ISSCC 2013 / SESSION 24 / ENERGY-AWARE DIGITAL DESIGN / 24.9
24.9

Intermittent Resonant Clocking Enabling Power
Reduction at any Clock Frequency for 0.37V 980kHz
Near-Threshold Logic Circuits

Hiroshi Fuketa1, Masahiro Nomura2, Makoto Takamiya1,Takayasu Sakurai1
University of Tokyo, Tokyo, Japan,Semiconductor Technology Academic Research Center, Yokohama, Japan

The proposed IRC is applied to a 0.37V near-Vt adder array. Fig. 24.9.3(b) showsa block diagram of a test chip. 32 arrays of 32b adders are implemented withinput/output latches. The critical path of each adder is 110 FO4 inverter delays.
In IRC, static CMOS latches, instead of flip-flops, are used, since CKB is not asignal with a 50% duty cycle but a pulse signal, as shown in Fig. 24.9.2(c). In
this paper, VDD = 0.37V is used, because the measured minimum energy of theadder array is achieved at VDD = 0.37V.

12In order to improve the energy efficiency of logic circuits, reductions in capacitance (C) and power supply voltage (VDD) are required, as energy consumption
is proportional to CVDD2. Near-threshold (Vt) operation achieves an energy minimum [1]. Resonant clocking [2-5] can reduce the effective capacitance of theclock distribution network [3]. In this work, a new resonant clocking scheme
enabling power reduction at any clock frequency is proposed and applied to a0.37V 980kHz near-Vt logic circuit in 40nm CMOS.
Figs. 24.9.1(a), (b), and (c) show conventional non-resonant clocking with abuffered H-tree, conventional resonant clocking with an unbuffered H-tree [4-5],and the proposed intermittent resonant clocking (IRC) with an unbuffered Htree, respectively. The conventional resonant clocking in Fig. 24.9.1(b) has threeproblems: 1) The clock frequency (fCLK) range is narrow, typically ±20% [3-5].
At fCLK lower than the resonant frequency (fRES), power higher than that of nonresonant clocking and functional errors due to ringing are observed [2], which
prohibit dynamic frequency scaling (DFS) and low-speed testing. 2) fCLK values
in previous papers [2-5] range from 100MHz to 5GHz and less-than-1MHz operation is difficult to achieve, because a large inductance for the resonance isrequired, which prevents the application of resonant clocking to near-Vt logic circuits. 3) A sinusoidal clock waveform increases the clock skew due to the lowslew rate. To solve these problems, the IRC in Fig. 24.9.1(c) is proposed. In conventional resonant clocking, the clock period (TCLK) is equal to the resonant period (TRES). In contrast, in IRC, TCLK is larger than TRES. Therefore, IRC has threeadvantages: 1) The selection of fCLK is flexible, and power reduction is achievedat any clock frequency. Thus, IRC can be applied to near-Vt logic circuits, andDFS and low-speed testing are possible. 2) The required inductance for the resonance is reduced to (TRES/TCLK)2 of conventional resonant clocking. 3) A small
clock skew owing to a high slew rate is obtained. The slew rate is increased toTCLK/TRES of conventional resonant clocking.
Details of IRC are shown in Fig. 24.9.2. Fig. 24.9.2(a) shows a schematic of thecircuit of an IRC buffer that drives the clock node (CKB). CCLK denotes the capacitance of CKB. A voltage doubler [6] is added to overdrive the gate of nMOS
(M1). Figs. 24.9.2 (b) and (c) show timing waveforms for the IRC circuit. To
illustrate the operating principles of IRC, Fig. 24.9.2(b) shows timing waveforms
with a step input applied. Fig. 24.9.2(c) shows actual IRC operation with a pulse
input. When Pulse is high, IRC is in a resonant mode. In contrast, when Pulse islow, IRC is in a non-resonant mode. In IRC, both the resonant mode and thenon-resonant mode are mixed within a clock period and TCLK is larger than TRES,
thereby enabling the flexible selection of fCLK. The pulse width (TPW) of Pulseshown Fig. 24.9.2(c) is an important parameter for IRC to minimize the clockingpower. In Fig. 24.9.2(b), after the step input, CKB shows ringing at around 0V.
To minimize the clocking power, the highest voltage in the ringing shown as“Point A” in Fig. 24.9.2(b) indicates the best timing for TPW, because the power
required to pull up CKB to VDD is minimized at Point A. The timing of Point A corresponds to TRES, as shown in Fig. 24.9.2(b). In contrast, the lowest voltage inthe ringing at T1 indicates the worst timing at which the clocking power is maximized. Similarly, T2 indicates the second worst timing.
To minimize the clocking power, the large ringing observed in Fig. 24.9.2(b) isrequired. Such ringing is determined by the resistance of the LC resonator,
which is dominated by the ON resistance of M1 in Fig. 24.9.2(a). In the 0.37V
near-Vt logic circuit, however, the ON resistance at VDD = 0.37V is very high. To
decrease the ON resistance with small area and power overhead, the gate of M1
is boosted by the voltage doubler. Fig. 24.9.3(a) shows a simulated comparisonof the gate widths and powers of M1 with and without gate boosting at the same
ON resistance. At the same ON resistance, the proposed gate boosting with thevoltage doubler reduces the gate width of M1 and the power dissipation to drive
M1 by 97% and 91%, respectively.

