Showing papers in "IEEE Transactions on Microwave Theory and Techniques in 2003"

Single-substrate integration technique of planar circuits and waveguide filters

Abstract: The integrated planar technique has been considered as a reliable candidate for low-cost mass production of millimeter-wave circuits and systems. This paper presents new concepts that allow for a complete integration of planar circuits and waveguide filters synthesized on a single substrate by means of metallized post (or via-hole) arrays. Analysis of the synthesized integrated waveguide and design criteria are presented for the post pitch and diameter. A filter design method derived from a synthesis technique using inductive post is presented. An experimental three-pole Chebyshev filter having 1-dB insertion loss and return loss better than 17 dB is demonstrated. Integrating such planar and nonplanar circuits on a substrate can significantly reduce size, weight, and cost, and greatly enhance manufacturing repeatability and reliability.

Advanced coupling matrix synthesis techniques for microwave filters

Abstract: A general method is presented for the synthesis of the folded-configuration coupling matrix for Chebyshev or other filtering functions of the most general kind, including the fully canonical case, i.e., N prescribed finite-position transmission zeros in an Nth-degree network. The method is based on the "N+2" transversal network coupling matrix, which is able to accommodate multiple input/output couplings, as well as the direct source-load coupling needed for the fully canonical cases. Firstly, the direct method for building up the coupling matrix for the transversal network is described. A simple non-optimization process is then outlined for the conversion of the transversal matrix to the equivalent "N+2" folded-configuration coupling matrix. The folded matrix may be used directly to realize microwave bandpass filters in a variety of technologies, but some of these could require awkward-to-realize cross-couplings. This paper concludes with a description of two simple procedures for transforming the transversal and folded matrices into two novel network configurations, which enable the realization of advanced microwave bandpass filters without the need for complex inter-resonator coupling elements.

Artificial neural networks for RF and microwave design - from theory to practice

Abstract: Neural-network computational modules have recently gained recognition as an unconventional and useful tool for RF and microwave modeling and design. Neural networks can be trained to learn the behavior of passive/active components/circuits. A trained neural network can be used for high-level design, providing fast and accurate answers to the task it has learned. Neural networks are attractive alternatives to conventional methods such as numerical modeling methods, which could be computationally expensive, or analytical methods which could be difficult to obtain for new devices, or empirical modeling solutions whose range and accuracy may be limited. This tutorial describes fundamental concepts in this emerging area aimed at teaching RF/microwave engineers what neural networks are, why they are useful, when they can be used, and how to use them. Neural-network structures and their training methods are described from the RF/microwave designer's perspective. Electromagnetics-based training for passive component models and physics-based training for active device models are illustrated. Circuit design and yield optimization using passive/active neural models are also presented. A multimedia slide presentation along with narrative audio clips is included in the electronic version of this paper. A hyperlink to the NeuroModeler demonstration software is provided to allow readers practice neural-network-based design concepts.

A small dual-frequency transformer in two sections

Abstract: One of the most useful transmission-line constructs is the quarter-wave transformer that is used to impedance match a line at a single frequency f/sub 0/. The feasibility of an electrically small transformer with two sections and capable of achieving ideal impedance matching at two arbitrary frequencies is demonstrated analytically. To achieve this, the exact solution to the resulting transcendental transmission-line equations for two sections is obtained with no restrictions. The parameters of the transformer are presented in explicit closed form, and are exact. The results of this study are useful for a number of practical design problems, including dual-band antennas and RF circuits in general. In particular, feasibility of ideal operation at the important first harmonic frequency 2f/sub 0/ is demonstrated.

Compact planar microstripline branch-line and rat-race couplers

Abstract: Both branch-line and rat-race couplers are easily realized using planar circuit technology as they employ only transmission lines without additional components. However, as the electrical lengths of the transmission line elements are either 90/spl deg/ or 270/spl deg/, such couplers consume a significant amount of circuit area. This paper shows the development of branch-line and rat-race couplers that use artificial transmission lines (ATLs) in place of conventional transmission lines resulting in significant size reduction. As the ATLs are constructed entirely from microstriplines, the couplers are easily fabricated using conventional printed-circuit processes. The design formulas developed for the ATLs are explicit. Full-wave simulation and experimental results were used to confirm the design approach for hybrids operating at 1.8 GHz. The frequency response of the proposed hybrids is similar to conventional hybrids.

