Gen Rad Primer

7/27/2019 Gen Rad Primer

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5 Clock Tow er Place, 210 East, M ayn ard , M assachusett s 01754TELE: (80 0 ) 253- 1230 , FAX: (978) 46 1- 4 295, INTL: (978) 4 61- 210 0

h t t p :/ / ww w.quad tech .com

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LCRLCR

MEASUREMENTMEASUREMENT

PRIMERPRIMER
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2


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3

This material is for informational purposes only and is subject to changewithout notice. QuadTech assumes no responsibility for any error or forconsequential damages that may result from the misinterpretation of anyprocedures in this publication.

Preface

The intent of this reference primer is to explain the basic definitions andmeasurement of impedance parameters, also known as LCR. This primerprovides a general overview of the impedance characteristics of an AC cir-

cuit, mathematical equations, connection methods to the device under testand methods used by measuring instruments to precisely characterizeimpedance. Inductance, capacitance and resistance measuring tech-niques associated with passive component testing are presented as well.

LCR Measurement Primer3rd Edition, July 2003

Comments: [email protected]

5 Clock Tower Place, 210 EastMaynard, Massachusetts 01754Tel: (978) 461-2100Fax: (978) 461-4295Intl: (800) 253-1230Web: http://www.quadtech.com
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4

Impedance 5

Definitions 5Impedance Terms 6Phase Diagrams 7Series and Parallel 7

Connection Methods 10Two-Terminal Measurements 10Four-Terminal Measurements 10Three-Terminal (Guarded) 11

Impedance Measuring Instruments 12

Methods 12Functions 13

Test Voltage 13Ranging 14Integration Time 14Median Mode 14Computer Interface 14

Test Fixtures and Cables 15

Compensation 15Open/Short 15Load Correction 16

Capacitance Measurements 17

Series or Parallel 17High & Low Value Capacitance 18ESR 20

Inductance Measurements 21

Series or Parallel 21Inductance Measurement Factors 21

DC Bias Voltage 22Constant Voltage (Leveling) 22Constant Source Impedance 22DC Resistance and Loss 23

Resistance Measurements 24

Series or Parallel 24

Precision Impedance Measurements 25

Measurement Capability 25Instrument Accuracy 26Factors Affecting Accuracy 27Example Accuracy Formula 28

Materials Measurement 30Definitions 30Measurement Methods, Solids 30

Contacting Electrode 30Air-Gap 31Two Fluid 32

Measurement Method, Liquids 33

Recommended LCR Meter Features 34

Test Frequency 34Test Voltage 34Accuracy/Speed 34Measurement Parameters 34Ranging 34

Averaging 34Median Mode 34Computer Interface 35Display 35Binning 36Test Sequencing 37Parameter Sweep 37Bias Voltage and Bias Current 37Constant Source Impedance 37Monitoring DUT Voltage and Current 38

Examples of High Performance Testers 39

Digibridge Component Testers 39

1600 Series 39

1659 391689/89M 391692 391693 391700 Series 40

1710 401730 401750 40

Precision LCR Meters 41

1900 Series 41

1910 Inductance Analyzer 41

1920 LCR Meter 417000 Series 417400 LCR Meter 427600 LCR Meter 42

Dedicated Function Test Instruments 42

Milliohmmeters 42Megohmmeters 42Hipot Testers 42

Electrical Safety Analyzers 42

Appendix A 43

Nationally Recognized Testing Laboratories

(NRTLs) and Standards Organizations 44Helpful Links 45

Typical Measurement Parameters 46

Impedance Terms and Equations 47

Application Note Directory 49

Glossary 53

Contents


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5

ImpedanceImpedance is the basic electrical parameterused to characterize electronic circuits, compo-nents, and materials. It is defined as the ratioof the voltage applied to the device and theresulting current through it. To put this anotherway, impedance is the total opposition a circuitoffers to the flow of an alternating current (ac)at a given frequency, and is generally repre-sented as a complex quantity, which can beshown graphically. The basic elements thatmake up electrical impedances are inductance,capacitance and resistance: L, C, and R,respectively.

In the real world electronic components are not

pure resistors, inductors or capacitors, but acombination of all three. Today's generation ofLCR meters are capable of displaying theseparameters and can easily calculate and dis-play many other parameters such as Z, Y, X, G,B, D, etc. This primer is intended as an aid inunderstanding which ac impedance measure-ments are typically used and other factors thatneed to be considered to obtain accurate andmeaningful impedance measurements.

Definitions

The mathematical definition of resistance for dc(constant voltage) is the ratio of applied voltageV to resulting current I. This is Ohms Law: R =V/I. An alternating or ac voltage is one thatregularly reverses its direction or polarity. If anac voltage is applied to a circuit containing onlyresistance, the circuit resistance is determinedfrom Ohms Law.

Complex Quantity

However, if capacitance or inductance arepresent, they also affect the flow of current. Thecapacitance or inductance cause the voltageand current to be out of phase. Therefore,

Ohms law must be modified by substitutingimpedance (Z) for resistance. Thus for ac,Ohm's Law becomes : Z = V/I. Z is a complexnumber: Z = R + jX . A complex number orquantity has a real component (R) and an imag-inary component (jX).

Phase Shift

The phase shift can be drawn in a vector dia-gram which shows the impedance Z, its real

part Rs, its imaginary part jXs (reactance), andthe phase angle . Because series imped-ances add, an equivalent circuit for an imped-ance would put Rs and Xs is series hence sub-script s. The reciprocal of Z is Admittance, Ywhich is also a complex number having a realpart Gp (conductance) and an imaginary part

jBp (susceptance) with a phase angle . Note = - . Because admittances in parallel add,an equivalent circuit for an admittance wouldput Gp and Bp in parallel. Note from the for-mulas below that, in general, Gp does notequal (1/Rs) and Bp does not equal -(1/Xs).

Refer to Table 1 for Impedance terms, units ofmeasure and equations.

Impedance

For DC, Resistance, R =I

VFor AC, Impedance, Z =

V

I= R + jX


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6

Table 1: Impedance Terms & Equations

Parameter Quantity Unit Symbol Formula

Z Impedance ohm, Z R jX

YZS S

j= + = =1

| |

|Z| Magnitude of Z ohm, | |

| |

Z R X

YS S= + =

2 2 1

Rsor ESR Resistance,Real part of Z

ohm, R

G

G BS

P

P P

=+2 2

=2

1 Q

RP

+

Xs Reactance,Imaginary part of Z

ohm, X

B

G BS

P

P P

= +2 2

Y Admittance siemen, SY G jB

ZYP P

j= + = =1

| |

|Y| Magnitude of Y siemen, S(was mho)

| || |

Y G BZ

P P= + =2 2 1

GP Real part of Y siemen, SG

R

R XP

S

S S

=

+2 2

BP Susceptance siemen, SB

X

R XP

S

S S

= +2 2

Cs Series capacitance farad, F CX

C DSS

P= = +1

1 2

( )

CP Parallel capacitance farad, FC

B C

DP

S= =+ 1 2

Ls Series inductance henry, H

LX

LQ

QS p= =

+

2

21

LP Parallel inductance henry, H LB

LQP P S

= = +1

11

2

( ) RP Parallel resistance ohm, R

GR QP

P

S= = +1

1 2( ) Q Quality factor none

tan1

====P

P

S

S

B

G

R

X

DQ

D, DF or

tan

Dissipation factor none tan)90tan(

1 0 =====P

P

S

S

G

B

X

R

QD

Phase angle of Z degree or radian =

Phase angle of Y degree or radian =

Notes:1. f = frequency in Hertz; j = square root (-1); = 2f2. R and X are equivalent series quantities unless otherwise defined. G and B are equivalent parallel quantities unless otherwise defined.

Parallel R (Rp) is sometimes used but parallel X (Xp) is rarely used and series G (Gs) and series B (Bs) are very rarely used.3. C and L each have two values, series and parallel. If no subscript is defined, usually series configuration is implied, but not necessarily, especially for C

(Cp is common, Lp is less used).4. Q is positive if it is inductive, negative if it is capacitive. D is positive if it is capacitive. Thus D = -1/Q.5. Tan is used by some (especially in Europe) instead of D. tan = D.


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Series and Parallel

At any specific frequency an impedance maybe represented by either a series or a parallelcombination of an ideal resistive element andan ideal reactive element which is either capac-itive or inductive. Such a representation iscalled an equivalent circuit and illustrated inFigure 1.

The values of these elements or parametersdepend on which representation is used, seriesor parallel, except when the impedance is pure-

ly resistive or purely reactive. In such casesonly one element is necessary and the series orparallel values are the same.

Since the impedance of two devices in series isthe sum of their separate impedances, we canthink of an impedance as being the series com-bination of an ideal resistor and an ideal capac-

itor or inductor. This is the series equivalent cir-

cuit of an impedance comprising an equivalentseries resistance and an equivalent seriescapacitance or inductance (refer to Figure 1).Using the subscript s for series, we have equa-tion 1:

For a complicated network having many com-ponents, it is obvious that the element values ofthe equivalent circuit will change as the fre-quency is changed. This is also true of the val-ues of both the elements of the equivalent cir-cuit of a single, actual component, although thechanges may be very small.

