There’s an “R” in Varistor

Mick Maytum

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

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r

Current – A

0 5000 10000 15000 20000 25000 30000 35000 40000 45000

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V

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R

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

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1400

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r

Current – A

0 5000 10000 15000 20000 25000 30000 35000 40000 45000

Volta

ge –

V

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R

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)

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)

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

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

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

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

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

Equation Fitting — Chinese Log(I) equation result

Current — A

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Volta

ge —

V

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400

500

600700800900

2000

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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

Equation Fitting —3-term power law

Equation C.3U = A + CIβ

Ais 815C is 4.32 β is 0.51

Current — A

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Volta

ge —

V

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Voltage versus current Voltage using equation C.3

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

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

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

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.

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

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

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

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

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

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

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

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

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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

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