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AN ULTRA-COMPACT ANTENNA TEST SYSTEM AND ITS ANALYSIS IN THE
CONTEXT OF WIRELESS CLOCK DISTRIBUTION
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
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
ACKNOWLEDGMENTS ................. ............................. ii
ABSTRACT ......... ........................................ ......... vi
1 INTRODUCTION .................................................1
1.1 Emergence of W wireless Interconnects ............................ 1
1.2 Intra-Chip Clock Distribution ............... ..................1
1.3 Overview of Thesis. ........................................... 6
2 ULTRA-COMPACT 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 Frequency-Dependent Measurements ............................ 65
5.4 Measurement Summary ..................................... .69
6 SUMMARY AND FUTURE WORK ..................................72
6.1 Summary ...................................................72
6.2 Future Work .................................................74
A DRAWINGS FOR THE ULTRA-COMPACT 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 ULTRA-COMPACT ANTENNA TEST SYSTEM AND ITS ANALYSIS IN THE
CONTEXT OF WIRELESS CLOCK DISTRIBUTION
Wayne R. Bomstad II
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 off-chip.
The concept of externally-transmitted wireless clock distribution (ECD), or
inter-chip clock distribution, has been studied in this work through the development of an
application-specific measurement setup. This setup was designed to serve as a test-bed for
the characterization of ECD systems. Also in this work, a prototype ECD system, consist-
ing of only transmit and receive antennas, was designed and then measured in this new
test-bed, called the Ultra-Compact Antenna Test System (UCATS).
The UCATS was developed to measure the gain in the near- to intermediate-field
region of a transmitting antenna on a 3-inch diameter wafer. For the initial tests, a proto-
type transmit-receive 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 evenly-spaced
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 receiver-transmitter 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 intermediate-field 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 present-day microprocessors.
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 high-speed operation of microprocessors,
even when using the state-of-the-art copper and low-K interconnect technology [Flo01].
Worse than this, typical systemic clock skew solutions involve use of H-tree 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 Intra-Chip Clock Distribution
Feasibility of using wireless interconnects to alleviate some of the interconnect
concerns of the semiconductor industry has been proposed  and components for
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 1-1. The transmitter has been placed in the middle of a group of integrated receivers.
RX RXh RXh RXh
RX RX4 RXs RXI
RXI RXI RXIs RXf
RXh RXh RXh RXh
Figure 1-1 Conceptual diagram of an intra-chip clock distribution system.
1.2.1 Propagation Inside an Intra-Chip Clock Distribution System
Figure 1-1 shows that, although placement of the transmitter and receiver can be
optimized from a systemic view, there will be differences in direct-path 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 1-2). To alleviate this problem, sophisticated techniques are required,
such as the inclusion of a properly engineered propagation layer underneath the silicon
Figure 1-2 Possible disruption of direct-path signals in the intra-chip wireless clock
1.2.2 Clock Receiver Architecture
A block diagram of the clock receiver is shown in Figure 1-3. To improve noise
immunity, differential mode circuitry was used throughout the system. To mate with the
differential mode circuitry, balanced-line 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 low-noise 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.
GCK / System
Block diagram of a typical clock receiver.
1.2.3 Inter-Chip Clock Distribution System
One way around this skew for intra-chip clock receivers is to use an inter-chip
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 off-chip (Figure 1-4). 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
I xxxx x xxxxx (PC Board/MCM)
Antenna (Plane Wave
Figure 1-4 Conceptual diagram of inter-chip clock distribution system.
1.3 Overview of Thesis
1.3.1 Ultra-Compact Antenna Test System (UCATS)
One of the goals set forth in this work was the design of a set-up capable of charac-
terizing the nature of the transmitter-to-receiver 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 set-up, for cost pur-
poses, but also had to allow for sensitive level adjustment and receiver-transmitter 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 1-5, where the four main parts of the UCATS can be seen: the
isolation chamber, vacuum ring, transmitter platform, and probe height-extenders. Finer
details on the measurement setup are in Chapter 2.
