LCLCRR MEASUREMENMEASUREMENTT PRIMEPRIMERR
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5 Clock Tower Place, 210 East, Maynard, Massachusetts 01754 TELE: (800) 253-1230, FAX: (978) 461-4295, INTL: (978) 461-2100 http:// www.quadtech.com 2 Preface
The intent of this reference primer is to explain the basic definitions and measurement of impedance parameters, also known as LCR. This primer provides a general overview of the impedance characteristics of an AC cir- cuit, mathematical equations, connection methods to the device under test and methods used by measuring instruments to precisely characterize impedance. Inductance, capacitance and resistance measuring tech- niques associated with passive component testing are presented as well.
LCR Measurement Primer 2nd Edition, August 2002 Comments: [email protected]
5 Clock Tower Place, 210 East Maynard, Massachusetts 01754 Tel: (978) 461-2100 Fax: (978) 461-4295 Intl: (800) 253-1230 Web: http://www.quadtech.com
This material is for informational purposes only and is subject to change without notice. QuadTech assumes no responsibility for any error or for consequential damages that may result from the misinterpretation of any procedures in this publication.
3 Contents
Impedance 5 Recommended LCR Meter Features 34 Definitions 5 Test Frequency 34 Impedance Terms 6 Test Voltage 34 Phase Diagrams 7 Accuracy/Speed 34 Series and Parallel 7 Measurement Parameters 34 Connection Methods 10 Ranging 34 Averaging 34 Two-Terminal Measurements 10 Median Mode 34 Four-Terminal Measurements 10 Computer Interface 35 Three-Terminal (Guarded) 11 Display 35 Impedance Measuring Instruments 12 Binning 36 Methods 12 Test Sequencing 37 Functions 13 Parameter Sweep 37 Test Voltage 13 Bias Voltage and Bias Current 37 Ranging 14 Constant Source Impedance 37 Integration Time 14 Monitoring DUT Voltage and Current 38 Median Mode 14 Computer Interface 14 Examples of High Performance Testers 39 Digibridge ® Component Testers 39 Test Fixtures and Cables 15 1600 Series 39 Compensation 15 1659 39 Open/Short 15 1689/89M 39 Load Correction 16 1692 39 Capacitance Measurements 17 1693 39 Series or Parallel 17 1700 Series 40 High & Low Value Capacitance 18 1710 40 ESR 20 1730 40 1750 40 Inductance Measurements 21 Precision LCR Meters 41 Series or Parallel 21 1900 Series 41 Inductance Measurement Factors 21 1910 Inductance Analyzer 41 DC Bias Voltage 22 1920 LCR Meter 41 Constant Voltage (Leveling) 22 7000 Series 41 Constant Source Impedance 22 7400 LCR Meter 42 DC Resistance and Loss 23 7600 LCR Meter 42 Resistance Measurements 24 Dedicated Function Test Instruments 42 Milliohmmeters 42 Series or Parallel 24 Megohmmeters 42 Precision Impedance Measurements 25 Hipot Testers 42 Measurement Capability 25 Electrical Safety Analyzers 42 Instrument Accuracy 26 Factors Affecting Accuracy 27 Appendix A 43 Example Accuracy Formula 28 Nationally Recognized Testing Laboratories Materials Measurement 30 (NRTLs) and Standards Organizations 44 Definitions 30 Measurement Methods, Solids 30 Helpful Links 45 Contacting Electrode 30 Typical Measurement Parameters 46 Air-Gap 31 Impedance Terms and Equations 47 Two Fluid 32 Measurement Method, Liquids 33 Application Note Directory 49 Glossary 53
4 Impedance Impedance Complex Quantity However, if capacitance or inductance are Impedance is the basic electrical parameter present, they also affect the flow of current. The used to characterize electronic circuits, compo- capacitance or inductance cause the voltage nents, and materials. It is defined as the ratio and current to be out of phase. Therefore, of the voltage applied to the device and the Ohms law must be modified by substituting resulting current through it. To put this another impedance (Z) for resistance. Thus for ac, way, impedance is the total opposition a circuit Ohm's Law becomes : Z = V/I. Z is a complex offers to the flow of an alternating current (ac) number: Z = R + jX . A complex number or at a given frequency, and is generally repre- quantity has a real component (R) and an imag- sented as a complex quantity, which can be inary component (jX). shown graphically. The basic elements that make up electrical impedances are inductance, capacitance and resistance: L, C, and R, Phase Shift respectively. The phase shift can be drawn in a vector dia- In the real world electronic components are not gram which shows the impedance Z, its real pure resistors, inductors or capacitors, but a part Rs, its imaginary part jXs (reactance), and combination of all three. Today's generation of the phase angle q. Because series imped- LCR meters are capable of displaying these ances add, an equivalent circuit for an imped- parameters and can easily calculate and dis- ance would put Rs and Xs is series hence sub- play many other parameters such as Z, Y, X, G, script ‘s’. The reciprocal of Z is Admittance, Y B, D, etc. This primer is intended as an aid in which is also a complex number having a real understanding which ac impedance measure- part Gp (conductance) and an imaginary part ments are typically used and other factors that jBp (susceptance) with a phase angle f. Note need to be considered to obtain accurate and q = - f. Because admittances in parallel add, meaningful impedance measurements. an equivalent circuit for an admittance would put Gp and Bp in parallel. Note from the for- mulas below that, in general, Gp does not Definitions equal (1/Rs) and Bp does not equal -(1/Xs). The mathematical definition of resistance for dc (constant voltage) is the ratio of applied voltage V to resulting current I. This is Ohms Law: R = Refer to Table 1 for Impedance terms, units of V/I. An alternating or ac voltage is one that measure and equations. regularly reverses its direction or polarity. If an ac voltage is applied to a circuit containing only resistance, the circuit resistance is determined from Ohms Law.
V V For DC, Resistance, R = For AC, Impedance, Z = = R + jX I I
5 Table 1: Impedance Terms & Equations
Parameter Quantity Unit Symbol Formula Z Impedance ohm, W 1 Z = R + jX = =| Z|e jq S S Y |Z| Magnitude of Z ohm, W 2 2 1 | Z|= R + X = S S |Y| R or ESR Resistance, ohm, W G s R = P Real part of Z S 2 2 GP + BP X Reactance, ohm, W B s X = - P Imaginary part of Z S 2 2 GP + BP Y Admittance siemen, S 1 Y = G + jB = =|Y|e jf P P Z |Y| Magnitude of Y siemen, S 2 2 1 |Y |= G + B = (was mho) P P |Z | G Real part of Y siemen, S R P G = S P 2 2 RS + XS B Susceptance siemen, S X P B = - S P 2 2 RS + XS C Series capacitance farad, F s 1 2 CS = - = CP (1+ D ) wXS C Parallel capacitance farad, F C P B S CP = = w 1+ D2 Ls Series inductance henry, H 2 X Q LS = = Lp w 1+ Q2 LP Parallel inductance henry, H 1 1 L = - = L (1+ ) P S 2 wBP Q R Parallel resistance ohm, W P 1 2 RP = = RS (1+ Q ) G P Q Quality factor none 1 X G Q = = S = P = tan q D RS BP
D, DF or Dissipation factor none 1 RS GP 0 tan d D = = = = tan(90 - q) = tan d Q XS BP q Phase angle of Z degree or radian q = -f
f Phase angle of Y degree or radian f = -q
Notes: 1. f = frequency in Hertz; j = square root (-1); w = 2pf 2. 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 d is used by some (especially in Europe) instead of D. tan d = D.
