Showing papers on "Q factor published in 2006"
TL;DR: In this article, a new class of rectangular plate and ring-shaped contour-mode piezoelectric aluminum nitride radio-frequency microelectromechanical system resonators that span a frequency range from 19 to 656 MHz showing high quality factors in air (Qmax=4300 at 229.9 MHz), low motional resistance (ranging from 50 to 700 Omega), and center frequencies that are lithographically defined.
Abstract: This paper reports theoretical analysis and experimental results on a new class of rectangular plate and ring-shaped contour-mode piezoelectric aluminum nitride radio-frequency microelectromechanical systems resonators that span a frequency range from 19 to 656 MHz showing high-quality factors in air (Qmax=4300 at 229.9 MHz), low motional resistance (ranging from 50 to 700 Omega), and center frequencies that are lithographically defined. These resonators achieve the lowest value of motional resistance ever reported for contour-mode resonators and combine it with high Q factors, therefore enabling the fabrication of arrays of high-performance microresonators with different frequencies on a single chip. Uncompensated temperature coefficients of frequency of approximately -25 ppm/degC were also recorded for these resonators. Initial discussions on mass loading mechanisms induced by metal electrodes and energy loss phenomenon are provided
614 citations
TL;DR: In this article, the authors proposed an ultrahigh quality factor (Q) photonic crystal slab nanocavity created by the local width modulation of a line defect, which has an intrinsic Q value of up to 7×107.
Abstract: We propose an ultrahigh quality factor (Q) photonic crystal slab nanocavity created by the local width modulation of a line defect. We show numerically that this nanocavity has an intrinsic Q value of up to 7×107. Transmission measurements for fabricated Si photonic-crystal-slab nanocavities directly coupled to input/output waveguides have exhibited a loaded Q value of ∼800000. These theoretical and experimental Q values are very high for photonic crystal nanocavities. In addition, we demonstrate that simply shifting two holes away from a line defect is sufficient to achieve an ultrahigh Q value both theoretically and experimentally.
511 citations
TL;DR: In this article, the characteristics of a local plasmon resonance of a metal nanostructure exhibit several general properties under the quasistatic approximation, and the effect of optical gain on the Q factor is also obtained.
Abstract: Under the quasistatic approximation, the characteristics of a local plasmon resonance of a metal nanostructure exhibit several general properties. The resonance frequency depends on the fraction of plasmon energy residing in the metal through the real dielectric function of the metal. For a given resonant frequency, the Q factor of the resonance is determined only by the complex dielectric function of the metal material, independent of the nanostructure form or the dielectric environment. A simple result describing the effect of optical gain on the Q factor is also obtained.
490 citations
TL;DR: The LCORR takes advantage of the high sensitivity, small footprint, and low sample consumption with the ring resonator, as well as the efficient fluidic sample delivery with the capillary, and will open an avenue to future multiplexed sensor array development.
Abstract: We have demonstrated a novel sensor architecture based on a liquid-core optical ring-resonator (LCORR) in which a fused silica capillary is utilized to carry the aqueous sample and to act as the ring resonator. The wall thickness of the LCORR is controlled to a few micrometers to expose the whispering gallery mode to the aqueous core. Optical characterization with a water-ethanol mixture shows that the spectral sensitivity of the LCORR sensor is approximately 2.6 nm per refractive index unit. A model based on Mie theory is established to explain the experimental results. The LCORR takes advantage of the high sensitivity, small footprint, and low sample consumption with the ring resonator, as well as the efficient fluidic sample delivery with the capillary, and will open an avenue to future multiplexed sensor array development.
469 citations
TL;DR: In this article, the authors defined stricter limits that apply to a class of antennas (or scatterers) consisting of any arrangement of conductors on a spherical surface, and the energy stored within the sphere is included in the analysis.
Abstract: Considerable work has been published to define the minimum possible antenna radiation Q as a function of the antenna size and gain. Many of the derivations assume an enclosing sphere and deal only with the fields external to this sphere. As a result, the limits tend to be overly optimistic, and realizable antennas generally have Q's considerably higher than the minimum values predicted by these theories. This paper defines stricter limits that apply to a class of antennas (or scatterers) consisting of any arrangement of conductors on a spherical surface. Energy stored within the sphere is included in the analysis. The minimum Q values are as much as three times the values based only on external fields. Recently published independent experimental data on electrically small antennas in this class reported Q values only slightly higher than the new limits provided in this paper
282 citations
TL;DR: It is shown that the Q factors of the latest high-Q cavities in two dimensional photonic crystals, measured experimentally to be ~1000000, are determined by losses due to imperfections in the fabricated structures, and not by the cavity design.
