Method and apparatus for testing crystal elements

A method and apparatus for determining anomalies in the frequency- or admittance-temperature characteristic of a piezoelectric crystal resonator by inserting a variable capacitance network in series with the crystal and electronically sweeping the value of the capacitance network by a control voltage applied thereto while the temperature remains constant and noting any abrupt change in the resonance frequency characteristic.

BACKGROUND OF THE INVENTION 
1. Field of the Invention 
This invention relates generally to the electronic measurement of crystal 
resonator temperature anomalies and more particularly to the frequency or 
admittance-temperature anomalies occurring in quartz crystal resonators. 
2. Description of the Prior Art 
Because of precision frequency control requirements for digital 
communication and position location systems currently in use, it is 
imperative that the crystal resonators utilized have very smooth and 
reproducible frequency-temperature characteristics. One reason why the 
characteristic is required to be smooth is because the temperature 
compensating network used in temperature compensated crystal oscillators 
must be capable of compensating for the usual "S" shaped curve of an 
AT-cut crystal, for example. Consequently, it is the usual practice to 
individually test each crystal resonator in an oven over a selected 
temperature range and monitor the oscillator frequency on a continuous 
basis. Such temperature runs require expensive apparatus and take 
considerable time for a careful scan. If the crystal is acceptable, the 
frequency-temperature characteristic will exhibit a substantially smooth 
"S" curve. If on the other hand the crystal has an anomaly in its 
frequency-or admittance-temperature characteristic, referred to as an 
"activity dip" or "band break," the curve exhibits an abrupt change or 
discontinuity. Either the frequency or resistance curve can be used as an 
indication of the presence of such an anomaly depending upon where on the 
"S" curve the "activity dip" occurs. 
These anomalies are generally considered to be caused by various 
combinations of different modal frequencies coming into coincidence at 
particular temperatures because of differing temperature coefficients. At 
least two distinct species of activity dips exist; one being 
"design-related" dips, while the other is termed "process-related" dips. 
The latter type arises from shortcomings in the processing phases, where 
for example, an improperly deposited electrode film peels or blisters in a 
reversible, temperature-dependent manner. Design-related activity dips are 
those for which structural configuration remains unaffected by temperature 
changes, but instead depends solely upon geometry and material constants. 
It is these latter type anomalies to which the present invention is 
directed. The presence of design-related activity dips is a persistent 
problem and as a consequence, necessitates a great deal of costly testing 
for medium and high precision resonator units in the manner mentioned 
above, i.e., temperature runs. Doubly rotated cuts generally could be 
expected to have even more problems in this regard than AT-cut crystals, 
since they exhibit less symmetry and have therefore a more complicated 
mode spectrum when lateral boundaries are taken into account. The 
exception appears to be the SC/TTC orientation for which activity dips 
have yet to be encountered. 
The modal interference that takes place can be either linear or non-linear. 
If the impressed voltage is capable of driving the desired thickness mode 
and at the same time drive a harmonic effectual mode, for example, then 
the vibrator admittance will reflect this fact as the linear superposition 
of the separate modal admittances. With temperature changes, it is 
possible for the two resonance frequencies to cross and produce an 
anomaly. Such linear activity dips have been described by several 
investigators in the following publications: "Activity Dips in AT-Cut 
Crystals," A. Wood, et al., Proceedings 21st Annual Frequency Control 
Symposium (AFCS), Ft. Monmouth, N.J., April, 1967, pp. 420-435, and "The 
Unwanted Responses of Crystal Oscillator Controlled by AT-Cut Plate," H. 
Fukuyo, et al., Bulletin Tokyo Inst. Tech., No. 82, September, 1967, pp. 
53-64; Proceedings 21st AFCS, April, 1967, pp. 402-419. 
Non-linear activity dips are less well understood and perhaps more 
important. The Wood, et al. publication also found that the AT-Cut 
fundamental thickness shear frequency to be effected by interfering modes 
at twice its frequency. In a publication entitled "On Activity Dips of AT 
Crystals At High Levels of Drive," C. Franx, Proceedings 21st AFCS, April, 
1967, pp. 436-454, the same type of coupling due to a mode at three times 
the fundamental frequency was reported. Similar results were obtained and 
reported by the aforementioned Fukuyo reference. In all cases, the 
sensitivity of mode coupling to power levels is a characteristic of 
non-linearity. 
