Precise Design of a Bandpass Filter Using High-Q Dielectric Ring Resonators

A precise design is presented for a bandpass filter constructed by placing TE/sub 01delta/ dielectric ring resonators coaxially in a TE/sub 01/ cutoff circular waveguide. On the basis of a rigorous analysis by the mode- matching technique, the interresonator coupling coefficients are determined accurately from the calculation of two resonant frequencies f/sub sh/ and f/sub op/ when the structurally symmetric plane is short- and open-circuited. For the TE/sub 01delta/ ring resonator,the resonant frequency f/sub 0/, the temperature coefficient tau/sub f/, the unloaded Q(Q/sub u/), and the other resonances are also calculated accurately in a similar way. From the calculations, the optimum dimensions are determined to obtain the maximum Q/sub u/, as F/sub r/ = f/sub r/ /f/sub 0/ is kept constant, where f/sub r/ is the next higher resonant frequency the ring resonator using low-loss ceramics (epsilon/sub r/ = 24.3, tan delta = 5 x 10/sup -5/) has Q/sub u/ = 16800 at 12 GHz and tau/sub f/ = 0.1+-0.5 ppm/° C, while the rod one has Q/sub u/ = 14700. A four-stage Chebyshev filter having ripple of 0.04 dB and equiripple bandwidth of 27.3 MHz at f/sub 0/ =11.958 GHz is fabricated using these resonator; the measured frequency responses agree well with theory. The insertion loss is 0.9 dB, which corresponds to Q/sub u/ = 9800.     

SAW Bandpass Filter Design for 1.6-GHz PCM Timing Tank Applications

A 1.6-GHz surface acoustic wave (SAW) timing tank for a self-timed regenerative repeater for an ultrahigh-speed PCM optical fiber transmission system is described. A SAW narrow bandpass filter with 0.74-mu m linewidth interdigital transducers with double electrode geometry and 20-nm aluminum metallization on AT-quartz substrate is realized by conventional optical photolithography. Typical performance obtained is as follows: center frequency f/sub 0/ is 1.5993 GHz; insertion loss is 22 dB; stopband attenuation is above 23 dB with respect to the passbaand; stability is |2Q/sub L//spl dot/Delta f /f/sub 0/| < 0.1, where Q/sub L/ is loaded Q value and Delta f is mistuning due to temperature effects. It is demonstrated that SAW quartz transversal filters can be made into new practical filters which have both high Q value and high stability fn the GHz range and are satisfactory from the standpoints of precise design, fabrication technique, and performance.     

Unloaded Q of Single Crystal Yttrium-Iron-Garnet Resonator as a Function of Frequency (Correspondence)

The practical feasibility of constructing magnetically tunable broad-tuning range microwave filters using single crystal yttriumiron-garnet resonators was demonstrated in a recent paper. Experimental results were presented on one- and two- resonator filters which can be tuned by varying a dc magnetic field bias over a full waveguide bandwidth and greater, at the same time maintaining an insertion loss performance which is comparable to mechanically-tuned cavity filters. The crucial parameter of the resonant elements in a band-pass filter is the unloaded Q, Q/sub u/. With a spherical single crystal of yttrium-iron-garnet the Q/sub u/ decreases with frequency below X-band frequencies reaching very low values at frequencies around 2000 Mc.     

Wideband coplanar waveguide-to-rectangular waveguide transition using fin-line taper

This letter introduces a new wideband coplanar waveguide-to-rectangular waveguide transition. The transition uses a uniplanar circuit in line with the waveguide, which eases the design and fabrication. The design does not require airbridges. Simulations and measurements of X-band (8.2-12.4 GHz) transitions based on both a low- and high-permittivity material (/spl epsiv//sub r/= 2.33 and 10.8) show that the transition works fine over the full frequency band. For /spl epsiv//sub r/= 2.33 the measured return and insertion loss of a back-to-back transition are more than 16 dB and less than 0.4dB, respectively. The corresponding values for /spl epsiv//sub r/= 10.8 are more than 10 dB and less than 1.0 dB, respectively, over 90% of the frequency band. The measured insertion loss values indicate losses of less than 0.14 dB and 0.36 dB at the center frequency for a single transition on a substrate with /spl epsiv//sub r/= 2.33 and 10.8, respectively.     