1.3.2 Prototype Transmitter-Receiver Pair
To verify the proper functionality of the UCATS and to provide a reference design
for future inter-chip clock distribution systems, a prototype transmit-receive antenna pair
was also designed as part of this work. Since an actual parabolic reflector antenna, as in
Figure 1-4, 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 plane-wave-like beam,
which is only diffraction-limited 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 Q-cm silicon substrate.
This work is also discussed in Chapter 3.
Upon measuring the received power gain using microwave scattering parameters
(s-parameters) 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 s-parameters and the
antenna properties has yielded a skew of 1.7% and 3% for receiver-transmitter 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.
Vacuum Ring,& Wafer
Antenna Chamber EM Absorbe
S1-5 C -s l o 7"UCA
Figure 1-5 Cross-sectional layout of the UCATS.
ULTRA-COMPACT ANTENNA TEST SYSTEM
2.1 Structural Design
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 receiver-transmitter 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 five-sided
box, consisting of four distinct pieces: side-walls (x2), a front panel with an access door,
back-panel, 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 2-1(a). Details, such as the screw holes and spacing, have been omitted
for simplicity, but the actual drawings have been included in Appendix A.
(Fron Panel) -4"--
-- -7" --
Figure 2-1 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
multi-step hole in the middle of the top surface, shown in Figure 2-2. 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
Cross section of antenna chamber top panel.
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 receiver-transmitter
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 specially-designed "L-clamps". 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 2-3 shows a cut-away
view of the platform, while Appendix A contains more detailed drawings.
\ Tx-Platfor ^
'"- _-'Adj. Screws '""
Transmitter Tx Platform
-,, "L"-Clamps ,
Figure 2-3 Cutaway view of transmitter platform inside antenna chamber.
2.1.4 Probe Height-Extender 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 3-inch diameter wafer secured on
the vacuum ring, a probe height-extender 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.
The probe height-extender assembly consists of two distinct pieces: the probe
arms and probe height-extenders. The probe height-extenders 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 2-4, while the engineering drawings can be
seen in Appendix A.
Figure 2-4 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 2-5, 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 3-inch wide wafer
(circular or square) to cover the aperture completely. Finally, the ring must provide ade-
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
3" Diameter 3" Square
Wafer ___ --
I..... |I (b)
Actual-size drawing of vacuum ring showing (a) wafer placement and (b)
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 line-of-sight (LOS) path, to propagate from transmitter to receiver. Appropriate
absorbing material had to be placed inside the antenna chamber to absorb any reflected
signals. The absorber is shown in Figure 2-6, a 0.5-inch 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.
\ Vacuum Ring
Antenna chamber with absorber.
2.2.2 Electromagnetic Absorber
Electromagnetic radiation absorption can best be understood on a fundamental
level using plane-wave theory. This plane-wave 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)
Here the wave has been chosen to propagate in the z-direction which represents toward
the wafer in Figure 2-6, 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 bold-faced
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 direct-path rays from
the gaussian optics horn transmitter. Thus, the convoluted form (egg-crate 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 1.5-inch 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 far-field of an antenna. This absorber was
compared to low-profile 0.5-inch thick flat absorber of the same polyurethan-based mate-
rial. To check these specifications for the UCATS, a near- to intermediate-field antenna
range, measurements were conducted with the set-up seen in Figure 2-7. The results of the
corresponding measurements are shown seen in Figures 2-8(a) and 2-8(b). As a bench-
mark for this experiment, these results were compared to the laboratory free-space mea-
surement of 2-7(c), which was performed in the laboratory by pointing the transmitter in a
direction with no LOS reflection path.
Figure 2-7 Absorber attenuation experiments: (a) control, (b) experiment, and (c)
laboratory free space (no absorber or aluminum).
t G- Flat Absorber
1 z A- Aluminum
S-. v...v" Laboratory
-20.0 Free Space
23.0 23.5 24.0 24.5 25.0
"-..... 7 Laboratory Free Space
Figure 2-8 Absorber experiments in the measurement bandwidth of the UCATS
using (a) flat absorber and (b) convoluted absorber as the
23.0 23.5 24.0 24.5 25.0
Figure 2-8 Absorber experiments in the measurement bandwidth of the UCATS
using (a) flat absorber and (b) convoluted absorber as the
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 free-space 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 worst-case 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 inter-chip 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 first-principle
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 =
RI-R2) as seen by plane waves propagating through opposite sides of the 2 cm wide wafer
as indicated in Figure 2-9,
Figure 2-9 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 cm-vertical over a 2 cm width horizontal, a ratio of 2850 tol horizontal to vertical
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 aluminum-tin alloy, half-pillbox 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 2-10.