Metallo-dielectric electromagnetic bandgap structures for suppression and isolation of the parallel-plate noise in high-speed circuits

Abstract: A novel approach for the suppression of the parallel-plate waveguide (PPW) noise in high-speed printed circuit boards is presented. In this approach, one of the two conductors forming the PPW is replaced by an electromagnetic bandgap (EBG) surface. The main advantage of the proposed approach over the commonly practiced methods is the omnidirectional noise suppression it provides. For this purpose, two EBG structures are initially designed by utilizing an approximate circuit model. Subsequently, the corresponding band structures are characterized by analytical solutions using the transverse resonance method, as well as full-wave finite-element simulations. The designed EBG surfaces were fabricated and employed in a number of PPW test boards. The corresponding frequency-domain measurements exhibited bandgaps of approximately 2.21 and 3.35 GHz in the frequency range below 6 GHz. More importantly, suppression of the PPW noise by 53% was achieved based on time-domain reflectometry experiments, while maintaining the signal transmission quality within the required specifications for common signaling standards.

Behavioral modeling of nonlinear RF power amplifiers considering memory effects

Abstract: This paper proposes a new behavioral model to treat memory effects in nonlinear power amplifiers (PAs) Phenomena such as asymmetries in lower and upper intermodulation terms, and variation of AM/AM and AM/PM, depending on signal history, are often observed in high-power PAs To treat these phenomena, this paper presents a model based on the previously developed memory polynomial model The contribution made in this paper is to augment the memory polynomial model to include a sparse delay tap structure that reduces the parameter space required for accurate model identification A figure-of-merit, called the memory effect ratio, is defined to quantify the relative level of distortion due to memory effects, as compared to the memoryless portion Another figure-of-merit is defined as the memory effect modeling ratio, which quantifies the degree to which the PA memory effects have been accounted for in the model This new technique is validated using a variety of RF PAs, including an 880-MHz and a 21-GHz high-power laterally diffused metal-oxide semiconductor PA and various signals such as two-tone, eight-tone, and IS-95B signals

Microstrip stepped impedance resonator bandpass filter with an extended optimal rejection bandwidth

Abstract: Bandpass filters with an optimal rejection bandwidth are designed using parallel-coupled stepped impedance resonators (SIRs). The fundamental (f/sub o/) and higher order resonant harmonics of an SIR are analyzed against the length ratio of the high-Z and low-Z segments. It is found that an optimal length ratio can be obtained for each high-Z to low-Z impedance ratio to maximize the upper rejection bandwidth. A tapped-line input/output structure is exploited to create two extra transmission zeros in the stopband. The singly loaded Q(Q/sub si/) of a tapped SIR is derived. With the aid of Q/sub si/, the two zeros can be independently tuned over a wide frequency range. When the positions of the two zeros are purposely located at the two leading higher order harmonics, the upper rejection band can be greatly extended. Chebyshev bandpass filters with spurious resonances up to 4.4f/sub o/, 6.5f/sub o/, and 8.2f/sub o/ are fabricated and measured to demonstrate the idea.

The class-E/F family of ZVS switching amplifiers

Abstract: A new family of switching amplifiers, each member having some of the features of both class E and inverse F, is introduced. These class-E/F amplifiers have class-E features such as incorporation of the transistor parasitic capacitance into the circuit, exact truly switching time-domain solutions, and allowance for zero-voltage-switching operation. Additionally, some number of harmonics may be tuned in the fashion of inverse class F in order to achieve more desirable voltage and current waveforms for improved performance. Operational waveforms for several implementations are presented, and efficiency estimates are compared to class-E.

Miniature and tunable filters using MEMS capacitors

Abstract: Microelectromechanical system (MEMS) bridge capacitors have been used to design miniature and tunable bandpass filters at 18-22 GHz. Using coplanar waveguide transmission lines on a quartz substrate (/spl epsiv//sub r/ = 3.8, tan/spl delta/ = 0.0002), a miniature three-pole filter was developed with 8.6% bandwidth based on high-Q MEMS bridge capacitors. The miniature filter is approximately 3.5 times smaller than the standard filter with a midband insertion loss of 2.9 dB at 21.1 GHz. The MEMS bridges in this design can also be used as varactors to tune the passband. Such a tunable filter was made on a glass substrate (/spl epsiv//sub r/ = 4.6, tan/spl delta/ = 0.006). Over a tuning range of 14% from 18.6 to 21.4 GHz, the miniature tunable filter has a fractional bandwidth of 7.5 /spl plusmn/ 0.2% and a midband insertion loss of 3.85-4.15 dB. The IIP/sub 3/ of the miniature-tunable filter is measured at 32 dBm for the difference frequency of 50 kHz. The IIP/sub 3/ increases to >50 dBm for difference frequencies greater than 150 kHz. Simple mechanical simulation with a maximum dc and ac (ramp) tuning voltages of 50 V indicates that the filter can tune at a conservative rate of 150-300 MHz//spl mu/s.