The Coupling Coefficients of an Unsymmetrical High-Q Lossy Waveguide Resonator

This paper determines the minimum insertion loss and the minimmn VSWR of a waveguide resonator constructed by spacing two, unequal, reactive, primarily-shunt, Iossy, reflecting elements approximately one-half-wavelength apart on a lossy transmission line. The requirement that the resonant loss be small, 10 db or less, limits the size of the loss parameters and permits an approximate solution of the problem within an error of the order of 1/Q/sub L/. These formulas can be expressed in terms of two "coupling coefficients. " Contrary to the familiar formulas derived from the low frequency analogue, however, these coupling coefficients depend, in general, on the parameters of both reflecting elements. Formulas for the loaded and unloaded Q of the resonator are derived. In general, it is not possible to determine the unloaded Q of the resonator from its loaded Q except by a limiting process. Within the order of the approximation involved, series losses cannot be distinguished from shunt losses. Accordingly they can be lumped together and one is led to the fact that a Iossy admittance inverter consists of a lossless admittance inverter surrounded on both sides by series losses. This is used to justify the application of the idea of "predistortion" to the design of narrow-band, Iossy, waveguide filters.     

Miniature and tunable filters using MEMS capacitors

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.     

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

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.     

High-Power Microwave Rejection Filters Using Higher-Order Modes

In order to obtain filters capable of handling very high power, the use of radial lines and uniform line discontinuities was investigated. Forty-five-degree tapers and uniform lines were used to design a high-power microwave filter capable of handling 700 kw at 15 pounds pressure in a 0.900 by 0.400 ID waveguide. In addition to the filtering which results from the discontinuities in the TE/sub 10/ mode in the waveguide, high insertion loss elements are effected when the enlarged uniform line section is larger than the TE/sub 10/ mode waveguide wavelength and when the length of the enlarged section is approximately (2n -1)lambda/sub g//4. Extremely large insertion losses are possible by the cascading of these elements. Tuning, in the standard-size waveguide, has no effect on the insertion loss of the higher-mode enlarged waveguide at its resonant frequency. Empirical design formulas are evolved and the design procedure for band-rejection filters is given, using these high insertion loss elements.     

Radiation from Bends in Dielectric Rod Transmission Lines

The radiation from the fundamental mode propagating around curved dielectric rod transmission lines is investigated experimentally with microwave frequencies. Three methods are used to determine the attenuation by radiation: measuring the insertion loss of bends, measuring the Q-factor of ring resonators, and measuring the Q-factor of sections of curved dielectric rod transmission lines terminated by large reflecting plates. The attenuation is found to depend mainly on the combination R lambda/sub 0//sup 2/ / r/sub 0//sup 3/ where R is the radius of curvature, lambda/sub 0/ the free space wavelength and r/sub 0/ a measure of the transverse field extent of the HE/sub 11/ mode. The experimental results are compared with theoretical predictions of other authors. The measured values of the attenuation constant are found to be smaller than the theoretical values. The distribution of the electromagnetic field near bends is recorded using a semiautomatic field plotter. From the field pictures, it can be concluded that the curved dielectric waveguide radiates tangentially from the outer side. The results presented will also be useful for understanding the mechanism of radiation from bent optical waveguides.     

Broad-Band Coupling to High-Q Resonant Loads

Broad-band coupling between a resistive source and a resonant load is considered for coupling networks consisting of a uniform transmission line of impedance Z/sub I/ and length equal to a quarter wavelength at the load resonant frequency. An approximate analysis is used to show that either maximally flat or ripple insertion loss frequency response can be obtained by proper choice of Z/sub I/, and the 3-dB bandwidth obtained in either case is always greater than 1/Q. Depending on the ratio of load and source resistances, the bandwidth may be greater than 1 octave. Network design curves for maximally flat operation with a variety of load parameters are computed without approximation. The design of lumped element approximations for the transmission line network is also described.     

Tables for Nonminimum-Phase Even-Degree Low-Pass Prototype Networks for the Design of Microwave Linear-Phase Filters

The element values of a selection of even-degree nonminimum phase low-pass prototype networks with equiripple passband amplitude and constant group delay in the least squares sense over a large percentage of the passband are tabulated. All the prototypes have passband insertion loss ripple R=0.01 dB and cutoff frequency omega/sub c/ = 1.0 rad/s at the 0.01-dB point. Five tables contain the element values of networks up to degree N=20. The tables are classified according to the number of transmission zeros at infinite frequency NZ/sub infin/ and the passband frequency to which the group delay is constant in ttse least squares sense omega/sub d/. The following combinations of NZ/sub infin/ and omega/sub d/ are tabulated: NZ/sub infin/ = 2 and omega/sub d/=0.9; NZ/sub infin/ =4 and omega/sub d/ =0.8; NZ/sub infin/ = 6 and omega/sub d/=0.7; NZ/sub infin/ =8 and omega/sub d/ = 0.6; and NZ/sub infin/ =10 and omega/sub d/= 0.5. The maximum phase and delay errors for each network are tabulated. Plots of the passband group delay and stopband insertion loss versus frequency, for each network, accompany the tables to facilitate selection of a prototype. The prototypes are suitable for the design of narrow-band generalized interdigital, generalized direct-coupled cavity waveguide, and generalized combline linear-phase filters A simple algorithm for the analysis of the prototypes is given.     

