A Variable-Capacitance Vibration-to-Electric Energy Harvester
IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS—I: FUNDAMENTAL THEORY AND APPLICATIONS
1
A Variable-Capacitance Vibration-to-Electric Energy Harvester Bernard C. Yen, Student Member, IEEE, and Jeffrey H. Lang, Fellow, IEEE
Abstract— Past research on vibration energy harvesting has focused primarily on the use of magnets or piezoelectric materials as the basis of energy transduction, with few experimental studies implementing variable-capacitance-based scavenging. In contrast, this paper presents the design and demonstration of a variable-capacitance vibration energy harvester that combines an asynchronous diode-based charge pump with an inductive energy flyback circuit to deliver 1.8 µW to a resistive load. A cantilever beam variable capacitor with a 650-pF DC capacitance and a 348pF zero-to-peak AC capacitance, formed by a 43.56 cm2 spring steel top plate attached to an aluminum base, drives the charge pump at its out-of-plane resonant frequency of 1.56 kHz. The entire harvester requires only one gated MOSFET for energy flyback control, greatly simplifying the clocking scheme and avoiding synchronization issues. Furthermore, the system exhibits a startup voltage requirement below 89 mV, indicating that it can potentially be turned on using just a piezoelectric film. Index Terms— Vibration energy harvesting, vibration energy scavenging, variable-capacitance-based energy conversion.
I. I NTRODUCTION
I
N RESPONSE to a growing interest in autonomous systems, such as RF sensor nodes that must operate for prolonged periods of time without human intervention, vibrationto-electric energy harvesters have attracted wide research interest. Three main strategies for energy transduction dominate: piezoelectric, magnetic, and electric. Magnetic harvesting can be further categorized into systems with a time-varying inductor and systems that employ moving permanent magnets. Likewise, electric harvesting employs either a time-varying capacitor or a moving permanent electret. Piezoelectric materials, such as quartz and barium titanate, contain permanently-polarized structures that produce an electric field when the materials deform due to imposed mechanical forces [1]. Such a mechanically excited element can be modeled as a current source with a capacitive source impedance [2] where the current amplitude depends on the applied force. Therefore, if the material is connected to a vibration source, it can harvest the vibration energy and generate electric power [3], [4]. Magnetic energy harvesters, on the other hand, convert vibration energy into an induced voltage across wire coils, which can then deliver power to a load. This is typically done by attaching either a permanent magnet, such as that made from Manuscript received March 25, 2005; revised June 1, 2005. This paper was recommended by Associate Editor M. K. Kazimierczuk. The authors are with the Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, Cambridge, MA 02139, USA (email: [email protected]; [email protected]).
Neodymium Iron Boron, or a coil of wire onto a cantilever beam that is vibrationally actuated; the other element remains fixed [5], [6]. In either scenario, the coil will cut through magnetic flux as the cantilever beam vibrates, creating an induced voltage at the terminals of the coil. Vibration energy can also be transduced using a variable inductor, although no such studies have been reported to date, presumably due to the inherent advantages of permanent magnets. Finally, electric energy harvesting transduces vibration energy through the electric fields between a parallel plate capacitor. Typically, charge is injected into the capacitor at maximum capacitance and pulled off at minimum capacitance. Between these points, vibration separates the plates against their attractive force, performing work on the injected charge, which is then harvested [7], [8], [9], [10]. Besides the variable capacitor, one can also employ a moving layer of permanently embedded charge, or electret, to carry out electric energy harvesting [11], although such systems currently have power densities inferior to those using variable capacitors. Roundy et al. prototyped a simple variable-capacitancebased charge pump and showed that mechanical-to-electrical energy transduction was possible, but they did not explore the regime where the harvester saturates due to the lack of an energy flyback path [12]. Mur-Miranda conducted extensive studies on a synchronously-excited capacitive energy harvester involving two active switches [8]. Although energy conversion was demonstrated, difficulties in gate clocking and inefficiencies of the power electronics prevented net energy conversion to a load. Miyazaki et al. improved the timing scheme of this topology and achieved 120 nW of converted power from a 45 Hz vibration [9]. However, they did not analyze whether energy injection from the clock signal contributed to the harvested energy. As this paper will show, such energy injection can be significant, and can be mistaken for converted energy. Here, we present an optimized asynchronous capacitive energy harvester that requires only one active switch, thereby greatly simplifying clocking. For this paper, emphasis is placed on the circuitry, not on the implementation of the variable capacitor. The circuit employs a charge pump in its forward harvesting path and an inductive energy flyback to return net energy to a central reservoir. The harvester is demonstrated experimentally using a spring steel variable capacitor with capacitance variation between 302 pF and 998 pF and an outof-plane resonant frequency of 1.56 kHz. It delivers 1.8 µW of power to a resistive load, translating to an efficiency of 19.1%. Experimental data prove that net energy conversion does not result from clock energy injection.
c 2005 IEEE 0000–0000/00$00.00
IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS—I: FUNDAMENTAL THEORY AND APPLICATIONS
2 , -$
, . /
( ) *+
(1
Fig. 1.
Block diagram of asynchronous capacitive energy harvester.
, *$ " 0
Buck-converter flyback is presented here as a highefficiency standard baseline implementation against which other schemes, such as switched-capacitor flyback, can be compared. Thus, even though the flyback circuitry involves an inductor, it is worthwhile examining. When employed as part of an integrated system, the required inductor in the flyback path could be implemented as an external component. Alternatively, planar inductors could be deposited or electroplated as part of the fabrication process [13]. II. P OWER E LECTRONICS Fig. 1 shows a block diagram of the capacitor-based energy harvester. The charge pump in the forward path transduces vibration energy into electric energy, which is then delivered to a temporary storage. Periodically, the inductive flyback circuit sends the harvested energy back to a reservoir that powers the attached load, priming the charge pump. A circuit implementation of the block diagram is shown in Fig. 2, with RLOAD representing the load. The charge pump consists of two diodes, D1 and D2 , that sandwich a variable capacitor CVAR . The flyback section includes a gated MOSFET, freewheeling diode DFLY , and inductor LFLY ; RWIRE and RCORE model the winding and core loss of the inductor respectively. Finally, the reservoir CRES and temporary storage CSTORE are each formed by a single capacitor under the requirement that CRES ≫ CSTORE . In this paper, the MOSFET gate drive is powered from an external power supply for simplicity. It is recognized that the gate drive, along with other required control logic, must ultimately be powered directly from the harvested energy. This appears to be feasible for an integrated system because power generation on the order of microwatts is demonstrated below. Based on a typical MOSFET gate-source capacitance of CGS = 100 pF, a drive voltage of vGS = 1 V for an IC implementation, and a drive frequency of fCLK = 475 Hz, the power dissipated in driving the MOSFET gate is 2 PCLK = CGS vGS fCLK = 50 nW .
(1)
Thus, the harvested energy should be adequate. A. Charge Pump Section To understand the transduction of vibration energy to electric energy, assume initially that vVAR = vRES = vSTORE and CVAR = CMAX , the maximum capacitance of the variable capacitor. At this point, both D1 and D2 are off, meaning that QVAR , the charge on the variable capacitor, cannot change. As ambient vibration pulls the capacitor plates apart, CVAR decreases, which causes vVAR to rise given constant QVAR . This voltage rise eventually turns on D2 , resulting in the partial
% & '
2 - *3
!"
% &!" '
#$
% & #$ '
45 6 7 89 : ; < = > ?
) *+
4 @ AB C 7 D E 5 F8D < FG 8B ?
