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AN ULTRACOMPACT ANTENNA TEST SYSTEM AND ITS ANALYSIS IN THE CONTEXT OF WIRELESS CLOCK DISTRIBUTION By WAYNE ROGER BOMSTAD II A THESIS PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE UNIVERSITY OF FLORIDA 2002 ACKNOWLEDGMENTS I would like to begin by thanking my advisor, Professor Kenneth O, for giving me the opportunity to work on this project. His passion and commitment are always a per sonal source of inspiration. I would also like to thank the rest of my mentoring professors (Leffew, Snider, Weller, and Zory) for their guidance, allowing me to wholeheartedly claim a future career path. Additionally, I give my deepest respect to my first mentors, and lifelong role mod els, my parents: Henrietta I. Shuminsky and Wayne R. Bomstad. Also this work would not be possible in any timely manner without my teammates. On the SRC Project I thank J. Caserta, X. Guo, R. Li, J. Branch, and T. Dickson. Proper thanks go out to graduated Ph.D. students B. Floyd and K. Kim for providing many enlightening discussions. Next, I am grateful to Bruce Smith of Precision Tool and Engi neering for his help in mechanical engineering throughout this project. I dedicate this work, and all future engineering work, to my beautiful wife, Aleasha. Her love, encouragement, and dedication are behind any achievement of mine. TABLE OF CONTENTS page ACKNOWLEDGMENTS ................. ............................. ii ABSTRACT ......... ........................................ ......... vi CHAPTER 1 INTRODUCTION .................................................1 1.1 Emergence of W wireless Interconnects ............................ 1 1.2 IntraChip Clock Distribution ............... ..................1 1.3 Overview of Thesis. ........................................... 6 2 ULTRACOMPACT ANTENNA TEST SYSTEM .......................... 7 2 .1 Stru ctural D esign ................... ................... ...... 7 2.2 Electrical Design Considerations ............... .............. 11 2.3 Data Extraction ..................................... .......... 19 2.4 Calibration ..................................................23 3 INTEGRATED RECEIVE ANTENNAS ...............................26 3.1 Infinitesimal Dipole Antennas ................. ......... ..... 26 3.2 Radiated vs. Input Power. ................ ................... 30 3.3 Integrated Antennas in the UCATS .............. ............. 34 4 PROTOTYPE TRANSMITTER AND WAVEGUIDE ASSEMBLY ........... 37 4.1 W aveguide A ssem bly .......................................... 37 4.2 Prototype Transmitter. ........................................42 5 PROTOTYPE SYSTEM MEASUREMENTS ............................. 51 5.1 Testchip Design ..................................... ........ 51 5.2 Spatial Wavefront Uniformity Measurements ...................... .52 5.3 FrequencyDependent Measurements ............................ 65 5.4 Measurement Summary ..................................... .69 6 SUMMARY AND FUTURE WORK ..................................72 6.1 Summary ...................................................72 6.2 Future Work .................................................74 APPENDIX A DRAWINGS FOR THE ULTRACOMPACT ANTENNA TEST SYSTEM. ..... 75 A.1 Engineering Drawings for the UCATS ............................ 75 A.2 Photographs of Assembled UCATS. ........................... 84 B FINITE ELEMENT SIMULATIONS .............................. 86 B.1 Electromagnetic Application of Finite Elements .......... ....... 86 B.2 Simulation of Prototype Transmitter ................. ........... 89 B.3 Standing Wave Simulations ............... ................... 92 LIST OF REFERENCES ................. ............................... 98 BIOGRAPHICAL SKETCH ....... ................................. 99 Abstract of Thesis Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Master of Science AN ULTRACOMPACT ANTENNA TEST SYSTEM AND ITS ANALYSIS IN THE CONTEXT OF WIRELESS CLOCK DISTRIBUTION By Wayne R. Bomstad II December 2002 Chair: Kenneth K. O Major Department: Electrical and Computer Engineering It has been proposed to generate and receive the clock signal using wireless com munication systems as an alternative means of microprocessor clock distribution. As a candidate to replace traditional wired interconnects, wireless clock distribution has several potential advantages over its conventional counterpart including synchronization over a larger area and smaller clock skew. Previous wireless clock distribution systems were investigated using integrated receivers and transmitters. However, operation of these sys tems is hindered by the interference caused by coplanar metal structures. The way to mitigate this effect is to generate the clock signal offchip. The concept of externallytransmitted wireless clock distribution (ECD), or interchip clock distribution, has been studied in this work through the development of an applicationspecific measurement setup. This setup was designed to serve as a testbed for the characterization of ECD systems. Also in this work, a prototype ECD system, consist vi ing of only transmit and receive antennas, was designed and then measured in this new testbed, called the UltraCompact Antenna Test System (UCATS). The UCATS was developed to measure the gain in the near to intermediatefield region of a transmitting antenna on a 3inch diameter wafer. For the initial tests, a proto type transmitreceive antenna set was characterized both as a benchmark for future designs and as a means of characterizing the test range. Specifically, a 24 GHz gaussian optics horn antenna was used as the transmitter. A test chip containing an evenlyspaced array of folded dipoles was designed and used as the set of receive antennas. Phase and amplitude distributions of the received wave front were characterized by individually probing the integrated antennas. Measurements were performed for two different receivertransmitter separation distances, and the results were compared in terms of the overall gain, magnitude, and phase distributions. Measurements have shown that a wave front can be generated and received with a maximum phase difference of 16 degrees and a mean amplitude difference of 3.77 dB. For the purposes of clock delivery for 3 GHz operation, this can be approxi mated as a planar wave front with a beam area of 3.8 cm x 3.1 cm, the measurable size of the receiver array. In conclusion, it was shown that a planar wave front can be generated and mea sured in the near to intermediatefield region of the transmitting antenna using the UCATS and a prototype ECD system. The clock skew, assuming typical clock receiver architecture, was calculated to be 3% and 1.7% of the period at a receiver distance of 3 and 7.5 inches, respectively. These measurements were made over an area of 1178 mm2, a span of over 3 times the average area of presentday microprocessors. CHAPTER 1 INTRODUCTION 1.1 Emergence of Wireless Interconnects The emergence of the technical field of wireless interconnects has occurred as a means of addressing the some of the bottlenecks facing the semiconductor industry. As recently as 2001 the Semiconductor Industry Association's International Technology Roadmap for Semiconductors (ITRS) [SIA01] has predicted that, in the next 5 years, microprocessors will have local clock frequencies approaching 7 GHz, transistor gate length will decrease to 45 nm, and the number of metal layers will increase to 9. However, restriction of the tolerable phase discrepancy of the clock signal, or clock skew require ment, has been reduced to 40 ps resulting from the increased frequency. As a result of these trends, the global clock skew can limit the highspeed operation of microprocessors, even when using the stateoftheart copper and lowK interconnect technology [Flo01]. Worse than this, typical systemic clock skew solutions involve use of Htree circuitry, tak ing up a large area and requiring symmetry [Rab96]. What this means in terms of clock delivery is that as the chip size and clock frequency are increased each passing year, the clock skew becomes harder to equalize across the chip, and the total area used in clock delivery increases. This problem is one of the grand challenges facing the semiconductor industry, that could place serious limitations on the growth of the industry. 1.2 IntraChip Clock Distribution Feasibility of using wireless interconnects to alleviate some of the interconnect concerns of the semiconductor industry has been proposed [099] and components for 1 such a system have been successfully evaluated at a global clock transmission frequency of 15 GHz using integrated receivers and transmitters fabricated on a 0.18 jPm silicon CMOS technology [Flo00, KimOO]. A conceptual diagram of the system is shown in Fig ure 11. The transmitter has been placed in the middle of a group of integrated receivers. IC edge RX RXh RXh RXh RX RX4 RXs RXI TX RXI RXI RXIs RXf RXh RXh RXh RXh RX= Receiver TX=Transmitter Figure 11 Conceptual diagram of an intrachip clock distribution system. 1.2.1 Propagation Inside an IntraChip Clock Distribution System Figure 11 shows that, although placement of the transmitter and receiver can be optimized from a systemic view, there will be differences in directpath propagation delays for skews even in the ideal situation because the receivers must be placed at varying distances from the transmitting antenna. The distribution of delays to the different receiv ers becomes more complex when considering that the signal can also travel under the sili con surface, through the silicon substrate, and reflect off surrounding metal layers [Kim01](Figure 12). To alleviate this problem, sophisticated techniques are required, such as the inclusion of a properly engineered propagation layer underneath the silicon surface. Figure 12 Possible disruption of directpath signals in the intrachip wireless clock distribution system. 1.2.2 Clock Receiver Architecture A block diagram of the clock receiver is shown in Figure 13. To improve noise immunity, differential mode circuitry was used throughout the system. To mate with the differential mode circuitry, balancedline antennas (BLAs) such as dipoles and loops are needed for signal reception. Sequentially, the transmitted signal at the global clock fre quency (GCK) is received by the BLA, buffered, amplified by the lownoise amplifier (LNA), and then fed to the frequency divider. Through the divider, the signal's frequency is divided by 8 to the system clock frequency. The signal is then buffered again before being sent to the adjacent circuitry. BLA + GCK / System SClock LNo Frequency ("L ADivider Block diagram of a typical clock receiver. Figure 13 1.2.3 InterChip Clock Distribution System One way around this skew for intrachip clock receivers is to use an interchip clock distribution system. Such a means of clock distribution also uses a distribution of integrated wireless clock receivers across a chip. However, the signal transmission is accomplished by a plane wave generator located offchip (Figure 14). The signal travels from the transmitter, through the silicon, and to the receivers. This kind of signal propaga tion renders the interference effect of surrounding metal structures negligible, and better ensures that the receivers synchronously receive the clock signal without regard to their placement onchip. Receiving Antennas I xxxx x xxxxx (PC Board/MCM) Integrated Circuits transmitted clock signal Transmitting Antenna (Plane Wave Emitter) Figure 14 Conceptual diagram of interchip clock distribution system. 1.3 Overview of Thesis 1.3.1 UltraCompact Antenna Test System (UCATS) One of the goals set forth in this work was the design of a setup capable of charac terizing the nature of the transmittertoreceiver propagation in a wireless clock distribu tion system using microwave scattering parameters. In terms of the mechanical design, the UCATS not only had to be able to fit within the existing measurement setup, for cost pur poses, but also had to allow for sensitive level adjustment and receivertransmitter spacing. Electrically, the system had to be able to absorb as much reflected radiation as possible, providing a ground for the absorbed radiation. Thus, an isolation chamber was designed to isolate the transmitter and receiver from all signals except the direct link between them. A rendition is shown in Figure 15, where the four main parts of the UCATS can be seen: the isolation chamber, vacuum ring, transmitter platform, and probe heightextenders. Finer details on the measurement setup are in Chapter 2. 