Single side band monolithic crystal filter

An improved monolithic piezoelectric bandpass filter unit, suitable for single side band applications, having a pair of finite poles introduced into one of its stopbands.

FIELD OF THE INVENTION 
The present invention relates to crystal filters in general and to those 
utilizing monolithic crystals in particular. 
BACKGROUND AND PRIOR ART OF THE INVENTION 
Copending application Ser. No. 681,438, filed Apr. 29, 1976, now U.S. Pat. 
No. 4,028,647, in the name of H. K. H. Yee as inventor, discloses an 
improved monolithic piezoelectric filter unit having two bilateral 
electrodes on one surface and a common electrode on the opposite surface 
with the common electrode connected to the common terminal of the filter 
unit via a capacitor (C.sub.c). The latter, in cooperation with the 
coupling between the two bilateral electrodes, introduces a pair of finite 
poles one in each of the upper and the lower stopbands on either side of 
the passband of the filter unit. An advantage of such arrangement is that 
the tolerance on the internal coupling coefficient of the monolithic 
crystal may be relaxed. 
In utilizing monolithic crystals to realize Single Side Band (SSB) filters, 
it is advantageous to have all finite poles in either of the upper or 
lower stopbands exclusively, depending on which sideband is involved. 
SUMMARY OF THE INVENTION 
In the above-mentioned copending application, the capacitor C.sub.c 
connecting the common electrode of the monolithic crystal to the common 
terminal of the filter unit introduces a pair of finite poles one on 
either side of the passband. It has been found that, instead, this 
capacitor could be used to virtually cancel the intra-crystal coupling 
with the following resultant advantages: 
(1) INTRODUCTION OF A PAIR OF FINITE POLES, BOTH OF WHICH ARE EITHER IN THE 
UPPER OR LOWER STOPBANDS; 
(2) FURTHER RELAXATION OF THE TOLERANCE ON THE INTRA-CRYSTAL COUPLING, 
WHICH IS NOW ALMOST FULLY CANCELLED; AND 
(3) PERMITTING THE DESIGN OF A SIMPLER FILTER HAVING ADEQUATE PERFORMANCE 
FOR THE GIVEN APPLICATION. 
In case both finite poles are to be in the lower stopband, the capacitor 
C.sub.c would be unusually large in capacitance value. If both finite 
poles are in the upper stopband, the capacitor C.sub.c would be unusually 
small in value. The term "unusually" large or small will become clearer 
when describing the preferred embodiment of the present invention. 
In essence, the novel filter unit permits the use of a monolithic two pole 
crystal to replace two discrete crystal resonators. 
Thus according to the present invention, the novel monolithic bandpass 
filter unit has an upper and a lower stopband and comprises: a monolithic 
piezoelectric crystal substrate having two adjacent electrodes on one 
surface thereof constituting two bilateral terminals of said filter unit, 
and a common electrode on the other surface opposite said two electrodes; 
a coupling capacitor between said two adjacent electrodes; and a capacitor 
interconnecting said one common electrode and a common terminal of said 
filter unit and having a predetermined capacitance value to substantially 
cancel intra-crystal coupling in said monolithic piezoelectric crystal 
substrate, and to introduce a pair of finite poles in only one of the 
upper and the lower stopband of the filter unit.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT 
FIG. 1a of the drawings depicts schematically the structure of a monolithic 
filter unit. In the prior art referred to above, the intra-crystal 
coupling and the capacitors C.sub.b and C.sub.c were utilized to produce 
two finite poles at the frequencies f.sub.1 and f.sub.2 as shown in FIG. 
1b of the drawings. In the present invention, however, the capacitor 
C.sub.c is utilized solely to substantially cancel intra-crystal coupling, 
and to cause the single AT cut monolithic crystal 10, with the thereon 
deposited electrodes 11, 12 and 13, to act as a substitute for two single 
crystal resonators coupled via the capacitor C.sub.b. As a result, two 
finite poles as shown in FIG. 1c at the same frequency f.sub.1 are 
produced. Such two finite poles at the same side of the passband (in FIG. 
1c the lower frequency side) are suitable for Single Side Band (SSB) 
filters, and permit the design of simpler filters with adequate 
performance. 
It is in order here to point out that a single crystal cut to have 
inherently very little or no intra-crystal coupling is not suitable for 
many applications, because such cuts are only suitable for low frequency 
operation. In addition, the maximum practicable bandpass width is only ca. 