Fig. 2. Capacitive energy harvester with source-referenced clock controlling the flyback switch.
discharge of CVAR into CSTORE with vVAR = vSTORE . When the vibration reverses direction, CVAR increases, causing vVAR to drop, thereby turning off D2 . As vVAR drops further, D1 turns on, which results in charge injection from CRES to CVAR . This charging causes vVAR to be held at vRES . The cycle repeats itself as charge and energy are pumped into CSTORE . Without the flyback section, vSTORE will eventually saturate. Because this saturation voltage impacts the overall energy harvester performance, it is now computed analytically. Let the variable capacitor exhibit CMIN ≤ CVAR ≤ CMAX , and define a complete energy harvesting cycle as one variation of CVAR from CMAX to CMIN and back to CMAX . Let vSTORE,n , where n is an integer index starting from 0, represent the voltage on CSTORE at the end of n cycles. Based on this definition, vSTORE,0 = vRES . Furthermore, since CRES ≫ CSTORE , approximate vRES as a constant voltage source. Finally, assume the diodes are ideal. Fig. 3(a) shows an equivalent circuit diagram at the start of cycle n. At this point, the total charge, QTOTAL , stored in CVAR and CSTORE is QTOTAL,n−1 = CMAX VRES + CSTORE vSTORE,n−1 .
(2)
Next, as CVAR decreases, vVAR rises so that D1 immediately turns off and QTOTAL remains constant. Eventually, vVAR increases enough so that D2 turns on and the equivalent circuit diagram shown in Fig. 3(b) results. During this part of the cycle, charge is transferred from CVAR to CSTORE , giving vSTORE =
CSTORE vSTORE,n−1 CMIN + CSTORE CMAX VRES + CMIN + CSTORE
(3)
at the end of the half cycle. Then, as CVAR increases and vVAR decreases, D2 immediately turns off, keeping the charge on CSTORE , and hence vSTORE , constant throughout the remainder of the cycle. Therefore, vSTORE,n = vSTORE
(4)
where vSTORE is taken from (3). Because charge is transferred from CVAR to CSTORE during the cycle, vVAR will head towards a voltage that is less than VRES as CVAR continues to increase. Therefore, D1 is guaranteed to turn on by the point when CVAR = CMAX , so Fig. 3(a) is again the equivalent
IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS—I: FUNDAMENTAL THEORY AND APPLICATIONS
H I
H J
T U RSO
K LMN
Z RSO
[ \
T U O P Q R S WX Y I
K OPQ RS
V
l efb
[]
^ _ `a
g ^ bcd ef h b c d e f ij
V
k
(a) Start of first half of cycle Fig. 3.
3
g h b c d e f ij k
(b) Start of second half of cycle
Equivalent circuit diagrams for different parts of the harvesting cycle. uvwx
p o n m u v wx
~
u v yz u v yz
{|
{}
Fig. 4.
q rs t
Q-V plane contour representing one energy harvesting cycle.
circuit diagram for the charge pump at the start of the next cycle. Define CSTORE α= (5) CMIN + CSTORE CMAX VRES (6) β= CMIN + CSTORE
B. Inductive Flyback Section
so that (3) and (4) can be rewritten as vSTORE,n = αvSTORE,n−1 + β ,
(7)
which is a recurrence relation in the variable vSTORE,i . From [14], the solution of this recurrence relation is CMAX vSTORE,n = VRES 1 − CMIN n CMAX CSTORE . (8) + × CMIN + CSTORE CMIN To determine the saturation value of vSTORE without energy flyback, substitute n = ∞ to obtain vSTORE,∞ =
CMAX VRES . CMIN
(9)
(9) indicates that the saturation value is related to the ratio CMAX /CMIN . This equation may be rewritten as vSTORE,∞
CDC + CAC VRES = CDC − CAC
The energy transduction process just described can also be viewed graphically as a Q-V plane contour shown in Fig. 4. In this diagram, Point 1 corresponds to the moment when both D1 and D2 are off and the capacitor plates are just starting to pull apart for the nth energy conversion cycle. At Point 2, D1 turns on, allowing charge to transfer from CVAR to CSTORE ; correspondingly QVAR falls from Point 2 to Point 3. During this part of the cycle, vVAR = vSTORE . At Point 3, vibration has pulled the capacitor plates to their maximum separation, decreasing CVAR to CMIN . Next, CVAR increases and vVAR falls, turning off D2 . Correspondingly, QVAR remains constant until Point 4, at which time D1 turns on and vVAR is held at VRES . The area within the closed curve in Fig. 4 equals the mechanical vibration energy converted to electrical energy and delivered to CSTORE . As the cycles advance, Point 2 moves to the right and Point 3 rises to meet it. At the same time, Point 4 rises to meet Point 1, and the converted energy shrinks to zero as vSTORE,n saturates. Because of this, it is important to send the energy stored in CSTORE back to CRES quickly enough to permit continuous energy conversion. This is the purpose of the flyback circuitry shown in Fig. 1 and Fig. 2.
(10)
where CDC represents the average value of CVAR and CAC represents its zero-to-peak capacitance variation. From (10), it is apparent that DC parasitic capacitances in parallel with CVAR must be minimized to prevent early saturation.
To power the attached load and prevent vSTORE from saturating, an inductive flyback circuit, modeled after a DC/DC buck converter and shown in Fig. 2, complements the charge pump. Nominally in its off state, the MOSFET switch turns on every few energy harvesting cycles to energize LFLY . The current iFLY ramps up according to diFLY vFLY = dt LFLY
(11)
where vFLY = vSTORE − vRES . After DTCLK , where D represents the clock duty ratio and TCLK represents the clock period, the MOSFET turns off, forcing iFLY to commutate to the freewheeling diode DFLY . This makes vFLY = −vRES , so vRES diFLY =− dt LFLY
(12)
until iFLY = 0 A, at which point the diode turns off. In this way, energy is transferred from CSTORE back to CRES where it can power the load, represented here by RLOAD . Note that it is not necessary for this process to be synchronized with the energy conversion cycles described in Section II-A. Indeed, it might be best to initiate the energy flyback whenever vSTORE rises to a threshold value. This simplifies the control of the
IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS—I: FUNDAMENTAL THEORY AND APPLICATIONS
4
TABLE I H ARVESTED POWER AS A FUNCTION OF vG USING GROUND - REFERENCED CLOCK .
vG (V)
vRES,0 (V)
vRES,∞ (V)
PCONV (W)
4.7
5.9995
5.9724
−5.50 × 10−6
10.7
5.9989
5.9921
−1.40 × 10−6
16.7
5.9990
6.0029
0.79 × 10−6
22.7
5.9991
6.0041
1.02 × 10−6 à ¸Â Ä ¹Å ¸Â Æ ¸À Ç Â
¡
¢
£ ¦§
³ ´°²
» ¹È É À Ê
£ ¤¥
µ
¯ ° ¬± ²
Î
®
£¨
Ì Í ¸À È
Ï ÐÑÒ £ § ©ª « ¬
¶ · ¸¹º » ¸¼ ½ ¹¾ ¼ ½ ¿ À Á Â
Ó » Ë Ë Â ¸Â ÈÀ Ç ¹· ¾
(a) Charge injection
(b) Charge leakage
Fig. 6.
Spring steel variable capacitor side view (not to scale).
Fig. 5. Cycle of circuit operation that results in energy injection from CLK.
