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Microwave and Millimeter-Wave High-Q Micromachined Resonators Microwave and Millimeter-Wave High-Q Micromachined Resonators Andrew R. Brown,1 Pierre Blondy,2 Gabriel M. Rebeiz1 1 Radiation Laboratory, Department of Electrical Engineering, University of Michigan, Ann Arbor, Michigan 48109; e-mail: [email protected] and [email protected] 2 IRCOM, University of Limoges, Limoges, France; e-mail: [email protected] Recei¨ed 29 June 1998; re¨ised 19 December 1998 ABSTRACT: Alternative techniques for integrating high-quality factor resonators using micromachining techniques have been investigated. Two methods are presented which include suspending microstrip lines on thin dielectric membranes, resulting in an effective dielectric constant of near unity, and integrating three-dimensional micromachined wave- guide cavity resonators with planar feedlines. These resonators show large improvements in quality factor over conventional techniques, and more importantly, allow for planar integra- tion in complex systems. Resonators were fabricated in suspended microstrip at 29, 37, and 62 GHz with quality factors of over 450 with very close agreement between simulated and measured results. An integrated micromachined cavity resonator was also fabricated with a TE011 resonance quality factor of 1117 at 24 GHz and a TE021 resonance quality factor of 1163 at 38 GHz. To the authors' knowledge, these are the highest quality factor planar resonators without the use of superconductive materials, and can be used in microwave and millimeter-wave low-loss ®lters and low-phase-noise oscillators. ᮊ 1999 John Wiley & Sons, Inc. Int J RF and Microwave CAE 9: 326᎐337, 1999. Keywords: millimeter wave; high-Q resonators; micromachining; packaging techniques I. INTRODUCTION Current millimeter-wave wireless front-end transceivers use a hybrid approach with a combi- Microwave and millimeter-wave communication nation of waveguide components, solid-state de- systems are expanding rapidly as they offer many vices, and dielectric resonatorsŽ. Fig. 1 . All of the advantages over conventional wireless links. They active componentsŽ. LNA, power ampli®er, mixer allow the use of very wideband radio links suit- are based on solid-state technology, and are im- able for intersatellite and personal communica- plemented using planar MMICs. However, the tions. Commercially available systems are under diplexer and other ®lters are implemented either development at 28 GHz for the local multipoint using high-Q structures such as resonant wave- distribution systemŽ. LMDSwx 1 , the PCS networks guide cavity ®lters or dielectric resonator ®lters. at 38 GHzwx 2, 3 , and also a new short-range These expensive components are needed in order telecommunication band at 60 GHz. Commercial to have a low insertion loss, high out-of-band systems demand high yield and the ability to rejection, and high channel-to-channel isolation. fabricate large volumes of systems using low-cost The theoretical insertion loss of a ®lter is given by techniques. wx4: Correspondence to: A. R. Brown cn ⌬ L Ž.dB f 8.686 Ž. 1 This work was supported by the United States Army Re- A ␻Q search Of®ce ASSERT under Contract DAAH04-95-1-0205. u ᮊ 1999 John Wiley & Sons, Inc. CCC 1096-4290r99r040326-12 326 Microwa¨e High-Q Micromachined Resonators 327 ⌬ where LAnŽ.dB is the in-band insertion loss, c where F is the noise ®gure of the active circuit is the ®lter prototype coef®cient and is a function with the positive feedback removed, k is the of the number of poles and passband ripple of the Boltzmann constant, T is the temperature, Pa¨ s is ␻ ®lter, is the ®lter fractional bandwidth, and Qu the available signal power, QL is the resonator is the unloaded quality factor of the resonator. loaded Q, f0 is the oscillation frequency, and fm Figure 2 shows the impact of the quality factor on is the frequency offset from the carrier where the the insertion loss of a 3 and an 8% ®lter. It is noise spectral power is measured. For frequencies evident that, in order to obtain high performance, near the carrier, the phase noise is a function of a resonator unloaded Q of 500 or higher should 1rQ2. Millimeter-wave oscillators are typically be used for a narrowband diplexer design. fabricated with either a waveguide cavity such as The local oscillator should also exhibit a very the case of Gunn or IMPATT diodeswx 5 or using low-phase-noise performance which is strongly a dielectric resonator as in the case of HEMT or dependent on the quality factor. The oscillator HBT deviceswx 6᎐8 . These resonators exhibit a Q phase noise, using a linear approximation, is given of 1000᎐3000 at 30᎐60 GHz, and result in excel- by: lent phase-noise performance. However, excellent performance is also achieved with a microma- 22 chined resonator with a Q of 500᎐1000. FkT 1 f0 NfŽ.s 1 q Ž.2 Micromachining has been used in the past to pn m 2 P 2Qf a¨ sLmž/ž/ implement high-Q on-chip mechanical resonators Figure 1. Typical millimeter-waveŽ. a transceiver front-end block diagram and Ž. b new-gen- eration K-band phased array for satellite communications. 