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In the test chip, conventional non-resonant clocking with an unbuffered clock
tree is also implemented for comparison, since clocking with an unbuffered tree
is more energy-efficient than that with a buffered tree in near/sub-Vt circuits [7].
Figures 24.9.4 (a) and (b) show conventional non-resonant clocking and the proposed IRC, respectively. For a fair power comparison, the unbuffered clock tree
is the same and the gate widths of the clock drivers are designed to have thesame slew rate. Compared with conventional non-resonant clocking, the total
gate width of the proposed IRC is reduced by 84%. Fig. 24.9.4 also shows themeasured waveforms of CKB at VDD = 0.37V and fCLK = 980kHz. The measured
waveform in Fig. 24.9.4(b) validates the qualitative waveform in Fig. 24.9.2(c).
The measured slew rates in Figs. 24.9.4(a) and (b) are similar. In IRC, the measured fRES is 19MHz with an off-chip inductor of 7µH, which corresponds to CCLKof 10pF. In this implementation, TCLK/TRES = 19. Therefore, the required inductance of IRC for the resonance is reduced to 1/192 = 1/361× that of conventional resonant clocking, and the slew rate is increased to 19× that of conventional
resonant clocking.
To validate the discussion on the optimum TPW in Figs. 24.9.2 (b) and (c), Fig.
24.9.5 shows the measured TPW dependence of the clock power of IRC. The
clock power of the conventional non-resonant clocking (Fig. 24.9.4(a)) is also
shown for comparison. As expected, the minimum clock power is achieved at
TPW = TRES with the power reduction of -36%.
To demonstrate power reduction at any clock frequency in the proposed IRC,Fig. 24.9.6 shows the measured fCLK dependence of the clock powers of conventional non-resonant clocking and the proposed IRC. In IRC, the clock power is
proportional to fCLK, which is different from that observed in conventional resonant clocking [2-5]. Compared with that of conventional non-resonant clocking,the clock power of IRC is reduced at all fCLK values, which is the most important
advantage of the proposed IRC. At fCLK = 980kHz, the clock power is reduced by
36% and the total power including the adder array is reduced by 10%. When theclock is stopped, the clock leakage power is reduced by 81%, owing to the 84%
gate width reduction in Fig. 24.9.4.
Fig. 24.9.7(a) shows a die micrograph of the test chip in 40nm CMOS. The area
overhead due to the voltage doubler is 0.6%. Fig. 24.9.7(b) shows a comparison
with prior work.
Acknowledgements:
This work was carried out as a part of the Extremely Low Power (ELP) project
supported by METI and NEDO.
References:[1] H. Kaul, et al., “A 320mV 56µW 411GOPS/Watt Ultra-Low Voltage Motion
Estimation Accelerator in 65nm CMOS,” ISSCC Dig. Tech. Papers, pp. 316-317,
2008.
[2] S. Chan, et al., “A Resonant Global Clock Distribution for the Cell BroadbandEngine Processor,” ISSCC Dig. Tech. Papers, pp. 512-513, 2008.
[3] V. Sathe, et al., “Resonant Clock Design for a Power-Efficient High-Volume
x86-64 Microprocessor,” ISSCC Dig. Tech. Papers, pp. 68-69, 2012.
[4] V. Sathe, et al., “A 0.8-1.2GHz Single-Phase Resonant-Clocked FIR Filter with
Level-Sensitive Latches,” IEEE Custom Integrated Circuits Conf., pp. 583-586,
2007.
[5] A. Ishii, et al., “A Resonant-Clock 200MHz ARM926EJ-STM Microcontroller,”
European Solid-State Circuits Conf., pp. 356-359, 2009.
[6] N. Verma, et al., “A 65nm 8T Sub-Vt SRAM Employing Sense-AmplifierRedundancy,” ISSCC Dig. Tech. Papers, pp. 328-329, 2007.
[7] M. Seok, et al., “Clock Network Design for Ultra-Low Power Applications,”
ACM/IEEE International Symp. Low-Power Electronics Design, pp. 271-276,
2010.

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ISSCC 2013 / February 20, 2013 / 5:00 PM

Figure 24.9.1: (a) Conventional non-resonant clocking; (b) conventional
resonant clocking [4-5]; (c) proposed intermittent resonant clocking (IRC).

Figure 24.9.2: (a) IRC buffer; (b) timing waveforms of IRC with a step input;(c) timing waveforms of IRC operation with a pulse input.

Figure 24.9.3: (a) Simulated comparison of gate widths and powers of M1;(b) block diagram of test chip including adder array and IRC.

Figure 24.9.4: Two clocking circuits in test chip for comparison.
(a) Conventional non-resonant clocking [7]; (b) proposed IRC.

24

Figure 24.9.5: Measured dependence of clock power on pulse width of Pulse
signal (TPW).

Figure 24.9.6: Measured fCLK dependence of clock powers of conventional
non-resonant clocking and proposed IRC.

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Figure 24.9.7: Die micrograph and compairison with previous works.

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