Lumped Element Transmission Line Research Articles

High Quality Factor Miniaturized CMOS Transmission Lines Using Cascaded T-Networks for 60 GHz Millimeter Wave Applications

This work presents an on-chip 60 GHz lumped element transmission line (TL) using cascaded T-networks with a high Quality factor. Each T-network consists of a series inductance with a shunt capacitance at its center. We have derived the design equations for this TL configuration and proved that a TL whose electrical length ≥ 60° achieves additional miniaturization when implemented with three or more cascaded T-networks. The inductance is implemented using a straight wire model with no ground below it, while the capacitance is implemented using a parallel plate model with a grounding pedestal. Both configurations guarantee maximum inductance per unit length and capacitance per unit area to further improve the miniaturization level. A quarter wavelength TL with three cascaded T-networks is fabricated as proof of concept. The measured and simulated results of the fabricated TL have good agreement, and the measured quality factor is 17 at 60 GHz.

Drifting plasmons in two-dimensional electron channels: circuit analogy.

Plasmons in two-dimensional electron channels have potential applications in the terahertz frequency range. Equivalent circuit models provide a convenient framework for analysing the plasmons. This article introduces a circuit model for plasmons in the presence of a dc current that flows in a gated channel. It is shown that drifting plasmons can be described by an LC-transmission line with distributed dependent sources. A circuit analogue of the Dyakonov-Shur instability is demonstrated. Then, a lumped-element transmission line with dependent sources is analysed, and non-reciprocity is demonstrated for examples of a right- and a left-handed transmission line. Effects of ohmic loss are discussed. The results could be used for the design of non-reciprocal transmission line devices. This article is part of the theme issue 'Celebrating the 15th anniversary of the Royal Society Newton International Fellowship'.

A dynamically tunable discrete-element transmission line pulse generator

The Frozen Wave Generator (FWG) is a megawatt-class radio frequency pulse forming network that converts DC input up to ones-of-GHz center frequency (fc) by superposing an ensemble of alternately charged reactive storage elements. In this work, we demonstrate an all-solid-state, dynamically tunable, and chirp-capable FWG using the lumped-element transmission line (LETL) topology. A 12-segment LETL-FWG switched using a MOSFET is demonstrated and directly compared with a literature standard coaxial-based system. Comparison metrics for pulse width (tpulse) are studied as a function of the transmission line length and respective LC parameters. The chirp- and dynamic-tuning-capability as well as the high volumetric power density of the system are demonstrated by comparing the predicted and measured bandwidth, rise-time, pulse width, and delay-time from a 7.5 × 30 × 3 cm3 printed circuit board. The experiment resulted in dynamically tunable pulse trains with 15–24 ns pulse widths (40–80 MHz) and >35% conversion efficiency and an ∼80% reduction in volume compared to vacuum-relativistic pulsers in the same peak power class.

Precise Configuration of Transmission Line Class-E Power Amplifier Operating at GHz Frequency

Power amplifier (PA) is a core part of microwave power transmission (MPT) system. Featuring simple topology and theoretical 100% efficiency, class-E PA is widely discussed both in industry and academia. This article centers around the precise configuration of transmission line class-E PA operating at GHz frequency. Based on the conversion between lumped element topology and transmission line topology of class-E PA, the equal resistance surface-based configuration method is proposed. Specific configuration method for different types of matching network is analyzed according to the corresponding characteristics. Then, an L-type matching network-based class-E PA is designed in detail for the MPT system. Besides, extended application of the proposed method is discussed for different derivate topologies of class-E PA. Finally, a 2.5-GHz/10-W transmission line class-E PA is fabricated in the lab and the proposed configuration method is fully verified with experiments.

Complementary Metal Oxide Semiconductor Digitally Controlled Passive Phase Shifter Circuit for Bearing Angle Control in Multiple Antenna System

A Complementary Metal Oxide Semiconductor (CMOS) digitally controller passive phase shifter circuit for bearing angle control in multiple antenna systems with the changes of the frequency angle or phase shift by using the passive component is presented. The circuit has been designed by using TSMC 0.18 um CMOS technology on the Advanced Design System (ADS) software. This project aims to look for multiple phase transition angles on the same circuit by using the switch in order to get different shifter pattern selectors in series with a digital phase tuning phase adapted using digital capacitors and inductors loading a lumped element transmission line. The phase shifter has a range of 360° with 5.6° resolution at 8-11 GHz frequency band. These CMOS phase shifter characteristics are attractive for multiple antennae and commercial phased array communication systems where cost, size, weight, power and high linearity are required.

