Modeling a longitudinally coupled dual-mode leaky-SAW resonator filter with enhanced upper-sideband suppression

Recently, it has been experimentally reported that enhanced upper-sideband suppression of a longitudinally coupled (first/third) dual-mode leaky SAW (LSAW) resonator filter may be obtained by incorporation of a selectively valued capacitor between input and output terminals. In this paper, coupling-of-modes (COM) and bandstop-filter modeling is applied to realize this enhanced suppression. Tradeoffs are examined between upper and lower sideband suppression levels caused by the ensuing capacitive coupling between input and output terminals. Good agreement is obtained between this theory and reported experimental results for an 800-MHz band cellular filter     

Transverse modes in one-port SAW resonators

The S(11) and equivalent S(21) frequency responses of a one-port surface acoustic wave (SAW) resonator with transverse modes derived from one-dimensional coupling-of-modes and transmission-matrix analysis. The two-dimensional nature of the problem is approximated by a summation of one-dimensional mode responses for each transverse mode. Comparison between theory and experimental data for a commercial 280-MHz one-port SAW resonator shows good agreement for the placement of transverse modes.     

A theoretical and experimental study of waveguide coupled SAWresonator filters

The coupling-of-modes (COM) formalism is extended to include coupled transducers and applied to the modelling of surface acoustic wave (SAW) coupled resonator filters. The models do not require the derivation of equivalent circuits and they accommodate finger reflections, electromagnetic feedthrough and external matching circuits. Frequency responses for waveguide-coupled devices are computed and compared to experimental results. Longitudinal mode profiles within the resonant cavities are presented     

Equivalent circuit modeling of coupled resonator filters

Using the stacked crystal filter (SCF) concept, a coupled resonator filter (CRF) can be interpreted as a device in which 2 piezoresonators are stacked on top of each other in such a way that a certain degree of acoustic interaction occurs. The work presented in this paper reports a novel all-electrical model for the CRF. The model associates acoustical coupling with an equivalent electrical coupling between resonators. The resulting equivalent circuit makes it possible to apply classical filter synthesis techniques directly based on the coupling control between resonators. It complements with a synthesis approach the analysis approach of the Mason model.     

Modelling the transverse-mode response of a two-port SAW resonator

An equation is derived for the transverse-mode frequencies of a two-port surface-acoustic-wave (SAW) resonator with uniform reflection gratings. It is postulated that only odd-order (symmetric) transverse modes should be excited in such a grating, due to its symmetrical placement with respect to the interdigital transducer (IDT). Frequency response modeling involves a summation of one-dimensional transmission-matrix computations for the fundamental mode and participating transverse ones. Excellent agreement is obtained between theory and experiment for a 360-MHz resonator with three close-in transverse modes, attributed to symmetric modes of odd order m=3, 5, 7.     

Modeling of bulk acoustic wave devices built on piezoelectric stack structures: impedance matrix analysis and network representation

The fundamental electro-acoustic properties of a solid layer are deduced in terms of its impedance matrix (Z) and represented by a network for modeling the bulk acoustic wave devices built on piezoelectric stacked structures. A piezoelectric layer is described by a three-port equivalent network, a nonpiezoelectric layer, and a short- or open-circuit piezoelectric layer by a two-port one. Electrical input impedance of the resonator is derived in terms of the Z-matrix of both the piezoelectric layer and an external load, the unique expression applies whether the resonator is a mono- or electroded-layer or a solidly mounted resonator (SMR). The loading effects of Al-electrodes on the resonating frequencies of the piezoelectric ZnO-layer are analyzed. Transmission and reflection properties of Bragg mirrors are investigated along with the bulk radiation in SMR. As a synthesizing example, a coupled resonator filter (CRF) is analyzed using the associated two-port equivalent network and by calculating the power transmission to a 50Omega-load. The stacked crystal filter is naturally included in the model as a special case of CRF. Combining a comprehensive matrix analysis and an instructive network representation and setting the problem with a full vectorial formalism are peculiar features of the presented approach.     