6 +jX +jX +jBX +jBX R G S +R Z Y P +G q q -j(1/wCs) d jwLs jwCp -j(1/wLp) d
d d q q +R +G Z RS GP Y -jX -jX -jB -jB
RS RS
CP RP LP RP or or CS LS G P GP
IMPEDANCE ADMITTANCE Capacitive Inductive Capacitive Inductive
Figure 1: Phase Diagrams Series and Parallel itor or inductor. This is the series equivalent cir- At any specific frequency an impedance may cuit of an impedance comprising an equivalent be represented by either a series or a parallel series resistance and an equivalent series combination of an ideal resistive element and capacitance or inductance (refer to Figure 1). an ideal reactive element which is either capac- Using the subscript s for series, we have equa- itive or inductive. Such a representation is tion 1: called an equivalent circuit and illustrated in Figure 1. j 1: Z = Rs + jXs = Rs + j wL = Rs - The values of these elements or parameters wC depend on which representation is used, series or parallel, except when the impedance is pure- ly resistive or purely reactive. In such cases For a complicated network having many com- only one element is necessary and the series or ponents, it is obvious that the element values of parallel values are the same. the equivalent circuit will change as the fre- Since the impedance of two devices in series is quency is changed. This is also true of the val- the sum of their separate impedances, we can ues of both the elements of the equivalent cir- think of an impedance as being the series com- cuit of a single, actual component, although the bination of an ideal resistor and an ideal capac- changes may be very small.
7 Admittance, Y, is the reciprocal of impedance Gp, Cp and Lp are the equivalent parallel as shown in equation 2: parameters. Since a pure resistance is the reciprocal of a pure conductance and has the 1 same symbol, we can use Rp instead of Gp for 2: Y = Z the resistor symbols in Figure 1, noting that Rp = 1/Gp and Rp is the equivalent parallel resist- It too is complex, having a real part, the ac con- ance. (By analogy, the reciprocal of the series ductance G, and an imaginary part, the sus- resistance, Rs, is series conductance, Gs, but ceptance B. Because the admittances of paral- this quantity is rarely used). lel elements are additive, Y can be represented Two other quantities, D and Q, are useful, not by a parallel combination of an ideal conduc- only to simplify the conversion formulas of tance and a susceptance, where the latter is Table 1, but also by themselves, as measures either an ideal capacitance or an ideal induc- of the "purity" of a component, that is, how tance (refer to Figure 1). Using the subscript p close it is to being ideal or containing only for parallel elements, we have equation 3: resistance or reactance. D, the dissipation fac- tor, is the ratio of the real part of impedance, or j admittance, to the imaginary part. Q, the quali- 3: Y = Gp + jBp = Gp + j wCp = Gp - ty factor, is the reciprocal of this ratio as illus- wL trated in equation 5.
Rs Gp 1 Note that an inductance susceptance is nega- 5: D = = = tive and also note the similarity or duality of this Xs Bp Q last equation and Equation 1. It is important to recognize that, in general, Gp is not equal to 1/Rs and Bp is not equal to 1/Xs A low D value, or high Q, means that a capaci- (or -1/Xs) as one can see from the calculation in tor or inductor is quite pure, while a low Q, or equation 4. high D, means that a resistor is nearly pure. In Europe, the symbol used to represent the dissi- 1 1 4: Y = = pation factor of a component is the tangent of Z Rs + jXs the angle delta, or tan d. Refer to Table 1. Some conventions are necessary as to the Rs Xs = - j signs of D or Q. For capacitors and inductors, Rs 2 + Xs2 Rs 2 + Xs2 D and Q are considered to be positive as long as the real part of Z or Y is positive, as it will be = Gp + jBp for passive components. (Note, however, that transfer impedance of passive networks can exhibit negative real parts). For resistors, a Thus Gp = 1/Rs only if Xs = 0, which is the case common convention is to consider Q to be pos- only if the impedance is a pure resistance, and itive if the component is inductive (having a Bp = -1/Xs (note the minus sign) only if Rs = 0, positive reactance), and to be negative if it is that is, the impedance is a pure capacitance or capacitive (having a negative reactance). inductance.
8 Formulas for D and Q in terms of the series and parallel parameters are given in Table 1. Note that the D or Q of an impedance is independent of the configuration of the equivalent circuit used to represent it. It should be emphasized that these series and parallel equivalent circuits both have the same value of complex impedance at a single fre- quency, but at any other frequency their imped- ances will be different. An example is illustrated in Figure 2.
Series Parallel
1kW
0.5uF 2kW DUT 0.1uF
+jX +jBX 1kW Y Z DUT = 1000 -j1000 W at 1.5915kHz +R q d w = 2p f jw0.5uF f = 10/2p kHz = 1.5915kHz /(w/(w0.1uF) - j d q w = 2p (10/2p)kHz +G Z 2kW w = 10 kHz -jX -jB
Figure 2: Complex Impedance
9 Connection Methods Connection to the device under test (DUT) is typical impedance measurement range for a crucial in determining the most accurate value two-terminal connection is limited to 100W to of the DUT’s impedance. The use of multiple 10kW. connections can reduce or remove impedance Four-Terminal Measurements measurement errors caused by series imped- ance in the connections or shunt impedance First let's jump into four-terminal measure- across the unknown. Refer to QuadTech appli- ments, which are simpler to explain and more cation note 035027 for an excellent tutorial on commonly used than a three-terminal measure- Multi-Terminal Impedance Measurements. For ment. With a second pair of terminals avail- the discussion in this primer we will illustrate 2, able, one can measure voltage across the 3 and 4-terminal connection methods. Note: device with one pair and apply current to the 1- terminal = 1 wire = 1 lead = 1 connection. device with the other pair. This simple improve- ment of independent leads for voltage and cur- Two-Terminal Measurements rent effectively removes the series inductance The impedance of a device is defined by Ohm's and resistance error factor (including contact Law as the ratio of the voltage across it to the resistance) and the stray capacitance factor current through it. This requires at least two discussed with two-terminal measurements. connections and therefore the arithmetic of ter- Accuracy for the lower impedance measure- minals starts with two. With only two terminals, ment range is now substantially improved down the same terminals must be used for both to 1W and below. There will be some mutual applying a current and measuring a voltage as inductance between the current leads and volt- illustrated in Figure 3. meter leads which will introduce some error, but much of this is eliminated by using shielded QuadTech PRECISION coaxial cabling. The most famous use of the 7600 LCR METER ! four-terminal connection is the Kelvin Bridge which has been widely used for precision DC resistance measurements. IL IH This circuitry associated Lord Kelvin's name so closely with the four-terminal connection tech- PL PH nique that "Kelvin" is commonly used to describe this connection.
