Alberto Padilla

Nonlinear Distributed Model for Bulk Acoustic Wave Resonators

This work expands the model proposed by Krimtholz, Leedom, and Matthaei (KLM) model to account for the nonlinear effects occurring in acoustic devices due to the nonlinear stiffened elasticity. We show that a nonlinear distributed capacitance in the acoustic transmission line of the KLM model can account for the distributed nature of the nonlinear effects. Specifically, we use the nonlinear telegraphers equation to find closed-form equations for intermodulation distortion and harmonic generation. We confirm the validity of these equations by comparing their results with those provided by a KLM equivalent circuit in which the nonlinear transmission line is implemented by cascading many L-C cells having a voltage-dependent capacitance. To further confirm the model, we show measured nonlinear effects in a thin film bulk acoustic resonator in close agreement with the equivalent circuit simulations.

Passive Intermodulation Due to Self-Heating in Printed Transmission Lines

This paper proposes a mechanism by which third-order intermodulation distortion, due to self-heating, is generated in transmission lines. This work shows how transmission lines made of several materials, whose properties are independent of the electric and magnetic fields, can generate important levels of intermodulation distortion. A circuit model supported by finite-element simulations is presented to account for the temperature generation and also for its impact on the nonlinear performance. Closed-form expressions are used to calculate the generated intermodulation products and are derived from the circuit model and compared with simulations. Finally, measurements and simulations of different transmission lines are presented, showing very good agreement.

Nonlinear distributed model for IMD prediction in BAW resonators

This work presents a distributed nonlinear equivalent circuit to asses the intermodulation distortion (IMD) occurring in a BAW resonator. Closed-form expressions for intermodulation distortion at 2f1-f2 are obtained. Comparisons between analytical and simulated results are in good agreement. Extension of this analysis could be used to predict the nonlinear performance of more complex systems using BAW resonators, such as filters. Finally, measurements are presented and explained using the proposed approach.

First-Order Elastic Nonlinearities of Bulk Acoustic Wave Resonators

We propose a procedure to characterize the intrinsic nonlinearities of bulk acoustic wave resonators by performing one-port measurements of the second harmonic and second-order intermodulation spurious signals. Closed-form expressions have been derived that relate the nonlinear stiffened elasticity with experimental observables. These formulas are valid in a wide range of frequencies around the resonance and have been verified with nonlinear circuit simulations. The measurement setup and its effects are also discussed in our approach. Measurements of a set of aluminum nitride-based devices from several manufacturers yield consistent model parameters and allow us to obtain a coefficient of the nonlinear stiffened elasticity intrinsic to this piezoelectric material.

Third-Order Intermodulation Distortion and Harmonic Generation in Mismatched Weakly Nonlinear Transmission Lines

This paper describes a procedure to obtain analytical expressions for the spurious signals generated in nonlinear transmission lines with impedance mismatch when they are subject to small-signals. Using these expressions one can rapidly extract the nonlinear parameters describing the nonlinear effects due to the conductor, L(i) and R(i) , such as in superconductors, and/or the nonlinear parameters due to the dielectric, C(v) and G(v) , such as in ferroelectrics. The resulting closed-form expressions have been validated by equivalent circuit simulations. Spurious signal measurements on several coplanar waveguide superconducting and ferroelectric transmission lines have been explained by the use of the resulting closed-form expressions.

Synthesis of 4 th order lossy filters with uniform Q distribution

This paper outlines the synthesis procedure for obtaining the folded coupling matrix of lossy filters of 4th order with uniform Q distribution. The method is applied to Butterworth, Chebyshev and Chebyshev with a single pair of symmetrical transmission zeros responses. Closed-form expressions to relate a prescribed insertion loss and filter bandwidth with the required resonator quality factor for an infinite Q flatness filter responses have been obtained. Experimental results on a Chebyschev microstrip filter coincide with the theoretical predictions.

Superconducting Multiplexer Filter Bank for a Frequency-Selective Power Limiter

This work proposes a superconducting multiplexer filter bank configuration to be used as a frequency-selective power limiter. The proposed configuration limits narrowband high-power signals within a single frequency band without degrading the signal performance in the rest of the frequency bands. To accomplish this, we need to calculate the limiting power of superconducting filters implemented by means of half-wavelength transmission line resonators. The limiting power is obtained as a function of the resonator geometry, filter bandwidth, and filter order. Practical issues occurring in superconducting filters operating at high power, such as the reduction of the quality factors and de-tuning, are also analyzed and shown to not adversely affect the overall multiplexer power limiter performance.

Comparison of lossy filters and predistorted filters using novel software

This paper compares several synthesis alternatives for a 4GHz filter with 36 MHz bandwidth. The alternatives considered are: classical synthesis, various forms of predistortion and lossy filter synthesis. Electrical performance of the various alternatives is discussed in detail and a brief description of the topologies is also given. The synthesis of the several alternatives presented in this paper has been performed with a novel software that generates the desired transfer response, obtains the filter transverse coupling matrix and transforms it into other topologies of technological interest. The paper includes a brief description of the software features.

On the Relation Between the Nonlinear Surface Impedance and the Superfluid Current Density in High-Temperature Superconductors

The nonlinear surface impedance is related to a local description of the nonlinear superfluid current density that depends on the condensate velocity, by use of the definition of surface impedance as the ratio between the electric field and magnetic field at the conductor surface. To obtain this relation, we follow a rigorous approach based on the time-domain nonlinear London equations and the two-fluid model. The formulation is compared with harmonic balance simulations of an equivalent transmission line circuit that models a plane wave propagating across a vacuum-superconductor boundary, and shows very good agreement for the resulting surface impedance as a function of current density at the surface.