Grid oscillators Citation Popovic, Zoya Basta (1990) Grid oscillators. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/721n-xr11. https://resolver.caltech.edu/CaltechETD:etd-03112007-121926 Abstract In the microwave and millimeter-wave frequency range, solid-state oscillators have limited output power levels. The alternative high-power sources are tubes, which are expensive, bulky, have a limited lifetime and require high-voltage power supplies. Combining a large number of low-power solid-state negative resistance devices becomes attractive. In this work a coherent oscillator that can combine thousands of solid-state devices is presented. The feasibility of a reliable high-power, monolithically integrated microwave and millimeter-wave source is demonstrated. In this approach, the active devices load a two-dimensional metal grid that radiates, and the power combining is done in free-space. Several MESFET grid oscillator designs are presented in this thesis, ranging from a 5 by 5 to a 10 by 10 grid in size. The 100-MESFET hybrid grid oscillator is a planar structure suitable for wafer-scale monolithic integration. This grid locks at 5 GHz, with an ERP of 24 Watts and a conversion efficiency of 20%. An equivalent embedding circuit for the devices in the grid predicts the oscillation frequency. The devices in the grid self-lock with no external locking signal present, but the grid can also be externally injection-locked. Measurements and analysis are presented for the injection-locked planar grid oscillator. Item Type: Thesis (Dissertation (Ph.D.)) Degree Grantor: California Institute of Technology Division: Engineering and Applied Science Major Option: Electrical Engineering Thesis Availability: Public (worldwide access) Research Advisor(s): Rutledge, David B. Thesis Committee: Unknown, Unknown Defense Date: 2 May 1990 Record Number: CaltechETD:etd-03112007-121926 Persistent URL: https://resolver.caltech.edu/CaltechETD:etd-03112007-121926 DOI: 10.7907/721n-xr11 Default Usage Policy: No commercial reproduction, distribution, display or performance rights in this work are provided. ID Code: 925 Collection: CaltechTHESIS Deposited By: Imported from ETD-db Deposited On: 12 Mar 2007 Last Modified: 16 Apr 2021 23:05 Thesis Files Preview PDF (Popovic_zb_1990.pdf) - Final Version See Usage Policy. 5MB Repository Staff Only: item control page

Grid Oscillators Thesis by Zoya Basta PopoviC In Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy California Institute of Technology Pasadena, California 1990 (Submitted May 2, 1990) To my family with love Acknowledgements I wish to thank my advisor David Rutledge for his enthusiasm which attracted me to microwaves and electromagnetics. Thanks for the knowledge and ideas he shared with us, for teaching me how to approach the world of research, and for the times we spent talking as friends. I consider myself privileged to be one of his students. I also wish to thank my fellow graduate students Bobby Weikle, Moonil Kim, Karen Lee, Scott Wedge, Yong Guo, Jon Hacker, as well as Dr. Phil Stimpson, Dr. Wyman Williams, Professor Rick Compton, Dale Yee and Kent Potter for many useful conversations and the good times we spent together. Many thanks to my friends Svetlana Tatik, Suzana and Tim Brown, Dana StevanoviC, Gabriel Rebeiz, Craig Leff, Dayalan Kasilingam and David Schweizer for being there when I needed them, and for making my years in graduate school more pleasant. This work would not have been possible without the love and advice of my parents, who showed me that hard work can be fun and rewarding. I am also dedicating this work to my grandmothers and to the memory of my grandfathers, who encouraged me to leave my country to continue my education and gave me much valuable and wise advice. Thanks to my dear sisters for all the love and good humor, with the hope that their work will be as exciting and as rewarding. Affectionately, I thank my husband Srdjan Basta for his love and patience. Grid Oscillators Abstract In the microwave and millimeter-wave frequency range, solid-state oscillators have limited output power levels. The alternative high-power sources are tubes, which are expensive, bulky, have a limited lifetime and require high-voltage power supplies. Combining a large number of low-power solid-state negative resistance devices becomes attractive. In this work a coherent oscillator that can combine thousands of solid-state devices is presented. The feasibility of a reliable high-power, monolithically integrated microwave and millimeter-wave source is demonstrated. In this approach, the active devices load a two-dimensional metal grid that radiates, and the power combining is done in free-space. Several MESFET grid oscillator designs are presented in this thesis, ranging from a 5 by 5 to a 10 by 10 grid in size. The 100-MESFET hybrid grid oscillator is a planar struc- ture suitable for wafer-scale monolithic integration. This grid locks at 5 GHz, with an ERP of 24 Watts and a conversion efficiency of 20%. An equivalent embedding circuit for the devices in the grid predicts the oscillation frequency. The devices in the grid self-lock with no external locking signal present, but the grid can also be externally injection-locked. Measurements and analysis are presented for the injection-locked planar grid oscillator. v Contents Chapter 1. Introduction 1.1 Microwave and Millimeter-wave Sources 1.2 Power Combining 1.3 Organization of the Thesis References Chapter 2. A 25-MESFET hybrid Grid Oscillator 2.1 The 5 by 5 MESFET Grid Oscillator 2.2 Calculating the Grid Far-Field pat tern References Chapter 3. The Bar-Grid Oscillator -- Theory 3.1 Unit Waveguide 3.2 Equivalent Circuit for the Bar-Grid Oscillator References Chapter 4. The Bar-Grid Oscillator -- Measurements 4.1 Locking and Reliability 4.2 Power and Pattern Measurements 4.2 Modulation References Chapter 5. The Planar Grid Oscillator 5.1 Equivalent Circuit 5.2 Mirror Tuning References Chapter 6. Injection Locking of the Planar Grid Oscillator 6.1 Inject ion-Locking Theory 6.2 The Grid Oscillator Receiving and Transmitting Pattern References Chapter 7. Conclusion and Suggestions for Future Work 7.1 Scaling 7.2 The Grid as a Receiver 7.3 System Integration References Chapter 1 Introduction The frequency range from 30 GHz to 300 GHz is usually called the millimeterwave region. These frequencies have applications in radio-astronomy, com- munication, radar, radiometry, remote sensing, plasma diagnostics and spectroscopy [I]. The effects of the atmospllere on wave propagation are important for most of these applications. The earth's atmosphere absorption spectrum has minima, or windows, in the millimeter-wave region around 35 GHz, 93 GHz, 130 GHz and 225 GHz. Millimeter waves propagate through dust, fog, smoke and clouds, making them attractive for radar used in adverse environmental conditions. These frequencies also pass through interstellar gases and dust. This is important for radio-astronomy [2], since many phenomena, such as star birth, occur deep within regions of space through which optical telescopes cannot penetrate. Recently there has been a lot of interest in the earth's ozone layer, and most of the chemicals in the ozone cycle have absorption lines in the xnillimeter and submillimeter-wave range. The high millimeter-wave frequencies haw some advantages over microwave frequencies. For a given beamwidth and gain, millimeter-wave antennas are very small. They also offer wide bandwidths for communication applications. 