LCD TVs, notebook computers, PCs, and the like. In particular, the structure of the dielectric multilayer capacitor has the advantage that the dielectric layer having a thickness of several micrometers to several tens of micrometers and the internal electrode side of several micrometers are laminated to each other to obtain a large capacity characteristic with a small structure. Therefore, the demand is rapidly increasing, replacing the conventional tantalum and electrolytic capacitors.

In general, in an ideal capacitor, voltage, capacity, and charge amount have a relationship as in Equation 1 below.

[Equation 1]

(Q : 전하량, C : 용량, V : 전압)

(Q: charge amount, C: capacity, V: voltage)

Therefore, in the ideal capacitor, since its capacity is fixed constantly, the relationship between the voltage and the amount of charge is represented by a graph having a linear characteristic as shown in FIG.

However, in the case of an actual dielectric stacked capacitor, the linear characteristics as shown in FIG. 1 do not appear as the voltage increases, that is, toward the high field. In fact, the capacitor increases as the charge increases. This is due to the decrease in capacitance of the dielectric multilayer capacitor as the high electric field is generated.

In particular, when designing a circuit such as an electronic device, the circuit is generally designed using an ideal capacitor (a capacitor having the characteristics of Equation 1) provided by circuit design software (for example, SPICE). The high field nonlinear nature of the same real capacitor is not reflected in the circuit design. Because of this, the circuits designed in the circuit design software do not match the characteristics of the actual fabricated circuits. To correct this, additional tuning according to the nonlinear characteristics of the capacitors is required.

In this way, the circuit design does not match the characteristics of the actual circuit, and apart from the simulation performed at the design stage of the circuit, the additional tuning after the circuit is manufactured requires additional product production processes and lowers productivity. This will occur.

Therefore, there is an urgent need in the art for equivalent circuits of dielectric multilayer capacitors capable of representing real capacitors having nonlinear characteristics in high electric fields so that they can be used in simulation software and the like in circuit design.

SUMMARY OF THE INVENTION The present invention has been made to solve the above problems, and when designing a circuit of an electronic device, a high-capacity capacitor of a capacitor capable of eliminating a separate tuning process by expressing a nonlinear characteristic of a voltage and a charge amount in a high electric field of an actual capacitor The purpose is to provide a method for analyzing nonlinear characteristics.

In order to achieve the above technical problem, the present invention,
In the analysis method for analyzing a high field nonlinear characteristic of a capacitor having a predetermined capacitance,
Setting two ideal capacitors having a capacity twice the capacitor capacity; And
Setting up a slave power supply connected in series between the two ideal capacitors,

It provides a high field nonlinear characteristic analysis method of a capacitor, characterized in that the capacitor is interpreted as an equivalent circuit composed of the two ideal capacitors and the cascade power supply connected in series therebetween.

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The nonlinear characteristic of the capacitor may be expressed as a polynomial of the voltage value V applied across the capacitor in Equation 1. In the present invention, the high field nonlinear characteristics of the capacitor may be expressed as in Equation 2 below.

[Equation 2]

In Equation 2, Q is an amount of charge stored in the capacitor, and V ₁ and V ₂ are voltages across the capacitor. That is, V ₁ -V ₂ is equal to V in Equation 1. And α ₁ to α ₄ are the doses of the respective terms. The values of α ₁ to α ₄ can be obtained by measuring the nonlinear characteristics of the capacitor and substituting the amount of charge and the voltage value into the equation (2).

In addition, the voltage value V _c of the slave power source is calculated from the above equation 2. The voltage value of the slave power supply is expressed as in Equation 3 below.

[Equation 3]

In Equation 3, V _c is a voltage value of the dependent power supply, and C _m is a capacitance value of an actual capacitor having a nonlinear characteristic to be expressed as an equivalent circuit.

Hereinafter, with reference to the accompanying drawings, it will be described in more detail the high electric field nonlinear characteristic analysis method of the capacitor according to the present invention.

The inventors of the present invention, through the research and experiment, as shown in Fig. 2, in order to express the nonlinear characteristics of the capacitor, two ideal capacitors 11 and 12 connected in series, and connected in series between them It was concluded that it is desirable to represent the capacitor using the equivalent circuit 10 consisting of the slave power source 13. The capacitor is a dielectric multilayer capacitor (MLCC) having a nonlinear characteristic in a high electric field, that is, a capacitance decreases toward a high electric field. In the following description, the term "condenser" mainly refers to a dielectric multilayer capacitor.

Since the two ideal capacitors 11 and 12 are connected in series with each other, the value should be twice the capacity of the original capacitor. That is, if the value of the original capacitor to be expressed by the equivalent circuit is 4.7 kW, the capacity of each of the ideal capacitors 11 and 12 is 9.4 kW.

