Slow-wave Transmission Lines Research Articles

A GCPW slow‐wave transmission line with improved wavelength reduction technique by adopting capacitor array

AbstractThis letter presents a grounded coplanar waveguide (GCPW) slow‐wave transmission line (SWTL) with an improved wavelength reduction technique by adopting capacitor array. By cross‐interleaving additional capacitors between a signal line and side ground planes, the total capacitance in the capacitor array increases approximately two times compared to the conventional structure, allowing designers to choose a smaller signal conductor's width for higher inductance, thus, improving wavelength reduction performance while preserving the same characteristic impedance. At the 150 GHz frequency of interest, the proposed GCPW SWTL shows approximately 20% and 62.16% reduction in wavelength compared to the reported GCPW SWTL and regular CPW, respectively, with the same characteristic impedance. To prove the effectiveness of the proposed SWTL concept, the proposed GCPW SWTL test patterns are fabricated in a 65 nm CMOS process.

Miniaturized wide‐band microstrip grid array antenna loaded with slow‐wave transmission line

AbstractA miniaturized microstrip grid array antenna (MGAA) in X‐band is proposed in the paper. The antenna consists of a radiation grid array, a feed network and a metal back cavity. The 2 × 2 planar grid array is constructed by using four MGAAs as subarrays. MGAA does not require complex feeders in contrast to microstrip patch arrays. Furthermore, a curved slow‐wave transmission line (SWTL) is adopted as the long side of grid. The SWTL not only reduces the physical size of the grid while keeping its electrical size unchanged, but also improves the impedance matching and greatly broaden the bandwidth of the antenna. A fabricated prototype was measured in the microwave chamber. The results indicate that the impedance matching band of |S11| < −10 dB is from 9 to 10.5 GHz (15.4%), and the maximum gain is 19.2 dBi. Meanwhile, the projected area of the antenna is reduced by about 40% by loading the SWTL.

Miniaturized, Slow-Wave Transmission Line-Based Annular Ring Antenna With Reconfigurable Circular Polarization and High Gain

A miniaturized, high-gain, circular polarization (CP)-reconfigurable antenna implemented by slow-wave transmission line (SW-TL)-based annular ring is developed. First, the detailed configuration of the CP reconfigurable antenna together with its biasing circuit is presented. Then, its working mechanism of CP radiation and miniaturization is comprehensively revealed by illustrating the evolution process from a conventional linearly polarized annular ring antenna. Further, the detailed resonant frequency of the miniaturized SW-TL-based antenna is calculated by the slow-wave factor (SWF) of the fan-shaped SW-TL. Finally, experiments were carried out to validate the design concept. Measured results, verified by the simulated ones, show that the developed CP reconfigurable antenna exhibits a high gain of 7.83dBic under a miniaturized annular ring radiator with radius of 0.136λ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> .

A Simple Circularly Polarized Beam-Scanning Antenna Using Modulated Slotline-Spoof Surface Plasmon Polariton Slow-Wave Transmission Line

This letter proposes a novel simple planar circularly polarized (CP) frequency beam-scanning (FBS) antenna using slotline (SL) and spoof surface plasmon polariton (SSPP) structure. A new SL-SSPP slow-wave transmission line (TL) is initiated by periodically introducing orthogonal tilted corrugated grooves on both sides of the SL, which can generate orthogonal electric-field components in the same cross-section along the TL, and its dispersion characteristic can be flexibly adjusted. In order to excite an effective radiating mode from the propagating slow-wave mode, a simple double-sided tilted modulation method is devised to periodically modulate the SL-SSPP TL. Further, to obtain the CP characteristic, a π/2 phase displacement between the sinusoidal modulation structures on both sides of the TL is designed. The configuration of presented CP beam-scanning antenna owns the merits of simpler structure, low profile, and single dielectric layer. A prototype is manufactured and then tested to verify the proposed design. The experimental results con-firm that, within the 3-dB axial ratio (AR) bandwidth (from 7.2 to 8.35 GHz), the designed antenna achieves a 35° beam-steering range with CP characteristic. This antenna also realizes appropriate gain and radiation efficiency in the working band.