Abstract: In this letter, we show that the Q factors of the latest high-Q cavities in two dimensional photonic crystals, measured experimentally to be ~1000000, are determined by losses due to imperfections in the fabricated structures, and not by the cavity design. Quantitative analysis shows that the dominant sources of loss include the tilt of air-holes within the cavity, the roughness of the inner walls of the air-holes, variation in the radii of the air-holes, and optical absorption by adsorbed material. We believe that cavities with experimental Q factors of the order of several millions will be obtained in the future by reducing the losses due to imperfections through improved fabrication techniques.
263 citations
TL;DR: In this paper, a method to obtain the electrical characteristics of complementary split ring resonators (CSRRs) coupled to planar transmission lines is presented, which is of actual interest for the design of microwave circuits and metamaterials based on these complementary resonant particles.
Abstract: In this letter, a method to obtain the electrical characteristics of complementary split ring resonators (CSRRs) coupled to planar transmission lines is presented. CSRRs have been recently proposed by some of the authors as new constitutive elements for the synthesis of metamaterials with negative effective permittivity, and they have been applied to the fabrication of metamaterial-based circuits in planar technology. The method provides the electrical characteristics of CSRRs (including the intrinsic resonant frequency and the unloaded Q-factor), as well as the coupling capacitance between line and CSRRs, and the parameters of the host line. Parameter extraction from the proposed method is applied to two different structures corresponding to the basic cells of left handed (LH) and negative permittivity lines. The method is of actual interest for the design of microwave circuits and metamaterials based on these complementary resonant particles
242 citations
TL;DR: In this paper, the authors demonstrate optical resonance from microfiber knots obtained by manipulating freestanding silica microfibers, which can be easily tuned by tightening the knot structure in air.
Abstract: We demonstrate optical resonance from microfiber knots obtained by manipulating freestanding silica microfibers. Q factors as high as 57 000 with finesse of 22 are observed in knots with sizes less than 1mm. The free spectral range of the resonator can be easily tuned by tightening the knot structure in air. The knot resonators are highly stable in water with Q factors up to 31 000 and finesse of 13. The possibility of supporting the knot resonator with a solid MgF2 substrate is also demonstrated.
239 citations
TL;DR: In this article, the authors used ultra-high-Q optical microcavities (Q>10 to the 7th) to detect D2O in H2O.
Abstract: Ultra-high-Q optical microcavities (Q>10 to the 7th) provide one method for distinguishing chemically similar species. Resonators immersed in H2O have lower quality factors than those immersed in D2O due to the difference in optical absorption. This difference can be used to create a D2O detector. This effect is most noticeable at 1300 nm, where the Q(H2O) is 10(to the 6th) and the Q(D2O) is 10(to the 7th). By monitoring Q, concentrations of 0.0001% [1 part in 10(to the 6th) per volume] of D2O in H2O have been detected. This sensitivity represents an order of magnitude improvement over previous techniques. Reversible detection was also demonstrated by cyclic introduction and flushing of D2O.
229 citations
TL;DR: In this paper, the authors present two approaches to analyze and calculate thermoelastic damping in micromechanical resonators, and demonstrate the use of the latter approach to identify the thermal modes that contribute most to damping.
Abstract: This paper presents two approaches to analyzing and calculating thermoelastic damping in micromechanical resonators. The first approach solves the fully coupled thermomechanical equations that capture the physics of thermoelastic damping in both two and three dimensions for arbitrary structures. The second approach uses the eigenvalues and eigenvectors of the uncoupled thermal and mechanical dynamics equations to calculate damping. We demonstrate the use of the latter approach to identify the thermal modes that contribute most to damping, and present an example that illustrates how this information may be used to design devices with higher quality factors. Both approaches are numerically implemented using a finite-element solver (Comsol Multiphysics). We calculate damping in typical micromechanical resonator structures using Comsol Multiphysics and compare the results with experimental data reported in literature for these devices
229 citations
TL;DR: The transmission and group delay of microring coupled-resonator optical waveguides (CROWs) was measured and it was found that the CROWs had a delay of 110-140 ps and a slowing factor of 23-29 over a 17 GHz bandwidth.
