Abstract:
Embodiments of apparatuses, systems and methods relating to temperature compensation of acoustic resonators in the electrical domain are disclosed. Other embodiments may be described and claimed.

Description:
TECHNICAL FIELD  
       [0001]    Embodiments of the present invention relate generally to the field of acoustic resonators, and more particularly, to temperature compensation of acoustic resonators in the electrical domain. 
       BACKGROUND  
       [0002]    Acoustic resonators used in radio frequency (RF) filters, such as surface acoustic wave (SAW) filters and bulk acoustic wave (BAW) filters, typically have a negative temperature coefficient of frequency (TCF) that is caused by a decrease of stiffness of materials when temperature increases. Acoustic velocity decreases with temperature and hence a filter&#39;s transfer function shifts toward lower frequencies. There are very few materials that show an irregular behavior in this regard. One example is amorphous silicon oxide. The introduction of amorphous silicon oxide to the propagation path of acoustic waves in a SAW or BAW filter may have a temperature-compensating effect and reduce the overall temperature drift of these devices. However, amorphous silicon oxide also introduces various challenges. 
         [0003]    Amorphous silicon oxide introduces additional propagation loss, and may thwart the objective of achieving low insertion loss in filters. Furthermore, any additional material introduced into a propagation path of an acoustic wave will reduce a coupling coefficient of a resonator, which relates to the efficiency at which the resonator will convert energy between an acoustic wave form and an electrical form. As a consequence, a maximum relative filter bandwidth that a certain piezo-material can provide may decrease steeply. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0004]    Embodiments are illustrated by way of example and not by way of limitation in the figures of the accompanying drawings, in which like references indicate similar elements and in which: 
           [0005]      FIGS. 1(   a )- 1 ( d ) illustrate temperature-compensated resonator circuits in accordance with some embodiments. 
           [0006]      FIG. 2  illustrates a ladder filter in accordance with some embodiments. 
           [0007]      FIG. 3  illustrates a ladder filter in accordance with some embodiments. 
           [0008]      FIGS. 4(   a ) and  4 ( b ) illustrate compensation capacitor pairs in accordance with some embodiments. 
           [0009]      FIG. 5  illustrates a wireless communication device in accordance with some embodiments. 
       
    
    
