there’s an “r” in varistor · 2019. 3. 4. · varistor (voltage dependent resistor), vdr:...
TRANSCRIPT
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There’s an “R” in Varistor
Mick Maytum
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What kind of “R”?
• Dynamic “r”
• Quotient of characteristic point values “R”
vri
∆=∆
VRI
=
Current – A
0 5000 10000 15000 20000 25000 30000 35000 40000 45000
Volta
ge –
V
0
200
400
600
800
1000
1200
1400
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2000
r
Current – A
0 5000 10000 15000 20000 25000 30000 35000 40000 45000
Volta
ge –
V
0
200
400
600
800
1000
1200
1400
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1800
2000
R
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Answer to “What kind of “R”?”
• Dynamic “r”
• Quotient of characteristic point values “R”
vri
∆=∆
VRI
=
Current – A
0 5000 10000 15000 20000 25000 30000 35000 40000 45000
Volta
ge –
V
0
200
400
600
800
1000
1200
1400
1600
1800
2000
r
Current – A
0 5000 10000 15000 20000 25000 30000 35000 40000 45000
Volta
ge –
V
0
200
400
600
800
1000
1200
1400
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1800
2000
R
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Why “R”?• Work done in China shows that “R” is a useful parameter
when working with Varistor voltage-current relationships
• Don’t we have a relationship given in Varistor definitions?varistor (voltage dependent resistor), VDR: component, whose conductance, at a given temperature range, increases rapidly with voltage within a given current range Note 1 to entry: This note applies to the French language only.Note 2 to entry: Varistor is graphically symbolized as Z. Note 3 to entry: This property is expressed by either of the following formulae:U = CIβ (1) or I = AUγ (2)whereI is the current flowing through the varistor; U is the voltage applied across the varistor;β is the non-linearity current index; γ is the non-linearity voltage index;A and C are constants. (IEC 61051-1 ED3, Varistors for use in electronic equipment - Part 1: Generic specification)
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The Chinese characteristic takeaway — 1
Single voltage-current characteristic line.
(ITU-T K.128)
A is leakage segment (typical)B is operational segment (maximum voltage)(ITU-T K.128)
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The Chinese characteristic takeaway — 2Three segment characteristicfor• d.c.,• a.c. and • impulse current operational regionsNOTE: In I = AUγ Chinese use αrather than γ. (ITU-T K.128) 0.8
1.0
1.2
1.4
1.6
1.8
2.0
2.2
Volta
ge ra
tio
U/U
1mA
Log I
AC 50Hz
8/20 impulse
DC
-5 -4 -3 -2 -1 0 1 2 3 4(1 A) (10 A) (100 A) (1 kA) (10 kA)(1 mA) (10 mA) (100 mA)(100 µA)(10 µA)
α=26 to 100
α=61 to 55
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The Chinese characteristic takeaway — 3• But wait – there’s more!
The impulse characteristic is di/dt dependent. NOTE: This is in addition to any inductive lead effects.(ITU-T K.128)
1.5
1.0
0.5
0
4/10
8/20
1/5
2 mspulse
101 102 103 104 105 106Peak impulse current — A
Peak
vol
tage
nor
mal
ised
to 8
/20,
10
kA v
olta
ge
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Modelling — Chinese dataThis analysis uses the measured and calculated values for an MOV arrester block shown in the right table
CurrentA
VoltageV
ResistanceΩ
276 880 3.18604 940 1.56864 960 1.11
1640 1000 0.6103280 1070 0.3267200 1220 0.169
14400 1400 0.097226400 1580 0.059844800 1840 0.0411
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Modelling — Chinese data plots
MOV sample, voltage versus current MOV sample, resistance versus current
MOV current — A
100 1000 10000 100000
MO
V vo
ltage
— V
300
400
500
600700800900
2000
3000
1000
Voltage versus current
MOV current — A
100 1000 10000 100000
MO
V re
sist
ance
—
0.01
0.1
1
10
Resistance versus current
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Equation Fitting — 2-term power law
MOV current — A
100 1000 10000 100000
MO
V vo
ltage
— V
300
400
500
600700800900
2000
3000
1000
Voltage versus currentCI versus current
Equation C.1U = CIβ
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Equation Fitting — Chinese Log(I) equation result
Current — A
100 1000 10000 100000
Volta
ge —
V
300
400
500
600700800900
2000
3000
1000
Voltage versus currentCalculated voltage using equation C.2
IIAAA IR log)log( 21010 ×⋅+×=
Equation C.2
A0 is 3.2306A1 is -1.2465 A2 is 0.05434
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Equation Fitting —3-term power law
Equation C.3U = A + CIβ
Ais 815C is 4.32 β is 0.51
Current — A
100 1000 10000 100000
Volta
ge —
V
300
400
500
600700800900
2000
3000
1000
Voltage versus current Voltage using equation C.3
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References• Wang zhen-lin, Li Sheng-tao “Engineering and Application of Zinc Oxide
Voltage Dependent Ceramics” [M] , Beijing: Science Press, 2009
• Panasonic Electronic Component Co., Ceramic Department “Application Manual of ‘ZNR’” (2nd.edition), 1981.