Analysis Technique for Asymmetrically Coupled Resonator Structures

Asymmetrical acoustically coupled structures are present in several acoustic applications. Specifically when they are used in filter design, some configurations provide unexplored and special response characteristics with high selectivity and relatively wide bandwidths. The relationships between geometries, configurations, and response specifications do not rely on a direct link. In this work, a novel approach to the analysis of these structures is presented as well as a model of an asymmetrical bulk acoustic wave coupled resonator filter obtained from the analysis presented.     

Idealized analysis of SAW longitudinally coupled resonator filters

A surface acoustic wave (SAW) longitudinally coupled resonator (LCR) filter consists of either two or three interdigital transducers located between two strongly reflecting gratings. The behavior of this structure is, in general, very complex because the transducers are of the single-electrode type, which gives strong electrode reflections. It is shown here that, for the filter passband, a number of realistic assumptions can be used to derive a very simple set of approximate relations for the device Y-matrix. The simplifications involve reciprocity, symmetry, and power conservation. The theory also uses the necessary fact that each grating, combined with its adjacent transducer, must have high directivity so that application of a voltage results in wave generation primarily toward the center of the device. For a three-transducer device, it is shown using symmetry that the central transducer behaves as if it were transparent, despite having strong electrode reflections. Hence, the device behaves as a single resonant cavity. The simple Y-matrix formulae are shown to agree very well with accurate results obtained by a coupling-of-modes (COM) analysis for both types of device. They also lead to simple formulae for the electrical loading required to obtain a flat, low-loss filter response. Equivalent circuits also are discussed.     

Ultra-miniature coupled resonator filter with single-layer acoustic coupler

Coupled resonator filters designed using a singlelayer coupler require coupling materials with an acoustic impedance less than 5.0 MRayl. Carbon-doped oxide, with an acoustic impedance of 4.8 MRayl and an acoustic attenuation of 200 to 600 dB/cm at 1 GHz, can be used as a single-layer coupler to produce a competitive 2-stage coupled resonator filter for cellular handset applications in the gigahertz frequency range. The electrical response of our filter is superior to that of coupled resonator filters using a traditional acoustic mirror as the coupling element. We present an ultra-miniature 0.58 mm x 0.38 mm coupled resonator filter operating at a frequency of 2.15 GHz.     

Fast,precise, and full extraction of the COM parameters for multielectrode-type gratings by periodic Green's function method

It is very important to extract all four coupling-of-modes (COM) parameters of the electrode cells for the simulation and optimal design of a low loss surface acoustic wave (SAW) filter. A new approach for fast and full extraction of the COM parameters for a multielectrode-type grating is proposed. The field distribution of the wave under the periodic shorted grating is calculated by the periodic Green's function method. The phase of the reflection is determined from the positions of the standing wave node. The transduction coefficient and its phase are determined by the charge distribution at low frequency. The COM parameters of the commonly used electrode width controlled (EWC) single phase unidirectional transducer (SPUDT) is computed. It shows that this is a simple and direct way to extract all the COM parameters for SPUDT and, accordingly, is a powerful tool for the optimization of the filter structure.     

Very small IF resonator filters using reflection of shear horizontal wave at free edges of substrate