Abstract: We measured the transmission and group delay of microring coupled-resonator optical waveguides (CROWs). The CROWs consisted of 12 weakly coupled, microring resonators fabricated in optical polymers (PMMA on Cytop). The intrinsic quality factor of the resonators was 18,000 and the interresonator coupling was 1%, resulting in a delay of 110-140 ps and a slowing factor of 23-29 over a 17 GHz bandwidth.
TL;DR: In this paper, the authors presented a silicon-on-insulator single ring resonator with a free spectral range equal to 47nm, which is the widest known value for this type of resonators.
Abstract: The authors present a silicon-on-insulator single ring resonator with a free spectral range equal to 47nm, which is the widest known value for this type of resonators. The ring radius is 2μm and is the smallest ring resonator ever reported, achieving experimentally such a wide spectral range. For this ring resonator, the authors demonstrate the quality factor to be equal to 6730±60. They thermally tune the resonant wavelength with 0.11nm∕°C, thus showing the ring resonator as an attractive component for on-chip ultracompact photonic add/drop filters and switches.
TL;DR: In this paper, the authors describe the fabrication, packaging and testing of a resonant mass sensor for the detection of biomolecules in a microfluidic format, which employs a suspended microchannel as the resonating element, thereby avoiding the problems of damping and viscous drag.
Abstract: There is a great need in experimental biology for tools to study interactions between biological molecules and to profile expression levels of large numbers of proteins. This paper describes the fabrication, packaging and testing of a resonant mass sensor for the detection of biomolecules in a microfluidic format. The transducer employs a suspended microchannel as the resonating element, thereby avoiding the problems of damping and viscous drag that normally degrade the sensitivity of resonant sensors in liquid. Our device differs from a vibrating tube densitometer in that the channel is very thin, which enables the detection of molecules that bind to the channel walls; this provides a path to specificity via molecular recognition by immobilized receptors. The fabrication is based on a sacrificial polysilicon process with low-stress low-pressure chemical-vapor deposited (LPCVD) silicon nitride as the structural material, and the resonator is vacuum packaged on the wafer scale using glass frit bonding. Packaged resonators exhibit a sensitivity of 0.8 ppm/(ngmiddotcm2) and a mechanical quality factor of up to 700. To the best of our knowledge, this quality factor is among the highest so far reported for resonant sensors with comparable surface mass sensitivity in liquid
IBM1
TL;DR: This work fabricated and characterized two complimentary types of SOI photonic wire based devices and found that instead of well-known waveguide bending and propagation losses, mode conversion loss in the coupling region of such resonators dominates when the air gap between the racetrack resonator and access waveguide is smaller than 120nm.
Abstract: Two complimentary types of SOI photonic wire based devices, the add/drop (A/D) filter using a racetrack resonator and the Mach-Zehnder interferometer with one arm consisting of an identical resonator in all-pass filter (APF) configuration, were fabricated and characterized in order to extract the optical properties of the resonators and predict the performance of the optical delay lines based on such resonators. We found that instead of well-known waveguide bending and propagation losses, mode conversion loss in the coupling region of such resonators dominates when the air gap between the racetrack resonator and access waveguide is smaller than 120nm. We also show that this additional loss significantly degrades the performance of the optical delay line containing cascaded resonators in APF configuration.
TL;DR: In this paper, an important design concept to suppress radiation loss is introduced: the envelope of the cavity mode field should have no abrupt changes and should ideally follow a Gaussian function.
Abstract: In this paper, we discuss methods to suppress the radiation loss of ultrasmall cavities, of the size of the optical wavelength, in two-dimensional photonic crystal slabs. An important design concept to suppress radiation loss is introduced: The envelope of the cavity mode field should have no abrupt changes and should ideally follow a Gaussian function. Cubic wavelength order cavities, with experimental Q factors of 100 000 and nearly 1 000 000 are obtained by tailoring the envelope functions using air-hole shifts and multistep heterostructures, respectively. In addition, the experimental Q factors of the latest cavities are shown to be determined by the imperfections in the fabricated structures and not by the cavity design. The differences between the experimental and the theoretical Q factors are investigated in order to demonstrate how higher Q factors could be realized in the future
TL;DR: It is confirmed that low-power nonlinear optical effects could be attributed to the ultra-high Q factor of the nanocavity, and this nonlinearity could be explained by coupled-mode theory.