• Wu wei-han, He jin-liang, Gao Yu-ming “properties and Applications of Nonlinear Metal Oxide Varistors” [M], Beijing, Qing Hua University Press, 1998
• ITU-T Recommendation K.128 (01/2018), Surge protective component application guide - metal oxide varistor (MOV) components
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Summary of foregoing• The characteristic point quotient “R” shows a strong correlation
with current. The voltage at the point is R x I.
• The Chinese Log(I) and 3-term power equations are reasonable curve fits to the voltage-current characteristic.
• A more accurate term and definition would be:metal oxide varistor, MOV: non-linear resistor made of a sintered mixture of zinc and other metal oxides whose conductance, at a given temperature and within a given current range, increases rapidly with current
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SPICE (Simulation Program with Integrated Circuit Emphasis)This section creates an LTspice model for a varistor using the modified power-law U = 815 + 4.32xI0.51 equation derived earlier expressed as a current I = (0.231*U-188.3)1.96.
LTspice comes with various Arbitrary Behavioural Voltage or Current Sources, which can be controlled by equations:
• Type E. Voltage Dependent Voltage Source• Type F. Current Dependent Current Source• Type G. Voltage Dependent Current Source• Type H. Current Dependent Voltage Source
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LTspice varistor Type G. Voltage Dependent Current SourceThis section creates an LTspice model for a varistor using the I= (0.2313*U-188.23)1.96 equation. This equation is unidirectional and needs to be made bidirectional and placed in LTspice equation format:
GRES 1 2 VALUE={sgn(V(1,2))*(0.2313*abs(V(1,2))-188.23)**1.96}
In words, the Type G voltage dependent current source (having terminals 1 and 2) draws a current equal to:The polarity of the terminal voltage multiplied by (0.2313 times the absolute terminal voltage minus 188.23) raised to the power of 1.96.
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LTspice varistor sub-circuit creation1. Insert a resistor symbol in the circuit
2. Change the symbol from a component into an Type G X1X2 sub-circuit (current source set by voltage) as described at https://electronics.stackexchange.com/questions/313333/ltspice-how-to-vary-resistances-in-a-simulation-depending-on-the-value-of-a-vol
3. Insert a SPICE sub-circuit statement referencing the Type G X1X2 sub-circuit and the equation.
https://electronics.stackexchange.com/questions/313333/ltspice-how-to-vary-resistances-in-a-simulation-depending-on-the-value-of-a-vol
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LTspice varistor test circuit — descriptionThe circuit components are:
• V1 is a double exponential surge generator having a peak voltage of 10 kV, a 1.5 µs front time and a 50 µs decay time.
• Series resistor R1 limits the peak generator current into the varistor
• Shunt resistor R2 simulates the varistor leakage resistance.