Z QuadTech PRECISION 7600 LCR METER Figure 3: Two Terminal Measurement ! When a device is measured in this way it might not be an accurate measurement. There are IL IH two types of errors and these are the errors that measurements with more connections will avoid, one is the lead inductance and lead PL PH resistance in series with the device and the other is stray capacitance between the two Z leads, both of which affect the measurement results. Because of these error sources, the Figure 4: Four Terminal
10 QuadTech PRECISION 7600 LCR METER ments are simply called guarded measure- ! ments. They are also called direct impedance measurements. Figure 6 illustrates one repre-
IL IH sentation of a passive 3-terminal network. The impedance Zx is that impedance directly between points A and B. As shown by equation PL PH 6, errors caused by Za and Zb have been changed. If it were not for the series imped- ances, the effect of Za and Zb would have been Z removed completely. The combination of series Z a b Z impedance and shunt impedance has given us two new types of errors. We'll call the first (z1/Za and z3/Zb) the "series/shunt" error. It's caused by a voltage, or current, divider effect. Figure 5: 7600 3-Terminal Kelvin The voltage between point A and guard is Three-Terminal (or Guarded) reduced because the attentuating or dividing Measurements effect of the impedances z1 and Za. Likewise, While the four-terminal measurement applies a Zb and z3 divide the current Ix so that it doesn't current and measures the resulting open-circuit all flow in the ammeter. Note that this error is a voltage, the three -terminal measurement does constant percent error, independent of the the opposite, it applies a voltage and measures value of Zx. It usually is very small at low fre- the short circuit current. The extra terminal, or quencies unless the series and shunt imped- third terminal, is called the guard. Any compo- ances are actual circuit components as they nents shunting the unknown can effectively be might be in in-circuit measurements. removed by connecting some point along the A three-terminal connection usually employs shunt to this guard terminal. two coaxial cables, where the outer shields are The effect of any stray path, capacitive or con- connected to the guard terminal of the LCR ductive, (shunting Zx) can be removed by inter- meter. The guard terminal is electrically differ- cepting it with a shield tied to the guard point. ent from the instrument ground terminal which Likewise, "shunting Zx" can effectively be is connected to chassis ground. Measurement removed in a series string of actual compo- accuracy is usually improved for higher imped- nents by connecting some point along the string ances, but not lower because lead inductance to the guard and making a three-terminal meas- and resistance are still present. urement. Sometimes three-terminal measure-
Figure 6: Three-Terminal Guarded z1 z3 using Delta Impedance Configuration A B Zx
V Equation 6: Z Z Z = V a b A m I formula for Figure 6 C
z z1 + z3 z1 z3 z5 Zx 5 = Zx 1 + + + - Zx Za Zb Za Zb
11 Impedance Measuring Instruments Digital LCR meters rely on a measurement Most recently instruments have been devel- process of measuring the current flowing oped which employ elaborate software-driven through the device under test (DUT), the volt- control and signal processing techniques. For age across the DUT and the phase angle example, the QuadTech 7000 LCR Meter uses between the measured V and I. From these a principle of measurement which differs signif- three measurements, all impedance parame- icantly from that employed by the traditional ters can then be calculated. A typical LCR measuring instruments. In particular, the 7000 meter has four terminals labeled IH, IL, PH and uses digital techniques for signal generation PL. The IH/IL pair is for the generator and cur- and detection. In the elementary measurement rent measurement and the PH/PL pair is for the circuit as shown in Figure 8, both the voltage voltage measurement. across the device under test (Zx) and the volt- age across a reference resistor (Rs) are meas- Methods ured, which essentially carry the same current. There are many different methods and tech- The voltage across Zx is Vx and the voltage niques for measuring impedance. The most across Rs is Vs. Both voltages are simultane- familiar is the nulling type bridge method illus- ously sampled many times per cycle of the trated in Figure 7. When no current flows applied sine wave excitation. In the case of the through the detector (D), the value of the 7000, there are four reference resistors. The unknown impedance Zx can be obtained by the one used for a particular measurement is the relationship of the other bridge elements, optimal resistor for the device under test, fre- shown in equation 7. quency, and amplitude of the applied ac signal. Z For both Vx and Vs a real and imaginary (in 7: Z = 1 Z phase and quadrature) component are comput- x Z 3 2 ed mathematically from the individual sample measurements. The real and imaginary components of Vx and Vs are by themselves meaningless. Z Z 1 X Differences in the voltage and current detection and measurement process are corrected via software using calibration data. The real and D Detector imaginary components of Vx (Vxr and Vxi) are combined with the real and imaginary compo- nents of Vs (Vsr and Vsi) and the known char- Z2 Z3 acteristics of the reference resistor to determine the apparent impedance of the complex imped- ance of Zx using complex arithmetic.
Oscillator
Figure 7: Bridge Method Various types of bridge circuits, employing com- binations of L, C, and R as bridge elements, are used in different instruments for varying appli- cations.
12 IH PH IH IX PH
ZX K VX PL IL VX ZX Differential PL K V Amplifiers RS S
VS
IL RS
- V (R ) Z = X S + V X V S S VX ZX =
VS RS 7000 Measurement Circuit, Simplified 7000 Measurement Circuit, Active 5-Terminal
Figure 8: 7000 Measurement Circuit
A source resistance (Rs, internal to the meter) is effectively connected in series with the ac output and there is a voltage drop across this resistor. When a test device is connected, the voltage applied to the device depends on the value of the source resistor (Rs) and the imped- ance value of the device. Figure 9: QuadTech 7600 LCR Meter Figure 10 illustrates the factors of constant Functions source impedance, where the programmed voltage is 1V but the voltage to the test device The demand on component testing is much is 0.5V. more than a resistance, capacitance or induc- Some LCR meters, such as the QuadTech tance value at a given test frequency and stim- 1900 have a voltage leveling function, where ulus voltage. Impedance meters must go the voltage to the device is monitored and beyond this with the flexibility to provide multi- maintained at the programmed level. parameters over wide frequency and voltage ranges. Additionally, an easily understood dis- 1910 Source Resistance play of test results and the ability to access and use these results has become increasingly RS=25W important. ZX= R+jX V V PROGRAM VP= 1V R = 25W DUT MEASURE X = 0W V = ? Test Voltage M R2+ X2 V = V The ac output of most LCR meters can be pro- M P I MEASURE (R + R) 2 + X2 grammed to select the signal level applied to S the DUT. Generally, the programmed level is obtained under an open circuit condition. Figure 10: Source Impedance Factors
13 Ranging tion. In median mode 3 measurements are In order to measure both low and high imped- made and two thrown away (the lowest and the ance values measuring instrument must have highest value). The remaining value then repre- several measurement ranges. Ranging is usu- sents the measured value for that particular ally done automatically and selected depending test. Median mode will increase test time by a on the impedance of the test device. Range factor of 3. changes are accomplished by switching range Computer Interface resistors and the gain of detector circuits. This Many testers today must be equipped with helps maintain the maximum signal level and some type of standard data communication highest signal-to-noise ratio for best measure- interface for connection to remote data pro- ment accuracy. The idea is to keep the meas- cessing, computer or remote control. For an ured impedance close to full scale for any given operation retrieving only pass/fail results the range, again, for best accuracy. Programmable Logic Control (PLC) is often Range holding, rather than autoranging, is a adequate, but for data logging it's a different feature sometimes used in specific applica- story. The typical interface for this is the IEEE- tions. For example, when repetitive testing of 488 general purpose interface bus or the RS- similar value components, range holding can 232 serial communication line. reduce test time. Another use of range hold These interfaces are commonly used for moni- occurs when measuring components whose toring trends and process control in a compo- value falls within the overlap area of two adja- nent manufacturing area or in an environment cent ranges, where if allowed to autorange the where archiving data for future reference is instrument’s display can sometimes change required. For example when testing 10% com- resulting in operator confusion. ponents, the yield is fine when components test Integration Time at 8% or 9%, but it does not take much of a shift The length of time that an LCR meter spends for the yield to plummet. The whole idea of pro- integrating analog voltages during the process duction monitoring is to reduce yield risks and of data acquisition can have an important effect be able to correct the process quickly if needed. on the measurement results. If integration An LCR Meter with remote interface capability occurs over more cycles of the test signal the has become standard in many test applications measurement time will be longer, but the accu- where data logging or remote control have racy will be enhanced. This measurement time become commonplace. is usually operator controlled by selecting a FAST or SLOW mode, SLOW resulting in improved accuracy. To improve repeatibility, try the measurement averaging function. In aver- aging mode multiple measurements are made and the average of these is calculated for the end result. All of this is a way of reducing unwanted signals and effects of unwanted noise, but does require a sacrifice of time. Median Mode
A further improvement of repeatability can be Figure 11: 7000 Series Computer Application obtained by employing the median mode func-
14 Test Fixtures and Cables Test fixtures (fixturing) and cables are vital com- Open/Short ponents of your test setup and in turn play an Open/Short correction is the most popular com- important role in the accuracy of your imped- pensation technique used in most LCR instru- ance measurements. Consider these factors ments today. When the unknown terminals are pertaining to test fixtures and cables. open the stray admittance (Yopen) is meas- ured. When the unknown terminals are shorted Compensation the residual impedance (Zshort) is measured. When the device is measured, these two resid- Compensation reduces the effects from error uals are used to calculate the actual impedance sources existing between the device under test of the device under test. and the calibrated connection to the measuring When performing an OPEN measurement it is instrument. The calibrated connection is deter- important to keep the distance between the mined by the instrument manufacturer, which unknown terminal the same as they are when can be front or rear panel connections, or at the attached to the device. It's equally important to end of a predefined length of cable. make sure that one doesn't touch or move their Compensation will ensure the best measure- hands near the terminals. When performing a ment accuracy possible on a device at the SHORT measurement a shorting device (short- selected test conditions. When a measurement ing bar or highly conductive wire) is connected is affected by a single residual component the between the terminals. For very low imped- compensation is simple. ance measurements it is best to connect the Take the case of stray lead capacitance unknown terminals directly together. (CSTRAY) in parallel with the DUT capacitance L L H H (CX), illustrated in Figure 12. The value of the CUR (-) POT POT (+) CUR Test stray capacitance can be measured directly Terminals with 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 simple when stray residuals are more than a single component. OPEN
Kelvin Kelvin Test Test Leads Leads
CSTRAY CSTRAY Z
CDUT SHORT
CDUT = CMEASURE - CSTRAY
Figure 12: Lead Compensation Figure 13: Open/Short
15 Load Correction Load Correction is a compensation technique which 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 the measuring instrument and for test fixture or lead effects which may be dependent on the test frequency , test voltage, impedance range, or other factors. Criteria for selecting the appropriate load include: a. Load whose impedance value is accurately known. b. Load whose impedance value is very close to the DUT (this ensures that the measuring instrument selects the same measurement range for both devices). c. Load whose impedance value is stable under the measurement conditions. d. Load whose physical properties allow it to be connected using the same leads or fixture as the DUT. A prerequisite for load correction is to perform a careful open/short compensation as previously discussed. This feature, found on a number of QuadTech LCR Meters, provides for an auto- matic load correction. The load's known value is entered into memory, the load then measured, and this difference then applied to ongoing measurements. Z actual = Z measure +/- delta Z delta Z = the difference between the known and the measured value of the load. Through the use of load correction it is possible to effectively increase the accuracy of the measuring instrument substantially, but this is only as good as the known accuracy of the load used in determining the correction.
