Patent Publication Number: US-6987488-B1

Title: Electromagnetic phase shifter using perturbation controlled by piezoelectric transducer and pha array antenna formed therefrom

Description:
CROSS-REFERENCE TO RELATED APPLICATION 
     This application claims benefit of U.S.C. § 119(e) of the provisional application having a title of “Tunable Circuits and Devices Controlled by Piezoelectric Transducers”, a filing date of Feb. 16, 2001, Ser. No. 60/269,569. 
    
    
     TECHNICAL FIELD OF THE INVENTION 
     This invention relates generally to electronic systems and more particularly to electromagnetic perturbation utilizing a piezoelectric transducer. 
     BACKGROUND OF THE INVENTION 
     Phase shifters are utilized to introduce a shift in phase of an electrical signal. There are many applications for the use of phase shifters in which shifting a phase in an electrical signal is desired. As one example, phase shifters are often used in antenna arrays. Other examples include timing recovery circuits and phase equalizers for data channels. 
     Antenna arrays may be designed with a plurality of antennas, each transmitting and receiving an electrical feed. Phase shifters are often used to introduce a phase shift into each of the feeds. The result of introducing phase shift into each of the feeds is a steering of the resulting beam projected by the antenna. Rather than utilizing an antenna that rotates or otherwise moves, the direction at which the antenna electrically points is affected by introducing phase shift into the feeds of the antennas. This is referred to as beam steering. 
     Many existing phase shifters suffer from various disadvantages. For example, many phase shifters are narrow band, meaning they can operate in only a narrow range of frequencies. In addition, such phase shifters are often high loss devices or provide only a small phase shift. Such devices include monolithic microwave integrated circuit, ferroelectric, solid-state, and photonically controlled phase shifters. Beam steering methods using a ferrite plate have been developed for low cost systems but require very high voltages up to several kV. One example of such a ferrite plate shifter requires impedance matching transformers to a polarization rotator for two dimensional arrays, large size lens, power consumption of 0.5 W, and forced air cooling. In addition these phase shifters are often expensive and inefficient. 
     SUMMARY OF THE INVENTION 
     Therefore, a need has arisen for an improved phase shifter and associated method. The present invention provides a system and method for introducting phase shift into an electric circuit, including phased array antennas and other devices. 
     According to one embodiment of the invention, an apparatus for introducing phase shift into an electric circuit includes a piezoelectric transducer configured to deflect in response to an applied voltage, a microstrip or other transmission line, and a perturber separated from the microstrip line by a gap and configured to deflect in response to deflection of the piezoelectric transducer. The deflection of the perturber causes a phase shift in an electric current flowing through the microstrip line. 
     According to another embodiment of the invention, a phased array antenna system includes an antenna array comprising a plurality of antennas, a plurality of microstrip lines connected in a one-to-one fashion with respective ones of the plurality of antennas, a perturber disposed proximate the plurality of microstrip lines, and a piezoelectric transducer coupled to the perturber such that deflection of the piezoelectric transducer causes deflection of the perturber with respect to the plurality of microstrip lines thereby introducing a phase shift in each of the microstrip lines. 
     Some embodiments of the invention provide numerous technical advantages. Other embodiments may realize some, none, or all of these advantages. For example, according to one embodiment, a piezoelectric transducer controlled multi-line phase shifter is provided that results in high bandwidth, low-loss, and large phase shift in a relatively inexpensive manner. Some embodiments do not require any impedance matching circuits, such as those found in ferrite plate shifters. Additional advantages of some embodiments include smaller size, lower power consumption (&lt;1 mw in one example) lower DC control voltage (approximately 60 volts in one example), and wider operating bandwidth due to a true time-delay type of phase shifting. The bandwidth of such a piezoelectric transducer phase shifter is very wide because the perturbation of the transmission line changes the phase in the transmission line but does not significantly affect its characteristic impedance. 
