Lumped-element Network Research Articles

Simple and fast modelling of radio frequency passives in view of beyond-5G and 6G applications: case study of an RF-MEMS multi-state network described by an equivalent lumped element network

Simple and fast modelling of radio frequency passives in view of beyond-5G and 6G applications: case study of an RF-MEMS multi-state network described by an equivalent lumped element network

Parameter identification of transformer lumped element network model through genetic algorithm‐based gray‐box modelling technique

AbstractThe lumped element network model has been proven to be an efficient tool for the interpretation of transformer Frequency Response Analysis. However, it is challenging to obtain parameters of the model if transformer design information is unavailable. In such a case, optimisation algorithms can be used for gray‐box model parameter estimation. A methodology is developed by the authors to establish a transformer network model without winding design data, and instead, end‐to‐end open circuit Frequency Response and other terminal test results are utilised; and Genetic Algorithm is applied to approximate the unknown parameters of the model. The modelling approach developed is independent of the unit number of the network model and therefore guarantees the accuracy of optimisation. Furthermore, it can deal with transformers with a complicated winding structure such as interleaved disc type winding. Two single windings, helical and interleaved disc type, and a single‐phase 144/13 kV 60 MVA transformer are used to demonstrate the method. FRA spectra produced by the best estimated gray‐box model and the corresponding white‐box model are compared. The main features in amplitude and phase spectra are well matched, with low values of Relative Standard Deviation, for both single windings and transformer. Estimated electrical parameters show a high consistency with reference values, which are calculated based on winding design data. This validates the methodology and gives confidence to apply grey‐box modelling for FRA interpretation.

Quantum fluctuations in electrical multiport linear systems

We present an extension of the classical Nyquist-Thevenin theorem for multiport classical electrical networks by Twiss to the quantum case. Conversely, we extend the quantum fluctuation-dissipation result for one port electrical systems to the multiport case, both reciprocal and nonreciprocal. Our results are extended to lossy systems by depicting resistive components as continuous limits of purely lossless lumped-element networks. Simple circuit examples are analyzed, including a linear system lacking a direct impedance representation.

Bondwire Model and Compensation Network for 60 GHz Chip-to-PCB Interconnects

This letter presents a bondwire model in the form of a lumped-element network, which is based on the geometry of the bondwire and landing pads. For the interconnection between a chip and the feedline on a printed circuit board (PCB) substrate, the associated parasitics are calculated, which are responsible for the performance degradation caused by the bondwire at millimeter-wave (mmWave) frequencies. A matching network is realized with planar-lumped elements on the PCB and integrated for impedance mismatch compensation at a center frequency of 60 GHz. Simulations show an operating bandwidth of 50–70 GHz. The proposed solution is first verified by the measurements of PCB-to-PCB bondwire interconnects. Then, as an application example, an antenna-switch chip is placed at the PCB feedline. Remarkable improvements in terms of input matching and insertion loss are observed compared with an unmatched bondwire interconnect.

Computer‐aideddesign methodology for inductive compensated microwaveclass‐Epower amplifier

This article presents a simulation-based analysis to first evaluate the impact of excessive transistor output capacitance on class-E power amplifiers and to second show how inductive compensation can be used to recover optimum class-E operating conditions. As a starting point, the finite-feed inductor in a parallel-circuit topology is replaced by a frequency-dependent inductor, which in turn can be substituted by a network composed of a series inductor and additional subharmonic resonators. This complex lumped-element network is then replaced by a generalized transmission line equivalent topology, suitable for microwaves. Calculation of the transmission line impedances and electrical lengths of the proposed generalized network is shown in detail and a design procedure for this modified class-E is provided. The analysis presented here is further extended by using a simplified large-signal model for the employed GaN HEMT device, which allows evaluating the effects of non-ideal switching as well as of capacitance voltage-dependency and feedback capacitance. The analysis is validated by simulation and design of a test board. Measurements of the test board showed a drain efficiency of 80.3%, power-added efficiency of 76.3% and output power of 40.1 dBm at 1.96 GHz, demonstrating the validity of the proposed approach.

