838 IEEE JOURNAL OF SOLID-STATE CIRCUITS, VOL. 40, NO. 4, APRIL 2005 A 233-MHz 80%–87% Efficient Four-Phase DC–DC Converter Utilizing Air-Core Inductors on Package Peter Hazucha, Member, IEEE, Gerhard Schrom, Jaehong Hahn, Bradley A. Bloechel, Associate Member, IEEE, Paul Hack, Gregory E. Dermer, Member, IEEE, Siva Narendra, Member, IEEE, Donald Gardner, Member, IEEE, Tanay Karnik, Senior Member, IEEE, Vivek De, Member, IEEE, and Shekhar Borkar, Member, IEEE Abstract—We demonstrate an integrated buck dc–dc converter for multi- CC microprocessors. At nominal conditions, the converter produces a 0.9-V output from a 1.2-V input. The circuit was implemented in a 90-nm CMOS technology. By operating at high switching frequency of 100 to 317 MHz with four-phase topology and fast hysteretic control, we reduced inductor and capacitor sizes by three orders of magnitude compared to previously published dc–dc converters. This eliminated the need for the inductor magnetic core and enabled integration of the output decoupling capacitor on-chip. The converter achieves 80%–87% efficiency and 10% peak-to-peak output noise for a 0.3-A output current and 2.5-nF decoupling capacitance. A forward body bias of 500 mV applied to PMOS transistors in the bridge improves efficiency by 0.5%–1%. Index Terms—Buck converter, CMOS, dc–dc converter. I. INTRODUCTION M ICROPROCESSOR designs with two different supply voltages are becoming attractive for achieving high performance under stringent power constraints [1]. Speed-critical circuits operate at high voltage while circuits with delay slacks operate at low voltage to save power without impacting processor frequency. In addition, large on-chip caches in 90 nm and beyond require higher voltage to maintain adequate SRAM cell stability, while lower voltage can be applied to logic cores and smaller arrays on the chip. Furthermore, on-chip analog circuits often require larger headroom and higher voltage than logic circuits. An efficient on-die dc–dc converter that delivers high currents with small area overhead and also meets supply noise constraints is desirable to reduce system complexity. A step-down voltage regulator can be implemented as a switched-capacitor charge pump, linear regulator, or switching dc–dc converter. Our feasibility study indicated that a charge pump with on-chip capacitors implemented in bulk CMOS achieves only 65% conversion efficiency and requires large silicon area of 1 mm for 100 mA of output current. A linear , which regulator theoretically achieves efficiency Manuscript received August 30, 2004; revised November 29, 2004. P. Hazucha, G. Schrom, B. A. Bloechel, T. Karnik, P. Hack, G. Dermer, S. Narendra, V. De, and S. Borkar are with Circuit Research, Intel Laboratories, Intel Corporation, Hillsboro, OR 97124 USA (e-mail: peter.hazucha@intel.com; gerhard.schrom@intel.com; bradley.a.bloechel@ intel.com; tanay.karnik@intel.com; paul.hack@intel.com; greg.dermer@ intel.com; siva.g.narendra@intel.com; vivek.de@intel.com; shekhar.y.borkar@ intel.com). J. Hahn is with Intel Corporation, Beaverton, OR 97006 USA (e-mail: jaehong.hahn@intel.com). D. Gardner is with Intel Corporation, Santa Clara, CA 95054 USA (e-mail: d.s.gardner@intel.com). Digital Object Identifier 10.1109/JSSC.2004.842837 is 66%–83% in this application. The most important advantage of a linear regulator is small silicon area and very fast load regulation. We report on a fast linear regulator in another paper in this issue [12]. A switching dc–dc converter often has conversion efficiency above 80% at the cost of bulky off-chip inductors and a fair amount of decoupling capacitance. In this paper, we demonstrate a four-phase buck converter operating at an ultra-high frequency ( 100 MHz) that leads to a three-orders-of-magnitude reduction in capacitor and inductor size. The capacitor was integrated on-chip and four size-402 SMT air core inductors were mounted on the package. In Section II, we describe the details of the dc–dc converter circuits. In Section III, we present dc and transient response measurements on the test chip. Finally, we compare performance of our design with previously published dc–dc