     DETAILED DESCRIPTION 
       [0010]    Various aspects of the illustrative embodiments will be described using terms commonly employed by those skilled in the art to convey the substance of their work to others skilled in the art. However, it will be apparent to those skilled in the art that alternate embodiments may be practiced with only some of the described aspects. For purposes of explanation, specific devices and configurations are set forth in order to provide a thorough understanding of the illustrative embodiments. However, it will be apparent to one skilled in the art that alternate embodiments may be practiced without the specific details. In other instances, well-known features are omitted or simplified in order not to obscure the illustrative embodiments. 
         [0011]    Further, various operations will be described as multiple discrete operations, in turn, in a manner that is most helpful in understanding the present disclosure; however, the order of description should not be construed as to imply that these operations are necessarily order dependent. In particular, these operations need not be performed in the order of presentation. 
         [0012]    The phrase “in one embodiment” is used repeatedly. The phrase generally does not refer to the same embodiment; however, it may. The terms “comprising,” “having,” and “including” are synonymous, unless the context dictates otherwise. 
         [0013]    In providing some clarifying context to language that may be used in connection with various embodiments, the phrases “A/B” and “A and/or B” mean (A), (B), or (A and B); and the phrase “A, B, and/or C” means (A), (B), (C), (A and B), (A and C), (B and C) or (A, B and C). 
         [0014]    The term “coupled with,” along with its derivatives, may be used herein. “Coupled” may mean one or more of the following. “Coupled” may mean that two or more elements are in direct physical or electrical contact. However, “coupled” may also mean that two or more elements indirectly contact each other, but yet still cooperate or interact with each other, and may mean that one or more other elements are coupled or connected between the elements that are said to be coupled to each other. 
         [0015]    Embodiments of the present invention provide resonator circuits that compensate for temperature drift characteristics of acoustic resonators that may otherwise compromise the effectiveness of the acoustic resonators. In particular, the temperature compensated resonator circuits may be incorporated into filters to prevent filter performance from being adversely affected by temperature drift. 
         [0016]    In many wireless applications there is a critical filter skirt on either the lower or upper side of a filter&#39;s transfer function. However, there is rarely a critical filter skirt on both sides of the transfer function. A critical filter skirt, as used herein, may be an operational specification most likely to be violated in the presence of temperature drift. 
         [0017]    Some of the embodiments described herein provide targeted temperature compensation for the elements that have an impact on the portion of the filter&#39;s transfer function that is adjacent to the critical filter skirt. By limiting temperature compensation to only a subset of elements in a filter, any negative impact of temperature compensation may have less impact on overall filter performance. 
         [0018]      FIG. 1(   a ) illustrates a temperature-compensated resonator circuit  100  in accordance with various embodiments. The resonator circuit  100  may include an acoustic resonator  104  coupled in parallel with a compensating capacitor  108 . The resonator circuit  100  may be incorporated into a radio frequency (RF) filter that is configured to provide a transfer function that exhibits a low in-band insertion loss and a high out-of-band insertion loss. 
         [0019]    The acoustic resonator  104  may be an electromechanical transducer configured to convert energy between an acoustic wave form and an electrical form. The resonator  104  may oscillate at certain frequencies, called resonance frequencies, with a greater amplitude than at other frequencies. The resonator  104  may generate an electrical signal that corresponds to the oscillations, or, conversely, generate oscillations that correspond to an electrical signal. 
         [0020]    The resonator  104  may be associated with a negative temperature coefficient of frequency (TCF) that changes resonance properties associated with the resonator  104  with temperature. In particular, a negative TCF may mean that velocity of acoustic waves will decrease with temperature and, when the resonator  104  is incorporated into an RF filter, this may result in a transfer function shifting toward a lower frequency. 
         [0021]    The compensating capacitor  108 , C_c, may at least partially compensate for temperature drift of the resonance of the resonator  104 . Hereinafter, “C_c” may refer to the capacitor  108  itself, or the capacitance associated with capacitor  108 , depending on the context in which it is used. Temperature compensation will be performed in the electrical domain, without modifying acoustic wave propagation on the resonator  104 . 
         [0022]    The capacitor  108  may be configured to exhibit a negative temperature coefficient of capacitance (TCC), e.g., a capacitance of the capacitor may decrease in response to corresponding increase in temperature. In some embodiments, a negative TCC may be accomplished by using a capacitor having a dielectric material with a high negative temperature coefficient of the dielectric constant (TCK). As used herein, a high negative TCK may refer to a TCK that is more negative than approximately −1,000 ppm/C. In some embodiments, the capacitor  108  may include a dielectric composed of a ceramic formulation that includes calcium titanate (CaTiO3), which may have a TCK of −4,000 ppm/C. The dielectric constant of calcium titanate may be around 160 and the tan-delta may be 0.003. 
         [0023]    An acoustic resonator may be modeled using a Butterworth-van-Dyke (BVD) equivalent circuit in which the resonator is represented by a capacitor, C — 0, coupled in parallel with a series segment that includes a resistor, R_a, a capacitor, C_a, and an inductor, L_a, coupled in series with one another. In the BVD equivalent circuit, temperature drift of a series resonance, which may also be referred to as resonance frequency, f_s, is dominated by C_a and L_a, while temperature drift of parallel resonance, which may also be referred to as anti-resonance frequency, f_p, is dominated by C_a, C — 0, and L_a. R_a models losses of a resonator. 
         [0024]    The addition of C_c may not change the resonance frequency of the resonator circuit  100 , but it may lower the anti-resonance frequency of the resonator circuit  100 . The anti-resonance frequency may be the frequency at which a local maximum of impedance occurs and the resonance frequency may be the frequency at which a local minimum of impedance occurs. The anti-resonance frequency may be given by: 
         [0000]    
       
