This article has been accepted for inclusion in a future issue of this journal. Content is final as presented, with the exception of pagination.

IEEE TRANSACTIONS ON VERY LARGE SCALE INTEGRATION (VLSI) SYSTEMS 1

All Digital Energy Sensing forMinimum Energy Tracking

Sagar Venkatesh Gubbi and Bharadwaj Amrutur

Abstract— Minimizing energy consumption is of utmost importance inan energy starved system with relaxed performance requirements. Thisbrief presents a digital energy sensing method that requires neither aconstant voltage reference nor a time reference. An energy minimizingloop uses this to find the minimum energy point and sets the supplyvoltage between 0.2 and 0.5 V. Energy savings up to 1 275% over existingminimum energy tracking techniques in the literature is achieved.

Index Terms— Droop detector, low power, minimum energypoint (MEP), minimum energy tracking.

I. INTRODUCTION

A whole class of systems, such as wireless sensor systems forremote monitoring, implantable medical electronic devices, and so on,has been made possible by ultralow-power very large scale integrationcircuits. These systems are often severely constrained in size, and thebattery supplying energy will therefore be of limited capacity [1].Since it is often inconvenient or infeasible to replace the battery, itis paramount to minimize the net energy consumed by the system tomaximize its lifetime.

The energy consumption of the system can be reduced by loweringthe supply voltage. However, at very low supply voltages, theleakage energy dominates [2], and the net energy consumed peroperation starts to increase (Fig. 1). The minimum energy point(MEP) depends on the activity factor and is also sensitive to processand temperature variations [3]. Therefore, the location of the MEPchanges during circuit operation. To track the MEP, it is necessaryto sense the energy consumed per operation at different supplyvoltages.

In this brief, we present a digital energy sensing technique thatdoes not require any sort of reference, is robust to process vari-ations and performs well over a wide range of system currentconsumption.

The existing energy sensing method in literature needs both a timeand voltage reference [4]. The approach to sensing energy in [4], letsthe supply capacitor discharge for a fixed number of clock cyclesand then measures the voltage droop via a time-based ADC, whichneeds a time and voltage reference. This scheme also performs poorlywhen there is a large variance in the system current consumption.Our work addresses these issues. Abdallah et al. [5] have jointlyoptimized the dc–dc converter and the load circuit. This however,does not undermine the importance of minimum energy tracking. Anall-digital voltage sensing method is proposed in [6] where voltageis digitized by measuring charge on a small capacitance, whereasthis brief measures small voltage differences by converting voltageto time.

We first describe how the energy minimizing loop works. Then,we present the proposed circuit and estimate the error it makes inmeasuring energy per operation. Finally, we present the performanceof a system using the proposed circuit and compare it with prior art.

Manuscript received October 8, 2013; accepted April 16, 2014.The authors are with the Department of Electrical and Communication

Engineering, Indian Institute of Science, Bangalore 560012, India (e-mail:sagar@ece.iisc.ernet.in; amrutur@ece.iisc.ernet.in).

Color versions of one or more of the figures in this paper are availableonline at http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TVLSI.2014.2320304

Fig. 1. System energy–VDD curve for a 32-tap finite-impulse response (FIR)filter obtained from schematic-level SPICE simulations.

Fig. 2. System incorporating the minimum energy tracking loop.

II. EXISTING MINIMUM ENERGY TRACKING SCHEME

A. Description of the System

A low-power system such as a biomedical sensing platform com-prises the minimum energy tracker, dc–dc converter, and the digitalload circuit (processor, filter etc.), we wish to operate at minimumenergy (Fig. 2). The minimum energy tracking loop locates theMEP dynamically.

B. Finding the MEP

The way the minimum energy tracking loop works is by sensingenergy at each supply voltage. Because, the energy–VDD curve is aconvex function, an algorithm similar to gradient descent can huntthe MEP. Once the minimum energy tracking loop is initiated, itperturbs the supply and measures energy per operation (Eop) at thenew voltage. If there is an increase in Eop, the direction is reversed.Now that the direction to proceed is found, the process is continueduntil there is no longer a decrease in the measured energy, and thealgorithm halts declaring the last chosen supply voltage as the MEP.