7

RS RS

RP RPCP

LSCS

LP

IMPEDANCE ADMITTANCE

InductiveCapacitive InductiveCapacitive

Z

+R

+jX

-jX

RS

-jXRS

+R

Z+jX

Y

+GGP

+jB

-jB

jLs

GP GP

or or

Y

+GGP

-jB

+jB

jCpL

P

1-jCS

1-j

Figure 1: Phase Diagrams

1: Z = Rs + jXs = Rs + jL = Rs -j

C


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Admittance, Y, is the reciprocal of impedanceas shown in equation 2:

It too is complex, having a real part, the ac con-ductance G, and an imaginary part, the sus-ceptance B. Because the admittances of paral-lel elements are additive, Y can be representedby a parallel combination of an ideal conduc-tance and a susceptance, where the latter iseither an ideal capacitance or an ideal induc-tance (refer to Figure 1). Using the subscript pfor parallel elements, we have equation 3:

Note that an inductance susceptance is nega-tive and also note the similarity or duality of thislast equation and Equation 1.

It is important to recognize that, in general, Gpis not equal to 1/Rs and Bp is not equal to 1/Xs(or -1/Xs) as one can see from the calculation in

equation 4.

Thus Gp = 1/Rs only if Xs = 0, which is the caseonly if the impedance is a pure resistance, andBp = -1/Xs (note the minus sign) only if Rs = 0,that is, the impedance is a pure capacitance orinductance.

Gp, Cp and Lp are the equivalent parallelparameters. Since a pure resistance is thereciprocal of a pure conductance and has thesame symbol, we can use Rp instead of Gp forthe resistor symbols in Figure 1, noting that Rp

= 1/Gp and Rp is the equivalent parallel resist-ance. (By analogy, the reciprocal of the seriesresistance, Rs, is series conductance, Gs, butthis quantity is rarely used).

Two other quantities, D and Q, are useful, notonly to simplify the conversion formulas ofTable 1, but also by themselves, as measuresof the "purity" of a component, that is, howclose it is to being ideal or containing onlyresistance or reactance. D, the dissipation fac-tor, is the ratio of the real part of impedance, oradmittance, to the imaginary part. Q, the quali-ty factor, is the reciprocal of this ratio as illus-trated in equation 5.

A low D value, or high Q, means that a capaci-tor or inductor is quite pure, while a low Q, or

high D, means that a resistor is nearly pure. InEurope, the symbol used to represent the dissi-pation factor of a component is the tangent ofthe angle delta, or tan . Refer to Table 1.

Some conventions are necessary as to thesigns of D or Q. For capacitors and inductors,D and Q are considered to be positive as longas the real part of Z or Y is positive, as it will befor passive components. (Note, however, thattransfer impedance of passive networks can

exhibit negative real parts). For resistors, acommon convention is to consider Q to be pos-itive if the component is inductive (having apositive reactance), and to be negative if it iscapacitive (having a negative reactance).

8

2: Y =1

Z

3: Y = Gp + jBp = Gp + jCp = Gp -L

j

4: Y =Z

1 1=

Rs

Rs + jXs

=Rs2 + Xs2

- jXs

Rs2 + Xs2

= Gp + jBp

5: D =Rs

Xs= =

Bp

Gp 1

Q


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Formulas for D and Q in terms of the series andparallel parameters are given in Table 1. Notethat the D or Q of an impedance is independentof the configuration of the equivalent circuitused to represent it.

It should be emphasized that these series andparallel equivalent circuits both have the samevalue of complex impedance at a single fre-quency, but at any other frequency their imped-ances will be different. An example is illustratedin Figure 2.

9

DUT

Series Parallel

0.05uF 2k

0.1uF

1k

Z

+R

+jX

-jX

1k

Z DUT= 1000 -j1000 at 1.5915kHz

= 2 (10/2) kHz

= 2 f

f= 10/2 kHz = 1.5915kHz

= 10 kHz

Y

+G

2k-jB

+jB

j0.05uF

0.1uF1

-j

Figure 2: Complex Impedance


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Connection to the device under test (DUT) iscrucial in determining the most accurate valueof the DUTs impedance. The use of multipleconnections can reduce or remove impedancemeasurement errors caused by series imped-

ance in the connections or shunt impedanceacross the unknown. Refer to QuadTech appli-cation note 035027 for an excellent tutorial onMulti-Terminal Impedance Measurements. Forthe discussion in this primer we will illustrate 2,3 and 4-terminal connection methods. Note:1- terminal = 1 wire = 1 lead = 1 connection.

Two-Terminal Measurements

The impedance of a device is defined by Ohm'sLaw as the ratio of the voltage across it to the

current through it. This requires at least twoconnections and therefore the arithmetic of ter-minals starts with two. With only two terminals,the same terminals must be used for bothapplying a current and measuring a voltage asillustrated in Figure 3.

Figure 3: Two Terminal Measurement

When a device is measured in this way it mightnot be an accurate measurement. There are

two types of errors and these are the errors thatmeasurements with more connections willavoid, one is the lead inductance and leadresistance in series with the device and theother is stray capacitance between the twoleads, both of which affect the measurementresults. Because of these error sources, the

typical impedance measurement range for atwo-terminal connection is limited to 100 to10k.

Four-Terminal Measurements

First let's jump into four-terminal measure-ments, which are simpler to explain and morecommonly used than a three-terminal measure-ment. With a second pair of terminals avail-able, one can measure voltage across thedevice with one pair and apply current to thedevice with the other pair. This simple improve-ment of independent leads for voltage and cur-rent effectively removes the series inductanceand resistance error factor (including contactresistance) and the stray capacitance factor

discussed with two-terminal measurements.Accuracy for the lower impedance measure-ment range is now substantially improved downto 1 and below. There will be some mutualinductance between the current leads and volt-meter leads which will introduce some error, butmuch of this is eliminated by using shieldedcoaxial cabling. The most famous use of thefour-terminal connection is the Kelvin Bridgewhich has been widely used for precision DCresistance measurements.

This circuitry associated Lord Kelvin's name soclosely with the four-terminal connection tech-nique that "Kelvin" is commonly used todescribe this connection.

Figure 4: Four Terminal

10

Connection Methods

IH

QuadTech

PH

IL

PL

7600 PRECISIONLCR METER!

Z

IH

QuadTech

PH

IL

PL


Z


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Three-Terminal (or Guarded)

MeasurementsWhile the four-terminal measurement applies acurrent and measures the resulting open-circuitvoltage, the three -terminal measurement doesthe opposite, it applies a voltage and measuresthe short circuit current. The extra terminal, orthird terminal, is called the guard. Any compo-nents shunting the unknown can effectively beremoved by connecting some point along theshunt to this guard terminal.

The effect of any stray path, capacitive or con-ductive, (shunting Zx) can be removed by inter-cepting it with a shield tied to the guard point.Likewise, "shunting Zx" can effectively beremoved in a series string of actual compo-nents by connecting some point along the stringto the guard and making a three-terminal meas-urement. Sometimes three-terminal measure-

ments are simply called guarded measure-ments. They are also called direct impedancemeasurements. Figure 6 illustrates one repre-sentation of a passive 3-terminal network.

The impedance Zx is that impedance directly

between points A and B. As shown by equation6, errors caused by Za and Zb have beenchanged. If it were not for the series imped-ances, the effect of Za and Zb would have beenremoved completely. The combination of seriesimpedance and shunt impedance has given ustwo new types of errors. We'll call the first(z1/Za and z3/Zb) the "series/shunt" error. It'scaused by a voltage, or current, divider effect.The voltage between point A and guard isreduced because the attentuating or dividingeffect of the impedances z1 and Za. Likewise,Zb and z3 divide the current Ix so that it doesn'tall flow in the ammeter. Note that this error is aconstant percent error, independent of thevalue of Zx. It usually is very small at low fre-quencies unless the series and shunt imped-ances are actual circuit components as theymight be in in-circuit measurements.

A three-terminal connection usually employstwo coaxial cables, where the outer shields are

connected to the guard terminal of the LCRmeter. The guard terminal is electrically differ-ent from the instrument ground terminal whichis connected to chassis ground. Measurementaccuracy is usually improved for higher imped-ances, but not lower because lead inductanceand resistance are still present.

11

Zx

Za

Zb

z1 z3

z5

A

V A

B

C

Figure 6:

Three-Terminal Guarded

using Delta Impedance Configuration

Zm =V

Zx 1=

I

+ ++z1 + z3

Zx Za

z1 z3Zb

-z5 ZxZa Zb

Equation 6:formula for Figure 6

IH

QuadTech

PH

IL

PL


Zb

Za

Z

Figure 5: 7600 3-Terminal Kelvin


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Digital LCR meters rely on a measurementprocess of measuring the current flowingthrough the device under test (DUT), the volt-age across the DUT and the phase anglebetween the measured V and I. From these

three measurements, all impedance parame-ters can then be calculated. A typical LCRmeter has four terminals labeled IH, IL, PH andPL. The IH/IL pair is for the generator and cur-rent measurement and the PH/PL pair is for thevoltage measurement.

MethodsThere are many different methods and tech-niques for measuring impedance. The mostfamiliar is the nulling type bridge method illus-

trated in Figure 7. When no current flowsthrough the detector (D), the value of theunknown impedance Zx can be obtained by therelationship of the other bridge elements,shown in equation 7.

Figure 7: Bridge Method

Various types of bridge circuits, employing com-binations of L, C, and R as bridge elements, areused in different instruments for varying appli-cations.

Most recently instruments have been devel-oped which employ elaborate software-drivencontrol and signal processing techniques. Forexample, the QuadTech 7000 LCR Meter usesa principle of measurement which differs signif-

icantly from that employed by the traditionalmeasuring instruments. In particular, the 7000uses digital techniques for signal generationand detection. In the elementary measurementcircuit as shown in Figure 8, both the voltageacross the device under test (Zx) and the volt-age across a reference resistor (Rs) are meas-ured, which essentially carry the same current.

