253 results found
This paper presents the state-of-the-art in polymer-based 3-D printing of metal-pipe rectangular waveguides (MPRWGs) with the first reported terahertz filters, all operating within the WR-2.2 band (325 to 500 GHz): a 5 mm-long thru line, two 399 GHz single-cavity resonators and two 403 GHz bandpass filters (BPFs). Our thru line exhibits a measured average insertion loss of only 0.9 dB, with a worst-case return loss of 13.3 dB, across the band. The single-cavity resonators, without and with corner rounding compensation (CRC) are investigated with the use of an RLC equivalent circuit model. The uncompensated resonator exhibits a 2.3% frequency downshift and an increase of 10.8 GHz in its 3 dB bandwidth. The compensated resonator exhibits a 2.2% frequency upshift and an increase of only 2.2 GHz in its 3 dB bandwidth; clearly demonstrating that CRC helps to mitigate against increased coupling into the resonators, as a result of manufacturing limitations with low-cost 3-D printing. Finally, the 3 rd order Butterworth and Chebyshev MPRWG BPFs both have a measured passband insertion loss of only 1.0 dB. The Butterworth filter exhibits a 0.8% passband frequency upshift and worst-case return loss of 16.6 dB; while the Chebyshev filter exhibits a 1.2% passband frequency downshift and worst-case return loss of 10.4 dB. With our low-cost polymer-based 3-D printing technology, we have demonstrated measured performances that are better than those using metal-based 3-D printing in the WR-2.2 band and this may, in the not too distant future, challenge components manufactured using traditional machining technologies.
Zhu L, Rossuck I, Payapulli R, et al., 2023, 3-D printed W-band waveguide twist with integrated filtering, IEEE Microwave and Wireless Technology Letters, Vol: 33, Pages: 659-662, ISSN: 2771-957X
This work demonstrates the integration of a low-pass filter into a 90 ∘ waveguide twist at W -band (75–110 GHz), manufactured using polymer-based 3-D printing. For the first time, a 1-D periodic electromagnetic bandgap (EBG) structure is incorporated within a waveguide twist. Unlike conventional filters, implemented using irises and septa, EBG structures employing hollow cavities are structurally robust and mechanically insensitive to 3-D printing. The measured average passband insertion loss is only 0.48 dB at the W -band while using our unconventional split-block solution ( H -plane a -edge split with raised lips). A nontwist thru filter has also been demonstrated, as a reference. Our approach demonstrates the potential for the low-cost manufacture of compact and high-performance multifunctional integrated waveguide components at millimeter-wave frequencies.
Payapulli R, Zhu L, Shin S-H, et al., 2023, Polymer-based 3-D printed 140 to 220 GHz metal waveguide thru lines, twist and filters, IEEE Access, Vol: 11, Pages: 32272-32295, ISSN: 2169-3536
This paper demonstrates the current state-of-the-art in low-cost, low loss ruggedized polymer-based 3-D printed G-band (140 to 220 GHz) metal-pipe rectangular waveguide (MPRWG) components. From a unique and exhaustive up-to-date literature review, the main limitations for G-band split-block MPRWGs are identified as electromagnetic (EM) radiation leakage, assembly part alignment and manufacturing accuracy. To mitigate against leakage and misalignment, we investigate a ‘trough-and-lid’ split-block solution. This approach is successfully employed in proof-of-concept thru lines, and in the first polymer-based 3-D printed 90° twist and symmetrical diaphragm inductive iris-coupled bandpass filters (BPFs) operating above 110 GHz. An inexpensive desktop masked stereolithography apparatus 3-D printer and a commercial copper electroplating service are used. Surface roughness losses are calculated and applied to EM (re-)simulations, using two modifications of the Hemispherical model. The 7.4 mm thru line exhibits a measured average dissipative attenuation of only 12.7 dB/m, with rectangular-to-trapezoidal cross-sectional distortion being the main contributor to loss. The 90° twist exhibits commensurate measured performance to its commercial counterpart, despite the much lower manufacturing costs. A detailed time-domain reflectometry analysis of flange quality for the thru lines and 90° twists has also been included. Finally, a new systematic iris corner rounding compensation technique, to correct passband frequency down-shifting is applied to two BPFs. Here, the 175 GHz exemplar exhibits only 0.5% center frequency up-shifting. The trough-and-lid assembly is now a viable solution for new upper-mm-wave MPRWG components. With this technology becoming less expensive and more accurate, higher frequencies and/or more demanding specifications can be implemented.