RF Probes Al-Sb
Si Wafer Vacuum Ring
Figure 2-10 Probe isolation module cross-section.
The importance of this module can be best seen by measurements taken with, and
without the probe isolation module in place in Figure 2-11. The module in these measure-
ments has effectively reduced the variance of the measurements by 1-3 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 non-negligible multipath environment.The
probe shield can be used to provide a degree of isolation from this type of environment.
2.3 Data Extraction
Like most microwave measurement tools, the UCATS measures the microwave
scattering parameters (s-parameters) of the device-under-test, 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 two-port 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 s-parameters. Equation (2.4) gives the
explicit form of how the s-parameters are expressed in terms of incident and reflected
powers for ports of equal characteristic impedance.
aI a .
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
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 s-parameters out of
the DUT, each one serving a particular function.Figure 2-11 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 set-up, while Chapter 4 contains the details on the receive side.
Figure 2-11 Block diagram of equipment hierarchy.
2.3.3 Balun and Semi-Rigid 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 coaxial-based 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 black-box in Figure 2-12, 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
To Network 180 Degree
Analyzer 180 Degree RF
Cou r Rigid Probes
50 2-1 B c -3dBdi
Figure 2-12 Balun connection diagram.
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 semi-rigid cables may be seen in Figures 2-13(a)
and 2-13(b). Minimum amplitude mismatch is more desirable, since the phase difference
between the two different cables was used to compensate for excessive phase mismatch.
14.0 19.0 24.0
5 176.0 -
S 14.0 19.0 24.0
Figure 2-13 Difference (mismatch) between balun ports 2 and 3 in terms of (a)
magnitude and (b) phase.
The semi-rigid 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
its own "assembly" of semi-rigid cables. Figures 2-13(a) and 2-13(b) show both the defi-
nition of mismatch and the measured mismatch using the scattering parameters of the
default balun assembly.
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 de-embed
the DUT's s-parameters from the measured data. A typical calibration procedure involves
measuring standardized loads with the extraneous equipment, and then comparing the
load's measured s-parameters with their factory-measured definitions (standard defini-
tions). In this manner the s-parameters of the extraneous devices are determined and then
de-coupled from the s-parameters of the DUT.
An example of two-port 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 two-port 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 Signal-Signal (SS) probes on
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
two-port 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 de-embedding the effects of the baluns, probes, and
waveguides. The resulting DUT is shown in Figure 2-14.
Figure 2-14 S-parameter 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
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, semi-rigid 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 Right-Hand 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, semi-rigid 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 re-mounted on the opposing probe station (Figure 2-15).Because the
differential-mode SS probes have been rotated in the process, measurements performed
with opposite-handed probe stations will be 180 degrees out-of-phase 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 left-or right-hand side.
SS Probes-.. + A--SS Probes
Safer center line
Figure 2-15 Left- and right-hand side measurements across a wafer's center-line.
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
inter-chip 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
d IR y
Figure 3-1 Cartesian and spherical coordinate description of an infinitesimal
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 3-1.
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 sinusoidally-varying current of angular
frequency (co), the angular global clock frequency, to the dipole antenna allows analysis
to proceed with a well-known 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 un-primed vector locates the point of observation.
PO ej(k (R R'))
A(R, t) J(R) dv (3.2)
47r IR R'|
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 time-retarded 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
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).
.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.