         
           
             
               
                 
                   
                     f 
                     p 
                   
                   = 
                   
                     
                       1 
                       
                         2 
                          
                         π 
                       
                     
                      
                     
                       
                         1 
                         
                           
                             
                               L 
                               a 
                             
                              
                             
                               
                                 
                                   ( 
                                   
                                     
                                       C 
                                       0 
                                     
                                     + 
                                     
                                       C 
                                       C 
                                     
                                   
                                   ) 
                                 
                                 × 
                                 
                                   C 
                                   a 
                                 
                               
                               
                                 
                                   C 
                                   0 
                                 
                                 + 
                                 
                                   C 
                                   C 
                                 
                                 + 
                                 
                                   C 
                                   a 
                                 
                               
                             
                           
                         
                       
                       . 
                     
                   
                 
               
               
                 
                   Equation 
                    
                   
                       
                   
                    
                   1 
                 
               
             
           
         
       
     
         [0025]    The derivative of f_p over C_c may be expressed as: 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       ∂ 
                       
                         f 
                         p 
                       
                     
                     
                       ∂ 
                       
                         C 
                         C 
                       
                     
                   
                   = 
                   
                     
                       - 
                       
                         
                           f 
                           p 
                         
                         2 
                       
                     
                     × 
                     
                       
                         
                           C 
                           a 
                         
                         
                           
                             ( 
                             
                               
                                 C 
                                 0 
                               
                               + 
                               
                                 C 
                                 C 
                               
                               + 
                               
                                 C 
                                 a 
                               
                             
                             ) 
                           
                            
                           
                             ( 
                             
                               
                                 C 
                                 0 
                               
                               + 
                               
                                 C 
                                 C 
                               
                             
                             ) 
                           
                         
                       
                       . 
                     
                   
                 
               
               
                 
                   Equation 
                    
                   
                       
                   
                    
                   2 
                 
               
             
           
         
       
     
         [0026]    Equation 2 may be further expressed in relative changes in the approximated by: 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         ∂ 
                         
                           f 
                           p 
                         
                       
                       
                         ∂ 
                         
                           f 
                           p 
                         
                       
                     
                     
                       
                         ∂ 
                         
                           C 
                           C 
                         
                       
                       
                         ∂ 
                         
                           ( 
                           
                             
                               C 
                               0 
                             
                             + 
                             
                               C 
                               C 
                             
                           
                           ) 
                         
                       
                     
                   
                   = 
                   
                     
                       
                         1 
                         2 
                       
                        
                       
                         
                           - 
                           
                             C 
                             a 
                           
                         
                         
                           ( 
                           
                             
                               C 
                               0 
                             
                             + 
                             
                               C 
                               C 
                             
                             + 
                             
                               C 
                               a 
                             
                           
                           ) 
                         
                       
                     
                     ≅ 
                     
                       
                         
                           1 
                           2 
                         
                          
                         
                           [ 
                           
                             
                               
                                 ( 
                                 
                                   
                                     f 
                                     s 
                                   
                                   
                                     f 
                                     p 
                                   
                                 
                                 ) 
                               
                               2 
                             
                             - 
                             1 
                           
                           ] 
                         
                       
                       . 
                     
                   
                 
               
               
                 
                   Equation 
                    
                   
                       
                   
                    
                   3 
                 
               
             
           
         
       
     
         [0027]    For an acoustic resonator with an effective coupling coefficient of k 2 _eff, the frequency ratio equals: 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       f 
                       s 
                     
                     
                       f 
                       p 
                     
                   
                   ≅ 
                   
                     1 
                     - 
                     
                       
                         4 
                         
                           π 
                           2 
                         
                       
                       × 
                       
                         
                           k 
                           eff 
                           2 
                         
                         . 
                       
