we have discovered that a remarkable improvement in the performance of a piezoelectric transformer can be achieved when the piezoelectric element is formed from a single crystal of a relaxor ferroelectric material . rosen - type transformers according to the invention have demonstrated five to six times the output power density of standard polycrystalline equivalents . generally , any of the various shapes and configurations of transformers developed since rosen ( e . g ., a multi - layer rosen - type transformer as described in u . s . pat . no . 5 , 872 , 419 , a single layer or multi - layer thickness mode vibration transformer as described in u . s . pat . no . 5 , 341 , 061 , or a high displacement bending type as described in u . s . pat . no . 6 , 114 , 797 ) may be improved by use of single crystal material . however , the material must be cut and electroded appropriately to take advantage of its higher piezoelectric coupling coefficients and more strongly coupled mechanical properties . relaxor piezoelectric materials include , for example , pb ( zr 1 - x nb x ) o 3 — pbtio 3 ( pzn - pt ) and pb ( mg 1 - x nb x ) o 3 — pbtio 3 ( pmn - pt ), and are described in detail in park & amp ; shrout , “ characteristics of relaxor - based piezoelectric single crystals for ultrasonic transducers ,” ieee trans . on ultrasonics , ferroelect . and freq . control , 44 ( 5 ): 1140 - 1147 ( september 1997 ), which is incorporated herein by reference . to illustrate the difference between polycrystalline and single crystal piezoelectric material , tables 1 and 2 list selected characteristics of each for some pzn - pt compositions . note the generally higher coupling coefficients of single crystal material , and the highly coupled compliance and modulus ( as evidenced by the ratio of the 13 terms to the 33 terms ). table 2 shows that the mechanical q of the single crystal material is not as good as the electrical q , and comparatively not as good as hard polycrystalline piezoelectric material . it also shows that the dielectric strengths can be much higher than hard materials . in single crystal relaxor compositions , lower loss factors ( higher mechanical q &# 39 ; s ) are generally exhibited in the harder compositions , such as the pmn - pt series . the single crystal properties of tables 1 and 2 are representative of a particular single crystal material , pzn - 4 . 5 % pt , cut in a nominal & lt ; 100 & gt ; direction and poled parallel and transverse to that cut . data provided by trs ceramics show even higher dielectrics and coupling factors for pmn - 33 % pt single crystal material . to date , typical transformers have been produced from hard polycrystalline piezoelectric compositions , because their extremely high mechanical q &# 39 ; s improve voltage gain . however , because of these materials &# 39 ; relatively low dielectric strengths , it is difficult to get energy into and out of the material . in contrast , we have found that single crystals are 7 - 10 times as compliant , but exhibit an equivalent directional modulus , and generally exhibit mechanical q &# 39 ; s of around 50 . these transmission q &# 39 ; s are on par with soft polycrystalline compositions , and therefore , standing alone , would seem to imply inferior performance . however , it is much easier to get energy into the single crystal piezoelectric material , to couple it to mechanical energy and back to output electrical energy , and to extract it from our device . in contrast to the polycrystalline ceramics , single crystal devices typically show slightly lower voltage gains but offer even higher current throughput capability ( are matched by lower output electrical impedances ), thus providing greater power density . gain and current output are both functions of design , including geometry , poling , and other factors which will be apparent to one of ordinary skill in the art . equivalent voltage gains to those of polycrystalline transformers can be achieved by the devices of the invention , but they will have different output impedances from similarly constructed prior art devices , which those of ordinary skill in the art will be able to accommodate with circuit designs . one design tailored to the use of our innovative transformer is described in the copending and commonly owned application of masters , et al ., “ tuned power ignition system .” fig1 shows a piezoelectric transformer according to the invention . the illustrated transformer is of the rosen type , but other known configurations of piezoelectric transformers , may also be used . ( a wide variety of piezoelectric transformer configurations are known in the art . for example , transformer designs suitable for use with the invention are disclosed in u . s . pat . nos . 5 , 118 , 982 ; 5 , 229 , 680 ; 5 , 241 , 236 ; 5 , 278 , 471 ; 5 , 402 , 031 ; 5 , 424 , 602 ; 5 , 504 , 384 ; 5 , 675 , 208 ; 5 , 757 , 106 ; 5 , 814 , 922 ; 5 , 834 , 882 ; 5 , 894 , 185 ; 6 , 215 , 227 ; and 6 , 278 , 227 , all of which are incorporated herein by reference ). single crystal relaxor ferroelectric piezoelectric element 10 is coupled to input electrodes 12 and output electrodes 16 . the electrodes may be , for example , gold patches plated onto the ceramic piezoelectric element . the piezoelectric element is polarized in the two regions as shown by arrows . the device of fig1 is excited by electrical input at frequencies near the second axial resonance mode of the ceramic construction . since the device is piezoelectric , this mechanical resonance mode is coupled to the electrical ( and thermal ) characteristics of the device and therefore has varying frequency with varying output electrical load . the use of the single crystal element allows lower impedance output loads to be used with a high power density . typical prior art piezoelectric ceramic transformers are capable of generating a maximum around 300 w / in 3 , while we have demonstrated that a single crystal transformer of a relaxor ferroelectric material can generate power densities as high as 1 . 8 kw / in 3 . fig2 - 4 show further suitable transformer configurations . in each case , a relaxor piezoelectric element 10 is coupled to input electrodes 12 and output electrodes 16 , and polarized as indicated by arrows . each of these transformer configurations will have different electrical and mechanical properties , and are suitable for different applications . the transformer shown in fig2 operates in extensional mode , and has the advantage that the entire piezoelectric element is poled in a single direction . the transformer shown in fig3 operates by expanding radially , and has a circular shape that may be advantageous in some situations . the transformer shown in fig4 represents an improvement upon the general shape shown in fig3 tending to produce a more balanced vibration , since the input electrodes are more symmetrically placed . it has been proposed in u . s . pat . no . 5 , 229 , 680 to sato et al . to use a single crystal linbo 3 piezoelectric in a transformer . linbo 3 is not a relaxor material , and its single crystal exhibits an increased mechanical q as compared to the polycrystalline material . thus , the substitution of a single crystal for a polycrystal in a linbo 3 transformer follows the conventional wisdom of the art in attempting to increase q in order to improve performance . our invention , in contrast , uses a material that exhibits a lower q , but nevertheless exhibits improved performance because of its greater coupling coefficients and dielectric constant . domain texturing and optimal crystallographic cuts can benefit the operation of transformers according to the invention much as they do in specific quartz and linbo 3 cuts for optimal thermal and acoustic performance . measurement of the directional properties of relaxor ceramics is a topic of continuing research . those of ordinary skill in the art will understand how to use published data on texture effects on mechanical q and transmission directions to optimize particular transformer designs . precision cutting of piezoelectric ceramics to form complicated transformer geometries with particular crystallographic textures can be performed as described in commonly owned u . s . pat . no . 6 , 337 , 465 to masters et al ., which is incorporated by reference herein . other embodiments of the invention will be apparent to those skilled in the art from a consideration of the specification or practice of the invention disclosed herein . it is intended that the specification and examples be considered as exemplary only , with the true scope and spirit of the invention being indicated by the following claims .