MOSFET switch by making it independent of the motion of the variable capacitor. III. C LOCK E NERGY I NJECTION As the previous section shows, the capacitive energy harvester uses a source-referenced clock to drive the MOSFET. Typically, this gate drive is undesirable because the floating reference voltage makes implementation difficult. Here, SPICE simulation explains the necessity of this choice. Table I shows simulated data when the clock is referenced to ground. Circuit parameters used in the simulation are CRES = 1 µF, CSTORE = 3.3 nF, RLOAD = 20 MΩ, LFLY = 2.5 mH, RCORE = 360 kΩ, RWIRE = 8 Ω, vth = 2.5 V, CDC = 1.22 nF, CAC = 300 pF, vRES = 6 V, fCLK = 475 Hz, and D = 0.0019. The simulation uses a SPICE Level-3 2N7002 nchannel MOSFET model and a realistic diode model based on the characteristics of a 1N6263 low-leakage Schottky barrier diode. In the table, vRES,0 and vRES,∞ represent the original and final voltages on CRES respectively. Furthermore, vG is the magnitude of the gate drive voltage. In all cases, vG exceeds the MOSFET threshold voltage, so the on-resistance of the MOSFET does not change much between simulations. The important point to observe is that the converted power PCONV rises significantly as vG increases. Given that all other parameters remain fixed, the additional harvested energy must come from the clock. This is important for two reasons. First, in an experimental system in which the MOSFET is not powered by CRES , energy injection from the clock through the MOSFET gate can be confused as net energy conversion when in fact net energy is not converted. Second, the energy injected into the harvester diminishes the energy that can actually be harvested during a cycle. To understand the source of clock energy injection, consider the simplified circuit diagram shown in Fig. 5. In this figure, CGS is the MOSFET gate-source capacitance, D3 is
the MOSFET body diode, and C1 is the parasitic junction capacitance of DFLY . When a rising clock places QGS onto CGS , the voltage at node X rises according to the capacitive divider involving C1 and CGS . If the voltage rises enough, D3 turns on and leaks a fraction of QGS onto CSTORE , which cannot be recovered when the clock goes low. Using a source-referenced clock prevents node X from being pulled up, thereby preventing the accidental turn-on of D3 and the corresponding energy injection. Table II shows the SPICE simulation when a sourcereferenced clock is used. Here, PCONV does not increase with vGS , indicating that clock energy injection has been eliminated. The first row in the table proves that if vGS is less than the MOSFET threshold voltage, the capacitive energy harvester cannot sustain itself. IV. VARIABLE C APACITOR To test the asynchronous capacitive energy harvesting circuit, a macro scale spring steel variable capacitor supported by eight cantilever beams was designed and fabricated. As shown
Fig. 7.
Spring steel variable capacitor prototype.
IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS—I: FUNDAMENTAL THEORY AND APPLICATIONS
5
TABLE II H ARVESTED POWER AS A FUNCTION OF vGS USING SOURCE - REFERENCED CLOCK .
vGS (V)
vRES,0 (V)
vRES,∞ (V)
2
6.0000
5.9752
−5.034 × 10−6
5
6.0000
6.0038
0.773 × 10−6
11
6.0000
6.0038
0.773 × 10−6
17
6.0000
6.0038
0.773 × 10−6
23
6.0000
6.0038
0.773 × 10−6
35
350
100 pF
30
PCONV (W)
300
100 K
V+ CVAR VBIAS
250 V-
+
CAC (pF)
CAC (pF)
25
+ vTEST
20
-
15
200 150
10
100
5
50
0 1000
0
1200
1400
1600
1800
2000
2200
0
100
200
300
400
Vamp,p-p (mV)
Frequency (Hz)
Fig. 8. Frequency sweep for spring steel variable capacitor with vAMP,p−p = 50 mV.
Fig. 9.
CAC as a function of shaking strength at f = 1560 Hz.
V. E XPERIMENTAL R ESULTS ′′
in Fig. 6 and Fig. 7, a square sheet of 0.05 thick 1095 bluetempered spring steel, with a mass density of 7850 kg/m3 and a Young’s Modulus of 205 GPa, measuring 6.6 cm on each side formed the flexible top plate of CVAR . A solid block of aluminum formed the base. Mylar tape acted as a spacer that defined the nominal gap between the plates. To prevent the top and bottom plates from shorting, nylon screws were used to hold the structure together. FEA optimization was used to keep the out-of-plane resonant mode close to 1500 Hz while pushing the torsion and rotation modes towards higher frequencies above 6000 Hz. The resulting springs have lengths of 0.8 cm and widths of 0.7 cm. Finally, fillets with 2 mm radii were inserted at all perpendicular intersections to help reduce stress levels in the bending capacitor plate. The prototype spring steel variable capacitor gave CDC = 650 pF when measured on a standard bridge, which is close to the calculated value of 566 pF. The capacitor was vibrated with a Ling Dynamic System V456 shaker table and its corresponding PA 1000L amplifier. Using the circuit shown in Fig. 8, in which vTEST is proportional to CAC , a frequency sweep was performed. The result in Fig. 8 shows the first resonant mode to be at f = 1560 Hz with a Q of approximately 3.5. Next, by applying 1560 Hz vibrations of varying strengths to the variable capacitor, created by changing the peak-to-peak voltage input vAMP,p−p to the PA 1000L amplifier, a plot of CAC as a function of vAMP,p−p was generated. Fig. 9 shows the collected data.
The circuit in Fig. 2 was fabricated using surface mount components to test the validity of SPICE simulation results and to demonstrate its operation. The components include a 2N7002 n-channel MOSFET, three 1N6263 low-leakage Schottky barrier diodes, and a CD4047 low power monostable multivibrator gate drive. Before every experiment, a shorting jumper connects a battery to precharge CRES up to vRES = 1.5 V, the starting steady-state voltage. The shaker table is then ramped up from no shaking to the desired test level and the jumper is disconnected. In all cases, the flyback circuit is activated after every 4 energy conversion cycles. Because a resistive load RLOAD formed by a 10 MΩ scope probe in series with a 10 MΩ resistor is attached to the reservoir, a rising vRES indicates positive energy conversion. Fig. 10 plots the evolution of vRES for various shaker table amplifier inputs vAMP,p−p . When vAMP,p−p = 120 mV (CAC = 84 pF), the energy harvester just barely sustains vRES while powering the 20 MΩ load. For vAMP,p−p = 360 mV (CAC = 260 pF), vRES charges up to 6 V, which means that the system delivers 1.8 µW to RLOAD . Although the energy harvester does not have an integrated acceleration sensor to determine the applied acceleration directly, an approximate value can be obtained at the resonant frequency. Assuming a sinusoidal travel of the upper variable capacitor plate and using Q ≈ 3.5 from Fig. 8, and the nominal dimensions of the variable capacitor, the applied acceleration per 100 mV of vAMP,p−p is approximately 8.4g where g =
IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS—I: FUNDAMENTAL THEORY AND APPLICATIONS
5
2.5
Saturation Vres (V)
320 mV
2
280 mV
0.5Vres (V)
6
240 mV
1.5
200 mV 1
160 mV 120 mV
4 3 2 1
0.5
0
1000
0 -5
0
5
10
15
20
25
30
35
40
45
Time (sec)
Fig. 10. Evolution of vRES as a function of time parameterized by vAMP,p−p . The factor of 0.5 in the vertical axis results from the 10 MΩ resistor in series with the scope probe.
3 Vgs = 4.5 V Vgs = 6.0 V
0.5Vres (V)
2.5 2 1.5 1 0.5 0 -10
0
10
20
30
40
50
Time (sec)
Fig. 11.
vRES as a function of source-referenced clocking voltage.
9.8 m/s2 . This translates to 40g when CAC = 350 pF. Notice that the plots in Fig. 10 all flatten out and saturate. This is due to the nonlinear core loss present in LFLY that increases as vFLY goes up. In Fig. 2, this nonlinearity is modeled as a nonlinear resistor RCORE whose resistance depends on vFLY . As vFLY varies between 0 V and 3 V, RCORE drops from its nominal value of 400 kΩ down to approximately 1 kΩ. To prove that the harvested energy does not include clock energy injection, two additional experiments are performed. First, the shaker table is stopped while the clock signal continued running. The scope probe attached to CRES shows that vRES decays to below 80 mV, much lower than the voltages sustained in Fig. 10. This strongly suggests that even if there is energy injection from the source-referenced clock, it is small compared to the transduced energy. Next,
1200
1400
1600
1800
2000
2200
Frequency (Hz)
Fig. 13. Plot of saturation vRES as a function of frequency with vAMP,p−p = 320 mV.
the MOSFET clock amplitude, or equivalently vGS , is varied to determined its effect on the harvested energy. The result, shown in Fig. 11, indicates that the amount of harvested energy is independent of vGS , consistent with SPICE simulations presented in Table II. Thus, it is believed that no energy injected through the MOSFET gate is present in Fig. 10. If the capacitive energy harvester is to be integrated onto an IC with a MEMS capacitor, the minimum vRES required for system startup is critical. A high requirement would necessitate electrochemical cells, defeating the purpose of using an energy harvester in the first place. Startup tests were conducted for the prototype circuit by lowering vRES using a voltage divider and observing whether vRES could still rise to the levels shown in Fig. 10. Fig. 12 plots a sample result with vAMP,p−p = 320 mV and vRES = 200 mV at the start. An iteration process shows that even at the noise floor of the oscilloscope, around vRES = 89 mV, the system can still startup, allowing for a piezoelectric film or an electret to jump start the harvester. In real world applications, the vibration frequency will have some spread, so the sensitivity of the capacitive energy harvester to frequency variations is also important. Fig. 13 shows the saturation point of vRES as a function of the drive frequency at vAMP,p−p = 320 mV. From this plot, a deviation of 150 Hz from the resonant frequency causes a 37% drop in the saturation voltage, which may be unacceptable. A reduction in the mechanical Q will lower this sensitivity at the cost of CAC , so a trade-off exists. If the frequency spectrum of the ambient vibration is not known a priori, the variable capacitor can be designed with a tunable resonant frequency, perhaps through an adaptive scheme employing electric spring stiffening.