Oscillators Based on Step-Impedance and Slow Wave Transmission Lines for Sensing Applications

This work investigates the capabilities of oscillators based on step-impedance and slow wave structures to sense dielectric constants. The material under test (MUT) is placed over the structure and the objective is to achieve a high sensitivity of the oscillation frequency with the advantage of low phase noise, enabled by the high quality factor of the structure. With the aid of simplified analytical models, we will initially study the variation of the resonance frequency of a istep-impedance transmission line with the dielectric constant of the MUT, paying attention to the influence of the number of line sections. The study includes the derivation of analytical expressions for the sensitivity of the resonance frequency. Next, the structure will be connected to the oscillator active core, which will be modeled with a numerical nonlinear admittance function extracted from harmonic-balance (HB) simulations. The resulting semianalytical formulation will provide insight into the variation of the oscillation frequency and amplitude with the dielectric constant of the MUT, as well as the variation of the phase-noise spectral density. It will also enable a versatile test and optimization of the various structures to achieve high sensitivity with low phase noise. The methods have been successfully applied to an field-effect transistor (FET)-based oscillator at about 2 GHz.

Electromagnetic Particle Algorithm for Beam–Wave Interaction in Traveling Wave Tube of Symmetry

In many fields, such as space astrophysics, plasma and vacuum electronics, there are many nonlinear strong coupling physical problems. In order to solve the problem of electron beam–wave interaction in cylindrical Traveling wave tube (TWT) with symmetrical structure, a multi particle simulation algorithm for beam circuit is designed. The algorithm allows aperiodic time input, nonuniform linearity and large space diagnosis for different particles. In this algorithm, the field of coupled slow-wave transmission line is simulated by finite difference method. Assuming that there is strong coupling between the beam and the circuit, the space center equation of transmission along the line is obtained, and the space charge field is modeled considering the space charge effect, which can easily be ignored. The Particle In Cell (PIC) method of frog leaping step scheme is adopted to evaluate the electric field of each particle center, determine the circuit and space charge field, and design the termination part to compensate for the loss in order to avoid self-excited agitation. Finally, a simple numerical simulation is carried out for the electromagnetic problem and the accuracy of the code is checked against the electromagnetic simulator CHPIC. Therefore, the algorithm can be used to solve the problem of beam–wave interactions in a fixed structure (cylindrical) in multiple fields and can accurately record the data in the process.

Broadband and compact folded substrate integrated waveguide phase shifter and its application to 180° directional coupler

Abstract In this paper, a broadband, low insertion loss, and compact folded substrate integrated waveguide (FSIW) phase shifter is proposed for the first time. By loading the complementary split-ring resonators (CSRRs) on the middle metal layer of the FSIW, a closed-type slow-wave transmission line (TL) is obtained, which can provide a wideband phase shift (39%) compared with the equal-length fast-wave one. The enclosed structure of the CSRR-loaded FSIW prevents the CSRRs from radiation as suffered in the previous reported CSRR-loaded TLs, resulting in a low insertion loss. This feature greatly reduces the amplitude imbalance between the main line and the reference line of the phase shifter. In addition, no transition structure is required between the FSIWs with and without CSRRs for broadband impedance matching, which makes the phase shifter more compact and easier to integrate with other FSIW devices. To validate the performance of the proposed phase shifter and to illustrate its ease integration, a novel FSIW 180° directional coupler that consists of an FSIW 90° coupler and an FSIW 90° phase shifter is designed, fabricated, and measured. The measured results agree well with the simulated data.

Average Power Handling Capability of Corrugated Slow-Wave Transmission Lines.

In this article, the average power handling capability (APHC) of corrugated slow-wave transmission lines (SWTLs) is investigated. Firstly, the attenuation constants of conductor and dielectric are extracted by the multiline method. Secondly, the thermal resistance of corrugated SWTLs is analyzed based on the constant-angle model. To deal with the non-uniform corrugated structure of SWTLs, the concept of average heat-spreading width (AHSW) is introduced. Finally, the APHC of the corrugated SWTL is calculated using the attenuation constant and the thermal resistance. In addition, the APHC considering the temperature-dependent resistivity of metal conductor is also presented. For validation, the APHCs of SWTLs with different geometric parameters are evaluated. The results agree well with those obtained by the commercial software.