A conventional surface acoustic wave (SAW) resonator filter requires reflectors consisting of numerous grating fingers on both sides of interdigital transducers (IDTs). On the contrary, it is considered that small-sized and low loss resonator filters without reflectors consisting of grating fingers can be realized by exploiting this characteristic of the shear horizontal (SH) wave or the Bleustein-Gulyaev-Shimizu (BGS) wave. There are two types of resonator filters: transversely coupled and longitudinally coupled. No transversely coupled filters (neither conventional nor edge-reflection) using the SH wave on a single-crystal substrate have been realized until now, because two transverse modes (symmetrical and asymmetrical modes) are not easily coupled. However, the authors have realized small low loss transversely coupled resonator filters in the range of 25 to 52 MHz using edge reflections of the BGS wave on piezoelectric ceramic (PZT: Pb(Zr,Ti)O/sub 3/) substrates for the first time by developing methods by which the two transverse modes could be coupled. Also the authors have realized small low loss longitudinally coupled resonator filters in the range of 40 to 190 MHz using edge reflection of BGS or SH waves on PZT or 36/spl deg/-rotated-Y X-propagation LiTaO/sub 3/ substrates for the first time. Despite being IF filters, their package (3/spl times/3/spl times/1.03 mm/sup 3/) sizes are as small as those of RF SAW filters.     

STW in-line acoustically coupled resonator filter on quartz

The scattering-matrix method was used for design of a surface transverse wave (STW) in-line acoustically coupled resonator filter on quartz. In this filter, two one-port STW resonators were coupled by means of a center reflector, grating phase shifters were placed between interdigital transducers and reflectors, and the pass band of the filter was located near the center frequency of the reflectors. At a frequency of about 509 MHz, insertion loss of about 5 dB and a 3 dB bandwidth of about 0.23 MHz was obtained. Differences between the measured and calculated amplitude responses are explained and design guidelines are presented. High STW velocity, low insertion loss, and very weak transverse mode make this filter attractive for high-frequency applications.     

SAW filters based on parallel-connected coupled resonator filters with offset frequencies

The concept of coupled resonators is applied to synthesize surface acoustic wave filters. Employing two parallel-connected filter tracks, with a frequency shift imposed between them, a wide passband with low insertion loss together with well-controlled rejections is achieved. The operation of the two-track device is based on the mutual interaction of the individual transfer functions for the pair of tracks. Each track serves to contribute a part of the passband, enabling a wide band. Outside of the passband, the signals passing through the two channels may cancel each other, thus facilitating efficient control over the rejections. However, obtaining rejection stopbands at just the predetermined frequencies requires precise values for the materials parameters and a reliable fabrication process. Prototype devices fabricated with this approach are demonstrated both on quartz and, for the first time, on 42 degrees-LiTaO3. Results for two-track devices having either two or three transducers per track and operating either single-ended or with a balanced output are presented. The devices are designed employing the coupling-of-modes model and transmission-matrix approach, and the separate tracks are optimized simultaneously and independently. The center frequencies are 868 MHz and 1960 MHz. On quartz, a minimum insertion loss of 4 dB and a passband width of 0.23% are achieved at 868 MHz. On 42 degrees-LiTaO3, the corresponding figures of merit are 1.3 dB for minimum insertion loss and 4.1% bandwidth at 1960 MHz. The filters on 42 degrees-LiTaO3 also have remarkably flat passbands.     

Orthogonal frequency coded filters for use in ultra-wideband communication systems

The use of ultra-short pulses, producing very wide bandwidths and low spectral power density, are the widely accepted approach for ultra-wideband (UWB) communication systems. This approach is simple and can be implemented with current digital signal processing technologies. However, surface acoustic wave (SAW) devices have the capability of producing complex signals with wide bandwidths and relatively high frequency operation. This approach, using SAW based correlators, eliminates many of the costly components that are needed in the IF block in the transmitter and receiver, and reduces many of the signal processing requirements. This work presents the development of SAW correlators using orthogonal frequency coding (OFC) for use in UWB spread spectrum communication systems. OFC and pseudonoise (PN) coding provide a means for UWB spreading of data. The use of OFC spectrally spreads a PN sequence beyond that of code division multiple access (CDMA) because of the increased bandwidth providing an improvement in processing gain. The transceiver approach is still very similar to that of a CDMA but provides greater code diversity. Experimental results of a SAW filter designed with OFC transducers are presented. The SAW correlation filter was designed using seven contiguous chip frequencies within the transducer. SAW correlators with a 29% fractional bandwidth were fabricated on lithium niobate (LiNbO3) having a center frequency of 250 MHz. A coupling-of-modes (COM) model is used to predict the SAW filter response experimentally and is compared to the measured data. Good correlation between the predicted COM responses and the measured device data is obtained. Discussion of the design, analysis, and measurements are presented. The experimental matched filter results are shown for the OFC device and are compared to the ideal correlation. The results demonstrate the OFC SAW device concept for UWB communication transceivers.     