1.3.2 Prototype TransmitterReceiver Pair To verify the proper functionality of the UCATS and to provide a reference design for future interchip clock distribution systems, a prototype transmitreceive antenna pair was also designed as part of this work. Since an actual parabolic reflector antenna, as in Figure 14, would not be compatible to the UCATS environment, a gaussian optics antenna [Gol82] was used in its stead. Analogous in many ways to an electromagnetic "spotlight", the gaussian optics antenna, can be used to emit a planewavelike beam, which is only diffractionlimited in the spreading of its amplitude and phase over propaga tion distance. A more detailed discussion of this horn transmitter is presented in Chapter 4. A test mask including receive antennas was designed in order to measure and char acterize the transmitted wave front at the wafer surface. Cells of varying integrated anten nas, were spaced at even intervals across the wafer surface. Using this mask, a wafer was fabricated at the UF Microelectronics Fabrication Facility on a 20 Qcm silicon substrate. This work is also discussed in Chapter 3. Upon measuring the received power gain using microwave scattering parameters (sparameters) at every antenna of the same type in each cell, the spatial phase and ampli tude distributions were obtained and plotted. Careful analysis of the sparameters and the antenna properties has yielded a skew of 1.7% and 3% for receivertransmitter separations of 7.5 inches and 3 inches, respectively. These measurements and data analyses are pre sented in Chapter 5. Finally, as part of Chapter 6, broader conclusions from the data were drawn, and future work was proposed. RF Probes Vacuum Ring,& Wafer Antenna Chamber EM Absorbe 14" 7. Probe Heightextenders S15 C s l o 7"UCA Figure 15 Crosssectional layout of the UCATS. CHAPTER 2 ULTRACOMPACT ANTENNA TEST SYSTEM 2.1 Structural Design 2.1.1 Overview The mechanical design of the UCATS was governed by three stipulations. First of all, for cost efficiency purposes, the system must fit within the existing RF probe station. Second, in the context of external clock distribution networks, the design must allow for accurate measurement of phase differences across the entire wafer surface [Wan88]. Finally, the design must permit fine adjustment in receivertransmitter spacing. 2.1.2 Isolation Chamber Design The external dimensions of the isolation chamber and structural foundation of the UCATS were determined so that the system could snugly fit within the existing RF probe station, could allow for adequate range of motion of the probes, and could provide housing of both the receive and transmit antennas. The chamber was designed to be a fivesided box, consisting of four distinct pieces: sidewalls (x2), a front panel with an access door, backpanel, and the top surface. These individual pieces were fabricated using Aluminum, which allow for a sturdy probing platform, a ground for absorbed radiation, and an inex pensive and lightweight alternative to stainless steel. The assembled antenna chamber is displayed in Figure 21(a). Details, such as the screw holes and spacing, have been omitted for simplicity, but the actual drawings have been included in Appendix A. Vacuum Ring (Top Panel) 3"  14" (. )13.25" Access Door (Fron Panel) 4" 13.25"  7"  7"  (a) (b) Figure 21 Diagram of assembled antenna chamber: (a) oblique and (b) top views. The need to explore the effects of layers placed between the wafer and transmitter and different vacuum ring configurations has led to the design of a modular vacuum ring system. To help accomplish this, the vacuum ring housing was designed as a large multistep hole in the middle of the top surface, shown in Figure 22. In addition, holes in the vacuum ring housing were placed to permit for level adjustment of the vacuum ring separately from the transmitter platform via adjustment screws. More detailed drawings Adjustment Screws Cross section of antenna chamber top panel. Figure 22 9 can be found, once again, in Appendix A. The discussion of the prototype vacuum ring has been included in the electrical design section. 2.1.3 Transmitter Platform The transmitter platform resides inside the antenna chamber. This piece accom plishes the sensitive task of both allowing for a continuous range of receivertransmitter spacing, and level adjustment of the transmitting antenna. The platform fastens to the chamber by four large screws, 6 inches in length and 0.5 inches in diameter. These screws mate into 4 speciallydesigned "Lclamps". Turning all screws equally in one direction varies the distance between the receiver and transmitter, and causes the platform to slide up or down along the inside walls of the antenna chamber. Turning only a couple of these screws at a time adjusts the level of the antenna platform. Figure 23 shows a cutaway view of the platform, while Appendix A contains more detailed drawings. \ TxPlatfor ^ '" _'Adj. Screws '"" Transmitter Tx Platform Ant. ,, "L"Clamps , Figure 23 Cutaway view of transmitter platform inside antenna chamber. 2.1.4 Probe HeightExtender Assembly The antenna chamber has been designed with a greater height than the existing probe station. To allow probing of the entire surface of a 3inch diameter wafer secured on the vacuum ring, a probe heightextender assembly was designed. Aluminum was again chosen for its rigid support and light weight. The latter quality was vital to prevent over loading the calipers, the mechanism for probe deployment. 10 The probe heightextender assembly consists of two distinct pieces: the probe arms and probe heightextenders. The probe heightextenders allow the probes to be rig idly supported well above the wafer surface, while the probes are mounted on the probe arms. Additionally, the probe arms were specified to have 2 degrees of freedom and their actual design was contracted out to Precision Tool and Engineering. Their assembly with the antenna chamber can be seen in Figure 24, while the engineering drawings can be seen in Appendix A. Probe Arms Antenna Chamber Probe Height Extender Probe Adjustment Caliper Figure 24 View of probe support assembly (shaded). 2.1.5 Vacuum Ring In considering its physical topology alone, the vacuum ring is perhaps the most complex of the components of the UCATS. First, the ring must fit within the ring housing in the antenna chamber and mate to the vacuum ring level adjustment screws. In looking at Figure 25, the design of the inner ring radius, or measurement aperture, must not only provide access to transmitted signals from below, but also allow for any 3inch wide wafer (circular or square) to cover the aperture completely. Finally, the ring must provide ade 11 quate air evacuation to secure the wafer in place against repeated probe landings. Thus, the holes in the vacuum ring should each apply an equal downward force on the wafer. With this idea as a guide, the vacuum ring contains an internal vacuum channel connect ing all the vacuum holes and providing an outlet for external connection to a vacuum pump. Once again, Appendix A contains more of the dimensional details of the vacuum ring. 3" Diameter 3" Square Circular Wafer Wafer ___  Figure 25 I..... I (b) Actualsize drawing of vacuum ring showing (a) wafer placement and (b) cross section. 2.2 Electrical Design Considerations 2.2.1 Antenna Chamber The antenna chamber was designed so that the signal would take only one path, the lineofsight (LOS) path, to propagate from transmitter to receiver. Appropriate absorbing material had to be placed inside the antenna chamber to absorb any reflected 12 signals. The absorber is shown in Figure 26, a 0.5inch thick flat absorber was used for all of the internal surfaces of the antenna chamber. As discussed in Section 2.2.2, it was determined by experimental means that this absorber was a better choice for absorption at 23.7 GHz, the resonant frequency of the transmitting antenna. Wafer \ Vacuum Ring Figure 26 Antenna chamber with absorber. 2.2.2 Electromagnetic Absorber Electromagnetic radiation absorption can best be understood on a fundamental level using planewave theory. This planewave radiation can be defined by the form seen in Equation (2.1) in terms of the electric field intensity (E) or magnetic field intensity (H) quantities as functions of position (x,y,z) and time (t). E(x,y,z,t) E (kzot) (2.1) tH(x,y,z,t)J Ho Here the wave has been chosen to propagate in the zdirection which represents toward the wafer in Figure 26, where the plane wave is defined by its polarized amplitude (Eo or Ho), wave vector (k), and angular frequency (co). Also the convention of using boldfaced type to indicate a vector quantity has been utilized. Partial absorption this propagating wave is allowed by the complex k inside the absorbing material. In other words, it was thought that there could be divergent directpath rays from the gaussian optics horn transmitter. Thus, the convoluted form (eggcrate absorber) should be an ideal shape which allows for a more efficient production of currents inside the polyurethane absorber. This can be directly observed from the maxwell boundary con ditions for the H field, given by [Wan88] (Hchamber Habsorber) x n = K. (2.2) The tangential magnetic fields in the chamber just outside the absorber are related to the magnetic fields just inside the absorber (Habsorber) by a surface current launched just inside the absorber (K). The absorbed energy is then carried by the current through the absorber to ground via the conductive antenna chamber walls. Note the unit vector (n) is directed out of the absorber. Experiments were conducted to verify the convoluted absorber as the initial choice to coat the inside of the transmitter platform. A 1.5inch thick convoluted absorber was specified by the Cumings Corporation, the supplier of the absorber, to have a 40 dB reflectivity at the frequency of 30 GHz in the farfield of an antenna. This absorber was compared to lowprofile 0.5inch thick flat absorber of the same polyurethanbased mate 14 rial. To check these specifications for the UCATS, a near to intermediatefield antenna range, measurements were conducted with the setup seen in Figure 27. The results of the corresponding measurements are shown seen in Figures 28(a) and 28(b). As a bench mark for this experiment, these results were compared to the laboratory freespace mea surement of 27(c), which was performed in the laboratory by pointing the transmitter in a direction with no LOS reflection path. __ (a) Tx Aluminum AbsorberUnderTest (b) Tx (c) Laboratory Free space Tx Figure 27 Absorber attenuation experiments: (a) control, (b) experiment, and (c) laboratory free space (no absorber or aluminum). (a) 0.0 t G Flat Absorber 1 z A Aluminum S. v...v" Laboratory 20.0 Free Space 25.0 23.0 23.5 24.0 24.5 25.0 S5.0 0) S10.0 Aluminum "..... 7 Laboratory Free Space 25.0 Frequency (GHz) Figure 28 Absorber experiments in the measurement bandwidth of the UCATS using (a) flat absorber and (b) convoluted absorber as the absorberundertest. 23.0 23.5 24.0 24.5 25.0 Frequency (GHz) Figure 28 Absorber experiments in the measurement bandwidth of the UCATS using (a) flat absorber and (b) convoluted absorber as the absorberundertest. A comparison between these two plots shows that the flat absorber is better for the antenna's resonant frequency of 23.7 GHz, attenuating the signal at least 15 dB better than the convoluted absorber and about 5 dB better than the freespace measurement. In fact, the convoluted absorber had even worse attenuation than the Aluminum control experi ment. As a result of these experiments, the flat absorber was chosen as the default absorber in the UCATS. Actual application of the flat absorber to the antenna chamber only increases its capability of attenuating reflected waves, as the experiments performed above sought to examine the worstcase scenario. These experiments measured reflectivity at normal inci dence, a situation which never occurs in the actual UCATS since the transmitter's effec tive beam aligns with the wafer and vacuum ring aperture. Thus, the UCATS uses the absorber to attenuate rays diverging from the LOS path, and scattered rays, which have oblique incidence to the absorbers in the UCATS. 2.2.3 Expected Level Adjustment Performance The specification for minimum range of motion for level adjustment had a basis in the system expectations for clock skew in an interchip clock distribution system. Even though the industry standard [SIA01] has set the global clock skew tolerance at 10% of the system clock period, optimal system performance often requires a tighter skew toler ance. Therefore, skew added by the measurement setup should be negligible, preferably less than 0.5%. In order to have a global skew of less than 0.5%, it has been determined that the interchip clock distribution system should contain less than 10 degrees of phase error over a 4 cm2 area at 24 GHz. In line with these initial performance benchmarks, it must be required of the system level adjustment to be at least 20x more sensitive, accounting for a phase difference of 10/20=0.5 degrees at 24 GHz. The level adjustment criterion can be directly determined using firstprinciple electromagnetic wave propagation theory. For a resolution of 20x greater than the speci fied phase error, the level adjustment must be able to correct for a phase error of 0.5 degrees at 24 GHz. Using the principle of optical path difference [Ped93], nominally 0.5 degrees for this case, the alignment must be able to correct for a difference in height (A = RIR2) as seen by plane waves propagating through opposite sides of the 2 cm wide wafer as indicated in Figure 29, silicon wafer Figure 29 Optical path difference and level adjustment of wafer. showing two different waves propagating with two different path lengths (R1 and R2). By looking at this picture, Equation (2.3) can then immediately be written down. 0.5 (R2 R) A (2.3) Here the left hand side can be seen to represent the optical path difference, while the right hand side has expressed that phase difference in terms of an electromagnetic wave's phase argument as a function of vertical misalignment (A), frequency (/), and speed of light (c). In this way the equation was solved for A at 24 GHz, and equated with its expectation over the 4 cm2 area. Thus, the minimum tolerable alignment resolution was found to be 0.0035 cmvertical over a 2 cm width horizontal, a ratio of 2850 tol horizontal to vertical length units. 