16 Capacitance Measurements Capacitors are one of the many components Series or Parallel used in electronic circuits. The basic construc- Advances in impedance measurement instru- tion of a capacitor is a dielectric material sand- mentation and capacitor manufacturing tech- wiched between two electrodes. The different niques coupled with a variety of applications types of capacitors are classified according to has evolved capacitor test into what might be their dielectric material. Figure 14 shows the considered a complex process. A typical equiv- general range of capacitance values according alent circuit for a capacitor is shown in Figure to their dielectric classification. Capacitance C, 15. In this circuit, C is the main element of dissipation factor D, and equivalent series capacitance. Rs and L represent parasitic com- resistance ESR are the parameters usually ponents in the lead wires and electrodes and measured. Rp represents the leakage between the capac- Capacitance is the measure of the quantity of itor electrodes. electrical charge that can be held (stored) between the two electrodes. Dissipation factor, also known as loss tangent, serves to indicate capacitor quality. And finally, ESR is a single L RS C resistive value of a capacitor representing all real losses. ESR is typically much larger than the series resistance of leads and contacts of the component. It includes effects of the capac- RP itor's dielectric loss. ESR is related to D by the formula ESR =D/wC where w =2pf. Figure 15: Capacitor Circuit
ALUMINUM ELECTROLYTIC
TANTALUM ELECTROLYTIC
METALIZED PLASTIC
CERAMIC
0.1 1.0 10 100 1000 0.01 0.1 1.0 10 100 1000 104 105 1F picofarad (pF) microfarad (uF)
Figure 14: Capacitance Value by Dielectric Type
17 When measuring a capacitor these parasitics If C = Low then Xc = High must be considered. Measuring a capacitor in and Rp becomes the most series or parallel mode can provide different significant resistance results, how they differ can depend on the qual- ity of the device, but the thing to keep in mind is CLOW Rp that the capacitor's measured value most close- ly represents its effective value when the more suitable equivalent circuit, series or parallel, is Rs used. To determine which mode is best, con- sider the impedance magnitudes of the capaci- tive reactance and Rs and Rp. For example, Figure 16: Rp more significant suppose the capacitor modeled in Figure 16 has a small value. If C = High then Xc = Low and Rs becomes the most Remember reactance is inversely proportional significant resistance to C, so a small capacitor yields large reactance which implies that the effect of parallel resist- C Rp ance (Rp) has a more significant effect than HIGH that of Rs. Since Rs has little significance in this case the parallel circuit mode should be Rs used to more truly represent the effective value. The opposite is true in Figure 17 when C has a large value. In this case the Rs is more signifi- Figure 17: Rs more significant cant than Rp thus the series circuit mode become appropriate. Mid range values of C requires a more precise reactance-to-resist- The menu selection, such as that on the ance comparison but the reasoning remains the QuadTech 7000 Series LCR Meter, makes same. mode selection of Cs, Cp or many other parameters easy with results clearly shown on The rule of thumb for selecting the circuit mode the large LCD display. should be based on the impedance of the capacitor: * Above approximately 10 kW - Measuring Large and Small Values of use parallel mode Capacitance * Below approximately 10W - High values of capacitance represent relatively use series mode low impedances, so contact resistance and * Between these values - residual impedance in the test fixture and follow manufacturers recommendation cabling must be minimized. The simplest form of connecting fixture and cabling is a two termi- nal configuration but as mentioned previously, it Translated to a 1kHz test: can contain many error sources. Lead induc- Use Cp mode below 0.01 mF and Cs mode tance, lead resistance and stray capacitance above 10 mF; and again between these values between the leads can alter the result substan- either could apply and is best based on the tially. A three-terminal configuration, with coax manufacturers recommendation. cable shields connected to a guard terminal,
18 can be used to reduce effects of stray capaci- OPEN/SHORT compensation by the measuring tance. This is a help to small value capacitors instrument. The open/short compensation but not the large value capacitors because the when properly performed is important in sub- lead inductance and resistance still remains. tracting out effects of stray mutual inductance For the best of both worlds a four terminal con- between test connections and lead inductance. figuration, discussed earlier and shown in The effect of lead inductance can clearly Figure 18, (often termed Kelvin) can be used to increase the apparent value of the capacitance reduce the effects of lead impedance for high being measured. Open/Short compensation is value capacitors. Two of the terminals serve for one of the most important techniques of com- current sourcing to the device under test, and pensation used in impedance measurement two more for voltage sensing. This technique instruments. Through this process each resid- simply removes errors resulting from series ual parameter value can be measured and the lead resistance and provides considerable value of a component under test automatically advantage in low impedance situations. corrected. One of the most important things to always IH keep in mind is a concerted effort to achieve PH consistency in techniques, instruments, and fix- + turing. This means using the manufacturers D recommended 4-terminal test leads (shielded V U T coax) for the closest possible connection to the - device under test. The open/short should be PL performed with a true open or short at the test terminals. For compensation to be effective the IL open impedance should be 100 times the DUT A impedance and the short impedance 100 times Figure 18a: 4-Terminal to DUT less than the DUT impedance. Of equal impor- tance, when performing open/short zeroing, the Besides a 4-terminal connection made as close leads must be positioned exactly as the device as possible to the device under test, a further under test expects to see them. enhancement to measurement integrity is an
QuadTech 1730 LCR Digibridge
D : 1.2345 PARA : Cs - D F3
NEXT PAGE 1/3 F4
1 0 L L H H CUR (-) POT POT (+) CUR Figure 18b: l 4-Terminal to DUT 1730 LCR Meter IH and Kelvin Clip Leads PH + DUT - PL IL