Coupled resonator distributed-element circuits for monolithic crystal filters

The distributed-element equivalent circuit of the monolithic crystal filter is useful for analyzing the characteristics of the filter, but it is not suitable for physical interpretation of the filter behavior. A more refined coupled resonator circuit is derived by application of a sequence of transformations of the original distributed-element circuit. The frequency dependences of the circuit elements are discussed and some approximations of the equivalent circuits are introduced based on the discussion. Moderately wideband filters are designed using an approximate circuit.     

Coupling-of-modes analysis and modeling of polymer-coated surface acoustic wave resonators for chemical sensors

The analysis and modeling of SAW resonator devices based on the coupling-of-modes (COM) theory are described, integrating the effect of polymer coating so that the sensor effects can be accounted for in the device transfer function. Based on the perturbation method, the effects of film coating are included in determining the parameters for the model. The COM parameters are, therefore, modified and its simple analytical approaches are presented. The model is validated using the experimental data of a two-port SAW resonator device fabricated on ST-X quartz substrate. The experimental results for a device coated with Parylene C are compared with the simulation results of the proposed model. The comparative results of the electrical characteristics and the frequency sensitivity to film thickness show a good agreement which proves the validity of the model. This analysis and model will provide insight into the influence of the device design parameters on the sensor performance and help in practical design and optimization of SAW-based chemical sensor systems.     

Mechanically coupled CMOS-MEMS free-free beam resonator arrays with enhanced power handling capability

Integrated CMOS-MEMS free-free beam resonator arrays operated in a standard two-port electrical configuration with low motional impedance and high power handling capability, centered at 10.5 MHz, have been demonstrated using the combination of pull-in gap reduction mechanism and mechanically coupled array design. The mechanical links (i.e., coupling elements) using short stubs connect each constituent resonator of an array to its adjacent ones at the high-velocity vibrating locations to accentuate the desired mode and reject all other spurious modes. A single second-mode free-free beam resonator with quality factor Q > 2200 and motional impedance R(m) < 150 kΩ has been used to achieve mechanically coupled resonator arrays in this work. In array design, a 9-resonator array has been experimentally characterized to have performance improvement of approximately 10× on motional impedance and power handling as compared with that of a single resonator. In addition, the two-port electrical configuration is much preferred over a one-port configuration because of its low-feedthrough and high design flexibility for future oscillator and filter implementation.     

Properties of regular polygons of coupled microring resonators

The resonant properties of a closed and symmetric cyclic array of N coupled microring resonators (coupled-microring resonator regular N-gon) are for the first time determined analytically by applying the transfer matrix approach and Floquet theorem for periodic propagation in cylindrically symmetric structures. By solving the corresponding eigenvalue problem with the field amplitudes in the rings as eigenvectors, it is shown that, for even or odd N, this photonic molecule possesses 1 + N/2 or 1+N resonant frequencies, respectively. The condition for resonances is found to be identical to the familiar dispersion equation of the infinite coupled-microring resonator waveguide with a discrete wave vector. This result reveals the so far latent connection between the two optical structures and is based on the fact that, for a regular polygon, the field transfer matrix over two successive rings is independent of the polygon vertex angle. The properties of the resonant modes are discussed in detail using the illustration of Brillouin band diagrams. Finally, the practical application of a channel-dropping filter based on polygons with an even number of rings is also analyzed.