     Other advantages may be readily ascertainable by those skilled in the art and the following FIGURES, description, and claims. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       For a more complete understanding of the present invention and the advantages thereof, reference is now made to the following description taken in conjunction with the accompanying drawings, wherein like reference numbers represent like parts, and which: 
         FIG. 1A  is an isometric drawing of one embodiment of a phase shifter according to the teachings of the present invention; 
         FIG. 1B  is a cross-sectional drawing of a portion of the phase shifter of  FIG. 1A  showing an enlarged view of the perturber, the microstrip line, and the substrate of  FIG. 1A ; 
         FIG. 2  is an isometric drawing of a piezoelectric transducer according to a second embodiment of the invention utilizing a plurality of microstrip lines and a triangular perturber; 
         FIG. 3  is an isometric drawing of an E-plane phased array antenna according to yet another embodiment of the invention; 
         FIGS. 4A and 4B  are plan views of a single stripline-fed Vivaldi antenna that may be used with the invention; 
         FIG. 5  is an isometric drawing of an H-plane phased array antenna according to the teachings of the invention; and 
         FIG. 6  is an isometric drawing of a H-plane phase array antenna using two differently aligned piezoelectric transducer phase shifters according to the teachings of the invention. 
     
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     Embodiments of the invention and its advantages are best understood by referring to  FIGS. 1A ,  1 B,  2 ,  3 ,  4 A,  4 B,  5 , and  6  of the drawings, like numerals being used for like and corresponding parts of the various drawings. 
       FIG. 1A  is an isometric drawing of a piezoelectric transducer phase shifter  10  according to the teachings of the invention. Piezoelectric transducer phase shifter  10  includes a piezoelectric transducer  12  supported at one end  14  by a supporter  16 . Piezoelectric transducer phase shifter  10  also includes a perturber  18  coupled to piezoelectric transducer  12 . Piezoelectric transducer phase shifter  10  also includes a microstrip line  20  formed on a substrate  22 . Microstrip line  20  has a length  28 . Also illustrated is a test fixture  24  for supporting substrate  22  and the remainder of piezoelectric transducer phase shifter  10 . In this embodiment, piezoelectric transducer  12  is attached to a direct current voltage source (not explicitly shown) by electrical lines  26 . 
     In operation, a voltage is applied on electrical lines  26  to piezoelectric transducer  12 . Application of such a voltage causes piezoelectric transducer  12  to displace up or down at a free end  15 , as denoted by arrow  27 . This displacement in turn causes perturber  18  to also displace up or down. Displacement of perturber  18  with respect to microstrip line  20  disturbs the electromagnetic field around microstrip line  20 . This disturbance results, in this embodiment, in a phase shift in microstrip line  20 . The amount of this phase shift may be controlled by the proximity of perturber  18  with respect to microstrip line  20 , the distance at which perturber  18  is positioned along length  28  of the microstrip line, and other parameters as described below. In this manner, a selectable phase shift can be introduced into an electrical current running through microstrip line  20 , which may be used for a variety of purposes, including steering a phased antenna array. Other applications of utilizing a piezoelectric transducer to disturb an electromagnetic field in a conductor, transmission line, dielectric resonator, or other device in which a disturbance of an electromagnetic field surrounding the device is desired, referred to herein as target device, include tuning microwave circuits, tuning photonic bandgap resonators, tuning dielectric resonator oscillators, and other suitable applications. In such examples instead of the disturbance of the electromagnetic field generating a phase shift, the disturbance of the field results in a frequency change that is used for tuning purposes. 
     Additional details of this embodiment are described in conjunction with  FIGS. 1A and 1B .  FIG. 1B  is a cross-sectional drawing of a portion of piezoelectric transducer phase shifter  10  showing a GROUND, perturber  18 , microstrip line  20 , and substrate  22 . In the illustrated embodiment, perturber  18  is a dielectric perturber. GROUND of  FIG. 1B  is an electrical ground. According to one embodiment, piezoelectric transducer  12  ( FIG. 1A ) is a piezoelectric ceramic; however, other types of piezoelectrics may be used. According to one embodiment, piezoelectric transducer  12  is formed with a rectangular shape having dimensions of 2.75 inches by 1.25 inches by 0.085 inches and is formed from Lead Zirconate Titanate; however other dimensions, configurations, and materials may be used. The amount of deflection of piezoelectric transducer  12  depends on the applied voltage. In this embodiment, a voltage of between 0 and 90 volts is applied. At 90 volts, piezoelectric transducer  12  deflects downward 1.325 mm and at 0 volts no deflection occurs; however, piezoelectric transducer  12  may operate at different voltage levels and may deflect upward rather than downward in response to an applied voltage. 