2.5
VI. E NERGY C ONVERSION E FFICIENCY 0.5Vres (V)
2
Having demonstrated the behavior of the capacitive energy harvester, the energy conversion efficiency of the circuit is now computed. As a figure of merit, the efficiency η will be defined as Power delivered to load . (13) η≡ Theoretical power harvested from Q-V cycle
1.5 1 System startup 0.5 0 -5
5
15
25
35
45
Time (sec)
Fig. 12. Plot of vRES as circuit starts up from vRES = 200 mV when vAMP,p−p = 320 mV.
The numerator represents the amount of useful energy the harvester can provide to a load while the denominator represents the theoretical maximum that the circuit can deliver if the process was 100% efficient.
IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS—I: FUNDAMENTAL THEORY AND APPLICATIONS
7
As mentioned in Section V, the prototype system presents 6 V to a 20 MΩ resistive load under heavy shaking. Hence, the amount of power delivered to the load for that experiment is 1.8 µW. To determine the denominator, we can compute the total enclosed area A1 + A2 in Fig. 4. For simplicity, approximate A2 as a triangle. Also, because the flyback switch is enabled every 4 harvesting cycles in this paper, take n = 2 in (8) to find the average energy harvested per cycle. Begin by considering Point 1, which corresponds to the moment when both D1 and D2 are off and the plates of the variable capacitor are beginning to pull apart. At this point,
Again, the value of hiD i = 10 µA comes from HSPICE simulation [10]. Adding these losses to the numerator, one obtains 3.8 µW = 40.4% . (25) η′ = 9.4 µW
v1 = VRES = 6 V
VII. S UMMARY AND C ONCLUSION
(14)
and therefore Q1 = Q2 = CMAX VRES = 6 × 10−9 C .
(15)
Point 2 occurs when D2 turns on, and this happens when vVAR is equal to the previous cycle’s vSTORE , which is just vSTORE,1 . From (8) with n = 1, vSTORE,1 = 7.2 V, so v2 = 7.2 V. The trace between Points 2 and 3 represents the charge transfer between CVAR and CSTORE when D2 turns on. By setting n = 2 in (8), it is obtained that v3 = 8.2 V. From this, one can also calculate that Q3 = Q4 = CMIN v3 = 2.5 × 10−9 C .
(16)
Finally, the capacitor plates move toward each other until D1 turns on, from which point on vVAR is held at VRES until the end of the cycle. Therefore, v4 = VRES = 6 V .
(17)
Having determined all the necessary values, areas A1 and A2 can be computed as A1 = (v2 − v1 ) (Q1 − Q4 ) = 4.2 × 10−9 J (18) 1 −9 A2 = (v3 − v2 ) (Q1 − Q4 ) = 1.8 × 10 J . (19) 2 Therefore, the average converted energy WCONV per cycle is WCONV = A1 + A2 = 6 nJ ,
(20)
which means that PCONV = WCONV f = 9.4 µW .
(21)
Finally, referring back to (13), η=
1.8 µW = 19.1% . 9.4 µW
[10]. On the other hand, diodes have a constant voltage drop, vD , across them when turned on, so their average conduction loss is related to the average current, hiD i. Using typical parameter values from the 1N6263 Schottky diode datasheet, hPD,COND i ≈ hiD i vD = 2 µW .
(24)
This paper demonstrates an asynchronous capacitive energy harvesting circuit employing a charge pump and inductive flyback. Coupled to an experimental variable capacitor, it delivers 1.8 µW of power to a 20 MΩ resistive load at a steady-state voltage of 6 V while exhibiting an efficiency of 19.1%. The spring steel variable capacitor used to drive the charge pump achieved a CMAX /CMIN ratio of 3.3 with a 1.56 kHz out-of-plane resonant frequency. Because the harvester employs only one asynchronous MOSFET switch, clocking is greatly simplified. However, this paper shows that in order to obtain accurate data, a source-referenced gate drive should be used to prevent spurious clock energy injection, which can artificially inflate the conversion efficiency and diminish actual conversion. Experiments conducted using a prototype circuit not only demonstrated close match between theory and actual data, but they also revealed an extremely low startup requirement of vRES ≤ 89 mV for the capacitive harvester. Finally, the system can tolerate a frequency variation of 150 Hz before the steady-state voltage drops to 2/3 of its peak value. ACKNOWLEDGMENT This paper is based in part on [10]. The authors would like to thank both Professor Alex Slocum and Alexis Weber for their assistance in designing and fabricating the spring steel variable capacitor. We are also indebted to Professor Charles Sodini, who helped us work out the clock energy injection issues associated with ground-referenced gate drives. Finally, Professor Dave Perreault provided us with invaluable suggestions on the diode selection as well as alternative energy flyback techniques.
(22) R EFERENCES
An efficiency that removes the losses of the MOSFET and diodes can also be calculated. This value corresponds to the deliverable power given lossless power electronics. Because the MOSFET on-resistance, RDS,ON , is approximately a constant when operated as a switch, the average conduction loss, hPFET,COND i, is related to the root-mean-square current, iRMS . Using typical parameter values from the 2N7002 nchannel MOSFET datasheet, hPFET,COND i ≈ i2RMS × RDS,ON = 0.36 nW .
(23)
The value of iRMS = 14 µA comes from HSPICE simulation
[1] “Materials by Design: Piezoelectric Materials,” http://www.mse.cornell.edu/courses/engri111/piezo.htm, 1996. [2] G. K. Ottman, H. F. Hofmann, A. C. Bhatt, and G. A. Lesieutre, “Adaptive Piezoelectric Energy Harvesting Circuit for Wireless Remote Power Supply,” IEEE Transactions on Power Electronics, vol. 17, no. 5, pp. 669–676, September 2002. [3] S. Roundy, B. Otis, Y.-H. Chee, J. M. Rabaey, and P. Wright, “A 1.9GHz RF Transmit Beacon using Environmentally Scavenged Energy,” in International Symposium on Low Power Electronics and Design, 2003. [4] G. K. Ottman, H. F. Hofmann, and G. A. Lesieutre, “Optimized Piezoelectric Energy Harvesting Circuit Using Step-Down Converter in Discontinuous Conduction Mode,” IEEE Transactions on Power Electronics, vol. 18, no. 2, pp. 696–703, March 2003.
IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS—I: FUNDAMENTAL THEORY AND APPLICATIONS
[5] P. Glynne-Jones, M. Tudor, S. Beeby, and N. White, “An Electromagnetic, Vibration-Powered Generator for Intelligent Sensor Systems,” Sensors and Actuators A, vol. 110, no. 1-3, pp. 344–349, February 2004. [6] C. Williams and R. Yates, “Analysis of a Micro-electric Generator for Microsystems,” in 8th International Conference on Solid-State Sensors and Actuators, vol. 1, June 1995, pp. 369–372. [7] P. Miao, A. S. Holmes, E. M. Yeatman, and T. C. Green, “MicroMachined Variable Capacitors for Power Generation,” March 2003, unpublished. [8] J. O. Mur-Miranda, “MEMS-Enabled Electrostatic Vibration-to-Electric Energy Conversion,” Ph.D. dissertation, Massachusetts Institute of Technology, 2003. [9] M. Miyazaki, H. Tanaka, G. Ono, T. Nagano, N. Ohkubo, T. Kawahara, and K. Yano, “Electric-Energy Generation Using Variable-Capacitive Resonator for Power-Free LSI: Efficiency Analysis and Fundamental Experiment,” in ISPLED 2003, August 2003, pp. 193–198. [10] B. C. Yen, “Vibration-to-Electric Energy Conversion Using a Mechanically-Varied Capacitor,” Master’s thesis, Massachusetts Institute of Technology, 2005. [11] T. Sterken, K. Baert, R. Puers, G. Borghs, and R. Mertens, “A New Power MEMS Component with Variable Capacitance,” in Pan Pacific Microelectronics Symposium, February 2003, pp. 27–34. [12] S. Roundy, P. K. Wright, and J. Rabaey, “A Study of Low Level Vibrations as a Power Source for Wireless Sensor Nodes,” Computer Communications, vol. 26, no. 11, pp. 1131–1144, July 2003. [13] D. P. Arnold, F. Cros, I. Zana, D. R. Veazie, and M. G. Allen, “Electroplated Metal Microstructures Embedded in Fusion-Bonded Silicon: Conductors and Magnetic Materials,” Journal of Microelectromechanical Systems, vol. 13, no. 5, October 2004. [14] K. H. Rosen, Discrete Mathematics and Its Applications, 4th ed. McGraw-Hill, New York, 1999.
8
Bernard C. Yen (S’05) received the B.S. degree in electrical engineering from the University of California, Berkeley, in 2003, and the S.M. degree in electrical engineering from the Massachusetts Institute of Technology (MIT), Cambridge, in 2005. He is currently working toward the Ph.D. degree in electrical engineering at MIT. His research interests include vibration-to-electric energy harvesting, power electronics, micro-electromechanical systems, and analog circuit design.
Jeffrey H. Lang (S’78–M’79–SM’95–F’98) received the S.B., S.M., and Ph.D. degrees in electrical engineering from the Massachusetts Institute of Technology (MIT), Cambridge, in 1975, 1977, and 1980, respectively. Currently, he is a Professor of Electrical Engineering at MIT and has been a faculty member since 1980. His research and teaching interests focus on the analysis, design, and control of electromechanical systems with an emphasis on rotating machinery, microsensors and actuators, and flexible structures. He has written over 180 papers and holds 11 patents in the areas of electromechanics, power electronics and applied control, and has been awarded four best paper prizes from various IEEE societies. Prof. Lang is a former Hertz Foundation Fellowand a former Associate Editor of Sensors and Actuators.
1
A Variable-Capacitance Vibration-to-Electric Energy Harvester Bernard C. Yen, Student Member, IEEE, and Jeffrey H. Lang, Fellow, IEEE
Abstract— Past research on vibration energy harvesting has focused primarily on the use of magnets or piezoelectric materials as the basis of energy transduction, with few experimental studies implementing variable-capacitance-based scavenging. In contrast, this paper presents the design and demonstration of a variable-capacitance vibration energy harvester that combines an asynchronous diode-based charge pump with an inductive energy flyback circuit to deliver 1.8 µW to a resistive load. A cantilever beam variable capacitor with a 650-pF DC capacitance and a 348pF zero-to-peak AC capacitance, formed by a 43.56 cm2 spring steel top plate attached to an aluminum base, drives the charge pump at its out-of-plane resonant frequency of 1.56 kHz. The entire harvester requires only one gated MOSFET for energy flyback control, greatly simplifying the clocking scheme and avoiding synchronization issues. Furthermore, the system exhibits a startup voltage requirement below 89 mV, indicating that it can potentially be turned on using just a piezoelectric film. Index Terms— Vibration energy harvesting, vibration energy scavenging, variable-capacitance-based energy conversion.
I. I NTRODUCTION
I
N RESPONSE to a growing interest in autonomous systems, such as RF sensor nodes that must operate for prolonged periods of time without human intervention, vibrationto-electric energy harvesters have attracted wide research interest. Three main strategies for energy transduction dominate: piezoelectric, magnetic, and electric. Magnetic harvesting can be further categorized into systems with a time-varying inductor and systems that employ moving permanent magnets. Likewise, electric harvesting employs either a time-varying capacitor or a moving permanent electret. Piezoelectric materials, such as quartz and barium titanate, contain permanently-polarized structures that produce an electric field when the materials deform due to imposed mechanical forces [1]. Such a mechanically excited element can be modeled as a current source with a capacitive source impedance [2] where the current amplitude depends on the applied force. Therefore, if the material is connected to a vibration source, it can harvest the vibration energy and generate electric power [3], [4]. Magnetic energy harvesters, on the other hand, convert vibration energy into an induced voltage across wire coils, which can then deliver power to a load. This is typically done by attaching either a permanent magnet, such as that made from Manuscript received March 25, 2005; revised June 1, 2005. This paper was recommended by Associate Editor M. K. Kazimierczuk. The authors are with the Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, Cambridge, MA 02139, USA (email: [email protected]; [email protected]).
Neodymium Iron Boron, or a coil of wire onto a cantilever beam that is vibrationally actuated; the other element remains fixed [5], [6]. In either scenario, the coil will cut through magnetic flux as the cantilever beam vibrates, creating an induced voltage at the terminals of the coil. Vibration energy can also be transduced using a variable inductor, although no such studies have been reported to date, presumably due to the inherent advantages of permanent magnets. Finally, electric energy harvesting transduces vibration energy through the electric fields between a parallel plate capacitor. Typically, charge is injected into the capacitor at maximum capacitance and pulled off at minimum capacitance. Between these points, vibration separates the plates against their attractive force, performing work on the injected charge, which is then harvested [7], [8], [9], [10]. Besides the variable capacitor, one can also employ a moving layer of permanently embedded charge, or electret, to carry out electric energy harvesting [11], although such systems currently have power densities inferior to those using variable capacitors. Roundy et al. prototyped a simple variable-capacitancebased charge pump and showed that mechanical-to-electrical energy transduction was possible, but they did not explore the regime where the harvester saturates due to the lack of an energy flyback path [12]. Mur-Miranda conducted extensive studies on a synchronously-excited capacitive energy harvester involving two active switches [8]. Although energy conversion was demonstrated, difficulties in gate clocking and inefficiencies of the power electronics prevented net energy conversion to a load. Miyazaki et al. improved the timing scheme of this topology and achieved 120 nW of converted power from a 45 Hz vibration [9]. However, they did not analyze whether energy injection from the clock signal contributed to the harvested energy. As this paper will show, such energy injection can be significant, and can be mistaken for converted energy. Here, we present an optimized asynchronous capacitive energy harvester that requires only one active switch, thereby greatly simplifying clocking. For this paper, emphasis is placed on the circuitry, not on the implementation of the variable capacitor. The circuit employs a charge pump in its forward harvesting path and an inductive energy flyback to return net energy to a central reservoir. The harvester is demonstrated experimentally using a spring steel variable capacitor with capacitance variation between 302 pF and 998 pF and an outof-plane resonant frequency of 1.56 kHz. It delivers 1.8 µW of power to a resistive load, translating to an efficiency of 19.1%. Experimental data prove that net energy conversion does not result from clock energy injection.
c 2005 IEEE 0000–0000/00$00.00
IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS—I: FUNDAMENTAL THEORY AND APPLICATIONS
2 , -$
, . /
( ) *+
(1
Fig. 1.
Block diagram of asynchronous capacitive energy harvester.