19 Equivalent Series Resistance (ESR) If we define the dissipation factor D as the ener- Questions continually arise concerning the cor- gy lost divided by the energy stored in a capac- rect definition of the ESR (Equivalent Series itor we can deduce equation 9. Resistance) of a capacitor and, more particular- energy lost ly, the difference between ESR and the actual 9: D = energy stored physical series resistance (which we'll call Ras), the ohmic resistance of the leads and Real part of Z = plates or foils. Unfortunately, ESR has often (-Imaginary part of Z) been misdefined and misapplied. The following is an attempt to answer these questions and Rs = clarify any confusion that might exist. Very (-) Xs briefly, ESR is a measure of the total lossiness of a capacitor. It is larger than Ras because the = RswC actual series resistance is only one source of the total loss (usually a small part). = (ESR) wC At one frequency, a measurement of complex impedance gives two numbers, the real part If one took a pure resistance and a pure capac- and the imaginary part: Z = Rs + jXs. At that itance and connected them in series, then one frequency, the impedance behaves like a series could say that the ESR of the combination was combination of an ideal resistance Rs and an indeed equal to the actual series resistance. ideal reactance Xs (Figure 19). If Xs is nega- However, if one put a pure resistance in paral- tive, the impedance is capacitive and the reac- lel with a pure capacitance (Figure 20a) creat- tance can be replaced with capacitance as ing a lossy capacitor, the ESR of the combina- shown in equation 8. tion is the Real part of Z = Real part of equation 10 as shown in Figure 20b. -1 1 Rp 8: Xs = 10: = wCs 1 1 + w2Cp2Rp2 + jwCp Rp
We now have an equivalent circuit that is cor- From Figure 21a, however, it is obvious that rect only at the measurement frequency. The there is no actual series resistance in series resistance of this equivalent circuit is the equiv- with the capacitor. Therefore Ras = 0, but alent series resistance: ESR > 0, therefore ESR > Ras. ESR = Rs = Real part of Z
R R = P S 2 2 2 1 + w CP RP
Cp Rp = DUT R 1 S C = C S P ( 1+ 2 2 2 ) w CP RP
XS CS a: parallel b: series
Figure 20: ESR Figure 19: Real Part of Z
20 Inductance Measurements An inductor is a coiled conductor. It is a device In the case where the inductance is large, the for storing energy in a magnetic field (which is reactance at a given frequency is relatively the opposite of a capacitor that is a device for large so the parallel resistance becomes more storing energy in an electric field). An inductor significant than any series resistance, hence consists of wire wound around a core material. the parallel mode should be used. For very Air is the simplest core material for inductors large inductance a lower measurement fre- because it is constant, but for physical efficien- quency will yield better accuracy. cy, magnetic materials such as iron and ferrites For low value inductors, the reactance are commonly used. The core material of the becomes relatively low, so the series resistance inductor, its’ length and number of turns direct- is more significant, thus a series measurement ly affect the inductor’s ability to carry current. mode is the appropriate choice. For very small inductance a higher measurement frequency Coil of Wire, Air core = Inductor will yield better accuracy. For mid range values of inductance a more detail comparison of reac- tance to resistance should be used to help determine the mode. Put Produce Current Magnetic Flux The most important thing to remember whenev- Through Linkage Wire Out er a measurement correlation problem occurs, is to use the test conditions specified by the component manufacturer. Independent of any series/parallel decision, it is not uncommon for Magnetic Flux Inductance = different LCR meters to give different measured Current Through results. One good reason for this is that induc- tor cores can be test signal dependent. If the programmed output voltages are different the Series or Parallel measured inductance will likely be different. As with capacitor measurements, inductor Even if the programmed output voltage is the measurements can be made in either a series same, two meters can still have a different or parallel mode, use of the more suitable mode source impedance. A difference in source results in a value that equals the actual induc- impedance can result in a difference in current tance. In a typical equivalent circuit for an to the device, and again, a different measured inductor, the series resistance (Rs), represents value. loss of the copper wire and parallel resistance Inductance Measurement Factors (Rp) represents core losses as shown in Figure Here are four factors for consideration in 21. measuring actual inductors: L R X S DC Bias Current Constant Voltage (Voltage Leveling) Constant Source Impedance DC Resistance & Loss R P There are other considerations such as core Figure 21: Inductor Circuit material and number of coils (turns) but those are component design factors not measure- ment factors.
21 DC Bias Current Since it is possible to apply large values of cur- To get an accurate inductance measurement, rent and voltage to an inductor, CAUTION must the inductor must be tested under actual (real be taken when the current through an inductive life) conditions for current flowing through the circuit is suddenly interrupted because a volt- coil. This cannot always be accomplished with age transient then occurs across the open cir- the typical AC source and a standard LCR cuit. Put another way, if the current could be meter as the typical source in an LCR meter is instantly switched off, then the voltage would in normally only capable of supplying small theory become infinite. This does not occur amounts of current (<1mA). Inductors used in because the high voltage develops an arc power supplies need a larger current supply. across the switch as contact is broken, keeping Instead of using a larger AC current source, di/dt from becoming infinite. This does not how- inductors are usually tested with a combination ever prevent the voltage from increasing to of DC current and AC current. DC bias current potentially lethal levels. If a person breaks the provides a way of biasing the inductor to normal contact without the proper protection, the induc- operating conditions where the inductance can tor induces a high voltage, forcing the current then be measured with a normal LCR meter. through the person. Refer to Figure 22. The bottom line is that the measured induc- Constant Source Impedance tance is dependent on the current flowing The current flowing through the inductor from through the inductor. the AC source in the LCR meter must be held Constant Voltage (Voltage leveling) constant. If the current is not held constant the Since the voltage across the inductor changes inductance measurements will change. This with impedance of the inductor and the imped- change is generally a function of the LCR ance of the inductor changes with current, a meter's open circuit programmed test voltage. typical LCR meter designed for measurements The programmed voltage in an LCR meter is on capacitive and resistive devices can cause obtained under an open circuit condition. A the inductance to appear to drift. The actual source resistance (Rs, internal to the meter) is inductance is not drifting but is caused by the effectively connected in series with the AC out- voltage across the inductor not being constant put and there is a voltage drop across this resis- so the current is not constant. A voltage level- tor. When a test device is connected, the volt- ing circuit would monitor the voltage across the age applied to the device depends on the value inductor and continually adjust the programmed of the source resistor (Rs) and the impedance source voltage in order to keep the voltage value of the device. The source impedance is across the inductor constant. normally between 5W and 100kW.
