Analysis of the volt-ampere characteristic curve of zinc oxide varistor under 8/20μS pulse current-EEWORLD

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1 Introduction

There have been many studies on the volt-ampere characteristics of zinc oxide varistors under 8/20μS pulse current ^[1-4] . It is generally believed that: under 8/20μS pulse current, the current peak and voltage peak of the varistor do not arrive at the same time, the voltage peak is earlier than the current peak, the volt-ampere characteristic curve of the rising edge and the volt-ampere characteristic curve of the falling edge do not overlap and form a loop feature; some believe that it is the hole hysteresis effect excited by the pulse current ^[3] , some believe that it is the hysteresis effect caused by electrostriction or thermal effect ^[4] , and some believe that it is affected by the impact current and the current change rate ^[2] .

The loop characteristics are naturally associated with the inductance effect. Although various methods have been used in previous tests to reduce or eliminate the inductance of the varistor in the 8/20μS pulse current test, the volt-ampere characteristic loop characteristics of the varistor cannot be eliminated. Is this because the inductance cannot be eliminated or is the loop characteristic an intrinsic characteristic of the varistor ceramic body?

In fact, because it is impossible to use zero lead for varistor ceramics, reducing the lead length, using hollow valve plates and Kevin wiring method can only reduce the inductance as much as possible. The inductance cannot be completely eliminated during the impact measurement of the varistor. Even if the current is passed into the surface electrode of the varistor ceramic body using a zero-length lead, the current must be redistributed to each point on the surface electrode, and the current channel of the surface electrode constitutes the equivalent inductance. The equivalent inductance of the varistor electrode and the lead inductance between the test points together constitute the lead-out inductance of the varistor. The lead-out inductance cannot be eliminated. The lead-out inductance definitely contributes to the loop characteristics.

This paper attempts to conduct a semi-quantitative analysis of the loop characteristics of the varistor's volt-ampere characteristic curve under 8/20μS pulse current to confirm whether the loop characteristics are the intrinsic characteristics of the varistor ceramic.

2. Build the model

As shown in Figure 1, the equivalent circuit of the zinc oxide varistor in the current region after the breakdown under the 8/20μS pulse current. Among them, L is the lead inductance of the varistor and the equivalent inductance of the ceramic body, RV is the sensitive resistance of the varistor ceramic body (including nonlinear grain boundaries and grains), Rs is the lead resistance, i _is the current flowing through the varistor, V ( i ) is the total voltage drop on the varistor, VV ( i ) is the sensitive resistance voltage drop of the varistor ceramic body, Vr ( i ) is the _voltage drop on the lead resistance, di / dt is the rate of change of current with time, and di / dt is a function of current during pulse current, then the voltage drop on the inductor is Ld i / dt .

According to the equivalent circuit diagram 1, the series inductance cannot be zero. The existence of inductance will definitely produce a loop of volt-ampere characteristics during the impact test. The voltage in the rising section is higher than that in the falling section, which is consistent with the loop characteristics of the varistor. Therefore, it is assumed that the loop is caused by the equivalent inductance, and the equivalent inductance is regarded as a constant. The resistance of the varistor is a pure variable resistor. The voltage drop on the lead-out resistor and the resistance of the varistor is only related to the current size and has nothing to do with the current time change rate. It can be concluded that:

At the rising edge of the 8/20μS pulse current, the voltage on the varistor can be expressed as formula (1):

At the falling edge of the 8/20μS pulse current, the voltage on the varistor can be expressed as formula (2):

(2)

At the falling edge of the 8/20μS pulse current, corresponding to the same current value, the voltage drop on the varistor ceramic body is the same, as shown in formula (3a); at the same time, the voltage drop on the lead-out resistor is the same, as shown in formula (3b).

(3a)

(3b)

At the falling edge of the 8/20μS pulse current, corresponding to the same current value, subtracting equation (1) from equation (2) yields equation (4). The rising and falling edge voltage difference on the equivalent inductor corresponding to the same current value at the rising and falling edges is a function of the difference in the time rate of change of the current at the rising and falling edges. When the rising and falling edge voltage difference on the equivalent inductor and the difference in the time rate of change of the current at the rising and falling edges are known, the equivalent inductance value can be calculated.

