EIA-512-1985 STANDARD METH0DS FOR MEASUREMENT OF THE EQUIVALENT ELECTRICAL PARAMETERS OF QUARTZ CRYSTAL UNITS 1 kHz to 1 GHz.pdf

1、7 h ir; L f EIA 512 85 3234600 O072832 9 f STANOARO ANSI/ETA- 512- 1985 APPROVED APRIL 10, 1985 EIA STANDARD STANDARD MEi“0DS FOR MEXUREME“ OF THE EQUIVALE“ ELECTRICAL PARAMETERS OF QUARTZ CRYSTAL UNITS, i kz to i mz 1 UA-512 I APRIL 1985 Engineering Department ELECTRONIC INDUSTRIES ASSOCIATION EIA

2、512 85 m 323Lib00 0072833 O m c. . NOTICE EIA Engineering Standards and Publications are designed to serve the public interest through eliminating misunderstandings between manufacturers and purchasers, facilitating interchangeability and improvement of products, and assisting the purchaser in selec

3、ting and obtaining with minimum delay the proper product for his particular need. Existence of such Standards and Pub- lications shall not in any respect preclude any member or non-member of EIA from manufacturing or selling products not conforming to such Standards and Publications, nor shall the e

4、.xistence of such Standards and Publications preclude their voluntary use by those other than EIA members, whether the standard is to be used either domestically or internationally. Recommended Standards and Publications are adopted by EIA without regard to whether or not their adoption may involve

5、patents on articles, materials, or processes. By such action, EIA does not assume any liability to any patent owner, nor does it assume any obligation whatever to parties adopting the Recom- mended Standard or Publication. This EIA Recommended Standard is considered to have international standardiza

6、tion implications, but the IEC activity has not progressed to the point where a valid comparison between the EIA Recommended Standard and the IEC Recommendations can be made. e Published ,by ELECTRONIC INDUSTRIES ASSOCIATION Ehgineering Department 2001 Eye Street, N.W. Washington, D.C. 20006 Copyrig

7、ht 198 5 Ail rights reserved ELECTRONIC INDUSTRIES ASSOCIATION PRICE: $15.00 Printed in U.S.A. 4 EIA 512 85 M 3234b00 0072834 2 1. -*% O EIA- 512 TABLE OF (XNIEC SCOPE 1 IMRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . 1 SECTION I THE PIEZOELECTRIC CRYSTAL UNIT AMI ITS ELECIRICALLY EQ

8、UIVllL,NNETWORK . . . . . . . . . . . . . . . . . . . . 2 SECTION II TWO-PORT CRYSTAL, UNIT MEASUREMENTS AT LOWER FREQUENCIES. . . 5 SECTION III SINGLE-PORT REFLECTOMETERMEASURFMEWT. . . . . . . . . . . . , 7 A - Calibration . . . . . . . . . . . . . . . . . . . . . . . 8 B - Corrected Measurements

9、. . . . . . :. . . . . . . . . . . 9 SECTION IV TWO-PORT S-PARAMETER MEiASlJIEhENTS . . . . . . . . . . . . . . 10 A - System Calibration . . . . . . . . . . . . . . . . . . . 11 B - Corrected Measurements . . . . . . . . . . . . . . . . . . 13 SECTION V DATA REWCTION METHOD. . . . . . . . . . . . .

10、 ., . . . . . . . 16 A - Calculation of Parameters. . . . . . . . . . . . . . . 16 B - Verification of Data Integrity . . . . . . . . . . . . . . 17 SECTION VI MEASUREMENTSYSTEl6 . . . . . . . . . . . . . . . . . . . . 18 A - Instmentation. . . . . . . . . . . . . . . . . . . . . 18 B - Test Fixture

11、s. . . , :. . . . . . . . . . . . . . . . . . 18 REFERENCES . . . . . . . . . . . :. . . . . . . . . . . . . . 20 TABLES TABLE I - SYMBOLS USED FOR DESCRIBING THE EQUIVALE“ ELECTRICAL “WORK OF A PIEZOELECTRIC CRYSTAL UNIT. . . . . . . 21 TABLE 2 - APPROXIMATE RELATIONSHIPS OF CHARAmISTIC FREQUENCIES

12、 . . . . . . . . . . . . . . . . . . . 24 EIA 512 85 = 3234b00 0072835 4 ETA-512 TABLE OF CONTENTS (cont) APPENDIX1 . 25 FIGURES FIGURE 1 - EQUIVALENT ELECTRICAL NETWORKS CCNMONLY USED TO REPRESENT A PIEZOELECTRIC CRYSTAL UNIT OVER A NARROW FREQUENCY RANGE NEAR AN ISOLATED KIDE OF VIBRATION . . 26 F

13、IGURE 2 - LOCI OF THE ADMITTANCE AND IMPEDANCE FUNCTIONS OF A PIEZOELECTRIC CRYSTAL UNIT FOR FREQUENCIES NEAR AN ISOLATEDMODE OF VIBRATION. 27 FIGUrG 3 - IMPEDANCE lZl , RESISTANCE Re, REACTANCE Xe, AND SERIES-ARM REACTANCE X1 OF A PIEZOELECTRIC CRYSTAL UNIT AS FUNCTIONS OF FREQUENCY NEAR AN ISOLATE