converters in Section IV. II. DC–DC CONVERTER DESCRIPTION A. Design Requirements applications with the main voltage of 1.2 V, For multithe desired output voltage is about 0.8–1.0 V, which results in of 0.66–0.83. The simplest stepa conversion ratio down switching converter utilizing just one inductor and two switches is a buck converter and is typically used for conversion ratios of 0.1–0.9. For lower conversion ratios, the small duty cycle significantly degrades efficiency and transformer-based topologies are preferred. The value of the duty cycle in our application permitted us to use the buck topology, which also eliminated the need for magnetic coupling between the windings. One of the design goals was to integrate the dc–dc converter on a single chip. The typical -factor of on-chip air core inductors ranges between 5 and 10, which is not sufficient for power delivery with efficiency above 80%. Moreover, an on-chip inrating of 0.3 A occupies a substantial silicon ductor for area. So implementing the inductor on-chip with present technology did not seem possible. Integrating the output capacitor would require that the capacitor size be reduced to several nanofarads. Otherwise, the silicon area and the power wasted in oxide leakage of the capacitor would become prohibitively large. The size of the capacitor is determined from two requirements. First, switching operation of the buck converter introduces a ripple current that flows through the inductor in addition to the load current. This ripple current is integrated on the output ca. To suppress the pacitor and produces a voltage ripple on voltage ripple to several millivolts, the output capacitor has to be 0018-9200/$20.00 © 2005 IEEE HAZUCHA et al.: A 233-MHz 80%–87% EFFICIENT FOUR-PHASE DC–DC CONVERTER UTILIZING AIR-CORE INDUCTORS ON PACKAGE large. However, this is only true for a single-phase dc–dc converter. If the converter is divided into phases, each phase deof output current, with their switching times livering staggered by 360 , then the switching ripple completely can. In our cels out for any conversion ratio that is a multiple of application, the conversion ratios are close to 0.75, which corresponds to a four-phase dc–dc converter. Since the inductor ripple current is not a limiting factor in a multiphase dc–dc converter, the inductors can be smaller. This reduces output impedance at high frequency and improves the transient response for a given size of output decoupling capacitor. The second requirement comes from load regulation. If the load suddenly increases, then the output capacitor has to provide current to the load until the dc–dc converter adjusts its current through the inductors. The charge available in a decoupling ca, where mV for a 10% pacitor equals of 0.9 V. For a current step of 50% of , the droop at converter has to adjust the output current within time For a 1-nF capacitor, the available response time is only 1.2 ns! Obviously, a dc–dc converter with an extremely fast response time is required. For a multiphase buck converter, this implies that the switching frequency has to be in a range of 100 MHz to 1 GHz and the response has to be within less than one switching cycle. However, the response time of a widely used pulse-width modulation (PWM) controller is about five to ten switching cycles. Hysteretic control techniques have advantages in their immediate response to a load transient and a simple feedback circuit. However, the lack of synchronization makes them difficult to apply in multiphase interleaved dc–dc converters. In fact, load response may be degraded if the output voltage ripple becomes prohibitively large and forces the inductor size to increase. It is attractive to develop a multiphase, interleaved dc–dc converter that would benefit from the fast loop response of a hysteretic control and still afford small inductor size due to ripple cancellation effect inherent to multiphase design [2]. The proposed topology enables a multiphase configuration by adding an external synchronization signal to a hysteretic converter. 