Abstract: We investigated the characteristics of an ultra-high-Q photonic nanocavity (Q = ~230,000 and modal volume = ~1.2 cubic wavelengths) at various input light powers. The cavity characteristics were red-shifted as the input power increased. This nonlinearity could be explained by coupled-mode theory, taking into account two-photon absorption, the associated free-carrier absorption, plasma effect, thermo-optic effect, and a Kerr effect. Nonlinear cavity characteristics were observed at an extremely low input light power of 10 μW. We confirmed that these low-power nonlinear optical effects could be attributed to the ultra-high Q factor of the nanocavity.
TL;DR: In this article, the authors used a parallel array of corner-coupled polysilicon square plate resonators to achieve a motional resistance reduction of 5.9X.
Abstract: Substantial reductions in vibrating micromechanical resonator series motional resistance Rx have been attained by mechanically coupling and exciting a parallel array of corner-coupled polysilicon square plate resonators. Using this technique with seven resonators, an effective Rx of 480 Omega has been attained at 70 MHz, which is more than 5.9X smaller than the 2.82 kOmega exhibited by a stand-alone transverse-mode corner-supported square resonator, and all this achieved while still maintaining an effective Q>9000. This method for Rx-reduction is superior to methods based on brute force scaling of electrode-to-resonator gaps or dc-bias increases, because it allows a reduction in Rx without sacrificing linearity, and thereby breaks the Rx versus dynamic range tradeoff often seen when scaling. This paper also compares two types of anchoring schemes for transverse-mode square micromechanical resonators and models the effect of support beam parameters on resonance frequency
TL;DR: In this paper, the authors introduced a first order accurate resonance model based on a second order Pade approximation of the reflection coefficient of a narrowband antenna, which is characterized by its Q factor.
Abstract: In this paper, we introduce a first order accurate resonance model based on a second order Pade approximation of the reflection coefficient of a narrowband antenna. The resonance model is characterized by its Q factor, given by the frequency derivative of the reflection coefficient. The Bode-Fano matching theory is used to determine the bandwidth of the resonance model and it is shown that it also determines the bandwidth of the antenna for sufficiently narrow bandwidths. The bandwidth is expressed in the Q factor of the resonance model and the threshold limit on the reflection coefficient. Spherical vector modes are used to illustrate the results. Finally, we demonstrate the fundamental difficulty of finding a simple relation between the Q of the resonance model, and the classical Q defined as the quotient between the stored and radiated energies, even though there is usually a close resemblance between these entities for many real antennas.
TL;DR: In this paper, the authors consider the in-plane vibration of uniform rings of rectangular cross-section and compare the relationship between ring geometry, scale and Q-factor, and the ability to choose resonator dimensions to control Q -factor due to thermoelastic loss.
TL;DR: In the paper, a novel three-port channel drop filter in two dimensional photonic crystals (2D PCs) with a wavelength-selective reflection micro-cavity with a coupled mode theory in time is proposed and simulation results imply that the design is feasible.
Abstract: In the paper, a novel three-port channel drop filter in two dimensional photonic crystals (2D PCs) with a wavelength-selective reflection micro-cavity is proposed. In the structure, two micro-cavities are used. One is used for a resonant tunneling-based channel drop filter. The other is used to realize wavelength-selective reflection feedback in the bus wave-guide, which consists of a point defect micro-cavity side-coupled to a line defect waveguide based on photonic crystals. Using coupled mode theory in time, the conditions to achieve 100% drop efficiency are derived thoroughly. The simulation results by using the finite-difference time-domain (FDTD) method imply that the design is feasible.
TL;DR: In this article, the authors analyzed the impact of resonator design (i.e., slots machined into flexural beams) on TED-limited quality factor for complex geometries of micromechanical resonators.
Abstract: Thermoelastic dissipation (TED) is analyzed for complex geometries of micromechanical resonators, demonstrating the impact of resonator design (i.e., slots machined into flexural beams) on TED-limited quality factor. Zener first described TED for simple beams in 1937. This work extends beyond simple beams into arbitrary geometries, verifying simulations that completely capture the coupled physics that occur. Novel geometries of slots engineered at specific locations within the flexural resonator beams are utilized. These slots drastically affect the thermal-mechanical coupling and have an impact on the quality factor, providing resonators with quality factors higher than those predicted by simple Zener theory. The ideal location for maximum impact of slots is determined to be in regions of high strain. We have demonstrated the ability to predict and control the quality factor of micromechanical resonators limited by thermoelastic dissipation. This enables tuning of the quality factor by structure design without the need to scale its size, thus allowing for enhanced design optimization
TL;DR: In this paper, a dual-band voltage-controlled oscillator (VCO) was used to reduce the size of multiple-band RF systems and which allows better tradeoff between phase noise and power consumption.