E(R, t) = cVx B(R, t) (3.4)
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 zero-valued 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 free-space 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
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 far-field form can be directly observed as the terms of
order R-2 and R-3 get vanishingly small. The resultant far-field 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)
B (R, t) = = B(R, t) (3.9)
In the near- and intermediate-field regions, the radiation characteristics of the
infinitesimal dipole contrasts with that for the far-field 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
R-1 terms vanish in significance next to the R-3 term. It is convention to call this region the
near-field region. The region between these two asymptotes at kR-1, forcing the inclusion
of all terms, is called the intermediate-field 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 far-field region is linearly-polarized, since the E and B fields are in phase with one
In the far-field 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 time-averaged 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 intermediate-field region, invocation of either
the near- or far-field 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 E-field 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 lumped-circuit 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 3-2 can be
used to illustrate how the dipole antenna's input impedance models may be derived.
Figure 3-2 Various levels of small dipole circuit models: (a) ideal case and (b) finite
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 3-2(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 3-2(b).
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).
D ma (3.12)
D(O, ) S() (3.13)
It is also typical to define a directivity pattern, which results from using the spa-
tially-dependent 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,
tx txDtx p (3.14)
G e D o- (3.15)
rx rx tx p .
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 RF-link, 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 free-space 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
S(1- |S112) 2(1 |S22l2)
S1 R i P t2R
F figure 3-3 Schematic for transmitter-receiver link visualization.
Figure 3-3 Schematic for transmitter-receiver link visualization.
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
s-parameters. 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 3-3 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, zig-zag, and folded dipole antennas on a 20 Q-cm substrate measuring 0.5
mm in thickness. These antennas have been photographed and shown in Figure 3-4.
For a comparison between the antennas, the two-port s-parameters were measured
in the range of 23-25 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 s-parameters.
Z. = Z 1-11(3.18)
in 0 1-S
Figure 3-4 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)
Input resistance (a) and reactance (b) for various .--Long Dipole
integrated antennas. Small Dipole
The input resistance and reactance have been plotted versus frequency in Figures
3-5(a) and 3-5(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 differential-mode probes and
The same 2-port s-parameter 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 3-6, it
can be seen that the folded and zig-zag 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 3-6 which has led to the selection of the folded dipole as the prototype
receive antenna used in the initial characterization of the UCATS.
0- Folded Dipole
-50.0 L- Linear Dipole (2 mm)
--- -Linear Dipole (1 mm) Zig Zag Dipole-
-5. 23.5 24.0 24.5 25.0
Figure 3-6 Comparison of the system gain using different integrated antennas
as the receive antennas, taken at R= 3 inches.
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 4-1
-- -I -
z- a a I
Figure 4-1 Rectangular waveguide: coordinates, dimensions, and cross-section.
Figure 4-1 Rectangular waveguide: coordinates, dimensions, and cross-section.
This drawing replicates the cross-section of the type WR-42 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 4-1, the four side walls together form the surface S, the
transverse boundary. While the fields are confined transversely, the solution in the z-direc-
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 plane-wave field expressions become trans-
versely dependent functions [E(x,y) and H(x,y)].
By assuming steady-state, sinusoidal sources, Maxwell's boundary conditions, and
the source-free forms of Maxwell's equations, the field expressions in Equation (4.2) can
be solved for using the partial differential equation eigenmode-eigenfunction technique
[Sni99]. The equation to be solved is of the form:
V2 + k2 = 0 (4.3)
Here y could be taken as the z-component 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 E-field is expressed as
being completely transverse to the direction of propagation, the z-direction and TM,
where the H-field is purely transverse to the z-direction. The eigenfunctions can be
expressed as functions of constrained wave vector (kc) and cross-sectional geometry (a, b):
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 non-zero for zero-valued modal indices, and
even then, only one index can be zero at a time.
The eigenvalues become evident when substituting the previously-listed eigen-
functions into the original wave equation, (4.3). The constrained wave vector then relates
the free-space wave vector (k) and the modal indices as
kc= k2 k2 2r (4.5)
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 zero-valued m or n.
When this result is applied directly to the measurement spectrum, 0.045-26.5 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 z-direction, and the eigenspectrum becomes more complicated
than before. However this represents a worst-case 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 Coax-Waveguide Transition
The coax-waveguide transition was used to transform the signal from the 3.5 mm
coaxial test cables to the WR-42 waveguide propagation environment required by the
horn. This is conceptually illustrated in Figure 4-2. 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
h Monopole Probe
Figure 4-2 Simplified drawing of coax-waveguide 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 (k2-k2)-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 free-space wave vector k, the permeability [go, and permittivity e0 of
free-space, 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 4-3.