V _up ( i ) - V _down ( i ) = L (d i _up /d t - di _down /d t )= f (d i/ d t ) (4)

3 Experimental conditions

The test samples are 20D101 (medium-pressure material), 20D620 (low-pressure material), 32D560 (low-pressure material) and 32D101 (low-pressure material), one each. The lead spacing of 20D products is 10mm, and the test points are the root of the leads and about 50mm from the leads. The lead spacing of 32D products is 15mm, and the test points are the root of the leads. The voltage drop of parallel leads with a spacing of 10mm and a length of 125mm is measured.

The impulse generator is SK-20KA, and the current is sampled by the shunt of the equipment. The voltage signal is directly sampled at the root of the two leads of the varistor, and the current and voltage signals are displayed and measured in sequence by the TDS102 oscilloscope. The impulse current waveform is 8/20μS, and the peak values are 2.0kA and 3.0kA.

4 Test results and analysis

4.1 Test data shows that the resistance effect on the lead cannot be ignored

Figure 2 is an example of the characteristic curve of the volt-ampere characteristic loop of the tested varistor under 8/20uS impact. The curve clearly shows obvious loop characteristics, and the rising edge voltage is greater than the falling edge. Figures 3 and 4 are the current and voltage waveforms captured by the oscilloscope. The voltage peak precedes the current peak. Unlike a simple inductor, the current time change rate is zero at the current peak, but it shows that the voltage between the first and last test points of the parallel leads is not equal at this time. The equal voltage value is reached after the peak current. The time difference between the current peak point and the zero voltage on the electrical lead in each test, and the current value at zero voltage are listed in Table 1. It can be said with certainty that the resistance effect on the lead cannot be ignored.

Figure 2 Partial volt-ampere characteristic curve of the product under 8/20μS pulse current of 3.1KA

Table 1 Differences between the voltage equalization points and current peaks at the beginning and end of product leads and pure leads under 8/20μS pulse current

Sample	Peak value of impulse current kA	Current value at zero voltage point of conductor kA	The time difference between the current peak point and the conductor voltage zero point μS
125mm wire	2	1.84	4.2
125mm wire	3	2.9	2.8
20D101	2	1.9	3
20D101	3	2.88	3.2
20D620	2	1.96	3.4
20D620	3	2.95	1.6

Table 2 shows the theoretically calculated resistance of a pair of parallel copper wires with a diameter of 1 mm and the corresponding voltage drop during impulse current. The data shows that the influence of the lead-out resistance cannot be ignored.

Table 2 Theoretical calculation results of the resistance of parallel double copper wires with a diameter of 1 mm

Current mA	resistance	Voltage drop V
Current mA	mΩ	@0.9kA	@2kA	@3kA
10	0.446	0.401	0.892	1.338
50	2.23	2.007	4.460	6.69
125	5.575	5.018	11.150	16.725

4.2 Calculate the equivalent inductance value from the test data

According to the current change rate and voltage difference at the rising and falling edges of the corresponding current obtained by the test, the equivalent inductance values of the 125mm parallel double copper wires, the lead wires and silver-clad ceramic body of 20D101, and the lead wires and silver-clad ceramic body of 20D620 are calculated according to formula (4), and are listed in Table 3, Table 4 and Table 5 respectively.

