Nonlinear Electronics

— The paper deals with a simulation of nonlinear networks based on a classical approach of Volterra series expansion. It is known that a multidimensional Laplace transform (MLT) of a time-domain nonlinear impulse response results in the respective Laplace-domain transfer function which helps in finding Volterra kernels, for example via a harmonic input method. After solving the system in the Laplace domain, a final step is to transfer the solution back into the time domain. For this purpose proper multidimensional numerical inverse Laplace transforms (MNILT) are applied with advantages avoiding the usage of rather impractical associate variables method required to receive a single-variable Laplace image. To ensure good convergence and stability of the method the networks are limited to be rather weakly nonlinear when usually the kernels into the third order already yield reasonable results. That is why, methods for up to the third-dimensional NILT (3D NILT) are discussed in the paper, both the FFT-based one with a quotient-difference algorithm and a hyperbolic one with the Euler transformation. All the discussed methods are programmed and tested in Matlab language while considering a proper model of a nonlinear electrical network.

Ba0.7Sr0.3TiO3 (BST) single and quadruple layer capacitors with Pt electrodes were fabricated together on polycrystalline alumina substrates with a SiO2-based multicomponent amorphous buffer layer (SiO2/Al2O3). This paper presents the results of the characterization of these capacitors, to demonstrate their suitability for application as decoupling (high value) capacitors and as components in tunable RF applications (e.g., phase shifters and filters). BST films of different compositions, (Ba0.7Sr0.3)TiO3 and (Ba0.5Sr0.5)TiO3, were grown by metal-organic decomposition (MOD) and RF magnetron reactive sputtering. The capacitance density of 90-140 nm thick BST films was in the range of 20 to 70 fF/μm 2. Parallel plate capacitors with areas from 16 μm 2 to 2.25 mm2 were fabricated using photolithography and ion milling techniques. For large capacitors (0.125 to 2.25 mm2), capacitance and tanδ were measured at low frequencies (1 KHz - 1 MHz) using an LCR meter. Smaller capacitors (16 μm 2 to 3600 μm 2) were additionally characterized in the frequency range of 50 MHz - 20 GHz. In such case, capacitance, tanδ and equivalent series resistance (ESR) were extracted from two port scattering parameters obtained using a vector network analyzer (VNA). The relationship between dielectric loss, tunability and calculated figure of merit vs. BST composition and deposition temperature was outlined. In addition, loss and ESR at high frequencies was investigated. The typical achieved leakage current density of sputtered BST films for 2.25 mm2 capacitors fabricated on SiO2/Al2O3 was 7.3x10-9 A/cm2 at 300 kV/cm (65 fF/μm2), about 2 times lower than for (Ba0.7Sr0.3)TiO3 films deposited by MOD (1.4x10-8 A/cm2 at 300 kV/cm, 34.5 fF/μm2). Furthermore, the tunability of (Ba0.7Sr0.3)TiO3 deposited by both methods on SiO2/Al2O3 was ~60% at 350 kV/cm.

The paper deals with a simulation of nonlinear networks based on a classical approach of Volterra series expansion. It is known that a multidimensional Laplace transform (MLT) of a time-domain nonlinear impulse response results in the respective Laplace-domain transfer function which helps in finding Volterra kernels, for example via a harmonic input method. After solving the system in the Laplace domain, a final step is to transfer the solution back into the time domain. For this purpose proper multidimensional numerical inverse Laplace transforms (MNILT) are applied with advantages avoiding the usage of rather impractical associate variables method required to receive a single-variable Laplace image. To ensure good convergence and stability of the method the networks are limited to be rather weakly nonlinear when usually the kernels into the third order already yield reasonable results. That is why, methods for up to the third-dimensional NILT (3D NILT) are discussed in the paper, both the FFT-based one with a quotient-difference algorithm and a hyperbolic one with the Euler transformation. All the discussed methods are programmed and tested in Matlab language while considering a proper model of a nonlinear electrical network.