Slow-wave Line Research Articles

An Approach to Focus the Sheet Electron Beam in the Planar Microstrip Line Slow Wave Structure

Planar microstrip line slow wave structures (PML-SWSs) have great prospects in the millimeter and terahertz wave fields. However, the development of the devices employing PML-SWSs is severely limited due to the focusing difficulties. Compared with the conventional sheet electron beam (SEB) SWS, the asymmetric boundary condition of PML-SWS and high local electric field further increase the instabilities of the SEB transport in PML-SWS. A new approach, named the uniform magnetic focusing system with the matching electric field (UMFS-MEF), is presented in this article, which can effectively solve these issues. The simulation results illustrate that the expansion rate of the SEB in UMFS-MEF is significantly lower than that in the conventional uniform magnetic focusing system (CUMFS) with the same magnetic field strength <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${B}_{z}$ </tex-math></inline-formula> . Moreover, the present calculation results show that the UMFS-MEF requires only 10.6% of the magnetic field strength of CUMFS for maintaining the same expansion rate. This means that the UMFS-MEF can effectively suppress the instabilities, and employ a very low magnetic field to maintain the stabilities of the SEB transport. Finally, we give several other schemes to realize the method.

Broadband-Printed Traveling-Wave Tube Based on a Staggered Rings Microstrip Line Slow-Wave Structure

To increase the output power of microstrip line traveling-wave tubes, a staggered rings microstrip line (SRML) slow-wave structure (SWS) based on a U-shaped mender line (U-shaped ML) SWS and a ring-shaped microstrip line (RML) SWS has been proposed in this paper. Compared with U-shaped ML SWS and RML SWS, SRML SWS has a wider transverse width, which means SRML SWS has a larger area for beam–wave interaction. The simulation results show that SRML SWS has a wider bandwidth than U-shaped ML SWS and a lower phase velocity than RML SWS. Input/output couplers, which consist of microstrip probes and transition sections, have been designed to transmit signals from a rectangular waveguide to the SWS; the simulation results present that the designed input/output structure has good transmission characteristics. Particle-in-cell (PIC) simulation results indicate that the SRML TWT has a maximum output of 322 W at 32.5 GHz under a beam voltage of 9.7 kV and a beam current of 380 mA, and the corresponding electronic efficiency is around 8.74%. The output power is over 100 W in the frequency range of 27 GHz to 38 GHz.

Green’s Functions of Multi-Layered Plane Media with Arbitrary Boundary Conditions and Its Application on the Analysis of the Meander Line Slow-Wave Structure

A method was proposed for solving the dyadic Green’s functions (DGF) and scalar Green’s functions (SGF) of multi-layered plane media in this paper. The DGF and SGF were expressed in matrix form, where the variables of the boundary conditions (BCs) can be separated in matrix form. The obtained DGF and SGF are in explicit form and suitable for arbitrary boundary conditions, owing to the matrix form expression and the separable variables of the BCs. The Green’s functions with typical BCs were obtained, and the dispersion characteristic of the meander line slow-wave structure (ML-SWS) is analyzed based on the proposed DGF. The relative error between the theoretical results and the simulated ones with different relative permittivity is under 3%, which demonstrates that the proposed DGF is suitable for electromagnetic analysis to complicated structure including the ML-SWS.

Inverse Design of a Microstrip Meander Line Slow Wave Structure with XGBoost and Neural Network

We present a new machine learning (ML) deep learning (DL) synthesis algorithm for the design of a microstrip meander line (MML) slow wave structure (SWS). Exact numerical simulation data are used in the training of our network as a form of supervised learning. The learning results show that the training mean squared error is as low as 5.23 × 10−2 when using 900 sets of data. When the desired performance is reached, workable geometry parameters can be obtained by this algorithm. A D-band MML SWS with 20 GHz bandwidth at 160 GHz center frequency is then designed using the auto-design neural network (ADNN). A cold test shows that its phase velocity varies by 0.005 c, and the transmission rate of a 50-period SWS is greater than −5 dB with the reflectivity below −15 dB when the frequency is from 150 to 170 GHz. Particle-in-cell (PIC) simulation also illustrates that a maximum power of 3.2 W is reached at 160 GHz with 34.66 dB gain and output power greater than 1 W from 152 to 168 GHz.