     Supporter  16  may be formed from any suitable material that can mechanically support piezoelectric transducer phase shift  12 , such as a metal, dielectric, or insulator. The electrical characteristics of supporter  16  may be insulative or conductive. Piezoelectric transducer  12  may be coupled to supporter  16  by screws or any other suitable manner. 
     In this embodiment, perturber  18  has a dielectric constant of 10.8, a height  34  ( FIG. 1B ) of 0.050 inches, and a length  36  ( FIGS. 1A ,  1 B) of 1.8 inches; however, other dimensions and parameters may be used depending on the application. Generally, the induced phase shift in microstrip line  20  is proportional to the length of the perturbed length of microstrip line  20 . Therefore, to achieve greater phase shift, the length of perturber  18  is increased. Although perturber  18  is perturbed in the Z-axis ( FIGS. 1A ,  1 B) in this embodiment, perturber  18  may move horizontally in the Y-axis ( FIGS. 1A ,  1 B), or rotate. Forming perturber  18  from a dielectric material is advantageous because such perturbers result in low loss operation; however, perturber  18  may also be formed from a metal, or a metal-covered dielectric. Width  32  ( FIG. 1B ) of microstrip line  20  is designed in this embodiment to result in a high characteristic impedance of approximately 55 ohms to compensate for decreased characteristic impedance due to dielectric perturbation; however, other suitable characteristic impedances may be prescribed. Although in this embodiment perturber  18  is distinct from transducer  12 , perturber  18  may also be formed integral with, or as a part of, transducer  12 . 
     The use of microstrip line  20  is desirable because of the resulting quasi-transverse electromagnetic mode without cutoff frequency and its easy fabrication with no waveguide transition required. Other transmission lines, or conductors, may also be employed, including coplaner wave guides, coplaner strips, slot lines, and other transmission lines. In this embodiment, microstrip line  20  has a length  28  of 3 inches and a width  32  of 0.022 inches; however, other dimensions may be used. 
     Perturbation of the electromagnetic fields surrounding microstrip line  20  changes the distributed capacitance, which corresponds to a variation of the effective permitivity and propagation constant, and thus, results in a phase shift. The characteristic impedance of microstrip line  20  is only slightly affected by the perturbation and no additional impedance matching circuit is required for broadband operation. 
     Substrate  22  may be formed from any material operable to support microstrip line  20 ; however, according to one embodiment substrate  22  is formed from RT/DUROID 6010.8 with a dielectric constant of 10.8 and a height of 0.025 inches. 
     As illustrated in  FIG. 1B , an air gap  30  exists between dielectric perturber  18  and microstrip line  20 . This distance varies in response to displacement of perturber  18 . Air gap  30  may be any suitable distance; however, gaps in the range of 0 to 3 mm have been found to be particularly advantageous, with most phase shift occurring where air gap  30  is reduced to less than 0.5 mm. 
     The above description provides example dimensions and parameters that are meant only as examples. In general, it has been determined that a higher permitivity of substrate  22  and perturber  18  results in more desirable operation, such as greater phase shift and less loss. It is additionally desirable to provide a thicker perturber  18 . For example one particularly advantageous criteria for construction of perturber  18  is a thickness  34  that is at least twice as great as the thickness of substrate  22 . It has also been determined that a narrower strip width  32  and a thinner substrate  22  are desirable. In addition, having a higher permitivity of perturber  18  than that of substrate  22  in most cases tremendously increases the amount of phase shift. 