2.2.4 Probe Isolation Module The probe isolation module, a separate piece which is positioned over the wafer and RF probes, is responsible for isolating the probes and wafer from errant signals. The user places the module, an aluminumtin alloy, halfpillbox structure lined on the inside with the same flat absorber as the antenna chamber. The module is placed in position after making connections to the antennas such that the circular top surface of the module is par allel to the vacuum ring. In position, the module looks like the rendering in Figure 210. RF Probes AlSb Exterior Shell 0.5" Flat Absorber Si Wafer Vacuum Ring Figure 210 Probe isolation module crosssection. The importance of this module can be best seen by measurements taken with, and without the probe isolation module in place in Figure 211. The module in these measure ments has effectively reduced the variance of the measurements by 13 dB depending on how close the measurements were to the noise floor. This picture has indicated that the laboratory area around the UCATS presents a nonnegligible multipath environment.The probe shield can be used to provide a degree of isolation from this type of environment. 19 2.3 Data Extraction 2.3.1 SParameters Like most microwave measurement tools, the UCATS measures the microwave scattering parameters (sparameters) of the deviceundertest, or DUT. Acting as the con trol center of the UCATS, the HP 8510C Vector Network Analyzer, connecting to both the receive and transmit antennas, directly administers the measurement of the twoport scat tering parameters [Poz98]. The 8510C sweeps the RF power at each port in frequency and measures the resulting power level at each port. Association of the measured signal in each port to its parent signal in ratio form gives the sparameters. Equation (2.4) gives the explicit form of how the sparameters are expressed in terms of incident and reflected powers for ports of equal characteristic impedance. b. S.. (2.1) aI a . a. O 1 Here the i orj index represent either port one or port two. When i andj are the same, Sii represents a reflection coefficient with bi representing the reflected voltage wave. When the indices are different, Sij becomes a transmission coefficient, meaning that bi is now the transmitted voltage wave [Poz98]. In either case, portj sends the incident voltage wave, aj. The network analyzer does not perform measurements with both port sources active at the same time. Therefore, it becomes necessary to have the inactive port matched and its source turned off. This is represented mathematically in equation (2.4) by setting ai equal to zero. A priori information about the DUT gives additional insights about its associated scattering parameters. In the case of passive DUT's, the network does not generate any signal. Therefore, the maximum value of any scattering parameter is one. If the DUT is a symmetric and bilateral network, such as a passive filter, ideal measurement of S12 and S2] yields the same value. Finally, if there is knowledge that the DUT is a lossless net work, this means that a power balance may be applied to either port, giving equation (2.5) below for measurements using the port one source. S112+ S21 2 1 (2.2) This just means that the power that the network analyzer sends to the DUT is either reflected back to port one, or transmitted without loss to port two. 2.3.2 Equipment Hierarchy The UCATs uses a chain of equipment in order to extract the sparameters out of the DUT, each one serving a particular function.Figure 211 shows the block diagram of the measurement setup. The setup has two branches of equipment flow, one flow going through the transmission side of the UCATS, the other is the receive side. The vector net work analyzer (VNA) forms the head of the equipment hierarchy, controlling the flow through each measurement branch. Chapter 3 gives more information on the transmit side of the setup, while Chapter 4 contains the details on the receive side. Figure 211 Block diagram of equipment hierarchy. 21 2.3.3 Balun and SemiRigid Cable Assembly The 180 degree hybrid couplers act as baluns, converting the signal from balanced to unbalanced transmission lines with minimal loss. The need for the balun comes from the fact that the VNA operates on a coaxialbased system, a transmission line with unbal anced center and outer conductors; and the integrated antennas typically used in the inte grated clock receivers possess a balanced pair of transmission lines [KimOO, Flo00]. One cannot simply connect the balanced lines to the unbalanced lines without deleterious effects [Bal97] These effects in the worst case could amount to a net current flow to ground, reflecting all power sent to the antenna. Therefore, the balun assembly becomes necessary to transition between balanced and unbalanced transmission lines. The balun used in the UCATS was of the same type of device used in previous works [KimOO] except that it operates over a broader frequency range. The design of the balun, shown as a blackbox in Figure 212, has been specified to split power between ports 2 and 3 equally in magnitude, all the while maintaining a phase difference of 180 degrees between the center conductors of these same two ports. The specifications that the A 3dB To Network 180 Degree Analyzer 180 Degree RF Hybrid Semi Cou r Rigid Probes Coupler Cables (Balun) 50 21 B c 3dBdi Figure 212 Balun connection diagram. 22 coupler should have less than 1 dB amplitude mismatch and 10 degrees phase mismatch between ports 2 and 3 were given to the vendor, Krytar. To verify the specifications, measurements were made on each of the 2 baluns pur chased from the vendor, each with varying results. The best of the two baluns was used throughout this work as the default balun. The mismatch in transmission coefficient mag nitude and phase for this balun with its semirigid cables may be seen in Figures 213(a) and 213(b). Minimum amplitude mismatch is more desirable, since the phase difference between the two different cables was used to compensate for excessive phase mismatch. (a) 0.80 S21S31 =Mismatch 0.60 c 0.40 E 0.20 (b) 0.00 14.0 19.0 24.0 W 182.0 ( S21S31=Mismatch ( 180.0 2 178.0 E 5 176.0  174.0 S 14.0 19.0 24.0 Frequency (GHz) Figure 213 Difference (mismatch) between balun ports 2 and 3 in terms of (a) magnitude and (b) phase. The semirigid cables in the UCATS have a wider function than just connecting the probes to a balun. As previously mentioned, the phase delay difference in between the cables are used to compensate for the phase mismatch of the balun. Thus, each balun has 23 its own "assembly" of semirigid cables. Figures 213(a) and 213(b) show both the defi nition of mismatch and the measured mismatch using the scattering parameters of the default balun assembly. 2.4 Calibration 2.4.1 Introduction When using a vector network analyzer, measurement apparatuses such as coaxial cables, probes, and transmission line transitions are often needed to connect the DUT to the VNA. These extraneous devices add error to the measurements due in part to internal mismatches, phase delays, and signal attenuation. Calibration is then needed to deembed the DUT's sparameters from the measured data. A typical calibration procedure involves measuring standardized loads with the extraneous equipment, and then comparing the load's measured sparameters with their factorymeasured definitions (standard defini tions). In this manner the sparameters of the extraneous devices are determined and then decoupled from the sparameters of the DUT. An example of twoport calibration method is the .\/,, t, Open, Load, Through (SOLT). A SOLT calibration is widely used for measurements involving 3.5 mm coaxial cables. It is performed by first measuring a .\l,N t, Open and 500 Load termination at the end of each cable. Next, the ports are connected together through their respective cable assemblies in the Through measurement. 2.4.2 Calibration in the UCATS For any twoport calibration procedure, it is vital to make a Through measure ment. The problem with the UCATS is that it uses two different types of transmission line antenna feeds: waveguide on the transmission side and RF SignalSignal (SS) probes on 24 the receive side. Currently, a calibration kit (standards and their definitions) exists for either the SS probes or the waveguide. However, no kit is commercially available for a twoport calibration using both transmission lines. As a result, all measurements performed in this work used the 3.5 mm SOLT method using the HP 85052A calibration kit. A reliable Through calibration was obtained using this method at the expense of deembedding the effects of the baluns, probes, and waveguides. The resulting DUT is shown in Figure 214. Port 2 180deg. RF Couple Probes Port Waveguide ,Mode Assembly Launc Figure 214 Sparameter reference planes in the UCATS (effective DUT). Due to the inclusion of the mismatch associated with using the baluns, probes, and waveguide assembly, the gain and S21 magnitude measurements taken in the UCATS were lower than the actual case by at least 1 dB. Some of the reasons for this degradation include attenuation in the waveguides and probes, and leakage radiation out of the probes and cable interfaces. Although the absolute gain measurements will be in error due to this calibration, the UCATS will still be able to accurately measure the relative gain across the 25 wafer surface. These types of measurement issues are discussed in more detail in Chap ters 4 and 5. The absolute S21 phase measurements were also be affected by this calibration. Propagation delay through the waveguides, baluns, semirigid cables, and probes added to a measured phase delay much higher than the true phase delay for the clock distribution system. However, only the phase differences across the wafer surface, not the absolute S21 phase, are needed to determine the clock skew. 2.4.3 Left versus RightHand Side Probe Stations Another calibration issue arises when measuring a wafer using both the left and right hand side probe stations and then comparing the data taken from each probe station. For these types of measurements, the same probe assembly (baluns, semirigid cables, and probes) is used to characterize antennas. When taking measurements on opposite sides of the wafer, the probe assembly must be taken off the probe arms, rotated 180 degrees, and then remounted on the opposing probe station (Figure 215).Because the differentialmode SS probes have been rotated in the process, measurements performed with oppositehanded probe stations will be 180 degrees outofphase from one another. Therefore, in order to compare measurements across the wafer's center line, 180 degrees must be added to the lowest set of S21 phase data of either the leftor righthand side. Lefthandedghthanded SS Probes.. + ASS Probes Safer center line Figure 215 Left and righthand side measurements across a wafer's centerline. CHAPTER 3 INTEGRATED RECEIVE ANTENNAS The application of integrated dipole and loop antennas to wireless links for clock distribution has been successfully demonstrated [KimOO, Flo00, and 098]. Accordingly, these antennas have been exclusively used as the receive antennas in the first testchip for use in evaluating the UCATS. The use of these integrated antennas has been continued here because of their small size, a fundamental consideration in microelectronic applica tions, and their balanced transmission line configuration. Thus, these antennas, particu larly the dipole antenna, are examined in order to understand measurement results of the interchip clock distribution system presented in this work. 3.1 Infinitesimal Dipole Antennas From the beginnings of antenna theory, the infinitesimal dipole, or Hertzian dipole, has been used as a benchmark for antenna design and an introduction to antenna theory in general [Bal97]. Furthermore, analysis of integrated dipole antennas follows directly from the analysis of this fundamental antenna. The Hertzian dipole is physically z (R, ,9) d IR y x Figure 31 Cartesian and spherical coordinate description of an infinitesimal dipole antenna. an infinitely thin rod of perfectly conducting material, which measures in electrical length much smaller than a wavelength of its exciting current. In terms of excitation, it is fed at the center of the rod, such that one arm of the dipole is 180 degrees out of phase with the other arm as in Figure 31. Starting the analysis, the vector potential can be used to define the magnetic potential. The first goal is to write down the vector potential in terms of the currents trav eling along the dipole. This is shown in (3.1). V.B = 0 B = VxA (3.1) The next step in the analysis process is to start with the description of the antenna as a source of electromagnetic fields. Application of a sinusoidallyvarying current of angular frequency (co), the angular global clock frequency, to the dipole antenna allows analysis to proceed with a wellknown equation (3.2) for the vector potential resulting from this current density [Jac99]. Here the primed position vector describes the distance from the origin to the source, while the unprimed vector locates the point of observation. PO ej(k (R R')) A(R, t) J(R) dv (3.2) 47r IR R' V Also in this equation, the wave vector (k) replaces the scalar wave number (k). The direc tion of k is the direction of propagation and its magnitude is equal to the wave number. This potential is more commonly known as the timeretarded potential [Ula99]. In this equation, the vector potential as a function of position vector and time A(R,t), is determined by integrating the current density, written in terms of its constant spatial dis tribution Io on the antenna, over the volume of the source. Also in the equation, R repre sents the relative distance from the dipole to the analysis point, k is the wave number, and 28 po is the permeability of free space, the medium for this analysis. This dipole's small size allows the integral to be easily solved for in the form seen in (3.3). j(kR at) .A(R, t) = R Iod (3.3) 4 7R 0 Next the equation is converted to spherical coordinates, and then (3.4) is used to deter mine the E and B fields. Here, c is the velocity of light in free space. 