It is an object therefore of the present invention to provide a new and 
improved method and apparatus for testing for activity dips in 
piezoelectric (quartz) resonators which obviates the heretofore required 
temperature runs. 
SUMMARY 
It has been discovered that the effect of inserting a capacitor in series 
with a crystal results in a shift of all resonance frequencies upwards by 
amounts roughly inversely proportional to the capacitance ratios of the 
modes and with the temperature coefficients of the various modes being 
similarly altered. As a result of this fact and because the interfering 
modes have differing temperature coefficients, it is possible to alter the 
activity dip temperature by a series load capacitance. 
Briefly then, the subject invention is directed to the method and apparatus 
for coupling a voltage variable capacitance network in series with a 
crystal resonator under test and applying a time varying control voltage 
to the capacitor network for sweeping the capacitance value while the 
temperature remains substantially constant and detecting the resonance 
frequency change as a function of the change in control voltage and 
thereafter observing whether or not an abrupt discontinuity or dip occurs 
in the frequency or resistance characteristic of the resonator. 
The means employed comprises an RF oscillator circuit including an 
amplifier having the resonator under test and a series coupled varactor 
diode network coupled thereto. An electronic sweep voltage generator under 
the control of a circuit means which may be programmed, for example, 
varies the capacitance of the varactor network in a predetermined 
time-varying fashion such as a linear sweep. The RF signal output from the 
oscillator is coupled to a signal mixer which also has applied thereto a 
reference frequency from a fixed reference oscillator. The two RF signals 
are mixed, i.e., heterodyned and the difference output frequency is 
coupled to a frequency discriminator the output of which is fed to not 
only a visual display, but also the control means. The control circuit 
means also has a signal applied thereto corresponding to the actual RF 
frequency output from the oscillator, which is developed, for example, by 
an RF amplifier and a frequency counter coupled to the oscillator itself. 
Output means for providing a print out of the resonator's frequency 
characteristic is also coupled to the control signal means for providing a 
record of the frequency variation of the resonator as provided by the 
output of the frequency discriminator.

DESCRIPTION OF THE PREFERRED EMBODIMENTS 
Referring now to the drawings, there is shown in FIG. 1 a crystal resonator 
10 which is represented by a Butterworth-Van Dyke equivalent electrical 
circuit consisting of the capacitance C.sub.0 shunted by a series 
combination of a resistance R.sub.1 and inductance L.sub.1 and a 
capacitance C.sub.1. The effect of inserting a load capacitor 12 of the 
value C.sub.L in series with the crystal 10 as shown in FIG. 2 can also be 
represented by a circuit of the same form but with modified values of a 
capacitance C.sub.0L shunted by series combination of resistance R.sub.1L, 
inductance L.sub.1L and capacitance C.sub.1L with modified values which 
are expressed by the appropriate formulas shown in Table I, which are 
given in terms of the crystal capacitance ratio r which is defined as: 
EQU r=C.sub.0 /C.sub.1 (1) 
and the load capacitance ratio alpha, which is defined as: 
EQU .alpha.=C.sub.0 /(C.sub.0 +C.sub.L). (2) 
whereas 
EQU f.sub.R .congruent.f.sub.s (3) 
the effect of the series load capacitor 12 is to shift the frequency 
f.sub.R to a higher frequency f.sub.L according to the expression: 
EQU f.sub.L =f.sub.s .sqroot.1+.alpha./r. (4) 
Where for example the resonator 10 comprises an AT cut quartz crystal 
operated at f.sub.s, a typical value for r is in the order of 250. 
Accordingly, by inserting the series load capacitor 12 in series with the 
resonator 10, the frequency f.sub.L can be pulled by changes in the value 
of C.sub.L. An interfering mode, on the other hand, is apt to have a very 
large capacitance ratio and so would be shifted very little by the 
presence of C.sub.L. Because the effective capacitance of the thickness 
modes, such as the desired AT-cut shear mode, varies with the square of 
the harmonic, the overtones will shift correspondingly less than the 
fundamental. The same is also true of their non-linearly produced 
sub-harmonics. The series load capacitance 12 thus shifts upwardly, the 
different modes by different amounts. Accordingly, the points of 
intersection of the modes will also change, as will be shown particularly 
with reference to FIG. 4. 