C. Issues With the Existing Scheme

The primary difficulty in the existing scheme is the way in whichenergy is sensed. Ramadass and Chandrakasan [4] propose shuttingoff the power supply for Nop cycles and monitoring the supplyvoltage droop to estimate the energy consumed. The energy consumedper operation is given by

E = C(V 2

1 − V 22

)

2Nop. (1)

1063-8210 © 2014 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission.See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.

This article has been accepted for inclusion in a future issue of this journal. Content is final as presented, with the exception of pagination.

2 IEEE TRANSACTIONS ON VERY LARGE SCALE INTEGRATION (VLSI) SYSTEMS

Here, C is the decoupling capacitance and V1 is the supply voltagejust before shutting off the power supply. V2 is the voltage to whichthe supply droops to Nop cycles after disconnecting the power supply.By choosing a sufficiently large decoupling capacitance, the droopV1 − V2 is kept small. Therefore, the approximation V1 + V2 ≈ 2V1is made

E ≈ CV1Vdroop

Nop(2)

V1 − V2 = Vdroop. (3)

The supply voltage V1 is already known. The droop Vdroop isdigitized using an ADC. A measure of energy consumed per operationis obtained by digitally multiplying V1 and Vdroop. To digitize Vdroop,Ramadass and Chandrakasan [4] employ a time-based ADC. Theproblems with this approach are as follows.

1) The ADC needs both a fixed voltage reference and a referenceclock.

2) The droop has to be much larger than the comparator offset(1 mV) of the comparator in the ADC to limit the error inestimating the MEP. This means that if the current consumptionis overestimated and the decoupling capacitor chosen is muchlarger than necessary, the error in estimating the MEP balloons.On the other hand, choosing too small a decoupling capacitorcould potentially cause the droop to be too large resulting infunctional failure.

3) Even if an accurate estimate of the maximum current con-sumption is made, the variance in current consumption posesan issue. For instance, if the circuit consumes only 20%of the maximum current under typical operating conditions,the decoupling capacitor still has to be sized to account forthe maximum possible current consumption, but the error inestimating MEP under typical conditions will be larger thandesirable. We will see in a later section that this happens in a32-tap FIR filter when the number of taps is reduced by gating.

III. PROPOSED MINIMUM ENERGY TRACKING SCHEME

A. Proposed Method for Energy Sensing

To circumvent the issues mentioned in the previous section, wepropose measuring energy per operation by keeping Vdroop fixedand computing V1/Nop as a measure of energy (2). That is tosay, the power supply to the load circuit is shut off and a counteris enabled (Fig. 3). The counter keeps incrementing until Vdroopreaches a certain fixed value. When this happens, the power supplyis reconnected, and the value of the counter is captured, whichgives Nop. The digital controller in Fig. 3 computes V1/Nop as ameasure of energy per operation. V1 is the digital code word ofthe supply voltage that the controller chose and is proportional tothe fraction of VBAT that the dc–dc converter is producing. Notethat it is not necessary to know the absolute value of V1 as longas VBAT remains fixed when the MEP is being located. Thus, voltagereferences are avoided.

Fig. 4 shows a critical path replica ring oscillator providing theclock to the entire system including the energy minimizing loop. Italso shows a delay line longer than the ring oscillator chain powereddirectly from the supply whereas the power supply to the ring oscil-lator and the digital system can be gated (Fig. 2). To measure energy,the power supply is shut off. As the voltage VDD droops, the ringoscillator time period increases exponentially. But, the delay producedby the delay chain remains as before because its power supply isnot gated. After some number of clocks, the delay of the longerdelay chain and the delay of the ring oscillator running at a slightlylower voltage become equal (Fig. 5). The number of clocks for this

Fig. 3. Proposed circuitry in the minimum energy tracking loop.

Fig. 4. Droop detection circuit.

to happen is counted. In this scheme, the signal CLKd is initially(when VDD ≈ Vsup) captured when it is high. Eventually (as VDDdroops), the falling edge of CLKd comes closer to the rising edge ofthe CLK. We should expect the flop to go metastable at this point.This is easily handled by adding a LO-skew inverter to the outputof the flop. This is because, the flop is initially known to capturea 1, then go metastable (possibly) and finally capture 0. Therefore, aLO-skew inverter will ensure that even if the flop goes metastable,the output remains low. The number of clocks elapsed between gatingthe power supply and Y going 1 gives Nop.