Digital receivers and transmitters using polyphase filter banks for wireless communications

Abstract: Provides a tutorial overview of multichannel wireless digital receivers and the relationships between channel bandwidth, channel separation, and channel sample rate. The overview makes liberal use of figures to support the underlying mathematics. A multichannel digital receiver simultaneously down-converts a set of frequency-division-multiplexed (FDM) channels residing in a single sampled data signal stream. In a similar way, a multichannel digital transmitter simultaneously up-converts a number of baseband signals to assemble a set of FDM channels in a single sampled data signal stream. The polyphase filter bank has become the architecture of choice to efficiently accomplish these tasks. This architecture uses three interacting processes to assemble or to disassemble the channelized signal set. In a receiver, these processes are an input commutator to effect spectral folding or aliasing due to a reduction in sample rate, a polyphase M-path filter to time align the partitioned and resampled time series in each path, and a discrete Fourier transform to phase align and separate the multiple baseband aliases. In a transmitter, these same processes operate in a related manner to alias baseband signals to high order Nyquist zones while increasing the sample rate with the output commutator.

Cross-coupling in coaxial cavity filters - a tutorial overview

Abstract: This paper presents a tutorial overview of the use of coupling between nonadjacent resonators to produce transmission zeros at real frequencies in microwave filters. Multipath coupling diagrams are constructed and the relative phase shifts of multiple paths are observed to produce the known responses of the cascaded triplet and quadruplet sections. The same technique is also used to explore less common nested cross-coupling structures and to predict their behavior. A discussion of the effects of nonzero electrical length coupling elements is presented. Finally, a brief categorization of the various synthesis and implementation techniques available for these types of filters is given.

Electromechanical considerations in developing low-voltage RF MEMS switches

Abstract: This paper reports on the design, fabrication, and testing of a low-actuation voltage Microelectromechanical systems (MEMS) switch for high-frequency applications. The mechanical design of low spring-constant folded-suspension beams is presented first, and switches using these beams are demonstrated with measured actuation voltages of as low as 6 V. Furthermore, common nonidealities such as residual in-plane and gradient stress, as well as down-state stiction problems are addressed, and possible solutions are discussed. Finally, both experimental and theoretical data for the dynamic behavior of these devices are presented. The results of this paper clearly underline the need of an integrated design approach for the development of ultra low-voltage RF MEMS switches.

A fully matched N-way Doherty amplifier with optimized linearity

Abstract: This paper presents a new fully matched N-way Doherty amplifier. The basic principles of operation and important features are described. For the experimental verification, 2.14-GHz Doherty amplifiers having two-, three-, and four-way structures are implemented using silicon LDMOSFETs and tested using down-link WCDMA signal. The linearity performances of the two-, three-, and four-way Doherty amplifiers are optimized for better efficiency versus linearity by a bias adjustment of the peaking amplifiers. For simultaneously improving the efficiency and linearity to achieve maximum efficiency versus linearity, the gate biases of the peaking amplifiers for the N-way Doherty amplifier are optimized. As a result, the efficiency versus linearity characteristics are drastically improved by N-way extension of the Doherty amplifier.

Finite-difference frequency-domain algorithm for modeling guided-wave properties of substrate integrated waveguide

Abstract: In multilayer microwave integrated circuits such as low-temperature co-fired ceramics or multilayered printed circuit boards, waveguide-like structures can be fabricated by using periodic metallic via-holes referred to as substrate integrated waveguide (SIW). Such SIW structures can largely preserve the advantages of conventional rectangular waveguides such as high-Q factor and high power capacity. However, they are subject to leakage due to periodic gaps, which potentially results in wave attenuation. Therefore, such a guided-wave modeling problem becomes a very complicated complex eigenvalue problem. Since the SIW are bilaterally unbounded, absorbing boundary conditions should be deployed in numerical algorithms. This often leads to a difficult complex root-extracting problem of a transcend equation. In this paper, we present a novel finite-difference frequency-domain algorithm with a perfectly matched layer and Floquet's theorem for the analysis of SIW guided-wave problems. In this scheme, the problem is converted into a generalized matrix eigenvalue problem and finally transformed to a standard matrix eigenvalue problem that can be solved with efficient subroutines available. This approach has been validated by experiment.