Referring now to FIG. 3, which is illustrative of prior art practice, there 
is demonstrated the effects of two different load capacitance values 
C.sub.L1 and C.sub.L2 in series with the crystal 10 having a resonance 
frequency of f.sub.R =20MHz. The S-shaped curves shown in the figure are 
illustrative of frequency vs. temperature characteristics typically of an 
AT-cut quartz crystal resonator. Curve 14, for example, is descriptive of 
the frequency vs. temperature characteristic of the crystal 10 without a 
load capacitor. The resonance frequency accordingly varies according to 
the curve 14 and exhibits an anomaly 16 at a temperature of approximately 
78.degree. C. as indicated by the arrow. A second type of curve 18 
corresponding to grid current vs. temperature and which is also 
illustrative of crystal admittance exhibits an anomaly 20 at the same 
temperature. These curves were obtained by a typical heat run obtained in 
a manner well known to those skilled in the art. It was observed, however, 
that when the load capacitor 12 of a value C.sub.L1 was placed in series 
with the crystal 10, curves 22 and 24 resulted exhibiting respective 
activity dips 26 and 28 which were displaced downward in temperature to 
approximately 58.degree. C. Where, for example, the value of C.sub.L1 
=35pF, the substitution of a relatively smaller capacitor C.sub.L2 =22pF 
produced curves 30 and 31 with a further downward shift of the activity 
dip to 44.degree. C. as evidenced by the dips 32 and 34 respectively. The 
downward shift in temperature for the anomaly means that the temperature 
coefficient of the interfering mode is negative. The .DELTA.f/f scale 
shown in FIG. 3 is meant to pertain to each of the three S-curves 14, 22 
and 30 individually; the vertical separation between the S-curves is not 
to scale but has been greatly reduced so that they can be compared more 
easily. The resistance curves 18, 24 and 31 have been similarly displaced 
for clarity and accordingly the relative position is unimportant. 
Referring now to FIG. 4, the shift of the activity dip as a function of 
temperature is further clarified. The temperature-frequency curve 36 
corresponds to curve 14 shown in FIG. 3. On the scale of the drawing, the 
curve is nearly horizontal; however, its vertical scale has been 
exaggerated by a factor of 10. Two curves 38 and 40 representing unwanted 
interfering modes have been drawn and intersect the curve 36 at a common 
point 42 located at approximately 80.degree. C. As noted with respect to 
the curves shown in FIG. 3, the addition of the series load capacitor 12 
shifts the resonant frequency upward. This is illustrated by curve 44. The 
points of intersection of curves 38 and 40 occur at points 46 and 48. Thus 
the mode associated with curve 40 produces a dip at 48.degree., while the 
mode evidenced by curve 38 produces a dip at -23.degree. C. 
While the fundamental interfering modes are meant to be represented by the 
curves shown in FIG. 4, it is only necessary that the harmonic or 
sub-harmonic producing the disturbance be represented as shown in FIG. 4, 
in which case the curve would be a virtual response of the figure. Thus, 
in the aforementioned case of Franx, if this interfering mode were to have 
its temperature behavior mapped and then to have its frequency divided by 
a factor of 3, it could be drawn as a virtual response on the figure along 
with the fundamental curve for the purpose of determining how the dip 
temperature changes with the value of C.sub.L, i.e., the series load 
capacitance. The virtual curve would appear similar to the curves 38 or 
40, while the actual interfering mode would appear at some harmonic 
frequency off the scale shown in FIG. 4. 
Whereas the prior art method of testing for activity dips required 
temperature runs according to FIG. 3 to be made, the observance of the 
effect that the resonant frequency as well as the activity dips shift as a 
function of the load capacitor placed in series with the crystal 
resonator, provides a method of eliminating time consuming temperature 
scans for determining the existence of activity dips. In other words, the 
temperature scan heretofore required can be eliminated by sweeping or 
scanning the value of capacitance placed in series with the resonator and 
tracking its resonance frequency change. This is accomplished by utilizing 
a variable load capacitance in the form of a voltage variable (varactor) 
diode network whose capacitance varies as a function of the applied 
voltage. 