     Based on these criteria, it has been determined that a phase shifter having the general configuration shown in  FIGS. 1A and 1B  is particularly advantageous when formed with the following parameters: a permitivity of perturber  18  of 10.8, a height, or thickness  34 , of 0.010 inches, and a width  32  of microstrip line  20  of 0.005 inches. This results in a characteristic impedance in microstrip line  20  of 64 ohms at 40 gigahertz. In addition, in such an embodiment, substrate  22  has a metal thickness of 17 micrometers with a root-mean-squared surface roughness of 0.3214 micrometers. Such an embodiment also allows a reduced length piezoelectric transducer of 1.2, a lower maximum bias voltage on electric lines  26  of 30 V and better linearing. 
     Thus, a relatively low cost phase shifter is provided that results in desirable operation. The above-described phase shifters in one embodiment may provide phase shifts of 460° with an increased insertion loss of less than 2 dB and a total loss of less than 4 dB at 40 GHz. 
       FIG. 2  is an isometric drawing of a multi-line phase shifter  110  according to the teachings of the invention. Multi-line phase shifter  110  may be substantially similar to piezoelectric transducer phase shifter  10  ( FIGS. 1A ,  1 B) except in two respects. First, multi-line phase shifter  110  includes a plurality of microstrip lines  120  rather than a single microstrip line. Microstrip lines  120  are identified as microstrip line  142 , microstrip line  144 , microstrip line  146 , and microstrip line  148 . In the multi-line phase shifter  110  shown in this embodiment, perturber  118  is formed in the configuration of a triangle rather than a rectangle or square to effect a progressive phase shift; however, other configurations for perturber  118  may be used, including rectangular. In all other respects, multi-line phase shifter  110  is similar to piezoelectric transducer phase shifter  10  ( FIGS. 1A ,  1 B). In one embodiment, perturber  118  contacts microstrip lines  120  at progressive locations along the lengths of microstrip lines  120 , as shown in FIG.  2 . 
     Although the dimensions and physical characteristics of multi-line phase shifter  110  may vary according to desired outcome, particular parameters used in one instance are as follows. Substrate  122  is formed from RT/DUROID 5870, a high frequency laminate, with a dielectric constant of 2.33 and a height of 0.031 inches. Microstrip lines  120  each have a length of three inches and a width of 0.0917 inches. Perturber  118  is generally triangular with a dielectric constant of 60 and a thickness of 0.05 inches. 
     The resulting phase shift through any of microstrip lines  20  is proportional to the length over which perturbation occurs. Therefore, perturber  118  is designed to have a length over each microstrip line  120  that is equal to 0, 0.7, 1.4 and 2.1 inches, for microstrip lines  148 ,  146 ,  144 , and  142 , respectively. This triangular configuration for perturber  118  accomplishes differential phase shifting of 0, Φ, 2Φ, and 3Φ required for beamed steering, where (D is the desired progressive phase shift angle. 
     In operation, a voltage is applied on electrical wires  126 , which causes deflection of piezoelectric transducer  112 . This in turn causes an up and down perturbation of perturber  118 , resulting in the disturbance of the electromagnetic fields along microstrip lines  142 ,  144  and  146 . The field surrounding microstrip line  148  is substantially undisturbed because perturber  148  is designed to not interact with that field. As a result of the perturbation, a phase shift is introduced into microstrip lines  146 ,  144  and  142 . The magnitude of such phase shift is approximately proportional to the length of perturber  118  over the microstrip line. Therefore, microstrip lines  148 ,  146 ,  144 , and  142  exhibit a generally linear phase shift characteristic. 
     As described in greater detail below, multi-line phase shifters  10  and  110  may be utilized in combination with antenna elements to provide a phase-array antenna system that is controlled by the multi-line phase shifters. Such phased array antenna systems are described below in conjunction with  FIGS. 3 ,  4 A,  4 B,  5 , and  6 . 