Microwave characterization of a double-barrier GaAs/AlAs resonant tunneling diodes for active microstrip transmission lines

We describe a method of parameters extraction for the lumped element network representing resonant tunneling diodes (RTDs). The method is based on onchip reflection coefficient measurements in a wide frequency range from 1 kHz up to 60 GHz in combination with differential resistance measurements. We have proposed and fabricated double-barrier GaAs/AlAs RTDs embedded into the 50-Ohm coplanar transmission line section, suitable for onchip RF-measurements using a probe station and a vector network analyzer. A good agreement between the experimental S11-parameter curves and the curves calculated from the equivalent lumped network is obtained for various RTD bias voltages. A possible operation of a distributed RTDs as an active microstrip transmission line (MTL) is also discussed. Experimentally extracted parameters of the lumped equivalent network are used to define amplification conditions in MTLs based on distributed RTDs.

Coupled electromechanical and electromagnetic simulation of radio frequency microelectromechanical-systems (RF-MEMS) based on compact models approach

In this work, a modelling approach of complete RF-MEMS (MicroElectroMechanical-Systems for radio frequency) passives is discussed. The methodology takes into account both the non-linear electromechanical and the RF behaviour, and is suitable for being implemented and automated within a standard circuit simulator. The intrinsic electromechanical core is based on a structural hierarchical model library implemented in the VerilogA programming language, compatible with most commercial EDA (Electronic Design Automation) tools and circuit development environments. A wrapping lumped element network, extracted from S-parameters measured data, accounts for the electromagnetic RF behaviour of the MEMS device. The complete non-linear network can be hierarchically instantiated within a fully functional schematic environment for mixed domain design optimisation. The model is successfully validated against static and dynamic electromechanical and RF on-wafer measurements, using an optical interferometry profilometer. In particular, this paper discusses how the mentioned approach can be extended in order to include the effects due to the presence of a wafer-level package on the RF characteristics.

Step on It Bringing Fullwave Finite-Element Microwave Filter Design up to Speed

There are many steps in the design of a microwave filter: mathematically describing the filter characteristics, representing the circuit as a network of lumped elements or as a coupling matrix, implementing the distributed elements, finding the initial dimensions of the physical structure, and carrying out numerical tuning using electromagnetic (EM) simulators. The whole process is painstaking and time-consuming, and it requires a great deal of engineering expertise. Microwave filters are extremely complex geometric structures, and their simple circuits are often quite hard to represent. Moreover, manufacturing them is costly: to be sure that the hardware resulting from the design will meet the performance goals, rigorous computer tools are used to determine the physical dimensions and evaluate all of the adjustments at the final stage. This last stage is particularly challenging, and advanced computational techniques are required.

Design of Compact D-Band Amplifiers With Accurate Modeling of Inductors and Current Return Paths in 55-nm SiGe BiCMOS

This letter presents 1-stage and 2-stage compact D-band amplifiers with lumped-element matching networks implemented in 55 nm SiGe BiCMOS. To correctly account for the effects of a nonideal ground plane, i.e., reactances in current return paths, and coupling of inductors with nearby layout structures, a shielded 2-port, 4-terminal simulation strategy for inductors is proposed. Validated by measurements, the approach allows very accurate design of compact amplifiers in D-band. The 1-stage design proves 11.8 dB gain at 152 GHz and 17.9 GHz bandwidth in 0.031 mm2. With the 2-stage amplifier, featuring 20.1 dB gain at 150 GHz with 24.5 GHz bandwidth in 0.058 mm2, from $2\times $ to $5.7\times $ area reduction is demonstrated against similar SiGe amplifiers in the same frequency band.

Narrowband Impedance Transformer With Extremely High Transformation Ratio of 200

This letter presents a hybrid narrowband radio frequency (RF) impedance transformer using an aluminum nitride (AlN) microelectromechanical system (MEMS) resonator and lumped elements. The hybrid transformer consists of an AlN Lamb wave resonator, a parallel inductor, and a set of three lumped-element networks on a printed circuit board (PCB). The AlN resonator and the parallel inductor form the narrowband response while the lumped element networks fulfill the high impedance transformation. The transformer has been theoretically predicted and experimentally shown to achieve a narrow fractional bandwidth (FBW) of 2.2% and an extremely high impedance transformation ratio (ITR) of 200.