A Concentric Arc Meander Line SWS for Low Voltage, High Efficiency, and Wide Bandwidth V-Band TWT With Dual Sheet Beam

A concentric arc meander line slow wave structure (CAML-SWS) for low voltage, high efficiency, and wide bandwidth V-band traveling wave tube (TWT) with dual sheet beam (DSB) is proposed. As a nonperiodic SWS, the CAML-SWS is utilized for obtaining low operational voltage and wide bandwidth performance. The DSB is employed for efficiency enhancement. The simulated reflection loss (|S <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><b>11</b></sub> |) is smaller than -30 dB covering the whole V-band. The 3-D particle-in-cell (PIC) simulation predicts that the output power of the proposed TWT can reach 58.6 W at 60 GHz, when the voltage is set at 940 V and the current of each sheet beam is 0.1 A. The corresponding peak gain and electron efficiency is 19.6 dB and 31.1% at 60 GHz, respectively. Furthermore, the 3-dB gain bandwidth is about 17 GHz from 51 to 68 GHz, where the output signal is steady and the frequency spectrums are quite clean.

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.

Broadband compact 180° phase shifter based on dumbbell shaped slow wave line

AbstractThis paper presents a compact 180° phase shifter with flat phase difference in a wide bandwidth. It is a hybrid structure based on a stub‐loaded line and a switched‐line phase shifter, in which a kind of periodic dumbbell‐shaped slow wave line and T‐shaped short‐ended stub are introduced for miniaturization. The proposed configuration shows a better broadband performance and compact geometric dimension compared with traditional phase shifters. The fractional bandwidths of the proposed structure defined by the return loss of 10 dB and the phase deviation of ±5° were 96% and 77%, respectively.

Low‐loss frequency scanning planar array with hybrid feeding structure for low‐altitude detection radar

A 1 × 4 low-loss frequency scanning planar array with hybrid feeding structure in Ku-band has been designed. In order to improve the array efficiency, the planar array was designed by four parallel sub-arrays and the waveguide slow-wave line structure with electromagnetic coupled slot on narrow side was used as feed line. The results of simulation show that, except at the centre frequency, the voltage standing wave ratio of the antenna array is below 1.2 at the operation band, the range of the scanning angles is (−30.5°, 29°), the beam width of the antenna is about 5.5°–6.6°, the sidelobe is below −20 dB, and the gain is more than 30 dBi.

Pseudo-elliptic slow wave line

Quasi elliptic filters are of great demand in the present day communication systems. Coupling matrix analysis of pseudo-elliptic low pass filter using conventional microstrip line is presented in this paper. The conventional microstrip line has no non-zero cut off frequency. The conventional microstrip line is transformed into a pseudo-elliptic low-pass filter using the concept of slow wave. The slow wave microstrip line exhibits pseudo-elliptic low-pass behavior with transmission zeros at finite frequencies unlike the conventional Butterworth and Chebyshev filters. The coupling matrix of the slow wave microstrip line is arrived at by using the generalized Chebyshev functions. The coupling matrix of the slow wave line is validated using the MATLAB tool box. Finally, the prototype is fabricated and the performance is measured.

Slow wave microstrip line and its application in miniaturization

This article presents a technique for miniaturization. The miniaturization is brought about by reducing the velocity of the wave, a phenomenon called slow wave propagation. The technique is demonstrated in this work using a microstrip line. Electromagnetic simulations show that the slow wave microstrip line has a cut-off frequency of 18.76 GHz and hence behaves like a low pass filter. The low pass nature is also confirmed from the lumped equivalence. The fabrication complexity is reduced by replacing a substrate filled with plated vias with a substrate bearing three rows of plated vias beneath the microstrip line, both of which show similar performances. The slow wave concept is confirmed from the value of group delay and is found to be enhanced in the slow wave line by 21.21%. Implementation of slow wave also results in a 36.3% increase in the effective permittivity. Parametric studies are conducted to analyze the slow wave phenomenon. For proof of concept, the technique is compared to the standard Chebyshev filter. The proposed structure reduces area by 40%. The proposed structure is then fabricated and performance is measured. The measured and simulated results are in good agreement.