Abstract: A switched resonator concept, which can be used to reduce the size of multiple-band RF systems and which allows better tradeoff between phase noise and power consumption, is demonstrated using a dual-band voltage-controlled oscillator (VCO) in a 0.18-/spl mu/m CMOS process. To maximize Q of the switched resonator when the switch is on, the mutual inductance between the inductors should be kept low and the switch transistor size should be optimized. The Q factor of switched resonators is /spl sim/30% lower than that of a standalone inductor. The dual-band VCO operates near 900 MHz and 1.8 GHz with phase noise of -125 and -123dBc/Hz at a 600-kHz offset and 16-mW power consumption. Compared to a single-band 1.8-GHz VCO, the dual-band VCO has almost the same phase noise and power consumption, while occupying /spl sim/37% smaller area.
15 Mar 2006
TL;DR: In this article, a tunable resonant frequency power harvesting device in cantilever beam form which will shift its resonant frequencies to match that of the external vibrations was developed and verified.
Abstract: Over the past years, there has been growing interests in the field of power harvesting technologies for low-power electronic devices such as wireless sensor networks and biomedical sensor applications. Methodologies of using piezoelectricity to convert mechanical power to electric power with a cantilever beam excited by external environmental vibration were widely discussed and examined. Operating in resonant mode of the cantilever beam was found to be the most efficient power harvesting condition, but in most cases that the resonant frequencies of the cantilever beam are hardly matching with the frequency of external vibration sources. The mechanical resonant has relatively high Q factor, and thus the harvesting output will be significantly lower compared to the condition when resonant matching to external vibration frequency. A tunable resonant frequency power harvesting device in cantilever beam form which will shift its resonant frequency to match that of the external vibrations will be developed and verified in this paper. This system utilizes a variable capacitive load to shift the gain curve of the cantilever beam and a low power microcontroller will sampling the external frequency and adjust the capacitive load to match external vibration frequency in real-time. The underlying design thoughts, methods developed, and preliminary experimental results will be presented. Potential applications of this newly developed power harvesting to wireless sensor network will also be detailed.
03 Apr 2006
TL;DR: In this article, the effect of loss on magneto-inductive waveguides based on coupled loop resonators is examined. And conditions for low reflection are identified in splitters, and it is shown that matched three-port splitters with arbitrary power division ratios may be achieved for a particular input port.
Abstract: Devices formed from magneto-inductive waveguides based on coupled loop resonators are considered using simple analytic theory, initially assuming lossless propagation and nearest-neighbour coupling. Two-port devices that were considered include mirrors, Fabry-Perot resonators, Bragg gratings and tapers, while more general N-port devices include power splitters and directional couplers. Conditions for multiple-beam resonance and Bragg reflection in two-port devices are identified, and it is shown that quasi-optical filters may be constructed by simple layout variations. Conditions for low reflection are identified in splitters, and it is shown that matched three-port splitters with arbitrary power division ratios may be achieved for a particular input port. However, matching is not possible for all ports simultaneously. Directional couplers are shown to operate well only at mid-band and with weak coupling. The effect of loss is then examined and it is shown that idealised performance is obtained using resonators with sufficiently high Q-factors.
TL;DR: A two-ring resonator configuration that can provide optical switching with high extinction ratio (ER), large modulation depth (MD) and low switching threshold, and compare it with two other conventional one-ring configurations is proposed.
Abstract: We propose a two-ring resonator configuration that can provide optical switching with high extinction ratio (ER), large modulation depth (MD) and low switching threshold, and compare it with two other conventional one-ring configurations. The achievable input threshold is n2IIN ~10-5, while maintaining a large ER (> 10dB) and MD (~ 1) over a 10-GHz (0.1 nm) optical bandwidth. This performance can also be achieved by the ring-enhanced Mach-Zehnder interferometer, and is one to two orders of magnitude better than the simple bus-coupled one-ring structures, because of the use of asymmetric Fano resonance as opposed to the usual symmetric resonance of a single ring. The sharpness and the asymmetricity of the Fano resonance are linked to the low switching threshold and the high extinction ratio, respectively, and also accounts for the different dependence on ring dimensions between the one- and two-ring structures.