14、D MODE OFVIBRATION, 28 FIGURE 4 - TEST CIRCUIT CONFIGURATION FOR IEASNT OF LOW- FREQUENCY CRYSTAL UNITS. 29 FIm 5 - EQUIVALENT TRANSMISSION NETWON( OF FIGURE 4 FOR ANALYSIS OF LOW FREQUENCY CRYSTAL UNIT MEACUREMEWS. . 30 FIGURE 6 - TEST CIRCUIT CONFIGURATION FOR SINGLE-PORT REFLECTION MEASREMENTS OF

15、 CRYSTAL UNITS AT FREQUENCIES HIGHER THANlOQkHz . 31 FIGURE 7 - FLOWGRAPH OF THE REFLECTION MEASUREMENT SYSTEM OF FIGURE 6, AND THE SYSTEM RESPONSE AS A FUNCTION OF TRUE DEVICE REFLECTION COEFFICIENT AND SYSTEM “ERROR“ VECTORS. . 32 FIGURE 8 - TEST CIRCUIT CONFIGURATION FOR TWO-PORT S-PARAMETER w-s

16、. 33 FIGURE 9 - S-PARAMETER MEASlJREibEW SYSTEM FLOWGRAPHS IN FORWARD ANDREVERSE CONNECTIONS. . 34 ii -_ EIA 512 85 m 3234b00 O072836 b m STANDARL) METHODS FOR MEASUREibEW OF THE EQUIVALm ELECTRICAL PARAMETERS OF QUARTZ CRYSTAL UNITS, 1 kiiz to. GHz (From EIA Standards Proposal No. 1792, formulated

17、under the cognizance of EIA P-5.4 Working Group on martz Crystals.) iii EIA 512 85 323VbOO 0072837 8 Jk e. 2 EIA-5 12 Page 1 STANDARD METHODS FOR MEASUREMENT OF THE EQUIVALENT ELECTRICAL PARAMETERS OF QUARTZ CRYSTAL UNITS, 1 kHz to 1 GHz SCOPE: Methods are described which permit determination of fhe

18、 values of the equivalent electrical parameters of piezoelectric quartz crystal units, utilizing automated measuring equipment. The methods described make use of standard coaxial terminations, standard calibrated mismatched terminations, coaxial air-lines, and short-circuit terminations for both cal

19、ibration of the instrument/ test fHture error terms, and for verification of instrument performance. These coaxial standards, designed for 50 ohm systems, are readily available, and can be standardized in terms of national standards of impedance over very wide frequency ranges. The measurement metho

20、ds described are intended to provide standard reference values of the electrical equivalent parameters. Manufacturers and users may employ any other methods of measurement de si red,“ however, when other methods are used, the values obtained shall be correlated to those obtained by the reference met

21、hods. This standard is concerned only with the equivalent electrical network which approximates the admittance/ impedance characteristic of a crystal unit over a relatively narrow range of frequencies near an isolated mode of vibration, at a particular excitation level. Non-linear amplitude behavior

22、, or the presence of interfering modes of vibration, not only interfere with the actual measurement, also render the accepted equivalent network representation invalid. INTRODUCTION The uses of piezoelectric crystal units in frequency control, filter and timing applications require accurate determin

23、ation of the value of their equivalent electrical parameters. This document presents a reference method for but measurement of the parameters of crystal units, based upon the use of automated state-of-the-art instrumentation systems which have become available in recent times. Using these methods, t

24、he measured parameter values are referenced to coaxial, traceable standards of impedance, and are essentially independent of the particular instruments used in the measurement. Two basic methods are described: one, utilizing a two-port transmission method, characterizes the crystal unit as a three-t

25、erminal network; the second, utilizing a single-port reflection method, characterizes the crystal unit as a two-terminal device. Both methods yield the same values for the motional-arm parameter (RI, L1, and Cl), but the static capacitance parameters are different as discussed below. Section I descr

26、ibes the equivalent electrical networks which characterize the crystal unit as a two-port and as a one-port device, and lists the parameters necessary to define the network behavior. O EIA 512 85 m 3234600 0072838 T m EIA-5 1 2 Page 2 Section 1% presents a description of the two-port transmission me

27、asurement method recommended for characterizing the three-terminal equivalent network at frequencies below 100 kHz, where directional couplers are difficult to obtain. Section III presents a description of a single-port reflectometer method for determining the two-terminal equivalent network paramet

28、ers from 100 kHz to 1 GHz. Section IV gives a description of the two-port s-parameter method for determining the two-port network parameters, recommended for frequencies from 100 kMz to 1 GHZ. Section V describes the calculations required to obtain the equivalent network parameters from the correcte

29、d values of transfer admittance obtained by any of the methods of Sections II, III, or IV. All of the techniques of instrument calibration, data correction, and data reduction require extensive calculations, and are based on the utilization of a large number of individual measurements, which would n

30、ot be feasible without the use of automated, software controlled instrumentation and computerized data reduction. However, it is the availability of these tools which permits the improved accuracy and reproducibility of results, and) renders previously used manual measurement methods obsolete. Secti

