RU2589509C1 - Method of determining current in channel of electric breakdown of dielectric material - Google Patents

Abstract

FIELD: measuring equipment; electricity.

SUBSTANCE: invention relates to physics of electric breakdown and can be used for determination of amplitude and duration of current pulse electric breakdown in dielectric materials. Summary: high constant voltage U from previously charged capacitor with capacitance C_d is supplied to electrodes with dielectric sample arranged between them. Voltage pulse across waveform is measured at breakdown on connected in series with electrodes measuring resistor R circular frequency ω and oscillation damping time τ. Resistance R₀ is determined by calculation, and desired values of amplitude and duration of current are found respectively using formulae I_m=U/R₀, Δt=R₀C.

EFFECT: high accuracy of determining current in channel of electric breakdown of dielectric materials.

1 cl, 5 dwg

Description

The invention relates to the field of physics of electrical breakdown and can be used to determine the amplitude and duration of the pulse of the current of electrical breakdown in dielectrics.

The problem of the dielectric strength is still relevant, despite the fact that research in the field of breakdown physics has continued for many decades. At present, there is no generally accepted model for the electrical destruction of dielectrics, in particular polymer ones, which are widely used as insulation. There is not even reliable data on the values of breakdown currents that cause the destruction of dielectrics. Knowing the true values of the breakdown currents will provide additional information on the breakdown mechanism and information on the conditions for the destruction of dielectrics in an electric field and, therefore, outline ways to increase their electric strength and performance.

A known method for determining the current of formation of a conducting channel by changing the intensity of the light emitted by a semiconductor light source (LED, laser) included in the circuit of a pointed electrode (H. Yamada, T. Fujiwara and Y. Suzuoki, Electrical breakdown time delay and breakdown propagation velocity in polypropylene under a highly nonuniform field condition., J.Phys. D: Appl. Phys., 26, 1993, 1328-1330). A polymer sample was placed between the flat and pointed electrodes and filled with transformer oil to prevent discharge in the air. The breakdown current was measured by a light emitting diode connected in series with a pointed electrode, using the dependence of the brightness of the diode on the magnitude of the current flowing through it. The signal from the diode was transmitted using a fiber to a photomultiplier connected to an oscilloscope.

The disadvantage of this method is the low accuracy of determining the current value of the breakdown channel, since the light source is connected in series with the sample. In addition, the use of light sources and receivers significantly reduces the frequency range of the measured currents or voltages.

A known method for determining the current through the sample by turning on the current meter in series with the capacity of the measuring cell with the sample (Liu D., Kao K.S. High-field hole injection, conduction, and breakdown in polyethylene films fabricated by plasma polymerization, J. Appl. Phys 69, 1991, P. 2489-2496). A flat polymer sample was placed between two flat electrodes, one of which was sprayed onto the surface of the polymer in vacuum. A linearly varying voltage was applied to the electrodes, and the conductivity and breakdown current were measured using a logarithmic ammeter connected in series with the electrodes.

The disadvantage of this method is the low accuracy of current measurement, because not the true breakdown current is measured, but the current determined by the elements of the measuring circuit (wire inductance, limiting resistors), the resistance of which can exceed the resistance of the breakdown channel.

Closest to the claimed method (prototype) is a method for measuring the conductivity of a sample (R. Rinkunas, S. Kuskevičius, Journal of Technical Physics, 2009, Volume 79, Issue 1, p. 135). A dielectric sample is placed between the conductive substrate (flat electrode) and the needle electrode. Before measurement, the capacitor included in the circuit with the sample is charged by a voltage source to the voltage necessary for breakdown between the surface of the sample and the needle-shaped electrode. At the same time, an additional capacitor of a larger capacity is also charged. The magnitude of this charge is measured when the capacitor is discharged through the measuring resistance using an oscilloscope. As the conductivity of the sample increases, an increasing charge accumulates in the capacitor. By the magnitude of this charge, one can judge the conductivity of the test sample.

The disadvantage of the prototype is the low accuracy of the current measurement, since the charge flowing during the breakdown is measured, not the current strength, and the resistance of the breakdown channel is not taken into account.

The present invention solves the problem of increasing the accuracy of determining the current (amplitude and duration) in the channel of electrical breakdown of the dielectric.

The problem is solved by the method of determining the current in the channel of dielectric electrical breakdown, including placing a dielectric sample between two electrodes, applying high DC voltage U to the electrodes with a pre-charged capacitor with capacitance C _d , measuring the voltage waveform during breakdown at a measurement resistor of R connected in series with the electrodes, in which, according to the claims, the circular frequency ω and the oscillation decay time τ are measured from the oscillogram, the value of R ₀ resistance of the electric breakdown channel of the dielectric from the ratio:

Where:

K = 1 + ωτ;

C is the capacity of the electrodes with the sample;

L is the inductance of the measuring circuit;

C ₁ - parasitic capacitance formed by conductors connected by a measuring resistor R,

and the desired values of the amplitude I _m and the duration Δt of the current pulse are found, respectively, from the relations: I _m = U / R ₀ , Δt = R ₀ C.

