Multi-tone Harmonic Balance Research Articles

Imbalance vibration suppression for asymmetric rotors via an enhanced automatic dynamic balancer

Automatic dynamic balancer (ADB) is a passive ball-bearing type of vibration control device and has been applied successfully on some rotating machineries, i.e., hand-held machine tools and optical disk drives. Recently, an enhanced automatic dynamic balancer (EADB) has been developed to extend the capability of the ADB and to achieve a perfect-balancing condition in a wider rotor speed operation range. However, the EADB cannot be applied directly to the imbalance vibration suppression for asymmetric rotors since a multi-frequency whirling limit cycle in the asymmetrically supported rotor/ADB systems prevents the assumed solution of a single-frequency whirling limit cycle for the symmetric supported rotor/ADB systems. To address the aforementioned limitation, this paper proposes an imbalance vibration suppression method for asymmetric rotors via an EADB, which can achieve rotor perfect balancing condition in a wider operation range. The non-autonomous equations of motion for an asymmetrically supported planar rotor with an EADB system is established via Lagrange's method. The perfect-balancing equilibrium of the system is solved analytically, and the multi-frequency whirling limit cycle is obtained via a multi-tone harmonic balance method whose tones are predetermined by the matrix pencil method. To destabilize the multi-frequency whirling limit cycle and to guarantee the stable perfect balancing conditions for an asymmetric rotor with an EADB, a numerical continuation method is adopted to design parameters for the EADB. The stability analysis of the perfect-balancing equilibrium and the multi-frequency whirling limit cycle are conducted by Floquet theory. The enlarged unstable whirling limit cycle solution proves the effectiveness of the proposed method.

Multi-Tone Harmonic Balance Optimization for High-Power Amplifiers through Coarse and Fine Models Based on X-Parameters.

In this study, we focus on automated optimization design methodologies to concurrently trade off between power gain, output power, efficiency, and linearity specifications in radio frequency (RF) high-power amplifiers (HPAs) through deep neural networks (DNNs). The RF HPAs are highly nonlinear circuits where characterizing an accurate and desired amplitude and phase responses to improve the overall performance is not a straightforward process. For this case, we propose a coarse and fine modeling approach based on firstly modeling the involved transistor and then selecting the best configuration of HAP along with optimizing the involved input and output termination networks through DNNs. In the fine phase, we firstly construct the equivalent modeling of the GaN HEMT transistor by using X-parameters. Then in the coarse phase, we utilize hidden layers of the modeled transistor and replace the HPA’s DNN to model the behavior of the selected HPA by using S-parameters. If the suitable accuracy of HPA modeling is not achieved, the hyperparameters of the fine model are improved and re-evaluated in the HPA model. We call the optimization process coarse and fine modeling since the evaluation process is performed from S-parameters to X-parameters. This stage of optimization can ensure modeling the nonlinear HPA design that includes a high number of parameters in an effective way. Furthermore, for accelerating the optimization process, we use the classification DNN for selecting the best topology of HPA for modeling the most suitable configuration at the coarse phase. The proposed modeling strategy results in relatively highly accurate HPA designs that generate post-layouts automatically, where multi-tone harmonic balance specifications are optimized once together without any human interruptions. To validate the modeling approach and optimization process, a 10 W HPA is simulated and measured in the operational frequency band of 1.8 GHz to 2.2 GHz, i.e., the L-band. The measurement results demonstrate a drain efficiency higher than 54% and linear gain performance more than 12.5 dB, with better than 50 dBc adjacent channel power ratio (ACPR) after DPD.

Electrical and Noise Modeling of GaAs Schottky Diode Mixers in the THz Band

This paper presents a simulation tool for the analysis and design of Schottky mixers which is able to evaluate self-consistently both the conversion losses and the noise temperature. The tool is based on a Monte Carlo model of the diode coupled with a multi-tone harmonic balance technique. A remarkable feature of this tool is that it avoids the need of analytical or empirical models. The validation of the tool has been carried out by comparing simulation results with measurements of mixers published in the literature up to 2.5 THz. The usefulness of Schottky diodes as frequency mixers above 2.5 THz is analyzed. Additionally, the range of application and the limitations of simpler simulation tools based on lumped equivalent circuits or drift-diffusion models have been evaluated using the Monte Carlo model as a reference.

Optimization setup based on multi-tone harmonic balance for the direct and accurate control of the locking range of rationally synchronized oscillators

In this work, a new approach for the optimization of the locking range of rationally synchronized oscillators (RSO) is presented. The proposed method is based on a non-linear optimization setup, easily implementable on commercial harmonic balance software packages, which involves two copies of the circuit. An auxiliary generator (AG) is connected to each copy. The AGs are used to set the working points of the two circuit copies around the limits of the locking range, through the control of the phase of the autonomous signals. A conventional optimization process is then used to increase the synchronization bandwidth by changing the working frequency of one or both AGs. The synchronization loci of the RSO will be calculated to determine the achieved locking range and to analyze its dependence with the amplitudes of the synchronizing harmonics.