Design of Broadband Compact Grid Array Antennas Using Gradient Slow-Wave Structures

Compact grid array antennas (GAAs) with the gradient slow-wave structures are designed in this letter. The electrical lengths of slow-wave transmission lines (SW-TLs) with gradient structures are investigated based on the equivalent microwave network. By utilizing SW-TLs with exponential gradient structure on the long sides of GAAs, the proposed antenna achieves an area-reduction factor of 24.4%, with a measured 10 dB impedance bandwidth from 27.50 to 33.86 GHz and a maximum gain of 15.71 dBi.

Tunable phase shifters using composite inductive-capacitive loaded slow-wave transmission lines

This article presents the analysis and design of a continuously tunable phase shifter based on composite inductive/capacitive loaded slow-wave transmission lines. Slow-wave transmission lines are suitable candidates for the design of compact phase shifters due to their inherent miniaturized structures and highly dispersive characteristics. The design is started by considering the conventional capacitive loaded slow-wave transmission line, where the capacitors are replaced with varactor diodes for tuning the phase response. Then, more practically implementable phase shifter design is proposed by considering composite inductive/capacitive loaded slow-wave transmission lines. A systematic circuit model-based design method has been developed for the design of the tunable phase shifters using an accurate dispersion analysis. Finally, the efficiency of the design procedure is validated by fabricating and measuring a tunable phase shifter prototype using a four unit cell slow-wave transmission line. The measurements show a 121° phase tunability at 2 GHz design frequency with a maximum insertion loss (IL) of 2.1 dB, whereas a 140° phase tunability at 2 GHz can be achieved at a cost of a higher insertion loss around 2.7 dB.

Frequency controlled beam scanning characteristic realized using a compact slow wave transmission line.

To simplify the design of a beam scanning device, we present a simple and compact structure to realize the frequency scanning characteristic based on a hybrid waveguide consisting of a spoof surface plasmon polariton (SSPP) transmission line and half-mode substrate integrated waveguide (HMSIW). Additionally, the radiation characteristic is implemented using periodically modulated slots. The scanning angle range covers backward to forward directions without an open stop band at the broadside. The results from both simulations and measurements show that the total scanning angle reaches 117° for a frequency range of 9-11.4 GHz. Owing to the inherent features of the HMSIW and the unique design of the SSPP transmission line, the entire structure is only 139.2mm×15mm in size. Moreover, the average gain is approximately 6.5 dBi. Overall, the compact size and good performance ensure that the proposed design is favorable for planar integrated communication systems.

Highly Sensitive Phase-Variation Dielectric Constant Sensor Based on a Capacitively-Loaded Slow-Wave Transmission Line

This paper presents a highly sensitive phase-variation sensor for dielectric constant measurements based on a capacitively-loaded periodic slow-wave transmission line. Such line is implemented in microstrip technology, and the loading capacitors are formed by closely spaced rectangular patches. The sensing area of the device is delimited by the region occupied by the capacitive patches, where the material under test (MUT) must be located. The presence of the MUT modifies the coupling capacitance between adjacent patches, thereby producing a variation in the electrical length, or phase of the transmission line, which is the output variable. A detailed analysis of the equivalent circuit model of the unit cell, useful for design purposes, is carried out in the paper. Based on such analysis, a prototype device sensor is designed and fabricated. It is demonstrated in the paper that the sensitivity of the proposed sensor is by far superior to the one achieved in an ordinary meandered line with similar sensing area. Thus, the proposed slow-wave structure constitutes a good alternative to meandered lines for the implementation of phase-variation sensors with simultaneously high sensitivity and compact size.

