ECE Department

Rice University

6100 Main Street

Houston, Texas 77005, USA

Email: aydin.babakhani AT rice.edu

Tel: (713) 348-3821

Fax: (713) 348-5685

Rice University

6100 Main Street

Houston, Texas 77005, USA

Email: aydin.babakhani AT rice.edu

Tel: (713) 348-3821

Fax: (713) 348-5685

**Large-Scale Radiating
Integrated (LSRI) Circuits**

**
In the last few years,
the dimensions of a typical silicon chip have become
larger than its potential range of operating wavelengths
(Figure 1). This important event has far reaching
implications which are, at present, poorly understood
and thus presents exciting new frontiers to explore. One
of these frontiers is the field of Large-Scale Radiating
Integrated (LSRI) circuits. This multidisciplinary field
is a generalization/superset of several classical fields
central to circuit design and encompasses applications
such as high-speed wireless communication, medical
imaging, bio-molecular sensing, security imaging, radar,
energy-efficient near-field short distance
communication, etc (Figure 2).**

Figure 1. Chip size and cut-off wavelength

Figure 2. Large-scale radiating integrated circuits

Recognition of the birth of the field of LSRI circuits and its implications motivates reflection and rethinking of classical electronic system design research and practice. The field of LSRI circuits represents an exciting opportunity not only for hardware designers, but theorists as well. During the last several decades, an extreme and narrow focus in the individual fields of digital, mixed-mode, analog, RF/microwave, and antenna has revolutionized the semiconductor industry and significantly impacted human life. This specific form of division in electronic research fields influenced research in other areas such as wireless communication theory, network theory, control theory, and optimization theory, i.e., many problems in these theoretical fields were motivated by specific applications and their physical implementation strategies. For example, wireless communication theory discusses concepts such as base-band signal modulation and RF carrier.This originates from the efficiency limitations of small antennas. In the past, due to the low frequency contents of a base-band signal, it was not practical to connect the base-band signal directly to an antenna. Thus, the base-band signal had to be up-converted to an RF signal before being able to be sent to an antenna. Fortunately, this is no longer a limitation in today's high-speed transmitters. Today's silicon process technology makes it possible to implement chips operating in RF wavelengths that are smaller than the size of the chip itself. In these chips, information can be generated by directly modulating an antenna's boundary conditions. This concept is called Near-Field Direct Antenna Modulation (NFDAM) and introduced in [1].

The birth of LSRI circuits is an inevitable outcome of the increasing number of transistors (Moore's law) and rising transistor speed. These two important factors cause the convergence of the conventional electronic research fields (digital circuits, analog circuits, antennas) into a unified area of LSRI circuits, as illustrated in Figure 3. In order to appreciate this convergence, the complexity levels of these research fields should be discussed. The conventional electronic research fields assume different levels of abstractions that could be described by their signal-level and system-level complexities (Figure 3). For example, in a typical wireless transceiver, such as a cell phone, there are usually few antennas (low system-level complexity). The signal of these antennas could be represented with an electromagnetic wave comprised of two components (electric and magnetic fields). Each of these components is a function of time, t, and coordinates, x, y, z (high signal-level complexity). Conversely, in a digital system, the signal is usually expressed with 0's and 1's (low signal-level complexity), but the system itself could comprise several hundred million transistors (high system-level complexity). In an LSRI circuit, the signal could be a radiating electromagnetic wave (high signal-level complexity) and the system could be composed of thousands of active and passive elements (high system-level complexity).

Figure 3. Signal- and system-level complexities

It should be noted that the differences in the
conventional electronic research fields can also be
classified by the relative size of the physical system
to the operating wavelength. For an efficient antenna,
the physical size is usually larger than *λ*/10, where
*λ* is the wavelength in air, but the
size of a digital chip could be orders of magnitude
smaller than the effective wavelength (Figure 3).
Traditionally, two separate approaches
have been used in these research fields. The first approach
originates from several decades of research on
non-radiating circuits, and the second one is
used primarily in studying wave-guiding and radiating structures.
In the first approach, it is assumed that the physical
size of a device is much smaller than the operating
wavelength. This fundamental assumption reduces the
complexity of Maxwell's partial differential equations
by converting them into Kirchhoff's current (KCL) and
voltage (KVL) laws. Although these laws are only valid
for non-radiating circuits that are much smaller than
the operating wavelength, they have been extremely
useful in designing large-scale non-radiating integrated
circuits. In the second approach, numerical techniques
are used to directly solve Maxwell's partial
differential equations, but, due to the practical limits
on available computational power, the complexity of
these systems is very limited.