The voltage across Zx is Vx and the voltageacross Rs is Vs. Both voltages are simultane-ously sampled many times per cycle of theapplied sine wave excitation. In the case of the7000, there are four reference resistors. Theone used for a particular measurement is theoptimal resistor for the device under test, fre-quency, and amplitude of the applied ac signal.For both Vx and Vs a real and imaginary (inphase and quadrature) component are comput-ed mathematically from the individual samplemeasurements.

The real and imaginary components of Vx and

Vs are by themselves meaningless.Differences in the voltage and current detectionand measurement process are corrected viasoftware using calibration data. The real andimaginary components of Vx (Vxr and Vxi) arecombined with the real and imaginary compo-nents of Vs (Vsr and Vsi) and the known char-acteristics of the reference resistor to determinethe apparent impedance of the complex imped-ance of Zx using complex arithmetic.

12

Impedance Measuring Instruments

Z1

Z3

Z2

ZX

D Detector

Oscillator

Z1Z

x Z2

= Z3

7:


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Figure 9: QuadTech 7600 LCR Meter

FunctionsThe demand on component testing is muchmore than a resistance, capacitance or induc-tance value at a given test frequency and stim-ulus voltage. Impedance meters must gobeyond this with the flexibility to provide multi-parameters over wide frequency and voltageranges. Additionally, an easily understood dis-play of test results and the ability to access anduse these results has become increasinglyimportant.

Test Voltage

The ac output of most LCR meters can be pro-grammed to select the signal level applied tothe DUT. Generally, the programmed level isobtained under an open circuit condition.

A source resistance (Rs, internal to the meter)is effectively connected in series with the acoutput and there is a voltage drop across thisresistor. When a test device is connected, thevoltage applied to the device depends on thevalue of the source resistor (Rs) and the imped-ance value of the device.

Figure 10 illustrates the factors of constantsource impedance, where the programmed

voltage is 1V but the voltage to the test deviceis 0.5V.

Some LCR meters, such as the QuadTech1900 have a voltage leveling function, wherethe voltage to the device is monitored andmaintained at the programmed level.

Figure 10: Source Impedance Factors

13

VX

VSRS

IL

VX

VS

ZX

IH

-

+

PL

PH

RS

DifferentialAmplifiers

VS

ZX

IX

K

K

7000 Measurement Circuit, Simplified 7000 Measurement Circuit, Active 5-Terminal

VS

VX

RS

ZX=

IH PH

IL PL

ZX VS

VX

(RS)

=

DUT

1910 Source Resistance

VMEASURE

VPROGRAM

I MEASURE

VP= 1V

RS=25

ZX= R+jX

R = 25X = 0

VM= VPR2+ X2

(RS+ R)2 + X2

VM= ?

Figure 8: 7000 Measurement Circuit


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Ranging

In order to measure both low and high imped-ance values measuring instrument must haveseveral measurement ranges. Ranging is usu-ally done automatically and selected depending

on the impedance of the test device. Rangechanges are accomplished by switching rangeresistors and the gain of detector circuits. Thishelps maintain the maximum signal level andhighest signal-to-noise ratio for best measure-ment accuracy. The idea is to keep the meas-ured impedance close to full scale for any givenrange, again, for best accuracy.

Range holding, rather than autoranging, is afeature sometimes used in specific applica-

tions. For example, when repetitive testing ofsimilar value components, range holding canreduce test time. Another use of range holdoccurs when measuring components whosevalue falls within the overlap area of two adja-cent ranges, where if allowed to autorange theinstruments display can sometimes changeresulting in operator confusion.

Integration Time

The length of time that an LCR meter spends

integrating analog voltages during the processof data acquisition can have an important effecton the measurement results. If integrationoccurs over more cycles of the test signal themeasurement time will be longer, but the accu-racy will be enhanced. This measurement timeis usually operator controlled by selecting aFAST or SLOW mode, SLOW resulting inimproved accuracy. To improve repeatibility, trythe measurement averaging function. In aver-aging mode multiple measurements are made

and the average of these is calculated for theend result. All of this is a way of reducingunwanted signals and effects of unwantednoise, but does require a sacrifice of time.

Median Mode

A further improvement of repeatability can beobtained by employing the median mode func-

tion. In median mode 3 measurements aremade and two thrown away (the lowest and thehighest value). The remaining value then repre-sents the measured value for that particulartest. Median mode will increase test time by a

factor of 3.Computer Interface

Many testers today must be equipped withsome type of standard data communicationinterface for connection to remote data pro-cessing, computer or remote control. For anoperation retrieving only pass/fail results theProgrammable Logic Control (PLC) is oftenadequate, but for data logging it's a differentstory. The typical interface for this is the IEEE-

488 general purpose interface bus or the RS-232 serial communication line.

These interfaces are commonly used for moni-toring trends and process control in a compo-nent manufacturing area or in an environmentwhere archiving data for future reference isrequired. For example when testing 10% com-ponents, the yield is fine when components testat 8% or 9%, but it does not take much of a shiftfor the yield to plummet. The whole idea of pro-duction monitoring is to reduce yield risks andbe able to correct the process quickly if needed.

An LCR Meter with remote interface capabilityhas become standard in many test applicationswhere data logging or remote control havebecome commonplace.

Figure 11: 7000 Series Computer Application

14


15/58

Test fixtures (fixturing) and cables are vital com-ponents of your test setup and in turn play animportant role in the accuracy of your imped-ance measurements. Consider these factorspertaining to test fixtures and cables.

Compensation

Compensation reduces the effects from errorsources existing between the device under testand the calibrated connection to the measuringinstrument. The calibrated connection is deter-mined by the instrument manufacturer, whichcan be front or rear panel connections, or at theend of a predefined length of cable.Compensation will ensure the best measure-ment accuracy possible on a device at theselected test conditions. When a measurementis affected by a single residual component thecompensation is simple.

Take the case of stray lead capacitance(CSTRAY) in parallel with the DUT capacitance

(CX), illustrated in Figure 12. The value of the

stray capacitance can be measured directlywith no device connected. When the device is

connected the actual DUT value can be deter-mined by subtracting the stray capacitance(CSTRAY) from the measured value (CMEASURE).

The only problem is, its not always this simplewhen stray residuals are more than a singlecomponent.

Figure 12: Lead Compensation

Open/Short

Open/Short correction is the most popular com-pensation technique used in most LCR instru-ments today. When the unknown terminals areopen the stray admittance (Yopen) is meas-

ured. When the unknown terminals are shortedthe residual impedance (Zshort) is measured.When the device is measured, these two resid-uals are used to calculate the actual impedanceof the device under test.

When performing an OPEN measurement it isimportant to keep the distance between theunknown terminal the same as they are whenattached to the device. It's equally important tomake sure that one doesn't touch or move their

hands near the terminals. When performing aSHORT measurement a shorting device (short-ing bar or highly conductive wire) is connectedbetween the terminals. For very low imped-ance measurements it is best to connect theunknown terminals directly together.

Figure 13: Open/Short

15

Test Fixtures and Cables

Z

CSTRAY

CDUT

= CMEASURE

CDUT

CSTRAY

CSTRAY

-

KelvinTest

Leads

KelvinTest

Leads

LCUR

HCUR

HPOT

LPOT(-) (+)

OPEN

SHORT

Test

Terminals


16/58

16

Load Correction

Load Correction is a compensation techniquewhich uses a load whose impedance is accu-rately known and applies a correction to meas-urements of similar components to substantial-

ly improve measurement accuracy. The pur-pose being to correct for non-linearity of themeasuring instrument and for test fixture orlead effects which may be dependent on thetest frequency , test voltage, impedance range,or other factors. Criteria for selecting theappropriate load include:

a. Load whose impedance value isaccurately known.

b. Load whose impedance value is very

close to the DUT (this ensures that themeasuring instrument selects the samemeasurement range for both devices).

c. Load whose impedance value is stableunder the measurement conditions.

d. Load whose physical properties allow itto be connected using the same leadsor fixture as the DUT.

A prerequisite for load correction is to perform acareful open/short compensation as previously

discussed. This feature, found on a number ofQuadTech LCR Meters, provides for an auto-matic load correction. The load's known value isentered into memory, the load then measured,and this difference then applied to ongoingmeasurements.

Z actual = Z measure +/- delta Z

delta Z = the difference between theknown and the measured value of theload.

Through the use of load correction it is possibleto effectively increase the accuracy of themeasuring instrument substantially, but this isonly as good as the known accuracy of the loadused in determining the correction.


17/58

17

Capacitors are one of the many componentsused in electronic circuits. The basic construc-tion of a capacitor is a dielectric material sand-wiched between two electrodes. The differenttypes of capacitors are classified according to

their dielectric material. Figure 14 shows thegeneral range of capacitance values accordingto their dielectric classification. Capacitance C,dissipation factor D, and equivalent seriesresistance ESR are the parameters usuallymeasured.

Capacitance is the measure of the quantity ofelectrical charge that can be held (stored)between the two electrodes. Dissipation factor,also known as loss tangent, serves to indicatecapacitor quality. And finally, ESR is a singleresistive value of a capacitor representing allreal losses. ESR is typically much larger thanthe series resistance of leads and contacts ofthe component. It includes effects of the capac-itor's dielectric loss. ESR is related to D by theformula ESR =D/C where =2f.