2 E(R, t) = cVx B(R, t) (3.4) JCo Now the field equations for all space and time can be written down in terms of spherical coordinates [Ula99], they have been recorded in (3.5), (3.6), and (3.7). Iodk j(kR ot) 1 j_ ER(R, t) 2T e 3 (k])3 cos (3.5) odkR 2KO4To) 1 j3 ER, 0 j(kR L + s in (3.6) 4L (kR)2 (kR) 4 7r IRe( k ) 23 S(R, t) =je(kR ot) J 1 2+ ] sin (3.7) B4(Rtr) I(kR) (kR)Z The zerovalued x and y components of A have forced the 0 component of E, and both the R and 0 components of B to vanish. Also, ro has been used to denote the freespace wave impedance of 377 Q. The field expressions for the Hertzian dipole over all space and time were solved analytically from the above integral expressions. This type of success is rarely paralleled for actual antennas. Often, the integrals are too complex to evaluate in closed form if the 29 same method of finding the retarded potential is used. In any case, simpler expressions are always found when the distance to the receiver (R) moves very far away, fulfilling the con dition of kR>> 1 in (3.5), (3.6), and (3.7). Exactly how far depends on the antenna. For the Hertzian dipole, this asymptotic farfield form can be directly observed as the terms of order R2 and R3 get vanishingly small. The resultant farfield expressions for the electric and magnetic fields can be seen in (3.8) and (3.9). jdl0kl0e j(kR cot) sin (38) E(R, t) 4R e s (3.8) PE6 B (R, t) = = B(R, t) (3.9) 110 In the near and intermediatefield regions, the radiation characteristics of the infinitesimal dipole contrasts with that for the farfield limit. Looking at (3.5),(3.6), and (3.7), and taking the limit as R goes to zero, we see that for the condition of kR<<1, the R1 terms vanish in significance next to the R3 term. It is convention to call this region the nearfield region. The region between these two asymptotes at kR1, forcing the inclusion of all terms, is called the intermediatefield region. As the radiated electromagnetic fields by the dipole are vector fields, they contain a fundamental direction, or polarization [Wan88]. It is convention to refer to the electric field polarization of the antenna as the polarization, since given an outward radiation direction [see (3.8)and (3.9)], the polarization of B follows. Thus, the polarization of the dipole antenna is in the z direction, parallel to the length of the antenna. The radiation in the farfield region is linearlypolarized, since the E and B fields are in phase with one another. 30 In the farfield region, the electric and magnetic fields are perpendicular to the R direction, which is the direction of power flow and the wave vector. In (3.10), the Poynt ing vector (S) has units of power density. Its timeaveraged form gives a real power flow towards infinity or radiation. S(R,t) = ExH (3.10) It should be noted that liberties may quite often be successfully taken using these limits. In approximating propagation in the intermediatefield region, invocation of either the near or farfield limit is sometimes justified for rough predictions if either limit is almost met. Such approximations were successfully taken in the past in clock distribution system analyses[Kim01]. These approximations will also be used in this work when cal culating the radiated Efield from the prototype transmitter of the UCATS at the wafer surface. This discussion is presented in Chapter 5. 3.2 Radiated vs. Input Power As time averaging of (3.10) gives the real power density at a distance R away from the antenna. Integrating over the area of the sphere formed by R yields the total power radiated. For the ideal case of a Hertzian dipole formed by perfect conductors, this power radiated is the same as the power input to the terminals of the antenna. However, imper fections in the conductors and application of the dipole to a silicon substrate complicate this situation. The power sent to the terminals of the antenna is, in general, not equal to the power radiated. A lumpedcircuit model may be used to simulate the power flow into and out of the antenna from an impedance standpoint. Power sent into free space via radiation can be modeled by a resistor, Rrad, the radiation resistance. The power dissipated by the substrate or conductors is similarly represented by a resistor with its value the same as the total power dissipated by the antenna. The circuit transformations shown in Figure 32 can be used to illustrate how the dipole antenna's input impedance models may be derived. V (a) Rrad Rloss (b) Figure 32 Various levels of small dipole circuit models: (a) ideal case and (b) finite conductivity dipole. Knowledge of the radiation resistance, dissipative resistance, and the spatial distri bution of the radiated power as a function of R translates directly to information on the radiation efficiency, directivity, and antenna gain. The typical engineering definition of efficiency is simply the power radiated divided by the power supplied to the two resis tances in Figure 32(b). Using the I2R definition of power, one can use the formula in (3.11) to represent the radiation efficiency for the simple series circuit in Figure 32(b). rad arad (3.11) rad diss The antenna directivity is determined by the fields description of the radiation. The directivity is a measure of the antenna's ability to focus radiated energy, as a conse quence, this value is a pure number often expressed in the (dB). The mathematical defini tions of the directivity are given in (3.12) and (3.13). Here, the average power density radiated (S,) at R, normalizes the maximum power density at the same distance (S,,m). S max D ma (3.12) S av D(O, ) S() (3.13) S av It is also typical to define a directivity pattern, which results from using the spa tiallydependent power density (3.13) instead of the maximum power density in (3.12). The normalization of S(0,0) versus its maximum value is customarily called the radiation pattern of an antenna. The antenna parameter which most directly relates to the measurements per formed in the UCATS is the antenna gain, which is just the directivity of an antenna scaled by the radiation efficiency. The physical definition is the power radiated over the power input to the antenna. These definitions are given in (3.14) and (3.15). The top equa tion shows how an antenna gain applies to an antenna operating in signal transmission mode with etx representing the transmitter's radiation efficiency. The abbreviation of tx and rx in subscripts will be used to denote parameters of the transmitter and receiver, respectively. Grad tx txDtx p (3.14) in G e D o (3.15) rx rx tx p . 17C Equation (3.15) depicts how to describe the gain of the antenna operating in receive mode. The power radiated is replaced by the power detected by the receiver at its terminals, and here the power input to the antenna is the incident radiation. Also, the receiver's radiation efficiency has been represented by ex. For the purposes of describing an RFlink, dependent on both a transmitting and a receiving antenna, a different description of gain may be used. In this case, the receiver antenna gain, transmitter antenna gain and the attenuation due to the spherical spreading of the freespace radiation are combined in (3.16) to form the system antenna gain (Gsys). G =G G (GxI (3.16) sys rx tx 4 R This equation describes the gain of an antenna system, which is perfectly matched at both the receive and transmit ports. In this special case, the system gain would be equal to IS212. Transmitter Receiver S(1 S112) 2(1 S22l2) Iin RI RL S1 R i P t2R F figure 33 Schematic for transmitterreceiver link visualization. Figure 33 Schematic for transmitterreceiver link visualization. 34 As a practical system of antennas with a finite amount of power reflection at either port, the UCATS must still be able to extract the system antenna gain out of the measured sparameters. These mismatch losses can be taken into consideration by revising (3.16) into the version seen in (3.17). This equation is illustrated in Figure 33 and represents the power traversing the reflection boundaries at the input or output ports. S21 2 = (1 S11 2)(1 S22 2)Gsys (3.17) This equation is called the Friis transmission formula (3.17), and has been widely utilized in the field of electromagnetic measurements to find an unknown antenna gain using a transmitting antenna whose gain pattern is known a priori. For the UCATS, the system gain without the extraction of the individual antenna gains is extensively used. In this work, the system antenna gain will be called the "gain". 3.3 Integrated Antennas in the UCATS The set of integrated antennas used in the UCATS represents the success of past research results [Kim00].[Kin91], and [Kat83]. Thus, the loop antenna was used along with linear, zigzag, and folded dipole antennas on a 20 Qcm substrate measuring 0.5 mm in thickness. These antennas have been photographed and shown in Figure 34. For a comparison between the antennas, the twoport sparameters were measured in the range of 2325 GHz, which is the default measurement frequency bandwidth of the UCATS. From the S]] data, the input impedance may be extracted using the formula given in (3.18), with Zo being the 50 Q characteristic impedance of the sparameters. (1 +S11) Z. = Z 111(3.18) in 0 1S Figure 34 Wafer photograph showing the integrated antennas used as the receiver in the UCATS. 1 100 L .3.5 24.0 24.5 25.0 23.0 23.5 24.0 24.5 Frequency (GHz) (b) Frequency (GHz) 25.0 Folded Dipole Input resistance (a) and reactance (b) for various .Long Dipole 'Loop integrated antennas. Small Dipole .ZigZag Dipole 150 U) c100 0 .L 50 U) v, Figure 35 The input resistance and reactance have been plotted versus frequency in Figures 35(a) and 35(b), respectively.Periodic resonances every 0.5 GHz can be observed in these plots. These resonances could be due in part to high coupling between the antennas on the test chip, or inaccuracies associated with the calibration [Bal89]. These plots also show that, for each antenna, the resistance peaks at the reactance zero crossings, corre sponding to resonance points. Over this bandwidth, the resistance of the folded dipole appears closer to the 100 Q characteristic impedance of the differentialmode probes and clock receivers. The same 2port sparameter data can be used to compare the gains among the dif ferent integrated antennas when using equation (3.17). These data were taken in the UCATS with a spacing of 3 inches between the transmitter and receiver. In Figure 36, it can be seen that the folded and zigzag dipole have the highest gain, depending on the fre quency of observation. Since its radiation pattern null is in the direction of the transmitter, the loop antenna had the lowest gain of all the measured integrated antennas. It was the gain data of Figure 36 which has led to the selection of the folded dipole as the prototype receive antenna used in the initial characterization of the UCATS. 35.0 40.0 45.0 0 Folded Dipole 50.0 L Linear Dipole (2 mm) Loop  Linear Dipole (1 mm) Zig Zag Dipole 55.03. 5. 23.5 24.0 24.5 25.0 Frequency (GHz) Figure 36 Comparison of the system gain using different integrated antennas as the receive antennas, taken at R= 3 inches. CHAPTER 4 PROTOTYPE TRANSMITTER AND WAVEGUIDE ASSEMBLY This chapter describes the prototype transmitting antenna used in the UCATS. As the antenna in question is a gaussian optics antenna (GOA), possessing a waveguide feed structure, this chapter also provides a quick guide to the applicable waveguide theory. The discourse then broaches the topic of GOAs and the type of fields they radiate. 