Microstrip angular log‐periodic slow wave structure on quartz substrate with coaxial input/output coupler

The microstrip angular log-periodic meander line slow wave structure (SWS) on quartz substrate with coaxial input/output coupler is studied. The effects of different structure parameters on transmission characteristics of the 25 periods SWS during Ka band are discussed in detail. The SWS with the total length of ∼6.5 mm, add coaxial input/output coupler and tapered impedance microstrip line to form an entire assembly. The testing result is accordant with that of simulation. The dispersion characteristics of the SWS were obtained to determine the work voltage. The beam-wave interaction results show that the output power is 11.4 W at the frequency of 32 GHz, with the electron efficiency of 3.3%.

Expedite Design of Variable-Topology Broadband Hybrid Couplers for Size Reduction Using Surrogate-Based Optimization and Co-Simulation Coarse Models

In this paper, we discuss a computationally efficient approach to expedite design optimization of broadband hybrid couplers occupying a minimized substrate area. Structure size reduction is achieved here by decomposing an original coupler circuit into low- and high-impedance components and replacing them with electrically equivalent slow-wave lines with reduced physical dimensions. The main challenge is reliable design of computationally demanding low-impedance slow-wave structures that feature a quasi-periodic circuit topology for wideband operation. Our goal is to determine an adequate number of recurrent unit elements as well as to adjust their designable parameters so that the coupler footprint area is minimal. The proposed method involves using surrogate-based optimization with a reconfigurable co-simulation coarse model as the key component enabling design process acceleration. The latter model is composed in Keysight ADS circuit simulator from multiple EM-evaluated data blocks of the slow-wave unit element and theory-based feeding line models. The embedded optimization algorithm is a trust-region-based gradient search with coarse model Jacobian estimation. We exploit a penalty function approach to ensure that the electrical conditions for the slow-wave lines are accordingly satisfied, apart from explicitly minimizing the area of the coupler. The effectiveness of the proposed technique is demonstrated through a design example of two-section 3-dB branch-line coupler. For the given example, we obtain nine circuit design solutions that correspond to the compact couplers whose multi-element slow-wave lines are composed of unit cells ranging from two to ten.

Microstrip slow‐wave line for phase shifting cells

The design, simulation and measurements of microstrip slow-wave lines implemented in a 0.25 µm SiGe bipolar CMOS (BiCMOS) process is addressed for Ku-band (10–15 GHz) applications. The simulation results and the measurements show better performances for the proposed microstrip slow-wave line compared with the classical microstrip transmission line. These lines present very low insertion losses and a high phase constant.

W-band phase shifter in 28-nm CMOS

In this article, a compact W-band differential I---Q phase shifter is designed and implemented using 28-nm CMOS technology. The phase shifter is capable of achieving phase shifts ranging from 45° to 315° with a resolution of 90°. The design employs transmission-line baluns for creating a differential signal, Gilbert-cell-type active switches for generating 0° and 180° phase shifts and a 90° differential hybrid for obtaining differential I---Q signals. The hybrid is developed using capacitive-loaded slow-wave differential lines, thereby making it 75 % smaller than a conventional 90° hybrid. Furthermore, the modelling of a slow-wave differential line for odd-mode and even-mode propagation is explained. The phase shifter exhibits 12 dB of insertion loss, and the root-mean-square (RMS) gain and phase error are 0.55 dB and 16.6°, respectively, at 100 GHz. The total power consumption is 39 mW when using a 1-V supply. The chip size of the implemented design is 0.48 mm2 including the probing pads. The phase shifter design is further modified by replacing the baluns with single-stage differential buffer amplifiers to mitigate the signal loss. This modified version of the design shows +1 dB insertion gain with a total power consumption of 122.9 mW from a 1-V supply and realized at 0.565 mm2. A 13-dB gain improvement is obtained from the modified version and the measured RMS gain and phase error are 1.5 dB and 13°, respectively, at 100 GHz. After redesigning the layout, a minimum RMS phase error of 1.7° is expected in the simulations.

Slow-Wave Broadside-Coupled Microstrip Lines and Its Application to the Rat-Race Coupler

This letter proposes a type of slow-wave broadside-coupled microstrip lines. The new structure only requires a single-layer substrate and has the independently controllable even- and odd-mode impedances and slow-wave factors by adjusting the corresponding structural parameters. This property greatly simplifies the circuit design. In addition, it provides a large coupling strength. A miniaturized wideband microstrip rat-race coupler with the high isolation and perfect balances is implemented using the proposed slow-wave coupled lines.