Series or Parallel

Advances in impedance measurement instru-mentation and capacitor manufacturing tech-niques coupled with a variety of applicationshas evolved capacitor test into what might be

considered a complex process. A typical equiv-alent circuit for a capacitor is shown in Figure15. In this circuit, C is the main element ofcapacitance. Rs and L represent parasitic com-ponents in the lead wires and electrodes andRp represents the leakage between the capac-itor electrodes.

Figure 15: Capacitor Circuit

Capacitance Measurements

0.1 0.011000100101.0 100101.00.1 1000 104 105 1F

picofarad (pF) microfarad (uF)

CERAMIC

METALIZED PLASTIC

ALUMINUM ELECTROLYTIC

TANTALUM ELECTROLYTIC

Figure 14: Capacitance Value by Dielectric Type

L

RP

RS

C


18/58

18

When measuring a capacitor these parasiticsmust be considered. Measuring a capacitor inseries or parallel mode can provide differentresults, how they differ can depend on the qual-ity of the device, but the thing to keep in mind is

that the capacitor's measured value most close-ly represents its effective value when the moresuitable equivalent circuit, series or parallel, isused. To determine which mode is best, con-sider the impedance magnitudes of the capaci-tive reactance and Rs and Rp. For example,suppose the capacitor modeled in Figure 16has a small value.

Remember reactance is inversely proportionalto C, so a small capacitor yields large reactancewhich implies that the effect of parallel resist-ance (Rp) has a more significant effect thanthat of Rs. Since Rs has little significance inthis case the parallel circuit mode should beused to more truly represent the effective value.The opposite is true in Figure 17 when C has alarge value. In this case the Rs is more signifi-cant than Rp thus the series circuit modebecome appropriate. Mid range values of Crequires a more precise reactance-to-resist-ance comparison but the reasoning remains the

same.The rule of thumb for selecting the circuit modeshould be based on the impedance of thecapacitor:

* Above approximately 10 k -use parallel mode

* Below approximately 10 -use series mode

* Between these values -follow manufacturers recommendation

Translated to a 1kHz test:

Use Cp mode below 0.01 F and Cs modeabove 10 F; and again between these valueseither could apply and is best based on themanufacturers recommendation.

Figure 16: Rp more significant

Figure 17: Rs more significant

The menu selection, such as that on theQuadTech 7000 Series LCR Meter, makesmode selection of Cs, Cp or many otherparameters easy with results clearly shown onthe large LCD display.

Measuring Large and Small Values ofCapacitance

High values of capacitance represent relativelylow impedances, so contact resistance andresidual impedance in the test fixture andcabling must be minimized. The simplest form

of connecting fixture and cabling is a two termi-nal configuration but as mentioned previously, itcan contain many error sources. Lead induc-tance, lead resistance and stray capacitancebetween the leads can alter the result substan-tially. A three-terminal configuration, with coaxcable shields connected to a guard terminal,

CLOW

Rp

Rs

If C = Low then Xc = High

and Rp becomes the most

significant resistance

Rs

CHIGH Rp

If C = High then Xc = Low

and Rs becomes the most

significant resistance


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19

can be used to reduce effects of stray capaci-tance. This is a help to small value capacitorsbut not the large value capacitors because thelead inductance and resistance still remains.

For the best of both worlds a four terminal con-

figuration, discussed earlier and shown inFigure 18, (often termed Kelvin) can be used toreduce the effects of lead impedance for highvalue capacitors. Two of the terminals serve forcurrent sourcing to the device under test, andtwo more for voltage sensing. This techniquesimply removes errors resulting from serieslead resistance and provides considerableadvantage in low impedance situations.

Figure 18a: 4-Terminal to DUT

Besides a 4-terminal connection made as closeas possible to the device under test, a furtherenhancement to measurement integrity is an

OPEN/SHORT compensation by the measuringinstrument. The open/short compensationwhen properly performed is important in sub-tracting out effects of stray mutual inductancebetween test connections and lead inductance.

The effect of lead inductance can clearlyincrease the apparent value of the capacitancebeing measured. Open/Short compensation isone of the most important techniques of com-pensation used in impedance measurementinstruments. Through this process each resid-ual parameter value can be measured and thevalue of a component under test automaticallycorrected.

One of the most important things to alwayskeep in mind is a concerted effort to achieveconsistency in techniques, instruments, and fix-turing. This means using the manufacturersrecommended 4-terminal test leads (shieldedcoax) for the closest possible connection to thedevice under test. The open/short should beperformed with a true open or short at the testterminals. For compensation to be effective theopen impedance should be 100 times the DUTimpedance and the short impedance 100 timesless than the DUT impedance. Of equal impor-

tance, when performing open/short zeroing, theleads must be positioned exactly as the deviceunder test expects to see them.

A

V

+

IL

PL-

D

U

T

PH

IH

1730 LCR Digibridge

LCUR HCURHPOTLPOT

QuadTech

(-) (+)01

l

F1

F4

F3

F2

NEXT PAGE 1/3

PARA : Cs - D

LEVEL : 1.00 V

FREQ. : 100 kHz

Cs : 1.2345 pF

D : 1.2345

+

-

DUT

IL

PL

IH

PH

Figure 18b:

4-Terminal to DUT

1730 LCR Meterand

Kelvin Clip Leads


20/58

20

Equivalent Series Resistance (ESR)

Questions continually arise concerning the cor-rect definition of the ESR (Equivalent SeriesResistance) of a capacitor and, more particular-ly, the difference between ESR and the actual

physical series resistance (which we'll callRas), the ohmic resistance of the leads andplates or foils. Unfortunately, ESR has oftenbeen misdefined and misapplied. The followingis an attempt to answer these questions andclarify any confusion that might exist. Verybriefly, ESR is a measure of the total lossinessof a capacitor. It is larger than Ras because theactual series resistance is only one source ofthe total loss (usually a small part).

At one frequency, a measurement of compleximpedance gives two numbers, the real partand the imaginary part: Z = Rs + jXs. At thatfrequency, the impedance behaves like a seriescombination of an ideal resistance Rs and anideal reactance Xs (Figure 19). If Xs is nega-tive, the impedance is capacitive and the reac-tance can be replaced with capacitance asshown in equation 8.

We now have an equivalent circuit that is cor-rect only at the measurement frequency. Theresistance of this equivalent circuit is the equiv-alent series resistance:

ESR = Rs = Real part of Z

Figure 19: Real Part of Z

If we define the dissipation factor D as the ener-gy lost divided by the energy stored in a capac-itor we can deduce equation 9.

If one took a pure resistance and a pure capac-itance and connected them in series, then onecould say that the ESR of the combination wasindeed equal to the actual series resistance.However, if one put a pure resistance in paral-lel with a pure capacitance (Figure 20a) creat-ing a lossy capacitor, the ESR of the combina-tion is the Real part of Z = Real part of equation10 as shown in Figure 20b.

From Figure 20a, however, it is obvious thatthere is no actual series resistance in serieswith the capacitor. Therefore Ras = 0, butESR > 0, therefore ESR > Ras.

Figure 20: ESR

8: Xs =

-1

Cs

RS

CSXS

DUT

9: D =energy lost

energy stored

=

Real part of Z

(-Imaginary part of Z)=

Rs

(-) Xs

= RsC

= (ESR) C

10:

1

Rp

1+ jCp

=

Rp

2Cp2Rp2+1

CS

RS

b: series

=R

P

1 + 2CP

2RP

2

= CP( 1+

2CP

2RP

2

1)

a: parallel

Cp

Rp

=


21/58

21

An inductor is a coiled conductor. It is a devicefor storing energy in a magnetic field (which isthe opposite of a capacitor that is a device forstoring energy in an electric field). An inductorconsists of wire wound around a core material.

Air is the simplest core material for inductorsbecause it is constant, but for physical efficien-cy, magnetic materials such as iron and ferritesare commonly used. The core material of theinductor, its length and number of turns direct-ly affect the inductors ability to carry current.

Series or Parallel

As with capacitor measurements, inductormeasurements can be made in either a seriesor parallel mode, use of the more suitable moderesults in a value that equals the actual induc-tance. In a typical equivalent circuit for aninductor, the series resistance (Rs), representsloss of the copper wire and parallel resistance(Rp) represents core losses as shown in Figure21.

Figure 21: Inductor Circuit

In the case where the inductance is large, thereactance at a given frequency is relativelylarge so the parallel resistance becomes moresignificant than any series resistance, hencethe parallel mode should be used. For very

large inductance a lower measurement fre-quency will yield better accuracy.

For low value inductors, the reactancebecomes relatively low, so the series resistanceis more significant, thus a series measurementmode is the appropriate choice. For very smallinductance a higher measurement frequencywill yield better accuracy. For mid range valuesof inductance a more detail comparison of reac-tance to resistance should be used to helpdetermine the mode.

The most important thing to remember whenev-er a measurement correlation problem occurs,is to use the test conditions specified by thecomponent manufacturer. Independent of anyseries/parallel decision, it is not uncommon fordifferent LCR meters to give different measuredresults. One good reason for this is that induc-tor cores can be test signal dependent. If theprogrammed output voltages are different themeasured inductance will likely be different.

Even if the programmed output voltage is thesame, two meters can still have a differentsource impedance. A difference in sourceimpedance can result in a difference in currentto the device, and again, a different measuredvalue.

Inductance Measurement Factors

Here are four factors for consideration inmeasuring actual inductors:

DC Bias Current

Constant Voltage (Voltage Leveling)Constant Source ImpedanceDC Resistance & Loss

There are other considerations such as corematerial and number of coils (turns) but thoseare component design factors not measure-ment factors.