Figure 22: Breaking Contact Across an Inductor
22 DC Resistance and Loss Eddy-Current Loss in iron and copper are due Measuring the DCR or winding resistance of a to currents flowing within the copper or core coil of wire confirms that the correct gauge of cased by induction. The result of eddy-currents wire, tension and connection were used during is a loss due to heating within the inductors cop- the manufacturing process. The amount of per or core. Eddy-current losses are directly opposition or reactance a wire has is directly proportional to frequency. Refer to Figure 24. proportional to the frequency of the current vari- Hysteretic Loss is proportional to the area ation. That is why DC resistance is measured enclosed by the hysteresis loop and to the rate rather than ACR. At low frequencies, the DC at which this loop is transversed (frequency). It resistance of the winding is equivalent to the is a function of signal level and increases with copper loss of the wire. Knowing a value of the frequency. Hysteretic loss is however inde- wire's copper loss can provide a more accurate pendent of frequency. The dependence upon evaluation of the total loss (DF) of the device signal level does mean that for accurate meas- under test (DUT). (Refer to Figure 23). urements it is important to measure at known Loss signal levels. Three possible sources of loss in an inductor measurement are copper, eddy-current and Direction hysteretic. They are dependent on frequency, of Magnetic signal level, core material and device heating. Flux
As stated above, copper Loss at low frequen- CURRENT cies is equivalent to the DC resistance of the Eddy winding. Copper loss is inversely proportional Current Current to frequency. Which means as frequency paths carrying wire increases, the copper loss decreases. Copper Solid loss is typically measured using an inductance Core analyzer with DC resistance (DCR) measure- ment capability rather than an AC signal. Figure 24: Eddy Currents induced in an iron core
Inductance, L is blue Loss is red 0.1
1H
100mH
1mH 10mH 1 R f 2 0.01 D ~ o + G wL + D f 2 e o f o 1 - w Lo r 2 f Ohmic Loss Do ~ 1/f r
Resonance Do De Dd Factor Ohmic Eddy Dielectric Loss Current Loss
Dissipation Factor D = -1/Q Loss Eddy Current Loss, De ~ f
Dielectric Loss, Dd ~ f 0.001 1kHz 10 100 1MHz Frequency
Figure 23: Factors of Total Loss (Df)
23 Resistance Measurements Of the three basic circuit components, resistors, Series or Parallel capacitors and inductors, resistors cause the So how does one choose the series or parallel least measurement problems. This is true measurement mode? For low values of resis- because it is practical to measure resistors by tors (below 1kW) the choice usually becomes a applying a dc signal or at relatively low ac fre- low frequency measurement in a series equiva- quencies. In contrast to this, capacitors and lent mode. Series because the reactive com- inductors always experience ac signals that by ponent most likely to be present in a low value their very nature are prone to fluctuation, thus resistor is series inductance, which has no these components are generally measured effect on the measurement of series R. To under changing conditions. Resistors are usu- achieve some degree of precision with low ally measured at dc or low frequency ac where resistance measurements it is essential to use Ohm's Law gives the true value under the a four-terminal connection as discussed earlier. assumption that loss factors are accounted for. The thing to keep in mind is that if resistors are This technique actually eliminates lead or con- used in high frequency circuits they will have tact resistance which otherwise could elevate both real and reactive components. This can the measured value. Also, any factor that be modeled as shown in Figure 25, with a affects the voltage drop sensed across a low series inductance (Ls) and parallel capacitance resistance device will influence the measure- (Cp). ment. Typical factors include contact resist- ance and thermal voltages (those generated by dissimilar metals). Contact resistance can be reduced by contact cleanliness and contact LS RX pressure.
For high values of resistors (greater than sev-
CP eral MW) the choice usually becomes a low fre- quency measurement in a parallel equivalent mode. Parallel because the reactive compo- Figure 25: Resistor Circuit nent most likely to be present in a high value For example, in the case of wire-wound resis- resistor is shunt capacitance, which has no tors (which sounds like an inductor) its easy to effect on the measurement of parallel R. understand how windings result in this L term. Even though windings can be alternately reversed to minimize the inductance, the induc- tance usually increases with resistance value (because of more turns). In the case of carbon and film resistors conducting particles can result in a distributed shunt capacitance, thus the C term.
24 Precision Impedance Measurements QuadTech manufactures several instruments standard deviation to 5 ppm. It is therefore pos- for the measurement and analysis of passive sible to measure the difference between two component parameters. The 7000 Series LCR impedances to approximately 10 ppm with the Meter is an automatic instrument designed for 7000. Averaging many measurements takes the precise measurement of resistance, capac- time, however an automatic impedance meter itance and inductance parameters and associ- like the 7000 can take hundreds of averaged ated loss factors. It is also suited for use in cal- measurements in the time it takes to balance a ibration and standards laboratories and can high-resolution, manual bridge. assume many tasks previously performed only Measurement precision and confidence can be by high priced, difficult to use, manually bal- further improved by using the 7000's median anced impedance bridges and meters. measurement mode. In the median measure- ment mode, the instrument makes three meas- urements rather than one and discards the high and 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 measurements Figure 26: 7400 Precision LCR Meter not only increases basic measurement preci- Measurement Capability sion, but will also yield measurements that are independent of a large errors caused by line The measurements of highest precision in a spikes or other non-Gaussian noise sources. standards lab are 1:1 comparisons of similar impedance standards, particularly comparisons The ppm resolution of the 7000 is also not lim- between standards calibrated at the National ited to values near full scale as is typically true Institute of Standards and Technology (NIST) on six-digit, manual bridge readouts. In the and similar reference standards. This type of case of a manually balanced bridge, the resolu- measurement requires an instrument with high tion of a six-digit reading of 111111 is 9 ppm. measurement resolution and repeatability in The 7000 does not discriminate against such order to detect parts-per-million (ppm) differ- values; it has the same 0 .1 ppm resolution at ences rather than instruments with extreme, all values of all parameters including dissipation direct-reading accuracy. In such applications, factor (D) and quality factor (Q), the tangent of two standards of very nearly equal value are phase angle. compared using "direct substitution"; they are measured sequentially and only the difference Measured Parameters between them is determined. The resolution of the 7000 is 0.1 ppm for the Cs 17.52510 pF direct measured values and such direct reading measurements, at a one/second rate, have a DF 0.000500 typical standard deviation of 10 ppm at 1 kHz. Measuring By using the instrument's AVERAGING mode, Freq 1.0000kHz AC Signal 1.000V the standard deviation can be reduce by Range AUTO Average 1 1/(square root of N) where N is the number of Delay 0ms Bias Off measurements averaged. Thus, an average of 5 measurements or more typically reduces the Figure 27: Parts Per Million Resolution
25 The 7000 instrument also provides a unique Basic Accuracy load correction feature that allows the user to Manufacturers of LCR meters specify basic enter known values for both primary and sec- accuracy. This is the best-case accuracy that ondary parameters, as illustrated in the load can be expected. Basic accuracy does not take correction display of Figure 28. The instrument into account error due to fixturing or cables. measures these values and automatically The basic accuracy is specified at optimum test applies the correction to ongoing measure- signal, frequencies, highest accuracy setting or ments. slowest measurement speed and impedance of Load Correction the DUT. As a general rule this means 1VAC
Measure Off On RMS signal level, 1kHz frequency, high accura- Primary Nominal 60.00000 pF cy which equates to 1 measurement/second, Secondary Nominal 4.000000 m and a DUT impedance between 10W and Measuring Correction 100kW. Typical LCR meters have a basic accu- Measured Primary 60.25518 pF Measured Secondary .0042580 racy between ±0.01% and ±0.5%. Freq 1.0000MHz Primary Cs Range 49 Secondary Df HIT
26 Factors Affecting Accuracy Calculations Accuracy and Speed DUT Impedance Accuracy and speed are inversely proportional. High impedance measurements increase the That is the more accurate a measurement the error because it is difficult to measure the cur- more time it takes. LCR meters will generally rent flowing through the DUT. For example if have 3 measurement speeds. Measurement speed can also be referred to as measurement the impedance is greater than 1MW and the test voltage is one volt there will be less than 1mA time or integration time. Basic accuracy is of current flowing through the DUT. The inabil- always specified with the slowest measurement ity to accurately measure the current causes an speed, generally 1 second for measurements increase in error. above 1kHz. At lower frequencies measure- ment times can take even longer because the Low impedance measurements have an measurement speed refers to the integration or increase in error because it is difficult to meas- averaging of at least one complete cycle of the ure the voltage across the DUT. Most LCR stimulus voltage. For example, if measure- Meters have a resistance in series with the ments are to be made at 10Hz, the time to com- source of 100k to 5 ohms. As the impedance of plete one cycle is 1/frequency = 1/10Hz = 100 the DUT approaches the internal source resist- milliseconds. Therefore the minimum meas- ance the voltage across the DUT drops propor- urement speed would be 100ms. tionally. If the impedance of the DUT is signifi- cantly less than the internal source resistance Dissipation Factor (D) or Quality Factor (Q) then the voltage across the DUT becomes D and Q are reciprocals of one another. The extremely small and difficult to measure caus- importance of D or Q is the fact that they repre- ing an increase in error. sent the ratio of resistance to reactance or vice versa. This means that the ratio Q represents Frequency the tangent of the phase angle. As phase is The impedance of reactive components is also another measurement that an LCR meter must proportional to frequency and this must be make, this error needs to be considered. When taken into account when it comes to accuracy. the resistance or reactance is much much For example, measurement of a 1mF capacitor greater than the other, the phase angle will at 1 kHz would be within basic measurement approach ±90° or 0°. As shown in Figure 29, accuracy where the same measurement at even small changes in phase at -90° result in 1MHz would have significantly more error. Part large changes in the value of resistance, R. of this is due to the decrease in the impedance of a capacitor at high frequencies however +jX Resistance R there generally is increased measurement error S +R at higher frequencies inherent in the internal q -j(1/wCs) design of the LCR meter. d Reactance X Resolution C Z Impedance Resolution must also be considered for low value measurements. If trying to measure 0.0005 ohms and the resolution of the meter is -jX 0.00001 ohms then the accuracy of the meas- Capacitive urement cannot be any better than ±2% which Figure 29: Phase Diagram for Capacitance is the resolution of the meter.