1.1 Microwave and Millimeter-wave Sources One of the key components in every -&llimeter-wave system is the oscillator, whether it is the high-power source for a radar transmitter, or a low-power local-oscillator for a radio-astronomy receiver. Two types of sources have been used so far : tubes (TWT, BWO, klystron, magnetron, carcinotron, gyrotron) and solid-state devices. The latter can be two terminal devices, such as the IMPATT and Gunn diodes, or three terminal transistors, such as the MESFET (Metal Semiconductor Field Effect Transistor), HEMT (High Electron Mobility Transistor), or HBT (Heterojunction Bipolar Transistor). Tubes are high-power sources and have higher efficiencies than the semiconductor devices. For example, gyrotrons have achieved hundreds of kilowatts CW with efficiencies close to 50%. The output powers of individual solid-state devices and tubes versus frequency Fig. 1. Comparison of output power levels of solid-state and tube sources in the microwave and millimeter-wave region. are given in Fig. 1. Solid-state technology is continually improving. Recent efforts in HEMT devices [3] have resulted in a 23% power-added efficiency at 93 GHz with an output power of 18mW. HBT's [4] have promising high-power applications with good yields and power-added efficiencies of 40% at 12 GHz with output powers of 10 W. Quantum-well devices have pushed the frequency limit to 420 GHz [5],with an output power of 200nW. The individual output power levels from solid-state devices are still low compared to tubes a t the millimeterwave end. However, their advantages give motivation for finding a way to get enough power from them to replace tubes. The most obvious applications are any space or airborne systems, since tubes require large DC power supplies and have a short lifetime, typically on the order of several hundred hours. In addition, solid-state devices are relatively inexpensive with the existing integrated-circuit 1.2 Power Combining A way of obtaining high power from semiconductor devices is to combine the outputs of several devices coherently. Most power-combining schemes so far [6],[7] involve placing a few (up to 12) devices in a waveguide cavity (Fig. 2a) and locking to an external injection signal. Pulsed IMPATT diodes have given 20, 40 and 48 Watts peak power from 2,4 and 6 rectangular waveguide modules respectively, where each device could deliver 10 to 13W [S]. Eight CW IMPATT's were combined in a cylindrical cavity with a dominant TMolo mode and an output power of 10 W at 35 GHz. Up to 4 InP Gunn diodes were combined 191 at 90 GHz, with combining efficiencies reaching 106%. Waveguide cavity power combiners become impractical at higher frequencies because of the losses in the metal walls and the small guide dimensions. Some free-space combining work has been done with two InP Gunn diodes in a spherical mirror resonator [lo] (Fig. 2b), as well as with three IhIPATT's feeding patch antennas [ll],but in all these examples each device had its own biasing and tuning circuit. This is not practical if a large number of devices, for example a thousand, is to be combined. This work describes a way to quasi-optically combine the output powers of a large number of semiconductor oscillators by loading a two-dimensional metal grid with active devices. The grid structure is convenient for both two- or threeterminal device. The experimental grids demonstrated in this work are hybrid MESFET circuits combining up to one hundred devices between 3 and 10 GHz. All the devices share one biasing circuit. They are spatially coupled through a Fabry-Perot cavity. Fig. 3 shows the dependence of the output power of some solid-state devices versus frequency [13], and in the millimeter-wave range it is a dependence. This means that in order to flatten out this curve a t higher frequencies, a source y WAVEGU(0E CAVITY OUTPUT :lfC 103 Fig. 2 (a) IMPATT diode X-bad waveguide combiner [6]. (b) Quasi-optical power combining of two I n P Gunn-diodes a t 60 GHz [9]. for which the power would grow as the square of the frequency is needed. Any two-dimensional structure is a good candidate, and this was one of the motivations for using a planar grid structure. IMPATT diodes Gunn diodes a Fig. 3. Dependence of output power versus frequency for IMPATT and Gunn diodes 1121. Fig. 4. Schematic of a grid loaded with negative resistance devices. The grid oscillator can be made monolithically on a single wafer and scaled to as high a frequency as the one at which the devices can oscillate at. Possible designs for monolithic grids at 30 to 90 GHz will be presented in the last chapter. The grids are planar, light weight, small volume, easily biased, and offer a large variety of applications. A schematic of a grid oscillator is shown in Fig. 4. If the grid is several free-space wavelengths across, and if the devices are a fraction of a wavelength apart, one can look at this grid as a continuous, uniform, active sheet. If the devices in the grid locked in phase, the radiated wave is a plane wave, which allows simple transmission-line analysis. 1.3 Organization of t h e Thesis The thesis describes several grid oscillators that were tested and analyzed. Parts of this work have been published in the articles [15], [16], and [17]. The first working hybrid 25-MESFET grid is described in Chapter 2. This grid proved that the grid oscillator concept works. The 36-MESFET bar grid is presented in Chapters 3 and 4. The theoretical analysis and simulations of this oscillator are based on the symmetry of an infinite loaded grid. The analysis predicts the oscillation frequency and gives an equivalent transmission-line circuit for the transistors in the grid, which makes it possible to design the oscillator. The measurements on the bar-grid oscillator are presented in Chapter 4. One of the most important ideas behind the grid oscillators is the fact that they can potentially be monolithically integrated on a single wafer. The grids described in Chapters 2-4 were not planar in the real sense. In Chapter 5 is presented a planar version of the oscillator with 100 MESFET's at 5 GHz. The grid oscillators lock without an external signal present. Holvever, for some applications it would be advantageous to lock the high-power grid to a low-power esternal oscillator. The injection-locking behaviour of the planar grid oscillator is described in Chapter 6. A general theory for injection-locked oscillators is also presented, and some measurcme~~ts made to confirm the results. In the last chapter are given some possible grid designs for wafer-scale integrated grids, which assume currently existing devices and available technology. The grid oscillator is an antenna as well as a source, and several potential applications that will be subjects of future are described. References [I] J.C. Wiltse, "Introduction and Overview of Millimeter Waves," Infrared and Millimeter Waves, Vo1.4, Academic Press Inc., 1981, pp. 1-18. [2] J. D. Icraus, Radio Astronomy, Cygnus-Quasar Books, 2nd Edition. [3] M. Kao, P. M. Smith, P. Ho, P. Chao, Ii. H. G. Duh, A. A. Jabra, J. M. Ballingall, "Very High Power-Added Efficiency and Low-Noise 0.15-pm GateLength Pseudomorphic HEMT's ," IEEE Electron Device Letters, Vol. 10, NO. 12, 580-582, December 1989. [4] P. M. Asbeck, M. F. Chang, I<. C. Wang, D. L. Miller, G. J . Sullivan, N. H. Sheng, E. Sovero, J. A. Higgins, "Heterojunction Bipolar Transistors for Microwave and Millimeter-Wave Integrated Circuits," IEEE Trans. on Microwave Theory and Techniques, Val. MTT-35, 1463-1470, December 1987. [5] E. R. Brown, T . C. L. G. Sollner, C. D. Parker, W. D. Goodhue, C. L. Chen, "Oscillations up to 420 GHz in GaAsIAlAs Resonant Tunneling Diodes," Applied Plzysics Letters, Vol. 55, Aro 17, 1777-1779, October 1989. (61 I<. J. Russel, "Microwave Power Combining Techniques," IEEE Transactions on Alicro~vaveTheory and Ted~niq ues, Vol. MTT-27, 472-478, May 1979. ['i]I<. Chang, C. Sun, "Millimeter-~~Tave Power Combining Techniques," IEEE Transactions on Micro~r-aveTheory and Techniques, Vol. MTT-31, 91-107, February 1983. [8] I<. Chang, R. L. Ebert, "W-Band Power Combiner Design ," IEEE ?kansactions of Microwave Theory and Tedzniques, Vol. MTT-28, 295, April 1980. (91 J. J. Sowers, 3. D. Crowley, F. B. F a d , "CW InP Gunn Diode Power Combining at 90 GHz," IEEE A4TT Symposium Digest, 503, Dallas, 1982. [lo] L. Iandinger, V. Nalbandian, "Millimeter-Wave Power Combiner Using Quasi- 0p t ical Techniques," IEEE Transactions on A/licrorvave Theory and Tedmiques, Vol. MTT-34, 273-279, February 1983. [Ill R. Dinger, D. White, D. Bowling, "A 10-GHz Space Power Combiner with Parasitic Injection Locking," Naval Weapons Center Technical Publication 6704, March 1986. [13]H. J. I<uno, "IMPATT Devices for Generation of Millimeter Waves," Infrared and Millimeter Waves, Vol. 1, 1979, pp. 96. [14] N. B. Earner, "Sources of Millimeter Wave Radiation: Travelling-Wave Tube and Solid-State Sources,'' Infrared and Millimeter IVaves, Vo1.4, Academic Press Inc., 1981, pp. 151-197. [I51 2. B. PopoviC, M. Kim, D. B. Rutledge, "Grid Oscillators," International Journal of Infrared and Millimeter Waves, Il'ol. 9, ATo. 7, July 1988, pp. 647654. [16] 2. B. PopoviC, R. M. Weikle, M. Kim, I<. -4. Potter, D. B. Rutledge, "BarGrid Oscillators," IEEE Trans. on Microlvave Tl2eo1-y and Techniques, IfoI. MTT-38, No. 3, h4arch 1990, pp. 225-230. [17] 2. B. PopoviC, R. h4. Weikle 11, M. Kim, D. B. Rutledge, "Planar Grid Oscillators," submitted for publication to the B E Transactions on Microrvave Theory and Tedzniques, April 1990. Chapter 2 A 25-MESFET Hybrid Grid Oscillator The grid oscillator configuration [I] is shown in Fig. 2.1. -4 metal