Zhu L, Shin S-H, Payapulli R, et al., 2023, 3-D printed rectangular waveguide 123-129 GHz packaging for commercial CMOS RFICs, IEEE Microwave and Wireless Technology Letters, Vol: 33, Pages: 157-160, ISSN: 2771-957X
This work demonstrates the hybrid integration of a complementary metal–oxide–semiconductor (CMOS) radio frequency integrated circuit (RFIC) into a host 3-D printed metal-pipe rectangular waveguide (MPRWG). On-chip Vivaldi antennas are used for TE 10 -to-thin-film microstrip (TFMS) mode conversion. Our packaging solution has a combined measured insertion loss of only 1 dB/transition at 126 GHz. This unique packaging and interconnect solution opens up new opportunities for implementing low-cost subterahertz (THz) multichip modules.
Zhu L, Shin S-H, Payapulli R, et al., 2023, Erratum to “3-D Printed Rectangular Waveguide 123–129 GHz Packaging forCommercial CMOS RFICs”, IEEE Microwave and Wireless Technology Letters, Vol: 33, Pages: 236-236, ISSN: 2771-957X
Shin S-H, Payapulli R, Zhu L, et al., 2022, 3-D Printed Plug and Play Prototyping for Low-cost Sub-THz Subsystems, IEEE Access, Vol: 10, Pages: 41708-41719, ISSN: 2169-3536
Polymer-based additive manufacturing using 3-D printing for upper-millimeter-wave ( ca. 100 to 300 GHz) frequency applications is now emerging. Building on our previous work, with metal-pipe rectangular waveguides and free-space quasi-optical components, this paper brings the two media together at G-band (140 to 220 GHz), by demonstrating a compact multi-channel front-end subsystem. Here, the proof-of-concept demonstrator integrates eight different types of 3-D printed components (30 individual components in total). In addition, the housing for two test platforms and the subsystem are all 3-D printed as single pieces, to support plug and play development; offering effortless component assembly and alignment. We introduce bespoke free-space TRM calibration and measurement schemes with our quasi-optical test platforms. Equal power splitting plays a critical role in our multi-channel application. Here, we introduce a broadband 3-D printed quasi-optical beamsplitter for upper-millimeter-wave applications. Our quantitative and/or qualitative performance evaluations for individual components and the complete integrated subsystem, demonstrate the potential for using consumer-level desktop 3-D printing technologies at such high frequencies. This work opens-up new opportunities for low-cost, rapid prototyping and small-batch production of complete millimeter-wave front-end subsystems.
Zhu L, Payapulli R, Shin S-H, et al., 2022, 3-D printing quantization predistortion applied to sub-THz chained-function filters, IEEE Access, Vol: 10, Pages: 38944-38963, ISSN: 2169-3536
This paper investigates physical dimension limits associated with the low-cost, polymer-based masked stereolithography apparatus (MSLA) 3-D printer, with 50 μm pixels defining the minimum print feature size. Based on the discretization properties of our MSLA 3-D printer, multi-step quantization predistortion is introduced to correct for registration errors between the CAD drawing and slicing software. This methodology is applied to G-band 5th order metal-pipe rectangular waveguide filters, where the pixel pitch has an equivalent electrical length of 8.5° at center frequency. When compared to the reference Chebyshev filter, our chained-function filter exhibits superior S-parameter measurements, with a low insertion loss of only 0.6 dB at its center frequency of 182 GHz, having a 0.9% frequency shift, and an acceptable worst-case passband return loss of 13 dB. Moreover, with measured dimensions after the 3-D printed parts have been commercially electroplated with a 50 μm thick layer of copper, the re-simulations are in good agreement with the S-parameter measurements. For the first time, systematic (quantization) errors associated with a pixel-based 3-D printer have been characterized and our robust predistortion methodology has been successfully demonstrated with an upper-millimeter-wave circuit. Indeed, we report the first polymer-based 3-D printed filters that operate above W-band. As pixel sizes continue to shrink, more resilient (sub-)THz filters with ever-higher frequencies of operation and more demanding specifications can be 3-D printed. Moreover, our work opens-up new opportunities for any pixel-based technology, which exhibits registration errors, with its application critically dependent on its minimum feature size.