The separation in these research approaches made sense in the
past, as the speed of transistors was not high enough to
justify the integration of radiating elements. Due to
the low operating frequency of transistors, the chip
size was always much smaller than the wavelength. Hence,
it was not possible to make efficient on-chip radiators.
Today's silicon process technology allows us to
implement silicon chips that are comparable to or even
larger than the operating wavelength. For example, in a
typical 130nm SiGe process, which has been accessible to
universities for the last 3-5 years, the length of a
typical chip could be as large as 6-7mm. This process
technology provides transistors with maximum cut-off
frequency (*f _{T}*) of close to 200GHz. In this process, the
minimum cut-off wavelength of the transistor,

As illustrated in Figure 1, we have passed the crossover
point where the chip size, *d*, and cut-off wavelength of
the transistors, *λ _{T}*, met each other. This means that the
unparalleled integration level of today's standard
silicon technology can be exploited to implement
thousands of active and passive radiating elements on a
single chip, with an unprecedented level of adaptivity
and reconfigureability. Finally, we are witnessing the
birth of large-scale radiating integrated circuits
(Figures 1, 2, 3).

It is important to realize that the fundamental laws of classic circuit theory, i.e., Kirchhoff's current (KCL) and voltage (KVL) laws, cannot be used to study LSRI circuits, because radiation effects cannot be ignored anymore. Since there are no analytical solutions for most of these radiation problems, numerical techniques are commonly used. During the last decade, in order to facilitate the design process of radiating structures, generic optimization techniques, such as genetic algorithms, have been widely employed. Because these genetic algorithms are usually slow and only find locally optimum solutions, they are not very effective when dealing with problems where hundreds or thousands of optimization variables are involved. In a recent paper [2], for the first time, a convex optimization method was introduced that is capable of finding globally optimum solutions for a broad class of large-scale radiating integrated circuits. In order to fully utilize the potential of today's silicon technology and speed up the progress of designing these radiating circuits, efficient tools for design and synthesis should be developed.

I believe the study of large-scale radiating integrated circuits will have a significant impact in several areas:

1) LSRI can greatly influence research on millimeter-wave and sub-millimeter-wave systems, which has been rapidly advancing in the last few years. This field encompasses applications such as high-speed wireless communication, radar, medical imaging, and security imaging, as well as spectroscopy and biomedical sensing. Fortunately, some of these applications, such as high-speed wireless communication in the 60GHz unlicensed band, as well as radar and security imaging in the 94GHz band, have received significant attention from government and industry, as evidenced by the recent allocation of funding to these areas. This has provided a great opportunity for funding academic research in the millimeter and sub-millimeter wavelength regimes.

2) The study of LSRI circuits presents a new opportunity for designing novel communication systems with unique properties such as the transmitter architectures based on the concept of Near-Field Direct Antenna Modulation (NFDAM). Unlike the conventional systems, NFDAM transmitters generate information after the antenna by modulating the antenna's boundary conditions. This allows them to transmit direction-dependent information using a single antenna. This property can be exploited to increase the security of wireless communication by preventing receivers in undesired directions from capturing the correctly modulated signal, i.e., undesired receivers will receive scrambled information. This also allows a single transmitter to increase the effective data rate by simultaneously sending independent information in different directions.

3) Traditional high data-rate links are reaching the point where the loss of copper-based connections is becoming a limiting factor. Many research groups have already started looking into replacements such as inductive and capacitive proximity communication as well as optical links [3]. The study of large-scale radiating integrated circuits will help us to explore the fundamental limits of high-speed near-field wireless links, and may provide insight into superior solutions to this problem.

4) The study of large-scale radiating integrated circuits, and developing design tools for these circuits, will help us explore complex near-field wave propagation problems. The nature of many of these problems is analogous to the problems that are studied in the growing area of near-field optics. The results of such a study could be used to improve the design of optical structures, such as nano-antennas [4].