                     
                   
                 
               
               
                 
                   Equation 
                    
                   
                       
                   
                    
                   4 
                 
               
             
           
         
       
     
         [0028]    A temperature dependence of the compensation capacitance itself may be: 
         [0000]        C   c  (Δ T )= C   C0 (1+ TCK×ΔT ),   Equation 5
 
         [0029]    where C_C0 is an initial, room-temperature capacitance of the capacitor  104 . 
         [0030]    To illustrate the effects of the temperature compensation, consider an example in which the resonator  104  is a BAW resonator with an initial effective coupling coefficient of 6.5%. Initially, it may be assumed that the resonator  104  has no temperature drift at all. For this example, C_c may be ¼ of C — 0. The shift in f_p may then be calculated as follows. 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         
                           ∂ 
                           
                             f 
                             p 
                           
                         
                         
                           ∂ 
                           
                             f 
                             p 
                           
                         
                       
                       
                         
                           ∂ 
                           
                             C 
                             C 
                           
                         
                         
                           ∂ 
                           
                             ( 
                             
                               
                                 C 
                                 0 
                               
                               + 
                               
                                 C 
                                 C 
                               
                             
                             ) 
                           
                         
                       
                     
                     ≅ 
                     
                       - 
                       0.02 
                     
                   
                   , 
                 
               
               
                 
                   Equation 
                    
                   
                       
                   
                    
                   6 
                 
               
             
             
               
                 
                   
                     
                       
                         
                           
                             
                               ∂ 
                               
                                 C 
                                 C 
                               
                             
                             
                               ∂ 
                               T 
                             
                           
                            
                           
                             
                               C 
                               C 
                             
                             
                               ( 
                               
                                 
                                   C 
                                   0 
                                 
                                 + 
                                 
                                   C 
                                   C 
                                 
                               
                               ) 
                             
                           
                         
                         = 
                           
                          
                         
                           
                             TCKC 
                             C 
                           
                           
                             
                               C 
                               0 
                             
                             + 
                             
                               C 
                               C 
                             
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           
                             - 
                             4000 
                           
                            
                           
                               
                           
                            
                           ppm 
                            
                           
                             / 
                           
                            
                           C 
                           × 
                           
                             
                               1 
                               5 
                             
                             
                               
                                 4 
                                 5 
                               
                               + 
                               
                                 1 
                                 5 
                               
                             
                           
                         
                       
                     
                   
                   
                     
                       
                         
                           = 
                             
                            
                           
                             
                               - 
                               800 
                             
                              
                             
                                 
                             
                              
                             ppm 
                              
                             
                               / 
                             
                              
                             C 
                           
                         
                         , 
                       
                     
                   
                 
               
               
                 
                   Equation 
                    
                   
                       
                   
                    
                   7 
                 
               
             
             
               
                 
                   
                     
                       
                         
                           
                             
                               ∂ 
                               
                                 f 
                                 p 
                               
                             
                             
                               ∂ 
                               T 
                             
                           
                            
                           
                             1 
                             
                               f 
                               p 
                             
                           
                         
                         = 
                           
                          
                         
                           
                             ( 
                             
                               - 
                               0.02 
                             
                             ) 
                           
                           × 
                           
                             ( 
                             
                               
                                 - 
                                 800 
                               
                                
                               
                                   
                               
                                
                               ppm 
                                
                               
                                 / 
                               
                                
                               C 
                             
                             ) 
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           
                             + 
                             16 
                           
                            
                           
                               
                           
                            
                           ppm 
                            
                           
                             / 
                           
                            
                           
                             C 
                             . 
                           