       FIG. 3  is a perspective drawing of a phased-array antenna system  200  according to the teachings of the invention. Phased-array antenna system  200  includes a multi-line phase shifter  210 , which may be similar to multi-line phase shifter  110 , and an antenna system  250 , which may be steered by multi-line phase shifter  210 . Antenna system  250  includes a plurality of antennas  252 ,  254 ,  256 , and  258 . 
     Phase shifter  210  includes a piezoelectric transducer  212 , a supporter  216  at a first end  214  of transducer  212 , a perturber  218 , and a substrate  222  found with a plurality of microstrip lines  220 . Microstrip lines  220  involve microstrip lines  242 ,  244 ,  246 , and  248 . These components of piezoelectric transducer  212  may be substantially similar to the corresponding components in piezoelectric transducer  110 , described above. In this example, a connector  213  is utilized to attach perturber  218  to piezoelectric (transducer  212 ; however, in other embodiments piezoelectric transducer may attach to perturber  218  without such a connector or transducer  212  and perturber  218  may be formed integral with one another. Attaching structure  213  may be any suitable mechanical structure for coupling piezoelectric transducer  212  to perturber  218 . Attaching structure  213  may be electrically conductive or insulative. A power divider  270  may be used to provide power to microstrip lines  242 ,  244 ,  246 ,  248 . 
     In operation, phase shifter  210  introduces a progressive phase shift into microstrip lines  242 ,  244 ,  246 ,  248 , as described above in conjunction with phase shifter  110 . The progressive phase shifts result is a desired beam steering angle of antenna system  250 . 
     The parameters and dimensions of multi-line phase shifter  210  varying depending upon desired characteristics for phased-array antenna system  200 . A description of how to select such parameters is provided below. 
     One method for effecting beam steering of the beam angle in antenna system  200  is providing a progressive phase shift Φ by multi-line phase shifter  210 . Thus beam steering is accomplished by introducing a phase shift of O in microstrip line  248 , (in microstrip line  246 , 2Φ in microstrip line  244 , and 3Φ in microstrip line  242 . The amount of phase shift (varies according to the desired operation of antenna system  200 ; however, 30° of beam steering is one desirable amount. 
     The parameters of multi-line phase shifter  210  that produce a phase shift of 30° is determined as follows. First an antenna spacing is determined for antennas  252 ,  254 ,  256 , and  255  according to conventional techniques, such as be those described in R. C. Hansen,  Phased Array Antennas , New York: John Wiley &amp; Sons, 1998; P. H. Schaubert &amp; J. Shin, “Parameter Study of Tapered Slot Antenna Arrays,”  IEEE Int. Antennas and Propagat. Symp. Digest , Newport Beach, Calif., 1995, and P. H. Schaubert, “A class of E-plane scan blindness in single-polarized arrays of tapered-slot antennas with a ground plane,  IEEE Trans. Antenna Propagat , Vol. 44, No. 7, July 1996, which are hereby incorporated herein by reference. This spacing determination may include considering grating lobes, and scanning blindness. In this embodiment, an antenna element spacing of 0.340 inches is determined. 
     With a set antenna spacing the phase shift angle α is determined from the following equation: 
               θ   o     =       sin     -   1       ⁡     (     Φ       k   o     ·   d       )               (   1   )             
 
where θ o  is the beam scanning angle, d is the distance between two neighboring antenna elements, k o  is the propagation constant in the free space, and Φ is the progressive phase shift, using values of θ o =30°; d=0.340 inches. This results in a phase shift angle Φ of 51.5° at 10 gigahertz.
 
     Thus, the phase shift of perturbed microstrip line  146  with respect to the phase of unperturbed microstrip line  148 , called a differential phase shift, is 51.5°. The differential phase shifts of  144  and  142  are 103° and 154°, respectively. 