The technical result achieved is to increase the accuracy of determining the electric breakdown current of dielectrics.

Reliable experimental data on the breakdown currents are currently lacking, because the existing methods for detecting current in the breakdown channel are imperfect, and their use leads to significant errors. Let us explain this with the help of FIG. 1, which shows a diagram of the flow of currents during breakdown of a dielectric,

Where:

1 - dielectric sample;

2 - electrode;

3 - electrode;

4 - capacitor with a capacitance C _d ;

5 - measuring resistor with resistance R;

6 - breakdown channel with resistance R ₀ ;

7 - limiting resistor.

To determine the current through the sample, the voltage drop is usually measured on a known (measuring) resistor 5 connected in series with a capacitor formed by sample 1 and electrodes 2 and 3.

The authors of the invention for the first time revealed the fact that the breakdown current consists not only of the current closing to the ground I ₁ (t), but also from the self-discharge current of the sample capacitor I (t), which cannot be measured directly, since it closes through breakdown channel resistance 6 in the sample volume. The self-discharge current of the sample can be tens of times higher than the measured current, due to which the true breakdown current is almost equal to the self-discharge current of the dielectric sample.

In the proposed method, the authors were able to determine the true breakdown current flowing in a circuit that is inaccessible to measurement (sample volume) according to the measurement data of the parameters of the breakdown voltage pulse at the measuring resistor 5 (the oscillation frequency ω and their decay time τ).

To illustrate the method, consider the equivalent circuit shown in FIG. 2

Where:

4 - capacitor with a capacitance C _d ;

5 - measuring resistor with resistance R;

6 - breakdown channel with resistance R ₀ ;

8 - capacitor with capacitance C (capacitance of sample 1 with electrodes 2 and 3);

9 - inductance of the measuring circuit value L;

10 - capacitor with stray capacitance value C ₁ .

The stray capacitor 10 is formed by conductors connected by a measuring resistor 5. I ₂ (t) is the current flowing through the capacitor 10.

The voltages and currents in the equivalent circuit are connected by a system of differential equations, the characteristic equation of which can be written in the form:

s ⁴ + bs ³ + cs ² + ds + e = 0,

Where:

We denote the roots of the characteristic equation as s ₁ , s _{2 /} s ₃ , s ₄ . Then, according to the decomposition theorem (Ango A. Mathematics for electrical and radio engineers. M .: Nauka, 1967. 779 pp.), The voltage across capacitor 10 with capacity C ₁ , which in absolute value is equal to the voltage across measuring resistance 5 with value R, can be represented in as follows:

The expression for the self-discharge current can be written as follows:

The amplitude of the current is obviously equal to I _m = U / R ₀ . The resistance of the breakdown channel is much less than the total resistance of the circuit, which consists mainly of measuring resistance 5 and inductance reactance. It should be borne in mind that the inductance of a piece of straight copper wire with a length of I ₀ = 10 cm and a diameter of 2r = 1 mm is approximately 10 ^-7 GN. This value is apparently close to the minimum parasitic inductance of the measuring circuits used. The reactance of this inductance at a frequency of 100 MHz is ~ 63 Ohms. Therefore, the duration of the breakdown current will be determined mainly by the resistance of the breakdown channel and is equal to Δt = R ₀ C.

In FIG. Figure 3 shows the change over time of the voltage U ₁ (t) at the measuring resistance and current I (t) at C = 3 pF, C ₁ = 10 F, C _d = 300 pF, R ₀ = 10 Ohm, R = 1600 Ohm, L = 0.3 μH, U = 1000 V. It is clearly seen that if the breakdown current is determined in a known manner, then dividing the maximum value of U ₁ (t), equal to approximately 1000 V, by the resistance of the measuring resistor, equal to 1600 Ohms, we obtain a current with an amplitude of about 0 , 6 A, which is many times smaller than the amplitude of the true current I (t), which is equal to I _m = 100 A. Since the calculation was made for the known parameters of the circuit, the proposed method can be easily checked by vibration parameters in FIG. 3. It can be seen that the amplitude of the voltage fluctuations U ₁ (t) decreases 2.7 times in τ≈21 ns, the period of oscillations T≈11 ns, and the oscillation frequency ω≈5.9 · 10 ⁸ rad / s. Substituting these values in the above formula (1) for the channel resistance, we obtain that R ₀ ≈10 Ohm, which was used for the calculation. The amplitude of the current is I _m = U / R ₀ = 1000/10 = 100 A. The duration of the breakdown current pulse is Δt = R ₀ C = 10 · 3 · 10 ^-12 = 0.03 ns.

