Alexandru Gabriel Gheorghe

New Nonlinear Circuit Models for Power BAW Resonators

New nonlinear circuits, modeling both the amplitude-frequency effect and the intermodulation effect are described. One model is validated using the measured dependence of the series resonance frequency on the incident power.

Circuit models for power BAW resonators - set-up and implementation

A critical description of the known models of power BAW resonators is presented. It is shown that behavioral models must be preferred to the physical ones and that linear parametric models cannot be implemented in commercial circuit analysis programs. New nonlinear circuits, modeling both the amplitude- frequency effect and the intermodulation effect are briefly decsribed.

An A.C. linear parametric behavioral model of a nonlinear BAW resonator

A new method for the parameter identification of a behavioral model of a nonlinear BAW resonator is proposed. This model contains two parametric elements whose resistance and capacitance depend on the r.m.s. value of the input current. The identification procedure is simpler than that corresponding to the known physical models. The model of a quartz resonator is built and implemented in the APLAC simulator.

Modeling and Simulation of Piezoelectric Devices

The piezoelectric effect occurs in materials for which an externally applied elastic strain causes a change in electric polarization which produces a charge and a voltage across the material. The converse piezoelectric effect is produced by an externally applied electric field, which changes the electric polarization, which in turn produces an elastic strain. The most known piezoelectric material is quartz crystal. Many other natural crystalline solids, as Rochelle salt, ammonium dihydrogen phosphate, lithium sulfate, and tourmaline as well as some man-made crystal as gallium orthophosphate, aluminium nitride (AlN), and langasite exhibit piezoelectric properties. A lot of artificial ceramics as barium titanate, lead titanate, lead zirconate titanate (PZT), potassium niobate, lithium niobate, and lithium tantalite have similar properties. The most known technical application is the piezoelectric transducer. In the last years electromechanical AlN resonators emerged as a very efficient solution for mobile communications filters due to the possibility to be integrated at a relatively low cost together with CMOS circuits in systems on a chip and systems in a package. In most applications the piezoelectric devices have a linear behaviour. In Section 2 the linear and nonlinear equations of the piezoelectric effect are described, a new iterative procedure for solving the nonlinear equations is given, and some aspects of the Finite Element solution are discussed. An electromechanical field analysis of a displacement transducer is presented in Section 3. Sections 4 and 5 show some recent applications in the mobile communication technology. The field analysis of a bulk acoustic wave (BAW) resonator using 3D linear models is presented in Section 4. Some nonlinear effects in power BAW resonators together with their circuit models are discussed in Section 5.

Pole/Zero Computation for Linear Circuits

An algorithm able to compute both the numerical values and the approximate symbolic expressions of poles and zeros of a circuit function is analyzed. At least for the given example, the numerical values obtained with this algorithm prove to be more accurate than those computed by HSPICE, SPECTRE and SAPWIN. The approximate symbolic pole expressions are also computed for this example. A comparison with known algorithms for the computation of the approximate pole/zero expressions as ANALOG INSYDES and SYMBA is performed. It follows that the symbolic LR algorithm, used in the proposed program, performs less drastic simplifications than the procedures used in ANALOG INSYDES and SYMBA. Difficulties arising in the computation of the approximate pole/zero expressions are discussed as well as some future developments in this area.

Measurement and modeling of nonlinear effects for power BAW filters with AlN

Two six-resonator power BAW filters using anti-series and anti-parallel connected resonators are measured, proving that the amplitude of the 2f component in the output power is very small. A behavioral model of a three-resonator power BAW filter is discussed.

Improved LR algorithm for computation of the approximate symbolic pole/zero expressions

The following improvements are made to the symbolic LR algorithm for the computation of the approximate pole/zero expressions: formulation of the “state-like” matrix in the case d=0 in the output equation by the implementation of the Sandberg-So and Davison algorithms, using of matrices so that their diagonal elements are not placed in the decreasing order of their modules, replacing the search for the eigenvalue clusters with the elimination of one or two line and column pair during symbolic LR iterations. The zero symbolic expressions in term of transistor parameters for a LNA in the 900 MHz band illustrates these improvements. The proposed algorithm is similar or better with respect to the best ones implemented in ANALOG INSYDES and SYMBA software packages.

Error control in circuit transient analysis

The frequency warping error occurring in transient circuit analysis and the manner to control it are revisited. A new algorithm for the time step choice, based on an energy balance error, is proposed. An example shows that this new algorithm rejects fewer time steps than the SPICE one.

A new approach to the computation of reduced order models for one-port and two-port RC circuits

A method for the computation of a reduced order circuit model, based on the approximation of |Y(jomega)| with a set of assymptotes corresponding to a simple RC admittance is presented. The circuit passivity is preserved unlike the majority of other approaches. A 1033 node RC circuit is reduced to admittance with one pole and two zeros for a frequency range of three decades

A new behavioral model for frequency domain analysis of power BAW filters

A new behavioral model for frequency domain analysis of power bulk acoustic wave (BAW) filters with sinusoidal excitation is proposed. It is built based on the measured S parameters and on the measured frequency characteristic of the second harmonic of the output reflected power, as functions of frequency and incident input power. This model gives better results than behavioral models build with nonlinear circuit elements for one tone driven filters, and can be used for multi-tone excitations as well.