The preferred embodiment of activity dip scanner apparatus utilized to 
practice the subject method is shown in block diagrammatic form in FIG. 5. 
There an RF oscillator circuit 50, configurations of which are shown in 
FIGS. 6A through 6C, is coupled to a varactor diode network 52 which has a 
periodic i.e., variable sweep voltage applied thereto from a sweep 
generator 54 which is adapted to apply a time varying voltage to the 
varactor network 52 for varying its capacitance characteristic in 
accordance with a predetermined scan procedure established by control 
circuit means 56 which may be a programmed control and signal processing 
unit implemented for example by a microprocessor or other type of 
programmable control apparatus, which is adapted to be responsive to 
resistance and frequency information for controlling system operation. The 
sweep generator 54 is adapted, for example, to supply a ramp voltage to 
the varactor network 52, which is operative to provide a variable C.sub.L 
in series with the crystal unit under test. In addition to being coupled 
to an RF amplifier 58, the output frequency from the oscillator 50 is fed 
to a mixer 60 which also receives a reference frequency from an oscillator 
62 which is adapted to operate at the nominal frequency of the crystal. 
The difference frequency output from the mixer 60 is applied to a 
frequency discriminator circuit 64 by means of an RF amplifier 66. The 
output voltage of the discriminator 64 is fed back to the control means 56 
which receives an additional input of the oscillator frequency from a 
counter circuit 70 coupled to the RF amplifier 58. Indicator means 72 
which may be, for example, an oscilloscope for providing a visual 
indication of the change of the resonance frequency of the crystal under 
test in the oscillator circuit 50 as a function of the sweep voltage 
applied to the varactor network 52 is provided by means of having the Y 
axis input coupled to the output of the discriminator circuit 64 while the 
X axis input also is coupled to the sweep voltage from the generator 54. 
The control means 56 is also adapted to be coupled to an output device 74 
which may be, for example, a printer or chart recorder for providing a 
permanent record of a capacitor scan. Additionally, the control means 56 
is adapted to be operable to provide information for "go-no go" acceptance 
or rejection of the unit under test for activity dips as well as 
evaluation of crystal parameter's output of results as well as sequencing 
and control of input and output flow on an assembly line basis. 
The oscillator circuit 50 requires care in its design, but its details are 
a matter of choice. However, one must be sure that the sought for 
anomalies originate in the crystal and not the oscillator so that unwanted 
frequency components must be strongly discriminated against. What is 
required is that the oscillator be such that it adjusts its frequency such 
that the crystal-load capacitor combination operates near or at its zero 
reactance point, i.e., resonance of f.sub.L. Schematically, the oscillator 
in its simplest form is shown in FIG. 6A and consists of a crystal unit 76 
under test, coupled to a feedback amplifier 78. One input to the amplifier 
is coupled to a reference potential shown as ground, while the other input 
is connected to a circuit junction 80 which is common to an output 
terminal 82 and a terminal 84 which connects to the varactor network 52. 
The output of the amplifier 78 couples to circuit junction 86, which is 
adapted to couple to one side of the crystal unit under test 76, while the 
other side of the crystal unit under test is connected to terminal 88, 
which is adapted to be connected to the other side of the varactor network 
52. A first fixed capacitor 90 is coupled to ground from circuit junction 
86, while a second fixed capacitor 92 is coupled to ground from circuit 
junction 80. Consideration of FIGS. 6B and 6C will be deferred for reasons 
which will become obvious when FIGS. 10 and 11 are discussed. 