The s-parameters were measured by connecting two coaxial-WG transitions
together in cascade with the port reference planes located at the coaxial input of each tran-
sition. The attenuation through one coax-RWG 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 one-transition, since the antenna is close to a matched
14.0 19.0 24.0
14.0 19.0 24.0
Figure 4-3 Scattering parameters for two cascaded coax-RWG 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-
4.2.1 Abrupt Junction
An abrupt rectangular-circular 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 cross-section before abruptly changing to a circular
waveguide cross-section. 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 cross-section. 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 n-th 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 n-th zero for the same m-th 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)
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
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 4-4. 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 4-5).
Figure 4-4 Gaussian lens-horn antenna shown with source and source impedance
->: t1 .- Horn
Figure 4-5 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 Gaussian-Hermite 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
intermediate-field region [Pad87, Gol82].
From a geometric optics perspective, the gaussian-spreading power in the far-field
region can be represented by a gaussian beam of rays [Ped93]. The application of the lens
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 quasi-optical 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
finite-elements simulator. The results are summarized in Table 4-1. The maximum antenna
gain measured by Millitech in their full-anechoic 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 far-field 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
B-2 shows the AGP of the horn antenna as simulated in HFSS. In such a plot, Half-Power
Beam Width (HPBW) can be directly determined by finding the amount of cross-sectional
angle in degrees the main lobe covers between the 3 dB points.
AGP(O,) = lOlog( G( -) (4.11)
Here G(0,4) is defined to be the transmitter's spatially-dependent antenna gain, measured
at an arbitrary R value in the far-field. 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 E-walls.
The finite element model has proven itself to be an acceptable computer model in
approximating the far-field radiation of the GOA. The results of the far-field comparison
can be seen in Table 4-1 below. This data tend to support the statement that the lens char-
acteristics tend to dominate the far-field characteristics of the GOA, which becomes
important later in making gaussian-beam approximations.
Table 4-1 Finite Element Model (FEM) vs. Measured Antenna Parameters for the GOA
Parameter FEM Measured Difference
Azimuthal HPBW 21 25.17 3.88
Elevational HPBW 24 27.23 3.23
Azimuthal Peak Gain 18.5 17.7 0.8
Elevational Peak Gain 18.5 17.8 0.7
The fields in the far-field region are much easier to calculate than the fields in the
near-field region for the GOA. Unfortunately, the UCATS operation is not in the far-field
of the antenna, as per optical gaussian beam theory [Ped93]. Equation (4.12) shows the
calculation of the far-field limit, RFF, The gaussian beam waist (see Figure 4-6), is the
minimum width (wo) of the gaussian beam, and ) is still the wavelength.The beam waist
RFF k (4.12)
in turn was found by using the far-field measurement data supplied by the manufacturer
using (4.13). Here 0 is the same as the measured HPBW.
In summary, for a 1.25 cm wavelength and 1.81 cm beam waist, far-field 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 receiver-transmitter separation to 7.5
inches, measurements taken using this system are in the intermediate- to near-field region.
For approximation purposes, propagation in the intermediate- to near-field regions
for a conical lens-horn 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)
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 4-6. 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.
Figure 4-6 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 time-averaged Poynting vector relationship of (3.10) and Maxwell's equations
(B.5). The E-field 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.
pw 2 Z
With the gaussian mode equations of the GOA, it is then convenient to predict the
measured power for two different transmitter-receiver spacings. Using Equations (4.13)
and (4.14), spatial distributions can be plotted for both power magnitude and E-field phase
with x and y as the dependent parameters for each constant-z 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
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.
PROTOTYPE SYSTEM MEASUREMENTS
Utilizing the ultra-compact 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 2-5), 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
Figure 5-1 Testchip layout showing measurement aperture.
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 5-1. Note that each cell has been labeled by row and
column in the array using a matrix-style notation.