The accuracy of determining the current depends on the accuracy of determining the frequency and decay time of the oscillations, as well as the accuracy of measuring the parameters of the measuring installation. The least accuracy (about 10%) characterizes the measurement of the decay time of the oscillations. Other parameters are measured with an accuracy of at least 1%. Compared with the known method of measuring breakdown current with low accuracy of the order of thousands of percent (0.6 A instead of 100 A), the use of the proposed method significantly increases the accuracy of the measurements.

The invention is illustrated by drawings:

In FIG. 1 diagram of the flow of currents during breakdown of a dielectric;

In FIG. 2 equivalent electrical circuit of the measuring circuit;

In FIG. 3 graphs of voltage and current in the circuit of FIG. 2;

In FIG. 4 scheme of the experimental setup;

In FIG. 5, the waveform obtained by the installation of FIG. four.

Example

The implementation of the invention is confirmed by the apparatus shown in FIG. 4, where:

1 - dielectric sample;

2 - ball electrode;

3 - flat electrode;

4 - capacitor;

5 - measuring resistor;

7 - limiting resistor;

11 - copper wire discharge circuit;

12 - teflon inserts;

13 - high-frequency high-voltage output;

14 - copper screen;

15 - getinaksovy substrate.

To illustrate, consider an example of determining the breakdown current of a film of polyethylene terephthalate (PET) based on experimental data obtained using ball-plane electrodes (ball diameter 5 mm). The film thickness was 2.5 μm. An equivalent circuit is shown in FIG. 2. The parameters (active and reactance) of the installation were measured using an AA-1400 antenna analyzer. The numerical values of the circuit elements were used above when calculating the voltage and current shown in FIG. 2, except for the unknown resistance of the breakdown channel. The value of the measuring resistor 5 is selected R = 1600 Ohms for better coordination with the measuring divider of the broadband oscilloscope. The experiments used the ADS-2332 broadband storage oscilloscope (1 ns sampling interval), with a TTHV250 high-voltage divider with a cutoff frequency of 300 MHz.

In FIG. Figure 5 shows the experimentally recorded waveform of the signal at the measuring resistor 5 during the breakdown of the PET film in the mode of voltage rise at a constant speed. The breakdown occurred at U = 1200 V. By using the fast Fourier transform, it was found that the largest spectral peak corresponds to a frequency of 106.8 MHz (ω = 2π · 106.8 · 10 ⁶ ). The amplitude of the oscillations decreases 2.7 times in about τ≈25 ns. Substituting the found values of ω and τ into formula (1) for the resistance of the breakdown channel, we obtain that R ₀ ≈6.5 Ω. From this we find that the amplitude of the breakdown current pulse is I _m = 1200 / 6.5≈185 A. Since the self-discharge current pulse has an approximately triangular shape (see Fig. 3), the effective current value will be about 90 A. The duration of the breakdown current pulse is Δt = R ₀ C = 6.5 · 3 · 10 ^-12 ≈0.02 ns.

Modern digital oscilloscopes have a built-in Fourier transform and markers for measuring the change in momentum over time. However, you can use oscilloscopes without this function, and process the captured waveform using the appropriate computer program, for example, MathCAD. The presented example confirms the feasibility of the invention.

Thus, in comparison with the known method of measuring the breakdown current with low accuracy, the use of the proposed method greatly increases the accuracy of the measurements. The feasibility of the invention is confirmed both theoretically and by staging special measurements. It is shown that instead of the currents recorded in a known manner, which comprise fractions of an ampere, the true breakdown currents can exceed a hundred amperes and lead to the destruction of the dielectric. Using the proposed method will allow to obtain new information about the conditions for the destruction of dielectrics in an electric field and to develop methods to increase their electric strength.

Claims (1)

A method for determining the current in the channel of dielectric electrical breakdown, including placing a dielectric sample between two electrodes, supplying high DC voltage U to the electrodes from a pre-charged capacitor with capacitance C _d , measuring a voltage pulse waveform during breakdown of a measuring resistor R in series with the electrodes, characterized in that is measured from the oscillogram the circular frequency ω and the decay time τ oscillations determine the value of resistance R ₀ channel elektricheskog the ratio of the dielectric breakdown

Where
K = 1 + ωτ;
C is the capacity of the measuring cell with the sample;
L is the inductance of the circuit;
C ₁ - parasitic capacitance formed by conductors connected by a resistor R,
and the sought values of the amplitude I _m and the current duration Δt are found, respectively, from the relations: I _m = U / R ₀ , Δt = R ₀ C.

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