Several new techniques, d i e l e c t r i c resonators, SAW resonatcrs, skimming mode b u l k a c o u s t i c resonators and h i g h overtone b u l k a c o u s t i c wave (PAW) rescnators a r e k i n g advanced f o r low noise s t a b i l i z a t i o n of vicrowave s i g n a l sources.
Ultra-high Q, X-band resonators, used in a frequency discriminator for stabilization of a low-noise signal generator, can provide a means of obtaining significant reduction in phase noise levels. Resonator unloaded Qs on the order of 500 K can be obtained in sapphire dielectric resonator (DR) operating on a low-order (i.e. TE(01)) mode at 77 K and employing high-temperature superconducting (HTS) films installed in the DR enclosure covers. Rigorous analysis for the determination of resonator frequency, modes, and unloaded Q have been carried out using mode matching techniques. Trade-off studies have been performed to select resonator dimensions for the optimum mode yielding highest unloaded Q and widest spurious mode separation. Field distributions within the resonator have been computed to enable practical excitation of the required mode. The results of both analysis and prototype device evaluation experiments are compared for resonators fabricated using enclosures consisting of conventional, metal sidewalls and covers employing HTS films as a function of cover conductivity.
The high overtone bulk acoustic resonator (HBAR) provides the basis for stable microwave sources. The HBAR's high Q, closely spaced, periodic resonances provide stabilization for multiple frequency microwave sources. Recently an L-band source with 5 MHz channels has been developed. This HBAR source has phase noise performance equivalent to that of sources based on low frequency quartz crystal stabilization and multiplication, but it requires only a fraction of the hardware.The resonators are fabricated by depositing film transducers on the resonator cr ystaf such as YAG, sapphire, lithlum niobate, or fithium tantalate. The low-loss material of the crystal gives a Q approximately 10 times that of quartz. Resonators have been fabricated at frequencies as high as 10 GHz and have achieved Q's in excess of 65,000 at 1.5 GHz using the compressional mode. Tuning of the resonators has been achieved by deposition of mass loadlng materials such as sificon dioxide. Tuning to within 1 kHz of a standard using an active feedback system during deposition has been accomplished. The resonator is assembled into a rigid housing that minimizes the ef feet of external vibration on the resonator. Vibration sensitivity of 1 x 10 -1l/g has been measured.
An approximate theory w i l l be discussed for the determination of acceleration sensitivity of a high overtone yttrim al&m garnet (YAG) bulk mode resonator plate operating directly a t micrcnuave frequencies. The high overtone bulk acoustic resonator f a c i l i t a t e s i m p l e n t a t i o n of l c n u phase noise multiple freqwncy microwave sources with much less hardware than has been required by other mans. Details of the oscillator design and tests are d i s a s s e d i n a c a r panion paper, see r e f e r e n e l .The vibration sensit i v i t y is treated both analytically and experimntally in this paper.Electrical masuremnts *re performed on a YAG bulk mode resonator device in both quiescent and vibrating states. The ccmputed value for the -11 acceleration sensitivity (K) of approxirrately 4x10 /G canpared favorably w i t h the tested value of 1.28xlO-'l/G. The masured value for the bulk d e plate is about two orders of magnitude less sensitive to m t i o n than a typical 3 pint AT cut quartz crystal. I N T w l D u c T I C NIn radar applications of oscillator devices, vibration will cause frequency d u l a t i o n (FM) of the resonator. The FM, i f excessive, will produce noise sidebands of sufficient magnitude t o n-ask real targets during radar operation. The degree of sensitivity of the oscillator to vibration is primarily dependent u p n the acceleration sensitivity (K) of the resonator.The resonator is driven by very thin, on the order of 4000a, ZnO transducers. "he problem of d e f o m t i o n ( s t r a i n ) is solved i n terms of its relationship to the frequency equation in the transpnded direction. Several simple formulas are obtained relating elastic deformtion to the acceleration sensitivity. &termination of the strain w a s achieved by f i r s t calculating the plate stresses. A brief description of the mthod for determining the plate stresses w i l l a l s o be included in the discussion which f o l l m . A N A L Y T I C A Z , APPFUIACHFor this analysis the plate w a s assunEd to be isotropic. It w a s further assumed t h a t the plate w a s fixed a t its interface with the munting preform, on three sides, as depicted in figures 1 and 2. The e l e c t r i c a l l y active area is about 8~1 O -~i n .~ ' Ihe problem of deformation caused by vibration of the resonator plate is solved in terms of its relaticnship to the frequency equation in the trans-(2) direction. The resonator frequency is 2t (1)where Vz is the velocity in the z direction and t is the initial plate thickness.The acceleration sensitivity is strain dependent and is caused primarily by the stresses that are developed a t the plate surfaces, i.e., a t the transducer munting surfaces, during vibration. I n terms of elastic constants, the generalized Hmke's law for strain in t h e t r a n s p d e d direction may be written asA t i s the change in thickness caused by the n o m 1 stresses Sx, S and S?., E is the d u l u s of e l a s t i c i t y and A i s Poisson's ratio. Once the plate is stressed equation 1 b e m s Y me + or -no...
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