Inductance Measurements

LX

RP

RS

PutCurrent

Through

Wire

Coil of Wire, Air core = Inductor

ProduceMagnetic Flux

Linkage

Out

Inductance =Current Through

Magnetic Flux


22/58

22

DC Bias Current

To get an accurate inductance measurement,the inductor must be tested under actual (reallife) conditions for current flowing through thecoil. This cannot always be accomplished with

the typical AC source and a standard LCRmeter as the typical source in an LCR meter isnormally only capable of supplying smallamounts of current (


23/58

23

DC Resistance and Loss

Measuring the DCR or winding resistance of acoil of wire confirms that the correct gauge ofwire, tension and connection were used duringthe manufacturing process. The amount of

opposition or reactance a wire has is directlyproportional to the frequency of the current vari-ation. That is why DC resistance is measuredrather than ACR. At low frequencies, the DCresistance of the winding is equivalent to thecopper loss of the wire. Knowing a value of thewire's copper loss can provide a more accurateevaluation of the total loss (DF) of the deviceunder test (DUT). (Refer to Figure 23).

Loss

Three possible sources of loss in an inductormeasurement are copper, eddy-current andhysteretic. They are dependent on frequency,signal level, core material and device heating.

As stated above, copper Loss at low frequen-cies is equivalent to the DC resistance of thewinding. Copper loss is inversely proportionalto frequency. Which means as frequencyincreases, the copper loss decreases. Copperloss is typically measured using an inductance

analyzer with DC resistance (DCR) measure-ment capability rather than an AC signal.

Eddy-Current Loss in iron and copper are dueto currents flowing within the copper or corecased by induction. The result of eddy-currentsis a loss due to heating within the inductors cop-per or core. Eddy-current losses are directly

proportional to frequency. Refer to Figure 24.Hysteretic Loss is proportional to the areaenclosed by the hysteresis loop and to the rateat which this loop is transversed (frequency). Itis a function of signal level and increases withfrequency. Hysteretic loss is however inde-pendent of frequency. The dependence uponsignal level does mean that for accurate meas-urements it is important to measure at knownsignal levels.

0.1

0.01

0.0011kHz 10 100 1MHz

1H

100mH

10mH

1mH

Frequency

DissipationFactorD

=-1/Q

Ohm

icLossDo~1/f

Eddy

Current

Loss,

De~f

Diele

ctric

Loss

,D

d~f

2

Inductance, L is blue Loss is red

D ~1

1 -ffr

2

Ro

Lo+ GeLo +

ffr

2

Do

De

Eddy

Current

Loss

Do

Ohmic

Loss

Dd

Dielectric

Loss

Resonance

Factor

CURRENT

Current

carrying

wire

Eddy

Current

paths

Solid

Core

Direction

of

Magnetic

Flux

Figure 23: Factors of Total Loss (Df)

Figure 24: Eddy Currents induced in an iron core


24/58

24

Of the three basic circuit components, resistors,capacitors and inductors, resistors cause theleast measurement problems. This is truebecause it is practical to measure resistors byapplying a dc signal or at relatively low ac fre-

quencies. In contrast to this, capacitors andinductors always experience ac signals that bytheir very nature are prone to fluctuation, thusthese components are generally measuredunder changing conditions. Resistors are usu-ally measured at dc or low frequency ac whereOhm's Law gives the true value under theassumption that loss factors are accounted for.The thing to keep in mind is that if resistors areused in high frequency circuits they will haveboth real and reactive components. This can

be modeled as shown in Figure 25, with aseries inductance (Ls) and parallel capacitance(Cp).

Figure 25: Resistor Circuit

For example, in the case of wire-wound resis-tors (which sounds like an inductor) its easy tounderstand how windings result in this L term.Even though windings can be alternatelyreversed to minimize the inductance, the induc-tance usually increases with resistance value(because of more turns). In the case of carbonand film resistors conducting particles canresult in a distributed shunt capacitance, thusthe C term.

Series or Parallel

So how does one choose the series or parallelmeasurement mode? For low values of resis-tors (below 1k) the choice usually becomes alow frequency measurement in a series equiva-

lent mode. Series because the reactive com-ponent most likely to be present in a low valueresistor is series inductance, which has noeffect on the measurement of series R. Toachieve some degree of precision with lowresistance measurements it is essential to usea four-terminal connection as discussed earlier.

This technique actually eliminates lead or con-tact resistance which otherwise could elevatethe measured value. Also, any factor that

affects the voltage drop sensed across a lowresistance device will influence the measure-ment. Typical factors include contact resist-ance and thermal voltages (those generated bydissimilar metals). Contact resistance can bereduced by contact cleanliness and contactpressure.

For high values of resistors (greater than sev-eral M) the choice usually becomes a low fre-

quency measurement in a parallel equivalentmode. Parallel because the reactive compo-nent most likely to be present in a high valueresistor is shunt capacitance, which has noeffect on the measurement of parallel R.

Resistance Measurements

LS

CP

RX


25/58

25

QuadTech manufactures several instrumentsfor the measurement and analysis of passivecomponent parameters. The 7000 Series LCRMeter is an automatic instrument designed forthe precise measurement of resistance, capac-

itance and inductance parameters and associ-ated loss factors. It is also suited for use in cal-ibration and standards laboratories and canassume many tasks previously performed onlyby high priced, difficult to use, manually bal-anced impedance bridges and meters.

Figure 26: 7400 Precision LCR Meter

Measurement Capability

The measurements of highest precision in astandards lab are 1:1 comparisons of similarimpedance standards, particularly comparisonsbetween standards calibrated at the NationalInstitute of Standards and Technology (NIST)and similar reference standards. This type ofmeasurement requires an instrument with highmeasurement resolution and repeatability inorder to detect parts-per-million (ppm) differ-ences rather than instruments with extreme,direct-reading accuracy. In such applications,two standards of very nearly equal value arecompared using "direct substitution"; they aremeasured sequentially and only the differencebetween them is determined.

The resolution of the 7000 is 0.1 ppm for thedirect measured values and such direct reading

measurements, at a one/second rate, have atypical standard deviation of 10 ppm at 1 kHz.By using the instrument's AVERAGING mode,the standard deviation can be reduce by1/(square root of N) where N is the number ofmeasurements averaged. Thus, an average of5 measurements or more typically reduces the

standard deviation to 5 ppm. It is therefore pos-sible to measure the difference between twoimpedances to approximately 10 ppm with the7000. Averaging many measurements takestime, however an automatic impedance meter

like the 7000 can take hundreds of averagedmeasurements in the time it takes to balance ahigh-resolution, manual bridge.

Measurement precision and confidence can befurther improved by using the 7000's medianmeasurement mode. In the median measure-ment mode, the instrument makes three meas-urements rather than one and discards the highand low results. The remaining median meas-urement value is used for display or further pro-cessing (such as averaging). Using a combina-tion of averaging and median measurementsnot only increases basic measurement preci-sion, but will also yield measurements that areindependent of a large errors caused by linespikes or other non-Gaussian noise sources.

The ppm resolution of the 7000 is also not lim-ited to values near full scale as is typically trueon six-digit, manual bridge readouts. In thecase of a manually balanced bridge, the resolu-tion of a six-digit reading of 111111 is 9 ppm.

The 7000 does not discriminate against suchvalues; it has the same 0 .1 ppm resolution atall values of all parameters including dissipationfactor (D) and quality factor (Q), the tangent ofphase angle.

Figure 27: Parts Per Million Resolution

Precision Impedance Measurements

Measured Parameters

Measuring

Freq 1.0000kHz

Range AUTODelay 0ms

AC Signal 1.000V

Average 1Bias Off

Cs 17.52510 pF

DF 0.000500


26/58

26

The 7000 instrument also provides a uniqueload correction feature that allows the user toenter known values for both primary and sec-ondary parameters, as illustrated in the loadcorrection display of Figure 28. The instrument

measures these values and automaticallyapplies the correction to ongoing measure-ments.

Figure 28: Entry of Values for Load Correction

Obviously, automatic instruments such as theQuadTech 7000 have the significant advantageof speed, since a balancing procedure is notrequired. Balancing manual ac bridges is tire-some, time consuming and frequently requireshighly skilled personnel. Another advantage of

programmable instruments is the ability to cre-ate a fully automated system by utilizing theinstrument's RS-232 and IEEE-488.2 bus inter-face capability. With a computer based system,correction calculations can be made without thechance of human errors, especially the all toocommon recording problems with + and - signs.

Instrument Accuracy

In determining how the instruments measure-ment capability is defined, take a look at thespecified accuracy of the instrument. Also, tomaintain the accuracy and repeatibility ofmeasurements, the calibration procedureshould be investigated. A DUTs measuredvalue is only as accurate as the instrumentscalibrated value (plus fixture effects).

Basic Accuracy

Manufacturers of LCR meters specify basicaccuracy. This is the best-case accuracy thatcan be expected. Basic accuracy does not takeinto account error due to fixturing or cables.

The basic accuracy is specified at optimum testsignal, frequencies, highest accuracy setting orslowest measurement speed and impedance ofthe DUT. As a general rule this means 1VACRMS signal level, 1kHz frequency, high accura-cy which equates to 1 measurement/second,and a DUT impedance between 10 and100k. Typical LCR meters have a basic accu-racy between 0.01% and 0.5%.

Actual AccuracyIf the measurements are to be made outside of"optimum" conditions for basic accuracy, theactual accuracy of the measurement needs tobe determined. This is done using a formula orby looking at a graph of accuracy versusimpedance and frequency (refer to Figure 31).