27 Example: Accuracy Formula The impedance range (ZRANGE) is specified 7600 Precision LCR Meter in this table: Test Conditions: In Voltage Mode In Current Mode ZRANGE= 100kW for Zm ³ 25kW 400W for I < 2.5mA 1pF Capacitor at 1MHz 6kW for 1.6kW £ Zm < 25kW 25W for I > 2.5mA 1VAC signal 6kW for Zm > 25kW and Fm > 25kHz Auto Range 400W for 100W £ Zm < 1.6kW Non-Constant Voltage 400W for Zm > 1.6kW and Fm > 250kHz Slow Measurement Speed 25W for Zm < 100W Df of 0.001 The Calculated Accuracy using the formula in Equation 11 is 3.7% substituting the values Basic Accuracy of the 7600 is ±0.05% listed herein. Kt = 1 Accuracy Formula for Slow Mode R, L, C, X, Zm = 1/(2p*frequency*C) G, B, |Z|, and |Y| is given in Equation 11. = 1/(2p*1000000*1x10-12) = 159 kohms Vs = Test voltage in voltage mode, ZRANGE = 400 ohms = I * Zm in current mode* V = 1 Zm = Impedance of DUT fs Multiply A% = 8 Fm = Test frequency A% = 0.46% o o Kt = 1 for 18 to 28 C o o = 2 for 8 to 38 C Multiply A% times 8 due to Zm > 64 times o o = 4 for 5 to 45 C ZRANGE
VFS = 5.0 for 1.000V < Vs £ 5.000V A% = 0.46% * 8 = 3.68% 1.0 for 0.100V < Vs £ 1.000V 0.1 for 0.020V £ Vs £ 0.100V Refer to Equation 12 to fill in the numbers.
For Zm > 4* ZRANGE multiply A% by 2 For Zm > 16* ZRANGE multiply A% by 4 For Zm > 64* ZRANGE multiply A% by 8
*: For I * Zm > 3, accuracy is not specified
2 .05 .02 Vfs (V - 1) Fm 300 A% = +/- 0.025 + 0.025 + + Z x 10-7 x + .08 x + S x 0.7 + + x K m 5 t Zm VS VS 4 10 Fm
Equation 11: 7600 Accuracy Formula
28 Equation 12: Completed 7600 Accuracy Formula
.05 .02 1 (1 - 1)2 1000000 300 A% = +/- 0.025 + 0.025 + + 159000 x 10-7 x + .08 x + x 0.7 + + x 1 159000 1 1 4 105 1000000
Example 7600 Accuracy Graph The accuracy could have been predicted with- Use the graph in Figure 30 and substitute Z out the use of a formula. If we calculate the for R. If we find the position on the graph for impedance of a 1pF capacitor at 159kHz we an impedance value of 1591ohms at 100kHz get a value of: we see a light blue or teal representing an accuracy of 3.45% to 3.65%. Overall the graph and formula point to the same accuracy Z = Xs = 1/(2p*frequency*capacitance) of ±3.5%.
Z = Xs = 1/(2p*1,000,000*0.000,000,000,001) = 159kohms
3.6500%-3.8500% Accuracy Z vs F Slow 3.4500%-3.6500% 3.2500%-3.4500% 0.1 3.0500%-3.2500% 1 2.8500%-3.0500% 2.6500%-2.8500% 10 2.4500%-2.6500% 2.2500%-2.4500% 100 2.0500%-2.2500% 1000 1.8500%-2.0500% 1.6500%-1.8500% Impedance 1.00E+04 1.4500%-1.6500% 1.2500%-1.4500% 1.00E+05 1.0500%-1.2500% 1.00E+06 0.8500%-1.0500% 0.00.20.40.60.81.01.21.41.61.82.02.22.42.62.83.03.23.43.63.8 50 0.6500%-0.8500% 1.00E+07 0 0.4500%-0.6500% 10 100 1000 1.00E+04 1.00E+05 5.00E+05 1.00E+06 2.00E+06 % 0.2500%-0.4500% Frequency 0.0500%-0.2500%
Figure 30: 7600 Accuracy Plot
29 Materials Measurements
Materials Measurement where eo is the permittivity of a vacuum, and e Many materials have unique sets of electrical the absolute permittivity. characteristics which are dependent on its e = 0.08854pF/cm dielectric properties. Precision measurements o of these properties can provide valuable infor- The capacitance of a parallel-plate air capaci- mation in the manufacture or use of these tor (two plates) is: materials. Herein is a discussion of dielectric constant and loss measurement methods. C = Ka eo Area / spacing
where Ka is the dielectric constant of air:
Ka = 1.00053
if the air is dry and at normal atmospheric pressure.
Figure 31: QuadTech 7000 Meter with LD-3 Cell Measurement Methods, Solids Definitions The Contacting Electrode Method There are many different notations used for This method is quick and easy, but is the least dielectric properties. This discussion will use K, accurate. The results for K should be within the relative dielectric constant, and D, the dissi- 10% if the sample is reasonably flat. Refer to pation factor (or tan d) defined as follows: Figure 32. The sample is first inserted in the cell and the electrodes closed with the micrometer K = e' = er until they just touch the sample. The electrodes should not be forced against the sample. The and micrometer is turned with a light finger touch e " and the electrometer setting recorded as h . D = tan d = r m er' The complex relative permittivity is: e er* = = er' - j (er") eo
h=ho ho
H H
L L Figure 32: Contact Electrode
G G Specimen Air
Cxm and Dxm Ca and Da 30 The LCR Meter should be set to measure par- The Air-Gap Method allel capacitance and the capacitance and dis- This method avoids the error due to the air sipation factor of the sample measured as Cxm layer but requires that the thickness of the and Dxm. sample is known. Its thickness should be The electrodes are opened and the sample measured at several points over its area and removed and then the electrodes closed to the the measured values should be averaged to same micrometer reading, h . C (parallel) and get the thickness h. The micrometer used m should have the same units as those of the D of empty cell are measured as Ca and Da. micrometer on the cell. Calculate Kx and Dx of the sample from: The electrodes are set to about .02 cm or .01 C inch greater than the sample thickness, h, and K = (1.0005) xm the equivalent series capacitance and D meas- x C a ured as Ca and Da. Note the micrometer set- ting as hm which can be corrected with the and micrometer zero calibration, hmo to get: D = (D - D ) x xm a ho = (hm + h mo)
The factor 1.0005 in the formula for Kx corrects The sample is inserted and measured as C for the dielectric constant of (dry) air. xa and D . Calculate: Subtracting Da from Dxm removes any constant xa phase error in the instrument. For even better D (h - h) M = o accuracy, the electrode spacing can be adjust- h ed until the measured capacitance is approxi- o mately equal to C , and then D measured. xm a Ca D = (Dxa - D a) Note that both Kx and Dx will probably be too Ca - MC xa low because there is always some air between the electrodes and the sample. This error is (1-M) C 1.0005 K = xa smallest for very flat samples, for thicker sam- x 2 Ca - MC xa 1 + D x ples and for those with low K and D values.
