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.

Longitudinal leaky SAW resonators and filters on YZ-LiNbO3.

The high-phase velocity (above 6100 m/s in an aluminum (Al) grating on lithium niobate (LiNbOs)) of the longitudinal leaky surface acoustic wave (SAW) (LLSAW) mode makes it attractive for application in high-frequency SAW ladder filters in the 2-5 GHz range. We investigate the dependence of one-port synchronous LLSAW resonator performance on YZ-LiNbO3 on the metallization thickness and metallization ratio, both experimentally and theoretically. Our results indicate a strong dependence of the Q factor and resonance frequency on the aluminum thickness, with the optimal thickness that produces the highest Q values being about 8%. The optimal thickness increases with the metallization ratio. The observed behavior is interpreted with the help of simulations using a combined finite element method (FEM)/boundary element method (BEM) technique. As an application, bandpass filters have been fabricated in the 2.8 GHz frequency regime, based on LLSAWs. The synchronous resonators constituting the ladder filters operate in the fundamental mode. The filters feature low insertion losses below 3 dB and wide relative passbands of 4.5-5%.

Low-loss, multimode 5-IDT SAW filter.

Longitudinally coupled resonator filters provide unbalanced-balanced operation with wide bandwidth, low loss, and high suppression levels. However, reducing the insertion loss in the 1.8-2.2 GHz range remains a challenging problem because at high frequencies the resistive losses arising from the relatively wide aperture of the filter may degrade the performance. A 5-interdigital transducer (IDT) filter has six gaps at which the periodicity of the grating is broken, resulting in additional loss due to scattering into the bulk. In this paper, we show that replacing the gaps between the transducers with short transducer sections having their pitch different from that of the main transducers reduces the insertion loss of the device. We present devices with balun operation at 1842 MHz with wide bandwidth of 4.5% and -40 dB suppression, with a minimum insertion loss less than 1 dB in the best devices, and a maximum insertion loss of -1.2 dB in the passband. The passband is quite flat, with <1 dB ripple. We also discuss the layout of the contact pads and the connections, and its effect on the device performance and balance characteristics.

Extraction of the SAW attenuation parameter in periodic reflecting gratings.

In this paper, the extraction of the coupling-of-modes (COM) model attenuation parameter gamma in a finite grating is considered. We use test structures comprising identical transmitting and receiving transducers and a grating centered in the acoustic channel along the propagation direction of the surface acoustic wave (SAW). The extraction procedure proposed is based on studying the magnitude of the ratio of the reflection and transmission coefficients of the grating, R/T, obtained through time gating from the S parameter measurements of the test devices. In particular, we found that the level of the notches of R/T directly depends on the attenuation of SAW in the grating. A simple closed-form expression for the attenuation normalized to the grating length, gamma lambda0, depending on the characteristics of absolute value R/T, is given. The proposed method is applied to the measurement data for selected grating topologies to yield estimates of the attenuation.

Quantum circuits for general multiqubit gates.

We consider a generic elementary gate sequence which is needed to implement a general quantum gate acting on n qubits-a unitary transformation with 4(n) degrees of freedom. For synthesizing the gate sequence, a method based on the so-called cosine-sine matrix decomposition is presented. The result is optimal in the number of elementary one-qubit gates, 4(n), and scales more favorably than the previously reported decompositions requiring 4(n)-2(n+1) controlled NOT gates.

Efficient decomposition of quantum gates.

Optimal implementation of quantum gates is crucial for designing a quantum computer. We consider the matrix representation of an arbitrary multiqubit gate. By ordering the basis vectors using the Gray code, we construct the quantum circuit which is optimal in the sense of fully controlled single-qubit gates and yet is equivalent with the multiqubit gate. In the second step of the optimization, superfluous control bits are eliminated, which eventually results in a smaller total number of the elementary gates. In our scheme the number of controlled NOT gates is O(4(n)) which coincides with the theoretical lower bound.

Short reflectors operating at the fundamental and second harmonics on 128 degree LiNbO3.

In this work, we study numerically the operation of surface acoustic wave (SAW) reflectors comprising a small number of electrodes on the 128 degree YX-cut lithium niobate (LiNbO3) substrate. The electrodes have a finite thickness, and they are either open circuited or grounded. The center-to-center distance between adjacent electrodes d corresponds roughly either to half of the characteristic wavelength d proportional to lambda0/2 or to d proportional to lambda0, for the reflectors operating at the fundamental and second harmonic modes, respectively. We use software based on the finite-element and boundary-element methods (FEM/BEM) for numerical experiments with a tailored test structure having 3 interdigital transducers (IDTs), simulating experimental conditions with an incident wave and reflected and transmitted SAWs. Using the fast Fourier transform (FFT) and time-gating techniques, calculation of the Y-parameters in a wide frequency range with rather a small step allows us to determine the reflection coefficients, and to estimate the energy loss due to bulk-wave scattering. The detailed dependences of the attenuation and reflectivity on the metallization ratio and the electrode thickness are given for the classic 128 degree-cut of LiNbO3.

