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IEEE TRANSACTIONS ON VERY LARGE SCALE INTEGRATION (VLSI) SYSTEMS
1
All Digital Energy Sensing for
Minimum Energy Tracking
Sagar Venkatesh Gubbi and Bharadwaj Amrutur
Abstract— Minimizing energy consumption is of utmost importance in
an energy starved system with relaxed performance requirements. This
brief presents a digital energy sensing method that requires neither a
constant voltage reference nor a time reference. An energy minimizing
loop uses this to find the minimum energy point and sets the supply
voltage between 0.2 and 0.5 V. Energy savings up to 1 275% over existing
minimum energy tracking techniques in the literature is achieved.
Index Terms— Droop detector, low
point (MEP), minimum energy tracking.
power,
minimum
energy
Fig. 1. System energy–VDD curve for a 32-tap finite-impulse response (FIR)
filter obtained from schematic-level SPICE simulations.
I. I NTRODUCTION
A whole class of systems, such as wireless sensor systems for
remote monitoring, implantable medical electronic devices, and so on,
has been made possible by ultralow-power very large scale integration
circuits. These systems are often severely constrained in size, and the
battery supplying energy will therefore be of limited capacity [1].
Since it is often inconvenient or infeasible to replace the battery, it
is paramount to minimize the net energy consumed by the system to
maximize its lifetime.
The energy consumption of the system can be reduced by lowering
the supply voltage. However, at very low supply voltages, the
leakage energy dominates [2], and the net energy consumed per
operation starts to increase (Fig. 1). The minimum energy point
(MEP) depends on the activity factor and is also sensitive to process
and temperature variations [3]. Therefore, the location of the MEP
changes during circuit operation. To track the MEP, it is necessary
to sense the energy consumed per operation at different supply
voltages.
In this brief, we present a digital energy sensing technique that
does not require any sort of reference, is robust to process variations and performs well over a wide range of system current
consumption.
The existing energy sensing method in literature needs both a time
and voltage reference [4]. The approach to sensing energy in [4], lets
the supply capacitor discharge for a fixed number of clock cycles
and then measures the voltage droop via a time-based ADC, which
needs a time and voltage reference. This scheme also performs poorly
when there is a large variance in the system current consumption.
Our work addresses these issues. Abdallah et al. [5] have jointly
optimized the dc–dc converter and the load circuit. This however,
does not undermine the importance of minimum energy tracking. An
all-digital voltage sensing method is proposed in [6] where voltage
is digitized by measuring charge on a small capacitance, whereas
this brief measures small voltage differences by converting voltage
to time.
We first describe how the energy minimizing loop works. Then,
we present the proposed circuit and estimate the error it makes in
measuring energy per operation. Finally, we present the performance
of 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 available
online at http://ieeexplore.ieee.org.
Digital Object Identifier 10.1109/TVLSI.2014.2320304
Fig. 2.
System incorporating the minimum energy tracking loop.
II. E XISTING M INIMUM E NERGY T RACKING S CHEME
A. Description of the System
A low-power system such as a biomedical sensing platform comprises the minimum energy tracker, dc–dc converter, and the digital
load circuit (processor, filter etc.), we wish to operate at minimum
energy (Fig. 2). The minimum energy tracking loop locates the
MEP dynamically.
B. Finding the MEP
The way the minimum energy tracking loop works is by sensing
energy at each supply voltage. Because, the energy–VDD curve is a
convex function, an algorithm similar to gradient descent can hunt
the MEP. Once the minimum energy tracking loop is initiated, it
perturbs the supply and measures energy per operation (E op ) at the
new voltage. If there is an increase in E op , the direction is reversed.
Now that the direction to proceed is found, the process is continued
until there is no longer a decrease in the measured energy, and the
algorithm 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 which
energy is sensed. Ramadass and Chandrakasan [4] propose shutting
off the power supply for Nop cycles and monitoring the supply
voltage droop to estimate the energy consumed. The energy consumed
per operation is given by
C V12 − V22
.