grid is loaded with solid-state negative resistance devices. The grid can be on a dielectric substrate. It is placed bet\veen a metal mirror and another dielectric slab, which acts as a partially transparent reflector. The mirror and the dielectric slab form a Fabry-Perot cavity. The devices lock to a mode of the cavity. Tkansparent Mirror Planar Grid Fig. 2.1. The grid oscillator configuration. Reflector Mirror Substrate (a) (b) Fig. 2.2. (a) 5 by 5 MESFET grid, and the bar-grid oscillator (b). Several different hybrid grid oscillators were made, measured and analyzed. The first working MESFET oscillator was a 5 by 5 array at 10 GHz 121, shown schematically in Fig. 2.2a. The grid is etched on a quarter dielectric wavelength thick grounded microstrip Duroid substrate. The ground plane of the substrate acts as the mirror, and another Duroid slab, with copper etched away from both sides, is placed in front of the grid as the partially transparent reflector. The mirror position in this case is fixed, so that there can be no mirror-tuning. The second MESFET grid oscillator, shown in Fig. 2.2b, eliminated the dielectric substrate. This grid will from now on be called the bar-grid oscillator, since 36 devices are soldered directly onto a stack of metal bars. The bars provide escellent heat-sinliing and DC bias, and they act as a partially transparent reflector as well. This grid oscillates around 3 GHz. It does not require the dielectric slab shown in Fig. 2.2b to lock. However, two slabs were used in the measurements for impedance-matching. In this oscillator the mirror can be translated for mechanical tuning, and electrical tuning can be obtained by modulating the gate or the drain bias. The third hybrid grid oscillator was a planar 100-h4ESFET oscillator at 5GH2,as shown in Fig. 2. 1. This grid is made on a dielectric substrate, and the mirror position can be changed. The grid itself is the partially transparent reflector. This grid demonstrates the possibility of wafer-scale, monolithically integrated, high-power grid oscillators. 2.1 The 5 by 5 MESFET grid oscillator The 5 by 5 MESFET grid is shown in Fig. 2.3. The devices are Fujitsu MESFET's (FSCll), made for satellite receivers at 4 GHz. These devices usually give about 20 mW in single-transistor microstrip oscillators. The substrate is a microstrip substrate Duroid, with a dielectric constant 6, = 10.5, and 2.35mm thick, which is a quarter of a dielectric wavelength at 10 GHz. Fig. 2.4 shows the orientation of the transistor leads in the grid. The vertical lines connected to the transistor drain and gate terminals support the flow of RF currents, and the radiated electric field vector is parallel to them. The horizontal lines are used for DC bias, and they should not affect the R F fields. Th'1s was confirmed by cross-polarization measurements. The grid dimensions have been chosen by experiment, and the period of the array is 13 mm. The gate lead is not connected to a DC bias. Its length (5mm) is chosen so that the RF embedding impedance for the gate is inductive. The horizontal drain tabs, which are 3.5 mm Fig. 2.3. Photograph of the 25-transistor oscillator grid at 9.7 GHz. I - Bias lines P P P P Source Fig. 2.4. The 5 by 5 MESFET grid oscillator layout. Frequency offset, KHz Fig. 2.5. Spectrum of locked 25-MESFET grid SUBSTRATE - REFLECTOR SPACING, mm Fig. 2.6. The radiated power and oscillation frequency vs. substrate-reflector spacing. long, are chosen empirically, and they help in matching the impedance of the device, since the pourer drops when they are removed. When biased at a drain voltage of 4 V, the grid oscillates at 9.7 GHz. The spectrum is shown in Fig. 2.5. Varying the spacing between the substrate and the reflector shifts the frequency over a 1% range, and produces large changes in the power, as shown in Fig. 2.6. The largest measured effective radiated power relative to an isotropic source (ERP) is 3'i\JT a t a spacing of 4.8mm. Fig. 2.7 shows the measured far-field pat tern where the peak ERP was 20.7 watts. Instabilities caused by reflections prevented pattern measurements a t the higher power levels. From the measured pattern, we can deduce the total radiated power, which is 464mW. This is roughly 25 times the power that we typically get from a single transistor oscillator. The DC to RF conversion efficiency is 14.5%. Fig. 2.7. Two-dimensional far-field pattern of the transistor grid. The vertical scale is linear i n power, the peak ER.P is 20.7W, and the directivity is 16.4dB. The angles y and 6-are indicated on the measurement setup shown i n the upper right-hand corner of the figure. The Gplane pattern is a scan of -y with 6 = 0, and the H-pane pattern is a scan of 6: with 7 = 0. 2.2 Calculatillg the Grid Far-field Pattern If we assume that the grid is infinite and that the devices are locked in phase, we can treat each transistor as a current source feeding a short dipole antenna. The dipole is on top of an infinite grounded dielectric, and above it is an air gap and a dielectric superstrate. The far field of such a dipole can be found by reciprocity [3,4]. A test dipole in the far-field will produce a field at the dielectric substrate surface. If the test dipole moves along the Eplane of the grid, as shown in Fig. 2.8a7 the incident field on the grid surface will be the same as the grid Eplane pattern, by reciprocity. Since the test dipole is in the far field, plane-wave analysis can be used. The equivalent transmission-line circuit is sho\vn in Fig. 2.Sb. The pattern is proportional to the square of the transmission coefficient at the plane of the grid: where Yois the free-space admittance. The T M incident wave gives the Eplane, and the TE incident wave gives the E-plane for a single dipole in the grid. The total grid pattern is found by assuming an array factor for which all transistors are equal current sources. The theoretical and measured patterns are shown in Fig. 2.9. The measured E-plane in Fig. 2.9a is shifted about 7 degrees, and the reason is a tilt in the dielectric slab with respect to the grid, which introduces a linear phase shift across the plane of the grid. 2, D i- YD v - I, YO 1, D * YD 1 Mirror Dielectric Air Dielectric Air Fig. 2.8. (a) The pattern of the grid is found by reciprocity. The fields of a test dipole are found as it is moved along the E and N planes. (b) Equivalent transmission-line circuit for calculating t h e far-field pattern of the grid. The TM polarization gives the E-plane, and the T M polarization the H-plane. The corresponding impedances in each of the layers are YTM = Yofi,/cosO, YTE = YoJSrcos0, and the electrical length of each of the layers is le = JT,d c o d . ANGLE (b) Fig. 2.9. (a) E p l a n e , (b) 13-plane of transistor grid, theory and experiment. T h e scale is linear in power. References [I] 2. B. PopoviC, D. B. Rutledge, "~iode-r rid Oscillators," 1988 IEEE Antennas and Propagation Symposium, Syracuse, New York, June 1988. [2] 2. B. PopoviC, M. Kim, D. B. Rutledge, "Grid Oscillators," International Journal of Infrared and Millimeter Waves, Vol. 9, No. 7, 647-654, July 1988. [3] D. B. Rutledge, D. P. Neikerk, D.P. ICasilingam, "Integrated Circuit Antennas," Infrared and Millimeter-Waves, Vol. 10, 1-87, 1983. [4] H. Y. Yang, N. G. Alex6poulos, "Gain Enhancement Methods for Printed Circuit Antennas Through Multiple Superstrates", IEEE Transactions on Antennas and Propagation, Vol. 35, No. 7, July 1987. Chapter 3 T h e Bar-Grid Oscillator - T h e o r y The side view of the bar-grid oscillator is shown in Fig. 3.1. It is a G by 6 grid. The devices (Fujitsu FSC11) are soldered directly onto a stack of metal bars. The bars provide excellent heat-sinking and bias connections. .Adjacent rows of the grid share gate and drain bias bars to minimize the number of bias lines, as shown in Fig. 3.2. The grid is 0.6 Xo across, and the period is 10 mm (Xo/lO)The 5 by 5 grid described in Chapter 2 demonstrated the locking and the pattern mas predicted. However, it is very hard to find the impedances presented at the device terminals in the grid. The dielectric is thick, and the source leads pass through it, so that the devices couple strongly through the substrate. The substrate modes have been calculated for two dipoles and slots [I],but the calculations ~vouldbe considerably more complicated for 25 antennas. The goal \vas to make a grid oscillator structure for wliicll the impedances presented to the devices could be calculated, and optimized for high-power output. The first step was to make a structure where all the currents were in one plane. The dielectric substrate mas left out for heat-sinking purposes. Fig. 3.1. Side view of the MESFET bar-grid oscillator. Fig. 3.2. Boundary conditions o n the symmetry lines define the unit cell. T h e solid lines on t o p and bottom represent electric walls, and the dashed lines o n the sides magnetic walls. Adjacent rows share drain and gate biases. 