TL;DR: Ultra-high-Q optical microcavities (Q>10(7)) provide one method for distinguishing chemically similar species by monitoring Q, and sensitivity represents an order of magnitude improvement over previous techniques.
Abstract: Ultra-high Q resonators immersed in H2O have a lower Q than those in D2O due to the higher optical absorption. By monitoring the cavity-Q, concentrations of .0001% (1ppmv) of D2O in H2O have been detected.
TL;DR: In this paper, a simple model for estimating viscous damping of fluid (gas or liquid) loaded mechanical resonators is presented, which applies to beams in flexural modes of vibration, and to thin beams and plates in longitudinal modes of vibrations.
Abstract: Simple models are presented for estimating viscous damping of fluid (gas or liquid) loaded mechanical resonators. The models apply to beams in flexural modes of vibration, and to thin beams and plates in longitudinal modes of vibration. Predictions of the associated quality factor are compared with measured values for several macroscale and microscale resonators. The scaling of viscous loss with oscillator size is discussed. The minimum detectable mass is estimated for several oscillator designs and it is shown that, for comparably sized devices, longitudinal resonators have the lowest threshold of detection. This minimum detectable mass is proportional to scale to the power 1.75 for all resonator architectures limited by viscous damping, and it is shown that the viscous loss is 220 times larger in water than in air.
11 Jun 2006
TL;DR: In this paper, a branch-line coaxial line with periodic dielectric straps is demonstrated. But the line is not considered in this paper, since the inner conductor cross-section is different from ours.
Abstract: A miniature non-uniform copper-air rectangular coaxial line with the inner conductor supported by periodic dielectric straps is demonstrated. The overall height of the line is 310mum with the outer conductor cross-section being 250mumtimes250mum. The measured loss is 0.22dB/cm at 26GHz, while the isolation between two parallel lines with a center-to-center separation of 700mum is better than 60dB. Several quasi-planar components are designed and fabricated on the same wafer, and presented here are a branch-line hybrid and a transmission line resonator. The through and coupled port transmissions for the hybrid at 26GHz are -3.25dB and -3.35dB respectively, with phase misbalance below 0.2deg. The transmission line resonator has an unloaded Q-factor of 110 at 25GHz
TL;DR: These devices, and an all-optical actuation and detection system, may provide insight into the physics of the interaction of nanoscale mechanical structures with their environments, greatly extending the viscosity range over which such small flexural resonant devices can be operated.
Abstract: We demonstrate the operation of radio frequency nanoscale flexural resonators in air and liquid. Doubly clamped string, as well as singly clamped cantilever resonators, with nanoscale cross-sectional dimensions and resonant frequencies as high as 145 MHz are driven in air as well as liquid with an amplitude modulated laser. We show that this laser drive technique can impart sufficient energy to a nanoscale resonator to overcome the strong viscous damping present in these media, resulting in a mechanical resonance that can be measured by optical interference techniques. Resonance in air, isopropyl alcohol, acetone, water, and phosphate-buffered saline is demonstrated for devices having cross-sectional dimensions close to 100 nm. For operation in air, quality factors as high as 400 at 145 MHz are demonstrated. In liquid, quality factors ranging from 3 to 10 and frequencies ranging from 20 to 100 MHz are observed. These devices, and an all-optical actuation and detection system, may provide insight into the physics of the interaction of nanoscale mechanical structures with their environments, greatly extending the viscosity range over which such small flexural resonant devices can be operated.
TL;DR: In this paper, Recta-Coaxial (recta-coax) transmission lines fabricated through a three-dimensional micromachining process are presented, and their design equations are presented for impedance, loss, and frequency range.
Abstract: Rectangular-coaxial (recta-coax) transmission lines fabricated through a three-dimensional micromachining process are presented. These lines are shown to have significant advantages over competing integrated transmission lines such as microstrip and coplanar waveguides. Design equations are presented for impedance, loss, and frequency range. The equations are confirmed with simulations and measurements. The quality factor of shorted lambda/4 resonators is measured to be 156 at 60 GHz. This corresponds to a line loss of 0.353 dB/cm. Advantages of these lines for passive millimeter-wave circuits including ease of signal routing, high isolation, and signal crossovers are demonstrated with realized lines and couplers