Dawood A, Lucyszyn S, 2021, Parasitic high Q-factor open-box modes with 3-D printed dielectric-filled metal waveguides, IEEE Access, Vol: 9, Pages: 134319-134334, ISSN: 2169-3536
High Q-factor open-box mode resonances have been found in the microwave measurements of several 3-D printed dielectric-filled metal-pipe rectangular waveguides (MPRWGs). These parasitic Fabry-Pérot eigenmodes are confined by the conductive walls in the transverse plane of the MPRWG and partially confined by the air-dielectric and dielectric-air boundaries in the longitudinal direction. The excitation of open-box modes was previously speculated to be due to the inhomogeneities and/or anisotropic nature of the 3-D printed dielectric-fillers. This has now been confirmed, by representing the inhomogeneous and anisotropic nature of the woodpile-like dielectric structure (physical realm), with an anisotropic dielectric constant tensor (simulation realm). Analytical and numerical eigenmode solvers, previously used by the authors with MPRWGs, are applied here to parallel-plate waveguides (PPWGs) and circular waveguides (CWGs); identifying all the individual parasitic open-box modes. With the former, its TM11 mode exhibits an ultra-high Q-factor of approximately 2,300 at X-band, which is considerably higher than those found with other modes and in other waveguide structures. Finally, a numerical full-wave frequency-domain simulator that employs the dielectric constant tensor is introduced in this paper. This new modeling technique independently confirms that open-box modes are excited in 3-D printed dielectric-filled MPRWG, PPWG and CWG structures. This paper provides the foundations for accurately modeling parasitic resonances associated with inhomogeneities and anisotropy in 3-D printed microwave components; not just the metal-walled waveguide structures considered here, but the methodology could also be extended to generic 3-D printed dielectric waveguides and substrate-based transmission lines.
Marquez-Segura E, Shin S-H, Dawood A, et al., 2021, Microwave characterization of conductive PLA and its application to a 12 to 18 GHz 3-D printed rotary vane attenuator, IEEE Access, Vol: 9, Pages: 84327-84343, ISSN: 2169-3536
This paper demonstrates an ultra-light weight microwave rotary vane attenuator (RVA) manufactured using polymer-based 3-D printing. In addition, for the first time, conductive polylactic acid (PLA) is rigorously characterized across both X- and Ku-bands (8 to 18 GHz); while acrylonitrile butadiene-styrene (ABS) has similarly been characterized across Ku-band (12 to 18 GHz). Using the results from the conductive PLA characterization process, an electromagnetic model was created for predicting the performance of the RVA. It is shown that, even with its complex internal geometrical features, a mix of both dielectric and conductive PLA building materials, an assembly of multiple parts and a mechanically rotating central section, our experimental proof-of-concept prototype RVA exhibits excellent measured performance across Ku-band. This tunable microwave control device represents a higher-level of functionality for additive manufacturing, when compared to a fixed (i.e., non-movable) 3-D printed structure, opening the way for other groups to routinely 3-D print custom microwave components and subsystems in the not too distant future.
Shin S, Shang X, Ridler N, et al., 2021, Polymer-based 3-D printed 140-220 GHz low-cost quasi-optical components and integrated subsystem assembly, IEEE Access, Vol: 9, Pages: 28020-28038, ISSN: 2169-3536
Few examples of individual polymer-based 3-D printed quasi-optical component types have been previously demonstrated above ca. 100 GHz. This paper presents the characterization of polymer-based 3-D printed components and complete subsystems for quasi-optical applications operating at G-band (140 to 220 GHz). Two low-cost consumer-level 3-D printing technologies (vat polymerization and fused deposition modeling) are employed, normally associated with microwave frequencies and longer wavelength applications. Here, five different quasi-optical component types are investigated; rectangular horn antennas, 90° off-axis parabolic mirrors, radiation absorbent material (RAM), grid polarizers and dielectric lenses. As an alternative to conventional electroplating, gold-leaf gilding is used for the polarizer. A detailed investigation is undertaken to compare the performance of our 3-D printed antennas, mirrors and RAM with their commercial equivalents. In addition, a fully 3-D printed, RAM-lined housing with central two-axis rotational platform is constructed for performing two-port measurements of a quasi-optical horn-mirror-polarizer-mirror-horn subsystem. Measured results generally show excellent performances, although the grid polarizer is limited by the minimum strip width, separation distance and metallization thickness. The ultra-low cost, `plug and play' housing is designed to give a fast measurement setup, while minimizing misaligning losses. Its RAM lining is designed to suppress reflections due to diffraction from components under test that may cause adverse multi-path interference. Our work investigates each component type at G-band and integrates them within subsystem assemblies; operating at frequencies well above those normally associated with low-cost consumer-level 3-D printing technologies. This opens-up new opportunities for rapid prototyping of complete low-cost front-end quasi-optical upper-millimeter-wave subsystems.