3.1 Unit Waveguide The goal of the analysis presented here is to find the reflection coefficient of an infinite grid for a plane wave at normal incidence. Strictly speaking, this analysis should be accurate only for grids that are much larger than a free-space wavelength. The symmetry of the grid imposes boundary conditions, which define a unit cell [2], shown in Fig. 3.2. This reduces the problem of analyzing the grid to that of analyzing an equivalent waveguide. The equivalent waveguide has electric walls (tangential electric field is zero) on the top and bottom, magnetic walls (tangential magnetic field is zero) on the sides, and extends in the +z and -z directions, with the transistors in the z = 0 plane. In order to model the behavior of the transistors in the grid, the impedances presented at the device terminals need to be found. The propagating mode has a real wave impedance and can be modeled with a TEM transmission line. The reactive impedances arise from the coupling between the currents in the leads and the evanescent modes. The method used to find these mode impedances is dual to the EMF analysis in the paper by Eisenhart and Icahn [3] for a post in a rectangular waveguide. Our problem is different, since there are two waveguides in the unit cell as shown in Fig. 3.3 (side view) and Fig. 3.4 (front view). This introduces an additional mutual capacitance and inductance, which can be found by considering the odd and even combinations of the currents and voltages, shown in Fig. 3.3. For example, when both the drain and the gate current are flo\ving into the transistor (Fig. 3.4a), the tangential magnetic fields cancel at the symmetry plane in the middle of the source bar, so we can place a magnetic wall (Fig. 3.4b). The currents and the fields are expanded in terms of the waveguide modes. Since the transistor leads are short compared to a wavelength, the currents are assumed to be uniform in the x and y directions. The total inductance for this case is: Drain waveguide llectric wall Vd? 1 Id I magnetic wall Fig. 3.3. O d d a n d even current a n d voltage modes reduce t h e two-waveguide unit cell t o a single step in a waveguide. Fig. 3.4. T h e unit cell consists of two waveguides: one excited by the drain current and t h e other by t h e gate. Odd and even combinations o f the currents reduce the unit cell (a) t o (b) and (c), where the electric walls are represented with solid lines, and the magnetic walls with dashed ones. If one of the currents changes direction, an electric wall can be placed a t the symmetry plane (Fig. 3 . 4 ~ ) .In this case, the total inductance is given by: 00 X" = Fa u m=l )sinc , 2( m n w M -- nnc (i + i)Ymo+ % C Ymnsinc (-g-) 2 The inductive self-reactance of each lead is the average of the electric wall and magnetic wall reactances, and the mutual inductive reactance is half of the difference of the two: In the formulae above, a, b, c and w are the dimensions in the unit cell from Fig. 3.2, and Y, is the mn-th mode admittance given by [4]: In a similar fashion, the capacitive self and mutual susceptances are found. These are capacitive reactances that correspond to a step in a rectangular wal-eguide [4]. They are given by n a B, = b odd 00 nnc a C yo, sincZ(x) - - C yo, sincZ 2b (7) n=l n odd n=z n even 3.2 Equivalent Circuit for the Bar-Grid Oscillator The equivalent circuit for the transistors in the grid is shown in Fig. 3.5. The center-tap transformer describes the coupling into free space. The center tap is the common source bar. The effect of the mirror from Fig. 3.1 is represented as a shunt reactance. The parameters at the 3GHz operating frequency, with a = lOmm, b = 5mm, c = 3mm, and w = 0.75mm are: ZTEM = 18852, BTEM = 45O, Xs = 3 0 n , X, = 0.25R, Bs= 1.33mS, B, = -0.57mS. The simulation of the circuit was done with a microwave CAD program called Puff, developed at Caltech [5]. The grid is simulated as the one-port from FIg. 3.5 looking into a matched load, as shown in Fig. 3.6a. In this case, the oscillation condition is: = O), the grid reflection coefficient This means that for a matched load (srOad becomes infinite. As the transistors are saturating, Sprid loops in the clockwise direction, trying to reach the point at infinity. Since the Smith chart is a bilinear transformation, this can happen if sgrid loops in the counterclockwise direction. Fig. 3.5. Equivalent transmission-line circuit for transistors in t h e grid. (b) Fig. 3.6. (a) T h e oscillator is simulated as a one-port looking into a matched load. (b) Simulation of t h e transmission-line equivalent circuit. T h e dashed line shows t h e circuit behavior when t h e transistors a r e not saturated. T h e solid line shows t h e saturated behavior with a counterclockwise loop. So, an instability is manifested as a counterclockwise loop on the Smith chart, and the oscillation frequency occurs where the magnitude of the reflection coefficient is the largest. The simulation predicts an oscillation frequency of 3 GHz, which agrees with experiment. Fig. 3.6b shows the grid reflection coefficient on a Smith chart with a radius of 4 (12 dB). To illustrate this behavior, also plotted on the same Smith-chart is the reflection coefficient with the small-signal transistor s-parameters. Saturation in oscillation is simulated by reducing the transistor s z l parameter by 3 dB, which shows the counterclockwise loop. References [I] R. L. Rogers, D. P. Neikerk,"Use of- roadside Twin Element Antennas to Increase Efficiency on Electrically Thick Dielectric Substrates," h t ernationd Journal of Infrared and Millimeter Waves, Vol. 9, No 11, 949-971, November 1988. [2] D. B. Rutledge, S. E. Schwarz, "Planar Multimode Detector Arrays for Infrared and Millimeter-Wave Applications," IEEE Journal of Quantum Electronics, Vol. QE-17, No.3, 407414, March 1981. (31 R. L. Eisenhart, P. J. Icahn, "Theoretical and Experimental Analysis of a Waveguide Mounting Structure," IEEE Trans. on Microwave Theory and Techniques, Vol. MTT-19, No. 8, August 1971, pp. 706-719. [4] R. F. Harrington, "Time-Harmonic Electromagnetic Fields," McGrarv Hill, 1961, pp. 171-1TG. [5] R. C. Compton, D. B. Rutledge, "Puff- Computer Aided Design for Microwave Integrated Circuits," program manual, pp. 26, 1987. Available from the authors. Chapter 4 T h e Bar-Grid Oscillator - M e a s u r e i ~ ~ e n t s 4.1 Locking a n d Reliability The photograph of the 36-MESFET bar-grid oscillator [I]is shown in Fig. 4.1. This grid locks at around 3 GHz, and the measured spectrum is shown in Fig. 4.2. It is stable to within 2 MHz during 24 hours of CW operation. It is not sensitive to vibrations, and this \vas verified when the antenna pattern of the grid was measured by rotating it in a mount with stepper motors. The grid has an interesting locking sequence that is illustrated in Fig. 4.3. These spectra were Fig. 4.1. Photograph of the 36-MESFET bar-grid oscillator Frequency 3.084G Hz 1 MHz Fig. 4.2. Spectrum of a locked 36-MESFET grid oscillator. recorded as the gate bias was varied over a range of 1V. Qualitative probing shows that first the devices in individual rows lock, and then adjacent rows lock together. A similar behal~ioris observed when the mirror position is varied. The effect of device failures was tested by removing devices indicated in Fig. 4.4a. Fig. 4.4b shows the received power after removing devices labeled according to their position in the grid. The oscillation mode was preserved even when up to 6 out of 36 devices were removed, but the power dropped considerably. The reduction in power should be a much smaller effect when the grid size is increased. 1 I 1 1 1 1 1 1 I - - - - M - - m . k $0 - - 11,- a &-j" ILL%: > - -c= .A -4J 2 "'% - - - - I 1 I Frequency I t 1 I 3536 GHZ 1 t I 1 I H 10 M H ~ Fig. 4.3. Locking sequence of the oscillator as the gate bias varies. I Removed devices I AP (dB) I (b) Fig. 4.4. Grid schematic (a) with removed devices indicated. T h e table ( b ) shows t h e degradation of power as devices were taken o u t of t h e grid. T h e first four rows a r e for devices removed o n e a t a time, a n d in the last three they are taken o u t consecutively. 