Linear Systems, Sparse Solutions, and Sudoku

In this paper, we show that Sudoku puzzles can be formulated and solved as a sparse linear system of equations. We begin by showing that the Sudoku ruleset can be expressed as an underdetermined linear system: ${mmb{Ax}}={mmb b}$, where ${mmb A}$ is of size $mtimes n$ and $n>m$. We then prove that the Sudoku solution is the sparsest solution of ${mmb{Ax}}={mmb b}$, which can be obtained by $l_{0}$ norm minimization, i.e. $minlimits_{mmb x}Vert{mmb x}Vert_{0}$ s.t. ${mmb{Ax}}={mmb b}$. Instead of this minimization problem, inspired by the sparse representation literature, we solve the much simpler linear programming problem of minimizing the $l_{1}$ norm of ${mmb x}$, i.e. $minlimits_{mmb x}Vert{mmb x}Vert_{1}$ s.t. ${mmb{Ax}}={mmb b}$, and show numerically that this approach solves representative Sudoku puzzles.      

Q-Band pHEMT and mHEMT Subharmonic Gilbert Upconversion Mixers

This letter makes a comparison between Q-band 0.15 $mu{rm m}$ pseudomorphic high electron mobility transistor (pHEMT) and metamorphic high electron mobility transistor (mHEMT) stacked-LO subharmonic upconversion mixers in terms of gain, isolation and linearity. In general, a 0.15 $mu{rm m}$ mHEMT device has a higher transconductance and cutoff frequency than a 0.15 $mu{rm m}$ pHEMT does. Thus, the conversion gain of the mHEMT is higher than that of the pHEMT in the active Gilbert mixer design. The Q-band stacked-LO subharmonic upconversion mixers using the pHEMT and mHEMT technologies have conversion gain of $-$7.1 dB and $-$0.2 dB, respectively. The pHEMT upconversion mixer has an ${rm OIP}_{3}$ of $-$12 dBm and an ${rm OP}_{1 {rm dB}}$ of $-$24 dBm, while the mHEMT one shows a 4 dB improvement on linearity for the difference between the ${rm OIP}_{3}$ and ${rm OP}_{1 {rm dB}}$. Both the chip sizes are the same at 1.3 mm $times$ 0.9 mm.      

Improved Microwave Noise Performance by SiN Passivation in AlGaN/GaN HEMTs on Si

Effects of silicon nitride (SiN) surface passivation by plasma enhanced chemical vapor deposition (PECVD) on microwave noise characteristics of AlGaN/GaN HEMTs on high-resistivity silicon (HR-Si) substrate have been investigated. About 25% improvement in the minimum noise figure $(NF_{min})$ (0.52 dB, from 2.03 dB to 1.51 dB) and 10% in the associate gain $(G_{rm a})$ (1.0 dB, from 10.3 dB to 11.3 dB) were observed after passivation. The equivalent circuit parameters and noise source parameters (including channel noise coefficient $(P)$, gate noise coefficient $(R)$, and their correlation coefficient $(C)$ ) were extracted. $P$ , $R$ and $C$ all increased after passivation and the increase of C contributes to the decrease of the noise figure. It was found that the improved microwave small signal and noise performance is mainly due to the increase of the intrinsic transconductance $(g_{{rm m}0})$ and the decrease of the extrinsic source resistance $(R_{rm s})$.      

2 MHz AO $Q$ -switched ${rm TEM}_{00}$ Grazing Incidence Laser With 3 at.% Neodymium Doped Nd:YVO$_{4}$

We present a detailed experimental and theoretical study of the ultrahigh repetition rate AO $Q$ -switched ${rm TEM}_{00}$ grazing incidence laser. Up to 2.1 MHz $Q$-switching with ${rm TEM}_{00}$ output of 8.6 W and 2.2 MHz $Q$ -switching with multimode output of 10 W were achieved by using an acousto-optics $Q$ -switched grazing-incidence laser with optimum grazing-incidence angle and cavity configuration. The crystal was 3 at.% neodymium doped Nd:YVO$_{4}$ slab. The pulse duration at 2 MHz repetition rate was about 31 ns. The instabilities of pulse energy at 2 MHz repetition rate were less than ${pm}6.7hbox{%}$ with ${rm TEM}_{00}$ operation and ${pm}3.3hbox{%}$ with multimode operation respectively. The modeling of high repetition rate $Q$-switched operation is presented based on the rate equation, and with the solution of the modeling, higher pump power, smaller section area of laser mode, and larger stimulated emission cross section of the gain medium are beneficial to the $Q$-switched operation with ultrahigh repetition rate, which is in consistent with the experimental results.      