Estimating materials parameters in thin-film BAW resonators using measured dispersion curves.

The dispersion curves of Lamb-wave modes propagating along a multilayer structure are important for the operation of thin-film bulk acoustic wave (BAW) devices. For instance, the behavior of the side resonances that may contaminate the electrical response of a thin-film BAW resonator depends on the dispersion relation of the layer stack. Because the dispersion behavior depends on the materials parameters (and thicknesses) of the layers in the structure, measurement of the dispersion curves provides a tool for determining the materials parameters of thin films. We have determined the dispersion curves for a multilayer structure through measuring the mechanical displacement profiles over the top electrode of a thin-film BAW resonator at several frequencies using a homodyne Michelson laser interferometer. The layer thicknesses are obtained using scanning electron microscope (SEM) measurements. In the numerical computation of the dispersion curves, the piezoelectricity and full anisotropy of the materials are taken into account. The materials parameters of the piezoelectric layer are determined through fitting the measured and computed dispersion curves.

Phases of the SAW reflection and transmission coefficients for short reflectors on 128 degree LiNbO3.

We study numerically the phase of surface acoustic waves reflected by or transmitted through short reflectors comprising only 1-3 aluminium electrodes on 128 degree YX-cut lithium niobate (LiNbO3). The electrodes have a finite thickness, and they are either open-circuited or grounded. The center-to-center distance between adjacent electrodes d corresponds roughly either to half of the characteristic wavelength d proportional to lambda0/2 or to d proportional to lambda0, for the reflectors operating at the fundamental and second harmonic modes, respectively. We use software based on the finite-element and boundary-element methods (FEM/BEM) for numerical experiments with a tailored test structure having 3 interdigital transducers (IDTs), simulating experimental conditions with an incident wave and reflected and transmitted surface acoustic wave (SAW). Using artificial enhancement of time resolution in conjunction with the fast Fourier transform (FFT) and time-gating, calculation of the Y-parameters in a relatively wide frequency range allows us to determine the phase of the reflection and transmission coefficients.

SPUDT filters for the 2.45 GHz ISM band.

Filters based on using single-phase, unidirectional transducers (SPUDT) consisting of lambda/4 and wider electrodes are presented. The design variants exploit the significant difference between the reflectivity of short-circuited lambda/4 electrodes and that of floating wide electrodes on 128 degree lithium niobate (LiNbO3). The surface acoustic wave (SAW) devices operating at 2.45 GHz have critical dimensions of about 0.3-0.4 microm, accessible to standard optical lithography. When matched, the fabricated SPUDT filters exhibit minimum insertion losses of 5.5-7.9 dB together with 3 dB passbands of 89-102 MHz. The majority of the insertion loss can be attributed to the attenuation on free surface and inside the grating, and to the resistivity of the electrodes.

Unidirectional SAW transducer for gigahertz frequencies.

A single-phase unidirectional transducer (SPUDT) structure using lambda/4 and wider electrodes is introduced. The considerable difference between the reflectivity of short-circuited lambda/4 electrodes and that of floating lambda/2-wide electrodes on 128 degree lithium niobate (LiNbO3) is exploited. The surface acoustic wave (SAW) device operating at 2.45 GHz has critical dimensions of about 0.4 microm, accessible for standard optical lithography.

Second-harmonic reflectors on 128 degrees LiNbO3.

In this work, we study theoretically the operation of long surface acoustic wave reflectors, comprising a large number of electrodes, at the fundamental and second harmonic frequencies on the 128 degrees LiNbO3 substrate for various electrode thicknesses and metallization ratios. Numerical simulations utilizing tailored test structures and time gating indicate that the reflectivity of the second-harmonic reflectors can be very high for certain geometries. Furthermore, our simulations suggest that inside the stopband the total losses for the second harmonic are of the same order as those for operation at the fundamental harmonic.

Optimal multiqubit operations for Josephson charge qubits.

We introduce a method for finding the required control parameters for a quantum computer that yields the desired quantum algorithm without invoking elementary gates. We concentrate on the Josephson charge-qubit model, but the scenario is readily extended to other physical realizations. Our strategy is to numerically find any desired double- or triple-qubit gate. The motivation is the need to significantly accelerate quantum algorithms in order to fight decoherence.