(1)
E=
2Nop
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IEEE TRANSACTIONS ON VERY LARGE SCALE INTEGRATION (VLSI) SYSTEMS
Here, C is the decoupling capacitance and V1 is the supply voltage
just before shutting off the power supply. V2 is the voltage to which
the supply droops to Nop cycles after disconnecting the power supply.
By choosing a sufficiently large decoupling capacitance, the droop
V1 − V2 is kept small. Therefore, the approximation V1 + V2 ≈ 2V1
is made
C V1 Vdroop
(2)
E ≈
Nop
V1 − V2 = Vdroop .
(3)
The supply voltage V1 is already known. The droop Vdroop is
digitized using an ADC. A measure of energy consumed per operation
is obtained by digitally multiplying V1 and Vdroop . To digitize Vdroop ,
Ramadass and Chandrakasan [4] employ a time-based ADC. The
problems with this approach are as follows.
1) The ADC needs both a fixed voltage reference and a reference
clock.
2) The droop has to be much larger than the comparator offset
(1 mV) of the comparator in the ADC to limit the error in
estimating the MEP. This means that if the current consumption
is overestimated and the decoupling capacitor chosen is much
larger than necessary, the error in estimating the MEP balloons.
On the other hand, choosing too small a decoupling capacitor
could potentially cause the droop to be too large resulting in
functional failure.
3) Even if an accurate estimate of the maximum current consumption is made, the variance in current consumption poses
an 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 for
the maximum possible current consumption, but the error in
estimating MEP under typical conditions will be larger than
desirable. We will see in a later section that this happens in a
32-tap FIR filter when the number of taps is reduced by gating.
III. P ROPOSED M INIMUM E NERGY T RACKING S CHEME
A. Proposed Method for Energy Sensing
To circumvent the issues mentioned in the previous section, we
propose measuring energy per operation by keeping Vdroop fixed
and computing V1 /Nop as a measure of energy (2). That is to
say, the power supply to the load circuit is shut off and a counter
is enabled (Fig. 3). The counter keeps incrementing until Vdroop
reaches a certain fixed value. When this happens, the power supply
is reconnected, and the value of the counter is captured, which
gives Nop . The digital controller in Fig. 3 computes V1 /Nop as a
measure of energy per operation. V1 is the digital code word of
the supply voltage that the controller chose and is proportional to
the fraction of VBAT that the dc–dc converter is producing. Note
that it is not necessary to know the absolute value of V1 as long
as VBAT remains fixed when the MEP is being located. Thus, voltage
references are avoided.
Fig. 4 shows a critical path replica ring oscillator providing the
clock to the entire system including the energy minimizing loop. It
also shows a delay line longer than the ring oscillator chain powered
directly from the supply whereas the power supply to the ring oscillator and the digital system can be gated (Fig. 2). To measure energy,
the power supply is shut off. As the voltage VDD droops, the ring
oscillator time period increases exponentially. But, the delay produced
by the delay chain remains as before because its power supply is
not gated. After some number of clocks, the delay of the longer
delay chain and the delay of the ring oscillator running at a slightly
lower 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 VDD
droops), the falling edge of CLKd comes closer to the rising edge of
the CLK. We should expect the flop to go metastable at this point.
This is easily handled by adding a LO-skew inverter to the output
of the flop. This is because, the flop is initially known to capture
a 1, then go metastable (possibly) and finally capture 0. Therefore, a
LO-skew inverter will ensure that even if the flop goes metastable,
the output remains low. The number of clocks elapsed between gating
the 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
Ki
(4)
i=1
tchain = Vsup e
−(1+η)Vsup
nVT
Ndelay
Ki
(5)
i=1
where K i and K i depend on transistor parameters, n is the ideality
factor, η is the Drain Induced Barrier Lowering factor, and VT is the
thermal voltage. The circuit in Fig. 4 detects a 1 when tring becomes
just equal to tchain . The droop at which this happens is given by
⎛
Ndelay ⎞
Vsup
nVT
i=1 K i ⎠
Vdroop =
.
(6)
ln ⎝
Nring
1+η
(Vsup − Vdroop )
K
i=1
i
Equation (6) shows that Vdroop has a weak dependence on the
supply voltage. If Vdroop is small
⎞
⎛
Ndelay Ki
nVT
i=1
⎠.