Resonant Frequency and Q of an Open-Ended Rectangular Cavity

A field analysis of the TE /sub 10m/ resonant mode in an open-ended rectangular cavity is presented. The cavity geometry consists of rectangular waveguide with thick H-plane bifurcations for the terminations at each end. The bifurcation problem is solved by the method of modal analysis and a resonance criterion is established. Expressions for the cavity fields are written and used to compute stored energy, power lost, and Q. Calculated values for resonant frequency and Q are given and compared with experimental data.     

Millimeter-wave CMOS design

This paper describes the design and modeling of CMOS transistors, integrated passives, and circuit blocks at millimeter-wave (mm-wave) frequencies. The effects of parasitics on the high-frequency performance of 130-nm CMOS transistors are investigated, and a peak f/sub max/ of 135 GHz has been achieved with optimal device layout. The inductive quality factor (Q/sub L/) is proposed as a more representative metric for transmission lines, and for a standard CMOS back-end process, coplanar waveguide (CPW) lines are determined to possess a higher Q/sub L/ than microstrip lines. Techniques for accurate modeling of active and passive components at mm-wave frequencies are presented. The proposed methodology was used to design two wideband mm-wave CMOS amplifiers operating at 40 GHz and 60 GHz. The 40-GHz amplifier achieves a peak |S/sub 21/| = 19 dB, output P/sub 1dB/ = -0.9 dBm, IIP3 = -7.4 dBm, and consumes 24 mA from a 1.5-V supply. The 60-GHz amplifier achieves a peak |S/sub 21/| = 12 dB, output P/sub 1dB/ = +2.0 dBm, NF = 8.8 dB, and consumes 36 mA from a 1.5-V supply. The amplifiers were fabricated in a standard 130-nm 6-metal layer bulk-CMOS process, demonstrating that complex mm-wave circuits are possible in today's mainstream CMOS technologies.     

Estimation of Q-factors and resonant frequencies

We estimate the quality factor Q and resonant frequency f/sub 0/ of a microwave cavity based on observations of a resonance curve on an equally spaced frequency grid. The observed resonance curve is the squared magnitude of an observed complex scattering parameter. We characterize the variance of the additive noise in the observed resonance curve parametrically. Based on this noise characterization, we estimate Q and f/sub 0/ and other associated model parameters using the method of weighted least squares (WLS). Based on asymptotic statistical theory, we also estimate the one-sigma uncertainty of Q and f/sub 0/. In a simulation study, the WLS method outperforms the 3-dB method and the Estin method. For the case of measured resonances, we show that the WLS method yields the most precise estimates for the resonant frequency and quality factor, especially for resonances that are undercoupled. Given that the resonance curve is sampled at a fixed number of equally spaced frequencies in the neighborhood of the resonant frequency, we determine the optimal frequency spacing in order to minimize the asymptotic standard deviation of the estimate of either Q or f/sub 0/.     

A Proposal of a New Dielectric Resonator Construction for MIC's

A compact and high-temperature-stable dielectric resonator having no shielding metal walls nor a conventional frequency tuning screw is described. This resonator consists of a high epsilon/sub r/ dielectric resonator element mounted on a low-loss dielectric mount, a dielectric disk with thin metal film fixed on the resonator element, and a microstrip line substrate on which to mount the constituents. The resonant frequency tuning is made by trimming the metal film on the disk. The TE/sub 01delta/ -mode resonant frequencies are analyzed through dielectric waveguide model application. Less than 1-percent analytical error is presented in comparison with the experimental data for a practical resonator. The frequency tuning limit by metal film trimming is about 7 percent. The unfoaded Q value of 2700 at 8.8 GHz and a 4.4-ppm/deg frequency temperature coefficient are obtained.     

High temperature dielectric stability of liquid crystal polymer at mm-wave frequencies

The temperature dependent dielectric stability and transmission line losses of liquid crystal polymer (LCP) are determined from 11-105 GHz. Across this frequency range, LCP's temperature coefficient of dielectric constant, /spl tau//sub /spl epsi/r/, has an average value of -42 ppm//spl deg/C. At 11GHz the /spl tau//sub /spl epsi/r/ is the best (-3 ppm//spl deg/C), but this value degrades slightly with increasing frequency. This /spl tau//sub /spl epsi/r/ average value compares well with the better commercially available microwave substrates. In addition, it includes information for mm-wave frequencies whereas standard values for /spl tau//sub /spl epsi/r/ are usually only given at 10 GHz or below. Transmission line losses on 3- and 5-mil LCP substrates increase by approximately 20% at 75/spl deg/C and 50% or more at 125/spl deg/C. These insertion loss increases can be used as a design guide for LCP circuits expected to be exposed to elevated operating temperatures.     