Subsequently, the following method was used to determine the voltage value of the slave power source 13.

As described above, in general, the relationship between the voltage and the amount of charge in an ideal capacitor can be expressed by Equation 1 below.

[Equation 1]

In Equation 1, C is a capacitance value of the capacitor, V is a potential difference across the capacitor, and Q is an amount of charge stored in the capacitor.

However, Equation 1 is a formula that can be applied to an ideal capacitor, and does not exhibit nonlinear characteristics in actual high electric field. Therefore, when designing a circuit of an electronic device or the like, when designing a circuit with a capacitor to which Equation 1 is applied in a simulation software or the like, an error occurs in the characteristic between the designed circuit and the actual circuit due to the nonlinear characteristic toward the high electric field. Therefore, an equivalent circuit of a capacitor having a nonlinear characteristic that can be applied to the simulation in the circuit design stage is needed.

The inventors of the present invention present Equation 2 below, which shows the non-linear characteristics of the capacitor to find the voltage value of the slave power source 13 in the equivalent circuit 10 of the capacitor as shown in FIG.

[Equation 2]

Equation 2 is a formula for expressing the non-linear characteristics between the voltage and the amount of charge in the capacitor. Q is the charge amount, and V ₁ and V ₂ are potentials at both ends of the capacitors 31 and 32. That is, V ₁ -V ₂ corresponds to V in Equation 1. The coefficients α ₁ to α ₄ of each term correspond to the dose of each term. Equation 2 expresses the charge amount in the fourth order of V ₁ -V ₂ to represent the non-linear characteristics of the capacitor, but the more higher the expression, the more accurate the non-linear characteristics can be represented. However, in the case of the fifth order term of V ₁ -V ₂ or more, since the capacity value of each term, which is the coefficient of each term, appears very small, it is most preferable to ignore it and to express it in the fourth order of V ₁ -V ₂ as in Equation 2.

Experimental equipment was configured as shown in FIG. 3 to obtain values of α ₁ to α ₄ satisfying Equation 2. In this experiment, a capacitor (1) for measuring nonlinear characteristics, a frequency response analyzer (2), an oscilloscope (3), and a power amplifier (4) for applying and analyzing a voltage (or current) having a predetermined frequency and magnitude are analyzed. An experimental apparatus composed of a current probe 5 and a computer 6 for converting current into voltage was used.

First, the current generated by the power supply 2g in the frequency response analyzer 2 is amplified by the power amplifier 4 and passed through the capacitor 1, and the current passing through the capacitor 1 is passed by the current probe 5. It is converted into a voltage value and input to the frequency response analyzer 2 and the oscilloscope 3. The voltage value thus measured is measured by the frequency response analyzer 1 and the relationship between the voltage and the amount of charge is displayed on the computer 6. The frequency response analyzer 2 and oscilloscope 3 are connected to the computer 6 using a General-Purpose Interface Bus (GPIB).

The curves indicated by squares in FIGS. 4A and 4B show the nonlinear characteristics of the capacitor 1 measured through the experimental apparatus. 4A is a characteristic curve of a 4.7 kV capacitor, and FIG. 4B is a characteristic curve of a 1.0 kV capacitor. As shown in FIGS. 4A and 4B, the capacitor exhibits a nonlinear characteristic in which an increase in charge amount decreases toward a high electric field. If the voltage-charge amount corresponding to any of the four points on the curve is input into Equation 2, the values of α ₁ to α _{4, which} are the capacity of each term, can be obtained.

Subsequently, both sides of Equation 2 were divided by the capacitance value C _m of the capacitor, and the voltage value V _c of the slave power source 13 of the equivalent circuit shown in FIG. 2 was derived as in Equation 3 below.

[Equation 3]

In Equation 3, V _c is the voltage value of the dependent power supply, C _m is the capacitance value of the capacitor. And, the last term on the right side of-(V ₁ -V ₂ ) is to express the nonlinear characteristics of the capacitor. Therefore, the dependent power source of the equivalent circuit used to express the nonlinear characteristics of the capacitor as shown in equation 3 is controlled by the potential difference across the capacitor.

4A and 4B are graphs of a voltage-charge relationship comparing the nonlinear characteristics of the capacitor actually measured by the experimental apparatus shown in FIG. 3 with the characteristics of the capacitor simulated by the equivalent circuit according to the present invention. The simulation results shown in FIGS. 4A and 4B used B ² SPICE (Beige Bag Software Co., Ltd.).