839 Fig. 1. Hysteretic controller with RC network across the inductor. where is the switching frequency and has to match the hysteresis window is the duty cycle. which sets the switching frequency The feedback network , provides stable operation in single-phase configuration, especially when the hysteresis is small. C. Voltage Positioning The optimum load response is achieved by designing the output impedance for a resistive response [3]. When that is the case and the converter is loaded by current, the output exhibits a dc error proportional to the output resistance. Since the output voltage at any time “positions” itself along a load line with the slope of the output resistance, this concept is called voltage positioning [4]. . The The average voltage at the comparator output is average voltage at the bridge output is reduced by the and is given by drop on the bridge series resistance is a weighted average of series resistances of high-side and low-side switches B. Hysteretic Controller Fig. 1 shows a buck converter with a hysteretic controller. The comparator hysteresis is set by resistors and . A cascade of buffers drives a high-side PMOS transistor and a low-side NMOS transistor of a bridge that switches inductor . The feedback network , works as a high-pass filter from to , and provides fast transient response. Since is relatively small and the voltage across is large compared to the ripple , the voltage across is an integral of the voltage at of the bridge output. Therefore, the RC integrator estimates the inductor current and current sensing is not required. , is The voltage variation at the feedback node, If resistor is introduced between the comparator output as shown in Fig. 2, then and Since equals the input reference due to the action is given of the negative feedback loop, the average output by By properly choosing , the dc output impedance can be adjusted for optimum load response. 840 Fig. 2. IEEE JOURNAL OF SOLID-STATE CIRCUITS, VOL. 40, NO. 4, APRIL 2005 Hysteretic controller with voltage positioning. Fig. 4. Derivation of a synchronization condition. In order to synchronize, the frequency angular voltage should be lower than should satisfy the condition Fig. 3. of the injected tri, and the amplitude Synchronization of the hysteretic controller by injection locking. Then the injected amplitude is D. Droop Control (see Fig. 1) As mentioned earlier, the feedback network works as a high-pass filter from to , which enables a very fast response of the controller. Whenever the load current , the controller will couple the inductor abruptly changes by . The inductor needs time to either to ground or to accommodate the current change for for The initial difference between inductor current and load current causes a droop The RC time constant is such that the voltage change across equals , and equals approximately after time for for E. Synchronization The hysteretic controller can be synchronized by injection of , as shown in Fig. 3, so that a synchronization signal at the switching instants can follow the envelope of the hysteretic is band according to Fig. 4. The free-running frequency , and the values of and determined by the hysteresis where . F. Single-Phase Implementation The complete circuit schematic of a single-phase dc–dc converter module, 1-phase, is shown in Fig. 5. A switched capacwith itor circuit, subtractor, generates a reference voltage respect to the local ground by subtracting the external referand . An integrator , ence voltages compensates for the input offset of comparator and and . Reother offsets induced by the synchronization current sistors with large values implemented in CMOS usually have large parasitic capacitance to ground that limits the bandwidth. in Fig. 3 is about larger than . Therefore, Resistor , was replaced by resisin Fig. 5, the resistive divider tors , and the R-2R ladder which do not require high-value resistors. The hysteresis window of comis digitally adjustable by changing the divider ratio parator . A sensed output voltage, , is coupled to of via a high-pass filter , and for fast response to , in Fig. 3 was load current transients. Resistive divider . By changing the divider replaced by the R-2R ladder, , the dc-level of can be programmed between ratio