4.2 Power and Pattern Measurements The bar-grid requires a mirror to lock. When the mirror is very close to the transistors - only 3mm away - the grid operates in a high-po~vermode, which is very stable. The power and pattern measurements were made with two dielectric slabs placed in front for impedance-matching. The dielectric constant of the slabs is 12, they are 2mm thick, and they are placed 20 and 35 mm in front of the grid. Fig. 4.5. Far-field radiation pattern of the bar-grid oscillator. The axes are given in terms of spherical coordinates by BE = Osin4 and OH = Ocosq5. The vertical scale is linear in power. The far-field pattern of the grid was measured in an anechoic chamber. The mount with the grid fixed to it was rotated with stepper motors controlled by a personal computer. A power meter and a wide-band horn with a 9 -dB gain were used to measure the power in the far field (1.5 m away). The measured ERP is 3.0 W. The input DC power is 1.0 W, and the calculated radiated power is 0.22 W. This gives a DC to RF efficiency of 22%, and an isotropic conversion gain of 4.8 dB. The isotropic conversion gain is a concept introduced by Stephan and Itoh [2] and is the product of the efficiency and the directivity. The measured radiation pattern is shown in Fig. 4.5, and Fig. 4.6 shows the E and H plane patterns (Fig. 4.6a) and the co-polar and cross-polarized patterns (Fig. 4.6b) in the 45" plane. In this mode of operation, the frequency of the grid can be tuned over 300 MHz by translating the mirror (10% tuning bandwidth). Angle, degrees Angle, degrees Fig. 4.6. The E and K plane patterns (a) of the bar-grid oscillator, and the 45O plane co- polar and cross- polarized pat terns (b). 4.3 Modulation Another mode of operation at a lower drain current and larger mirror spacing gives lower pou7er,but allows electrical modulation through the bias lines. The gate voltage modulates the frequency over 300 MHz (250 MHz/V). The drain voltage has more effect on the amplitude, so there is a possibility for AM or FM. Fig. 4.7 shows a measured FM spectrum, with a modulation frequency of 5 MHz and a modulation index fi of 2. The FM spectrum is given by [3]: The calculated Bessel coefficie~~ts are indicated in Fig. 4.7, and they agree \\yell with the experiment. Frequency Fig. 4.7. Measured bar-grid oscillator FM spectrum. The scale is linear .in voltage and the numbers at the X'Sgive Bessel-function coefficients. References [I] 2. B. PopoviC, R. M. Weikle, M. Kim, I<. A. Potter, D. B. Rutledge, "BarGrid Oscillators," IEEE Trans. on Microwave Theory and Techniques, Vol. MTT-38, No. 3, 225-230, March 1990. [2] C. Stephan, T. Itoh,"Planar Quasi-Optical Subharmonically Pumped Mixer Characterized by Isotropic Conversion Loss ," IEEE Trans. on Microwave Theory and Techniques, Vol. MTT-32, No. 1, 97-102, January 1984. [3] R. E Ziemer, W. H. Tranter, "Principles of Communications," Houghton Mifflin Co.,Boston, 1976, pp. 117. Chapter 5 The PIanar Grid Oscillator The planar grid oscillator is shown in Fig. 1. The transistors are Fujitsu GaAs MESFET's (FSC1I), made for satellite receivers at 4 GHz, which typically produce 20mW in a microstrip oscillator. The devices in adjacent rows share the gate and drain bias lines. The symmetry of the grid forces cancellation of RF currents along the horizontal bias lines, so that the radiation is primarily Fig. 5.1. The 100-MESFET planar grid oscillator. The horizontal lines are the bias lines. Ferrite beads are added to the bias lines to suppress lower-frequency oscillations. All the gates, drains and sources are connected, so there are a total of three wires used for the grid bias. The vertical leads are gates and drains, and the radiated electric field is polarized in this direction. 0 1 2 3 Separation distance. I\-avelengths Fig. 5.2. Calculated power diffraction loss per round trip for different modes a s a function of the cavity length. T h e dimensions of t h e cavity correspond t o the planar grid oscillator dimensions [3]. from the vertical drain and gate leads. The grid is made on a 0.5 mxn thick low-dielectric constant ( e , = 2.2) material on top of a 2.5 mm thick Duroid slab with e , = 10.5. There is a flat metal mirror behind the grid. The mirror and the grid form a Fabry-Perot cavity about a wavelength long. T17hen the bias to the transistors is turned on, oscillations build up, and all the cavity modes compete. The mode with the lowest diffraction loss per round trip survives, and the devices in the grid lock to this mode. Analysis similar to that of Fox and Li [2] was done for the case of a FabryPerot metal-reflector resonator of the same size as the grid [3]. Fig. 5.2 shows the calculated loss per round trip for different modes. The lowest-order mode has about 2dB lower loss per round trip than the next mode. This can also be ( 0 . 0 ) mode (1.0) mode (2.1) mode (2.2) mode Fig. 5.3. Calculated mode patterns for the (0,O)mode (a), (1.0) mode (b), ( 2 , l ) mode (c), and (2,2) mode(d). In the simulations, it typically took ten round trips for the mode t o converge [3]. Fig. 5.4. T h e measured radiation pattern of the planar grid. T h e vertical scale is linear in power. T h e axes are given in terms o f spherical coordinates by OE = Usin4 and O H = O C O S ~ . This grid locks at 5 GHz, and in Fig. 5.4 is shown the measured pattern with the mirror 57mm away from the back of the substrate. The effective radiated power (ERP) is 22 Watts, and the directivity 16 dB. The RF to DC efficiency is 20%) and the isotropic conversion gain [S] is 8.5 dB. The cross-polarized compo- nent is 30 dB below the co-polar one at the pattern peak. 5.1. Equivalent Circuit In an infinite grid with all the devices locked in phase, symmetry allows us to represent the grid as an equivalent waveguide unit cell. This waveguide has magnetic walls on the sides and electric walls on the top and bottom, as shown in Fig. 5.5. It extends in the +z and -2 directions, with the grid in the z = 0 plane. The propagating mode is TEM, and the evanescent modes couple to the currents in the transistor leads and present reactive impedances to the device terminals. These reactances can be found by the EMF method [4].Their values depend on the electrical thickness of the dielectric that supports the grid, on the geometry of the grid, and on the assumed current distribution on the transistor leads. The analysis is similar to that of the bar-grid oscillator described in Chapter 3. A set of TE and T M basis vectors is chosen for the unit waveguide. The currents and fields are expanded in terms of these basis vectors. The power is given by Fig. 5.5. Boundary conditions are imposed by the grid symmetry. The solid lines are electric walls (Etons= 0) and the dashed lines are magnetic walls ( H t o n g = 0). where j,, are the current expansion coefficients for the m, n-th mode. Z, the parallel combination of the mode impedances in the is + and - z-direction, and it can include any mirrors or dielectric slabs. The results presented here are derived from a first-order assumption for the currents: A uniform current in the gate and drain leads a linear current in the source lead. The latter is set to zero at the magnetic walls to satisfy the boundary conditions. The current distribution is shown in Fig. 5.6. The equivalent embedding circuit for the device in the grid is sho\vn ill Fig. 5.7. The inductors L in the gate and the drain are the lead inductances. The circuit elements are given by mrw C sinc2 (T) 22: 00 1 L =JW rn12 rn even rn even x sinc2 (z ( F ) + -) m7iw n a ma-w nodd 1 nrw mrw 2 z,,T E (b) (4 Fig. 5.6. (a) Transistor in unit waveguide, with source (b) a n d d r a i n a n d g a t e (c) current distributions. T h e magnitudes of t h e g a t e a n d drain c u r r e n t s a r e different. T h e current distribution inside t h e device is assumed t o b e linear to avoid discontinuities. Fig. 5.7. T h e equivalent circuit for a device in an infinite grid. The given reactance values are for the symmetric grid with a = 8 mm, w = I mm, and a 2.5 m m thick dielectric with c = 10.5. where 22: and 21ft4 are the impedances of the mn-th TE and TM modes 151. Each of these is a parallel combination of the impedances in the +z and -2 directions, and kk, = ( F)2 -(zl2 - ( z)*. The transformer describes coupling into free space, which is represented as a 375 R transmission-line. The mirror is represented as a shunt reactance j B. The entire grid is in this way reduced to a one-port equivalent. The measured small-signal transistor s-parameters were used, and saturation is taken into account by reducing IszlI by 3 dB. The impedance looking into the oscillator from the 37752 load was examined as a function of frequency. When this impedance becomes -3'i7R, an oscillation should occur, and the model from Fig. 5.7 predicts 4.93 GHz for a mirror distance of 57mm. The grid oscillates a t 5 GHz for this mirror distance. We tested the equivalent circuit by building two grids with the same dimensions [6], but with shorting strips instead of transistors, as shown in Fig. 5.8a and 5.Sb. The substrates are Rogers Duroid lOcm square, with a nominal dielectric constant of 10.5, copper cladding on the back, and 2.5 mm thick. The and 5.8d, use the same equivalent circuits for these two grids, shown in Fig. 5 . 