Design Principles for Higher (Prime) Order Composite Directional Couplers

The theoretical construction of ideal (lossless) 3 $,times,$3, 4 $,times,$4, and 5 $,times,$5 dimensional directional couplers from 2$,times,$ 2 directional couplers is demonstrated. Such devices could be fabricated as planar waveguide circuit elements.      

$S$ - and $C$ -Band Ultra-Compact Phase Shifters Based on All-Pass Networks

Ultra-compact phase shifters are presented. The proposed phase-shifting circuits utilize the lumped element all-pass networks. The transition frequency of the all-pass network, which determines the size of the circuit, is set to be much higher than the operating frequency. This results in a significantly small chip size of the phase shifter. To verify this methodology, 5-bit phase shifters have been fabricated in the $S$ - and $C$ -band. The $S$ -band phase shifter, with a chip size of 1.87 mm $,times,$0.87 mm (1.63 mm $^{2}$), has achieved an insertion loss of ${hbox{6.1 dB}} pm {hbox{0.6 dB}}$ and rms phase-shift error of less than 2.8$^{circ}$ in 10% bandwidth. The $C$ -band phase shifter, with a chip size of 1.72 mm $,times,$0.81 mm (1.37 mm $^{2}$), has demonstrated an insertion loss of 5.7 dB $pm$ 0.8 dB and rms phase-shift error of less than 2.3 $^{circ}$ in 10% bandwidth.      

Preprocessing and Partial Rerouting Techniques for Accelerating Reconfiguration of Degradable VLSI Arrays

This paper presents novel techniques to accelerate the reconfiguration of degradable very large scale integration arrays. A preprocessing step is used to derive the upper and lower size bounds of the maximum logical array (MLA) such that only those subarrays that possibly contain the MLA are reconfigured, thereby reducing the reconfiguration time and also obtaining a same-sized logical array. In addition, the partial rerouting approach is generalized so that as many as possible previous routing results can be reused in the current rerouting step. The reconfiguration time is reduced from $ O((1-rho)cdot beta cdot m cdot n)$ to its lower bound $ O((1-rho)cdot mcdot n)$ for $ mtimes n$ host arrays with small fault density $ rho $, where $ beta $ is the expected routing length required per logical column.      

10-GHz and 20-GHz Channel Spacing High-Resolution AWGs on InP

This letter reports on 10-GHz and 20-GHz channel-spacing arrayed waveguide gratings (AWGs) based on InP technology. The dimensions of the AWGs are 6.8$,times,$8.2 mm$^{2}$ and 5.0$,times,$6.0 mm$^{2}$, respectively, and the devices show crosstalk levels of $-$12 dB for the 10-GHz and $-$17 dB for the 20-GHz AWG without any compensation for the phase errors in the arrayed waveguides. The root-mean-square phase errors for the center arrayed waveguides were characterized by using an optical vector network analyzer, and are 18 $^{circ}$ for the 10-GHz AWG and 28$^{circ}$ for the 10-GHz AWG.      

Analysis and Design of a CMOS UWB LNA With Dual- -Branch Wideband Input Matching Network

A wideband low-noise amplifier (LNA) based on the current-reused cascade configuration is proposed. The wideband input-impedance matching was achieved by taking advantage of the resistive shunt–shunt feedback in conjunction with a parallel LC load to make the input network equivalent to two parallel $RLC$-branches, i.e., a second-order wideband bandpass filter. Besides, both the inductive series- and shunt-peaking techniques are used for bandwidth extension. Theoretical analysis shows that both the frequency response of input matching and noise figure (NF) can be described by second-order functions with quality factors as parameters. The CMOS ultra-wideband LNA dissipates 10.34-mW power and achieves ${ S}_{11}$ below $-$8.6 dB, ${ S}_{22}$ below $-$10 dB, ${ S}_{12}$ below $-$26 dB, flat ${ S}_{21}$ of 12.26 $pm$ 0.63 dB, and flat NF of 4.24 $ pm$ 0.5 dB over the 3.1–10.6-GHz band of interest. Besides, good phase linearity property (group-delay variation is only $pm$22 ps across the whole band) is also achieved. The analytical, simulated, and measured results agree well with one another.      

Low-Threshold Strained Quantum-Well GaSb-Based Lasers Emitting in the 2.5- to 2.7-$mu$ m Wavelength Range

GaInAsSb–GaSb strained quantum-well (QW) ridge waveguide diode lasers emitting in the wavelength range from 2.51 to 2.72 $ mu{hbox {m}}$ have been grown by molecular beam epitaxy. The devices show ultralow threshold current densities of 44 $hbox{A}/{hbox {cm}}^{2}$ (${L}rightarrow infty $) for a single QW device at 2.51 $ mu{hbox {m}}$, which is the lowest reported value in continuous-wave operation near room temperature (15 $^{circ}hbox{C}$) at this wavelength. The devices have an internal loss of 3 ${hbox {cm}}^{-1}$ and a characteristic temperature of 42 K. By using broader QWs, wavelengths up to 2.72 $mu{hbox {m}}$ could be achieved.      