4.1 Waveguide Assembly 4.1.1 Basic Waveguide Theory As the feed to the prototype transmitter is a waveguide, it becomes immediately neces sary to understand the characteristics of the electromagnetic fields inside a waveguide. Instead of a general treatment using an arbitrary waveguide, found in such sources as [Bal89], [Jac99], or [Col60], only the structure of interest to the measurement system, the rectangular waveguide (RWG) is considered. The coordinate system used for the discus sion is shown in Figure 41  I  z a a I Figure 41 Rectangular waveguide: coordinates, dimensions, and crosssection. Figure 41 Rectangular waveguide: coordinates, dimensions, and crosssection. This drawing replicates the crosssection of the type WR42 waveguide used in the UCATS, with the large lateral dimension (a) measuring 0.42 inches and the small lateral dimension (b) equal to 0.17 inches. Referring still to Figure 41, the four side walls together form the surface S, the transverse boundary. While the fields are confined transversely, the solution in the zdirec tion resembles that of plane wave propagation. Thus the functional dependence of the vec tor field expressions takes the form [Jac99]: E(x, y, z, t) E(x, y) j+(kz cot) H(x, y, z, t) = H(x,y) (4.2) Here the constant amplitude terms of the planewave field expressions become trans versely dependent functions [E(x,y) and H(x,y)]. By assuming steadystate, sinusoidal sources, Maxwell's boundary conditions, and the sourcefree forms of Maxwell's equations, the field expressions in Equation (4.2) can be solved for using the partial differential equation eigenmodeeigenfunction technique [Sni99]. The equation to be solved is of the form: V2 + k2 = 0 (4.3) Here y could be taken as the zcomponent of either E or H, depending on the mode of propagation. The transverse solutions are found by substituting the eigenfunctions into Maxwell's equations (B.4). As this solution is described in a vast number of microwave and advanced electro magnetics sources [Jac99], [Poz98], [Col66], [Bal89], the eigensolutions are just quoted here. The solutions can be classified into two forms: TE, where the Efield is expressed as being completely transverse to the direction of propagation, the zdirection and TM, where the Hfield is purely transverse to the zdirection. The eigenfunctions can be expressed as functions of constrained wave vector (kc) and crosssectional geometry (a, b): (mx'\ (ny1 z(x, y, z) Emnsinma b )s y) I Jk c(44) [H(XY,z ) H cos m7x Cos ny mn a eb In this above equation, the TM eigenfunction is represented by the top eigenfunction (Ez), while the TE eigenfunction (Hz) is displayed in the bottom entry. The eigenfunctions are in turn linked to their respective eigenvalues by the indices m and n, and the corresponding arbitrary constants (Amn and Bmn). The transverse vector component solutions and the dual field expression, can then be determined from the eigenfunctions using expressions derived directly from Maxwell's Equations [Jac99] (Appendix B). It should be particularly noted that only the TE eigenfunction can be nonzero for zerovalued modal indices, and even then, only one index can be zero at a time. The eigenvalues become evident when substituting the previouslylisted eigen functions into the original wave equation, (4.3). The constrained wave vector then relates the freespace wave vector (k) and the modal indices as kc= k2 k2 2r (4.5) k^ This expression reduces easily to the cutoff mode expression when evanescent modes are excluded [Col60]. This means that the square root argument must be greater than or equal to zero in (4.5). Now the expression for the lowest frequency that a mode can propagate down the wave guide, the cutoff frequency (fcmn), can be derived: jnn 1 (mn n f +ifAn I If(4.6) Here pL and e are respectively the relative permeability and relative permittivity. A signifi cant observation is that the TE mode can propagate at lower frequencies than the TM mode, since only the TE can have zerovalued m or n. When this result is applied directly to the measurement spectrum, 0.04526.5 GHz, of the UCATS, key statements can be made. First, only the TElo mode can be detected propagating inside this frequency band. The TE10 cutoff frequency was calculated at 14.05 GHz, while the cutoff for the next mode, TE20 was found to be 28.10 GHz. The word, "ideally", must be inserted in the above statements with the cutoff frequency value since all of the equations were derived for a section of waveguide with infinitely conducting walls. Also fabrication process variation, and measurement resolution can also be labeled as reasons for deviation from this ideal cutoff frequency calculation. If a waveguide is finite in length, capped by metal ends in the z direction, it becomes a resonant cavity. This means that the waveguide eigensolutions must include another indexed term in the zdirection, and the eigenspectrum becomes more complicated than before. However this represents a worstcase scenario, and since ideally both ends of the waveguide are matched in the UCATS, the eigenspectrum more resembles that of a waveguide than that of a resonant cavity. 4.1.2 CoaxWaveguide Transition The coaxwaveguide transition was used to transform the signal from the 3.5 mm coaxial test cables to the WR42 waveguide propagation environment required by the horn. This is conceptually illustrated in Figure 42. The particular coupling mechanism used in the assembly was a monopole probe. This device was selected for its efficient cou pling to the TElo mode [Pozar]. The complete analysis of this structure can be quite com plex, and is covered in such works as [Col60] and [Mar48], and is beyond the scope of this S > 3.5 mm Coax h Monopole Probe Figure 42 Simplified drawing of coaxwaveguide transition. work. The assumption that only the TElo mode has been excited greatly simplifies the analysis [Poz98] and a first order expression for the input resistance is given by the (4.7). R. k (k2k2)1/2 (4.7) in a f0 c Here, the height of the probe has been approximated to the first order of b. Also we have continued to use the freespace wave vector k, the permeability [go, and permittivity e0 of freespace, and the waveguide transverse dimensions (a and b). From (4.7) the scattering parameters can then be directly determined using basic microwave relations. SiI can be expressed as a function of characteristic and input imped ance. Furthermore, (2.5) can be invoked to find an equation for the transferred power, IS21 2, shown in (4.8). However, for the purposes of calculating the path gain in terms of S21 2 = 1 S 112 (4.8) the Friis formula, it has sufficed to simply measure the attenuation on the network ana lyzer, the results can be seen in Figure 43. The sparameters were measured by connecting two coaxialWG transitions together in cascade with the port reference planes located at the coaxial input of each tran sition. The attenuation through one coaxRWG transition was measured at 0.37 dB, this means that the attenuation through one transition would be about 0.2 dB. Return loss should be greater than 10 dB for onetransition, since the antenna is close to a matched load. 0.0 5.0 J 10.0 U0 15.0 14.0 19.0 24.0 0.0 10.0 S20.0 30.0 14.0 19.0 24.0 Frequency (GHz) Figure 43 Scattering parameters for two cascaded coaxRWG transitions 4.2 Prototype Transmitter The prototype transmitter consists of an abrupt junction mode launcher and the GOA. The mode launcher converts the modes from the TElo modes propagating in the rectangular waveguide to the TE11 and TM11 modes. The latter modes are needed by the GOA to launch gaussian waves, which resemble plane waves at sufficiently large dis tances. 4.2.1 Abrupt Junction An abrupt rectangularcircular waveguide transition has been built into the horn, mating directly to the rectangular waveguide described in the previous section. The abrupt junction first broadens its rectangular crosssection before abruptly changing to a circular waveguide crosssection. In terms of modes, this junction has been shown to excite the HE11 mode, a combination of the TE11 and TM11 modes, in the circular wave guide sec tion of the junction [Eng73]. This mode has been thoroughly researched in the past an effi cient mode for the production of gaussian beams [Cla69, Cla71]. 4.2.2 Circular Waveguide The transition to the circular waveguide necessitates the need to know the type of modes allowed by this structure. Like the previous section, the development of the field theory involves finding the eigensolutions which satisfy both the wave equation and the boundary conditions on the edge of the circular waveguide crosssection. As the detailed and complete solution may be found in most graduate electromagnetics textbooks, such as those listed in the previous section, here simply the solutions, showing first the eigenfunc tions in (4.9) in cylindrical coordinates (p,4,z) are summarized. E (p, t) A J(mnP Ez(, t) mnn m a eJ (kz cot)4.9) [Hz(p, z, t) = J '(mnpn Z(PB J ' mn m( a I The J(...) is the Bessel function of the first kind of order m, using the radius, a, of the cir cular waveguide in the argument forces the function to meet the boundary conditions at the nth zero (mn) of the Bessel function. Similarly, J'(...) is the derivative of the Bessel function of the first kind of order m. The ,n term is the nth zero for the same mth order derivative of the Bessel function. Linked to the eigenfunctions by the modal indices, the equations for the eigenval ues dictate the modes propagating above cutoff in the transmitting antenna. Following again the procedure outlined in 4.1.1, the TE eigenvalue equation is k = 2 (4.10) _2 k^ Thus, from the above expressions the modes propagating in the feed of the GOA are deter mined. The cutoff frequency can be found using the same procedure as in the rectangular waveguide case. 4.2.3 Gaussian Optics Horn Antenna The GOA consists of two main parts: the conical horn with tapered corrugation, or scalar horn, and the spherical lens which covers the scalar horn's aperture. The GOA and its components are shown in Figure 44. The horn antenna is, by itself, already a highly directive antenna, the addition of the lens only increases its ability to focus RF power. The ability of the horn to launch gaussian waves even in the near field is what has led to its selection as the prototype transmit antenna. The internal geometry which causes the HE11 spherical modes to expand to a gaus sian mode is the corrugation on the inside surface of the horn. Its corrugation teeth are lin early tapered from length (L1) to the shorter length (L2) located near the aperture of the horn. Also, the thicknesses of the teeth (tj) and gaps (wl) increase to t2 and w2 as the cor rugation approaches the aperture of the horn (Figure 45). Corrugated RWG Feed Abrupt Junction Dielectric Lens Figure 44 Gaussian lenshorn antenna shown with source and source impedance (Zs). Iti t1^ Lw1 >: t1 . Horn Lrt2 Aperture Circular WG Feed Figure 45 Tapered corrugation on one half of the conical horn antenna. The spherical modes propagating across the corrugation surface are readily expandable in terms of a GaussianHermite series. The radiated fields are also of this form, allowing the fields to be expressed in terms of gaussian modes even in the near to intermediatefield region [Pad87, Gol82]. From a geometric optics perspective, the gaussianspreading power in the farfield region can be represented by a gaussian beam of rays [Ped93]. The application of the lens Antenna to the antenna limits the divergence of the beam, increasing both the directivity and gain of the antenna. The application of geometric optics to submillimeter wave antenna design is termed quasioptical analysis. The GOA was designed, fabricated and tested by Milltech, LLC. Using the draw ings supplied by the manufacturer, the antenna was simulated using Ansoft HFSS, a finiteelements simulator. The results are summarized in Table 41. The maximum antenna gain measured by Millitech in their fullanechoic chamber was 17.7 dBi, given in decibels with respect to an isotropic radiators, while the finite element program calculated a gain of 18.5 dBi. For definitions of these farfield antenna parameters, [Bal89] or [Ula99] can be consulted. The Antenna Gain Pattern (AGP) in units of decibels with respect to an isotro pic radiator (dBi) is defined by (4.11). AGP is often plotted versus spatial 0 and 0. Figure B2 shows the AGP of the horn antenna as simulated in HFSS. In such a plot, HalfPower Beam Width (HPBW) can be directly determined by finding the amount of crosssectional angle in degrees the main lobe covers between the 3 dB points. AGP(O,) = lOlog( G( ) (4.11) iso Here G(0,4) is defined to be the transmitter's spatiallydependent antenna gain, measured at an arbitrary R value in the farfield. This gain is normalized by the gain of an isotropic point radiator (Giso) for the same distance. This difference between the simulated and calculated values of the GOAs maxi mum gain and HPBW's is considered acceptable in terms of a first order approximation. The difference stems mainly from the boundary conditions imposed on the finite element model of the horn and the exclusion of the corrugation. For reasons of convergence and simulation size in terms of a good aspect ratio [Sad91], corrugation inside the horn has been left out of the model. Keeping the corrugation in the model would cause simulation size to exceed available computer resource. Also, for simplicity the walls of the horn antenna have been defined as perfect electric conductors, or Ewalls. The finite element model has proven itself to be an acceptable computer model in approximating the farfield radiation of the GOA. The results of the farfield comparison can be seen in Table 41 below. This data tend to support the statement that the lens char acteristics tend to dominate the farfield characteristics of the GOA, which becomes important later in making gaussianbeam approximations. Table 41 Finite Element Model (FEM) vs. Measured Antenna Parameters for the GOA Parameter FEM Measured Difference Azimuthal HPBW 21 25.17 3.88 (Degrees) Elevational HPBW 24 27.23 3.23 (Degrees) Azimuthal Peak Gain 18.5 17.7 0.8 (dBi) Elevational Peak Gain 18.5 17.8 0.7 (dBi) The fields in the farfield region are much easier to calculate than the fields in the nearfield region for the GOA. Unfortunately, the UCATS operation is not in the farfield of the antenna, as per optical gaussian beam theory [Ped93]. Equation (4.12) shows the calculation of the farfield limit, RFF, The gaussian beam waist (see Figure 46), is the minimum width (wo) of the gaussian beam, and ) is still the wavelength.The beam waist 212 RFF k (4.12) in turn was found by using the farfield