8 ~ (4 (dl Fig. 5.8. Inductive (a) and capacitive (b) grids made o n a 2.5 m m thick dielectric ( Duroid, cr = 10.5). T h e dimensions of the unit cell are the same as for t h e MESFET grid. Equivalent circuits for the inductive (c) and capacitive ( d ) grids. formulas for inductances and capacitance as the transistor grid. The phase of the reflection coefficient of the grid mas measured from 2 GHz to 18 GHz in an anechoic chamber with a wide-band horn and an HP 8510 network analyzer. The calibration mas quasi-optical. Microwave absorber a t a 45O angle served as the matched load, and a copper sheet as a short. The copper sheet was translated to provide a delayed short as the third standard. The reflection-coefficient phases are shown in Fig. 5.9a and 5.9b. The theoretical phase calculated from the Frcqucncy, G Hz Fig. 5.9. Measured (dashed line) and theoretical (solid line) phase of the reflection coefficient for the inductive grid (a) and capacitive grid (b). Note that the two phase scales are quite different. equivalent models is shown in solid line for comparison. The substrate electrical thickness is used in the model was measured by stripping the grid pattern and repeating the reflection-phase measurement. The close agreement between theory and experiment gives us confidence in the equivalent circuit model. 5.2. Mirror tuiliilg The position of the mirror has a strong effect on the frequency of oscillation, the grid output power, and the radiation pattern. The equivalent circuit in Fig. 5 predicts frequency tuning as a function of the mirror position. In this simple transmission-line model, the oscillation frequency does not change if the mirror spacing is increased by X/2, as shown in solid line in Fig. Sa. The experimental results, shown with dots, agree with the theory. The mirror position affects the width of the main lobe and the size of the sidelobes, as shown in Fig. 9a and 9b. The pattern of the grid is found as that of a unifonn array of short dipoles on an infinite dielectric and with an infinite mirror in the back [7]. The distances at which the theory predicts similar patterns are several ~llillimeterslarger than seen in the experiment. For some mirror distances, the pattern has a null in the middle, which will prevent locking and will correspond to the region where the grid does not lock. h?irror distance, mrn 0.040 M 60 70 80 90 100 110 120 130 Mirror distance, mrn (b) Fig. 5.10. The simulated (solid line) and measured (dots) frequency (a) and power (b) mirror-tuning of the grid. (b) Fig. 5.11. Experimental (solid line) patterns for mirror distances of 54 mm (a) and 82 mm (b). Theoretical (dashed line) patterns [3] for mirror distances of 62 mm (a) and 88 mm (b). References [I] 2. B. PopoviC, R. M. Weikle, M. Kim, R. D. Rutledge, "A 100-MESFET Planar Grid Oscillator," submitted to IEEE Transaction on Microwave Theory and Techniques, April 1990. [2] A. G. Fox, T. Li, "Resonant Modes in a Maser Interferometer," Bell Sys. Tech. J., Vol. 40, 453488, March 1961. [3] Moonil Kim, private communication. [4] R. L. Eisenhart, P. J. I<ahn, "Theoretical and Experimental Analysis of a Waveguide Mounting Structure," IEEE Trans. on Microrvave Theory and Techniques, Vol. MTT-19, No. 8, 706-719, August 1971. [5] R. F. Harrington, "Time-Harmonic Electromagnetic Fields," McGra~vHill., New York, 1961, pp. 349. [6] Robert M. Weikle, 11, private communication. [TI D. B. Rutledge, D. P. Neikerk, D.P. I<asilingarn, "Integrated Circuit Antennas," Infrared and MiIIimet er- Waves, Vol. 10, 1-S7, 1983. Chapter 6 Injection-Locking of t h e P l a n a r G r i d Oscillator In the measured results presented so far, the MESFET's were locked together with no external locking signal present. For some applications it is convenient to be able to lock the devices to an externally injected signal. For example, an electrically modulated low-power oscillator can frequency-modulate the source. The injected signal can also stabilize the frequency, as shown in Fig. 6.1. The injection-locking was performed quasi-optically, as shown in Fig. 6.2. The mea- -70 -70 -100 0 100 Frequency offset, kHz -1 00 0 100 nequency offset, kHz Fig. 6.1. The free-running (a) and injection-locked (b) grid spectra. The center frequency is 5.2 GHz. HP5350A Frequency Counter L H P 435B Power Meter I rn Grid Injected Wave 7 HP 8620C 1 Sweep Oscillator 1OdBCoupIer J 10dBQu~Ier C Lf-'+ -u-' Radiated Wave F i g . 6.2. Quasi-optical injection-locking measurement setup. sured injection-locking bandwidth as a function of the relative injected power is shown in Fig. 6.3, and it is proportional to the square root of the injected power, or, equivalently, to the injected field magnitude, as expected [4]. Fig. 6.3. T h e dependence of t h e grid locking range o n t h e power ratio of t h e injected and free-running signal for a mirror distance of D = 54 mm. 6.1. Injection-Locking T h e o r y Previous injection-locking analysis [4]is based on the assumption that the device impedance is a function of the amplitude only, and that the load impedance is a function of frequency. For the grid, the impedance is a function of both power and frequency, while the load, which is free space, is independent of power and frequency. This suggests a different approach. We use the equivalent circuit shown in Fig. 6.4a. The grid is represented by a reflection coefficient sJp, f ) , which is a function of the transmitted power p and frequency f . Free space is represented by a load with a reflection coefficient of zero. The radiated signal is represented by a wave amplitude a, where the magnitude of a is the square root of the radiated power. The injected signal is written as c, where tlie magnitude of c is the square root of the injected power. From the circuit model we can write the relation Fig. 6.4b is a plot of s , ( p * f ) in the complex plane. This is a convenient representation, because the origin represents the free-running oscillation condition. The contours of constant power and frequency may be drawn as straight lines in a small neighborhood about the origin. -4s the frequency varies, the tip of the c / a arrow will trace out a semicircle, provided the injected power remains the same, and that the deviation of the radiated power is small. For a given 1$1, the fre- quency deviation varies symmetrically around the free-running frequency from -A fmaz to +A f,,, , where 2A fmaz is the injection-locking bandwidth. The power deviation Ap inside the locking range is not symmetrical in general; for example, in Fig. 6.4(b) it grows in the direction of the arrow, reaching the largest value a t the contour Apmaz. From Fig. 6.4(b), the frequency and amplitude of an injection-locked oscillator are given by (b) Fig. (5.4. (a) T h e equivalent circuit of the injection-locked grid oscillator. a is the power wave radiated from the grid, and c is the injected signal power wave. The reflection coefficient of the grid s g ( p ,f ) is a function of both power and frequency. (b) Contours of constant Ap and A f in the $ = complex plane. - = g P f) where 6' is the angle between the contours of constant A f and Ap, and q5 changes from 4 2 to + x / 2 inside the locking range. Apo is the change in oscillator power at the free-running frequency after it has been injection-locked. This means that it is suacient to measure A f,,, , Ap,,, and Apo in order to predict the injection-locked oscillator behaviour. Fig. 6.5 showvs measured and calculated power variation of the injection-locked grid for two different mirror positions. Fig. 6.4(b) corresponds to the curve in Fig. 6.5(a). Starting from -A f m a z and moving along the c/a circle, Ap is first negative, tlle11crosses the Ap = 0 contour, grows to its maximum, and finally starts dropping at the upper end of the locking range. The tip of the c/a arrow traces a whole circle in the complex plane, but only one half of this circle corresponds to stable solutions. The stability of oscillation is discussed in Fig. 6.6. The contours of growing power are indicated with the direction