, *$ " 0
Buck-converter flyback is presented here as a highefficiency standard baseline implementation against which other schemes, such as switched-capacitor flyback, can be compared. Thus, even though the flyback circuitry involves an inductor, it is worthwhile examining. When employed as part of an integrated system, the required inductor in the flyback path could be implemented as an external component. Alternatively, planar inductors could be deposited or electroplated as part of the fabrication process [13]. II. P OWER E LECTRONICS Fig. 1 shows a block diagram of the capacitor-based energy harvester. The charge pump in the forward path transduces vibration energy into electric energy, which is then delivered to a temporary storage. Periodically, the inductive flyback circuit sends the harvested energy back to a reservoir that powers the attached load, priming the charge pump. A circuit implementation of the block diagram is shown in Fig. 2, with RLOAD representing the load. The charge pump consists of two diodes, D1 and D2 , that sandwich a variable capacitor CVAR . The flyback section includes a gated MOSFET, freewheeling diode DFLY , and inductor LFLY ; RWIRE and RCORE model the winding and core loss of the inductor respectively. Finally, the reservoir CRES and temporary storage CSTORE are each formed by a single capacitor under the requirement that CRES ≫ CSTORE . In this paper, the MOSFET gate drive is powered from an external power supply for simplicity. It is recognized that the gate drive, along with other required control logic, must ultimately be powered directly from the harvested energy. This appears to be feasible for an integrated system because power generation on the order of microwatts is demonstrated below. Based on a typical MOSFET gate-source capacitance of CGS = 100 pF, a drive voltage of vGS = 1 V for an IC implementation, and a drive frequency of fCLK = 475 Hz, the power dissipated in driving the MOSFET gate is 2 PCLK = CGS vGS fCLK = 50 nW .
(1)
Thus, the harvested energy should be adequate. A. Charge Pump Section To understand the transduction of vibration energy to electric energy, assume initially that vVAR = vRES = vSTORE and CVAR = CMAX , the maximum capacitance of the variable capacitor. At this point, both D1 and D2 are off, meaning that QVAR , the charge on the variable capacitor, cannot change. As ambient vibration pulls the capacitor plates apart, CVAR decreases, which causes vVAR to rise given constant QVAR . This voltage rise eventually turns on D2 , resulting in the partial
% & '
2 - *3
!"
% &!" '
#$
% & #$ '
45 6 7 89 : ; < = > ?
) *+
4 @ AB C 7 D E 5 F8D < FG 8B ?
Fig. 2. Capacitive energy harvester with source-referenced clock controlling the flyback switch.
discharge of CVAR into CSTORE with vVAR = vSTORE . When the vibration reverses direction, CVAR increases, causing vVAR to drop, thereby turning off D2 . As vVAR drops further, D1 turns on, which results in charge injection from CRES to CVAR . This charging causes vVAR to be held at vRES . The cycle repeats itself as charge and energy are pumped into CSTORE . Without the flyback section, vSTORE will eventually saturate. Because this saturation voltage impacts the overall energy harvester performance, it is now computed analytically. Let the variable capacitor exhibit CMIN ≤ CVAR ≤ CMAX , and define a complete energy harvesting cycle as one variation of CVAR from CMAX to CMIN and back to CMAX . Let vSTORE,n , where n is an integer index starting from 0, represent the voltage on CSTORE at the end of n cycles. Based on this definition, vSTORE,0 = vRES . Furthermore, since CRES ≫ CSTORE , approximate vRES as a constant voltage source. Finally, assume the diodes are ideal. Fig. 3(a) shows an equivalent circuit diagram at the start of cycle n. At this point, the total charge, QTOTAL , stored in CVAR and CSTORE is QTOTAL,n−1 = CMAX VRES + CSTORE vSTORE,n−1 .
(2)
Next, as CVAR decreases, vVAR rises so that D1 immediately turns off and QTOTAL remains constant. Eventually, vVAR increases enough so that D2 turns on and the equivalent circuit diagram shown in Fig. 3(b) results. During this part of the cycle, charge is transferred from CVAR to CSTORE , giving vSTORE =
CSTORE vSTORE,n−1 CMIN + CSTORE CMAX VRES + CMIN + CSTORE
(3)
at the end of the half cycle. Then, as CVAR increases and vVAR decreases, D2 immediately turns off, keeping the charge on CSTORE , and hence vSTORE , constant throughout the remainder of the cycle. Therefore, vSTORE,n = vSTORE
(4)
where vSTORE is taken from (3). Because charge is transferred from CVAR to CSTORE during the cycle, vVAR will head towards a voltage that is less than VRES as CVAR continues to increase. Therefore, D1 is guaranteed to turn on by the point when CVAR = CMAX , so Fig. 3(a) is again the equivalent
IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS—I: FUNDAMENTAL THEORY AND APPLICATIONS
H I
H J
T U RSO
K LMN
Z RSO
[ \
T U O P Q R S WX Y I
K OPQ RS
V
l efb
[]
^ _ `a
g ^ bcd ef h b c d e f ij
V
k
(a) Start of first half of cycle Fig. 3.
3
g h b c d e f ij k
(b) Start of second half of cycle
Equivalent circuit diagrams for different parts of the harvesting cycle. uvwx
p o n m u v wx
~
u v yz u v yz
{|
{}
Fig. 4.
q rs t
Q-V plane contour representing one energy harvesting cycle.
circuit diagram for the charge pump at the start of the next cycle. Define CSTORE α= (5) CMIN + CSTORE CMAX VRES (6) β= CMIN + CSTORE
B. Inductive Flyback Section
so that (3) and (4) can be rewritten as vSTORE,n = αvSTORE,n−1 + β ,
(7)
which is a recurrence relation in the variable vSTORE,i . From [14], the solution of this recurrence relation is CMAX vSTORE,n = VRES 1 − CMIN n CMAX CSTORE . (8) + × CMIN + CSTORE CMIN To determine the saturation value of vSTORE without energy flyback, substitute n = ∞ to obtain vSTORE,∞ =
CMAX VRES . CMIN
(9)
(9) indicates that the saturation value is related to the ratio CMAX /CMIN . This equation may be rewritten as vSTORE,∞
CDC + CAC VRES = CDC − CAC
The energy transduction process just described can also be viewed graphically as a Q-V plane contour shown in Fig. 4. In this diagram, Point 1 corresponds to the moment when both D1 and D2 are off and the capacitor plates are just starting to pull apart for the nth energy conversion cycle. At Point 2, D1 turns on, allowing charge to transfer from CVAR to CSTORE ; correspondingly QVAR falls from Point 2 to Point 3. During this part of the cycle, vVAR = vSTORE . At Point 3, vibration has pulled the capacitor plates to their maximum separation, decreasing CVAR to CMIN . Next, CVAR increases and vVAR falls, turning off D2 . Correspondingly, QVAR remains constant until Point 4, at which time D1 turns on and vVAR is held at VRES . The area within the closed curve in Fig. 4 equals the mechanical vibration energy converted to electrical energy and delivered to CSTORE . As the cycles advance, Point 2 moves to the right and Point 3 rises to meet it. At the same time, Point 4 rises to meet Point 1, and the converted energy shrinks to zero as vSTORE,n saturates. Because of this, it is important to send the energy stored in CSTORE back to CRES quickly enough to permit continuous energy conversion. This is the purpose of the flyback circuitry shown in Fig. 1 and Fig. 2.
(10)
where CDC represents the average value of CVAR and CAC represents its zero-to-peak capacitance variation. From (10), it is apparent that DC parasitic capacitances in parallel with CVAR must be minimized to prevent early saturation.