The delay of the chain of inverters constituting the ring oscillator(tring) and delay of the delay chain above the ring oscillator (tchain)can be shown [3] to be

tring = VDD e−(1+η)VDD

nVT

Nring∑

i=1

Ki (4)

tchain = Vsup e−(1+η)Vsup

nVT

Ndelay∑

i=1

K′i (5)

where Ki and K′i depend on transistor parameters, n is the ideality

factor, η is the Drain Induced Barrier Lowering factor, and VT is thethermal voltage. The circuit in Fig. 4 detects a 1 when tring becomesjust equal to tchain. The droop at which this happens is given by

Vdroop = nVT

1 + ηln

⎛

⎝ Vsup

(Vsup − Vdroop)

∑Ndelayi=1 K

′i

∑Nringi=1 Ki

⎞

⎠. (6)

Equation (6) shows that Vdroop has a weak dependence on thesupply voltage. If Vdroop is small

Vdroop ≈ nVT

1 + ηln

⎛

⎝∑Ndelay

i=1 K′i

∑Nringi=1 Ki

⎞

⎠. (7)

We shall later examine the impact of supply voltage on the droopdetected by the circuit. Nring is dictated by the critical path of the

This article has been accepted for inclusion in a future issue of this journal. Content is final as presented, with the exception of pagination.

IEEE TRANSACTIONS ON VERY LARGE SCALE INTEGRATION (VLSI) SYSTEMS 3

Fig. 5. Illustration of how the droop detection circuit works.

Fig. 6. Layout of the droop detector.

digital system. From (7), Ndelay is chosen to give a reasonable droopsuch as 15 mV. When making the calculation, all K ’s and K

′’s are

taken to be equal.Although the droop detected is sensitive to temperature, the energy

minimizing loop works without problems because it does not needVdroop to be well specified so long as it is a small constant for allsupply voltages chosen by the loop. The time taken for temperatureto change is much larger than the time taken by the loop to findthe MEP. Hence, the droop remains fixed when the loop is huntingthe MEP.

The proposed droop detector circuit works without needing avoltage reference or time reference. In constructing the minimumenergy tracking loop, the only requirement is that the supply voltagegiven by the dc–dc converter is proportional to the value requestedby the digital controller. The precise value of the supply voltage isnot relevant. Thus, the energy minimizer avoids references altogether.

B. Impact of Process Variations

Equation (7) shows that global process variations have no impacton the droop detected by the circuit. All the Ks are process dependent,but global variations affect the numerator and denominator in anidentical manner and thus Vdroop is left unaffected.

Local variations cause a small variation in the droop detected.However, the proposed energy sensing scheme does not need a precisedroop target. It is sufficient if the droop is kept constant and withintolerable limits across all supply voltages of interest and (7) showsthat the summation averages out the local variations and the droopcan be well controlled.

C. Limitations

This circuit works only at subthreshold voltages, and the droopdetected by the circuit is sensitive to temperature. When the currentconsumption of the load circuit is on the low end of the spectrum, thedroop detector takes many more cycles to detect the droop becausethe voltage droop is slower. Therefore, the energy sensing is slower

Fig. 7. Thousand-point Monte Carlo simulation of the droop detector with10% Vth variation across process corners and 1.5%–4% within die mismatch.

Fig. 8. Thirty-two-tap FIR filter.

when the current consumption is low or the temperature is high. Theenergy sensing can be speeded up by having a programmable delayline in Fig. 4 that changes Ndelay to control the droop depending onthe number of clock cycles it is taking for droop detection. Futurework will include the performance of this circuit in the presence ofpower supply noise and clock jitter.

IV. ERROR ESTIMATION

There are two sources of error in the measurement of energy. Onedue to the approximation made in arriving at (2) and the other dueto variation in the droop detected at different supply voltages.