A Compact, High-Efficiency, Reflectionless Leaky-Wave Antenna

A compact, high-efficiency leaky-wave antenna (LWA) is presented in this letter. Comprised by a novel periodic transmission line structure, the developed LWA could radiate its input power by a peak radiation efficiency of 93% with a compact size of 3.63λ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">L</sub> × 0.24λ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">L</sub> . Besides, the LWA exhibits good reflectionless performance characteristics from dc to 19 GHz. The equivalent circuit representations are utilized to reveal its operation mechanism. It is verified that the LWA operates as a slotted half-mode substrate integrated waveguide with high-efficiency leaky-wave radiation in the upper leaky band. Meanwhile, it could serve as a low-loss slow-wave transmission (SW-TL) line with spoof surface plasmon polariton structure in the lower band. For verification, an LWA prototype was fabricated and measured, which has experimentally confirmed its simulated radiation performances.

Tilted-Beam Antenna Based on SSPPs-TL with Stable Gain.

In this paper, a titled-beam antenna based on spoof surface plasmon polaritons (SSPPs) transmission lines (TLs) is proposed. The parallel SSPPs-TL is a slow-wave TL, which is able to limit waves in the TL strictly. By periodically introducing a set of tapered stubs along the SSPPs-TL, the backward endfire beams are formed by the surface waves in the slow-wave radiation region. Then, through the placement of a big metal plate below the endfire antenna, the backward endfire beams are tilted, and the tilted angle of the beams are steered by the distance of the metal plate and antenna. Over the band of 5.7 GHz~7.0 GHz, the tilted antenna performs constant shapes of radiation patterns. The gain keeps stable at around 12 dBi and the 1-dB gain bandwidth is 20%. The measured results of the fabricated prototypes confirm the design theory and simulated results.

A narrow‐band circularly polarized leaky‐wave antenna with open stopband suppressed

In this paper, a narrow-band circularly polarized (CP) microstrip leaky-wave antenna (LWA) with open stopband suppressed is proposed. Coupled meandered slow-wave lines are adopted to realize narrow-band beam scanning. The asymmetric elements are employed as radiators to realize CP and zero-crossing scanning. We modulated the antenna by loading the ground inductance and asymmetric capacitors on the meandered slow-wave transmission line. The antenna consists of ten asymmetrical structural elements connected by coupling, the antenna size of L × W is 170 mm × 25 mm. In the operating band of 8.1 to 8.5 GHz, the measured scanning angel of the fabricated antenna is from −31°to +6°. The antenna axial ratios (ARs) are all below 3 dB at the corresponding beam directions. The gain is above 9.1 dBi and the relative bandwidth is only 4.8%. In the operating band, the radiation efficiency is above 60%. It has potential applications in radar detection and wireless communication systems for its simple and low-profile structure with CP, beam-scanning, and narrow-band performance.

Transmission lines characteristic impedance versus Q-factor in CMOS technology

AbstractThis paper presents a systematic comparison of the relationship between transmission line characteristic impedance and Q-factor of CPW, slow-wave CPW, microstrip, and slow-wave microstrip in the same CMOS back-end-of-line process. It is found that the characteristic impedance for optimal Q-factor depends on the ground-to-ground spacing of the slow-wave transmission line. Although the media are shown to be similar from a mode of propagation point of view, the 60-GHz optimal Q-factor for slow-wave transmission lines is achieved when the characteristic impedance is ≈23 Ω for slow-wave CPWs and ≈43 Ω for slow-wave microstrip lines, with Q-factor increasing for wider ground plane gaps. Moreover, it is shown that slow-wave CPW is found to have a 12% higher optimal Q-factor than slow-wave microstrip for a similar chip area. The data presented here may be used in selecting Z0 values for S-MS and S-CPW passives in CMOS that maximize transmission line Q-factors.