Full-Wave Methodology to Compute the Spontaneous Emission Rate of a Transmon Qubit

The spontaneous emission rate (SER) is an important figure of merit for any quantum bit (qubit), as it can play a significant role in the control and decoherence of the qubit. As a result, accurately characterizing the SER for practical devices is an important step in the design of quantum information processing devices. Here, we specifically focus on the experimentally popular platform of a transmon qubit, which is a kind of superconducting circuit qubit. Despite the importance of understanding the SER of these qubits, it is often determined using approximate circuit models or is inferred from measurements on a fabricated device. To improve the accuracy of predictions in the design process, it is better to use full-wave numerical methods that can make a minimal number of approximations in the description of practical systems. In this work, we show how this can be done with a recently developed field-based description of transmon qubits coupled to an electromagnetic environment. We validate our model by computing the SER for devices similar to those found in the literature that have been well-characterized experimentally. We further cross-validate our results by comparing them to simplified lumped element circuit and transmission line models as appropriate.

Compact wideband CMOS lumped‐element Wilkinson power divider with asymmetric negative capacitance circuit

The authors developed a wideband on-chip Wilkinson power divider (WPD) using lumped-element transmission lines (LE TLs) with 2-port negative capacitance (NCAP) circuits that provide the phase response with a positive slope and broadband port impedance. The bandwidth of the WPD was increased using the broadband quarter-wavelength ( λ /4) LE TLs with port-matched NCAP circuits. The WPD was implemented in the Global Foundry 8SF 130-nm RF CMOS IC technology. The size of the core chip is 1100 µm × 400 µm. The S-parameter measurements showed an absolute bandwidth ranging between 0.76 and 1.6 GHz, and a fractional bandwidth of 71.2%. In the frequency range of the bandwidth, the insertion loss was 0.4–3.4 dB, with the isolation between the two output ports was >18 dB, and the noise figures were 11–12 dB. The input-referred 1-dB gain compression point at the frequency of 1 GHz was ‒6 dBm.

Analysis and Design of Distributed Power Detectors

The distributed power detector is an alternative detector topology to overcome the wideband input matching limits of traditional matching techniques. A distributed power detector absorbs the bandwidth limiting parasitic junction capacitance of the diode in a traveling-wave structure. This paper presents a detailed theoretical analysis of the diode-based distributed power detectors. A lumped-element transmission line model is used to design the power detector with wideband RF input matching. Furthermore, a generalized analytical expression for the current and voltage responsivities of an ${n}$ -section power detector is derived. The noise analysis of the power detector is also carried out to predict its frequency-dependent noise equivalent power (NEP). The analysis is experimentally validated by designing two- and three-section distributed power detectors using packaged Schottky diodes on a PCB substrate. The three-section design demonstrates a measured video bandwidth of at least 46 MHz and a measured $S_{11}$ below −10 dB from 0.1 to 5.3 GHz. A maximum voltage responsivity of 17.57 kVW−1 is measured at 5.3 GHz. It achieves a measured input-referred square-law dynamic range of at least 51 dB for a ±1-dB error. The design has a measured NEP of less than 9.6 pW/ $\sqrt {\mathrm{ Hz}}$ for the entire bandwidth of operation. Simulations and measurements show a very good agreement with the developed theory.

A Highly Compact 2.4-GHz Passive 6-bit Phase Shifter With Ambidextrous Quadrant Selector

An extremely compact architecture for a passive 6-bit digital phase shifter is presented. The phase shifter has a range of 360° with 5.6° resolution at 2.4 GHz. The architecture is composed of an ambidextrous quadrant selector in series with a digital finetuned phase shifter that makes use of high-ratio symmetrical digitally variable capacitors loading a lumped element transmission line. The phase shifter achieves a 50 Ω match in all 64 states. The circuit occupies approximately 0.47 mm2 on die, and the entire test chip measured 0.84 mm2, including bond pads and ESD structures. The 1-dB compression point was +23 dBm. The chip was fabricated in a commercial 0.13-μm silicon-on-insulator CMOS process.

Stepped Impedance Magnetic Compression Line Pulse Generator

A novel and improved magnetic compression-based stepped impedance transmission line pulse generator circuit is presented. It is shown that discharging an initially charged lumped element transmission line with saturable inductor switches in each cell can result in complete energy transfer between cells provided the cell capacitances are in a certain fixed sequence independent of the cell inductances. The use of precharge voltage and proper capacitance sequence in such stepped impedance magnetic compression line provides voltage multiplication in addition to pulse compression.