A. Error Due to Approximation in Computation

Ramadass and Chandrakasan [4] have shown that the error incomputing E because of the approximation V1 + V2 ≈ 2V1 is

δE

E= V1 − V2

V1 + V2. (8)

A constant relative error in energy estimation does not affect theenergy minimizing loop. However, a relative error that changes withthe supply voltage limits the energy resolution. For typical valuessuch as Vdroop = 20 mV and V1+V2 = 250 + 230 = 480 mV at thelowest operating point, this error is 4.166% of energy per operationat 250 mV. To obtain an estimate of the energy resolution, assumethat the energy per operation Eop at VDD = 300 mV is the same asat VDD = 250 mV. The error in estimating Eop at VDD = 300 mVis 3.448% of Eop. Thus the limit on energy resolution due to thisapproximation is 4.166%−3.448% = 0.718% of Eop. This is becausean increase of up to 0.718% in energy per operation at VDD = 300 mVwill not be detected by the circuit and the system continues to operateat VDD = 300 mV, which is no longer the MEP.

This article has been accepted for inclusion in a future issue of this journal. Content is final as presented, with the exception of pagination.

4 IEEE TRANSACTIONS ON VERY LARGE SCALE INTEGRATION (VLSI) SYSTEMS

TABLE IPERFORMANCE OF THE ENERGY MINIMIZING LOOP

B. Error Due to Variation in Droop

For a number of reasons including finite width of the flop’smetastability window, variation in the position of the metastabilitywindow as the supply voltage changes and nonzero droop duringone clock cycle, the droop (Vdroop) fixed by the circuit in Fig. 4 isnot constant across the range of possible supply voltages, rather itis a weak function of the supply voltage. Let δV be the maximumdifference in the droop between two successive supply voltages setby the minimum energy tracking loop. The error in computing energydue to this uncertainty in the detected droop is

δE = Ecomputed − Eactual = CVDDδV

Nop. (9)

The relative error isδE

E= δV

δV + Vdroop. (10)

For typical values of Vdroop = 20 mV and δV = 1 mV, the errorcomes to 4.7%, which limits the energy resolution of this energysensing scheme.

The total error in estimating energy is thus bound by 4.7% +0.718% = 5.418% of the energy per operation (Emin) at MEP.

V. RESULTS

A 32-tap FIR filter and the proposed minimum energy trackingloop were built on the UMC 65-nm 1 Poly, 10-metal-layer low-leakage process (Fig. 6). The simulation results of the droop detectorfollowing post layout extraction are reported. The power data for theFIR filter are from transistor level SPICE simulations of a singlemultiplier.

A. Droop Detector

The performance of the droop detector was analyzed by modelingthe voltage on the decoupling capacitor with the power supply shutoff as a decreasing ramp. The maximum difference between thedroop detected at successive supply voltages is the metric of theperformance.

The distribution of the maximum variation in the droop detected bythe circuit with the supply voltage swept in steps of 50 mV is shownFig. 7. The low-leakage transistors used to construct the ring oscillatorand delay chain have a threshold voltage of about 450 mV. Since theexponential dependence of delay on supply voltage is true only in thesubthreshold region, the performance of the droop detector declinesrapidly when the threshold voltage is crossed as can be observed inFig. 7. If the supply voltage is kept below 0.45 V, the maximumdroop difference is expected to be below 1.414 mV in 99.9% of thechips at the 95% confidence level.

B. Energy Minimizing Loop

Fig. 8 shows a 32-tap FIR filter. It consists of 32 8-bit multipliers,31 adders ranging from 16 to 19 bit, and 31 flops, which totals to21 020 gates. The power consumed by the FIR filter was modeledby testing the multiplier under different input combinations. Thefirst input combination was having the multiplier fixed to 0×FFand the multiplicand swinging between 0×FF and 0×00 onevery clock cycle. This refers to be swinging input case inTable I and is used to estimate the maximum possible currentconsumption of each multiplier. The second input combinationwas keeping the multiplier fixed and having a digital ramp as themultiplicand that reflects the typical power consumption of themultiplier.