Ren H, Shin S, Lucyszyn S, 2020, Enhanced cognitive demodulation with artificial intelligence, Scientific Reports, Vol: 10, Pages: 1-16, ISSN: 2045-2322
The low-cost ‘THz Torch’ wireless link technology is still in its infancy. Until very recently, inherent limitations with available hardware has resulted in a modest operational figure of merit performance (Range × Bit Rate). However, a breakthrough was reported here by the authors, with the introduction of ‘Cognitive Demodulation’. This bypassed the thermal time constant constraints normally associated with both the thermal emitter and sensor; allowing step-change increases in both Range and Bit Rate with direct electronic modulation. This paper concentrates on advancements to the bit error rate (BER) performance. Here, separate techniques are introduced to the demodulation software that, when combined, result in enhanced Cognitive Demodulation. A factor of more than 100 improvement in BER was demonstrated within the laboratory and approximately a 60-fold improvement in a non-laboratory environment; both at the maximum Range and Bit Rate of 2 m and 125 bps, respectively, demonstrated recently. Moreover, demodulation speed is increased by almost a factor of 10,000; allowing for real-time demodulation while easing future computational hardware requirements. In addition to these software advancements, the paper demonstrates important improvements in hardware that has brought the technology out of the laboratory, with field trials being performed within an office corridor.
Jones A, Lucyszyn S, Marquez-Segura E, et al., 2020, 3-D printed standards for calibration of microwave network analysers, Measurement, Vol: 158, Pages: 1-10, ISSN: 0263-2241
This paper describes the design, fabrication and testing of 3-D printed primary standards for use with the calibration of microwave vector network analysers. The standards are a short-circuit and a quarter wavelength section of line that are designed for use with the Thru-Reflect-Line calibration technique. The standards are realised in metal-pipe rectangular waveguide, covering the frequency range from 12 GHz to 18 GHz (i.e., Ku-band). The standards are polymer-based 3-D printed, which is subsequently metal plated to provide the required electrical conductivity. The performance of the standards is compared with conventionally machined standards that are used as part of the UK’s primary national measurement system for microwave scattering parameters. The authors believe that this is the first time that 3-D printing techniques have been used to produce such calibration standards, and, that this could lead to a new approach to providing metrological traceability for these types of measurement.
Ren H, Lucyszyn S, 2020, Thermodynamics-based cognitive demodulation for `THz Torch' wireless communications links, Scientific Reports, Vol: 10, ISSN: 2045-2322
The low-cost ‘THz Torch’ technology, which exploits the thermal infrared spectrum (ca. 10 to 100 THz), was recently introduced to provide secure low data rate communications links across short distances. In this paper, a thermodynamics-based approach is proposed for greatly enhancing the sensitivity of detection with non-stationary thermal radiation, generated by thermal emitters that have been modulated well beyond their thermal time constants. Here, cognitive demodulation is employed and, unlike all previous demonstrators, allows truly asynchronous operation by dynamically predicting the thermal transients for the next bit to be received. The result is a five-fold increase in the reported operational figure of merit (Range × Bit Rate) for ‘THz Torch’ wireless communications links. A single-channel (2 m × 125 bps) prototype and an 8-channel frequency-division multiplexed (0.5 m × 1,000 bps) prototype are demonstrated as proof-of-principle exemplars for the enhanced method of demodulation. Measurements show superior bit error rate performance with an increase in range and bit rate, when compared with conventional threshold detection. This work represents a paradigm shift in thermal-based modulation-demodulation of digital data, and offers a practical solution for the implementation of future ubiquitous secure ‘THz Torch’ wireless communications links; as well as other applications.
Shin S-H, Lucyszyn S, 2020, Benchmarking a Commercial (Sub-)THz Focal Plane Array Against a Custom-Built Millimeter-Wave Single-Pixel Camera, IEEE Access, Vol: 8, Pages: 191174-191190
Lucyszyn S, Ridler N, 2019, 3D-Printed Microwave-to-THz Technologies: ICL-NPL Landscape
Application space for the collaborative work between Imperial College London and the National Physical Laboratory.
Hanham S, Watts C, Ahmad M, et al., 2019, Photonic crystal resonators as bio-liquid sensing platforms in the terahertz band, META 2019
We describethe development of high quality(Q)factor photonic crystal resonators(PCRs)integrated with microfluidic systems to formthe basis ofhighly sensitive liquid sensing platformsforthe terahertz band.The strong confinement of the terahertz fieldincombinationwith the high Q-factor provided bythe PCR allows the measurement of thedielectric properties of sub-nanoliter liquid volumes. We demonstrate the utility of thisapproach by measuring the complex permittivity of several bio-liquids at 100 GHz.