                         
                       
                     
                   
                 
               
               
                 
                   Equation 
                    
                   
                       
                   
                    
                   8 
                 
               
             
           
         
       
     
         [0031]    Equation 8 shows that f p may shift approximately +16 ppm/C in this scenario. A typical BAW filter may exhibit approximately −15 to −17 ppm/C of TCF. Thus, the anti-resonance frequency of the resonator circuit  100  may become temperature stable in this embodiment. 
         [0032]    The insertion of the capacitor  108  in this embodiment may reduce the effective coupling coefficient to approximately 5.3%, down from the initial effective coupling coefficient of 6.5%. Such a coupling coefficient loss is less than other methods of attempting temperature compensation and is within an acceptable range of loss. 
         [0033]    It may be noted that the temperature drift of the series resonance of the resonator  104  is dominated by C_a and L_a, hence the temperature dependency of C — 0 can be ignored in the above calculations. 
         [0034]      FIG. 1(   b ) illustrates a temperature-compensated resonator circuit  112  in accordance with various embodiments. The resonator circuit  112  may include an acoustic resonator  116  coupled in series with a compensating capacitor  120 . 
         [0035]    The temperature compensation of the resonator circuit  112  may be similar to that of resonator circuit  100  except that resonator circuit  112  acts to compensate the temperature drift of the resonance frequency, rather than the temperature drift of the anti-resonance frequency. 
         [0036]    Assuming the resonator  116  is a BAW resonator with characteristics similar to those described above, the compensation capacitance for this embodiment may have a value approximately 4 times the static capacitance, C — 0, of the resonator  116 . In this embodiment, the resonance frequency of the resonator circuit  112  may become temperature stable by placing this compensation capacitance in series with the resonator  116 . Degradation of the coupling coefficient may be similar to that described above. 
         [0037]      FIG. 1(   c ) illustrates a temperature-compensated resonator circuit  124  in accordance with various embodiments. The resonator circuit  124  may include an acoustic resonator  128  coupled in series with compensating capacitor  132  and further coupled in parallel with compensating capacitor  136 . 
         [0038]    The temperature compensation of the resonator circuit  124  may compensate for temperature drift of both the resonance frequency and the anti-resonance frequency. However, resonator circuit  124  may be associated with more degradation of the coupling coefficient than resonator circuits  100  and/or  112 . 
         [0039]      FIG. 1(   d ) illustrates a temperature-compensated resonator circuit  138  in accordance with various embodiments. The resonator circuit  138  may include an acoustic resonator  140  coupled in series with a variable capacitor  142  and/or coupled in parallel with a variable capacitor  144 . The variable capacitors  142  and/or  144  may be coupled with an active control circuit  146  that controls one or both of the variable capacitors  142  and/or  144  such that they exhibit a TCC similar to that described above. The active control provided by the active control circuit  146  may emulate a similar temperature compensation as that described above with respect to capacitors having high TCK dielectric materials. The active control circuit  146  may include control logic  148  and a sensing device  150 . The sensing device  150  may sense temperature associated with the acoustic resonator  140 , and the control logic  148  may use the sensed temperature to serve as a basis for control of the variable capacitors  142  and/or  144  such that they exhibit desired negative TCC. The variable capacitors  142  and/or  144  may be varactors, tunable capacitors, switched capacitors, etc. 
         [0040]    Each of the resonator circuits  100 ,  112 ,  124 , and  138  may be specifically suited for particular applications.  FIGS. 2 and 3  show examples of some of these particular applications. 
         [0041]      FIG. 2  illustrates a ladder filter  200  in accordance with some embodiments. The ladder filter  200  may be used in an embodiment in which a lower filter skirt is the critical filter skirt. This may be, e.g., when the ladder filter  200  is used as a receive filter for a wireless code division multiple access (WCDMA) band 2 or 25 application. As will be described below, ladder filter  200  may be designed with temperature compensation for elements associated with a lower portion of a transfer function. 