Compact, low insertion-loss, sharp-rejection, and wide-band microstrip bandpass filters

Abstract: This paper presents a new compact, low insertion-loss, sharp-rejection, and wide-band microstrip bandpass filter. A bandstop filter is introduced that uses a ring resonator with direct-connected orthogonal feed lines. A new bandpass filter based on the bandstop filter uses two tuning stubs to construct a wide-band passband with two sharp stopbands. Without coupling gaps between feed lines and rings, there are no mismatch and radiation losses between them and, therefore, the new filters show low insertion loss. In addition, a dual-mode characteristic is used to increase the stopband bandwidth of the new filters. A simple transmission-line model used to calculate the frequency responses of the filters shows good agreement with measurements. The filter using three cascaded rings has 3-dB fractional bandwidth of 49.3%, an insertion loss of better than 1.6 dB in the passband, a return loss of larger than 13 dB from 4.58 to 7.3 GHz, and two rejections of greater than 40 dB within 2.75-4.02 and 7.73-9.08 GHz. The high-performance, compact-size, and low-cost filter was designed for reducing the interference in full duplex systems in satellite communications.

Voltage-controlled RF filters employing thin-film barium-strontium-titanate tunable capacitors

Abstract: Tunable lowpass and bandpass lumped-element filters employing barium-strontium-titanate (BST)-based capacitors are presented A new metallization technique is used, which improves the quality factor of the tunable BST capacitors by a factor of two The lowpass filter has an insertion loss of 2 dB and a tunability of 40% (120-170 MHz) with the application of 0-9 V DC bias The bandpass filter (BPF) has an insertion loss of 3 dB and a tunability of 57% (176-276 MHz) with the application of 0-6 V DC The third-order intercept point of the BPF was measured to be 19 dBm with the application of two tones around 170 MHz

Compact elliptic-function low-pass filters using microstrip stepped-impedance hairpin resonators

Abstract: A compact elliptic-function low-pass filter using microstrip stepped-impendance hairpin resonators and their equivalent-circuit models are developed. The prototype filters are synthesized from the equivalent-circuit model using available element-value tables. To optimize the performance of the filters, electromagnetic simulation is used to tune the dimensions of the prototype filters. The filter using multiple cascaded hairpin resonators provides a very sharp cutoff frequency response with low insertion loss. Furthermore, to increase the rejection-band bandwidth, additional attenuation poles are added in the filter. The filters are evaluated by experiment and simulation with good agreement. This simple equivalent-circuit model provides a useful method to design and understand this type of filters and other relative circuits.

Complex permittivity measurements of common plastics over variable temperatures

Abstract: In this paper, we present complex permittivity data at microwave frequencies (approximately 10 GHz) for many common plastics over a temperature range of 122 to 375 K. The measurements were made with a TE/sub 01/spl delta// dielectric resonator placed inside an environmental chamber. Data are presented for the following materials: acrylonitrile butadiene styrene, polytetrafluoroethylene, cross-linked polystyrene, tetrafluorethylene-perfluorpropylene, polypropylene, polysulfone, polymethylmethacrylate, polyvinyl chloride, polycarbonate, high-density polyethylene, polyoxy-methylene (acetal homopolymer), and polyamide.

An unconditionally stable scheme for the finite-difference time-domain method

Abstract: In this work, we propose a numerical method to obtain an unconditionally stable solution for the finite-difference time-domain (FDTD) method for the TE/sub z/ case. This new method does not utilize the customary explicit leapfrog time scheme of the conventional FDTD method. Instead we solve the time-domain Maxwell's equations by expressing the transient behaviors in terms of weighted Laguerre polynomials. By using these orthonormal basis functions for the temporal variation, the time derivatives can be handled analytically, which results in an implicit relation. In this way, the time variable is eliminated from the computations. By introducing the Galerkin temporal testing procedure, the marching-on in time method is replaced by a recursive relation between the different orders of the weighted Laguerre polynomials if the input waveform is of arbitrary shape. Since the weighted Laguerre polynomials converge to zero as time progresses, the electric and magnetic fields when expanded in a series of weighted Laguerre polynomials also converge to zero. The other novelty of this approach is that, through the use of the entire domain-weighted Laguerre polynomials for the expansion of the temporal variation of the fields, the spatial and the temporal variables can be separated.