Shin S, Alyasiri D, D’Auria M, et al., 2019, Fully 3-D printed tunable microwave subsystem, International Microwave Workshop Series on Advanced Materials and Processes (IMWS-AMP), Publisher: IEEE
M´arquez-Segura E, Otter W, Lucyszyn S, et al., 2019, Fabricación aditiva de atenuadores variables de veleta rotatoria en guía de onda, Simposium Nacional de la Unión Científica Internacional de Radio (URSI 2019), Publisher: URSI
Lim YP, Toh YL, Cheab S, et al., 2019, Coupling matrix synthesis and design of a chained-function waveguide filter, Asia-Pacific Microwave Conference 2018, Publisher: IEEE, Pages: 103-105
This paper presents, for the first time, the coupling matrix synthesis for the application of a chained-function to waveguide filters. The realization of this filter is carried out by successively adding one resonator at a time by comparing the simulated responses of each stage with those obtained using the coupling matrix synthesized from the chained-function. A sixth-order chained-function waveguide bandpass filter centered at 28 GHz with a fractional bandwidth of 2% is demonstrated. The simulated S-parameter responses and the sensitivity analysis pertaining to the manufacturing errors is included. The chained-function waveguide has the lowest percentage changes in terms of the return loss performance given the same amount of distortion as compared with those of the Chebyshev response filters. This results in a lower sensitivity rate with respect to the manufacturing errors, leading to achieving a high-performance filter implementation with a minimum tuning effort.
Shin S-H, Alyasiri DF, D'Auria M, et al., 2019, Polymer-Based 3-D Printed Ku-Band Steerable Phased-Array Antenna Subsystem, IEEE Access, Vol: 7, Pages: 106662-106673
Sun J, Dawood A, Otter WJ, et al., 2019, Microwave Characterization of Low-Loss FDM 3-D Printed ABS With Dielectric-Filled Metal-Pipe Rectangular Waveguide Spectroscopy, IEEE Access, Vol: 7, Pages: 95455-95486
AL-JUBOORI B, ZHOU J, HUANG Y, et al., 2018, Lightweight and low-loss 3-D printed millimeter-wave bandpass filter based on gap-waveguide, IEEE Access, Vol: 7, Pages: 2624-2632, ISSN: 2169-3536
This paper presents a comprehensive study of a groove gap waveguide (also known as a waffle-iron) bandpass filter at Ka-band (26.5-40 GHz), fabricated using a high resolution polymer jetting (Polyjet) 3-D printing technology. The same filter was previously fabricated using brass CNC milling technology. The metalized Polyjet 3-D printed filter has lower loss, is lighter in weight and more cost-effective, when compared to the solid metal case. The filter operates at a center frequency of 35.65 GHz, has a 500 MHz bandwidth (1.4% fractional bandwidth), and has a transmission zero below and above the passband. Without any design iterations, the measured S-parameters for the Polyjet 3-D printed filter are presented and compared with simulated results, showing excellent agreement. A comparison is then made between the measured results and that of its brass machined counterpart. The new Polyjet 3-D printed filter is 85% lighter than the conventional machined version. All these features prove the important potential of 3-D printing technology for millimeter-wave applications, which includes aerospace.
Lucyszyn S, Shang X, Otter W, et al., 2018, Polymer-based 3D printed millimeter-wave components for spacecraft payloads, International Microwave Workshop Series on Advanced Materials and Processes (IMWS-AMP), Publisher: IEEE MTT-S
This paper summarizes the current state of research & development within the U.K. for polymer-based 3D printed guided-wave and quasi-optical components for spacecraft payloads. Preliminary measured results look promising and show that this emerging technology may well overtake existing machined technologies in the not too distant future for general aerospace applications.