measurement data supplied by the manufacturer using (4.13). Here 0 is the same as the measured HPBW. 2h w0 (4.13) In summary, for a 1.25 cm wavelength and 1.81 cm beam waist, farfield measure ments should be taken at distances much larger than 8.23 cm, or 3.24 inches [Gol82]. Since measurements in the UCATS are limited in receivertransmitter separation to 7.5 inches, measurements taken using this system are in the intermediate to nearfield region. For approximation purposes, propagation in the intermediate to nearfield regions for a conical lenshorn with tapered corrugation can be put into gaussian mode form[Gol82]. For simplicity, coupling to higher order modes has been neglected. Using these approximations, the complex electric field solution can be written in the form of equations (4.14), the equation for the fundamental gaussian mode (TEMoo). EOWO jkz )z jkp2) x p2 2 E(p,z) e exp jatan exp ( exp 2 w(z) 2 2R(z) w(z) where: w(z) = w0+f 2 R(z) = z 1+ (4.14) (Az (4.14) It should be observed that both the phase and amplitude of the above expression have gaussian distributions. Therefore, both the phase and amplitude approach a uniform distri bution for large distances from the transmitter, as depicted in Figure 46. This approxima tion also involves placing the location of the beam waist at the beginning of the lens [Gol82]. The location of the beam waist determines the origin of the coordinate system. wafer GOA Origin Wo y z Figure 46 Gaussian mode radiation from the GOA. Using the knowledge that the GOAs radiation can be described according to gaus sian beam theory, an expression for power can be derived. Equation (4.15) is the result of using the timeaveraged Poynting vector relationship of (3.10) and Maxwell's equations (B.5). The Efield in this equation is the same as (4.14). This equation is the power in a plane wave (Ppw), where Zo is the wave impedance of free space. The results of these cal culations were used to compare with the measured data in Chapter 5. P (4.15) pw 2 Z With the gaussian mode equations of the GOA, it is then convenient to predict the measured power for two different transmitterreceiver spacings. Using Equations (4.13) and (4.14), spatial distributions can be plotted for both power magnitude and Efield phase with x and y as the dependent parameters for each constantz surface. These equations, however, should not be used to calculate the absolute gain between the transmitter and receiver. They do not account for the transmission through the wafer, standing waves between the wafer and lens, diffraction through the measurement aperture, or reflected 50 waves inside the antenna chamber. However, the gaussian mode equations are useful to predict the power and phase differences across the wafer surface. Conveniently, this type of difference analysis is what is most important for analyses of clock skew in a clock dis tribution system. Chapter 5 contains the results of the gaussian mode calculations the in the context of UCATS measurements. CHAPTER 5 PROTOTYPE SYSTEM MEASUREMENTS Utilizing the ultracompact antenna test system, measurements were performed using a testchip designed to characterize the planar quality of the wave form incident upon the chip in the context of wireless clock distribution. In addition, the data were taken in order to verify the measurement consistency of the UCATS. 5.1 Testchip Design The testchip used in this chapter was designed so that the spatial distribution of power across the wafer surface could be determined. The chip contained a 13 x 13 array of antenna cells. Each cell contained a collection of 6 different integrated antennas. The pres ence of the vacuum ring limited the total number of measurable antennas. Since portions of the wafer were covered by the vacuum ring (Figure 25), there were antennas which either fully or partially blocked by the vacuum ring. These antennas had impedance and ' I" iZ 1 ' ~   \ "' __1"1~~ ~ 7   .. . Measurement \. 7/ Aperture , , Footprint S.  Figure 51 Testchip layout showing measurement aperture. 51 52 radiation characteristics much different than those antennas in the more central cells and were omitted in the statistical analyses. The total array along with the footprint of the mea surement aperture, as shown in Figure 51. Note that each cell has been labeled by row and column in the array using a matrixstyle notation. 5.2 Spatial Wavefront Uniformity Measurements 5.2.1 Wavefront Uniformity Mapping at 3Inch Separation In order to verify the uniformity of the transmitted waveform, a critical parameter for clock applications, measurements were made on the folded dipole element in each cell. The collection of cells was chosen to be a 7x9 set of cells away from the edge of the vac uum ring. For comparison purposes, four antennas lying on the edge of the measurement aperture were included in some of the plots. Also, two sets of data were gathered: one with a receivertransmitter spacing of 3 inches, and the other at the UCATS' maximum spacing of 7.5 inches. The data were assembled into a series of spatial distribution plots of relative gain and phase in order to better visualize the uniformity. The spatial gain plots were extracted using equation (3.12) and the relative phase distributions were plotted directly as the phase of S21. All the data used in these plots have been normalized to the center cell, #66, and analyzed at 23.7 GHz, where the S]] of the transmitter is a minimum. Correspondingly, the phase also had to be normalized. Phase data on the rightside of the wafer was consistently 180 degrees outofphase with data on the leftside of the wafer due to the probing issues discussed in Section 2.4.3. The relative gain and phase data for a receivertransmitter spacing of 3 inches were collected and plotted in Figures 52 and 53. The gain from this center cell, was observed to be considerably higher in value than that of adjacent cells, by about 6.8 dB. The antennas lying over the edge of Figure 52 Spatial distribution of relative gain from center for 3inch separation (mean= 7.52 dB, standard deviation= 2.85 dB). Spatial distribution of relative phase for 3inch separation (mean = 30 degrees, standard deviation= 18.5 degrees). Figure 53 55 the vacuum ring, seen as the four corer points in Figures 52 and 53, were measured to have gain lower than the center by approximately 25 dB. Overall the average gain relative to the peak value at the center was 7.52 dB with a standard deviation of 2.85 dB exclud ing the four corner points. The phase distribution for the 3inch separation measurements varied in both the positive and negative directions from the central datum. However, the points which varied in the positive direction from the center were cell locations 64, 65, and 67. Again, the cor ner points deviated significantly at an average of 77 degrees from the center value. Alto gether the measurement statistics for the phase data amounted to an average relative phase shift of 30 degrees from cell #66 with a standard deviation of 18.5 degrees. 5.2.2 Wavefront Uniformity Mapping at 7.5Inch Separation Even though practical application of the wireless clock distribution requires the receiver and transmitter to be placed at a minimum distance from one another, for compar ison it was useful to perform the same measurements at a distance closer to the farfield of the transmitter. The distance of 7.5 inches was chosen because it coincides with the maxi mum range possible in the UCATS. However, the low S21 measured at this spacing, from the range of (between 45 and 58 dB), meant more variance in the measurements due to the closer proximity to the 75 dB noise floor of the measurement system. The spatial dis tribution pattern of the gain (Figure 54), like its 3inch separation counterpart, was peaked at the center cell of the measurement array. However, the rest of the distribution did not fall off in the same monotonic manner as the data set in Figure 52. Instead, there was a set of peaks and nulls located just outside the center, varying about 3 dB from crest to trough. Nevertheless, excluding the edge points located on the edge of the measurement Figure 54 Spatial distribution of relative gain for 7.5inch separation (mean= 3.77 dB, standard deviation= 2.90 dB). Figure 55 Spatial distribution of relative phase for 7.5inch separation (mean= 15.6 degrees, standard deviation= 10.5 degrees). aperture, the data did have less variance than the 3inch data with a mean relative gain of 3.77 dB and a standard deviation of 2.90 dB. Interestingly enough, the corner points var ied less from the center than the first set of data, ranging from 10 to 20 dB down from the center. Correspondingly, the phase data also saw a set of minima and maxima, distributed around the center point. Also following in the same trend as the 3inch separation data, the positive deviation was clustered around the center, with cell #67 having a value of 12 degrees above the center point. The mean for this set of data was 15.6 degrees phase delay relative to the center, while the standard deviation was 10.5 degrees. 5.2.3 Estimated Clock Skew from the Uniformity Data One of the defining metrics in the analysis of clock distribution systems is the clock skew. Therefore, it is desirable to be able to determine the total clock skew of the transmitterreceiver system under test inside the UCATS. Finding a conservative estimate for clock skew of the prototype GOA/folded dipole combination involves simply deter mining the range of deviation, dividing by 8, and then dividing by 360 degrees to find the clock skew as a percent of the period. The factor of 8 in the denominator is due to the fact that the current wireless clock distribution receivers feature a divideby8 counting archi tecture. Using the data from the uniformity measurements in the previous sections and the formula for clock skew, explicitly written in equation (5.1). Skew (MaxMin\ 0 (5.1) 8 360 J Clock skew for the prototype system may now be determined. Equation (5.1) only calcu lates skew based on phase data, the fact that skew may also be dependent on the signal amplitude deviation across the wafer is also concern. This, however, is left for future work, as it is currently believed that the skew is much more sensitive to phase mismatches. The result of the skew calculation at 3 GHz has been tabulated in Table 51. A clock skew of 1.7% of the period found for the 7.5inch separation data and 3% clock skew was calculated for the 3inch case. Both are well within the current skew tolerance limits for microprocessors. In addition, these skew values represented synchronization over a 3.8 cm x 3.1 cm area at 3 GHz, which is a much larger area than previously thought possible. Table 51Clock skew for prototype external clock distribution system Measurement Mean Range Skew Set (Degrees) (Degrees) (% Period) 3 inch 15.6 75 3.0 7.5 inch 10.6 50 1.7 5.2.4 Comparison with Gaussian Beam Theory and FEM Simulations The gaussian mode equations of the lenshorn antenna (4.14) can be used with varying success to predict the measured wave fronts detected when the folded dipoles are probed. The varied success may be particularly seen when the data collected during the previously described uniformity measurement sets at 23.7 GHz are organized by rows and compared with the plots according to equation (4.15) using the coordinate system defined in Figure 45. The results of this comparison between the gaussian optics (GO) and FEM calculations and the measured data for row 6, gain and phase, have been plotted in Figures 56(a) and 56(b), respectively. There were two sets of measured data, corresponding to 5.0 10.0 15. Figu 60 the data taken from probe stations on opposite sides of the wafer. For these two plots the measured data correlated more with the calculated towards the edge of the wafer, and the correlation was the worst when the distance from the wafer center (p) ranged between 0.5 to 1 cm. a) (b) 10.0 5.0 0.0 5.0 10.0 15.0 20.0 25.0 30.0 GO 35.0 GO RightSide Probe 40.0 e RightSide Pro LeftSide Probe LeftSide Probe FEM 45.0 FEM 50.0 2.0 1'.0 0.0 1.0 2.0 55.2.U 1.U UU 1.U 2 Distance from Center (cm) ire 56 Center row comparison between GO calculated, FEM simulated, and measured (a) gain and (b) phase at 3inch transmitterreceiver spacing. In addition, these plots show that the FEM simulations agreed much better with the measured phase data than the gaussian optics calculations with the exception of the p=1.9 cm points. The FEM phase simulations on the edge of the wafer were possibly affected by edge currents, which were caused by edge diffraction in the FEM model (Figure B4). Conversely, the GO calculations were largely in error for the middle three data points, but more closely matched the measured data at the edge points. (This disagreement between the GO calculations and the measured data was expected since the gaussianbeam calcula tions did not account for any reflected signals or standing waves between the wafer and lens.) 0.S The rest of the rows are plotted against their respective GO and FEM calculations in Figures 57(a) and 57(b). The difference between the measured curves and the GO cal culations is smaller as cell rows farther from the center are plotted. The GO calculations shown in these figures were slightly better at predicting the measurements since the stand ing wave magnitude has decreased in this region. However in each set of plots, the differ ence between the GO calculated and measured phase was always much higher than the gain differences.Overall, the FEM calculations were better than the GO calculations at predicting the measured gain and phase variations across the wafer. a) 0 10 ~5~10 30 5 108 FE 40 2.0 .5 20 10 0.0 1.0 20 2.0 1.0 0.0 1.0 2.0 10 5 51 c4 / GO Calculated (D (D06 Right Side Probe 25 Left Side Probe \  8 FEM Y 35 10__________________ 45 2.0 1.0 0.0 1.0 2.0 2.0 1.0 0.0 1.0 2.0 Distance from Center (cm) Distance from Center (cm) Figure 57 Measured versus GOpredicted gain and S21 phase values at (a) row 7 and (b) row 8 at R=3 inches. 