5) Historically, control theory has had a significant impact in the field of circuit design, such as the analysis and synthesis of passive linear systems in the frequency domain. Since the seminal work [5], there has been remarkable progress in characterizing passive (dissipative) systems using the concept of positive real functions. The application of control theory in circuit and communication areas evidently goes beyond the passivity concept. Indeed, the emerging optimization tools developed by control theorists, such as linear matrix inequalities (LMIs) [6] and sum-of-squares (SOS) [7], have been successfully applied to a number of fundamental problems in these fields. The study of large-scale radiating integrated circuits motivates many new challenging problems in control theory and optimization. For instance, in reference [2], a convex optimization method is introduced for finding the global optimum solution for a broad class of passive large-scale radiating circuits. Another interesting problem would be the stability analysis of large-scale radiating integrated circuits, where thousands of passive and active radiating elements are highly coupled to each-other. Some of these problems cannot be modeled using finite dimensional networks and require a stability study of Maxwell equations in the presence of continuous active boundary conditions.

6) Recently, there has been a growing interest in
studying smart antennas for increasing the effective
data rate in MIMO systems and wireless networks. The
concept of near-field direct antenna modulation
introduced in [1] is an ultimate smart antenna system
where signal modulation and beam steering are done
concurrently at the antenna level. A study of
fundamental limitations of data transmission in the
near-field direct antenna modulation systems opens many
collaboration opportunities among researchers in
communication theory, wireless network theory,
optimization theory, circuit design, and
electromagnetics. This can potentially affect the
research being done on the capacity limits of MIMO
systems, as well as that being done on developing the
scheduling and beam-steering algorithms in wireless
networks.

**Self-Healing Mixed-Signal Integrated Circuits**

**As
transistors become smaller, their performance becomes
more vulnerable to process variation and mismatch. This
can significantly lower the yield of a system in high
volume production. Fortunately, the increasing number of
available active and passive devices can be used to
alleviate the problem by implementing self-healing
circuits (Figure 4). These circuits, which contain
sensing and controlling blocks, could constantly measure
the performance of the system and autonomously vary some
predefined knobs to minimize the performance
degradation. As an example, in a transmitter, RF and DC
power detectors, temperature sensors, and diode peak
detectors can be used to measure a transmitter's gain,
input and output power, linearity, and efficiency.
Having these parameters, an on-chip processing unit can
be used to control on-chip actuators, hence minimizing
performance degradation due to process, mismatch,
temperature, aging, and environment variation. These
actuators could be variable impedances, variable
transmission lines, gain control circuitry, etc.**

** **

Figure 4. Self-healing increases the yield in high-volume production

**References:**

[1] A. Babakhani, D. B. Rutledge, and A. Hajimiri, "Transmitter Architectures Based On Near-Field Direct Antenna Modulation (NFDAM)," in IEEE J. Solid-State Circuits, vol. 43, no. 12, pp. 2674-2692, Dec. 2008.

[2] J. Lavaei, A. Babakhani, and A. Hajimiri, and J.C. Doyle, "Solving Large-Scale Linear Circuit Problems Via Convex Optimization," in IEEE Conference on Decision and Control, Dec. 2009.

[3] D. A. B. Miller, "Device Requirements for Optical Interconnects to Silicon Chips," Proc. IEEE, pp. 1166 - 1185, 2009.

[4] P. J. Schuck, et. al., "Improving The Mismatch Between Light And Nanoscale Objects With Gold Bowtie Nanoantennas," Phys. Rev. Lett. 94, 017402, 2005.

[5] O. Brune, "Synthesis Of A Finite Two Terminal Network Whose Driving Point Impedance Is A Prescribed Function Of Frequency," Journal of Mathematics and Physics, vol. 10, pp. 191-236, 1931.

[6] S. Boyd, L. E. Ghaoui, E. Feron, and V. Balakrishnan, "Linear Matrix Inequalities In System And Control Theory," SIAM, 1994.

[7] P. A. Parrilo, "Structured Semidefinite Programs And Semialgebraic Geometry Methods In Robustness And Optimization," Ph.D. dissertation, California Institute of Technology, 2000.