The varactor network 52 is shown schematically in FIG. 7 and consists of a 
balanced network of four voltage variable or varactor diodes 94, 96, 98 
and 100 coupled between the terminals 88 and 84, by means of a combination 
of fixed capacitors and resistors such that a sweep voltage applied across 
terminals 102 and 104 is applied across each of the varactor diodes. It 
can be seen that the fixed capacitors 106, 108, 110 and 112 are coupled 
between the varactor diodes 94, 96, 98 and 100 so as to form a string of 
series connected capacitances between the terminals 84 and 88. The 
capacitance vs. voltage characteristic for the varactor network shown in 
FIG. 7 is shown in FIG. 8. The curve 114 of FIG. 8 is non-linear and 
indicates that the value of capacitance C.sub.L is inversely proportional 
to the DC voltage applied across terminals 102 and 104. 
Referring now to FIG. 9, there is disclosed a set of graphs illustrative of 
the subject method for determining activity dips in a crystal resonator by 
means of the apparatus shown in FIG. 5, wherein the sweep generator 54 
shown in FIG. 5 comprises a ramp voltage up to a predetermined value and 
then ramps back to its starting point at the same rate. The set of graphs 
shown in FIG. 9 illustrate the operation of the subject method and 
comprises curves which would appear, for example, on the oscilloscope 72 
or on the output means 74 for three fixed temperatures T.sub.1, T.sub.2 
and T.sub.3 wherein T.sub.1 &lt;T.sub.2 &lt;T.sub.3 and for three separate power 
levels, P.sub.1, P.sub.2 and P.sub.3 wherein P.sub.1 &lt;P.sub.2 &lt;P.sub.3. It 
can be seen with reference to curves 116, 118 and 120 that for a first 
constant temperature T.sub.1, that as the power level is varied, the 
activity dip shows up as an abrupt change in the slope of the curves. At 
the low power level P.sub.1, the curve 116 exhibits a slight break 122 as 
the varactor voltage applied to the network as shown in FIG. 7 is varied. 
As the power level is increased to P.sub.2 and P.sub.3, the activity dip 
is manifested by the presence of respective hysteresis loops 124 and 126 
in the curves 118 and 120 with the arrows indicating the direction of 
traverse of the frequency shift during the sweep of the capacitance value 
C.sub.L achieved by the varactor network 52 coupled in series with the 
crystal resonator unit under test 76. 
Where, however, the power level is held constant, e.g. P.sub.2 and the 
varactor network 52 is swept at different constant temperatures, T.sub.1, 
T.sub.2 and T.sub.3, the hysteresis loop 124' and 124" on the curves 118' 
and 118" moves downward with increasing temperature. This indicates that 
the interfering mode has a negative temperature coefficient of frequency. 
This may readily be explained, since C.sub.L of the varactor network 52 
decreases with increasing varactor voltage, as evidenced from FIG. 8 and 
since a decrease in C.sub.L increases the shift of f.sub.L from f.sub.R as 
shown in FIG. 3. Therefore, high varactor voltages mean large f.sub.L 
shifts. If the anomaly occurs at large varactor voltage at T.sub.1 and 
again at a lower voltage at a higher temperature T.sub.3, then the 
coefficient of the undesired interfering mode is negative. 
It should be observed that the hysteresis loop characteristic depends upon 
the power level at which the system is operating and therefore depends 
upon operator choice. When no activity dip is present, the 
.DELTA.f-.DELTA.v curve will be substantially smoothly monotonic, although 
not necessarily linear, as evidenced by the curves 116, 118 and 120. 
However, when an activity dip is present, the slope of the smooth curve 
experiences an abrupt change, indicating the existence of an anomaly. By 
the addition of a differentiating network, not shown, coupled to the 
output of the frequency discriminator 64, the dip can be detected more 
readily. Alternatively, the system shown in FIG. 5 can be arranged to use 
a voltage proportional to the crystal resistance (admittance) i.e., the 
grid current parameter shown in FIG. 3 as the input to the Y axis for the 
oscilloscope indicator 72 as shown in FIG. 5. 
In different crystals, the anomaly may be more pronounced in either the 
frequency or the resistance shift mode of operation, and either may be 
used as a step in the detection of the anomaly as the value of the series 
load capacitance is swept in a manner previously described. 
It should be pointed out that the series load capacitance 12 shown in FIG. 
2 by itself can only shift the frequency f.sub.L of the crystal resonator 
10 between the limits of f.sub.R &lt;f.sub.L &gt;f.sub.A, that is between the 
resonance f.sub.R and anti-resonance f.sub.A of the crystal unit 76 (FIG. 