Designs and Experiments of a Novel Radial Line Slot Antenna for High-Power Microwave Application

A radial line slot antenna (RLSA) is a nonresonant multimode waveguide slotted array. To improve the power handing capacity, we design a radial line slow wave structure which replaces a traditional dielectric sheet. At the same time, the structure of the radiator unit is redesigned and optimised. This high-power microwave (HPM) RLSA is fed from a double-layered radial line waveguide to realize the directional radiation of high-power microwave. However, the slots spirally arrayed for circular polarization give rise to serious reflection in higher order modes, which disturbs the normal antenna operation. A reflection cancelling slot is added to the conventional one and the antenna return-loss is effectively improved. An antenna operating at 9.42 GHz was designed with a length of 15 cm and an aperture radius of 27 cm. Numerical simulation results show that the calculated aperture efficiency reaches 44.8%, the reflectance is less than -20 dB, the radiation efficiency is more than 99%. Experimental measurements are accomplished for the prototype. In the range of 9.30-9.45 GHz, the reflection of the antenna is below -10 dB. The antenna gain reaches 29.0 dBi, and the axial ratio is below 1.6 dB. In addition, the high-power experiment proves that this antenna has a power-handing capacity of more than 1 GW.

Analysis of a high power microwave radial line slot antenna

A traditional radial line slot antenna (RLSA) is a high gain planar array. To improve the power handling capacity, we design a radial line slow wave structure which replaces a traditional dielectric sheet in the radial waveguide of the traditional RLSA. This high power microwave (HPM) RLSA is fed from a double-layered radial line waveguide to realize the directional radiation of the microwave. However, the track of the widen slot array on the upper waveguide could cause large reflection, which disturbs the normal antenna operation, accordingly a reflection canceling slot is added to the lower waveguide, the key technology employed in the design of the HPM RLSA and the antenna return-loss is effectively improved. This article mainly gives the design theory of this antenna, which is confirmed by the simulations and experiments. At 9.4 GHz, the calculated aperture efficiency reaches more than 40%, the reflectance is less than 0.1, the radiation efficiency is more than 99% and its measured power-handling capacity exceeds 700 MW.

A High Slow-Wave Factor Microstrip Structure With Simple Design Formulas and Its Application to Microwave Circuit Design

This paper proposes a new microstrip slow-wave structure. The unit cell comprises a Schiffman section of meander line and a shunt open-circuited stub. No via-holes and ground-plane patterns are required. Simple design formulas can be used to obtain line parameters, such as the characteristic impedance and phase velocity. According to the analysis, the characteristic impedance and slow-wave factor of the proposed slow-wave line can be independently controlled by merely two layout parameters. The proposed uniplanar structure only requires a single-layer substrate and is simply constructed using the conventional printed circuit board manufacturing process. A branch-line and a rat-race coupler were designed and fabricated using the proposed structure to demonstrate its feasibility. Their sizes are only 8.49% and 4.87% of the conventional ones, respectively. This novel slow-wave structure should find wide applications in compact microwave circuits.

Metamaterial-based wideband rat-race hybrid coupler using slow wave lines

Based on derived convenient design equations for slow wave transmission lines and metamaterial line, a very compact and wideband rat-race hybrid coupler is proposed using three -90° slow wave lines and one -90° metamaterial line. The closed-form solutions for circuit parameters based on both phase and phase slope matching conditions are derived. At the design frequency of 2 GHz, the size of the proposed coupler is about 2.0 × 2.0 cm, which is a 85% reduction compared with the conventional one. In addition, the phase balance bandwidths based on ∠ S 21 -∠ S 31 (0±10°) and ∠ S 24 -∠ S 34 (180±10°) have been found to be 150 and 125%, which are 1.8 and 3.0 times improvements compared with those of the conventional one. The measured results are in reasonable agreement with the circuit- and EM-simulated ones.

Bandwidth-Enhanced Electrically Small Printed Folded Dipoles

This letter presents a wire folding scheme to enhance the bandwidth of an electrically small resonant microstrip antenna. As an example, meandered two-wire slow-wave lines spread on both sides of a dielectric slab short-circuited at both ends form a vertically folded printed dipole. It is found that the radiation resistance increases by about a factor of 4, and the energy storage increases by about a factor of 2, using a folded dipole. It is shown through both measurement and simulation that the Q-factor is reduced by about 50% through antenna folding. A 0.14 ¿-long folded dipole resonant at 2.43 GHz shows a bandwidth of about 4.8%. The proposed folding method facilitates planar antenna miniaturization with sufficient bandwidth.