Area-Efficient Extended 3-D Inductor Based on TSV Technology for RF Applications

Lossless positive-real systems have been widely studied in the literature. They are systems in which the energy is entirely transferred between input and output. In this paper, new aspects related to the linear quadratic gaussian (LQG) control of lossless positive-real systems are reported including both the continuous-time and the discrete-time cases. Direct formulas for the calculation of the optimal gains will be introduced and the properties of the different structures of the LQG compensator obtained for the continuous-time and the discrete-time cases will be emphasized, also in view of designing positive-real LQG compensators. Numerical examples related to low-damped structures are also discussed to verify the possibility to design the LQG compensator on the basis of a lossless approximation.

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“…Substituting Eqs. (7) in the D-CARE ( 13), after including the relationship for K c in (15), it follows that…”

Section: The Discrete-time Casementioning

confidence: 99%

“…of the optimal compensator, choosing as positive definite solution the matrix P satisfying (7). It yields…”

Section: Proof the Proof Is Based On The Evaluation Of The Discretetime Lyapunov Equation For The State Matrix Amentioning

confidence: 99%

LQG control of linear lossless positive-real systems: the continuous-time and discrete-time cases

Bucolo

Buscarino

Fortuna

et al. 2021

Int. J. Dynam. Control

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“…Recently, with the advancement of 3D integration technology, a through-silicon-via (TSV) based on-chip inductor was introduced in [7][8][9][10][11][12][13][14]. It was found that a toroidal TSV-inductor, as shown in Fig.…”

Section: Introductionmentioning

confidence: 99%

“…Other applications such as resonant clocking [12] and RF circuits [13] are implemented using TSV inductors, with the physics-based modeling approach detailed in [12]. To improve its inductance and quality factor, a magnetic core can be inserted into the structure to achieve high quality factor and L/Rdc [6,7,[16][17][18][19][20][21][22]. As demonstrated in Fig.…”

Section: Introductionmentioning

confidence: 99%

“…The fabricated structure has achieved an inductance density of 111nH/mm2, 2× compared with a TSV-inductor without a magnetic core and 16× compared with a conventional planar inductor. Based on that, several works have extended the proposed 3D magnetic core inductors to various applications from high efficiency DC-DC converter, radio-frequency circuit, to biomedical implants [16,[19][20][21][22]. For example, a three-dimensional insilicon TSV magnetic-core toroidal inductor was designed for power supply in package, which has 3× inductance and 30% higher quality factor compared with similar TSV air-core inductors [16].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Magnetic Core TSV-Inductor Design and Optimization for On-chip DC-DC Converter

Wen

Xiao

Chen

et al. 2022

ACM Trans. Des. Autom. Electron. Syst.

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The conventional on-chip spiral inductor consumes a significant top-metal routing area, thereby preventing its popularity in many on-chip applications. Recently through-silicon-via (TSV) based inductor (also known as TSV-inductor) with a magnetic core has been proved to be a viable option for the on-chip DC-DC converter. The operating conditions of these inductors play a major role in maximizing the performance and efficiency of the DC-DC converter. However, there is a critical need to study the design and optimization details of magnetic core TSV-inductors with the unique 3D structure embedding magnetic core. This paper aims to provide a clear understanding of the modeling details of a magnetic core TSV-inductor and a design and optimization methodology to assist efficient inductor design. Moreover, a machine learning assisted model combining physical details and artificial neural network (ANN) is also proposed to extract the equivalent circuit to further facilitate DC-DC converter design. Experimental results show that the optimized TSV-inductor with the magnetic core and air-gap can achieve inductance density improvement of up to 7.7 × and quality factor improvements of up to 1.6 × for the same footprint compared with the TSV-inductor without a magnetic core. For on-chip DC-DC converter applications, the converter efficiency can be improved by up to 15.9% and 6.8% compared with the conventional spiral and TSV-inductor without magnetic core, respectively.

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A two-step optimization strategy for the inductance control of TSV-based 3-D inductor based on the SAE model

Wang,

Yang,

Chen

et al. 2024

Struct Multidisc Optim

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Area-Efficient Extended 3-D Inductor Based on TSV Technology for RF Applications

Cited by 14 publications

References 24 publications

LQG control of linear lossless positive-real systems: the continuous-time and discrete-time cases

LQG control of linear lossless positive-real systems: the continuous-time and discrete-time cases

Magnetic Core TSV-Inductor Design and Optimization for On-chip DC-DC Converter

A two-step optimization strategy for the inductance control of TSV-based 3-D inductor based on the SAE model

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