0.3% of the operating frequency, so that, for instance, a crystal filter 
at 100 KHz is capable of only ca. 0.3 KHz band-pass width. This is 
insufficient for many applications. 
Beginning with FIG. 2, a step by step design procedure for a composite 
filter with finite poles only in the lower stopband according to the 
present invention, will be described. 
FIG. 2 is the schematic of a conventional insertion loss synthesized SSB 
filter having two adjacent pairs of identical pole frequencies f.sub.1 and 
f.sub.2 (FIG. 1c shows only one pair f.sub.1 -- usually f.sub.2 would be 
only slightly lower than f.sub.1 as will be shown in a numerical example, 
infra). The schematic shown has identical inductances, which is achievable 
by capacitance transformation. Such filter design is well known and is 
described, for instance, in "Filter Design Using Transformed Variables" by 
H. J. Orchard in IEEE Transactions on Circuit Theory, Dec. 1968, pp. 
385-407, and in "On The Design of Filters by Synthesis" by R. Saal and E. 
Ulbrich in IRE Transactions on Circuit Theory, Dec. 1958, pp. 284-327. 
The filter of FIG. 2 is converted into its lattice equivalent shown in FIG. 
3. Such conversion needs no further explanation as it is clear from the 
two figures. 
In order to take the crystal static capacity C.sub.o in consideration, the 
lattice circuit of FIG. 3 is modified into that of FIG. 4. In FIG. 4 the 
primed capacitors C.sub.b1 ', C.sub.b3 ', C.sub.A ', C.sub.B ', C.sub.D ' 
and C.sub.E ' are given by: 
EQU C.sub.b1 '.sub., 3 = 2C.sub.b1, 3 + C.sub.o 
and 
EQU C.sub.A '.sub., B, D, E = C.sub.A, B, D, E - C.sub.o. 
Since it is desired to obtain the lowest possible coupling within the 
crystal, the two electrodes 11 and 12 would be placed as far apart as 
possible. This, of course, is limited by the size of the crystal 10 and 
its quality factor Q. The actual "residual" coupling must then be 
determined to a reasonable accuracy, either by measuring or calculation 
and preferably by both. This coupling may be represented by a capacitance 
value C.sub.m. 
Given C.sub.m, the left-hand lattice section in FIG. 5 (corresponding to 
each of the lattice sections in FIG. 4) in which C.sub.s and -C.sub.s have 
been introduced, is determined. C.sub.s is given by: 
##EQU1## 
The right-hand lattice section in FIG. 5 is then determined by absorbing 
C.sub.s into the series arm tuned circuit to produce L', C.sub.1 ' and 
C.sub.b ". In the shunt arm a portion of C.sub.s is absorbed into the 
tuned circuits to yield the same inductance L' as in the series arm, with 
the remainder series capacitance being C.sub.c /2. C.sub.c is actually 
very close in magnitude to C.sub.m but opposite in sign. Of course, 
circuit transformations such as those of absorbing capacitance etc. are 
standard in the art, and are given, for example, in the "Handbook of 
Filter Synthesis" by Anatol I. Zverev, published 1967 by John Wiley and 
Sons, Inc. (cf. p. 526-527 for an example calculation). 
From the lattice section (excluding for the moment, -C.sub.s) of FIG. 5 the 
first bridged T section in FIG. 6 is obtained (the component values are 
related as shown). -C.sub.s is then absorbed by capacitance transformation 
and the bridged T section is transformed into the lattice section in FIG. 
6, which also contains the denormalized inductance L instead of L'. The 
denormalization is accomplished by impedance scaling and capacitance 
transformation. Now the lattice section is again transformed into its 
bridged T equivalent as shown in FIG. 6. The values of the capacitors in 
FIG. 6 are as follows: 
##EQU2## 
Generally speaking, the final value of C.sub.m ' may deviate slightly from 
the original design value C.sub.m by an error in the order of 0.1%, which 
is acceptable and is compensated by adjustment of the capacitor C.sub.b. 