Computational simulation of clarinet-like models

The presentation will review the computational simulation of two clarinet-like models. The Stewart and Strong model (J. Acoust. Soc. Am. 68, July 1980) consisted of a uniform cylindrical tube with an attached clarinet mouthpiece and reed. The tube was represented by 0.25-cm sections of lumped element transmission line. The tapered mouthpiece was similarly represented with 0.1-cm sections. The reed was represented as a non-uniform bar clamped at one end. The simulation was carried out on a DEC PDP-15 computer and had a running time of roughly 250,000 times real time. The Sommerfeldt and Strong model (J. Acoust. Soc. Am. 83, May 1988) was similar to the Stewart model, but included seven toneholes. The impedance of the tube with mouthpiece was calculated and used to calculate the impulse response. This was used to determine the interaction between pressure and flow at the reed opening. A player's airway was also included in the model because, at the time, there was some interest in its effect on tone production. Computational and experimental results will be presented. The two examples will illustrate some limits to simulation of models when computational power is inadequate as was true at the time.

Oscillating Pulse Generator Based on a Nonlinear Inductive Line

A chain of cascading LC sections consisting of series nonlinear inductors and parallel linear capacitors can be used to generate oscillating pulses. When a rectangular pulse is injected into the input of such a nonlinear inductive line (NLIL), the pulse undergoes modulation and exits at the output with oscillations in the waveform. This paper describes the implementation of high-voltage NLILs using commercial-off-the-shelf components. A pulser comprising of a storage capacitor and a fast semiconductor switch is used to provide the input pulse with approximate rectangular pulse shape. The design of the NLIL, which is a type of nonlinear lumped element transmission line (NLETL), is based on a NLETL circuit model developed earlier in-house. The nonlinear inductors made of ferrites are modeled using a simplified form of the Landau-Lifshitz-Gilbert (LLG) equation. A simple novel approach is proposed to determine the characteristic parameters in the LLG equation. Simulation results from the NLETL model are compared to the experimental results, and analyses on the voltage modulation and frequency content of the output pulses are performed. The use of crosslink capacitors in the line to modify the dispersive characteristics to enhance the performance is also investigated. With the results, the conditions and trends for producing oscillating pulses in NLILs are discussed.

Pulsed RF oscillations on a nonlinear capacitive transmission line

A nonlinear lumped element transmission line (NLETL) that consists of a nonlinear LC ladder network whose capacitors are nonlinear and inductors are linear can be used to produce oscillating pulses. This article describes the implementation of an oscillating pulse generator based on such high voltage nonlinear capacitive lines (NLCL) using commercial-off-the-shelf (COTS) components. Instead of using complex pulse forming networks or pulse forming lines, a storage capacitor and a fast semiconductor switch are used to provide an input pulse onto the cascading LC-elements of the NLCL with good approximation of a rectangular pulse-shape. The design of the NLCL is based on the NLETL circuit model that was developed earlier in-house. Experimental results are compared with simulations predicted by this NLETL model. The voltage modulation and the frequency content of the output pulses are analyzed. The conventional single NLCL produces a signal with a DC offset and a decoupling capacitor is needed at the end of the line to extract the AC component before injecting onto a load such as an antenna. A novel method of directly extracting the AC component without the use of a decoupling capacitor is proposed and investigated. Results of this direct AC extraction, which show the possibility of better performance, are discussed. The frequency tunability of this nonlinear line was also demonstrated.

An optimized surface plasmon photovoltaic structure using energy transfer between discrete nano-particles

Surface plasmon enhancement has been proposed as a way to achieve higher absorption for thin-film photovoltaics, where surface plasmon polariton(SPP) and localized surface plasmon (LSP) are shown to provide dense near field and far field light scattering. Here it is shown that controlled far-field light scattering can be achieved using successive coupling between surface plasmonic (SP) nano-particles. Through genetic algorithm (GA) optimization, energy transfer between discrete nano-particles (ETDNP) is identified, which enhances solar cell efficiency. The optimized energy transfer structure acts like lumped-element transmission line and can properly alter the direction of photon flow. Increased in-plane component of wavevector is thus achieved and photon path length is extended. In addition, Wood-Rayleigh anomaly, at which transmission minimum occurs, is avoided through GA optimization. Optimized energy transfer structure provides 46.95% improvement over baseline planar cell. It achieves larger angular scattering capability compared to conventional surface plasmon polariton back reflector structure and index-guided structure due to SP energy transfer through mode coupling. Via SP mediated energy transfer, an alternative way to control the light flow inside thin-film is proposed, which can be more efficient than conventional index-guided mode using total internal reflection (TIR).