of the arrow. For oscillations in the top half of the circle (Fig. 6.6b), a perturbation 6a at a frequency A f causes c / a to move from the contour Ap to a contour of larger power (Ap + 6p). This corresponds to an unstable oscillation. The same perturbation mill cause a decrease in power for stable solutions lying on the bottom half of the circle (Fig. 6.6a). To decide which half of the c l a circle corresponds to stable solutions, we draw a line from -A f,,, to +A f,,,, and pick the semicircle to which the power-gradiant arrow points. The described analysis can be potentially useful for characterizing noise, since the oscillator noise can be represented as a collection of injected signals of different powers and frequencies. The presented measurements on the injection-locked oscillator Frequency deviation A f , MHz -12 -4 4 12 20 Frequency deviation A f , MHz (b) Fig. 6.5. Variation of the oscillator output power inside the locking range for different ,Ap,,, mirror positions. The solid lines are calculated from measured values of A f,, and Apo. Fig. 6.6. Stable oscillations correspond t o t h e bottom half of t h e c / a circle, and unstable ones to t h e t o p half of the circle. T h e power gradient is in t h e direction of t h e arrow. are scalar measurements. The interesting possibility of measuring contours of constant power and frequency in the c l a complex plane with a vector network analyzer is the subject of future work . 6.2. T h e G r i d Oscillator Receiving and Dansmnitting P a t t e r n s The injection-locking bandwidth of the grid is a function of the incident angle of the injected signal. It is maximum for normal incidence, and decreases sharply as the angle varies from the normal (Fig. 6.7). The pattern is very similar to the transmitting field pattern, which is indicated on the same figure. It might seem surprising that the injection-locking bandwidth has the same pattern as the transmitting grid, but this is actually a consequence of reciprocity. We can understand this by considering a general equivalent circuit for an injection-locked grid, shown in Fig. G.S. The grid reflection coefficient is s,, and the source of the injection signal has a reflection coefficient si. The scattering matrix S(6,d) takes into account the grid pattern, free-space attenuation, and the horn pattern. It is linear, reciprocal and we assume it is matched. The radiated wave from the grid al produces a wave b2 in the far field. A wave a2, which feeds the horn from the injection source, produces the injected wave bl at the grid, so we have where s*l(6,4) is effectively the transmitting grid pattern, and s12(6,4) is effectively the receiving pattern. By reciprocity, these must be equal. From Fig. 6.3, the injection-locking bandwidth is proportional to the injected field magnitude Ibll, which is in turn proportional to s12(8,4), and to the transmitted \vave lb21. Fig. 6.8 confirms this interesting result. 0.0 -90 -60 -30 0 33 60 90 H-plcmc, dcgrccs Fig. 6.7. Normalized injection-locking bandwidth (dots) measured as the incidence angle of the injected signal was changed in the II-plane. T h e solid line shows the measured free-running far-field H-plane pattern. These two curves a r e the grid receiving and transmitting patterns, and they are closely related by reciprocity. At large angles the injected signal power is not sufficient for locking the grid. Fig. 6.8. Equivalent circuit for the grid as a receiving and transmitting antenna. T h e radiated wave from t h e grid is a l , and the injected wave is b l . T h e two-port S(O,+) takes into account t h e grid pattern, free-space attenuation, and t h e horn pattern. References [I] 2. B. PopoviC, R. M. Weikle, 11, M. i<irn, R. D. Rutledge, "A 100-MESFET Planar Grid Oscillator," submitted to IEEE Transaction on Microwave Theory and Techniques, March 1990. [2] S. Nogi, I<. Fukui, "Locking Behaviour of a Microwave Multiple- Device Ladder Oscillator," IEEE Transactions on Alicrowave Theory and Techniques, Vol. MTT-33, No. 3, pp. 253-262, March 1985. [3] I<. Daikoku, Y. Mizushima, "Properties of Injection Locking in the Non-Linear Oscillator," Int. J. Electronics, Vol. 31, No 3, 279-292, 1971. [4] I(. I<uroka\va, "Injection-Locking of Microwave Solid-state Oscillatoss," Proc. IEEE, Vol. 61, 1386-1410, October 1973. [5] R. Adler, "A study of Locking Phenomena in Oscillators," Procedings of the IRE and 'L'l'a,ves and Electrons, 351-357, June 1946. [6] S. Hamaya, "Stability of the Oscillation Mode in a Multiple-Oscillator System," IEEE Transact ions on Microrvave Theory and Techniques, 1701. A..iTT-33, No. 7, 593-599, July 1985. Chapter 7 Conclusioil and Suggestions for Future Work The work presented in this thesis demonstrates the feasibility of a highpower, solid-state source at microwave and millimeter-wave frequencies. Experiments on hybrid grid oscillators with MESFET's show that the devices lock to each other and that their po\17er is combined. The oscillators are planar and can be fabricated with the existing semiconductor technology. Any two- ter- minal or three-terminal devices that have negative resistance at the frequency of interest can be integrated in a grid. Although it can combine thousands of devices, the grid oscillator is a simple structure, since all of the devices share the same biasing and matching circuit. This type of source is especially attractive for millimeter-wave frequencies. In this range the waveguide dimensions become impractically small, and losses in the metal waveguide walls high, so that quasioptical techniques have many advantages. At higher frequencies, a single wafer is many wavelengths across, so high gains and ERP's can be expected. Measurements made on the three grids described in this thesis indicate that the grids can be used for a variety of applications. The grid is an antenna as well as a source. In an antenna application, the pattern and ERP would be of interest. In a source application, the power radiated from the grid and the conversion efficiency would be important parameters. The grid is a self-oscillating mixer, so it can be used as a receiver. In this case the noise characteristics and conversion gain need to be determined. The locking mechanism as well as the power distribution across the grid would be important to investigate. Probi-ng the near fields of the grid and making a field map across the grid surface could prove to be a useful tool for designing future grids. A field picture recorded at different stages of the locking process could help in the understanding of the locking mechanism of such a large number of oscillators. 7.1 Scaling Since the devices in the grid are closely spaced compared to a free-space wavelength, the entire grid can be viewed as a continuous active sheet. In this case, the scaling properties of the grid will be related to its area in wavelengths. The directivity is proportional to the area. The radiated power is proportional to the number of devices, i. e., to the area as well. This means that the ERP grows as the square of the area. In any application where the power is used in the far field, the total power radiated, as well as the directivity is of interest, because both contribute to the power density in the far field. In addition, if the noises of the individual devices are uncorrelated, the noise power is proportional to the area. This means that the signal-to-noise ratio (ERPIN) improves as the area of the grid increases. If the devices are more than a half of a substrate wavelength apart, the number of substrate modes in the dielectric will grow. The period of the grid is limited by heat considerations and the device geometry at the lower end, and by efficiency at the higher end. The grids described in this thesis have periods from Xo/10 to Xo/3, where Xo is the free-space wavelength. Existing state-of-the-art device technology allows some predictions for future monolithic grids. For a high-power application, a Heterojunction Bipolar Transistor (HBT) grid at 90 GHz on a 100 mm diameter wafer could have an ERP of 800 kWatts. This ERP can be achieved if the devices are 1 mm (Xo/3) apart and if each device can give 10 m l a t t s [I]. This gives a total power of 19 dBJV, and the directivity of such an active sheet is 40 dB. High-power devices like HBT's require good heat-sinking. A combination of the bar grid oscillator and the planar grid oscillator would be convenient. The HBT wafer can be placed against metal bars, which would be the radiator as well as p a t of the impedance-matching circuit. Bipolar transistors also require a resistive biasing circuit