The maximum current drawn from the circuit at 0.5 V (Vdd,max) isused to arrive at the decoupling capacitance (off-chip) by finding theminimum capacitance needed to prevent the droop from exceeding20 mV when the power supply is shut off for 100 clock cycles in theproposed circuit and 32 clock cycles for the method in [4]. For theproposed circuit, the needed capacitor is 100 nF and for the methodin [4], it is 32 nF.

It has been suggested that a realistic estimate of energy requiresconsideration of the efficiency of the dc–dc converter. The efficiencyof the dc–dc converter, we have assumed is based on the resultsin [7]. Fig. 1 shows system energy per operation versus VDD, whichincludes losses in the dc–dc converter.

The relative loss of energy by operating at the MEP found byboth the technique presented in [4] and ours when compared withoperating at the actual MEP is shown in Table I. Vdroop for theproposed method was chosen randomly between 20 and 21.4 mVat every voltage step and the maximum error over 10 trials isreported.

The proposed method performs well irrespective of the loadwhereas the method in [4] performs poorly when the current con-sumed is much lower than the estimated maximum because the droopover 32 clock cycles is small and consequently there is a largerrelative error in digitizing the droop.

The energy overhead associated with the proposed scheme inlocating the MEP is equal to the energy of 11 477 operations at MEPof the FIR filter operating with only one tap enabled and the restpower gated, whereas only 463 operations is the overhead in [4].The huge disparity is in part due to the fact that the loop in [4] haltsprematurely before finding the actual MEP. The proposed schemetakes a maximum of 3 s to locate the MEP in the worst-case scenario.This time is much smaller than the time taken for ambient temperatureto change substantially. Thus, the operation of the proposed circuitis independent of ambient temperature.

This article has been accepted for inclusion in a future issue of this journal. Content is final as presented, with the exception of pagination.

IEEE TRANSACTIONS ON VERY LARGE SCALE INTEGRATION (VLSI) SYSTEMS 5

VI. CONCLUSION

We have presented a method of energy sensing that is completelydigital and that does not rely on any fixed references. This makes thesystem robust even at very low voltages. We have demonstrated thatsensing energy by shutting off the power supply works better whenthe droop is fixed rather than when the number of clock cycles isfixed. This also eases the choice of the decoupling capacitance andan overestimate of current consumption will not hurt the performanceof the energy sensing circuit.

REFERENCES

[1] M. Seok et al., “The Phoenix processor: A 30 pW platform forsensor applications,” in Proc. IEEE Symp. VLSI Circuits, Jun. 2008,pp. 188–189.

[2] M. Alioto, “Ultra-low power VLSI circuit design demystified andexplained: A tutorial,” IEEE Trans. Circuits Syst. I, Reg. Papers, vol. 59,no. 1, pp. 3–29, Jan. 2012.

[3] B. H. Calhoun, A. Wang, and A. Chandrakasan, “Modeling andsizing for minimum energy operation in subthreshold circuits,”IEEE J. Solid-State Circuits, vol. 40, no. 9, pp. 1778–1786,Sep. 2005.

[4] Y. K. Ramadass and A. P. Chandrakasan, “Minimum energy trackingloop with embedded DC–DC converter enabling ultra-low-voltage oper-ation down to 250 mV in 65 nm CMOS,” IEEE J. Solid-State Circuits,vol. 43, no. 1, pp. 256–265, Jan. 2008.

[5] R. A. Abdallah, P. S. Shenoy, N. R. Shanbhag, and P. T. Krein, “Systemenergy minimization via joint optimization of the DC-DC converter andthe core,” in Proc. Int. Symp. Low Power Electron. Design, Aug. 2011,pp. 97–102.

[6] R. Ramezani, A. Yakovlev, F. Xia, J. Murphy, and D. Shang, “Voltagesensing using an asynchronous charge-to-digital converter for energy-autonomous environments,” IEEE Trans. Emerg. Sel. Topics CircuitsSyst., vol. 3, no. 1, pp. 35–44, Mar. 2013.

[7] Y. Pu et al., “Misleading energy and performance claims in sub/nearthreshold digital systems,” in Proc. IEEE/ACM Int. Conf. Comput.-AidedDesign, Nov. 2010, pp. 625–631.