Circuit Modeling of Nonlinear Lumped Element Transmission Lines Including Hybrid Lines

A nonlinear lumped element transmission line (NLETL) that consists of an <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">LC</i> -ladder network can be used to convert a rectangular input pump pulse into a series of RF oscillations at the output. The discreteness of the <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">LC</i> sections in the network contributes to the line dispersion while the nonlinearity of the <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">LC</i> elements produces the nonlinear characteristics of the line. Both of these properties combine to produce wave trains of high frequency. This paper describes an NLETL circuit model that is used to simulate RF generation for a given input pump pulse and the experiments used to validate the simulated results. The circuit model is used to study a nonlinear capacitive line that comprises nonlinear <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">C</i> but linear <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">L</i> and a nonlinear inductive line that comprises nonlinear <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">L</i> but linear <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">C</i> . Extensive and comprehensive parametric studies were carried out for the various NLETLs to understand the behavior and characteristics of these lines. Interesting observations were made, and explanations were given for their occurrence. A hybrid line that comprises both nonlinear elements <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">L</i> and <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">C</i> was also investigated using the circuit model with the goal of better matching to a resistive load. Simulations of the hybrid line indicate promising results.

Combined lumped element network and transmission line synthesis for passive microwave structures

Abstract. Compact circuit models of electromagnetic structures are a valuable tool for embedding distributed circuits into complex circuits and systems. However, electromagnetic structures with large internal propagation delay are described by impedance functions with a large number of frequency poles in a given frequency interval and therefore yielding equivalent circuit models with a high number of lumped circuit elements. The number of circuit elements can be reduced considerably if in addition to capacitors, inductors, resistors and ideal transformers also delay lines are included. In this contribution a systematic procedure for the generation of combined lumped element/delay line equivalent circuit models on the basis of numerical data is described. The numerical data are obtained by numerical full-wave modeling of the electromagnetic structure. The simulation results are decomposed into two parts representing a lumped elements model and a delay line model. The extraction of the model parameters is performed by application of the system identification procedure to the scattering transfer function. Examples for the modeling of electromagnetic structures are presented.

Broadband Mag-Noise of Patterned Permalloy Thin Films

A Y-factor noise figure (NF) measurement method is developed to characterize high-frequency mag-noise of a 550 nm wide Permalloy strip array under different dc bias currents. The noise voltage density is obtained. The proposed lumped element transmission line model describes noise properties of the patterned Py array well. Measurement data show that rapid ferromagnetic resonance frequencies (FMR) shift induced by dc bias current is related to the excess magnetization fluctuation thermally created by the combined dc current Joule heating effects and orthogonal Oersted fields.

High-Power Pulsed RF Extraction From Nonlinear Lumped Element Transmission Lines

Electrical soliton bursts are generated on a range of simulated and experimental nonlinear lumped element transmission lines (NLETLs). The design parameters necessary to achieve high frequency waveforms with peak voltage amplification are investigated, and the control over output frequency is demonstrated. An explanation of the fundamental problem of extracting extended bursts of solitons to linear load resistances is offered, along with the results from successful novel NLETL-based soliton burst generators tested at low voltages.

Fabrication of a Nb-Based 180-Degree IF Hybrid for Balanced SIS Mixers

180-degree IF hybrids are potentially useful for balanced superconductor-insulator-superconductor (SIS) mixers. We have developed a compact Nb-based 180-degree hybrid for 4-12 GHz which addresses concerns of element size, ohmic loss, and IF bandwidth. The fabrication scheme developed for these elements will be discussed, including the use of a thin overlayer Au process for via contacts, RF diode sputtered SiOx in lieu of sublimated SiOx films in order to improve the wafer yield, and diagnostic Nb capacitors to evaluate these SiOx films. Experimental results will be presented and compared with simulations of these lumped element transmission line rat-race hybrids. It should be noted that the hybrids can be used in cryogenic balanced mixers for any RF band.

Spark gap optimization by electrodynamic simulations

When switching times are no longer dominated by the plasma formation time, such as for photoconductive switching of high-voltage spark gaps, electrodynamic details of the switching process determine the rise time and pulse shape of the switched pulse. We show that the commonly used zero-dimensional lumped element and one-dimensional transmission line theory are no longer sufficient for optimizing such fast-switching devices, because important electromagnetic-field propagation in three dimensions is neglected. In order to improve the output of the photoconductively switched spark gap, we developed an optimization procedure for spark gap geometries based on full three-dimensional electrodynamic simulations. By monitoring the electromagnetic-field propagation in time, it will be shown that the initial electromagnetic-field disturbance in the gap reflects at the outer conductor and interferes with the initial field. The reflection and interference are essential for the shape of the output signal. We propose the following optimization procedure to improve the output of the photoconductively switched coaxial spark gap. Initially, the reflection and interference can be influenced by reshaping the inner conductor. The outer conductor can be used to fine-tune the system to get an output pulse with a sharp rising edge and no significant oscillations. We also present the optimal spark gap geometry that gives the best output signal at photoconductive switching.