Circular TE/sub 0n/ Mode Filters for Guided Millimeter-Wave Transmission

A millimeter-wave circular TE/sub 01/ mode waveguide generates undesired circularly symmetric modes (TE/sub 02/, TE/sub 03/ modes, etc.) in bends or at discontinuities along a waveguide line. This paper describes the theory and experiment on the TE/sub 02/ and TE/sub 03/ mode filters developed for guided millimeter-wave transmission. The experimental results of two improved TE/sub 03/ mode filters show that the attenuation of the TE/sub 03/ mode is more than 16 dB for one type over the 40-70-GHz range. The TE/sub 01/-mode insertion loss of another type is about 0.2 dB over the 40-80-GHz range. The present mode filters can be applied to various high-speed guided rnillimeter-wave systems currently under development.     

A millimeter-wave bandpass waveguide filter using a width-stacked silicon bulk micromachining approach

A 30-GHz bandpass filter is realized in a novel waveguide topology, through the use of bulk micromachining of standard (low-resistivity) silicon wafers. In this new design, the width of the rectangular waveguide structure is created through the stacking of etched silicon wafer pieces. This width-stacking approach eliminates the presence of convex corners in the design, resulting in more controllable etching. Also, this design enables the simple implementation of the split-block technique, which alleviates Ohmic contact resistance issues. This latter aspect, combined with a double-sided etching strategy that enables deep cavities to be formed, leads to very high-Q silicon micromachined resonators (Q/sub 0//spl ap/4500). A three-cavity bandpass filter was fabricated and tested leading to a deembedded insertion loss of 1dB at a center frequency of 29.7GHz, with a 3-dB bandwidth of 0.654GHz (2.2%). These results validate this new micromachined waveguide approach, and demonstrates a significant improvement over other millimeter-wave micromachined waveguide filters.     

Coaxial E-Field Probe for High-Power Microwave Measurement (Short Papers)

Open-ended semirigid coaxial cable is characterized for use as a coupling element for the measurement of high-power microwaves. There are many high-power microwave experiments where a high vacuum must be maintained, and yet it is necessary to measure the power and frequency of the microwave energy in a cavity or waveguide. Semirigid coaxial cable which is left open-ended and inserted no more than fresh with the inner waveguide wall is a convenient way to couple out a known sample of the power. The cable is inserted into the waveguide in a direction parallel to the electric field. The coupling value is expressed in terms of an area multiplier which is applied to the area of the end of the center conductor. The induced charge Q on the center conductor is then determined from Q =/rarr over D· and/n·(effective area), and the coupled power is calculated from P = ( omega Q)/ sup 2//(2Z/sub 0/). For a flush mounted Z/sub 0/=50-Omega with PTFE dielectric, the area multiplier is shown to be 3.846 theoretically and 3.77 experimentally. The area multiplier is also determined for various withdrawal depths of the coax into the waveguide wall.     

Magnetically Tunable Nonreciprocal Band-Pass Filters Using Ferrimagnetic Resonators

Possibilities of a small-bandwidth, small-insertion loss, magnetically tunable band-pass filters with nonreciprocal characteristics have been studied. the unloaded Q(Q/sub u/) for a ferrimagnetic sample has been derived, considering the fundamental definition of Q for a resonator. Theoretical analysis is given for coupling due to ferrimagnetic resonance, between two RF transmission circuits when the RF magnetic fields due to the two circuits are circularly polarized or, in general, elliptically polarized. The analysis gives the open-circuit impedance parameters for the equivalent circuit representing the ferrimagnetic coupling mechanism, from which the external-loading Q's (Q/sub e1/ and Q/sub e2/) are obtained. This analysis, applied to the case of the waveguides, shows that the behavior of the Q/sub e/ vs frequency characteristic depends upon the ellipticity of the RF magnetic field, and hence, upon the location of the off-axis position of the ferrimagnetic resonator. Also, the nonreciprocity depends upon the ellipticity of the RF magnetic field--the nonreciprocal behavior being optimum when the RF magnetic field is circularly polarized. Thus, again, for the case of waveguide circuits, the off-axis position determines the reverse-coupling-vs-frequency characteristic. The measurements on the experimental filters, tunable from 8.2 to 12.4 kMc, verify the results obtained from the theory. The forward and the reverse directions of the operation of these filters can be interchanged by reversing the dc magnetic field. Power limiting with these filters is briefly described.