Topological semantics for lumped parameter systems modeling

Behaviors of many engineering systems are described by lumped parameter models that encapsulate the spatially distributed nature of the system into networks of lumped elements; the dynamics of such a network is governed by a system of ordinary differential and algebraic equations. Languages and simulation tools for modeling such systems differ in syntax, informal semantics, and in the methods by which such systems of equations are generated and simulated, leading to numerous interoperability challenges. Logical extensions of SysML aim specifically at unifying a subset of the underlying concepts in such languages.We propose to unify semantics of all such systems using standard notions from algebraic topology. In particular, Tonti diagrams classify all physical theories in terms of physical laws (topological and constitutive) defined over a pair of dual cochain complexes and may be used to describe different types of lumped parameter systems. We show that all possible methods for generating the corresponding state equations within each physical domain correspond to paths over Tonti diagrams. We further propose a generalization of Tonti diagram that captures the behavior and supports canonical generation of state equations for multi-domain lumped parameter systems.The unified semantics provides a basis for greater interoperability in systems modeling, supporting automated translation, integration, reuse, and numerical simulation of models created in different authoring systems and applications. Notably, the proposed algebraic topological semantics is also compatible with spatially and temporally distributed models that are at the core of modern CAD and CAE systems.

Reciprocity in diffusive spin-current circuits

Similarly to their purely electric counterparts, spintronic circuits may be presented as networks of lumped elements. Due to interplay between spin and charge currents, each element is described by a matrix conductance. We establish reciprocity relations between the entries of the conductance matrix of a multi-terminal linear device, comprising normal metallic and strong ferromagnetic elements with spin-inactive interfaces between them. In particular, reciprocity equates the spin transmissions through a two-terminal element in the opposite directions. When applied to "geometric spin ratchets", reciprocity shows that certain effects, announced for such devices, are, in fact, impossible. Finally, we discuss the relation between our work and the spintronic circuit theory formalism.

Thermal boundary layer limitations on the performance of micromachined microphones.

This work examines the extent to which thermal boundary layer effects limit the performance of micromachined microphones. The acoustic impedance of the cavity formed by the microphone enclosure is calculated using both analytical and finite-element methods. A thermal correction to the cavity impedance is included to account for the transition of compression and expansion within the enclosure from adiabatic to isothermal when the thermal boundary layer that forms at the walls of the enclosure becomes large compared to the enclosure dimensions. The thermal correction to the cavity impedance contains a resistive term that results from thermal relaxation losses and contributes thermal-acoustic noise to the system. A lumped-element network model for the microphone response which includes the thermally corrected enclosure impedance is presented and compared to measured results for a case study device. The relative noise power contribution of each noise source considered in the model is calculated. It is shown that the noise due to the resistive term of the enclosure cavity impedance becomes significant when the enclosure volume is small. This sets a theoretical limit on the noise floor that can be achieved by a micromachined microphone with given enclosure dimensions.

Thermal boundary layer limitations on the performance of micromachined microphones

The extent to which thermal boundary layer effects limit the performance of micromachined microphones is examined. A lumped element network model for a micromachined microphone is presented which includes a ladder network in parallel with the adiabatic back volume compliance to account for the transition of the enclosure from adiabatic to isothermal conditions when the thermal boundary layer becomes large compared to the enclosure dimensions. The thermal correction to the cavity impedance contains a resistive component which contributes thermal-acoustic noise to the system. The model results are compared to measurements taken from commercially available microphone units with various back volume sizes, and the simulated relative noise power contribution of each acoustic noise source is calculated. The impedance of the back volume, including the thermal correction factor, is compared to the adiabatic compliance and the impedance derived from thermoacoustic finite element analysis. It is shown that the noise due to the thermal component of the back volume impedance becomes significant in microphones with small back volumes and effectively sets an upper bound on the signal-to-noise ratio of a microphone of given package dimensions.

General Coupling Matrix Synthesis for Decoupling MRI RF Arrays.

Multi-channel radio-frequency (RF) arrays, composed of multiple resonant coils, provide significant benefits for MRI during both signal reception (receive) and excitation (transmit). Demonstration of increased signal-to-noise ratio (SNR) and acceleration factors during parallel acquisitions has lead to the development of receive arrays. Conversely, transmit arrays have demonstrated considerable potential for mitigating excitation inhomogeneity arising at ultra-high magnetic field strengths ( ≥ 7 T) , present due to wave-like interactions inside the sample. Due to geometric constraints, the design of both receive and transmit arrays requires the resonating coils to be closely spaced. Significant overlap in the near-field distributions from each coil results in coupling. Without an adequate decoupling strategy applied between individual elements in an RF array, the MRI performance of the array can be significantly degraded. This work presents a method to design decoupling networks for arbitrarily large RF arrays based on direct synthesis of a coupling matrix. Reflection coefficients are fitted to transfer polynomials with transmission coefficients simultaneously minimized through a nonlinear optimization. The method demonstrates the design of nth-order distributed filters and lumped element networks that compensate for all first-order and cross-coupling terms arising in an RF array suitable for MRI. The synthesis results are computed for 4-, 8-, and 32-channel RF arrays. Monte Carlo analyses and experimental results for two RF array constructions demonstrate the robustness of this approach.