It is also important to understand that the meas-urement range is really more a display range.For example an LCR will specify a measure-

ment range of 0.001nH to 99.999H this doesnot mean you can accurately measure a0.001nH inductor or a 99.9999H inductor, butyou can perform a measurement and the dis-play resolution will go down to 0.001nH or up to99.999H. This is really why it is important tocheck the accuracy of the measurement youwant to perform. Do not assume that justbecause the value you want to measure is with-in the measurement range you can accuratelymeasure it.

The accuracy formulas take into account eachof the conditions effecting accuracy. Most com-mon are measurement range, accuracy/speed,test frequency and voltage level. There areaddition errors including dissipation factor Df ofthe DUT, internal source impedance andranges of the instrument, that effect accuracy.

Load Correction

Measure

Measuring Correction

Primary Nominal

FreqRange

HIT TO RETURN TO MAIN MENU

Off On

Secondary Nominal60.00000 pF4.000000 m

Measured PrimaryMeasured Secondary

60.25518 pF.0042580

1.0000MHz49

Primary CsSecondary Df

HIT TO CHANGE VALUESHIT TO MEASURE CORRECTION


27/58

27

Factors Affecting Accuracy Calculations

DUT Impedance

High impedance measurements increase theerror because it is difficult to measure the cur-rent flowing through the DUT. For example ifthe impedance is greater than 1M and the testvoltage is one volt there will be less than 1mAof current flowing through the DUT. The inabil-ity to accurately measure the current causes anincrease in error.

Low impedance measurements have anincrease in error because it is difficult to meas-ure the voltage across the DUT. Most LCRMeters have a resistance in series with thesource of 100k to 5 ohms. As the impedance of

the DUT approaches the internal source resist-ance the voltage across the DUT drops propor-tionally. If the impedance of the DUT is signifi-cantly less than the internal source resistancethen the voltage across the DUT becomesextremely small and difficult to measure caus-ing an increase in error.

Frequency

The impedance of reactive components is alsoproportional to frequency and this must be

taken into account when it comes to accuracy.For example, measurement of a 1F capacitorat 1 kHz would be within basic measurementaccuracy where the same measurement at1MHz would have significantly more error. Partof this is due to the decrease in the impedanceof a capacitor at high frequencies howeverthere generally is increased measurement errorat higher frequencies inherent in the internaldesign of the LCR meter.

ResolutionResolution must also be considered for lowvalue measurements. If trying to measure0.0005 ohms and the resolution of the meter is0.00001 ohms then the accuracy of the meas-urement cannot be any better than 2% whichis the resolution of the meter.

Accuracy and Speed

Accuracy and speed are inversely proportional.That is the more accurate a measurement themore time it takes. LCR meters will generallyhave 3 measurement speeds. Measurement

speed can also be referred to as measurementtime or integration time. Basic accuracy isalways specified with the slowest measurementspeed, generally 1 second for measurementsabove 1kHz. At lower frequencies measure-ment times can take even longer because themeasurement speed refers to the integration oraveraging of at least one complete cycle of thestimulus voltage. For example, if measure-ments are to be made at 10Hz, the time to com-plete one cycle is 1/frequency = 1/10Hz = 100milliseconds. Therefore the minimum meas-urement speed would be 100ms.

Dissipation Factor (D) or Quality Factor (Q)

D and Q are reciprocals of one another. Theimportance of D or Q is the fact that they repre-sent the ratio of resistance to reactance or viceversa. This means that the ratio Q representsthe tangent of the phase angle. As phase isanother measurement that an LCR meter mustmake, this error needs to be considered. When

the resistance or reactance is much muchgreater than the other, the phase angle willapproach 90 or 0. As shown in Figure 29,even small changes in phase at -90 result inlarge changes in the value of resistance, R.

Figure 29: Phase Diagram for Capacitance

Z

+R

+jX

-jX

RS

-j(1/Cs)

Capacitive

XC Impedance

Reactance

Resistance


28/58

28

Example: Accuracy Formula

7600 Precision LCR Meter

Test Conditions:

1pF Capacitor at 1MHz

1VAC signalAuto RangeNon-Constant VoltageSlow Measurement SpeedDf of 0.001

Basic Accuracy of the 7600 is 0.05%

Accuracy Formula for Slow Mode R, L, C, X,G, B, |Z|, and |Y| is given in Equation 11.

Vs = Test voltage in voltage mode,

= I * Zm in current mode*

Zm = Impedance of DUT

Fm = Test frequency

Kt = 1 for 18o to 28oC

= 2 for 8o to 38oC

= 4 for 5o to 45oC

VFS = 5.0 for 1.000V < Vs 5.000V

1.0 for 0.100V < Vs 1.000V

0.1 for 0.020V Vs 0.100V

For Zm > 4* ZRANGE multiply A% by 2



*: For I * Zm > 3, accuracy is not specified

The impedance range (ZRANGE) is specified

in this table:In Voltage Mode In Current Mode

ZRANGE= 100k for Zm 25k 400 for I < 2.5mA

6k for 1.6k Zm < 25kW 25 for I > 2.5mA

6k for Zm > 25k and Fm > 25kHz400 for 100 Zm < 1.6k

400 for Zm > 1.6k and Fm > 250kHz

25 for Zm < 100

The Calculated Accuracy using the formula inEquation 11 is 3.7% substituting the valueslisted herein.

Kt = 1

Zm = 1/(2*frequency*C)

= 1/(2*1000000*1x10-12)

= 159 kohms

ZRANGE = 400 ohms

Vfs = 1

Multiply A% = 8

A% = 0.46%

Multiply A% times 8 due to Zm > 64 times

ZRANGE

A% = 0.46% * 8 = 3.68%

Refer to Equation 12 to fill in the numbers.

A% = +/- 0.025 + 0.025 +.05

Zm+ Zm 10

-7 +xx.02

VS+ .08 x

VS

Vfs (VS - 1)2

4x 0.7 +

Fm

105+

300

Fmx Kt

Equation 11: 7600 Accuracy Formula


29/58

29

Example 7600 Accuracy Graph

The accuracy could have been predicted with-out the use of a formula. If we calculate theimpedance of a 1pF capacitor at 1MHz we geta value of:

Z = Xs = 1/(2*frequency*capacitance)

Z = Xs = 1/(2*1,000,000*0.000,000,000,001)

= 159kohms

Use the graph in Figure 30 and substitute Zfor R. If we find the position on the graph foran impedance value of 159kohms at 1MHz wesee a light blue or teal representing an accura-cy of 3.45% to 3.65%. Overall the graph andformula point to the same accuracy of 3.5%.

0.1

1

10

100

1000

1.00E+04

1.00E+05

1.00E+06

1.00E+07

10 100 1000 1.00E+04 1.00E+05 5.00E+05 1.00E+06 2.00E+06

0.0

50

0

%

0.2

50

0

%

0.4

50

0

%

0.6

50

0

%

0.8

50

0

%

1.0

50

0

%

1.2

50

0

%

1.4

50

0

%

1.6

50

0

%

1.8

50

0

%

2.0

50

0

%

2.2

50

0

%

2.4

50

0

%

2.6

50

0

%

2.8

50

0

%

3.0

50

0

%

3.2

50

0

%

3.4

50

0

%

3.6

50

0

%

3.8

50

0

%

Impedance

Frequency

Accuracy Z vs F Slow3.6500%-3.8500%

3.4500%-3.6500%

3.2500%-3.4500%

3.0500%-3.2500%

2.8500%-3.0500%

2.6500%-2.8500%

2.4500%-2.6500%

2.2500%-2.4500%

2.0500%-2.2500%

1.8500%-2.0500%

1.6500%-1.8500%

1.4500%-1.6500%

1.2500%-1.4500%

1.0500%-1.2500%

0.8500%-1.0500%

0.6500%-0.8500%

0.4500%-0.6500%

0.2500%-0.4500%

0.0500%-0.2500%

Figure 30: 7600 Accuracy Plot

A% = +/- 0.025 + 0.025 +.05

159000+ 159000 10-7 +xx

.02

1+ .08 x

1

1 (1 - 1)2

4x 0.7 +

1000000

105+

300

1000000x 1

Equation 12: Completed 7600 Accuracy Formula


30/58

30

Materials Measurement

Many materials have unique sets of electricalcharacteristics which are dependent on itsdielectric properties. Precision measurementsof these properties can provide valuable infor-

mation in the manufacture or use of thesematerials. Herein is a discussion of dielectricconstant and loss measurement methods.

Figure 31: QuadTech 7000 Meter with LD-3 Cell

Definitions

There are many different notations used fordielectric properties. This discussion will use K,the relative dielectric constant, and D, the dissi-pation factor (or tan ) defined as follows:

and

The complex relative permittivity is:

where o is the permittivity of a vacuum, and

the absolute permittivity.

The capacitance of a parallel-plate air capaci-tor (two plates) is:

where Ka is the dielectric constant of air:

if the air is dry and at normal atmosphericpressure.

Measurement Methods, Solids

The Contacting Electrode Method

This method is quick and easy, but is the leastaccurate. The results for K should be within10% if the sample is reasonably flat. Refer toFigure 32. The sample is first inserted in the celland the electrodes closed with the micrometeruntil they just touch the sample. The electrodesshould not be forced against the sample. The

micrometer is turned with a light finger touchand the electrometer setting recorded as hm.