To power the attached load and prevent vSTORE from saturating, an inductive flyback circuit, modeled after a DC/DC buck converter and shown in Fig. 2, complements the charge pump. Nominally in its off state, the MOSFET switch turns on every few energy harvesting cycles to energize LFLY . The current iFLY ramps up according to diFLY vFLY = dt LFLY
(11)
where vFLY = vSTORE − vRES . After DTCLK , where D represents the clock duty ratio and TCLK represents the clock period, the MOSFET turns off, forcing iFLY to commutate to the freewheeling diode DFLY . This makes vFLY = −vRES , so vRES diFLY =− dt LFLY
(12)
until iFLY = 0 A, at which point the diode turns off. In this way, energy is transferred from CSTORE back to CRES where it can power the load, represented here by RLOAD . Note that it is not necessary for this process to be synchronized with the energy conversion cycles described in Section II-A. Indeed, it might be best to initiate the energy flyback whenever vSTORE rises to a threshold value. This simplifies the control of the
IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS—I: FUNDAMENTAL THEORY AND APPLICATIONS
4
TABLE I H ARVESTED POWER AS A FUNCTION OF vG USING GROUND - REFERENCED CLOCK .
vG (V)
vRES,0 (V)
vRES,∞ (V)
PCONV (W)
4.7
5.9995
5.9724
−5.50 × 10−6
10.7
5.9989
5.9921
−1.40 × 10−6
16.7
5.9990
6.0029
0.79 × 10−6
22.7
5.9991
6.0041
1.02 × 10−6 à ¸Â Ä ¹Å ¸Â Æ ¸À Ç Â
¡
¢
£ ¦§
³ ´°²
» ¹È É À Ê
£ ¤¥
µ
¯ ° ¬± ²
Î
®
£¨
Ì Í ¸À È
Ï ÐÑÒ £ § ©ª « ¬
¶ · ¸¹º » ¸¼ ½ ¹¾ ¼ ½ ¿ À Á Â
Ó » Ë Ë Â ¸Â ÈÀ Ç ¹· ¾
(a) Charge injection
(b) Charge leakage
Fig. 6.
Spring steel variable capacitor side view (not to scale).
Fig. 5. Cycle of circuit operation that results in energy injection from CLK.
MOSFET switch by making it independent of the motion of the variable capacitor. III. C LOCK E NERGY I NJECTION As the previous section shows, the capacitive energy harvester uses a source-referenced clock to drive the MOSFET. Typically, this gate drive is undesirable because the floating reference voltage makes implementation difficult. Here, SPICE simulation explains the necessity of this choice. Table I shows simulated data when the clock is referenced to ground. Circuit parameters used in the simulation are CRES = 1 µF, CSTORE = 3.3 nF, RLOAD = 20 MΩ, LFLY = 2.5 mH, RCORE = 360 kΩ, RWIRE = 8 Ω, vth = 2.5 V, CDC = 1.22 nF, CAC = 300 pF, vRES = 6 V, fCLK = 475 Hz, and D = 0.0019. The simulation uses a SPICE Level-3 2N7002 nchannel MOSFET model and a realistic diode model based on the characteristics of a 1N6263 low-leakage Schottky barrier diode. In the table, vRES,0 and vRES,∞ represent the original and final voltages on CRES respectively. Furthermore, vG is the magnitude of the gate drive voltage. In all cases, vG exceeds the MOSFET threshold voltage, so the on-resistance of the MOSFET does not change much between simulations. The important point to observe is that the converted power PCONV rises significantly as vG increases. Given that all other parameters remain fixed, the additional harvested energy must come from the clock. This is important for two reasons. First, in an experimental system in which the MOSFET is not powered by CRES , energy injection from the clock through the MOSFET gate can be confused as net energy conversion when in fact net energy is not converted. Second, the energy injected into the harvester diminishes the energy that can actually be harvested during a cycle. To understand the source of clock energy injection, consider the simplified circuit diagram shown in Fig. 5. In this figure, CGS is the MOSFET gate-source capacitance, D3 is
the MOSFET body diode, and C1 is the parasitic junction capacitance of DFLY . When a rising clock places QGS onto CGS , the voltage at node X rises according to the capacitive divider involving C1 and CGS . If the voltage rises enough, D3 turns on and leaks a fraction of QGS onto CSTORE , which cannot be recovered when the clock goes low. Using a source-referenced clock prevents node X from being pulled up, thereby preventing the accidental turn-on of D3 and the corresponding energy injection. Table II shows the SPICE simulation when a sourcereferenced clock is used. Here, PCONV does not increase with vGS , indicating that clock energy injection has been eliminated. The first row in the table proves that if vGS is less than the MOSFET threshold voltage, the capacitive energy harvester cannot sustain itself. IV. VARIABLE C APACITOR To test the asynchronous capacitive energy harvesting circuit, a macro scale spring steel variable capacitor supported by eight cantilever beams was designed and fabricated. As shown
Fig. 7.
Spring steel variable capacitor prototype.
IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS—I: FUNDAMENTAL THEORY AND APPLICATIONS
5
TABLE II H ARVESTED POWER AS A FUNCTION OF vGS USING SOURCE - REFERENCED CLOCK .
vGS (V)
vRES,0 (V)
vRES,∞ (V)
2
6.0000
5.9752
−5.034 × 10−6
5
6.0000
6.0038
0.773 × 10−6
11
6.0000
6.0038
0.773 × 10−6
17
6.0000
6.0038
0.773 × 10−6
23
6.0000
6.0038
0.773 × 10−6
35
350
100 pF
30
PCONV (W)
300
100 K
V+ CVAR VBIAS
250 V-
+
CAC (pF)
CAC (pF)
25
+ vTEST
20
-
15
200 150
10
100
5
50
0 1000
0
1200
1400
1600
1800
2000
2200
0
100
200
300
400
Vamp,p-p (mV)
Frequency (Hz)
Fig. 8. Frequency sweep for spring steel variable capacitor with vAMP,p−p = 50 mV.
Fig. 9.
CAC as a function of shaking strength at f = 1560 Hz.
V. E XPERIMENTAL R ESULTS ′′
in Fig. 6 and Fig. 7, a square sheet of 0.05 thick 1095 bluetempered spring steel, with a mass density of 7850 kg/m3 and a Young’s Modulus of 205 GPa, measuring 6.6 cm on each side formed the flexible top plate of CVAR . A solid block of aluminum formed the base. Mylar tape acted as a spacer that defined the nominal gap between the plates. To prevent the top and bottom plates from shorting, nylon screws were used to hold the structure together. FEA optimization was used to keep the out-of-plane resonant mode close to 1500 Hz while pushing the torsion and rotation modes towards higher frequencies above 6000 Hz. The resulting springs have lengths of 0.8 cm and widths of 0.7 cm. Finally, fillets with 2 mm radii were inserted at all perpendicular intersections to help reduce stress levels in the bending capacitor plate. The prototype spring steel variable capacitor gave CDC = 650 pF when measured on a standard bridge, which is close to the calculated value of 566 pF. The capacitor was vibrated with a Ling Dynamic System V456 shaker table and its corresponding PA 1000L amplifier. Using the circuit shown in Fig. 8, in which vTEST is proportional to CAC , a frequency sweep was performed. The result in Fig. 8 shows the first resonant mode to be at f = 1560 Hz with a Q of approximately 3.5. Next, by applying 1560 Hz vibrations of varying strengths to the variable capacitor, created by changing the peak-to-peak voltage input vAMP,p−p to the PA 1000L amplifier, a plot of CAC as a function of vAMP,p−p was generated. Fig. 9 shows the collected data.
