A. Arsenovic

810 Labs LLC

In this paper we present the application of a projective geometry tool known as Conformal Geometric Algebra (CGA) to transmission line theory. Explicit relationships between the Smith Chart, Riemann Sphere, and CGA are developed to illustrate the evolution of projective geometry in transmission line theory. By using CGA, fundamental network operati...

Measurements at microwave frequencies can require a significant amount post-processing and analysis, especially in research and prototyping environments. From our experience, none of the existing software products satisfy the needs of these environments in which the abilities to understand, modify, and extend existing functionality are vital. In an...

Building on the work in [1], this paper shows how Conformal Geometric Algebra (CGA) can be used to model an arbitrary two-port network as a rotation in four dimensional space, known as a spinor. This spinor model plays the role of the wave-cascading matrix in conventional network theory. Techniques to translate two-port scattering matrix in and out...

In this paper, we analyze one dimensional periodic structures using an operator framework in Spacetime Algebra (STA). The Bloch Impedance and propagation constant are found for a variety of periodic structures, and band diagrams are presented.

Clifford is a numerical Geometric Algebra (a.k.a. Clifford algebra) package for python. https://github.com/pygae/clifford/

With the rapid proliferation of telecommunication and RF applications, so, too, has demand grown for tools to design and characterize these devices. scikit-rf is a Python package designed to make RF/microwave engineering both robust and approachable. The package provides a modern, object-oriented library for RF network analysis, circuit building, c...

Building on the work in [1], this paper shows how Conformal Geometric Algebra (CGA) can be used to model an arbitrary two-port scattering matrix as a rotation in four dimensional Minkowski space, known as a spinor. This spinor model plays the role of the wave-cascading matrix in conventional microwave network theory. Techniques to translate two-por...

This paper presents an approach to special relativity which is more in line with electrical engineering , namely as the time-harmonic analysis of a linear system. The approach is derived from Hestenes' Zitter model for the electron[1], [2], which assumes an internal structure of a light-like helix in spacetime. A time-harmonic model is constructed...

One and Two-port microwave calibration techniques are formulated with spinors. This provides a more geometric view of the process, and makes the algorithms more readable by scientists in other fields. Since the spinor model is itself basis invariant [1], so are all the algorithms developed within the framework.

A proof-of-concept demonstration of on-wafer electronic calibration in the submillimeter-wave band (325—500 GHz) is presented. A GaAs Schottky diode shunting a coplanar transmission line is employed as an electronic standard that is tuned by bias applied through wafer probes. Error-corrected scattering parameter measurements, based on a Thru-Reflec...

Modern Geometric Algebra software systems tend to fall into one of two categories, either fast, difficult to use, statically typed, and syntactically different from the mathematics or slow, easy to use, dynamically typed and syntactically close to the mathematical conventions. Gajit is a system that aims to get the best of both worlds. It allows us...

This letter reports on a method for extracting parasitic equivalent-circuit model parameters at submillimeter-wave frequencies. The devices investigated are quasi-vertical gallium arsenide Schottky diodes integrated on silicon. The technique utilizes measurements of coplanar waveguide-fed passive structures in the WR-2.2 band (325-500 GHz), which a...

Presenting a method to interpolate transmissive two-port networks using a new type of network model, producing more accurate results and significantly faster convergence rates than existing techniques.

A prototype imaging reflectometer based on the coded aperture technique and operating in the WR-1.5 (500–750 GHz) frequency band is described. Masks for the coded aperture system are realized through optical modulation of the conductivity of a high-resistivity silicon wafer. A network model representation of the imaging system is developed and appl...

The continued emergence of new terahertz devices has created a need for improved approaches to packaging, integration, and measurement tools for diagnostics and characterization in this portion of the spectrum. Rectangular waveguide has for many years been the primary transmission medium for terahertz and submillimeter-wave systems operating from 3...

Recent advances in technology have enabled the measurements of S-parameters in waveguide devices at frequencies well above 1 THz, which push the mechanical limits of flanges used to interconnect the devices under test. New IEEE standards have been adopted to address some the limitations and this work illustrates, through measurement, some of the is...

We present a closed form solution to re-flectometer self-calibration that allows for two partially known standards. The solution is developed explicitly for a pair lossless reflects standards, but could be applied to any calibration set with similar constraints. Related techniques presented previously are simplified in the new formulation and shown...