5.2 Spatial Wavefront Uniformity Measurements
5.2.1 Wavefront Uniformity Mapping at 3-Inch 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 receiver-transmitter 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 right-side
of the wafer was consistently 180 degrees out-of-phase with data on the left-side of the
wafer due to the probing issues discussed in Section 2.4.3. The relative gain and phase
data for a receiver-transmitter spacing of 3 inches were collected and plotted in Figures
5-2 and 5-3. 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 5-2 Spatial distribution of relative gain from center for 3-inch separation
(mean= -7.52 dB, standard deviation= 2.85 dB).
Spatial distribution of relative phase for 3-inch separation
(mean = -30 degrees, standard deviation= 18.5 degrees).
the vacuum ring, seen as the four corer points in Figures 5-2 and 5-3, 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 3-inch 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 7.5-Inch 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 far-field 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 5-4), like its 3-inch 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 5-2. 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 5-4 Spatial distribution of relative gain for 7.5-inch separation
(mean= -3.77 dB, standard deviation= 2.90 dB).
Figure 5-5 Spatial distribution of relative phase for 7.5-inch separation
(mean= -15.6 degrees, standard deviation= 10.5 degrees).
aperture, the data did have less variance than the 3-inch 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
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 3-inch 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
transmitter-receiver 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 divide-by-8 counting archi-
Using the data from the uniformity measurements in the previous sections and the
formula for clock skew, explicitly written in equation (5.1).
Skew (Max-Min\ 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 5-1. A
clock skew of 1.7% of the period found for the 7.5-inch separation data and 3% clock
skew was calculated for the 3-inch 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
Table 5-1Clock 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 lens-horn 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 4-5. 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
5-6(a) and 5-6(b), respectively. There were two sets of measured data, corresponding to
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.
GO -35.0 GO
Right-Side Probe -40.0 -e Right-Side Pro
Left-Side Probe Left-Side Probe
FEM -45.0 FEM
2.0 -1'.0 0.0 1.0 2.0 55.2.U -1.U UU 1.U 2
Distance from Center (cm)
ire 5-6 Center row comparison between GO calculated, FEM simulated, and
measured (a) gain and (b) phase at 3-inch transmitter-receiver 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 B-4).
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 gaussian-beam calcula-
tions did not account for any reflected signals or standing waves between the wafer and
The rest of the rows are plotted against their respective GO and FEM calculations
in Figures 5-7(a) and 5-7(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
-108 FE -40 2.0
-20 -10 0.0 1.0 20 -2.0 -1.0 0.0 1.0 2.0
-10 -5 -51
c4 / GO Calculated (D
(D0-6- Right Side Probe -25
Left Side Probe \ -
-8- -FEM Y -35
-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 5-7 Measured versus GO-predicted gain and S21 phase values at (a) row 7
and (b) row 8 at R=3 inches.
The data for the R=7.5-inch 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 5-8). In addition, due to computer resource limitations and convergence difficul-
ties, the 7.5-inch separation case could not be simulated by FEM.
(a) 0 20
S -6 --10
-8 -20 -
-1.0 -1.0 0.0 1.0 2.0 -3.0 -1.0 0.0 1.0 2.0
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
0 m 15
1-5 \- -5
-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 5-8 Gaussian calculation comparisons -Cal
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=3-inch 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=7.5-inches 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 5-6 and 5-7), the disagreement between the GO calcu-
lations and measured data can be reconciled when one assumes the existence of a spa-
tially-confined standing wave. This standing wave, thoroughly researched in laser
resonators [Ver89], is created between the wafer and the lens inside the UCATS (Figure
B-4). Due to the curvature of the lens and the planar boundary formed by the wafer,
E-field waves incident upon the center of the lens are gradually guided with each
lens-reflection 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 one-way propagation along the LOS path,
only the FEM simulations were of use in describing this effect. The simulations for the
3-inch 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 5-5). However, for the
R=7.5-inch case, due to computer resource limitations, the standing wave could not be
simulated using finite elements.
5.2.6 Right- versus Left-Hand-Side Measurements
In order for the UCATS to be a useful measurement platform, the measurement
offsets using the right- versus left-hand 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 5-2 Center-row reliability check data
Separation/ Max Ma.