of and . Buffers , and are sized to minimize the short circuit current through bridge transistors and . The rectangular voltage across creates a tri. Current creates a staircase angular waveform at waveform at that pulls the free-running oscillation fre. The bridge operates with quency to the frequency of independently adjusted, fixed dead times between the turn-off and turn-on instants of the high-side and low-side switches. G. Four-Phase DC–DC Converter The block diagram of the four-phase dc–dc converter is shown in Fig. 6. The chip contains four single-phase modules HAZUCHA et al.: A 233-MHz 80%–87% EFFICIENT FOUR-PHASE DC–DC CONVERTER UTILIZING AIR-CORE INDUCTORS ON PACKAGE Fig. 5. 841 Complete schematic of a single-phase dc–dc converter module (1-phase) featuring hysteretic control, voltage positioning, and synchronization. Fig. 6. Block diagram of a high-frequency four-phase interleaved dc–dc converter. that operate as stand-alone converters and receive synchronization signals from block synchronizer. In a multiphase topology, the switching times of the inductors are staggered to cancel out the output voltage ripple. For a four-phase design the phase difference is 90 , allowing a complete ripple cancellation for duty cycles of 25%, 50%, and 75%. Current reference generates reference voltage which is shielded by and fed differentially to the synchronization circuits inside each single-phase module. The only output decoupling capacitor integrated on-chip. was a 2.5-nF capacitor H. On-Chip Load The load current demand is emulated by an on-chip current , with a programmable dc offset, amplitude, and source, ramp time (Fig. 6). The range of ramp times is from 100 to 500 ps. The load can be triggered either by an internal ring os. cillator or by an external clock I. Test Chip Layout The test chip was implemented in a 90-nm CMOS technology [5]. The dc–dc converter was a part of a 3500 m 4500 m die out of which it occupied a silicon area of 1280 m 990 m (see Fig. 7). After subtracting the area of iload, decoupling capacitors, and overhead circuitry used for scanning the config- Fig. 7. DC–DC converter microphotograph. uration and internal signal probing, the area occupied by the 140 m. Each singlebridges and controllers is 1000 m phase module utilized four C4 bumps for bridge output, ground ), , and . ( Fig. 8 shows the chip packaged in a flip-chip BGA package attached to the circuit board. Four air core surface-mount inductors manufactured by Coilcraft [6] were soldered to pads on the die side of the package. According to the measurements in [6], these inductors achieve factors of 20 at 100 MHz, 30 at 300 MHz, and 90 at 2 GHz. For high-frequency measurement 842 IEEE JOURNAL OF SOLID-STATE CIRCUITS, VOL. 40, NO. 4, APRIL 2005 Fig. 8. Photograph of the prototype. Four air core inductors are mounted on the package. Fig. 9. Bridge outputs showing four-phase operation of a dc–dc converter. of the droop, a probe signal on output was routed via a 50- series-terminated connection to a dedicated C4 bump, a 50- package trace, and a miniature 50- coaxial cable that connected directly to the die side of the package. The oscilloscope had a bandwidth of 4 GHz. III. MEASUREMENT RESULTS The dc–dc converter test chip was designed to operate at a switching frequency from 100 MHz to about 600 MHz. Power loss in charging of the gate capacitance of the bridges increases with frequency while the resistive loss due to the ripple current in the inductors and the bridges decreases with frequency. The optimum frequency is selected such that the total loss is minimized and the efficiency maximized. The optimum point depends on the value of the inductors. A. Four-Phase Operation Fig. 9 shows the bridge outputs probed on the leads of the inductors on top of the package. The bridges operate with a duty cycle of 75% and are shifted by 90 to cancel out the ripple. For an inductor of 6.8 nH/phase, the optimum switching frequency is 233 MHz. B. Efficiency Measured efficiencies for 1.2 V/0.9 V and 1.4 V/1.1 V conversion are shown in Figs. 10 and 11, respectively. For a load current of about 0.2 A, the efficiency improves at larger inductance