Numerical Example 
A numerical example for a filter suitable for a channel bank according to 
the following requirements will now be given: 
______________________________________ 
Passband Ripple 0.1 dB peak-to-peak 
Passband 8,140,250 Hz to 8,143,400 Hz 
2 pole frequencies at 
8137.0 KHz 
2 pole frequencies at 
8139.2 KHz 
Predistorted filter width 
Crystal Q 100,000 
______________________________________ 
Based on the above specifications a ladder network is synthesized having 
equal inductances. The inductance, of course, is a crystal parameter which 
is determined by the approximate frequency of operation. This also 
determines the other crystal parameters, which could be as follows: 
______________________________________ 
Crystal inductance L 
= 24 mH 
Static Capacity C.sub.o 
= 3.2 pF 
Plate Size (diameter) 
= 0.560 inch 
Coupling C.sub.m 
= -2200 pF .+-. 1% 
______________________________________ 
The ladder network values designated by the symbols in accordance with FIG. 
2 are as follows: 
______________________________________ 
L = 24.00 mH 
C.sub.1 = 0.015931826 pF 
C.sub.2 = 0.0159404432 pF 
C.sub.b1 = 23.550085 pF 
C.sub.b2 = 7.2825777 pF 
C.sub.b3 = 3.8442388 pF 
C.sub.A = 13.52966 pF 
C.sub.B = 3.347053 pF 
C.sub.D = 3.760389 pF 
C.sub.E = 11.83077 pF 
______________________________________ 
The impedance of the left-hand port is 594.943 ohms, and that of the 
right-hand port is 22528.0 ohms. 
The ladder network is converted into its equivalent lattice network, and 
then the crystal static capacity C.sub.o is included ending with the 
configuration shown in FIG. 4 with the following values: 
______________________________________ 
L = 24.00 mH 
C.sub.o = 3.2 pF 
C.sub.1 = 0.015931824 pF 
C.sub.2 = 0.01590404432 pF 
C.sub.b1 ' = 50.3001707 pF 
C.sub.b2 = 7.2825777 pF 
C.sub.b3 ' = 10.888477 pF 
C.sub.A ' = 10.329666 pF 
C.sub.B ' = 0.14705319 pF 
C.sub.D ' = 0.5603896 pF 
C.sub.E ' = 8.63077815 pF 
______________________________________ 
C.sub.s is then computed, one for each lattice section (C.sub.s1 and 
C.sub.s2): 
##EQU3## 
with C.sub.b1 ' = 50.3001707 pF for the left section, and 
C.sub.b3 ' = 10.888477 pF for the right section. 
Hence, 
C.sub.s1 = -16190.6836 pF, and C.sub.s2 = -2642.91419 pF. 
Absorbing the capacitances -C.sub.sj into the lattice as explained before 
slightly lowers the crystal inductance from its design value, which are, 
therefore, scaled back to their design value by impedance scaling and 
capacitance transformation. 
From the formula C.sub.bp = .sqroot.(L/L.sub.b) C.sub.o given before in 
conjunction with FIG. 6, the shunt capacitance C.sub.bp is computed for 
C.sub.o to be equal to the final design value 3.2 pF of the final circuit. 
The lattices are then unbalanced into bridged T's and the final circuit is 
obtained. The values of the elements in accordance with FIG. 7 are as 
follows: 
______________________________________ 
L = 24.00 mH 
C.sub.o = 3.2 pF 
C.sub.b1 = 0.01593184219 pF 
C.sub.b1 ' = 23.476907 pF 
C.sub.b2 = 7.205404841 pF 
C.sub.b3 = 0.1594053963 pF 
C.sub.b3 ' = 3.8283979 pF 
C.sub.m1 ' = 2200.0196 pF 
C.sub.m3 ' = 2202.3269 pF 
C.sub.c1 ' = 2193.1653 pF 
C.sub.c3 ' = 2193.165 pF 
C.sub.A ' = 10.315262 pF 
C.sub.B ' = 0.14238557 pF 
C.sub.D ' = 0.533784952 pF 
C.sub.E ' = 8.5191941 pF 
Z.sub.1 = 599.42 ohms 
Z.sub.2 = 22863.0 ohms 
______________________________________ 
The remaining crystal parameters are: 
M.mu.1: k.sub.1 = 0.000724168193%; f.sub.1 = 8139169 Hz. 
M.mu.2: k.sub.2 = 0.0007238044306%; f.sub.2 = 8136949 Hz. 
FIG. 8 shows the schematic of the actual filter. Some of the capacitors are 
made variable to compensate for deviations from the calculated theoretical 
values. The component values are as given in the Figure. They do not 
differ substantially from the theoretical values.