6A). If at the temperature of the test the unwanted interfering mode 
causing the activity does not occur between these limits, then the anomaly 
will go undetected by the test and the curves 116, 120, etc., will not 
exhibit a break in the relatively smooth .DELTA.f-.DELTA.v curve. 
The present invention contemplates a means of extending the testing range 
of the method already described and consists in either adding an inductor 
11 in series with the crystal 10 coupled to the series load capacitor 12 
as shown in FIG. 10 or coupling an inductance 13 in parallel with the 
crystal 10 coupled to the series load capacitor 12 as shown in FIG. 11. 
The associated FIGS. 12 and 13 respectively disclose the effect of the 
series and parallel inductances 11 and 13 on the poles (x) where the 
reactance is infinite, i.e., where f.sub.A occurs and zeroes (o) where the 
reactance is zero, which occurs at the resonance frequency f.sub.R. FIGS. 
12 and 13 indicate the effect on the frequencies f.sub.R and f.sub.A 
between f=0 and f=.infin.. The effect of the series inductance 11 which 
may be referred to as a "stretching coil" lowers the first reactance zero 
(0) the resonance frequency f.sub.R towards f=0, i.e., to the point 
f'.sub.R. The inclusion of the series load capacitance 12, on the other 
hand, again moves the resonance frequency upward to the point f".sub.R but 
which is less than the original resonance frequency f.sub.R. 
With respect to the addition of the parallel inductance 13 (FIG. 11), it 
has the effect of shifting the anti-resonance frequency f.sub.A upward to 
the frequency f'.sub.A while the resonance frequency remains the same at 
f.sub.R. However, the addition of the load capacitance 12 causes a shift 
of the resonance frequency to f'.sub.R as shown in FIG. 13. 
The implementation of either the inclusion of the series inductance 11 or 
the parallel inductance 13 is shown in FIGS. 6B and 6C respectively, it 
being understood, however, that both implementations can be combined into 
a single embodiment when desirable. 
Referring first to FIG. 6B, the series inductor 11 can be electronically 
switched by means of a control signal (s) from the program control means 
56 coupled to switch diodes, e.g., PIN diodes or SCR's 128 and 130 with 
one being adapted to be rendered conductive while the other is 
non-conductive. Thus, for example, when diode 128 is rendered conductive 
while diode 130 is non-conductive, the inductance is out of the circuit 
and a circuit configuration as shown in FIG. 6A is provided while on the 
other hand, by rendering diode 130 conductive with diode 128 being 
non-conductive, the inductor 11 is connected in series with the unit under 
test 76, including the resonator 10. 
On the other hand, the parallel inductance 13 can be implemented as shown 
in FIG. 6C with a switch diode 132 coupled in series with the inductance 
13 across the unit under test 76. Thus when diode 132 is rendered 
non-conductive, the inductance 13 is not in the circuit and a 
configuration as shown in FIG. 6A is provided, however, with diode 132 
conductive, the inductance 13 is applied in parallel with the resonator 10 
implementing the combination shown in FIG. 13. 
Thus what has been shown and described is a simple, rapid and electronic 
means of detecting frequency or resistance (admittance) anomalies known as 
activity dips in piezoelectric crystals which is adapted to provide, for 
example, a rapid "go-no go" inspection method for eliminating resonator 
units having obvious and easily detected activity dips prior to making the 
costly temperature runs heretofore required. Also, when desirable, the 
apparatus described above provides instrumentation for readily determining 
other crystal parameters such as C.sub.0, C.sub.1, R.sub.1 and L.sub.1. 
Also, when desirable, a hybrid method may be utilized combined with the 
prior art temperature runs for interpolating between temperatures where, 
for example, the oven is programmed to dwell at each of a number of fixed 
temperatures, whereupon the varactor sweep method is used to search for 
dips between fixed temperatures. 
Although the present invention is described with a certain degree of 
particularity, it should be understood that the present disclosure has 
been made by way of example only, and that various modifications and 
alterations may be resorted to and equivalents substituted without 
departing from the spirit and scope of the invention. Accordingly,