Roles of epsilon-near-zero (ENZ) and mu-near-zero (MNZ) materials in optical metatronic circuit networks.

The concept of metamaterial-inspired nanocircuits, dubbed metatronics, was introduced in [Science 317, 1698 (2007); Phys. Rev. Lett. 95, 095504 (2005)]. It was suggested how optical lumped elements (nanoelements) can be made using subwavelength plasmonic or non-plasmonic particles. As a result, the optical metatronic equivalents of a number of electronic circuits, such as frequency mixers and filters, were suggested. In this work we further expand the concept of electronic lumped element networks into optical metatronic circuits and suggest a conceptual model applicable to various metatronic passive networks. In particular, we differentiate between the series and parallel networks using epsilon-near-zero (ENZ) and mu-near-zero (MNZ) materials. We employ layered structures with subwavelength thicknesses for the nanoelements as the building blocks of collections of metatronic networks. Furthermore, we explore how by choosing the non-zero constitutive parameters of the materials with specific dispersions, either Drude or Lorentzian dispersion with suitable parameters, capacitive and inductive responses can be achieved in both series and parallel networks. Next, we proceed with the one-to-one analogy between electronic circuits and optical metatronic filter layered networks and justify our analogies by comparing the frequency response of the two paradigms. Finally, we examine the material dispersion of near-zero relative permittivity as well as other physically important material considerations such as losses.

Enhanced Modelling of Split-Ring Resonators Couplings in Printed Circuits

An enhanced equivalent circuit approach for the magnetic/electric interaction of single split-ring resonators (SRRs) with printed lines is presented in this paper. A very simple and efficient lumped-element network is proposed to model the behavior of metamaterial-based printed lines over a wide frequency band. The same circuit topology can be used for the single- and two-mirrored SRRs loaded microstrip line. The corresponding circuit parameters are obtained from the multiconductor transmission line theory as well as from closed-form expressions that make use of just the resonance frequency and minimum of the reflection coefficient (which should be previously extracted from experiments or full-wave simulations). The comparison of our equivalent circuit results with measurements and full-wave simulations has shown a very good agreement in a considerably wider frequency band than other previously proposed simple equivalent circuits.

An eight-channel T/R head coil for parallel transmit MRI at 3T using ultra-low output impedance amplifiers

Parallel transmit is an emerging technology to address the technical challenges associated with MR imaging at high field strengths. When developing arrays for parallel transmit systems, one of the primary factors to be considered is the mechanism to manage coupling and create independently operating channels. Recent work has demonstrated the use of amplifiers to provide some or all of the channel-to-channel isolation, reducing the need for on-coil decoupling networks in a manner analogous to the use of isolation preamplifiers with receive coils. This paper discusses an eight-channel transmit/receive head array for use with an ultra-low output impedance (ULOI) parallel transmit system. The ULOI amplifiers eliminated the need for a complex lumped element network to decouple the eight-rung array. The design and construction details of the array are discussed in addition to the measurement considerations required for appropriately characterizing an array when using ULOI amplifiers. B1 maps and coupling matrices are used to verify the performance of the system.

Continued Discussion About "Propagation and Negative Refraction" [Backscatter

It is good that it is now accepted (at least by Prof. Gwarek) that a homogenous material with negative parameters can never exist because it would be noncausal. The argument then turns to metamaterials, which are completely defined by linear passive lumped element networks. These must exhibit all of the normal positive real properties, and, in particular, they must be causal. The entire preamble is irrelevant to the technical discussion, and everything revolves around the networks shown in Figure 3 and the lowpass equivalent as shown here.

A Practical Thermal Model for the Estimation of Permanent Magnet and Stator Winding Temperatures

A thermal model for the determination of the temperatures of interior permanent magnets and stator windings is presented in this paper. The innovation of the model relies on one temperature sensor being located in the stator core of the machine. Such sensor is simple to implement in many applications such as traction or EV, where reliability is critical. The estimated stator winding and permanent magnet temperatures are determined by a simplified thermal lumped element network model with only two time constants. It is shown that the proposed thermal model is very robust due to the structure of the model and the measured stator core temperature. The distortion of the temperature estimates caused by the cooling circuit is inherently accounted for such that the model can be used for robust online prediction of temperatures. Experimental results based on a forced water-cooled interior permanent magnet synchronous machine setup are presented to validate the effectiveness of the presented model.