Narrow bandpass filters using dual-behavior resonators

Abstract: This paper reports on a new concept of narrow bandpass filters leading to perfectly controlled electrical responses within both the required operating bandwidth and adjacent undesired bands. A specific topology is considered for such a "global synthesis": in comparison with conventional filter performances, it provides significant improvements in terms of rejection control. The attenuated frequencies are each located apart from the bandpass frequencies and controlled by means of n transmission zeros introduced through original dual-behavior resonators (DBRs). These resonators are based on the association of different parallel open-ended stubs and allow the designer to independently control the in-band and out-of-band responses of the filter. A global synthesis approach is also discussed on a simplified architecture based on stepped impedance stubs, and the experimental results shown clearly validate the proposed concept. This simplification reduces the number of degrees of freedom when designing a DBR, and consequently the two transmission zeros become dependent.

A compact second-order LTCC bandpass filter with two finite transmission zeros

Abstract: A novel implementation and associated design formula for a compact low-temperature cofired ceramics (LTCC) lumped-element second-order bandpass filter are proposed in this paper. The filter schematic that provides two finite transmission zeros is well known. It is shown in the paper that the filter schematic is built on a pair of conventional inductive coupled resonator tanks with a feedback capacitor between input and output. While revealing its working mechanism both graphically and mathematically, a simple design procedure for such a compact filter is also given. The proposed filter has been implemented in a six-layer ceramic substrate using LTCC technology, showing promising application potentials in miniaturized mobile terminals and Bluetooth RF front-ends. The measured results agree very well with the full-wave electromagnetic designed responses.

Intermodulation distortion and power handling in RF MEMS switches, varactors, and tunable filters

Abstract: This paper presents a theoretical and experimental study of the nonlinear effects generated RF-microelectromechanical system (MEMS) varactors and capacitive switches. The theoretical part includes an analytic derivation, as well as an electromechanical model suitable for computer-aided design (CAD) simulation. The simulations agree very well with measurements performed on a 24-GHz three-pole MEMS tunable filter. It is shown that MEMS capacitive components with a spring constant k>10 N/m generate very low intermodulation, as compared to semiconductor devices, and lead to a two-tone third-order intermodulation intercept point (IIP3) greater than +40 dBm for /spl Delta/f>3-5f/sub 0/, where f/sub 0/ is the mechanical resonant frequency. In fact, the IIP3 increases to +80 dBm for a difference signal (/spl Delta/f) of 5 MHz. The CAD model also allows the evaluation of the power-handling capabilities of the tunable filter and, it is seen that, for the case presented here, distortions become significant for an input power greater than +20 dBm. Noise generation due to thermal effects on a movable membrane (Brownian noise) is also modeled and it is shown that the tunable filter results in a very low phase-noise level close to the carrier.

Measurement of the dielectric constant and loss tangent of high dielectric-constant materials at terahertz frequencies

Abstract: Low-loss high dielectric-constant materials are analyzed in the terahertz frequency range using time-domain spectroscopy. The dielectric constant and loss tangent for steatite, alumina, titania loaded polystyrene, and zirconium-tin-titanate are presented and compared to measurements on high-resistivity silicon. For these materials, the real part of the dielectric constant ranges from 6 to 90. All of the samples were found to have reasonable low-loss tangents. Applications as photonic crystal substrates for terahertz frequency antenna are envisaged.

A first multigigahertz digitally controlled oscillator for wireless applications

Abstract: A novel digitally controlled oscillator (DCO) architecture for multigigahertz wireless RF applications, such as short-range wireless connectivity or cellular phones, is proposed and demonstrated. It deliberately avoids any use of an analog tuning voltage control line. Fine frequency resolution is achieved through high-speed dithering, yet the resulting spurious tones are very low. This enables to employ fully digital frequency synthesizers in the most advanced deep-submicrometer digital CMOS processes, which allow almost no analog extensions. It promotes cost-effective integration with the digital back-end onto a single silicon die. The demonstrator test chip has been fabricated in a digital 0.13 /spl mu/m CMOS process together with a digital signal processor to investigate noise coupling. The 2.4 GHz DCO core consumes 2.3 mA from a 1.5 V supply and has a very large tuning range of 500 MHz. The phase noise is -112 dBc/Hz at 500 kHz offset. The presented ideas have been incorporated in a commercial Bluetooth transceiver.