Hanham S, Watts C, Ahmad M, et al., 2018, Photonic crystal resonators for terahertz sensing applications, Progress in Electromagnetics Research Symposium, Publisher: IEICE, Pages: 803-803
Sun J, Lucyszyn S, 2018, Extracting complex dielectric properties from reflection-transmission mode spectroscopy, IEEE Access, Vol: 6, Pages: 8302-8321, ISSN: 2169-3536
Material characterization of homogeneous dielectric slabs using reflection-transmission mode spectroscopy can be problematic due to the ambiguity from a phasor term. A comprehensive analytical review of methods for calculating the normalized power spectra, to extract the effective complex dielectric properties of a sample, is undertaken. Three generic power response models (zero-order, power propagation and electric field propagation) are derived; these models act as a common mathematical framework for the whole paper. With our unified engineering approach, the voltage-wave propagation, transmission line and telegrapher’s equation transmission line models are then independently derived; the first two giving the same mathematical solutions, while the third generates the same numerical results, as the exact electric field propagation model. Mathematically traceable simulation results from the various models are compared and contrasted using an arbitrarily chosen dataset (window glass) from 1 to 100 THz. We show how to extract the approximate effective complex dielectric properties using time-gated time-domain spectroscopy and also the exact values with our graphical techniques from the first-order reflectance and transmittance. Our approach is then taken further by considering all the Fabry-Perot reflections with frequency- and space-domain spectroscopy. With scalar reflection-transmission mode infrared spectroscopy, we model the threshold conditions between the solution space that gives the single (exact) solution for the complex refractive index and that which gives multiple mathematical solutions. By knowing threshold conditions, it is possible to gain a much deeper insight, in terms of sample constraints and metrology techniques that can be adopted, to determine the single solution. Finally, we propose a simple additional measurement/simulation step to resolve the ambiguity within the multiple solution space. Here, sample thickness is arbitrary and no initia
Otter W, Ridler NM, Lucyszyn S, 2017, 3D printed waveguides: A revolution in low volume manufacturing for the 21st century, ARMMS RF & Microwave Society Conference, Publisher: ARMMS RF & Microwave Society, Pages: 1-6
3D printing is a disruptive technology, offering the inherent capabilities for creating truly arbitrary 3D structures, with low manufacturing costs associated with low volume production runs. This paper provides an overview of the current progress in 3D printing of metal-pipe rectangular waveguide (MPRWG) components, from 10 GHz to 1 THz, at Imperial College London. First, measurements performed at the UK National Physical Laboratory demonstrate that 3D printed MPRWG performance is comparable to standard commercial waveguides at X-band and W-band. Then, a fully 3D printed X-band dielectric flap tuneable phase shifter and W-band 6th-order inductive iris bandpass filter are demonstrated experimentally. Finally, an optically-controlled 500 GHz IQ vector modulator will also be presented; packaged laser diodes and high resistivity silicon implants are integrated within a hybrid 3D printed split-block module, representing a paradigm shift in additive manufacturing for realizing tuneable THz applications.
Otter WJ, Lucyszyn S, 2017, Hybrid 3-D-Printing Technology for Tunable THz Applications, PROCEEDINGS OF THE IEEE, Vol: 105, Pages: 756-767, ISSN: 0018-9219
Otter WJ, Lucyszyn S, 2017, Printing: the future of THz, Electronics Letters, Vol: 53, Pages: 443-443, ISSN: 0013-5194
3D printing allows for record-breaking, low-cost waveguides operating at 1.1 THz
Abstract:For the first time, 3D printed metal-pipe rectangular waveguides (MPRWGs) have been demonstrated in the WM-380 (500-750 GHz) and WM-250 (750 GHz-1.1 THz) waveguide bands. The ultra-high spatial resolution offered by the new RECILS additive manufacturing technology enables the precision fabrication of these prototype MPRWGs at such high frequencies. This enabling technology avoids the need for access to expensive microfabrication resources and, thus, opens up the terahertz spectrum to the low-cost manufacture of passive components.
Muller AA, Sanabria-Codesal E, Moldoveanu A, et al., 2017, Extended Capabilities of the 3-D Smith Chart with Group Delay and Resonator Quality Factor, IEEE Transactions on Microwave Theory and Techniques, Vol: 65, Pages: 10-19, ISSN: 0018-9480
This paper extends the capabilities of the 3D Smith chart for representing positive and negative differential-phase group delay and the associated loaded resonator quality factor, displayed simultaneously with scattering (S)-parameters. Here, mathematical concepts, inspired from elementary differential geometry and topology, are used to implement 3D projections. It is shown that a condition for a circuit to exploit negative differential-phase group delay is that its S-parameter winding number should be ≥ 0 (relative to its origin). Finally, exemplar network responses that exhibit both positive and negative differential-phase group delay and loaded resonator quality factor are shown with the 3D Smith chart. The convenience of being able to simultaneously display a wider range of parameters on one visualization platform, with the 3D Smith chart, may help to speed-up the design and analysis of microwave circuits by the user.
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