Materials Measurements

K = ' = r

D = tan =r"

r'

r* = o

= r' - j (r")

o = 0.08854pF/cm

C = Ka o Area / spacing

Ka = 1.00053

SpecimenCxm and Dxm

h=ho

H

L

G

ho

H

L

G

AirCa and Da

Figure 32:

Contact Electrode


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31

The LCR Meter should be set to measure par-allel capacitance and the capacitance and dis-sipation factor of the sample measured as Cxmand Dxm.

The electrodes are opened and the sampleremoved and then the electrodes closed to thesame micrometer reading, hm. C (parallel) and

D of empty cell are measured as Ca and Da.

Calculate Kx and Dx of the sample from:

and

The factor 1.0005 in the formula for Kx corrects

for the dielectric constant of (dry) air.Subtracting Da from Dxm removes any constant

phase error in the instrument. For even better Daccuracy, the electrode spacing can be adjust-ed until the measured capacitance is approxi-mately equal to Cxm, and then Da measured.

Note that both Kx and Dx will probably be too

low because there is always some air betweenthe electrodes and the sample. This error issmallest for very flat samples, for thicker sam-ples and for those with low K and D values.

The Air-Gap Method

This method avoids the error due to the airlayer but requires that the thickness of thesample is known. Its thickness should bemeasured at several points over its area and

the measured values should be averaged toget the thickness h. The micrometer usedshould have the same units as those of themicrometer on the cell.

The electrodes are set to about .02 cm or .01inch greater than the sample thickness, h, andthe equivalent series capacitance and D meas-ured as Ca and Da. Note the micrometer set-

ting as hm which can be corrected with themicrometer zero calibration, hmo to get:

The sample is inserted and measured as Cxaand Dxa. Calculate:

Kx = (1.0005)CxmCa

=Dx (Dxm - Da)

Specimen and AirCxa and Dxa

ho

H

L

G

h

H

L

G

AirCa and Da

Figure 33:

Air Gap Method

=ho (hm + hmo)

CaCa - MCxa

Kx =Cxa(1-M)

Ca - MCxa

1.0005

1 + Dx2

=D (Dxa - Da)

=M(ho - h)

ho


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The factor (1 + Dx2) converts the series value of

Cx to the equivalent parallel value and is not

necessary if Dx is small. The factor of 1.0005

corrects for the dielectric constant of air (if dry).The formula for D

xassumes that the true D of

air is zero and it makes a correction for a con-stant D error in the instrument.

The Two-Fluid Method

This method is preferred for specimens whosethickness is difficult to measure and for bestaccuracy which will be limited by the accuracyof the C and D measurements. However itrequires fourmeasurements, two using a sec-

ond fluid (the first being air). The dielectricproperties of this fluid need not be known, but itmust not react with the specimen and it must bestable and safe to use. A silicone fluid such as

Dow Corning 200, 1 centistoke viscosity, ismost generally satisfactory.

The four measurements of series capacitanceand D are outlined in the Figure 34. Note thespacing is the same for all measurements and

should be just slightly more than the specimenthickness. The accuracy will be limited mainlyby the accuracy of the measurements made.

From these measurements calculate:

which is the ratio of the equivalent seriescapacitance of the sample to Ca.

Specimen and AirCxa and Dxa

ho

H

L

G

h

H

L

G

AirCa and Da

ho

H

L

G

h

H

L

G

FluidCf and Df

Specimen and FluidCxfand Dxf

Figure 34: Two

Fluid Method

CaCf (Cxf- Cxa)=h

ho1 -

Cxa Cxf (Cf- Ca)

Cxser

Ca=

Cxf Cxa (Cf- Ca)

Ca (CxaCf- CxfCa)


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33

If Dx is close to Df or larger use:

If Dx is very small use:

which makes a zero D correction.

From the above results calculate:

As before, the factor of 1.0005 corrects for thedielectric constant of air (if dry) and the factor

(1 + Dx2) converts Cx to equivalent parallel

capacitance.

Measurement Methods, Liquids

Measurements on liquids are simple, the onlydifficulty is with handling and cleanup.

Equivalent parallel capacitance and D of air (Caand Da), is measured first and then that of the

liquid (Cxm and Dxm)

Determine Kx and Dx:

Note that the spacing is not critical but shouldbe narrow enough to make the capacitancelarge enough to be measured accurately.

(Cxf- Cxa) (Dxf- Df)CaDxf += (CxaCf- CxfCa)Dx

Dx =(Dxa - Da) Cxf (Cf- Ca)

(CxaCf- CxfCa)

Kx =h

ho

CxserCa

1.0005

1 + Dx2

Kx

=Cxm

Ca1.0005

=Dx (Dxm - Da)


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34

As with most test instrumentation, LCR meterscan come with a host of bells and whistles butthe features one most often uses aredescribed herein.

Test FrequencyElectrical components need to be tested at thefrequency in which the final product/applicationwill be utilized. An instrument with a wide fre-quency range and multiple programmable fre-quencies provides this platform.

Test Voltage

The ac output voltage of most LCR meters can

be programmed to select the signal levelapplied to the DUT. Generally, the programmedlevel is obtained under an open circuit condi-tion. A source resistance (Rs, internal to themeter) is effectively connected in series withthe ac output and there is a voltage drop acrossthis resistor. When a test device is connected,the voltage applied to the device depends onthe value of the source resistor (Rs) and theimpedance value of the device.

Accuracy/Speed

Classic trade-off. The more accurate yourmeasurement the more time it takes and con-versely, the faster your measurement speed theless accurate your measurement. That is whymost LCR meters have three measurementspeeds: slow, medium and fast. Depending onthe device under test, the choice is yours toselect accuracy or speed.

Measurement Parameters

Primary parameters L, C and R are not the onlyelectrical criteria in characterizing a passivecomponent and there is more information in theSecondary parameters than simply D and Q.Measurements of conductance (G), suscep-

tance (B), phase angle () and ESR can morefully define an electrical component or material.

Ranging

In order to measure both low and high imped-ance values measuring instrument must haveseveral measurement ranges. Ranging is usu-ally done automatically and selected dependingon the impedance of the test device. Rangechanges are accomplished by switching rangeresistors and the gain of detector circuits. Thishelps maintain the maximum signal level andhighest signal-to-noise ratio for best measure-ment accuracy. The idea is to keep the meas-ured impedance close to full scale for any given

range, again, for best accuracy.

Averaging

The length of time that an LCR meter spendsintegrating analog voltages during the processof data acquisition can have an important effecton the measurement results. If integrationoccurs over more cycles of the test signal themeasurement time will be longer, but the accu-racy will be enhanced. This measurement timeis usually operator controlled by selecting aFAST or SLOW mode, SLOW resulting inimproved accuracy. To enhance accuracy, themeasurement averaging function may be used.In an averaging mode many measurements aremade and the average of these is calculated forthe end result.

Median Mode

A further enhancement to accuracy can beobtained by employing the median mode func-tion. In a median mode 3 measurements mightbe made and two thrown away (the lowest andthe highest value). The median value then rep-resents the measured value for that particulartest.

Recommended LCR Meter Features


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Computer Interface

Many testers today must be equipped withsome type of standard data communicationinterface for connection to remote data pro-cessing, computer or remote control. For an

operation retrieving only pass/fail results theProgrammable Logic Control (PLC) is oftenadequate, but for data logging it's a differentstory. The typical interface for this is the IEEE-488 general purpose interface bus or the RS-232 serial communication line.

These interfaces are commonly used for moni-toring trends and process control in a compo-nent manufacturing area or in an environmentwhere archiving data for future reference is

required. For example when testing 10% com-ponents, the yield is fine when components testat 8% or 9%, but it does not take much of a shiftfor the yield to plummet. The whole idea of pro-duction monitoring is to reduce yield risks andbe able to correct the process quickly if needed.

An LCR Meter with remote interface capabilityhas become standard in many test applicationswhere data logging or remote control havebecome commonplace.

Display

An instrument with multiple displays providesmeasured results by application at the press ofa button. Production environments may prefera Pass/Fail or Bin Summary display. R&D Labs

may need a deviation from nominal display.The 7000 series instruments have seven dis-play modes: measured parameters, deviationfrom nominal, % deviation from nominal,Pass/Fail, Bin Summary, Bin Number and NoDisplay. Refer to Figure 35. Figure 36 illus-trates three of the 7000 Series display modes.

IH

QuadTech

PH

IL

PL


CAUTION

HIGH VOLTAGE

DISPLAY ENTRYSELECT TEST

0

10

987

.-

654

321 MENU

CNCL

ENTER

FREQUENCY Hz

IZI

255.2

153.4

204.3

102.5

51.59

10.00 572.9 32.82k 2.000M

START

STOP

Pass / Fail

Bin

4

2

1213

HIT TO RETURN TO MAIN MENU

NO CONTACT

110.00 k

3100.00 k110.00 k

511

120.00 k130.00 k

90.00 k

14

PRI Pass SEC FailLOW

PRI Fail SEC Pass

PRI Pass SEC FailHI

PRI Fail SEC Fail

Freq

DelayRange

PASS

Pass / Fail

Ls 158.450uH Q 1.000249

AC SignalAverageBias

Bin Totals

1

15

Totals: Pass 595 Fail 190 785

140.00 k130.00 k120.00 k

150.00 k

250

8090

100

Low LIMIT High LIMIT Total

7560555020

5

Measured Parameters

Measured Parameters

Measuring

Freq

RangeDelay

AC Signal

AverageBias

Cs 17.52510 pF

DF 0.000500

Setup I/O Analysis UtilitiesDisplay

Measured Parameters

% Deviation from NominalDeviation from Nominal

Pass / FailBin SummaryBin NumberNo Display

HIT MENU TO RETURN TO MAIN MENU

Figure 35: 7600 Display Menu

Figure 36: Example 7600 Display Modes


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Binning

A necessary production application, binning

sorts components by test results quickly by apredetermined value set by the test engineer.Two of the most common methods of sortingresults into bins are using nested limits orsequential limits.