         [0042]    The ladder filter  200  may include a number of series segments, e.g., series segments  204 _ 1 - 5 , with series segments  204 _ 2 - 5  each having at least one of five series resonators  208 _ 1 - 5  of the ladder filter  200 . The series resonators  208 _ 1  and  208 _ 2  may be coupled with one another to form a cascaded pair. The series resonators  208  may each have a common resonance frequency. 
         [0043]    The ladder filter  200  may also include four shunt segments  212 _ 1 - 4 , with each including at least one of four shunt resonators  216 _ 1 - 4  of the ladder filter  200 . Shunt resonators  216 _ 1  and  216 _ 4  may include a common resonance frequency f_s1, while shunt resonators  216 _ 2  and  216 _ 3  include a common resonance frequency f_s2, where f_s2−f_s1=14 megahertz in accordance with some embodiments. 
         [0044]    The ladder filter  200  may also include a number of inductors  218 . These inductors  218  may have small values and may be bond wires or small printed traces on the laminate module. 
         [0045]    The ladder filter  200  may include two compensation capacitors, C_c1  220 _ 1  and C_c2  220 - 2 , each having a negative TCC. The compensation capacitors  220  may include calcium titanate, for example, to provide a strong negative TCK. The values of the compensation capacitors  220  may be set to a fixed factor relative to the static capacitance of the resonator in the corresponding shunt segment. For example, C_c1 may be 4 times the capacitance associated with resonator  216 _ 2  and C_c2 may be 4 times the capacitance associated with resonator  216 _ 3 . 
         [0046]    With application of the ladder filter  200  being only (or at least primarily) concerned with temperature drift in a lower portion of the transfer function, it may be unnecessary to provide temperature compensation for any of the series resonators  208 . Further, it may be that temperature compensation is only desirable on a subset of the shunt segments that provide the largest influence on the portion of the transfer function adjacent the lower, critical skirt. In this embodiment, it may be that shunt segments  212 _ 2 - 3  have the largest impact on the portion of the transfer function of interest. Therefore, only the shunt segments  212 _ 2 - 3  may have temperature-compensated resonator circuits. This may further reduce any coupling coefficient losses that may be associated with temperature compensation. 
         [0047]      FIG. 3  illustrates a ladder filter  300  in accordance with some embodiments. The ladder filter  300  may be used in an embodiment in which an upper filter skirt is the critical filter skirt. This may be, e.g., when the ladder filter  300  is used as a transmit filter for a WCDMA band 2 or 25 application. Therefore, the ladder filter  300  may be designed with temperature compensation for elements associated with an upper portion of the transfer function. 
         [0048]    The ladder filter  300  may include a number of series segments, e.g., series segments  304 _ 1 - 5 , with series segments  304 _ 2 - 5  each having at least one of four series resonators  308 _ 1 - 4  of the ladder filter  300 . 
         [0049]    The ladder filter  300  may also include four shunt segments  312 _ 1 - 4 , with each including at least one of four shunt resonators  316 _ 1 - 4  of the ladder filter  300 . 
         [0050]    The ladder filter  300  may also include a number of inductors  318 . These inductors  318  may have small values and may be bond wires or small printed traces on the laminate module. 
         [0051]    The ladder filter  300  may include two compensation capacitors, C_c1  320 _ 1  and C_c2  320 _ 2 , that have a strong negative TCK. The compensation capacitors  320  may include calcium titanate, for example, to provide the strong negative TCK. The values of the compensation capacitors  320  may be set to a fixed factor relative to the compensation capacitance of the resonator in the corresponding series segment. For example, C_c1 may be ¼ the capacitance associated with resonator  308 _ 3  and C_c2 may be ¼ the capacitance associated with resonator  308 _ 4 . 
         [0052]    With application of the ladder filter  300  being only (or at least primarily) concerned with temperature drift in an upper portion of the transfer function, it may be unnecessary to provide temperature compensation for any of the shunt resonators  316 . Further, it may be that temperature compensation is only desirable on a subset of the series segments that provide the largest influence on the portion of the transfer function adjacent the upper, critical filter skirt. In this embodiment, it may be that series segments  304 _ 3 - 4  have the largest impact on the portion of the transfer function of interest. Therefore, only the series segments  304 _ 3 - 4  may have temperature-compensated resonator circuits. This may further reduce any coupling coefficient losses that may be associated with temperature compensation. 