Diff e Location Difference
(cell #) (Offset)
3"/ 2.55 #62 1.35
3"/ 13 #63 5.5
7.5"/ 3.05 #67 1.2
7.5"/ 31 #68 13
5.3 Frequency-Dependent 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 probe-transmitter coupling effect (Figure 5-9). The transmitter's
0.023.0 23.5 24.0 24.5 25.0
230 .0 23.5 24.0 24.5 25.0
R= 3 inch
-5.0 -...-- R= 7.5 inch
-2002 Uo 2..5b 24.0 24.5 25.0
Figure 5-9 SII stability for various same-row cell locations: (a) R = 3 inches, (b) R =
7.5 inches, (c) no wafer.
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 5-9 (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
S 2-60.0 .0 28.5 24.0 24.5 2,.0
(b) _jn n I -- I
-uu.23.0 23.5 24.0 24.5 25.0
Figure 5-10 Frequency-dependent gain plots for: (a) R = 3 inches, (b) R= 7.5 inches.
(Figure 5-10). Also in each plot, on every cell location, there are frequency-dependent
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 5-10 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 5-11). The high phase
delay was observed due to its proximity to the vacuum ring. In order for the signal to be
23.0 23.5 24.0
( -400 -Cell 61
e.-600 .-- Cell 64
-803.0 23.5 24.0
Figure 5-11 Frequency-dependent S21 phase plots for: (a) R= 3 inches, (b) R=7.5
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 gain-frequency plots could be a
combination of coupling between the antenna elements, measurement reliability, standing
wave effects, or resonance in the isolation chamber. Figure 5-12 shows another collection
of gain data, which further illustrates the gain variations. These plots contain the same
trend as both of the gain-versus-frequency plots in Figure 5-10: the gain decreases in over-
all magnitude for cell sites farther from the center. In Figure 5-12(b), both the gain and
23.0 23.5 24.0 24.5 25.0
-50.0 Cell 62
", Cell 82
= Cell 63
-55.0 Cell 83
23.0 23.5 24.0 24.5 25.0
Figure 5-12 Column-wise comparisons of frequency-dependent 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 5-12 and 5-10 further emphasizes the need to
identify the sources of the nulls at the 7.5-inch 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
receiver-transmitter 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 5-3 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 3-inch sepa-
ration varied more on average than the data for the 7.5-inch 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 5-1 Uniformity statistics for relative gain and phase
Separation/ Mean LHS/RHS Max-
Parameter Deviation Offset Min
3" -7.52 2.85 8.55 +/- 1.5 14.7
3" -30 18.5 55.5 +/- 5.5 97
7.5" -3.77 2.90 8.7 +/- 1.2 13.6
7.5" -16 10.5 31.5 +/- 13 51
From the phase data, the clock skew was calculated assuming a divide-by-8
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 3-inch 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 5-7).
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 frequency-dependent nulls, which
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.
SUMMARY AND FUTURE WORK
An ultra-compact antenna test system (UCATS) has been developed for specific
application to externally-transmitted clock distribution systems (ECDS) operating at the
global clock frequency range of 14-26 GHz. Some of the user-friendly features included
continuously-variable receiver-transmitter (RX-TX) 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 intermediate-field electromagnetic measure-
ment environment in terms of its small physical size relative to frequency bandwidth, the
use of a densely-packed (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
GO-calculated 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-
The measurements performed at an RX-TX spacing of 7.5 inches, the maximum
separation allowed in the UCATS, were both promising and surprising. Unlike the results
for the 3-inch 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 receiver-transmitter 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 inter-chip clock distribution system suggest that it
may be possible to increase the size of multi-GHz 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 standing-wave
analysis capabilities, and investigation using further wavefront uniformity mappings at a
wider range of RX-TX distances. Finally, the inclusion of a matching layer below the
wafer could effectively take out the dependence on the spatially-confined 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 electrical-length antenna into a smaller area is still an open task. Possible antenna
structures include log-periodic 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 lens-horn 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
DRAWINGS FOR THE ULTRA-COMPACT 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
14" l 25 6.12
I 1.5" 3" 3" In 3.5"
Figure A-i Isolation chamber sidewalls.