     In order to achieve this phase shift, the length of perturber  118  at the intersection of each of microstrip lines  120  may be selected according to the following description. The length of perturber  118  is calculated from the equation
 
ΔΦ n =L pert, n  ·Δβ n   (2) 
 
where ΔΦ n  is a differential phase shift, L pert, n  is the perturbed length, and a differential propagation constant Δβ n  is (β 4 -β pn ). In one embodiment, P 4  refers to a propagation constant of a fourth microstrip line. The fourth microstrip line&#39;s value is used as a reference to calculate Δβ n . Here β pn  is a perturbed propagation constant line n. In addition, Δβ n  is proportional to the frequency, and so is ΔΦ n . The non-linear frequency dependence of Δβ n , i.e. dispersion, is included in a variational calculation. Such analysis may be performed according to M. Kirsching and R. H. Jansen, “Accurate model for effective dielectric constant of microstrip with validity up to millimeter-wave frequencies,”  Electron. Lett ., Vol 18, no 6, pp. 272-273, Mar. 18, 1982; A. K. Verma and G. H. Sadr, “Unified dispersion model for multilayer microstrip line,”  IEEE Trans. Microwave Theory and Tech ., Vol. 40, No. 7, pp. 1587-1591, July 1992, which and hereby incorporated by reference.
 
     According to such analysis, microstrip lines  120  are formed on a RT/DUROID 6010.8 substrate  222  with a dielectric constant of 10.8 and thickness of 0.025 in. A high dielectric-constant of 10.8 is used for a substrate  222  of phase shifter  210  to reduce the length of phase shifter  210 . The distance between microstrip lines  242 ,  244 ,  246 ,  248  is the same as the antenna element spacing of 0.340 in. A total length of 2 inches for microstrip lines  242 ,  244 ,  246 ,  248  is sufficient to obtain the desired phase shifts for beam steering of 30°. A width  232  of 0.022 inches for microstrip lines  242 ,  244 ,  246 ,  248  is designed for a high characteristic impedance of 55 Ω to compensate for a decreased characteristic impedance due to dielectric perturbation. At the maximum perturbation, i.e. when the dielectric perturber is placed on the microstrip line, the characteristic impedance of microstrip lines  242 ,  244 ,  246 ,  248  is close to 50 Ω. 
     As described above, the particular dimensions and parameters used for the phase shifter may vary depending on application; however, the following dimensions and parameters were used in this embodiment. Dielectric perturber  218  has a dielectric constant of 10.8 and thickness of 0.050 inches. The length of perturber  218  at each microstrip line  242 ,  244 ,  246 ,  248  is varied linearly (0.6, 1.2, and 1.8 in). Piezoelectric transducer  212  has a size of 2.75 (length)×1.25 (width)×0.085 in 3  (thickness including supporter  214 ) with a composition of Lead Zirconate Titanate. Thus the total size of the phase shifter is 4×2 in 2 . A smaller size can be realized if a smaller piezoelectric transducer is available. 
     As shown, antenna array  250  comprises a plurality of antennas  252 ,  254 ,  256 ,  258  formed on substrate  222 . Therefore antenna array  250  is in the E-plane. E-plane refers to a plane parallel to the electric field of the radiation emitted by an antenna. 
     An advantage of the E-plane phased array antenna array  250  is its simple fabrication. Antenna array  250  may be fabricated on substrate  222 , the same substrate on which microstrip  220  is formed. In this example, antennas  252 ,  254 ,  256 , and  258  are microstrip-fed Vivaldi antennas. A strip line  260  ( FIG. 4 ) feeds the Vivaldi antennas. 
     As with substrate  122  of  FIG. 2 , substrate  222  is fabricated, in this embodiment, from RT/DUROID 5870 with a dielectric constant of 2.33 and thickness of 0.031 inches; however other suitable dimensions and parameters may be used. Selecting a substrate material with a higher dielectric it constant provides a larger phase shift as compared to one with a lower dielectric constant. Because a dielectric constant of 2.33 is relatively low, the length of substrate  222  and microstrip lines  242 ,  244 ,  246 , and  248  is 3 inches, rather than the 2 inches configuration of piezoelectric phase shifters  10  and  110  to compensate for the lower dielectric constant. In one embodiment power divider  270  has low loss and small amplitude and phase imbalance and operates at 20 GHz; however, other power dividers may be used. 