Multitone harmonic-balance simulations of an x-ray transition-edge sensor characterized at BESSY II

We present multitone harmonic-balance (MTHB) simulations of a Ti–Au x-ray transition-edge sensor (TES) microcalorimeter in a 5×5 pixel spectrometer array. The dynamic response of the TES microcalorimeter under simulation has been extremely well characterized at the BESSY II Synchrotron Radiation Facility in Berlin. We compare our simulated results directly with these measurements, and show that the MTHB algorithm is able to simulate to great accuracy the dynamic behavior of the TES, even when saturated by 6 keV photons. In this paper, we provide a detailed account of the MTHB simulations, and discuss the impact of this work on future missions such as the International X-ray Observatory.

Steady state analysis of electronic circuits by cubic and exponential splines

Multitone Harmonic Balance (HB) is widely used for the simulation of the quasiperiodic steady state of RF circuits. HB is based on a Fourier expansion of the unknown waveforms and is state-of-the-art. Unfortunately, trigonometric polynomials exhibit poor convergence properties in cases where the signal is not quasi-sinusoidal which leads to a prohibitive run-time even for small circuits. Moreover, the approximation of sharp transients leads to the well-known Gibbs phenomenon, which cannot be reduced by an increase of Fourier coefficients. In this paper, we present an alternative approach based on alternatively cubic or exponential splines for a (quasi-) periodic steady state analysis. Unlike trigonometric basis function, a spline basis solves for a variational problem, i.e., the cubic spline minimizes the curvature. Because of their compact support, spline bases are better suited for waveforms with sharp transients. Furthermore, we show that the amount of work for coding of splines is negligible if an implementation of HB is available. In general, designers are mainly interested in spectra and not in waveforms. Therefore, a method for calculating the spectrum from a spline basis is derived too.

Large-signal simulation of semiconductor lasers on device level: numerical aspects of the harmonic balance method

Large-signal modulation characteristics are key specifications in analog and digital applications of optoelectronic devices. In this work we present a novel approach for the modeling of these characteristics for semiconductor lasers on device level. A multi-tone harmonic balance method for a physics-based electro-thermal-optical model is utilized. The numerical aspects of the framework are described and illustrated for a realistic VCSEL example.

Electrothermal CAD of power devices and circuits with fully physical time-dependent compact thermal modeling of complex nonlinear 3-d systems

An original, fully analytical, spectral domain decomposition approach is presented for the time-dependent thermal modeling of complex nonlinear (3-D) electronic systems, from metallized power FETs and MMICs, through MCMs, up to circuit board level. This solution method offers a powerful alternative to conventional numerical thermal simulation techniques, and is constructed to be compatible with explicitly coupled electrothermal device and circuit simulation on CAD timescales. In contrast to semianalytical, frequency space, Fourier solutions involving DFT-FFT, the method presented here is based on explicit, fully analytical, double Fourier series expressions for thermal subsystem solutions in Laplace transform s-space (complex frequency space). It is presented in the form of analytically exact thermal impedance matrix expressions for thermal subsystems. These include double Fourier series solutions for rectangular multilayers, which are an order of magnitude faster to evaluate than existing semi-analytical Fourier solutions based on DFT-FFT. They also include double Fourier series solutions for the case of arbitrarily distributed volume heat sources and sinks, constructed without the use of Green's function techniques, and for rectangular volumes with prescribed fluxes on all faces, removing the adiabatic sidewall boundary condition. This combination allows treatment of arbitrarily inhomogeneous complex geometries, and provides a description of thermal material nonlinearities as well as inclusion of position varying and non linear surface fluxes. It provides a fully physical, and near exact, generalized multiport network parameter description of nonlinear, distributed thermal subsystems, in both the time and frequency domains. In contrast to existing circuit level approaches, it requires no explicit lumped element, RC-network approximation or nodal reduction, for fully coupled, electrothermal CAD. This thermal impedance matrix approach immediately gives rise to minimal boundary condition independent compact models for thermal systems. Implementation of the time-dependent thermal model as N-port netlist elements within a microwave circuit simulation engine, Transim (NCSU), is described. Electrothermal transient, single-tone, two-tone, and multitone harmonic balance simulations are presented for a MESFET amplifier. This thermal model is validated experimentally by thermal imaging of a passive grid array representative of one form of spatial power combining architecture.

An efficient Fourier transform algorithm for multitone harmonic balance

A novel Fourier transform technique is proposed for use in multitone harmonic-balance (HB) simulations. It is shown that computations of multitone distorted spectra reduce to efficient one-dimensional fast Fourier transform operations when certain relationships exist between the sampling rate and frequency components of the signal. The algorithm requires minimal initialization time and is readily incorporated into existing HE tools. It is especially useful when the number of input tones is very large, such as spectral regrowth and noise-power ratio simulations. The method is demonstrated on the example of a 5-GHz MESFET amplifier driven by a quadrature phase shift-keying modulated carrier.