         [0053]    The compensating capacitors used in the embodiments described herein may be thin-film capacitors integrated onto a filtered chip, thick-film capacitors embedded into a substrate or package, or discrete components. As there may be only two interconnections needed to connect a compensation capacitance to a filter, there may be a wide variety of implementation variations. Furthermore, due to the high relative dielectric constant of calcium titanate, at approximately 160 as mentioned above, the compensation capacitors may be relatively small. This may further facilitate their incorporation into various filter designs without difficulty. 
         [0054]    Materials with strongly negative TCK are usually ferroelectric in nature and tend to exhibit a small electrical field dependency of the dielectric constant, which may result in changes in capacitances occurring as a result of changes in voltage. In order to avoid nonlinear distortion that could result from such a behavior, the compensation capacitors may be used in pairs so that the electrical fields of the two capacitances are inverse. For example,  FIG. 4(   a ) illustrates a pair of compensating capacitors  404 _ 1 - 2  arranged in a cascade configuration in accordance with an embodiment. The two capacitors  404  are coupled in series with one another with their polarities inversed. In particular, a bottom terminal  408 _ 1  of the capacitor  404 _ 1  is coupled with a bottom terminal  408 _ 2  of the capacitor  404 _ 2 . 
         [0055]    For another example,  FIG. 4(   b ) illustrates a pair of capacitors  412 _ 1 - 2  arranged in an anti-parallel configuration in accordance with some embodiments. In particular, a top terminal  416 _ 1  of capacitor  412 _ 1  and a bottom terminal  420 _ 2  of capacitor  412 _ 2  are coupled to the same node  424 . 
         [0056]    Filters having temperature-compensated resonator may be used in a number of embodiments including, for example, a wireless communication device  500  as shown in  FIG. 5  in accordance with some embodiments. In various embodiments, the wireless communication device  500  may be, but is not limited to, a mobile telephone, a paging device, a personal digital assistant, a text-messaging device, a portable computer, a base station, a radar, a satellite communication device, or any other device capable of wirelessly transmitting and/or receiving RF signals. 
         [0057]    The wireless communication device  500  may have an antenna structure  504 , a duplexer  508 , a transceiver  512 , a main processor  516 , and a memory  520  coupled with each other at least as shown. 
         [0058]    The main processor  516  may execute a basic operating system program, stored in the memory  520 , in order to control the overall operation of the wireless communication device  500 . For example, the main processor  516  may control the reception of signals and the transmission of signals by the transceiver  512 . The main processor  516  may be capable of executing other processes and programs resident in the memory  520  and may move data into or out of memory  520 , as desired by an executing process. 
         [0059]    The transceiver  512  may include a transmitter  524  for transmitting RF signals, communicating outgoing data, through the duplexer  508  and antenna structure  504 . The transceiver  512  may additionally/alternatively include a receiver  528  for receiving RF signals, communicating incoming data, from the duplexer  508  and antenna structure  504 . The transmitter  524  and receiver  528  may include respective filters  532  and  536 . The filters  532  and  536  may have selected temperature-compensated resonator circuits to benefit the functions to which the respective filter is employed. For example, in some embodiments, the filter  532  may be similar to ladder filter  200 , while filter  536  may be similar to ladder filter  300 . 
         [0060]    In various embodiments, the antenna  504  may include one or more directional and/or omnidirectional antennas, including, e.g., a dipole antenna, a monopole antenna, a patch antenna, a loop antenna, a microstrip antenna or any other type of antenna suitable for OTA transmission/reception of RF signals. 
         [0061]    Although the present disclosure has been described in terms of the above-illustrated embodiments, it will be appreciated by those of ordinary skill in the art that a wide variety of alternate and/or equivalent implementations calculated to achieve the same purposes may be substituted for the specific embodiments shown and described without departing from the scope of the present disclosure. Those with skill in the art will readily appreciate that the teachings of the present disclosure may be implemented in a wide variety of embodiments. This description is intended to be regarded as illustrative instead of restrictive.