Nested Limits

Nested limits are a natural choice for sortingcomponents by % tolerance around a singlenominal value with the lower bins narrower than

the higher numbered bins. Nested limits forthree bins are illustrated in Figure 37. Note thatthe limits do not have to by symmetrical (Bin 3is -7% and +10%).

Sequential Limits

Sequential limits are a natural choice whensorting components by absolute value. Figure38 illustrates the use of sequential limits for atotal of three bins. Sequential bins do not haveto be adjacent. Their limits can overlap or havegaps depending upon the specified limit. Anycomponent that falls into an overlap betweenbins would be assigned to the lower numberedbin and any component that falls into a gapbetween bins would be assigned to the overallfail bin.

MeasuredValue

Bin 3Bin 2Bin 1

85.00k 100.00k90.00k 120.00k

N

Bin 1

Bin 3

Bin 2

MeasuredValue

Nominal Value100.00k

-7%

-5%

-1% +1%

+5%

+10%

Figure 37:

Nested Limits

Figure 38:

Sequntial Limits


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Test Sequencing

A sequence of tests, each with different testparameters and conditions can be performedon a single component. Combined with the bin-ning process, test sequencing enables multiple

tests on a single component and then sorting bytest. This is a great electrical characterizationtool for finding out under which conditions yourparticular component fails.

Parameter Sweep

Another excellent device characterization toolof LCR meters is the parameter sweep function.

A sweep is a user-defined number of measure-ments for a particular test. The QuadTech 7000

Series instruments display a table or plot ofmeasured results versus a test variable such asfrequency, voltage or current. The user definesthe lower boundary of the sweep in Hz, Volts or

Amps; the upper boundary in Hz, Volts orAmps; the step or number of increments in thesweep and the format (table or plot).

Figure 39 illustrates the parameter sweep func-tion of the 7000 Series instrument.

Bias Voltage and Bias Current

A bias voltage or bias current function enablesreal time operating conditions to be applied tothe device under test. Bias an inductor withDC current of 1-2mA to simulate the currentrunning through it in its real application (suchas in a power supply).

Constant Source Impedance

An LCR meter with a constant source imped-ance, will provide a source resistance (Rs) that

will hold the current constant. Therefore oneknows what the voltage at the DUT will be. Rsis in series with the ac output such that the pro-grammed voltage is 1V but the voltage to thetest device is 0.5V. Refer to Figure 40.

Setup I/O Analysis UtilitiesSweep

Parameter

Sweep End

Sweep Begin

Sweep Step

Sweep Format

HIT MENU TO RETURN TO MAIN MENU

Freq Voltage Current= 10.0 Hz

= 1.0000 kHz

25 50 100 200

Table Plot

Plot Table

Frequency1.0000kHz

1.6681kHz1.2915kHz

2.1544kHz

Frequency Hz

200.0

50.000k

Cs DF

2.7825kHz

3.5938kHz

4.6415kHz

5.9948kHz

7.7426kHz

10.000kHz

471.4576nF

470.4563nF469.8878nF

468.9983nF

466.4532nF

462.6634nF

460.6645nF

459.7892nF

458.7845nF

456.5454nF

0.003135

0.0036750.003867

0.010035

0.010078

0.011045

0.012895

0.014786

0.016782

0.018544

PrevPage

NextPage

180.0

160.0

140.0

120.0

100.0

51.000k 54.000k 62.000kIZI

Sweep Table Sweep Plot

Sweep Parameter Setup

Figure 39:

Parameter Sweep Function


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Figure 40: Constant Source Impedance

Monitoring DUT Voltage & CurrentMonitoring the voltage across or currentthrough the DUT during test enables real timeanalysis of the device. If the voltage can bekept level (constant) across a DUT then theimpedance can be measured accurately. Ininductor measurements it is necessary to keepthe voltage across the inductor constantbecause the voltage across an inductorchanges with the impedance of the inductorwhich changes with the current through it. Sothe ability to monitor the voltage and current tothe DUT will provide the most accurate condi-tions for impedance measurement.

DUT

1910 Source Resistance

V MEASUREV PROGRAM

I MEASURE

VP= 1V

RS=25

ZX= R+jX

R = 25X = 0

VM= VPR2+ X2

(RS+ R)2 + X2

VM= ?

Figure 41: Digibridge Family: 1689 & 1689M


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Examples of passive component measuringinstrumentation manufactured by QuadTech,Inc of Maynard Massachusetts is providedherein. Included are: Digibridges, PrecisionLCR Meters and Impedance Analyzers.

Digibridges

The 1600 and 1700 Series digital bridges arehigh performance passive component testers.

1600 Series

Common Features

Full five digit display for primary L,C & R

Four digit display for secondary D, Q

Continuous or Triggered Measurement Mode

Open & Short Circuit Compensation

DC Bias: Internal to 2V, External to 60V

Auto Ranging with Manual Hold

Pass/Fail Bins for Component Sorting

Charged Capacitor Protection

Optional IEEE 488 and Handler Interfaces

Full Range of Accessory Options

1659 LCR Digibridge Measurement Parameters: R/Q, L/Q, C/R, C/D

Test Frequency: 100Hz, 120Hz, 1kHz, 10kHz

Accuracy: 0.1% LCR; 0.0005 DQ

Applied Voltage: 0.3V maximum

2, 4 or 8 Measurements per second

1689/89M LCR Digibridge

Measurement Parameters: R/Q, L/Q, C/R, C/D

Programmable Test Frequency: 12Hz to 100kHz


Programmable Test Voltage: 5mV to 1.275V

1689: Up to 30 measurements/second*

1689M: Up to 50 measurements/second*

Constant Voltage Mode (25 Source)

Median Value Mode

* With High Speed Option

1692 LCR Digibridge

Measurement Parameters: R/Q, L/Q, C/R, C/D

Test Frequency: 100Hz, 120Hz, 1kHz, 10kHz

and 100kHz


Applied Voltage: 0.3V to 1.0V maximum 2, 4 or 8 measurements/second


Single Triggered Measurement or 1-10 Averaged

1693 LCR Digibridge

Measurement Parameters: R/Q, L/Q, C/R, C/D,R/X, G/B, Z/, Y/

500 Test Frequencies: 12Hz to 200kHz

Accuracy: Primary 0.02% L,C,R, G, Z, Y

Secondary: 0.0002 DQ; 0.01o


Up to 50 measurements/second*


Median Value Mode

* With High Speed Option

Examples of High Performance Testers

Figure 42: 1692 Digibridge



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1700 Series

Common Features

Guarded 4-Terminal Kelvin Connection

Selectable Test Voltage & Frequency

Selectable Measurement Rate

External DC Bias Voltage

Full Range of Accessory Options

1710 LCR Digibridge

Measurement Parameters: Primary: L, C, R

Secondary: D/Q, Q/R, Q/L, R/C, R/L

Test Frequency: 120Hz or 1kHz

Basic Accuracy: 0.2% LCR; 0.0005 D; 0.001 Q

Applied Test Voltage: 0.25V or 1.0V

3 measurements/second

External DC Bias Voltage: 0-60V

Internal Zeroing Function

1730 LCR Digibridge

12 Measurement Parameters


7 Test Frequencies: 100Hz to 100kHz


Up to 62 measurements/second

Programmable Source Impedance

IEEE-488 & Handler Interfaces, Standard

Monitor DUT Voltage & Current

Storage/Recall of 50 Setups

Pass/Fail Binning

Measurement Averaging (1-256)

Measurement Delay (0-10 seconds)

DC Bias Voltage: 0-5V

Automatic Open/Short Zeroing

1750 Digibridge


Basic Accuracy: 0.1% LCR; 0.001 DQ

43 Preset Test Frequencies: 1kHz to 200kHz

500 Programmable Frequencies: 20Hz-200kHz



Programmable Source Impedance

IEEE-488 & Handler Interfaces, Standard

Monitor DUT Current

Storage/Recall of 10 Setups

Pass/Fail Binning


DC Bias Voltage: 0-35V External

Open/Short Compensation

Load Correction

Median Value Mode





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Programmable Test Frequency: 10Hz to 500kHz


Programmable Test Voltage: 250uA to 100mA


DC Bias Voltage: 0V to 2.0V, Internal

DC Bias Voltage: 0V to 200V, External

DC Bias Voltage: 0V to 500V, External (7400A)

Internal Storage/Recall of 25 Setups

15 Pass/Fail Bins


Measurement Delay (0 to 1000 ms)


Displays Usage & Calibration Data




Programmable Test Frequency: 10Hz to 2MHz


Programmable Test Voltage: 250uA to 100mA


DC Bias Voltage: 0V to 2.0V, Internal DC Bias Voltage: 0V to 200V, External

DC Bias Voltage: 0V to 500V, External (7600A)

Internal Storage/Recall of 25 Setups

15 Pass/Fail Bins


Measurement Delay (0 to 1000 ms)


Displays Usage & Calibration Data

Dedicated Function Test Instruments

In addition to passive compent test instrumen-tation, QuadTech manufactures milliohmme-ters, megohmeters, AC/DC

Gen Rad Primer

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