Back-panel of isolation chamber.
Top view of back-panel.
+ + +
Figure A-4 Front-panel of isolation chamber with access door.
1.25" (typical spacing)
0.75"spacing from edge
~ 9/16 smoot
Figure A-5 Transmitter platform.
1/8" diameter circular
holes drilled completely through part
Figure A-6 Vacuum ring.
1/a6" diam. hL
1/8" diam. hemispherical groove (h. g. )
1/16" diam. h. g.
- ( for O-ring)
1/8" diam. screw drilled
1/4 "sdwy (countersunk)
1/8" h. g.
(note all measurements
are the same as
Vacuum ring cross section.
to accommodate 6 1/2" diameter SHC screws
Figure A-8 Threaded "L" steps.
Vacuum ring platform.
2.25" diameter hole
4.125" diameter cut
A.2 Photographs of Assembled UCATS
The UCATS was photographed, and the results are shown below in Figure A-1.
The top panel of the antenna chamber has been taken off to reveal the GOA transmitter on
Figure A-11 Photographs of the assembled UCATS: (a) inside the antenna chamber
and (b) top-down view showing through the vacuum ring.
the transmitter platform, surrounded by absorber [Figure A-1 l(a)]. Figure A- l(b) shows
a top-down view of the UCATS. Here, the transmitter can be seen through the measure-
ment aperture in the white-colored polyethylene vacuum ring.
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
3-dimensional 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 =
V D = p VxH= J+D
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 time-harmonic current density
source, the complex permittivity, C' in (B.4), and the time-harmonic 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
V p-H = 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
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 lens-horn antenna, as
in (B.6). The domain discretizes into N small tetrahedron-shaped subdomains (Qi), or
Sf [Vx (Vx E) k2E] W = 0 (B.6)
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, non-trivial, 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 E-field locally on each
subdomain in the form of(B.7).
E = x nW (B.7)
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&).
(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.
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 E-field distribution over the
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 re-meshing 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 user-defined stopping criterion, the re-meshing
stops and the field solution after the last mesh is the final solution to the problem.
B.2 Simulation of Prototype Transmitter
The gaussian lens-horn antenna, in order to verify manufacturer specifications,
was drawn inside Ansoft HFSS using its CAD-style 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
B-l shows the simulated system.
Port (and origin) z omLens (Rexolite)
I Horn r= 1.25
1 (Perfect E) PMLxyz
The prototype transmitter, as drawn inside Ansoft HFSS.
B.2.2 Sources and Boundaries
The model, drawn above in figure B-l, was then assigned a set of boundary condi-
tions. The cross-sectional plane of the model was given the H-symmetry boundary. When
this boundary condition is applied to a surface, HFSS assumes symmetry with respect to
the selected surface, keeping the H-fields 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 E-fields 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 semi-circular 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 4-1, but the phi and theta plots for the antenna gain pattern are shown in Figures in
Antenna Gain Pattern (AGP) plots for (a) 0=90 degrees, (b) 0= 90 degrees
in spherical coordinates.
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 5-2. However,
Ix Surrounding PMLs
(Ideal Absorber) virtual boxes
(Iused to optimize
Impedance BC at wafer surface y
Finite element model used to simulate R=3-inch separation case inside
due to its larger size compared to the previous model of only the lens-horn antenna, the
convergence criterion was relaxed to under 0.008 (W/m2) in order to prevent overflow of
computer resource. In Figure B-4, 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 diffraction-induced currents in Section 5.2.5
Distance from Wafer Center (cm)
Plot of EO 's power and phase over lateral dimension of wafer.
Next, the spatial distribution of E-field strength across the simulated wafer is
shown in Figure B-5. 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. .
Figure B-5 Distribution of FEM-simulated E-field strength across the area of the
Figure B-6 shows a spatial distribution on the x-z plane of the typical minima and
maxima associated with standing waves along the y-dimension between the wafer and
GOA. The power and phase of the standing wave are plotted single-dimensionally versus y
in Figure B-7.