     To achieve a larger phase shift, perturber  218  is formed to have a higher dielectric constant of 6. As a side effect, this reduces the operating frequency of phase shifter  210 , in one embodiment, from 40 to 24 GHz because the higher dielectric constant perturber  218  produces not only a larger phase shift but also a higher loss. The total size of phased array antenna system  200  is 7.7 (length)×4.5 (width)×0.6 (height) in 3 , which is relatively small and therefore desirable. 
     Thus, an antenna system is provided that is steered by a relatively low cost phase shifter according to the teachings of the invention. 
       FIG. 4A  is a plan view and  FIG. 4B  is an end view of an example stripline-fed Vivaldi antenna  244 . As described in conjunction with  FIG. 3 , in this embodiment substrate  222  is RT/DUROID 5870 with a dielectric constant of 2.33 and thickness (t) of 40 mil, as shown in  FIG. 4B ; however other materials and parameters may be used according to the desired application. A transition part of antenna  244  has a strip line width (W ST ) of 29.4 mil, transition length of the strip line (L ST ) of 102.4 mil, slotline width (W SL ) of 7.87 mil, and transition length of the slot line (a) of 86.6 mil as shown in  FIG. 4A ; however other materials and parameters may be used according to the desired application. These parameters were determined from a full-wave analysis using the method of moment software having the name IE3D®, a simulation and optimization software solving current distribution of 3D and multilayer structures of general shape. In this embodiment, the length of strip line feeding and transition (L FT ) is 0.5 in, and the length of the exponentially tapered and round-end antenna (L A ) is 1.47 in (=1.25 λ o  at 10 GHz), and the rounded end design has a radius (R) of about 0.35 in and a height (H) of 1.5 in. The array operates over 8 to 26 GHz. 
       FIG. 5  is a perspective drawing of a phased array antenna system  300  according to the teachings of the invention. Phased array antenna system  300  is substantially similar to system  200  except that it includes a Vivaldi antenna array  350  oriented in the H-plane rather than the E-plane. H-plane refers to the plane of an antenna in which lies the magnetic field vector of linearly polarized radiation. 
     As shown in  FIG. 5 , the H-plane phased array antenna system  300  includes a power divider  360 , a progressive multi-line phase shifter  310 , and a round-end stripline-fed Vivaldi antenna array  350 . A direct vertical transition  370  between microstrip lines  320  and an antenna array  350  is much simpler and reduces the size and cost of the system since no extra connector is used. 
     Particular dimensions utilized in this embodiment, which may be varied according to application, are: the spacing between each antenna  342 ,  344 ,  346 ,  348  is designed to be 0.340 inches and is equal to the spacing of microstrip lines  320  in piezoelectric phase shifter  310 , and phased array antenna system  300  has a size of 4.6×4×1.75 in 3 . The stripline-fed structure gives a better cross-polarization characteristic than the microstrip line-fed one due to the symmetry. 
     Antenna system  300  operates in substantially the same manner as antenna system  200  of  FIG. 3 , but operates in the H-plane rather than the E-plane. Thus an antenna system that operates in the H-plane is provided that is controlled by a phase shifter constructed according to the teachings of the invention. 
       FIG. 6  is an isometric drawing of a bi-directionally steered phased array antenna system  400  controlled by a dual piezoelectric transducer phase shifter  410 . Antenna system  400  includes a stripline-fed Vivaldi antenna array  450  coupled to dual piezoelectric transducer phase shifter  410 . Dual piezoelectric transducer phase shifter  410  includes dual piezoelectric transducers  412   a ,  412   b  supported by respective supporters  414   a ,  414   b . Phase shifter  410  also includes perturbers  418   a ,  418   b  and a plurality of microstrip lines  420  found on a substrate  422 . Microstrip lines  420  include microstrip lines  442 ,  444 ,  446 , and  448 . Vivaldi antenna array  450  includes Vivaldi, or exponentially tapered slot, antennas aligned in the H-plane. Antenna system  400  also includes a power divider  460  for providing power to phase shifter  410  and antenna array  450 . 