328 Brown, Blondy, and Rebeiz II. DEFINITION OF QUALITY FACTOR The de®nition for the Q factor is given by: energy stored resonator Q s ␻ Ž.3 energy dissipated The equivalent circuit for a distributed resonator is taken as a parallel RLC lumped element model Ž.Fig. 3 . In order to excite the resonator, energy must be coupled into the resonator with either magnetic or electric coupling. To take into ac- count the effects of inputroutput loading, the quality factor of a structure can be broken down into different ®gures of merit, namely, the loaded QQŽ.Lu, the unloaded QQ Ž., and the external Q Ž.Qext . The loaded Q is the measured quality factor taking into account the loading effects of the resonator itself, and also the loading of the external circuit. Only the loaded Q of a resonator Figure 2. Theoretical insertion loss for 3 and 8% can actually be measured, and the unloaded Q ®lters. The estimated type of resonator is based on data and the external Q of a resonator have to be from 30᎐60 GHzwx 10 . extrapolated. There are two main resonator con®gurations typically encountered in microwave and millime- ter-wave circuits, namely, the bandpass and the bandstop con®gurations. The bandpass con®gu- rationŽ. Fig. 4a uses the resonator as a single- with an unloaded quality factor of 20,000 at 70 wx resonator bandpass ®lter re¯ecting power at fre- MHz on a silicon substrate 9 , and it is predicted quencies away from resonance and passing power that mechanical resonators may reach 1 GHz in wx at frequencies at resonance. The bandstop con- the future 10 . However, the mechanical res- ®gurationŽ. Fig. 4b allows power to pass by the onator approach is process intensive, requires the resonator away from resonance, and then absorbs resonators to be vacuum sealed, and only to oper- power from the line at resonance, increasing the ate with reasonable Qs at low frequencies. This effective impedance and causing more re¯ection. paper discusses alternative methods for obtaining For a resonator in a bandpassŽ. bandstop con- planar microwave and millimeter-wave high-Q el- ®guration with a resistive matched source and ements by using micromachining techniques to load impedance, the loaded quality factor can be alter the geometry of a silicon substrate. The obtained from measuring the 3 dB bandwidth of paper presents two methods: the ®rst technique is the SS21Ž. 11 as shown below: based on thin dielectricŽ. membrane technology, and the second technique is based on three- f0 Q s Ž.4 dimensional etching in a cavity formation of a L ⌬ f silicon wafer. The micromachined resonators are 3dB fully compatible with MMIC technology, and most where f is the resonant frequency and ⌬ f is importantly, do not require low-loss millimeter- 03dB wave transitions which are necessary in waveguide technology. Also, micromachined resonators are lithographically de®ned, and therefore do not re- quire exact placement and manual tuning such as in dielectric resonator designs. It is expected that micromachining techniques will be very use- ful in future millimeter-wave communication and Figure 3. Equivalent parallel RLC model for dis- phased-array systems. tributed resonator. Microwa¨e High-Q Micromachined Resonators 329 onator, the quality factor can be found by: ␲ Q s Ž.8 ␭␣ where ␭ is the guided wavelength and ␣ is the attenuation in nepers per meter, including atten- uation by radiation, substrate loss, and ohmic loss. Distributed resonators using microstrip structures on conventional substrates have been used extensively for applications at X-band and below with reasonable values of Q Ž100᎐150 on quartzrTe¯on. However, with increasing fre- quency, thinner substrates must be used to re- duce radiation loss in substrate modes. This re- Figure 4. Typical resonator con®gurations for mag- sults in narrow line dimensions for a given netic coupling inŽ. a bandpass and Ž. b bandstop con- impedance, which greatly increases the ohmic loss, ®guration. and drastically reduces the resonator Q. Micro- machining techniques are used to produce a mi- cropackaged, air dielectric line with wide trans- the 3 dB bandwidth of the SS21Ž. 11 response. The external Q can then be obtained from the loaded verse dimensions resulting in high-Q resonators Q and the insertion loss of the resonator at the at millimeter-wave frequencies. resonant frequency by solving: Membrane-supported microstrip structures are formed by removing the silicon substrate and ␮ QQLLsuspending a microstrip line on a thinŽ. 1.4 m Q s or Q s Ž.5 extŽ. ext Ž. dielectric membrane. A ground plane is formed Sf21 0ž/ Sf 11 0 by another micromachined substrate, and is at- w x tached to the top of the circuit.
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