3-D FDTD design analysis of a 2.4-GHz polarization-diversity printed dipole antenna with integrated balun and polarization-switching circuit for WLAN and wireless communication applications

Abstract: Detailed numerical simulation, fabrication, and experimental measurements of a 2.4-GHz polarization-diversity printed dipole antenna are presented for wireless communication applications. Two orthogonal printed dipole antennas, each with a microstrip via-hole balun feeding structure, are combined and fabricated on an FR-4 printed-circuit-board substrate. A p-i-n diode circuit is used to switch and select the desired antenna polarization. In the antenna design simulation, a full-wave method of a three-dimensional finite-difference time-domain (FDTD) method is employed to analyze the entire structure of the printed antenna including the lumped elements of the polarization-selected p-i-n diode switching circuit. The Berenger perfectly matched layer absorbing-boundary condition is used for the FDTD computation. Numerical and measured results of antenna radiation characteristics, including input standing-wave ratio, radiation patterns, and polarization diversity are presented.

Varactor-loaded transmission-line phase shifter at C-band using lumped elements

Abstract: The design of varactor-loaded transmission-line phase shifters using lumped elements is discussed in this paper. A monolithic-microwave integrated-circuit (MMIC) phase shifter is fabricated to verify the proposed topology. Only one control voltage is required for phase control. Within a continuously adjustable phase-control range of 360/spl deg/ and a frequency range from 5 to 6 GHz, a low transmission loss of 4 dB/spl plusmn/1.7 dB is measured. The phase shifter is realized with a commercial 0.6-/spl mu/m GaAs MESFET process and requires a chip area of only 0.8 mm/sup 2/. To the knowledge of the authors, the best results reported to date are reached for a continuously adjustable passive phase shifter with comparable circuit size. The presented circuit is well suited to wireless adaptive antenna transceivers, operating in accordance with the 802.11a, high-performance radio local-area-network and high-speed wireless-access-network type-a standard.

Experimental feasibility study of confocal microwave imaging for breast tumor detection

Abstract: Initial experimental verification of confocal microwave imaging for breast tumor detection is described. Simple phantoms, consisting of a PVC pipe and objects representing tumors, are scanned with resistively loaded monopole or horn antennas. Successful reduction of clutter and detection of a variety of two-dimensional objects is demonstrated.

Compact single-channel rotary joint using ridged waveguide sections for phase adjustment

Abstract: A new design for single-channel waveguide rotary joints for high-power applications is presented. In order to obtain correct signal phase conditions along the ring and, at the same time, reduce the diameter of the rotary joint, tapered ridged waveguide sections are introduced. Design guidelines with respect to general transmission characteristics, H-plane aperture couplers, and ridge waveguide analysis are presented. Measurements of a 9.05-GHz prototype show less than 1-dB insertion loss over a 250-MHz bandwidth and, hence, verify the design concept.

Very low-loss distributed X-band and Ka-band MEMS phase shifters using metal-air-metal capacitors

Abstract: 2-bit wide-band distributed coplanar-waveguide phase shifters have been developed on a 500-/spl mu/m quartz substrate for X- and Ka-band operation. The designs utilize microelectromechanical system (MEMS) switches in a distributed MEMS transmission line periodically loaded by MEMS switches and high Q (/spl ges/250 at 30 GHz) metal-air-metal capacitors. The MEMS switches are actuated by a /spl plusmn/20-V voltage waveform using a high-resistance bias line. Estimated spring constant and switching time is 30 N/m and 9 /spl mu/s, respectively. The Ka-band 2-bit design results in a reflection coefficient better than -11.5 dB, an average insertion loss of -1.5 dB and phase shifts of 0/spl deg/, 89/spl deg/, 180/spl deg/, and 270/spl deg/ at 37.7 GHz. The X-band 2-bit design results in a reflection coefficient better than -12.5 dB, an average insertion loss of -1.2 dB and phase shifts of 0/spl deg/, 94/spl deg/, 176/spl deg/, and 270/spl deg/ at 13.6 GHz. These results are very competitive with switched transmission-line and reflection-based phase shifters. The distributed design can be easily scaled to V- and W-band frequencies for wide-band low-loss performance.