ho h
H H
Figure 33: Air Gap Method L L
G G Air Specimen and Air
Ca and Da Cxa and Dxa
31 2 The factor (1 + Dx ) converts the series value of Dow Corning 200, 1 centistoke viscosity, is most generally satisfactory. Cx to the equivalent parallel value and is not The four measurements of series capacitance necessary if Dx is small. The factor of 1.0005 and D are outlined in the Figure 34. Note the corrects for the dielectric constant of air (if dry). spacing is the same for all measurements and The formula for D assumes that the true D of x should be just slightly more than the specimen air is zero and it makes a correction for a con- thickness. The accuracy will be limited mainly stant D error in the instrument. by the accuracy of the measurements made. From these measurements calculate: The Two-Fluid Method h C C (C - C ) This method is preferred for specimens whose = 1 - a f xf xa h C C (C - C ) thickness is difficult to measure and for best o xa xf f a accuracy which will be limited by the accuracy of the C and D measurements. However it C C C (C - C ) requires four measurements, two using a sec- xser = xf xa f a ond fluid (the first being air). The dielectric Ca Ca (CxaCf - C xf Ca) properties of this fluid need not be known, but it must not react with the specimen and it must be which is the ratio of the equivalent series stable and safe to use. A silicone fluid such as capacitance of the sample to Ca.
ho h
H H
L L
G G Air Specimen and Air
Ca and Da Cxa and Dxa Figure 34: Two Fluid Method
ho h
H H
L L
G G Fluid Specimen and Fluid
Cf and Df Cxf and Dxf 32 If Dx is close to Df or larger use:
Ca (Cxf - C xa) (Dxf - D f) Dx = Dxf + (CxaCf - C xf Ca)
If Dx is very small use:
(Dxa - D a) Cxf (Cf - C a) Dx = (CxaCf - C xf Ca) which makes a zero D correction.
From the above results calculate:
h C 1.0005 K = xser x 2 ho Ca 1 + D x
As before, the factor of 1.0005 corrects for the dielectric constant of air (if dry) and the factor 2 (1 + Dx ) converts Cx to equivalent parallel capacitance.
Measurement Methods, Liquids
Measurements on liquids are simple, the only difficulty is with handling and cleanup.
Equivalent parallel capacitance and D of air (Ca and Da), is measured first and then that of the liquid (Cxm and Dxm)
Determine Kx and Dx:
Cxm Kx = 1.0005 Ca
Dx = (Dxm - D a)
Note that the spacing is not critical but should be narrow enough to make the capacitance large enough to be measured accurately.
33 Recommended LCR Meter Features As with most test instrumentation, LCR meters tance (B), phase angle (q) and ESR can more can come with a host of bells and whistles but fully define an electrical component or material. the features one most often uses are described herein. Ranging Test Frequency In order to measure both low and high imped- ance values measuring instrument must have Electrical components need to be tested at the several measurement ranges. Ranging is usu- frequency in which the final product/application ally done automatically and selected depending will be utilized. An instrument with a wide fre- on the impedance of the test device. Range quency range and multiple programmable fre- changes are accomplished by switching range quencies provides this platform. resistors and the gain of detector circuits. This helps maintain the maximum signal level and highest signal-to-noise ratio for best measure- Test Voltage ment accuracy. The idea is to keep the meas- The ac output voltage of most LCR meters can ured impedance close to full scale for any given be programmed to select the signal level range, again, for best accuracy. applied to the DUT. Generally, the programmed level is obtained under an open circuit condi- tion. A source resistance (Rs, internal to the Averaging meter) is effectively connected in series with The length of time that an LCR meter spends the ac output and there is a voltage drop across integrating analog voltages during the process this resistor. When a test device is connected, of data acquisition can have an important effect the voltage applied to the device depends on on the measurement results. If integration the value of the source resistor (Rs) and the occurs over more cycles of the test signal the impedance value of the device. measurement time will be longer, but the accu- racy will be enhanced. This measurement time is usually operator controlled by selecting a Accuracy/Speed FAST or SLOW mode, SLOW resulting in Classic trade-off. The more accurate your improved accuracy. To enhance accuracy, the measurement the more time it takes and con- measurement averaging function may be used. versely, the faster your measurement speed the In an averaging mode many measurements are less accurate your measurement. That is why made and the average of these is calculated for most LCR meters have three measurement the end result. speeds: slow, medium and fast. Depending on the device under test, the choice is yours to select accuracy or speed. Median Mode A further enhancement to accuracy can be obtained by employing the median mode func- Measurement Parameters tion. In a median mode 3 measurements might Primary parameters L, C and R are not the only be made and two thrown away (the lowest and electrical criteria in characterizing a passive the highest value). The median value then rep- component and there is more information in the resents the measured value for that particular Secondary parameters than simply D and Q. test. Measurements of conductance (G), suscep-
34 Computer Interface Display Many testers today must be equipped with An instrument with multiple displays provides some type of standard data communication measured results by application at the press of interface for connection to remote data pro- a button. Production environments may prefer cessing, computer or remote control. For an a Pass/Fail or Bin Summary display. R&D Labs operation retrieving only pass/fail results the may need a deviation from nominal display. Programmable Logic Control (PLC) is often The 7000 series instruments have seven dis- adequate, but for data logging it's a different play modes: measured parameters, deviation story. The typical interface for this is the IEEE- from nominal, % deviation from nominal, 488 general purpose interface bus or the RS- Pass/Fail, Bin Summary, Bin Number and No 232 serial communication line. Display. Refer to Figure 35. Figure 36 illus- These interfaces are commonly used for moni- trates three of the 7000 Series display modes. toring trends and process control in a compo- nent manufacturing area or in an environment Setup I/O Analysis Utilities Display where archiving data for future reference is Measured Parameters required. For example when testing 10% com- Deviation from Nominal ponents, the yield is fine when components test % Deviation from Nominal Pass / Fail at 8% or 9%, but it does not take much of a shift Bin Summary for the yield to plummet. The whole idea of pro- Bin Number duction monitoring is to reduce yield risks and No Display be able to correct the process quickly if needed. HIT MENU TO RETURN TO MAIN MENU An LCR Meter with remote interface capability has become standard in many test applications Figure 35: 7600 Display Menu where data logging or remote control have become commonplace.
QuadTech DISPLAY SELECT ENTRY TEST PRECISION 7400 LCR METER MENU ! 255.2 1 2 3 CAUTION 204.3 HIGH VOLTAGE CNCL STOP 153.4 4 5 6
102.5 IL IH 51.59 7 8 9 ENTER START
IZI W 10.00 572.9 32.82k 2.000M - 0 . FREQUENCY Hz PL PH 0 1
Measured Parameters Pass / Fail Bin Low LIMIT High LIMIT Total 1 90.00 k 110.00 k 250 Ls 158.450uH Q 1.000249 2 100.00 k 120.00 k 100 3 110.00 k 130.00 k 90 Cs 17.52510 pF 4 120.00 k 140.00 k 80 5 130.00 k 150.00 k 75 PRI Pass SEC Fail 11 60 DF 0.000500 LOWPRI Pass SEC Fail PASS 12 55 HI 13 PRI Fail SEC Pass 50 Measuring 14 PRI Fail SEC Fail 20 15 NO CONTACT 5 Freq AC Signal Freq AC Signal Totals: Pass 595 Fail 190 785 Range Average Range Average Delay Delay Bias Bias HIT