Compact Series-Fed Microstrip Patch Arrays Excited With Dolph–Chebyshev Distributions Realized With Slow Wave Transmission Line Feed Networks

Compact series-fed microstrip patch arrays are presented that are excited with Dolph–Chebyshev distributions realized with periodic stub-loaded slow wave transmission line (SW-TL) feed networks. The methodology to design these SW-TL feed networks is described in detail. The developed equivalent circuit representation reveals that their characteristic impedance can be modulated while maintaining their propagation constant (guided-wavelength) simply by modifying the widths of their stubs. These stub-loaded SW-TL feed networks are seamlessly integrated with uniformly spaced microstrip patch arrays. The desired Dolph–Chebyshev excitations are realized simply by modulating the widths of their stubs. Moreover, the slow wave property of the SW-TLs facilitates an advantageous closely spaced Dolph–Chebyshev current distribution, i.e., a very compact array with $0.3\lambda _{0}$ spacing between the array elements is attained. The Dolph–Chebyshev SW-TL feed networks are employed to excite microstrip patch arrays that radiate a broadside main beam with −30 dB sidelobe levels and a grating-lobe-free 50° tilted main beam. A measured prototype of the broadside-radiating array confirms its simulated performance characteristics. In comparison with conventional Dolph–Chebyshev arrays implemented with standard microstrip transmission line (MTL) feed networks, the optimized designs are grating-lobe-free and have enhanced bandwidths.

A 48 Gb/s PAM-4 Transmitter With 3-Tap FFE Based on Double-Shielded Coplanar Waveguide in 65-nm CMOS

A power and area-efficient pulse-amplitude modulation 4 (PAM-4) transmitter using 3-tap feed-forward equalizer (FFE) based on a slow-wave transmission line is presented. Passive delay line is adopted for generating equalizer tap to overcome the high clocking power consumption. The transmission line achieves high slow-wave factor of 15 with double floating metal shields around the differential coplanar waveguide. The physical dimensions of the transmission line are determined to have low loss and a high slow-wave factor with a small chip area by optimization with 3-D electromagnetic simulations. The transmitter includes 4:1 multiplexers (MUXs) and a quadrature clock generator for high-speed data generation in a quarter-rate system. The 4:1 MUX utilizes 2-UI pulse generator and the input configuration is determined by qualitative analysis. The chip is fabricated in 65-nm CMOS technology and occupies area of 0.151 mm2. The proposed transmitter system exhibits the energy efficiency of 3.03 pJ/b at the data rate of 48 Gb/s with PAM-4 signaling.

Compact Fully Metallic Millimeter-Wave Waveguide-Fed Periodic Leaky-Wave Antenna Based on Corrugated Parallel-Plate Waveguides

A compact fully metallic millimeter-wave (MMW) periodic leaky-wave antenna (LWA) based on corrugated parallel-plate waveguides with high radiation efficiency and low machining complexity is presented in this letter. The LWA consists of a smooth plate and a corrugated plate that integrates the corrugation for slow-wave transmission line and the radiating slots. By introducing two different elements into one radiating unit, the open stopband effect is improved and the broadside scanning is realized. As an experimental verification, a prototype in Ka-band is designed, fabricated, and measured. The scanning beams with an angular range of 48° (from −42.5° to 5.5°) and the peak gains between 11.9 and 16.0 dBi are obtained in the frequency range from 28 to 40 GHz. The radiation efficiency is higher than 85%. The results indicate its application potential in the MMW imaging and radar systems.

Design of a 77-GHz LC-VCO With a Slow-Wave Coplanar Stripline-Based Inductor

The objective of this paper is to demonstrate that the use of a distributed approach for the design of the inductance of an LC-tank millimeter-wave (mm-wave) voltage-controlled oscillator (VCO) can lead to higher performance. Performance is improved in both frequency tuning range and power consumption thanks to a reduction of the cross-coupled pair size. The direct comparison of VCOs designed in different technologies is not straightforward, since the performance of the varactors and the inductance widely differ for different fabrication technologies. Hence, two VCOs were designed and integrated in the same CMOS 55-nm technology by using the same varactors. A “classical” VCO using an inductor available in the technology and serving as reference, and a distributed-inductance-based VCO using a slow-wave transmission line were considered. A detailed and efficient approach is adopted for the synthesis of slow-wave transmission line-based inductance without using time-consuming EM simulations. The slow-wave VCO permits to limit the overall size linked to a distributed approach while improving the electrical performance. The experimental results on the proof-of-concept demonstrators at a working frequency of 77 GHz allow validating our proposal.