to prevent thermal runaway. In a hybrid microstrip version of a bipolar transistor grid oscillator, an alternative to using chip resistors is to use a special alumina substrate with two-layer metalization [2] that can be used to fabricate thin film resistors by etching. Two masks are needed to fabricate the grid. The first one defines the whole grid structure together with the bias resistors. The second mask defines the places where the copper is etched away, leaving the second layer exposed. Baking the substrate results in oxidation of this layer, which then becomes resistive, with a surface resistance on the order of 25 0. For a very high-frequency application, quantum-well resonant tunneling diodes can give 1pW at 200 GHz (31 with good yields. The directivity of a 100mm diameter grid is 40 dB. Assuming a 0.15 mm (Xo/lO) period, the radiated power \vould be 25 dBm, and the ERP 3 kWatts. Since the grid oscillator consists of a very large number of devices, the reliability of the oscillator is an important issue. If a device fails as an open ciricuit, and the grid is several wavelengths across, the hope is that the mode will not be affected, as was shown in measurements with the bar grid. If a device fails as a short, it shorts out the whole grid, fusing the rest of the devices. In a monolithic version, fuses should be integrated in series with each device. An important issue is the effect of the failure of devices at different positions in the grid. Future investigation on reliability could be done by probing the near fields of the grid when different devices are taken out of the grid, simulating an open-circuit failure. 7.2 The grid as a receiver The injection-locking experiments described in Chapter 6 also indicate that the grid oscillator is a receiver. Outside the locking range, the free-running and injected signal give mixing products that can be detected as the IF on the bias lines. Since the ferrite beads on the bias wires are a high impedance for IF frequencies, the IF can be taken out differentially, as shown in Fig. 7.1. A wire is pulled through the first ferrite bead on the source bias lines, and its two ends soldered to a coaxial connector. In this way the IF is transformer-coupled to an oscilloscope, as shown in Fig. 7.2. In order to characterize the grid oscillator as a receiver, its noise figure and conversion gain need to be measured. Coaxial cable Ferrite bead Fig. 7.1. Transformer-coupling can be used t o detect the IF o n t h e bias lines when the grid is used as a receiver. Mirror Fig. 7.2. Test setup for the grid as a receiver. The sweeper signal is incident on the free-running grid. The two signals produce an IF, which can be detected on the bias lines. 7.3 S y s t e m Integration In the previous section several high-frequency grid oscillators with fundamental frequency devices were discussed. An alternative high-frequency grid oscillator can use a subharmonic high-power grid together with a grid of multiplying devices. It is easier to make high-power devices across a wafer with high yield at 30 GHz than it is at 90 GHz. The 30 GHz grid output is incident on a planar grid multiplier [4]. The multiplier can be optimized for a second harmonic oscillator at 60 GHz, or a third harmonic oscillator at 90 GHz. In this case the other harmonics need to be filtered out, and this can be done with passive grids [5].Such an oscillator can be used as the LO for a receiver. An example of an integrated system is shown in Fig. 7.3. The back-to-back horn array indicated in the figure is a focal plane imaging array [7]. The RF is incident on the front detector array. The LO is brought to the detector from the back side, and the IF circuitry is integrated between the wafers of the front and back array. The grid oscillator itself is both a transmitter and a receiver, so the grid can be used as a radar. One way to modulate the grid is through the DC bias. For example, if the frequency changes linearly with the gate voltage, as shown for the bar-grid, a sawtooth modulation on the gate DC bias mill cause a sawtooth change in the frequency. This is the principle of CW FM ranging radar. The radiated wave and the wave coming back from the target are offset in frequency, and the beat frequency is determined by the range of the target. This beat frequency can be detected on the bias lines. The frequency can also be modulated mechanically by translating the mirror. In this case the output power changes as well, as described in Section 5.2. The planar grid has a high-power mode and a low-power mode, and the two are offset in frequency by about 200 MHz as shown in Fig. 7.4, which corresponds to Fig. 5.10; The grid can transmit a high-@wer pulse, and can receive in the low- power mode. It would be more convenient to do the mirror-tuning electrically. In principle, the mirror can be a grid of-bias-dependentreactive devices, such as varactor diodes. By changing the bias of such a grid, the reflection coefficient is varied, and this is similar to changing the position of the mirror. Such a varactor-diode grid is effectively a variable-impedance surface. Several other applications of the grid oscillator with other grid structures seem attractive. If the grid oscillator main lobe is incident on a phase-shifting surface, the beam can be steered. A monolithic phase-shifting grid at 90 GHz has been demonstrated [s], where the phase of an incident plane wave was shifted by linearly changing the bias on the rows of Schottky diodes across the grid. For some applications, the radiated beam would need to be turned off and on. This can be done without turning off the grid itself. A second grid of switching devices, for example, p-i-n diodes 191, can be placed in front of the grid oscillator Tuning platcs ij ij Band pass filtcrs Tuning plates Fundamental Oscillator grid Multiplier grid Back- to- back horn array FIg. 7.3. The grid oscillator as the LO in a millimeter-wave imaging-array system. Fig. 7.4. T h e power variation with of the planar grid oscillator. Both the power and frequency are changed by translating the mirror over 15 mm. and its transmission coefficient changed electrically. An active-device grid that does not oscillate can be a wave amplifier. In this application the input has to be isolated from the output to prevent positive feedback. One way to do this is to use different polarizations for the input and output waves. For example, if the gate and drain leads were perpendicular in a MESFET grid, the gate would receive one polarization, and the drain would radiate an amplified perpendicularly polarized wave. In conclusion, the grid oscillator is a planar device convenient for large-scale microwave and millimeter-wave power combining. The quasi-optical approach is easy to implement, and suggests using passive and active grids combined in versatile systems. The work presented in this thesis leads to a number of interesting and useful applications that can be investigated in the future. References [I] P. M. Asbeck, M. F. Chang, I<. C. .Wang, D. L. Miller, G. J. Sullivan, N. H. Sheng, E. Sovero, J. A. Higgins, "Heterojunction Bipolar Transistors for Microwave and Millimeter-Wave Integrated Circuits," IEEE Trans. on Microwave Theory and Techniques, Vol. MTT-35, 1462-1470, December 1987. [2] Rogers Corporation, "Omega-Ply Clad RT/duroid Laminates," product specification sheet RT 1.99.1. [3] E. R. Brown, T. C. L. G. Sollner, C. D. Parker, W. D. Goodhue, C. L. Chen, "Oscillations up to 420 GHz in GaAs/AlAs Resonant Tunneling Diodes," Applied Physics Letters, Vol. 55, No 17, 1777-1779, October 1989. [4] C. F. Jou, W. W. Lam, H. 2. Chen, I<. S. Stolt, N. S. Luhmann, D. B. Rutledge, "Millimeter-Wave Diode-Grid Frequency Doubler," IEEE Trans. on Microrvave Theory and Techniques, Vol. MTT-36, No. 1l, 1507-1514, November 1988. [5] J. A. Amaud, F. A. Pelow, "Resonant-Grid Quasi-Optical Duplexers," The Bell System Technical Journal, Vol. 54, No. 2, 263-283, February 1985. [6] R. J. Hwu, N. C. Luhmann, Jr., C. F. Jou, M. Kim, 2. B. PopoviC, and D. B. Rut ledge, "Array concepts for solid-state and vacuum microelectronics for millimeter-wave generation," 1st International Vacuum Microelectronics Conference, Williamsburg, Virginia, June 1988. [7] Yong Guo, private communication. [S] W. W. Lam, C. F. Jou, H. 2. Chen, I(. S. Stolt, N. S. Luhmann, D. B. Rutledge, "Millimeter-Wave Diode-Grid Phase Shifters," IEEE Trans. on Ahcrowave Theory and Techniques, Vol. MTT-36, No.5, 902-907, May 1988. [9] A. Armstrong, S. Parisi, C. M. Howell, "High-Power Waveguide Diode-ArraySwitch Element," MSN &. CT, 8-19, November 1987.