Recursive Pseudo-Exhaustive Two-Pattern Generation

Pseudo-exhaustive pattern generators for built-in self-test (BIST) provide high fault coverage of detectable combinational faults with much fewer test vectors than exhaustive generation. In $(n, k)$-adjacent bit pseudo-exhaustive test sets, all $2^{k}$ binary combinations appear to all adjacent $k$-bit groups of inputs. With recursive pseudoexhaustive generation, all $(n, k)$-adjacent bit pseudoexhaustive tests are generated for ${k}leq{n}$ and more than one modules can be pseudo-exhaustively tested in parallel. In order to detect sequential (e.g., stuck-open) faults that occur into current CMOS circuits, two-pattern tests are exercised. Also, delay testing, commonly used to assure correct circuit operation at clock speed requires two-pattern tests. In this paper a pseudoexhaustive two-pattern generator is presented, that recursively generates all two-pattern $(n, k)$-adjacent bit pseudoexhaustive tests for all ${k}leq{n}$. To the best of our knowledge, this is the first time in the open literature that the subject of recursive pseudoexhaustive two-pattern testing is being dealt with. A software-based implementation with no hardware overhead is also presented.      

A Low-Voltage Mobility-Based Frequency Reference for Crystal-Less ULP Radios

The design of a 100 kHz frequency reference based on the electron mobility in a MOS transistor is presented. The proposed low-voltage low-power circuit requires no off-chip components, making it suitable for application in wireless sensor networks (WSN). After a single-point calibration, the spread of its output frequency is less than 1.1% (3$sigma $) over the temperature range from $-{hbox{22}},^{circ}{hbox{C}}$ to 85$,^{circ}{hbox{C}}$ . Fabricated in a baseline 65$~$nm CMOS technology, the frequency reference circuit occupies 0.11$ hbox{mm}^{2}$ and draws 34 $ muhbox{A}$ from a 1.2 V supply at room temperature.      

W-Band Active Down-Conversion Mixer in Bulk CMOS

A W-band (76–77 GHz) active down-conversion mixer has been demonstrated using low leakage (higher ${rm V}_{{rm T}}$) NMOS transistors of a 65-nm digital CMOS process with 6 metal levels. It achieves conversion gain of ${-}8$ dB at 76 GHz with a local oscillation power of 4 dBm (${sim-}2$ dBm after de-embedding the on-chip balun loss), and 3 dB bandwidth of 3 GHz. The SSB noise figures are 17.8–20 dB (11.3–13.5 dB after de-embedding on-chip input balun loss) between 76 and 77 GHz. ${rm IP}_{1{rm dB}}$ is ${-}6.5$ dBm and IIP3 is 2.5 dBm (${sim-}13$ and ${sim}-4$ dBm after de-embedding the on-chip balun loss). The mixer consumes 5 mA from a 1.2 V supply.      

A 36–80 GHz High Gain Millimeter-Wave Double-Balanced Active Frequency Doubler in SiGe BiCMOS

This letter presents a high conversion gain double-balanced active frequency doubler operating from 36 to 80 GHz. The circuit was fabricated in a 200 GHz ${rm f}_{rm T}$ and ${rm f}_{max}$ 0.18 $mu$m SiGe BiCMOS process. The frequency doubler achieves a peak conversion gain of 10.2 dB at 66 GHz. The maximum output power is 1.7 dBm at 66 GHz and ${-}3.9$ dBm at 80 GHz. The maximum fundamental suppression of 36 dB is observed at 60 GHz and is better than 20 dB from 36 to 80 GHz. The frequency doubler draws 41.6 mA from a nominal 3.3 V supply. The chip area of the active frequency doubler is 640 $mu$m $,times,$424 $mu$m (0.272 mm $^{2}$) including the pads. To the best of authors' knowledge, this active frequency doubler has demonstrated the highest operating frequency with highest conversion gain and output power among all other silicon-based active frequency doublers reported to date.      

Highly Compact Interconnect Test Patterns for Crosstalk and Static Faults

The effect of crosstalk-induced errors becomes more significant in high-performance circuits and systems. In this paper, compact crosstalk test patterns are introduced for a system-on-a-chip and board level interconnects considering physically effective aggressors. By being able to target multiple victim lines, $6n$, where $n$ is the number of nets patterns are drastically reduced to a constant number $6D$, where $D$ indicates the effective distance among interconnect nets. The test quality for static and crosstalk faults are completely preserved with $6D$ patterns.      