Table 3 Experimental deduced inductance values of 125 mm parallel twin copper conductors

2kA	Current A	900	1200	1500	1800	2000
	Rising current change rate A/μS	368	272	192	100	0
	Falling edge current change rate A/μS	-65.6	-73.6	-76.8	-60.8	0
	The difference of the current change rate between the rising and falling edges is A/μS	433.6	345.6	268.8	160.8	0
	Rising edge voltage V	63.6	48.8	35.6	24.8	8.8
	Falling edge voltage V	-5.6	-6	-4	-0.8	8.8
	Voltage difference between rising and falling edges V	69.2	54.8	39.6	25.6	0
	Equivalent inductance nH	159.6	158.6	147.3	159.2
3kA	Current A	900	1500	2000	2500	3000
	Rising current change rate A/μS	580	420	328	220	0
	Falling edge current change rate A/μS	-88	-120	-126	-108	0
	The difference of the current change rate between the rising and falling edges is A/μS	668	540	454	328	0
	Rising edge voltage V	93.8	71	58	42.8	9.6
	Falling edge voltage V	-10	-12	-12.8	-8.4	9.6
	Voltage difference between rising and falling edges V	103.8	83	70.8	51.2	0
	Equivalent inductance nH	155.4	153.7	155.9	156.1

Table 4 Experimental deduced inductance values of 20D101 lead wire and silver ceramic body

2kA	Current A	900	1200	1500	1800	2000
	Rising current change rate A/μS	368	272	192	80	0
	Rising current change rate A/μS	-65.6	-73.6	-76.8	-60.8	0
	The difference of the current change rate between the rising and falling edges is A/μS	433.6	345.6	268.8	140.8	0
	Root rising edge voltage V	220	227	230	235	234
	Root falling edge voltage V	181	194	207	223	234
	Rising edge voltage V at 5cm wire	249	250	249	244	237
	Falling edge voltage V at 5cm wire	178	192	205	222	237
	The rising edge voltage V of the 5cm wire	29	twenty three	19	9	3
	Falling edge voltage V of 5cm wire	-3	-2	-2	-1	3
	The voltage difference V between the rising and falling edges of the silver ceramic	39	33	twenty three	12	0
	5cm wire rising and falling edge voltage difference V	32	25	twenty one	10	0
	Silver ceramic chip inductance nH	89.9	95.5	85.6	85.2
	5cm wire inductance nH	73.8	72.3	78.1	71.0
3kA	Current A	900	1500	2000	2500	3000
	Rising current change rate A/μS	580	424	328	220	0
	Rising current change rate A/μS	-88	-120	-126	-108	0
	The difference of the current change rate between the rising and falling edges is A/μS	668	544	454	328	0
	Root rising edge voltage V	232	250	260	268	268
	Root falling edge voltage V	174	198	218	238	268
	Rising edge voltage V at 5cm wire	275	281	285	288	272
	Falling edge voltage V at 5cm wire	170	191	212	234	272
	The rising edge voltage V of the 5cm wire	43	31	25	20	4
	Falling edge voltage V of 5cm wire	-4	-7	-6	-4	4
	The voltage difference V between the rising and falling edges of the silver ceramic	58	52	42	30	0
	5cm wire rising and falling edge voltage difference V	47	38	31	twenty four	0
	Silver ceramic chip inductance nH	86.8	95.6	92.5	91.5
	5cm wire inductance nH	70.4	69.9	68.3	73.2

Table 5 Experimental deduced inductance values of 20D620 lead wire and silver ceramic body