and lower frequency due to reduced switching loss and to the resistive loss associated with the ripple current. However, Fig. 10. Measured efficiency for 1.2 to 0.9 V conversion with I = 0:3 A. Fig. 11. Measured efficiency for 1.4 to 1.1 V conversion with I = 0:4 A. at a larger load current of about 0.3 A, the resistive loss due to the load current is significant. Inductors with the same form factor and technology, e.g., air core with copper wires, exhibit about the same factor at a given frequency. A larger induc. Therefore, the tance comes with a larger series resistance efficiency of a dc–dc converter with a larger inductance and higher peak efficiency degrades faster when the load current increases and eventually becomes worse than the efficiency of a dc–dc converter with a smaller inductance that runs at higher frequency. C. Efficiency With Body Bias To improve efficiency we applied a forward bias of 500 mV to the N-well of the PMOS transistors in the bridges. Forward body bias reduced the series resistance and the resistive loss of the bridges by about 10%. Since this type of loss contributes about one-third of the total loss, the overall loss reduction is about 3%. For a dc–dc converter efficiency of 85%, the total loss is 15% of the input power. A 3% reduction translates into about a 0.5% improvement in efficiency, which is in agreement with the measurements in Fig. 12. At larger load currents, the improvement is as much as 1%. D. Transient Response The transient response of the dc–dc converter was measured by changing the load current between two values with a 100-ps ramp time. From the analysis of typical circuits on a microprocessor, it was found that the maximum instantaneous load change is about 50% of the maximum load current. For 1.2 V/0.9 V conversion, the maximum load current is 300 mA. Fig. 13 shows the response of the converter for a load step from 0 to 150 mA. In all cases, the on-chip decoupling capacitor was HAZUCHA et al.: A 233-MHz 80%–87% EFFICIENT FOUR-PHASE DC–DC CONVERTER UTILIZING AIR-CORE INDUCTORS ON PACKAGE Fig. 12. Efficiency with (solid) and without (hollow) a 0.5-V forward body bias applied to the PMOS transistor of the bridge. 843 Fig. 14. Tradeoff between output decoupling requirement, inductor size, switching frequency, and efficiency. TABLE I SUMMARY OF PERFORMANCE Fig. 13. Output voltage noise for 1.2 to 0.9 V conversion with a 50% load step from 0 to 150 mA in 100 ps. 2.5 nF. At 3.6 nH, the response time of the converter is limited both by the delay in the controller and the bridges, and the slew rate of current in the inductors. As the inductance increases to 15 nH, the response time becomes dominated by the slew degrades rate of the inductor current. Therefore, droop for larger inductance values. The specified 10% droop is met for a 3.6 nH and 6.8 nH inductance per phase. The output has a steady-state error of about 50 mV which was intentionally introduced by voltage positioning. TABLE II PERFORMANCE COMPARISON E. Design Tradeoffs It is apparent from Figs. 10 and 13 that higher inductance improves efficiency and degrades transient response. However, excessive droop can be corrected by adding more decoupling capacitance either on-chip or off-chip. So for a constant droop, there is a tradeoff between the efficiency and the size of the decoupling capacitance. Fig. 14 illustrates the tradeoffs for a 10% droop. For a 2.5-nF decoupling, the maximum efficiency is 83.2%. This efficiency is achieved by operating at 233 MHz with an inductor of 6.8 nH. However, if the decoupling capacitor increases to 6.8 nF, the efficiency improves to 87% if the converter operates at 100 MHz with 36 nH/phase. IV. PERFORMANCE COMPARISON Table I gives a summary of the measured performance for 1.2 V/0.9 V and 1.4 V/1.1 V conversion. Power efficiencies of 82.5% and 83.2% are achieved at bridge current densities of 15 A/mm and 20 A/mm , respectively. These current densities give the ultimate limit that could be achieved for a large dc–dc converter with the controller circuits occupying much less area than the bridges. Table II shows a comparison with previously reported on-chip converters [7]–[11]. All the designs had a similar output rating of about 0.3 A and comparable efficiency. Our dc–dc converter was implemented in a standard 90-nm low-voltage CMOS 844 IEEE JOURNAL OF SOLID-STATE CIRCUITS, VOL. 40, NO. 4, APRIL 2005 process. The combined switching and resistive losses for these transistors are about 10% of the output power at frequencies as high as 100 MHz. The sizes of the inductors and the decoupling capacitor decrease linearly with frequency resulting in about 100–300 reduction. The combination of four-phase topology and hysteretic control reduced the decoupling capacitance by additional 5–10 . At that point, the sizes of the inductors and the decoupling capacitor were reduced by three orders of magnitude and we could utilize low-cost small-size high-frequency air-core inductors instead of inductors with magnetic cores that operate at frequencies of a few megahertz. V. CONCLUSION We have demonstrated an integrated dc–dc converter implemented in a 90-nm logic technology with off-chip air-core inductors soldered to the package. High switching frequency (100–317 MHz), fast hysteretic control, and four-phase design enable a 1000 reduction in inductor and capacitor size and elimination of the inductor magnetic core. The die area overhead of the integrated converter circuits is estimated to be 3%–4% for a 2-cm microprocessor with an 80-A current demand and an on-chip decoupling capacitor of 670 nF. Such a capacitance would be present on the power grid as nonswitching circuit capacitance and decoupling capacitance. To our knowledge, integration of inductors for 80 A of load current on the package or on the chip has not been demonstrated yet. REFERENCES [1] S. Mathew, M. Anders, B. Bloechel, T. Nguyen, R. Krishnamurthy, and S. Borkar, “A 4 GHz 300 mW 64 b integer execution ALU with dual supply voltages in 90 nm CMOS,” in IEEE Int. Solid-State Circuits Conf. (ISSCC) Dig. Tech. Papers, vol. 519, Feb. 2004, pp. 162–163. [2] J. A. Abu-Qahouq, N. Pongratananukul, I. Batarseh, and T. Kasparis, “Multiphase voltage-mode hysteretic controlled VRM with DSP control and novel current sharing,” in Proc. IEEE Int. Caracas Conf. Devices, Circuits and Systems, Apr. 2002, pp. P017-1–P017-7. [3] R. Redl, B. P. Erisman, and Z. Zansky, “Optimizing the load transient response of the buck converter,” in Proc. IEEE Applied Power Electronics Conf. Expo. (APEC), vol. 1, Feb. 1998, pp. 170–176. [4] A. Waizman and C.-Y. Chung, “Resonant free power network design using extended adaptive voltage positioning (EAVP) methodology,” IEEE Trans. Adv. Packag., vol. 24, no. 3, pp. 236–244, Aug. 2001. [5] K. Kuhn et al., “A 90 nm communication technology featuring SiGe HBT transistors, RF CMOS, precision R-L-C RF elements and 1 mm 6-T SRAM cell,” in Int. Electron Devices Meeting (IEDM) Tech. Dig., Dec. 2002, pp. 73–76. [6] Coilcraft. [Online]. Available: http://www.coilcraft.com [7] M. Mino, K. Tsukamoto, K. Yanagisawa, A. Tago, and T. Yachi, “A compact buck-converter using a thin-film inductor,” in Proc. IEEE Applied Power Electronics Conf. Expo. (APEC), vol. 1, Mar. 1996, pp. 422–426. [8] S. Sakiyama, J. Kajiwara, M. Kinoshita, K. Satomi, K. Ohtani, and A. Matsuzawa, “An on-chip high-efficiency and low-noise DC/DC converter using divided switches with current control technique,” in IEEE Int. Solid-State Circuits Conf. (ISSCC) Dig. Tech. Papers, Feb. 1999, pp. 156–157. [9] Y. Katayama, S. Sugahara, H. Nakazawa, and M. Edo, “High-powerdensity MHz-switching monolithic DC-DC converter with thin-film inductor,” in Proc. IEEE Power Electronics Specialists Conf., vol. 3, June 2000, pp. 1485–1490. [10] J. Kim and M. A. Horowitz, “An efficient digital sliding controller for adaptive power-supply regulation,” IEEE J. Solid-State Circuits, vol. 37, no. 5, pp. 639–647, May 2002. [11] K. H. Kim, J. Kim, H. J. Kim, S. K. Han, and H. J. Kim, “A megahertz switching DC/DC converter using FeBN thin film inductor,” IEEE Trans. Magn., vol. 38, no. 5, pp. 3162–3164, Sep. 2002. [12] P. Hazucha, T. Karnik, B. A. Bloechel, C. Parsons, D. Finan, and S. Borkar, “Area-efficient linear regulator with ultra-fast load regulation,” IEEE J. Solid-State Circuits, vol. 