• X1 is the varistor sub-circuit drawing a current defined byGRES 1 2 VALUE={sgn(V(1,2))*(0.2313*abs(V(1,2))-188.23)**1.96}
• The simulation run time is 200 µs
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LTspice varistor test circuit — diagram
V1
EXP(0 10000 0 1.5u 0 50u)
R1
0.15
X1X2
X1R21Meg
.tran 0 200us 0
.SUBCKT X1X2 1 2GRES 1 2 VALUE={sgn(V(1,2))*(0.2313*abs(V(1,2))-188.23)**1.96}.ENDS
Voltagesurge
generator
VaristorType G
sub-circuit
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LTspice varistor test circuit — voltage and current
0 20 40 60 80 100 120 140 160 180 2000.0
0.2 kV
0.4 kV
0.6 kV
0.8 kV
1.0 kV
1.2 kV
1.4 kV
1.6 kV
1.8 kV
2.0 kV
0
5 kA
10 kA
15 kA
20 kA
25 kA
30 kA
35 kA
40 kA
45 kA
50 kA
Voltage
Current
Time — µs
Varis
tor v
olta
ge
Varis
tor c
urre
nt
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LTspice dual varistor test circuit — one 10 % high, other 10 % low in voltage from typical
V1
EXP(0 10000 0 1.5u 0 50u)
R1
0.09
X1X2
X1R21Meg
X3X4
X2
.tran 0 200us 0
.SUBCKT X1X2 1 2GRES 1 2 VALUE={sgn(V(1,2))*(0.2313*abs(V(1,2))-169.4)**1.96}.ENDS
.SUBCKT X3X4 3 4GRES 3 4 VALUE={sgn(V(3,4))*(0.2313*abs(V(3,4))-207)**1.96}.ENDS
Voltagesurge
generator
10 % lowvaristor
10 % highvaristor
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LTspice dual varistor test circuit — voltage and current waveforms
0µs 20 40 60 80 100 120 140 160 180 2000.0
0.2 kV
0.4 kV
0.6 kV
0.8 kV
1.0 kV
1.2 kV
1.4 kV
1.6 kV
1.8 kV
2.0 kV
2.2 kV
2.4 kV
0
4 kA
8 kA
12 kA
16 kA
20 kA
24 kA
28 kA
32 kA
36 kA
40 kA
44 kA
48 kA
Voltage
X1 CurrentX2 Current
Time — µs
Varis
tor V
olta
ge
Varis
tor C
urre
nt
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Summary of LTspice results• LTspice sub-circuits can model varistor voltage-current behaviour
over a wide current range. (Spot point voltage and current tables can also be used)
• Key to this is having a robust equation (best fit in region where accuracy is critical) relating the voltage and current values.
• If a full range of voltage and current values is available the d.c.operating range could have also been modelled
• LTspice is free and can be downloaded from:https://www.analog.com/en/design-center/design-tools-and-calculators/ltspice-simulator.html
Questions?
https://www.analog.com/en/design-center/design-tools-and-calculators/ltspice-simulator.html
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14 mm MOV — large current range exampleTop left: Selected MOV data sheet characteristicBottom left: transcribed MOV characteristicBottom middle: calculated and equation resistanceBottom right: Data sheet and equation characteristics
Best fit equation: v = 482 + 4.59*(i)0.5 + 15.4*LN(i)over current range of 10 µA to 6 kA
MOV current — A
1e-5 1e-4 1e-3 1e-2 1e-1 1e+0 1e+1 1e+2 1e+3 1e+4
MO
V vo
ltage
— V
100
200
300
400
500
600
700800900
1000
Data sheet
MOV current — A
1e-5 1e-4 1e-3 1e-2 1e-1 1e+0 1e+1 1e+2 1e+3 1e+4
MO
V vo
ltage
— V
100
200
300
400
500
600
700800900
1000
Data sheetEquation
MOV current — A
1e-5 1e-4 1e-3 1e-2 1e-1 1e+0 1e+1 1e+2 1e+3 1e+4
MO
V re
sist
ance
—
1e-1
1e+0
1e+1
1e+2
1e+3
1e+4
1e+5
1e+6
1e+7
1e+8
Data sheetEquation
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There’s an “R” in Varistor
Mick Maytum
There’s an “R” in VaristorWhat kind of “R”?Answer to “What kind of “R”?”Why “R”?The Chinese characteristic takeaway — 1The Chinese characteristic takeaway — 2The Chinese characteristic takeaway — 3Modelling — Chinese dataModelling — Chinese data plotsEquation Fitting — 2-term power lawEquation Fitting — Chinese Log(I) equation resultEquation Fitting —3-term power lawReferencesSummary of foregoingSPICE (Simulation Program with Integrated Circuit Emphasis)LTspice varistor Type G. Voltage Dependent Current SourceLTspice varistor sub-circuit creationLTspice varistor test circuit — descriptionLTspice varistor test circuit — diagramLTspice varistor test circuit — voltage and currentLTspice dual varistor test circuit — one 10 % high, other 10 % low in voltage from typicalLTspice dual varistor test circuit — voltage and current waveformsSummary of LTspice results14 mm MOV — large current range exampleThere’s an “R” in Varistor