     In this embodiment, phased array antenna system  400  is designed to operate over the X, Ku, K bands from 8 to 26 GHz; however, other suitable frequency ranges may be prescribed. Power divider  460  is a low loss and broadband 1×4 power divider and was designed using the Chebyshev 4 th  order transformations to operate from 2 to 29 GHz with a small phase difference of less than 4°; however, other suitable power dividers may be used. 
     Oppositely aligned piezoelectric transducers  412   a ,  412   b  are controlled, in this embodiment, by only one voltage supply. One is aligned for top-down perturbation and the other for bottom-up perturbation. Twin bias wires  426   a ,  426   b  of both piezoelectric transducers  412   a ,  412   b  are oppositely connected together. Thus if one piezoelectric transducer phase shifter is going down, the other one is going up simultaneously, and vice versa, by one control voltage. In one embodiment, the first and second transducers  412   a  and  412   b  are configured to deflect in opposite directions in response to a common applied voltage. 
     In operation, a voltage applied to lines  426   a ,  426   b  results in displacement of piezoelectric transducer  412   a  in one direction and  412   b  in the other. This results in a progressive phase shift in microstrip lines  442 ,  444 ,  446 ,  448  as described above in conjunction with FIG.  3 . However, the magnitude of such phase shift may double because while one perturber is displaced upward, the other is displaced downward. This results in a swing in phase shift between microstrip lines  442  and  448  of between a maximum negative value and a maximum positive value, rather than between zero and a maximum value. 
     Particular dimensions and parameters utilized in this example embodiment are provided below; however, other parameters and dimensions may be used. As described above, the amount of the differential phase shift can be maximized with a higher permitivity substrate  422  and perturber  418   a ,  418   b ; thicker perturber  418   a ,  418   b ; narrower strip width of microstrips  420 ; and thinner substrate  422 . The optimization results in a reduction of the required control voltage applied to lines  426   a ,  426   b  and an improvement of the linearity of the phase shifting versus frequency. 
     Additional particular dimensions and parameters utilized in this example embodiment are provided below; however, other parameters and dimensions may be used. In this embodiment, each perturber  418   a ,  418   b  has a dielectric constant of 10.8, thickness of 0.050 inches, and perturbation length of 1.2 inches on a substrate  422  having a dielectric constant of 10.8, thickness of 0.010 inches, and a line width of 0.005 inches; however, other suitable dimensions and parameters may be used. In this example, substrate  422  is RT/DUROID 5870 with a dielectric constant of 2.33, thickness (t) of 40 mil, and the stripline width of 29.4 mil, and the length of antenna is 1.47 in (=1.25 λ o  at 10 GHz). The round-end design has a radius of about 0.35 in and the height is 1.5 in. The total size of the system is 4×6 in 2 . A smaller size can be realized if a smaller piezoelectric transducer  412   a ,  412   b  is available. The four microstrip-lines of the piezoelectric transducer phase shifter are directly, perpendicularly connected to stripline-fed antennas so that extra connectors are unnecessary, and the system size and cost is thus reduced. 
     Antennas in antenna array  450  are spaced 0.010 inches from each other. This spacing is determined according to the procedure described above, and includes: considering grating lobes, and scanning blindness. To achieve 30° of beam steering, the progressive phase shift of each line is designed to be about 60° at 10 GHz. To obtain the maximum phase shift of 180° (=3×60°), the chosen perturbation length of the perturber is 1.8 in. The length of triangular dielectric perturber is varied linearly (0.6, 1.2, and 1.8 in) at each line. The Vivaldi antenna of this example embodiment operates from 8 to 26.5 GHz. A round-end Vivaldi antenna results in an improved return loss response. The stripline-fed structure gives a better cross-polarization characteristic than a single microstrip line-fed piezoelectric transducer due to the symmetry. 
     Thus, another embodiment at an antenna system that is controlled by a piezoelectric transducer is provided. 
     Although the present invention has been described with several example embodiments, various changes and modifications may be suggested to one skilled in the art. It is intended that the present invention encompass those changes and modifications as they fall within the scope of the claims.