2kA	Current A	900	1200	1500	1800	2000
	Rising current change rate A/μS	368	272	192	80	0
	Rising current change rate A/μS	-65.6	-73.6	-76.8	-60.8	0
	The difference of the current change rate between the rising and falling edges is A/μS	433.6	345.6	268.8	140.8	0
	Root rising edge voltage V	186	197	205	211	214
	Root falling edge voltage V	157	172	185	201	214
	Rising edge voltage V at 5cm wire	212	218	220	220	217
	Falling edge voltage V at 5cm wire	155	168	182	200	217
	The rising edge voltage V of the 5cm wire	26	twenty one	15	9	3
	Falling edge voltage V of 5cm wire	-2	-4	-3	-1	3
	The voltage difference V between the rising and falling edges of the silver ceramic	29	25	20	10	0
	5cm wire rising and falling edge voltage difference V	28	25	18	10	0
	Silver ceramic chip inductance nH	66.9	72.3	74.4	71.0
	5cm wire inductance nH	64.6	72.3	67.0	71.0
3kA	Current A	900	1500	2000	2500	3000
	Rising current change rate A/μS	620	424	328	220	0
	Rising current change rate A/μS	-88	-120	-126	-108	0
	The difference of the current change rate between the rising and falling edges is A/μS	708	544	454	328	0
	Root rising edge voltage V	196	216	231	244	246
	Root falling edge voltage V	153	177	198	219	246
	Rising edge voltage V at 5cm wire	237	247	255	259	250
	Falling edge voltage V at 5cm wire	148	172	192	214	250
	The rising edge voltage V of the 5cm wire	41	31	twenty four	15	4
	Falling edge voltage V of 5cm wire	-5	-5	-6	-5	4
	The voltage difference V between the rising and falling edges of the silver ceramic	43	39	33	25	0
	5cm wire rising and falling edge voltage difference V	46	36	30	20	0
	Silver ceramic chip inductance nH	60.7	71.7	72.7	76.2
	5cm wire inductance nH	65.0	66.2	66.1	61.0

4.3 It is a reasonable method to derive lead inductance by experiment

Table 6 compares the theoretical lead inductance calculated using equation (5) ^[5] and the equivalent lead inductance derived from experiments.

(5)

Table 6 Comparison of theoretically calculated lead inductance and experimentally derived equivalent lead inductance

Theoretical calculation of inductance	product	125mm wire	20101	20620
	Spacing a mm	10.3	12.2	12.2
	Lead wire diameter d mm	1	1	1
	Lead length l mm	125	56	50
	Theoretical calculation of inductance nH	150	71.2	63.5
2kA derivation inductor	Mean nH	156.2	73.8	68.7
	Range ratio%	7.86%	9.62%	11.29%
	and theoretical deviation rate%	4.11%	3.68%	8.23%
3kA derivation inductance	Mean nH	155.3	70.4	64.6
	Range ratio%	1.54%	6.94%	8.06%
	and theoretical deviation rate%	3.52%	-1.10%	1.65%

It can be seen from Table 6 that within a reasonable error range, the theoretical calculated value of the lead inductance is very close to the experimentally derived value. The lead inductance is a constant, and the method of deriving the equivalent inductance value by experiment is a feasible method.

4.4 The equivalent inductance of the silver-clad ceramic body of the varistor is a constant

The equivalent inductance values of the silver-clad ceramic resistors of 20D101 and 20D620 varistors derived from the experiments in Tables 4 and 5 are listed in Table 7. It is obvious that within a reasonable experimental error range, the impact equivalent inductance of the silver-clad ceramic resistor is a constant.

Table 7 Experimental derivation of equivalent inductance of 20D product silver-clad ceramic body

product	2kA test data		3kA test data
product	Average value of equivalent inductance nH	Range Ratio	Average value of equivalent inductance nH	Range Ratio
20D101	89.1	11.52%	91.6	9.57%
20D620	71.2	10.57%	70.3	22.02%

4.5 The ceramic body has a large equivalent inductance

Silver-clad ceramic equivalent inductance, including the electrode equivalent inductance of the ceramic equivalent inductance. The voltage difference between the rising and falling edges of the tested 32D560 and 32D101 products is compared, and the comparison results of the equivalent inductance and thickness of the silver-clad ceramic bodies of 32D101 and 32D560 are listed in Table 8. The comparison of the equivalent inductance and thickness of the silver-clad ceramic bodies of 20D101 and 20D560 is listed in Table 9. As shown in Table 8, the thickness of 32D101 is 1.25 times that of 32D560, and the equivalent inductance of the silver-clad ceramic body of the former is 1.16 times that of the latter. The thickness of 20D101 is 0.76 times that of 20D620, and the equivalent inductance of the silver-clad ceramic body of the former is 1.28 times that of the latter.