4A shows a comparison between the measured value and the simulation value using the equivalent circuit of the present invention using a 4.7 kV capacitor. For a 4.7 kV capacitor, the nonlinear characteristics represented by Equation 2 are Q = 5 × 10 ^-6 V-8 × 10 ^-19 V ² -2 × 10 ^-8 V ³ + 3 × 10 ^-20 V ⁴ (V is Potential difference across the capacitor). If the voltage value of the slave power supply used in the equivalent circuit is obtained using this equation, Vc = 1.1 V-1.7 x 10 ^-13 V ² -4 x 10 ^-3 V ³ +6 x 10 ^-15 V ⁴ -V (V is the potential difference across the capacitor). Two and one an ideal capacitor has a capacitance of the ideal capacitor 9.4㎌ in series instead of in the simulation software 4.7㎌ connected therebetween ^{Vc = 1.1V-1.7 × 10 -13} V 2 -4 × 10 -3 V 3 + 6 × 10 - ^The result of simulating the charge amount-voltage characteristic by substituting an equivalent circuit composed of a subordinate power supply having a voltage value of ¹⁵ V ⁴ -V (V is a potential difference across the capacitor) is shown by a curve indicated by a plurality of circles in FIG. 4A. As shown in Fig. 4a, the characteristic curve of the 4.7 kV capacitor measured by experimental equipment (square curve) and the characteristic curve of the capacitor simulated by the equivalent circuit configured as described above (characteristic curve indicated by circle) Is almost identical.

4B compares the measured value and the simulation value using the equivalent circuit of the present invention using a 1.0 kV capacitor. In the case of a 1.0 kV capacitor, the nonlinear characteristic represented by Equation 2 is Q = 1 × 10 ^-6 V + 5 × 10 ^-19 V ² -5 × 10 ^-10 V ³ -2 × 10 ^-21 V ⁴ (V is Potential difference across the capacitor). If the voltage value of the slave power supply used in the equivalent circuit is obtained using this equation, Vc = V + 5 × 10 ^-13 V ² -5 × 10 ^-4 V ³ -2 × 10 ^-15 V ^4- V is the potential difference across the capacitor. In the simulation software, instead of the ideal capacitor of 1.0 ㎌, two ideal capacitors with a capacity of 2.0 직렬 in series and between them Vc = V + 5 × 10 ^-13 V ² -5 × 10 ^-4 V ³ -2 × ^10-15 The result of simulating the charge amount-voltage characteristic by substituting an equivalent circuit composed of a subordinate power supply having a voltage value of V ⁴ -V (V is the potential difference across the capacitor) is shown by a curve indicated by a plurality of circles in FIG. 4B. As shown in Fig. 4b, the characteristic curve of the 1.0 kV capacitor measured by the experimental equipment (curved in a square) and the characteristic curve of the condenser simulated by the equivalent circuit configured as described above (indicated by a circle) Almost identical.

As described above, when the equivalent circuit of the capacitor according to the present invention is used, the nonlinear characteristics of the dielectric multilayer capacitor (MLCC) exhibited in the high field can be accurately represented, and thus have the same characteristics as those of the capacitor operating in the actual circuit. Simulation of the capacitors becomes possible. Therefore, since the nonlinear characteristics of the capacitor can be considered from the circuit design stage, an additional tuning process according to the nonlinear characteristics is unnecessary after the actual circuit fabrication.

As described above, according to the present invention, it is possible to accurately represent the non-linear characteristics of the dielectric multilayer capacitor (MLCC) appearing in the high field, it is possible to simulate the capacitor having the same characteristics as the characteristics of the capacitor operating in the actual circuit in the circuit design stage It is effective. In addition, since the nonlinear characteristics of the capacitor can be taken into account from the circuit design stage, the additional circuit tuning process according to the nonlinear characteristics can be omitted after the actual circuit fabrication, thereby improving productivity and reducing manufacturing costs.

Claims (3)

In the analysis method for analyzing a high field nonlinear characteristic of a capacitor having a predetermined capacitance, Setting two ideal capacitors having a capacity twice the capacitor capacity; And Setting up a slave power supply connected in series between the two ideal capacitors, And analyzing the capacitor as an equivalent circuit composed of the two ideal capacitors and the cascaded power supply connected in series therebetween. The method of claim 1, wherein the capacitance of the capacitor in the high field, A high field nonlinear characteristic analysis method of a capacitor, which is represented by Equation 2 below. [Equation 2]

(Q: amount of charge stored in the capacitor, V ₁ , V ₂ : voltage at each end of the capacitor, α ₁ ~ α ₄ : capacity of each term) The method of claim 1, wherein the dependent power source, A high field nonlinear characteristic analysis method of a capacitor, characterized by the following Equation 3. [Equation 3]

(V _c : Voltage value of slave power, C _m : Capacitor capacity)

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