31、on VI outlines measurement system considerations with respect to instrumentation and fixturing. H. THE PIEZOELECTRIC CRYSTAL UNIT AND ITS ELECTRICALLY EQUIVALENT NETWORK A crystal unit consists of a mechanically resonant piezoelectric vibrator (usually a plate, bar, or tuning fork) with electrodes a

32、ttached to or supported near to the element to excite one of its resonant frequencies. The electrical behavior of the crystal unit, as evidenced by the electrical admittance (or impedance) observed from its terminals, over a narrow range of frequencies near a resonance, can be represented by an equi

33、valent electrical network. When the resonant mode of interest is sufficiently isolated from other modes of motion, the parameters of the equivalent network may be considered to be independent of frequency, and the equivalency will be nearly exact over a frequency band of at least a few percent. (If

34、the mode of interest is not essentially isolated, the methods of measurement presented may still be used to determine the impedances of the unit, but any attempts to relate the frequency dependence of its impedance to the electrically equivalent network of Figure 1 will be futile!) Figure 1A shows t

35、he three-terminal equivalent-circuit representation of a crystal unit which is valid over a few percent band centered at resonance for an isolated mode of vibration. There are six parameters shown: .- . - . : :., ., . - -“.: *: . i;:.; . . . .- EIA-5 12 Page 3 C13 = Static capacitance from pin 1 to

36、enclosure C23 = Static capacitance from pin 2 to enclosure Co = Static capacitance from pin 1 to pin 2, including the capacitance between electrodes and between support structures R1 = Series resonant resistance L, = Motional inductance Cl = Motional capacitance If the crystal unit is considered to

37、be a two-terminal element (enclosure connection neglected), it has an electrical equivalent as shown in Figure 1B. The motional parameters (R1, L1, and Cl) are the same as above; however, the value of Co will include the series combination of Cl, and C, as well as some effects of the capacitance fro

38、m enclosure to ground. The frequency dependence of device impedance will only be modeled as well as the various components of the composite Co are known. Consequently, the two-terminal equivalent circuit is recommended for use only in those applications where operation at a single frequency near ser

39、ies resonance is anticipated. The static capacitance values are quite easily measured by conventional means, as they are relatively independent of frequency and not related to the resonant properties of the vibrator. Co will be slightly influenced by the impedance of the measuring circuit, as the fr

40、ee and clamped values for piezoelectric materials are different, depending on the piezoelectric coupling coefficient; for quartz crystals, however, the effect is small, and a quite satisfactory value of Co can be obtained, for example, as the average of a value measured a few percent below resonance

41、, and a second value measured a few percent above anti-resonance. The trans-admittance (admittance between pins 1 and 2) of the crystal unit is quite accurately modeled by that of the equivalent network in Figure lA, over a band of frequencies extending several percent above and below resonance. For

42、tunately, this bandwidth is adequate to describe the behavior of almost any circuit in which the device will be used. The admittance characteristic is shown in Figure 2A, which is the admittance-plane locus of the vector relationship . - +j OC, - . 11 I R1 1 y12 = Ri2 + (wL1 - -)2 OC1 This circular

43、locus in the Y-plane clearly maps into a corresponding circular locus in the Z-plane, as shown in Figure 2B. There are several characteristic values which are commonly used in describing crystal units, whose relationship becomes clear from examination of Figure 2. The “fundamental“ constants which d

44、epend only on the motional properties of the vibrator are the series resonant frequency, f, and the values of Rl, L1, and Cl, associated with the motional arm circuit. The other frequencies of interest are: EIA 512 85 36334laOO I072840 8 = EIA-512 Page 4 fm = frequency of minimum impedance fr = freq

45、uency of zero-phase, low impedance fa = frequency of zero-phase, high impedance fn = frequency of maximum impedance fp = parallel resonance frequency (lossless) Clearly, all of these frequencies depend to at least some degree upon the effective value of Co; since connection into any use-circuit will

46、 almost inevitably produce some additional stray capacitance at the terminals and therefore modify the effective Co value, best correlation of measurements will be obtained if the series resonant frequency, f, is referenced. A list of symbols used for the equivalent electrical network is given in Ta

47、ble 1. The values of effective resistance at each of the characteristic frequencies can be determined from the real components of the impedance and admittance vectors, as shown in Figure 2. The motional inductance (or Capacitance), however, can only be determined from a knowledge of the frequency-de

48、pendence of the imaginary component. Figure 3 is a graphical presentation of the magnitudes of the real and imaginary components of device impedance versus frequency, with the characteristic frequencies marked. It can be shown2 that the value of motional inductance is very accurately determined from

49、 the derivative of reactance with respect to frequency, evaluated at f, after the admittance circle has been translated to have its center lie on the real axis in the Y-plane. This translation is accomplished mathematically by subtracting an amount o, Co = Bo from the susceptance component of each measured admittance vector. Then, the remaining admittance vectors, representing only the components due to the motional arm parameters, are transformed to impedance vectors; and the reactance component, X, may be fitted to a function of frequency. f, the ser