(7)
ln ⎝ N
Vdroop ≈
ring
1+η
K
i=1
i
We shall later examine the impact of supply voltage on the droop
detected by the circuit. Nring is dictated by the critical path of the
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IEEE TRANSACTIONS ON VERY LARGE SCALE INTEGRATION (VLSI) SYSTEMS
Fig. 5.
3
Illustration of how the droop detection circuit works.
Fig. 7. Thousand-point Monte Carlo simulation of the droop detector with
10% Vth variation across process corners and 1.5%–4% within die mismatch.
Fig. 6.
Layout of the droop detector.
digital system. From (7), Ndelay is chosen to give a reasonable droop
such 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 need
Vdroop to be well specified so long as it is a small constant for all
supply voltages chosen by the loop. The time taken for temperature
to change is much larger than the time taken by the loop to find
the MEP. Hence, the droop remains fixed when the loop is hunting
the MEP.
The proposed droop detector circuit works without needing a
voltage reference or time reference. In constructing the minimum
energy tracking loop, the only requirement is that the supply voltage
given by the dc–dc converter is proportional to the value requested
by the digital controller. The precise value of the supply voltage is
not relevant. Thus, the energy minimizer avoids references altogether.
There are two sources of error in the measurement of energy. One
due to the approximation made in arriving at (2) and the other due
to variation in the droop detected at different supply voltages.
B. Impact of Process Variations
A. Error Due to Approximation in Computation
Equation (7) shows that global process variations have no impact
on the droop detected by the circuit. All the Ks are process dependent,
but global variations affect the numerator and denominator in an
identical 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 precise
droop target. It is sufficient if the droop is kept constant and within
tolerable limits across all supply voltages of interest and (7) shows
that the summation averages out the local variations and the droop
can be well controlled.
Ramadass and Chandrakasan [4] have shown that the error in
computing E because of the approximation V1 + V2 ≈ 2V1 is
δE
V1 − V2
.
(8)
=
E
V1 + V2
A constant relative error in energy estimation does not affect the
energy minimizing loop. However, a relative error that changes with
the supply voltage limits the energy resolution. For typical values
such as Vdroop = 20 mV and V1 +V2 = 250 + 230 = 480 mV at the
lowest operating point, this error is 4.166% of energy per operation
at 250 mV. To obtain an estimate of the energy resolution, assume
that the energy per operation E op at VDD = 300 mV is the same as
at VDD = 250 mV. The error in estimating E op at VDD = 300 mV
is 3.448% of E op . Thus the limit on energy resolution due to this
approximation is 4.166%−3.448% = 0.718% of E op . This is because
an increase of up to 0.718% in energy per operation at VDD = 300 mV
will not be detected by the circuit and the system continues to operate
at VDD = 300 mV, which is no longer the MEP.
C. Limitations
This circuit works only at subthreshold voltages, and the droop
detected by the circuit is sensitive to temperature. When the current
consumption of the load circuit is on the low end of the spectrum, the
droop detector takes many more cycles to detect the droop because
the voltage droop is slower. Therefore, the energy sensing is slower
Fig. 8.
Thirty-two-tap FIR filter.
when the current consumption is low or the temperature is high. The
energy sensing can be speeded up by having a programmable delay
line in Fig. 4 that changes Ndelay to control the droop depending on
the number of clock cycles it is taking for droop detection. Future
work will include the performance of this circuit in the presence of
power supply noise and clock jitter.
IV. E RROR E STIMATION
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IEEE TRANSACTIONS ON VERY LARGE SCALE INTEGRATION (VLSI) SYSTEMS
TABLE I
P ERFORMANCE OF THE E NERGY M INIMIZING L OOP
B. Error Due to Variation in Droop
B. Energy Minimizing Loop
For a number of reasons including finite width of the flop’s
metastability window, variation in the position of the metastability
window as the supply voltage changes and nonzero droop during
one clock cycle, the droop (Vdroop ) fixed by the circuit in Fig. 4 is
not constant across the range of possible supply voltages, rather it
is a weak function of the supply voltage. Let δV be the maximum
difference in the droop between two successive supply voltages set
by the minimum energy tracking loop. The error in computing energy
due to this uncertainty in the detected droop is
C VDD δV
.