62 The data for the R=7.5inch separation measurements appeared to be less con forming to calculations, possibly suggesting other interfering phenomena, such as reflected waves in the isolation chamber, or diffraction through the measurement aperture (Figure 58). In addition, due to computer resource limitations and convergence difficul ties, the 7.5inch separation case could not be simulated by FEM. (a) 0 20 2 10 S 6 10 8 20  (b) 1.0 1.0 0.0 1.0 2.0 3.0 1.0 0.0 1.0 2.0 4 .40 2 20 0 0  2 a 20 42.0 1.0 0.0 1.0 2.0 42.0 1.0 0.0 1.0 2.0 5 35 25  0 m 15 15 \ 5 E15 10 25 2.0 1.0 0.0 1.0 2.0 2.0 1.0 0.0 1.0 2.0 Distance from Center (cm) Distance from Center (cm) Figure 58 Gaussian calculation comparisons Cal Calculated for R=7.5 inches: (a) row 6, (b) Right Side Probe row 7, (c) row 8. Left Side Probe The diffraction could come from the currents excited around edge of the measure ment aperture by the transmitted wavefront. At the R=3inch separation, this was not a problem, since the transmitted beam did not sufficiently spread from its beam waist diam eter to excite these edge currents. At R=7.5inches a wider, more plane wave beam is transmitted by the GOA, inducing edge currents in the absorber around the measurement aperture. From electromagnetic theory [Jac99], significant currents circulating around the edge of an aperture on an opaque screen (transmitter platform) are sources for diffraction. However, more work is needed to fully understand the differences between the measured and simulated data. 5.2.5 Standing Waves When R= 3 inches (Figures 56 and 57), the disagreement between the GO calcu lations and measured data can be reconciled when one assumes the existence of a spa tiallyconfined standing wave. This standing wave, thoroughly researched in laser resonators [Ver89], is created between the wafer and the lens inside the UCATS (Figure B4). Due to the curvature of the lens and the planar boundary formed by the wafer, Efield waves incident upon the center of the lens are gradually guided with each lensreflection away from p=0, towards the absorbing walls in the antenna chamber. Inter ference with other waves, including the direct path, is limited to only a few passes. Thus, the standing wave is confined in space, and is responsible for a series of minima and max ima across the wafer surface. Since the GO calculations assume only oneway propagation along the LOS path, only the FEM simulations were of use in describing this effect. The simulations for the 3inch separation case showed that there is a variation in power and phase over the surface of the wafer in agreement with the measured data (Figure 55). However, for the R=7.5inch case, due to computer resource limitations, the standing wave could not be simulated using finite elements. 5.2.6 Right versus LeftHandSide Measurements In order for the UCATS to be a useful measurement platform, the measurement offsets using the right versus lefthand side (RHS versus LHS) probe stations, which allows mapping of a 3.8 cm x 3.1 cm area, must be analyzed. This analysis can be per formed by checking the center row. Since a probe mounted on one of the two opposing probe stations can reach exactly half of the wafer plus the center row, measurement offset may be studied by performing center row measurements from probes mounted on each side. As the measurements from each side are performed at different times, under different calibrations, and with different probe landings, this can also be seen as a way to gauge measurement robustness in the UCATS. The data for the maximum and average gain and phase differences across the rows for both separation distances have been included in Table 52. Table 52 Centerrow reliability check data Max. Mean Separation/ Max Ma. Diff e Location Difference Parameter Difference (cell #) (Offset) 3"/ 2.55 #62 1.35 Gain (dB) 3"/ 13 #63 5.5 Phase (deg.) 7.5"/ 3.05 #67 1.2 Gain (dB) 7.5"/ 31 #68 13 Phase (deg.) 65 5.3 FrequencyDependent Measurements 5.3.1 Measurement Dependence on Probes For an acceptable measurement set across the wafer surface, the impedance of the transmitter should not be changed upon varying the location of the probes on the wafer surface [Rep88] and [Pet93]. The S11 has been measured for various probe locations across the wafer at the two separations used in the uniformity measurements. This can be used to investigate the probetransmitter coupling effect (Figure 59). The transmitter's 0.0 5.0 10.0 15.0 20.0 0.023.0 23.5 24.0 24.5 25.0  10.0 CO cE 20.0 30. 230 .0 23.5 24.0 24.5 25.0 0. R= 3 inch 5.0 ... R= 7.5 inch 10.0 15.0  2002 Uo 2..5b 24.0 24.5 25.0 Frequency(GHz) Figure 59 SII stability for various samerow cell locations: (a) R = 3 inches, (b) R = 7.5 inches, (c) no wafer. 66 return loss data are affected by less than 0.5 dB for different probe locations. Also shown in this figure is the shifting of the 24.5 GHz null as the distance is increased from R=3 inches to R= 7.5 inches. Figure 59 (c) shows how the S11 of the GOA decreases by about 4 dB when there is no wafer on the vacuum ring. This is a clear indication of the presence of a standing wave, since with a wafer over the transmitter, there would be a significantly larger amount of the power reflected back into the GOA. 5.3.2 Frequency Dependent Gain Data As indicated in the wafer uniformity data, the frequency dependent gain of the folded dipole varied significantly from one cell location to another. Going down a row on the test chip, the gain towards the center of the wafer tended to be peaked at 23.7 GHz, the frequency of uniformity analysis and the resonant frequency of the transmit antenna (a) 30.0 40.0 : 50.0 60.0 S 260.0 .0 28.5 24.0 24.5 2,.0 (b) _jn n I  I * 50.0 C0 uu.23.0 23.5 24.0 24.5 25.0 Figure 510 Frequencydependent gain plots for: (a) R = 3 inches, (b) R= 7.5 inches. (Figure 510). Also in each plot, on every cell location, there are frequencydependent nulls.Furthermore, the location of the nulls changed for different cell locations. Finally, as in the uniformity data, there was more gain variation across the frequency range when the separation distance is increased to 7.5 inches. The data for cell location 61, previously left out of the uniformity data, have been included in Figure 510 for comparative purposes. Compared to cell locations not border ing on the aperture edge, it had the poorest gain over the frequency band, the steepest dip of all the cell locations, and a much higher phase delay (Figure 511). The high phase delay was observed due to its proximity to the vacuum ring. In order for the signal to be (a)200 c 200 U) C 400 600 23.0 23.5 24.0 (b) 0200  ( 400 Cell 61 Cell 62 Cell 63 e.600 . Cell 64 Cell 65 803.0 23.5 24.0 Frequency (GHz) Figure 511 Frequencydependent S21 phase plots for: (a) R= 3 inches, (b) R=7.5 inches. 68 detected by this antenna, part of the signal had to propagate through the dielectric vacuum ring with a higher permittivity. The reasons for the significant variation in the gainfrequency plots could be a combination of coupling between the antenna elements, measurement reliability, standing wave effects, or resonance in the isolation chamber. Figure 512 shows another collection of gain data, which further illustrates the gain variations. These plots contain the same trend as both of the gainversusfrequency plots in Figure 510: the gain decreases in over all magnitude for cell sites farther from the center. In Figure 512(b), both the gain and (a) 30.0 40.0 _ c 50.0 60.0 23.0 23.5 24.0 24.5 25.0 (b) 40.0 45.0 50.0 Cell 62 ", Cell 82 = Cell 63 55.0 Cell 83 Cell 86 Cell 86 60.0 23.0 23.5 24.0 24.5 25.0 Frequency (GHz) Figure 512 Columnwise comparisons of frequencydependent gain data for: (a) R= inches, (b) R= 7.5 inches. null magnitudes increase along all three columns as the row number changes from 6 to 8. The relation between the data of Figures 512 and 510 further emphasizes the need to identify the sources of the nulls at the 7.5inch separation, since the null severity and gain degradation increase with distance in any direction from the center cell. 5.4 Measurement Summary 5.4.1 Uniformity Measurements As discussed earlier, spatial plots of relative gain and S21 phase at two different receivertransmitter separations were assembled with the purpose of determining the uni formity of the transmitted wavefront. The data were collected by individually probing the folded dipole antennas in each cell over a 3.8 cm x 3.1 cm area on the test chip. The statis tics are summarized in Table 53 below along with the offset for RHS versus LHS probe measurements. All data are referenced to the center cell measurement. The data indicate that, when fit to a unimodal normal distribution, the shape of the gain distribution is roughly the same for each separation value. However, measured gain for the 3inch sepa ration varied more on average than the data for the 7.5inch separation. For the phase data, the uniformity improved in both shape and average deviation when the receiver is moved from 3 inches to 7.5 inches away from the transmitter. Table 51 Uniformity statistics for relative gain and phase Separation/ Mean LHS/RHS Max a 30 Parameter Deviation Offset Min 3" 7.52 2.85 8.55 +/ 1.5 14.7 Gain 3" 30 18.5 55.5 +/ 5.5 97 Phase 7.5" 3.77 2.90 8.7 +/ 1.2 13.6 Gain 7.5" 16 10.5 31.5 +/ 13 51 Phase From the phase data, the clock skew was calculated assuming a divideby8 receiver architecture. Measurements taken at R=3 inches yielded a skew of 3.0%, while. measurements for full separation (R=7.5 inches) corresponded to a skew at 1.7% 5.4.2 Uniformity Measurements versus Predictions There was only partial agreement of the above measured data with the theoretical gaussian optics (GO) calculations at the 3inch separation due to the proposed presence of a standing wave confined to the center of the wafer. The data agreed better with the GO calculations when the data were analyzed along row 8, the row farthest from the center row. There was little agreement between the GO calculations and the data taken at row 6, the center row of the wafer, except at the edges of the wafer. However, the simulations per formed using the finite element method (FEM) agreed better with the phase data in the central region of this row. In fact, overall the FEM calculations agreed with the measured data much better than the GO calculations. This can be seen when the measured gain and phase are plotted with the two calculation methods along row 7 and row 8 (Figure 57). The gaussian calculations did not have any correlation with the data when the sep aration was increased to 7.5 inches. Also, because of the prohibitive size, no FEM solution could be generated at this separation. The lack of agreement between the GO calculations and the data could possibly stem from diffraction through the vacuum ring aperture, or reflected waves and resonances inside the antenna chamber. 5.4.3 Frequency Dependence When the gain was analyzed versus frequency, the measured data between the two different separations became even more disparate. In both row and column analysis, the gain plots for R=7.5 inches showed that there were frequencydependent nulls, which 71 became worse for increasing distance away from the center cell. For both separation plots the gain magnitude over the entire bandwidth decreased as the distance from the center of the wafer increased, in agreement with the uniformity data. The measured S11 data for both separations showed how probing different loca tions minimally influenced these measurements. However, the Si1 was strongly influenced by the separation distance. CHAPTER 6 SUMMARY AND FUTURE WORK 6.1 Summary An ultracompact antenna test system (UCATS) has been developed for specific application to externallytransmitted clock distribution systems (ECDS) operating at the global clock frequency range of 1426 GHz. Some of the userfriendly features included continuouslyvariable receivertransmitter (RXTX) spacing, modular vacuum ring design, and compatibility with standard vector network analyzers and RF probe stations. The UCATS is also the first known near to intermediatefield electromagnetic measure ment environment in terms of its small physical size relative to frequency bandwidth, the use of a denselypacked (spacing< [Wan88, Pet94, and Rep88]. In order to characterize the measurement system and to provide a benchmark for future designs, a prototype ECDS was also designed as part of this work. A gaussian optics horn antenna (GOA) was used as the transmitter due to its capability of emitting gaussian waves, which closely approximate plane waves. An array of integrated antennas typically used in wireless clock receivers were used as the receive antennas. From initial measurement results, the folded dipole was chosen as the default antenna for characteriza tion of the UCATS. Measurement results using the UCATS showed promising results for the measure ment set collected at a spacing of 3 inches. To facilitate usefulness to clock distribution development, data were expressed as