40, no. 4, pp. 933–940, Apr. 2005. Peter Hazucha (M’01) was born in Slovakia. He received the Ph.D. degree in physics from Linkoping University, Sweden, in 2000. Since 2001, he has been with the Circuit Research Laboratory at Intel Corporation. For the past five years, he has been actively working on neutron soft error rate characterization of CMOS processes including P1262, and soft error hardening techniques. Since 2001, he has also been involved in design of high-frequency voltage regulators and dc–dc converters. Gerhard Schrom received the M.S. and Ph.D. degrees from the Technical University Vienna, Austria, in 1992 and 1998, respectively. His Ph.D. research work encompassed device and circuit simulation, device modeling, and low-voltage/low-power CMOS technology. After joining Intel Corporation in 1998, he worked on the development of Intel’s 0.13-m technology. Since 2001, he has been with Intel Laboratories, Hillsboro, OR, where he has worked on device parameter variation analysis and the design of on-chip dc–dc converters. He has authored or co-authored over 20 papers. His research interests include device and circuit simulation, circuit design and synthesis, process technology and device design, signal and image processing, and TCAD framework aspects. Jaehong Hahn received the B.S. degree from Seoul National University, Seoul, Korea, in 1989, and the Ph.D. degree from Texas A&M University, College Station, in 2002. From 1989 to 1994, he was a Design Engineer at the Research and Development Center, Daewoo Heavy Industries, Incheon, Korea. From 1994 to 1995, he was a Field Application Engineer with Linear Technology Corporation. From 1995 to 1996, he was with Maxim Integrated Products, Inc., as a Senior Field Application Engineer. He joined the Mobile Platforms Group at Intel in 2002 and is currently working as a Platforms Engineer. His research interest is power electronics application to power quality and clean power converters. Bradley A. Bloechel (M’95–A’96) received the A.A.S. degree in electronic engineering technology from Portland Community College, Portland, OR, in 1986. He joined Intel Corporation, Hillsboro, OR, in 1987 as a Graphics Design Technician for the iWarp project supporting the RFU and ILU design effort. In 1991, he transferred to Supercomputer Systems Division Component Technology, where he supported VLSI test/validation effort and extensive fixturing support for accurate high-speed test and measurement of the interconnect component used in the Tera ops computer project (Intel, DOE, and Sandia). In 1995, he joined the Circuits Research Laboratory, Microcomputer Research Laboratory, where he is a Senior Laboratory Technician specializing in on-chip dc and high-speed I/O measurements and characterization. Mr. Bloechel is a member of Phi Theta Kappa. Paul Hack, photograph and biography not available at the time of publication. HAZUCHA et al.: A 233-MHz 80%–87% EFFICIENT FOUR-PHASE DC–DC CONVERTER UTILIZING AIR-CORE INDUCTORS ON PACKAGE Gregory E. Dermer (M’78) received the B.S degree in electrical engineering from Indiana Institute of Technology, Fort Wayne, in 1977 and the M.S. degree in electrical and computer engineering from the University of Wisconsin, Madison, in 1983. From 1979 to 1992, he held a variety of processor architecture, logic design, and physical design positions at Cray Research, Inc., Nicolet Instrument Company, Astronautics Corporation of America, and Tandem Computers, Inc. In 1992, he joined Intel Corporation’s Supercomputer Systems Division. While there, he worked on clock system design and reliability modeling for the Intel ASCI Red supercomputer. For the past six years, he has worked in the circuits research area of Intel Laboratories, Hillsboro, OR, on physical design and measurements for high-speed interconnections. Siva Narendra (M’99) received the B.E. degree from the Government College of Technology, Coimbatore, India, in 1992, the M.S. degree from Syracuse University, Syracuse, NY, in 1994, and the Ph.D. degree from the Massachusetts Institute of Technology, Cambridge, in 2002. He has been with Intel Laboratories since 1997, where his research areas