As waveguide measurements continue to push upwards in frequency, waveguide misalignment becomes a severe problem. In this paper we combine two known calibration algorithms; the SDDL and Usuggest that inaccuracies in the predicted response of the radiating open limits the perfornknown Thru, to create a two-port calibration insensitive to flange misa...

Terahertz imaging systems have received substantial attention from the scientific community for their use in astronomy, spectroscopy, plasma diagnostics and security. One approach to designing such systems is to use focal plane arrays. Although the principle of these systems is straightforward, realizing practical architectures has proven deceptive...

A micromachined on-wafer probe has been designed to facilitate the development of integrated circuits in the 600–900 GHz frequency range. The probe tip is fabricated on a 5-micrometer thick high-resistivity silicon substrate using a silicon-on- insulator fabrication process. This letter updates previous work on WR-1.2 wafer probes and presents for...

Anritsu and Virginia Diodes Inc. (VDI) are working jointly to deliver a measurement solution that enables the development of many of applications and demonstrate the use of a vector network analyzer (VNA) with THz frequency extenders to accurately characterize materials using a quasi-optical measurement technique. The test solution can be configure...

This paper presents a study characterizing the connection repeatability and reflection coefficient of submillimeter waveguide flanges in the 500–750 GHz band (WR-1.5 or WM-380). The connection repeatability of four types of flange was measured using one-port measurements and a “load-reference” technique with a vertically mounted system to mitigate...

An experimentally based technique for characterizing calibration uncertainty is presented. The approach described calculates uncertainty metrics at the output of the calibration processing chain as opposed to the input. In doing so, this method replaces the complexities of error propagation with the computational effort associated with performing n...

An improved micromachined on-wafer probe covering frequencies 500-750 GHz is demonstrated in this paper to address sub-millimeter-wave integrated-circuit testing. Measurements of a prototype WR-1.5 micromachined on-wafer probe exhibit a return loss better than 12 dB and a mean insertion loss of 6.5 dB from 500 to 750 GHz. The repeatability of on-wa...

Two competing delay-short calibration standard designs for WM-380/WR-1.5 rectangular waveguide (500-750GHz) are evaluated. Quantitative estimates of the connector uncertainty are made and it is shown that an end-milled design out-performs the shim design. The effect of each standard's repeatability on calibration uncertainty is used to determine co...

A micromachined on-wafer probe designed for WR-1.2 rectangular waveguide is demonstrated in this paper to further enable submillimeter-wave integrated circuits testing. Initial measurements of a prototype WR-1.2 micromachined on-wafer probe exhibit an insertion loss better than 9 dB for the lower half of the WR-1.2 band.

The mechanical design and characterization of a micromachined on-wafer probe scalable to submillimeter-wave frequencies is presented. The design consists of a silicon micro- machined probe with a ground-signal-ground configuration on a 15 m thick silicon substrate. This micromachined chip is housed in a metal waveguide block that provides mechanica...

The electromagnetic design and characterization of a micromachined submillimeter-wave on-wafer probe is presented. The mechanical design and fabrication of the probe is presented in the companion paper (Part I). Finite element simulations are applied to design an integrated probe chip to couple between rect- angular waveguide and the ground-signal-...

Terahertz components and devices are typically interfaced with measurement instrumentation and characterized using fixtures equipped with waveguide flanges or antennas. Such fixtures are known to introduce significant uncertainty and error in measurements. It is preferable to characterize such devices insitu, where the device under test can be meas...

Although progress has been made in the development of submillimeter-wave monolithic integrated circuits, the evaluation of these circuits still relies on test fixtures, which makes testing expensive and time consuming. Based on a W-band prototype, a micromachined on-wafer probe covering frequencies 500-750 GHz is built to simplify submillimeter-wav...

Waveguide twists are often necessary to provide polarization rotation between waveguide-based components. At terahertz frequencies, it is desirable to use a twist design that is compact in order to reduce loss; however, these designs are difficult if not impossible to realize using standard machining. This paper presents a micromachined compact wav...

The accuracy of an on-wafer probe system operating at 625 GHz is analyzed. A weighted least squares analysis is applied to the calibration of a one-port measurement system to propagate the non-systematic errors introduced by probe contact and probe placement variation. The worst-case errors of the 625 GHz on-wafer probe system are found and the com...

A micromachined on-wafer probe is designed, fabricated and measured at W-Band as a proof of concept for probes operating at sub-millimeter wavelengths. A fabrication process is developed to create devices that combine a waveguide probe with a GSG probe tip on a 15 μm silicon substrate. This device is housed in a metal machined waveguide block that...