relative gain and phase to those of the wafer center. The measurements along array rows showed agreement with the gaussian beam theory. However, the agreement was better for data from the cell rows away from the middle of the wafer, particularly along row 8. Data from the center row was largely different than the GOcalculated data, suggesting a standing wave between the wafer and lens. Finite ele ment simulations confirmed these assumptions, and overall agreed better with the mea surements at the center row than the GO calculations. Measurements at this range showed a clock skew of 3% at 3 GHz over a 3.4 x 3.1 cm. This was well within the suggested 10% global skew tolerance over an area well beyond the current or projected size of micropro cessors [SIA01]. The measurements performed at an RXTX spacing of 7.5 inches, the maximum separation allowed in the UCATS, were both promising and surprising. Unlike the results for the 3inch case, the measurements strongly disagreed with gaussian beam predictions. However, even with this variation, the results yielded a measured clock skew of 1.7% over a 3.4 x 3.1 cm area. In conclusion, the UCATS proved to be a reliable platform for ECDS characteriza tion. The fact that the antenna measurements agreed better with the underlying theory for decreasing receivertransmitter spacing, should not mitigate its usefulness to the micro processor industry. In fact, in a practical ECDS, the transmitter should be placed at a min imum distance from the receiver for compactness, making decreased spacing desirable. Measurements taken with a prototype interchip clock distribution system suggest that it may be possible to increase the size of multiGHz synchronous systems well beyond what is currently believed possible 6.2 Future Work There is much work which could improve the performance of wireless clock distri bution using the UCATS. Such efforts could include an improved vacuum ring design to eliminate multipath, numerical algorithms such as wavelets to increase standingwave analysis capabilities, and investigation using further wavefront uniformity mappings at a wider range of RXTX distances. Finally, the inclusion of a matching layer below the wafer could effectively take out the dependence on the spatiallyconfined standing wave. In addition, the task of developing the transmitter and receiver for the interchip clock distribution systems is also a critical area for future development work. Fitting a longer electricallength antenna into a smaller area is still an open task. Possible antenna structures include logperiodic and fractal antennas. Likewise, further work studying the feasibility of the ECDS could prove to be technically challenging. Such work would eventually involve the insertion of the heatsink and packaging between the receiver and transmitter link. The continued development of external clock transmitters should proceed in line with the feasibility studies. Practical transmitters should be more planar in structure than the lenshorn combination prototype used in this work, making their size easier to fit inside a computer system. Such structures could include microstrip arrays, which could give the freedom of aligning gain maxima with receivers. APPENDIX A DRAWINGS FOR THE ULTRACOMPACT ANTENNA TEST SYSTEM A. 1 Engineering Drawings for the UCATS The assembly drawings are shown here as they were sent out to the machine shop. All parts were fabricated in Aluminum, except for vacuum ring, which was fabricated in polyethylene. Graphics may appear distorted, since they have been reshaped to fit the for mat of this document. In addition, photographs of the assembled UCATS are shown in the final section, A.6. /    / 6 4" 5" 1/4 I 1/4" 7" 6.125 2" 1 I I 14" l 25 6.12 2" I 1.5" 3" 3" In 3.5" 1.5" I 13.25" 0.5" Figure Ai Isolation chamber sidewalls. Figure A2 II/ I11i  Backpanel of isolation chamber. Top View 6" I 4 0.5" Top view of backpanel. Figure A3 <" + + + Figure A4 Frontpanel of isolation chamber with access door. 1.25" (typical spacing) 2.75" 44 ow 0.75"spacing from edge typicaF 12.25" ~ 9/16 smoot bored hole Figure A5 Transmitter platform. 41 wo 1/8" diameter circular groove IXCB holes drilled completely through part Figure A6 Vacuum ring. 7/16" 1 1/a6" diam. hL 1/8" diam. hemispherical groove (h. g. ) I i 1/16" diam. h. g.  ( for Oring) 1/8" diam. screw drilled 1/4 "sdwy (countersunk) 1/8" h. g. 5/16"  . (note all measurements on grooves are the same as XCA Vacuum ring cross section. 0.5" XCB Figure A7 1.5"  3/4" I I I 3/4" t 2" 3/4" 0.5" Top View to accommodate 6 1/2" diameter SHC screws Figure A8 Threaded "L" steps. 1.25" I 2.5" 3/4' .M Figure A9 Vacuum ring platform. 3.5" ,, /Ai" 0.5" 11 2.25" diameter hole 0 4.125" diameter cut 4 C ZI 0 rC C) *1 Q 0 C) 00 I A.2 Photographs of Assembled UCATS The UCATS was photographed, and the results are shown below in Figure A1. The top panel of the antenna chamber has been taken off to reveal the GOA transmitter on Figure A11 Photographs of the assembled UCATS: (a) inside the antenna chamber and (b) topdown view showing through the vacuum ring. 85 the transmitter platform, surrounded by absorber [Figure A1 l(a)]. Figure A l(b) shows a topdown view of the UCATS. Here, the transmitter can be seen through the measure ment aperture in the whitecolored polyethylene vacuum ring. APPENDIX B FINITE ELEMENT SIMULATIONS B. 1 Electromagnetic Application of Finite Elements B. 1.1 Introduction to the Theory of Finite Elements The theory of finite elements was originally applied by civil engineers to the anal ysis of structures. However, this numerical technique for solving partial differential equa tions has been generalized to all engineering fields. In electrical engineering, this technique is used to provide numerical solutions to Maxwell's Equations, (Eq. B.1), in 3dimensional physical space. The sources, or particular solutions to the partial differen tial equation, are represented by p, the charge density in the medium, and the current den sity source, J. VB = 0 VxE = at V D = p VxH= J+D 6t (B.1) Now the constitutive equations (B.2) are used to express in terms of the H and E fields. Here a has been taken as the conductivity of the domain being analyzed. J = aE D = eE B = pH (B.2) Using this relation between J and E, assumption of a timeharmonic current density source, the complex permittivity, C' in (B.4), and the timeharmonic field = e+j (B.3) expressions, Maxwell's equations may be expressed as (B.4). Note that p has disappeared. It is assumed that our system is purely electrodynamic, or no initial charge exists prior to source application. V pH = 0 VxE = joctH V. E = 0 VxH = jo'E (B4) With this suggestive form, Maxwell's equations condense into the vector wave equation, (B.5). In this equation, k is the same as o2pe. This is the partial differential equation to which the software package, Ansoft's HFSS, now applies the finite element method. Vx(Vx E) kE = 0 (B.5) The finite element method starts by projecting the above equation over the domain of analysis (Q) using a collection of weights (W,), for example, the lenshorn antenna, as in (B.6). The domain discretizes into N small tetrahedronshaped subdomains (Qi), or finite elements. N Sf [Vx (Vx E) k2E] W = 0 (B.6) i= li The space spanned by the projecting basis functions is typically a piecewise poly nomial space [Bre94], and must adequately represent the variation of the fields over each small tetrahedron. For a given, nontrivial, field distribution, the choice of a simple basis function implies decomposition into a larger number of elements than a more complex basis function. In other words, the solver must be able to write the Efield locally on each subdomain in the form of(B.7). N E = x nW (B.7) n= 1 In order to incorporate surface boundary conditions (BC) into the solution, (B.8) can be written, with the help of Green's theorem, in the form of (B.8). The boundary inte gral is evaluated over the surface of the domain (8&). (B.8) (Vx W ) (Vx E) k2 (E W )] d = BCdQ The software then solves for the fields by using the expansion of E, with (B.7) in (B.8). Equation (B.9) represents this development. (B.9) I x [(Vx W ).(Vx W k2(WW W)]d d = BCdQa This equation, summed over m and n, enables matrix formulation of the form: Ax=b with x and b as column vectors. Solution of this equation is the Efield distribution over the entire domain. B. 1.2 Convergence by Error Analysis Because the initial mesh, or decomposition of the domain into subdomains, might not lead to an acceptably accurate solution, a mesh must be refined to obtain a more accu rate solution. The analysis of the error and remeshing of the domain into smaller subdo mains allow this eventual convergence upon the desired solution. The software computes the percent difference in power of the fields, AS, after each mesh. If the percent difference in the fields is equal to or less than the userdefined stopping criterion, the remeshing stops and the field solution after the last mesh is the final solution to the problem. B.2 Simulation of Prototype Transmitter B.2.1 Model The gaussian lenshorn antenna, in order to verify manufacturer specifications, was drawn inside Ansoft HFSS using its CADstyle interface. Due to the symmetry of the structure, and the resulting symmetry of the fields inside, it was necessary to draw only half of the structure, and in fact it could also be done with a quarter of the system. Figure Bl shows the simulated system. Port (and origin) z omLens (Rexolite) I Horn r= 1.25 1 (Perfect E) PMLxyz PMLyz The prototype transmitter, as drawn inside Ansoft HFSS. Figure Bl B.2.2 Sources and Boundaries The model, drawn above in figure Bl, was then assigned a set of boundary condi tions. The crosssectional plane of the model was given the Hsymmetry boundary. When this boundary condition is applied to a surface, HFSS assumes symmetry with respect to the selected surface, keeping the Hfields tangentially continuous across either side. Next, the inside of the horn was designated a Perfect E boundary, effectively making this surface a perfect conductor and forcing the Efields to be normal at this boundary. Also, the wall framing the lens and horn aperture was also assigned a Perfect E boundary. Around the lens, a bounding box of Perfectly Matched Layers (PMLs) were placed. These boundaries, drawn and defined automatically using a macro inside HFSS, have been developed by Ansoft to efficiently solve for radiated fields from an antenna. The notation, xy,xyz,x, etc., has been used to designate the axis of anisotropy, as the PMLs are basically a virtual anisotropic material. Finally, the semicircular cap at the end of the horn was assigned a port designa tion. This source has been defined as an ideal waveguide source, exciting the waveguide feed of the horn, as if the waves were sent from an infinite distance away. In each simula tion, excitation control of the entire model is given to the port source. B.2.3 Single Frequency Simulation at 23.7 GHz A single frequency simulation at 23.7 GHz was performed in order to find an accu rate field solution at the UCATS frequency of analysis. A convergence value of 0.001 W/ m2 using 40,000 tetrahedra was achieved using this model. The results are summarized in Table 41, but the phi and theta plots for the antenna gain pattern are shown in Figures in Figure B1. 20.0 15.0 10.0 5.0 0.0 5.0 10.0 15.0 20.0 25.0( 20.0 Phi (degrees) Antenna Gain Pattern (AGP) plots for (a) 0=90 degrees, (b) 0= 90 degrees in spherical coordinates. Theta (degrees) Figure B2 92 B.3 Standing Wave Simulations Instead of analysis using complicated special function theory, the standing wave inside the UCATS was investigated using Ansoft HFSS. This was accomplished by the inclusion of the wafer into the model used in Section B.3, and reduction to half of the model size using symmetry. The new model has been defined as in Figure 52. However, X .Z Ix Surrounding PMLs (Ideal Absorber) virtual boxes (Iused to optimize source meshing) I 1,4 of \\ afei lenshorn symmetry combination planes Figure B3 Impedance BC at wafer surface y Finite element model used to simulate R=3inch separation case inside the UCATS. due to its larger size compared to the previous model of only the lenshorn antenna, the convergence criterion was relaxed to under 0.008 (W/m2) in order to prevent overflow of 93 computer resource. In Figure B4, the phase and power of E is plotted versus the dis tance from the wafer. The increase in the gain around 2 cm is what was referred to as the gain due to the diffractioninduced currents in Section 5.2.5 130.0 Figure B4 Distance from Wafer Center (cm) Plot of EO 's power and phase over lateral dimension of wafer. Next, the spatial distribution of Efield strength across the simulated wafer is shown in Figure B5. Note, again, that the maximum shown at the edge of the wafer did not corroborate with the measured data, and could be a simulation artifact resulting from the fact that our wafer is "suspended" in free space in the model. Therefore, this area of high field strength in the simulator could be due to the edge diffraction of the incident radiation around the edge of the wafer. . . uII.ECr' m 3 Figure B5 Distribution of FEMsimulated Efield strength across the area of the wafer. Figure B6 shows a spatial distribution on the xz plane of the typical minima and maxima associated with standing waves along the ydimension between the wafer and GOA. The power and phase of the standing wave are plotted singledimensionally versus y in Figure B7. 