(9)
δ E = E computed − E actual =
Nop
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 to
21 020 gates. The power consumed by the FIR filter was modeled
by testing the multiplier under different input combinations. The
first input combination was having the multiplier fixed to 0×FF
and the multiplicand swinging between 0×FF and 0×00 on
every clock cycle. This refers to be swinging input case in
Table I and is used to estimate the maximum possible current
consumption of each multiplier. The second input combination
was keeping the multiplier fixed and having a digital ramp as the
multiplicand that reflects the typical power consumption of the
multiplier.
The maximum current drawn from the circuit at 0.5 V (Vdd,max ) is
used to arrive at the decoupling capacitance (off-chip) by finding the
minimum capacitance needed to prevent the droop from exceeding
20 mV when the power supply is shut off for 100 clock cycles in the
proposed circuit and 32 clock cycles for the method in [4]. For the
proposed circuit, the needed capacitor is 100 nF and for the method
in [4], it is 32 nF.
It has been suggested that a realistic estimate of energy requires
consideration of the efficiency of the dc–dc converter. The efficiency
of the dc–dc converter, we have assumed is based on the results
in [7]. Fig. 1 shows system energy per operation versus VDD , which
includes losses in the dc–dc converter.
The relative loss of energy by operating at the MEP found by
both the technique presented in [4] and ours when compared with
operating at the actual MEP is shown in Table I. Vdroop for the
proposed method was chosen randomly between 20 and 21.4 mV
at every voltage step and the maximum error over 10 trials is
reported.
The proposed method performs well irrespective of the load
whereas the method in [4] performs poorly when the current consumed is much lower than the estimated maximum because the droop
over 32 clock cycles is small and consequently there is a larger
relative error in digitizing the droop.
The energy overhead associated with the proposed scheme in
locating the MEP is equal to the energy of 11 477 operations at MEP
of the FIR filter operating with only one tap enabled and the rest
power 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] halts
prematurely before finding the actual MEP. The proposed scheme
takes 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 temperature
to change substantially. Thus, the operation of the proposed circuit
is independent of ambient temperature.
The relative error is
δE
δV
.
(10)
=
E
δV + Vdroop
For typical values of Vdroop = 20 mV and δV = 1 mV, the error
comes to 4.7%, which limits the energy resolution of this energy
sensing scheme.
The total error in estimating energy is thus bound by 4.7% +
0.718% = 5.418% of the energy per operation (E min ) at MEP.
V. R ESULTS
A 32-tap FIR filter and the proposed minimum energy tracking
loop were built on the UMC 65-nm 1 Poly, 10-metal-layer lowleakage process (Fig. 6). The simulation results of the droop detector
following post layout extraction are reported. The power data for the
FIR filter are from transistor level SPICE simulations of a single
multiplier.
A. Droop Detector
The performance of the droop detector was analyzed by modeling
the voltage on the decoupling capacitor with the power supply shut
off as a decreasing ramp. The maximum difference between the
droop detected at successive supply voltages is the metric of the
performance.
The distribution of the maximum variation in the droop detected by
the circuit with the supply voltage swept in steps of 50 mV is shown
Fig. 7. The low-leakage transistors used to construct the ring oscillator
and delay chain have a threshold voltage of about 450 mV. Since the
exponential dependence of delay on supply voltage is true only in the
subthreshold region, the performance of the droop detector declines
rapidly when the threshold voltage is crossed as can be observed in
Fig. 7. If the supply voltage is kept below 0.45 V, the maximum
droop difference is expected to be below 1.414 mV in 99.9% of the
chips at the 95% confidence level.
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VI. C ONCLUSION
We have presented a method of energy sensing that is completely
digital and that does not rely on any fixed references. This makes the
system robust even at very low voltages. We have demonstrated that
sensing energy by shutting off the power supply works better when
the droop is fixed rather than when the number of clock cycles is
fixed. This also eases the choice of the decoupling capacitance and
an overestimate of current consumption will not hurt the performance
of the energy sensing circuit.
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5
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