Evaluation of High-Temperature Absorption Coefficients of Ionized Gas Plasmas in Optical Fibers

The large absorption coefficient $alpha$ of a fiber core at high temperatures is closely related to the generation of a fiber fuse. When silica glass is heated to a temperature above 4500 K, it forms Si $^{+}$ and O $^{+}$ ions and electrons in the ionized gas plasma state. We estimate the $alpha$ value for the plasma in the fiber core at high temperatures. $alpha$ begins to increase at 3500 K, then increases rapidly with increasing temperature above 4000 K, reaching a value of $1times 10^{7}$ m$^{-1}$ at 6000 K. This value is about 300 times that necessary for initiating a fiber fuse.      

Compact Microracetrack Resonator Devices Based on Small SU-8 Polymer Strip Waveguides

Compact microracetrack resonator (MRR) devices are presented with small SU-8 polymer strip waveguides. The SU-8 strip waveguide has an SU-8 polymer core $(n {sim} 1.573)$ , a SiO$_{2}$ buffer $(n {sim} 1.445)$, and an air cladding. The fabricated straight waveguide has a low propagation loss of about 0.1 dB/mm. With such a high index-contrast optical waveguide, a compact MRR with a small bending radius ( $sim$150 $mu$m) are designed and fabricated. The measured spectral responses of the through/drop ports show a $Q$-factor of 8000.      

Extended Fault-Tolerant Cycle Embedding in Faulty Hypercubes

We consider fault-tolerant embedding, where an $n$-dimensional faulty hypercube, denoted by $Q_{n}$, acts as the host graph, and the longest fault-free cycle represents the guest graph. Let $F_{v}$ be a set of faulty nodes in $Q_{n}$. Also, let $F_{e}$ be a set of faulty edges in which at least one end-node of each edge is faulty, and let ${cal F}_{e}$ be a set of faulty edges in which the end-nodes of each edge are both fault-free. An edge in $Q_{n}$ is said to be critical if it is either fault-free or in $F_{e}$. In this paper, we prove that there exists a fault-free cycle of length at least $2^{n}-2vert F_{v}vert$ in $Q_{n} (ngeq 3)$ with $vert{cal F}_{e}vertleq 2n-5$, and $vert F_{v}vert+vert{cal F}_{e}vertleq 2n-4$ , in which each node is incident to at least two critical edges. Our result improves on the previously best known results reported in the literature, where only faulty nodes or faulty edges are considered.      

17 GHz RF Front-Ends for Low-Power Wireless Sensor Networks

A 17 GHz low-power radio transceiver front-end implemented in a 0.25 $mu{hbox {m}}$ SiGe:C BiCMOS technology is described. Operating at data rates up to 10 Mbit/s with a reduced transceiver turn-on time of 2 $mu{hbox {s}}$, gives an overall energy consumption of 1.75 nJ/bit for the receiver and 1.6 nJ/bit for the transmitter. The measured conversion gain of the receiver chain is 25–30 dB into a 50 $Omega$ load at 10 MHz IF, and noise figure is 12 $pm$0.5 dB across the band from 10 to 200 MHz. The 1-dB compression point at the receiver input is $-$37 dBm and ${hbox{IIP}}_{3}$ is $-$25 dBm. The maximum saturated output power from the on-chip transmit amplifier is $-$1.4 dBm. Power consumption is 17.5 mW in receiver mode, and 16 mW in transmit mode, both operating from a 2.5 V supply. In standby, the transceiver supply current is less than 1 $mu{hbox {A}}$.      

1580-V–40-$hbox{m}Omegacdot hbox{cm}^{2}$ Double-RESURF MOSFETs on 4H-SiC $(hbox{000}bar{hbox{1}})$

Double-reduced-surface-field (RESURF) MOSFETs with $hbox{N}_{2}hbox{O}$ -grown oxides have been fabricated on the 4H-SiC $(hbox{000} bar{hbox{1}})$ face. The double-RESURF structure is effective in reducing the drift resistance, as well as in increasing the breakdown voltage. In addition, by utilizing the 4H-SiC $(hbox{000}bar{hbox{1}})$ face, the channel mobility can be increased to over 30 $hbox{cm}^{2}/hbox{V}cdothbox{s}$, and hence, the channel resistance is decreased. As a result, the fabricated MOSFETs on 4H-SiC $( hbox{000}bar{hbox{1}})$ have demonstrated a high breakdown voltage $(V_{B})$ of 1580 V and a low on-resistance $(R_{rm ON})$ of 40 $hbox{m}Omega cdothbox{cm}^{2}$. The figure-of-merit $(V_{B}^{2}/R_{rm ON})$ of the fabricated device has reached 62 $hbox{MW/cm}^{2}$, which is the highest value among any lateral MOSFETs and is more than ten times higher than the “Si limit.”