include low voltage MOS analog and digital circuits and impact of MOS parameter variation on circuit design. He is an Adjunct Faculty with the Department of Electrical and Computer Engineering, Oregon State University, Corvallis. He has authored or coauthored 44 papers and has 41 issued and 15 pending patents in these areas. Dr. Narendra is an Associate Editor for the IEEE TRANSACTIONS ON VERY LARGE SCALE INTEGRATION (VLSI) SYSTEMS and a member of the ISLPED, ISQED, and DAC/ISSCC Student Design Contest Technical Program Committees. Donald Gardner (M’77) received the Ph.D. degree in engineering from Stanford University, Stanford, CA. He has been with Intel Corporation since 1991 and is currently a Senior Research Engineer in the Circuits Research Laboratory. He is also a Visiting Scientist at Stanford University. He has had appointments as a Visiting Research Scientist at Hitachi Research Laboratories, Japan, and as an Instructor at Stanford University. He is the inventor or co-inventor of 38 patents including for Al-Ti layered metal for interconnections, reflow of copper metal, embedded ground planes, and high-frequency magnetic materials. He has published and presented over 100 electrical engineering, materials science and computer science papers. He enjoys bringing new life to old technologies by blending them with different technologies or recent science and materials. His current interests include silicon-based optoelectronic devices, magnetic materials for inductors, nanostructure design, and process technology. Dr. Gardner has received three Best Paper and Poster awards at international conferences and his recent paper on RF inductors was judged the best at the IEEE IITC conference. 845 Tanay Karnik (M’88–SM’04) received the Ph.D. degree in electrical and computer engineering from the University of Illinois at Urbana-Champaign in 1995. From 1995 to 1999, he worked in the Strategic CAD Laboratory at Intel Corporation working on RTL partitioning and special circuits layout. Since March 1999, he has led the power delivery, soft error rate, and optoelectronics research in the Circuits Research, Intel Laboratories. He worked at Larsen and Toubro (India) Ltd. during 1987–1988 and at AT&T Bell Laboratories during summer 1994. His research interests are in the areas of power delivery, soft errors, VRM circuits, optoelectronics, and physical design. He has published over 25 technical papers and has 10 issued and 25 pending patents in these areas. Dr. Karnik serves on the ICCAD, ISQED, DAC, and ICICDT committees. Vivek De (M’89) received the Ph.D. degree in electrical engineering from Rensselaer Polytechnic Institute, Troy, NY, in 1992. He is a Senior Principal Engineer and Manager of Low Power Circuit Technology research at Intel Labs. in Hillsboro, OR. He is an author of 109 technical papers in refereed international conferences and journals, and three book chapters on low-power design. He has 56 patents issued, with 50 more patents filed (pending) in low-power and high-performance circuits and devices. Dr. De has served as General Chair and Technical Program Chair of the ISLPED, ISQED, and GLSVLSI conferences, and on the technical program committees of DAC and ISQED. He also served as the guest editor of a special issue on low-power electronics for the IEEE TRANSACTIONS ON VERY LARGE SCALE INTEGRATION (VLSI) SYSTEMS. He was the recipient of a Best Paper Award at the 1996 International ASIC Conference in Portland, OR. Shekhar Borkar (M’97) received B.Sc. and M.Sc. degrees in physics from the University of Bombay, Bombay, India, in 1977 and 1979, respectively, and the M.S.E.E. degree from the University of Notre Dame, Notre Dame, IN, in 1981. He joined Intel Corporation, Hillsboro, OR, in 1981, where he worked on the design of the 8051 family of microcontrollers, high-speed communication links for the iWarp multicomputer, and Intel Supercomputers. He is an Intel Fellow, and Director of Circuit Research in the Intel Laboratories, researching low-power high-performance circuits and high-speed signaling. He is also an Adjunct Faculty Member of Oregon Graduate Institute, Beaverton, and teaches digital CMOS VLSI.