The above non-corresponding relationship between inductance and ceramic body thickness shows that the thickness of the ceramic body is not the main influencing factor of the equivalent inductance of the silver-clad ceramic body. It can be explained that the ceramic thickness is a factor that forms the electrode equivalent inductance. The area surrounded by the electrode is not more than 1/20 compared with the area surrounded by the 5cm wire, which can be ignored. In this way, the electrode equivalent inductance will be less than 5nH. Of course, it is really nothing in the equivalent inductance of the ceramic body above 70nH. Such a large silver-clad ceramic body equivalent inductance is significantly positively correlated with the varistor voltage of the product, and the varistor voltage is proportional to the number of grain boundaries. It shows that the equivalent inductance of the silver-clad ceramic body mainly comes from the grain boundary, so only a small part of the equivalent inductance of the silver-clad ceramic body comes from the electrode equivalent inductance, and the ceramic body equivalent inductance coming from the grain boundary is much larger than the electrode equivalent inductance.

This shows that the varistor ceramic body has a large impact equivalent inductance, which will cause the varistor's volt-ampere characteristic loop characteristics when the impact current is 8/20μS. The loop characteristics are the intrinsic characteristics of the varistor ceramic body. Even if the inductance is completely eliminated, the loop characteristics cannot be eliminated.

Table 8 Comparison of equivalent inductance and thickness of 32D101 and 32D560 silver-clad ceramic bodies

product		32D101	32D560	Inductance ratio of 101 and 560	Thickness ratio of 101 and 561
Current A		Silver-clad ceramic rising and falling edge voltage difference V		Inductance ratio of 101 and 560	Thickness ratio of 101 and 561
2kA	900	37	32	1.16	1.25
	1200	32	27	1.19
	1500	26	twenty two	1.18
	1800	17	15	1.13
	Ratio Mean			1.16
3kA	900	55	46.5	1.18
	1500	50	42	1.19
	2000	42	36	1.17
	2500	30	27	1.11
	Ratio Mean			1.16

Table 9 Comparison of equivalent inductance and thickness of 20D101 and 20D560 silver-clad ceramic bodies

product	20D101	20D620	Inductance ratio of 101 and 620	Thickness ratio of 101 and 621
Current A	The average equivalent inductance value nH derived by the silver ceramic sheet		Inductance ratio of 101 and 620	Thickness ratio of 101 and 621
2kA	89.1	71.2	1.25	0.76
3kA	91.6	70.3	1.30	0.76

5 Conclusion

The volt-ampere characteristic of the zinc oxide varistor under 8/20μS pulse current presents a loop characteristic, which is an intrinsic characteristic of the varistor ceramic. The varistor ceramic itself has a constant equivalent inductance under 8/20μS pulse current, which is related to the number of grain boundaries and the ceramic material, causing the loop characteristic of the volt-ampere characteristic.

References

[1] Liang Yujin. Application of Metal Oxide Nonlinear Resistors in Power Systems. Wuhan: Huazhong University of Science and Technology Press, 1993.

[2] Wu Weihan, He Jinliang, Gao Yuming, et al. Tsinghua University Academic Monograph: Characteristics and Applications of Metal Oxide Nonlinear Resistors. Beijing: Tsinghua University Press, 1998.

[3] Sun Danfeng, Ji Youzhang, Yao Xueling, Chen Jingliang, Zhang Junfeng, et al. Volt-ampere characteristics of zinc oxide varistor under 8/20us impulse current. Paper presented at the 14th Annual Conference on Voltage Sensitive Technology of the Sensitive Technology Branch of the Chinese Institute of Electronics, Semiconductor Device Application, 2007: 1~5

[4] Zhang Junfeng, Xia Bo, Sun Danfeng, et al. Further exploration of the aging mechanism of zinc oxide varistors. Semiconductor Device Applications, Special Issue of the 16th Annual Conference on Voltage Sensitive Technology, Chinese Institute of Electronics, 2009: 68~72

[5] [Soviet Union] Heitvisi. Inductance Calculation. Beijing: National Defense Industry Press. 1960.

Reference address：Analysis of the volt-ampere characteristic curve of zinc oxide varistor under 8/20μS pulse current

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