The circuit in Fig. 2 was fabricated using surface mount components to test the validity of SPICE simulation results and to demonstrate its operation. The components include a 2N7002 n-channel MOSFET, three 1N6263 low-leakage Schottky barrier diodes, and a CD4047 low power monostable multivibrator gate drive. Before every experiment, a shorting jumper connects a battery to precharge CRES up to vRES = 1.5 V, the starting steady-state voltage. The shaker table is then ramped up from no shaking to the desired test level and the jumper is disconnected. In all cases, the flyback circuit is activated after every 4 energy conversion cycles. Because a resistive load RLOAD formed by a 10 MΩ scope probe in series with a 10 MΩ resistor is attached to the reservoir, a rising vRES indicates positive energy conversion. Fig. 10 plots the evolution of vRES for various shaker table amplifier inputs vAMP,p−p . When vAMP,p−p = 120 mV (CAC = 84 pF), the energy harvester just barely sustains vRES while powering the 20 MΩ load. For vAMP,p−p = 360 mV (CAC = 260 pF), vRES charges up to 6 V, which means that the system delivers 1.8 µW to RLOAD . Although the energy harvester does not have an integrated acceleration sensor to determine the applied acceleration directly, an approximate value can be obtained at the resonant frequency. Assuming a sinusoidal travel of the upper variable capacitor plate and using Q ≈ 3.5 from Fig. 8, and the nominal dimensions of the variable capacitor, the applied acceleration per 100 mV of vAMP,p−p is approximately 8.4g where g =
IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS—I: FUNDAMENTAL THEORY AND APPLICATIONS
5
2.5
Saturation Vres (V)
320 mV
2
280 mV
0.5Vres (V)
6
240 mV
1.5
200 mV 1
160 mV 120 mV
4 3 2 1
0.5
0
1000
0 -5
0
5
10
15
20
25
30
35
40
45
Time (sec)
Fig. 10. Evolution of vRES as a function of time parameterized by vAMP,p−p . The factor of 0.5 in the vertical axis results from the 10 MΩ resistor in series with the scope probe.
3 Vgs = 4.5 V Vgs = 6.0 V
0.5Vres (V)
2.5 2 1.5 1 0.5 0 -10
0
10
20
30
40
50
Time (sec)
Fig. 11.
vRES as a function of source-referenced clocking voltage.
9.8 m/s2 . This translates to 40g when CAC = 350 pF. Notice that the plots in Fig. 10 all flatten out and saturate. This is due to the nonlinear core loss present in LFLY that increases as vFLY goes up. In Fig. 2, this nonlinearity is modeled as a nonlinear resistor RCORE whose resistance depends on vFLY . As vFLY varies between 0 V and 3 V, RCORE drops from its nominal value of 400 kΩ down to approximately 1 kΩ. To prove that the harvested energy does not include clock energy injection, two additional experiments are performed. First, the shaker table is stopped while the clock signal continued running. The scope probe attached to CRES shows that vRES decays to below 80 mV, much lower than the voltages sustained in Fig. 10. This strongly suggests that even if there is energy injection from the source-referenced clock, it is small compared to the transduced energy. Next,
1200
1400
1600
1800
2000
2200
Frequency (Hz)
Fig. 13. Plot of saturation vRES as a function of frequency with vAMP,p−p = 320 mV.
the MOSFET clock amplitude, or equivalently vGS , is varied to determined its effect on the harvested energy. The result, shown in Fig. 11, indicates that the amount of harvested energy is independent of vGS , consistent with SPICE simulations presented in Table II. Thus, it is believed that no energy injected through the MOSFET gate is present in Fig. 10. If the capacitive energy harvester is to be integrated onto an IC with a MEMS capacitor, the minimum vRES required for system startup is critical. A high requirement would necessitate electrochemical cells, defeating the purpose of using an energy harvester in the first place. Startup tests were conducted for the prototype circuit by lowering vRES using a voltage divider and observing whether vRES could still rise to the levels shown in Fig. 10. Fig. 12 plots a sample result with vAMP,p−p = 320 mV and vRES = 200 mV at the start. An iteration process shows that even at the noise floor of the oscilloscope, around vRES = 89 mV, the system can still startup, allowing for a piezoelectric film or an electret to jump start the harvester. In real world applications, the vibration frequency will have some spread, so the sensitivity of the capacitive energy harvester to frequency variations is also important. Fig. 13 shows the saturation point of vRES as a function of the drive frequency at vAMP,p−p = 320 mV. From this plot, a deviation of 150 Hz from the resonant frequency causes a 37% drop in the saturation voltage, which may be unacceptable. A reduction in the mechanical Q will lower this sensitivity at the cost of CAC , so a trade-off exists. If the frequency spectrum of the ambient vibration is not known a priori, the variable capacitor can be designed with a tunable resonant frequency, perhaps through an adaptive scheme employing electric spring stiffening.
2.5
VI. E NERGY C ONVERSION E FFICIENCY 0.5Vres (V)
2
Having demonstrated the behavior of the capacitive energy harvester, the energy conversion efficiency of the circuit is now computed. As a figure of merit, the efficiency η will be defined as Power delivered to load . (13) η≡ Theoretical power harvested from Q-V cycle
1.5 1 System startup 0.5 0 -5
5
15
25
35
45
Time (sec)
Fig. 12. Plot of vRES as circuit starts up from vRES = 200 mV when vAMP,p−p = 320 mV.
The numerator represents the amount of useful energy the harvester can provide to a load while the denominator represents the theoretical maximum that the circuit can deliver if the process was 100% efficient.
IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS—I: FUNDAMENTAL THEORY AND APPLICATIONS
7
As mentioned in Section V, the prototype system presents 6 V to a 20 MΩ resistive load under heavy shaking. Hence, the amount of power delivered to the load for that experiment is 1.8 µW. To determine the denominator, we can compute the total enclosed area A1 + A2 in Fig. 4. For simplicity, approximate A2 as a triangle. Also, because the flyback switch is enabled every 4 harvesting cycles in this paper, take n = 2 in (8) to find the average energy harvested per cycle. Begin by considering Point 1, which corresponds to the moment when both D1 and D2 are off and the plates of the variable capacitor are beginning to pull apart. At this point,
Again, the value of hiD i = 10 µA comes from HSPICE simulation [10]. Adding these losses to the numerator, one obtains 3.8 µW = 40.4% . (25) η′ = 9.4 µW
v1 = VRES = 6 V
VII. S UMMARY AND C ONCLUSION
(14)
and therefore Q1 = Q2 = CMAX VRES = 6 × 10−9 C .
(15)
Point 2 occurs when D2 turns on, and this happens when vVAR is equal to the previous cycle’s vSTORE , which is just vSTORE,1 . From (8) with n = 1, vSTORE,1 = 7.2 V, so v2 = 7.2 V. The trace between Points 2 and 3 represents the charge transfer between CVAR and CSTORE when D2 turns on. By setting n = 2 in (8), it is obtained that v3 = 8.2 V. From this, one can also calculate that Q3 = Q4 = CMIN v3 = 2.5 × 10−9 C .
(16)
Finally, the capacitor plates move toward each other until D1 turns on, from which point on vVAR is held at VRES until the end of the cycle. Therefore, v4 = VRES = 6 V .
(17)
Having determined all the necessary values, areas A1 and A2 can be computed as A1 = (v2 − v1 ) (Q1 − Q4 ) = 4.2 × 10−9 J (18) 1 −9 A2 = (v3 − v2 ) (Q1 − Q4 ) = 1.8 × 10 J . (19) 2 Therefore, the average converted energy WCONV per cycle is WCONV = A1 + A2 = 6 nJ ,
(20)
which means that PCONV = WCONV f = 9.4 µW .
(21)
Finally, referring back to (13), η=
1.8 µW = 19.1% . 9.4 µW
[10]. On the other hand, diodes have a constant voltage drop, vD , across them when turned on, so their average conduction loss is related to the average current, hiD i. Using typical parameter values from the 1N6263 Schottky diode datasheet, hPD,COND i ≈ hiD i vD = 2 µW .
(24)
This paper demonstrates an asynchronous capacitive energy harvesting circuit employing a charge pump and inductive flyback. Coupled to an experimental variable capacitor, it delivers 1.8 µW of power to a 20 MΩ resistive load at a steady-state voltage of 6 V while exhibiting an efficiency of 19.1%. The spring steel variable capacitor used to drive the charge pump achieved a CMAX /CMIN ratio of 3.3 with a 1.56 kHz out-of-plane resonant frequency. Because the harvester employs only one asynchronous MOSFET switch, clocking is greatly simplified. However, this paper shows that in order to obtain accurate data, a source-referenced gate drive should be used to prevent spurious clock energy injection, which can artificially inflate the conversion efficiency and diminish actual conversion. Experiments conducted using a prototype circuit not only demonstrated close match between theory and actual data, but they also revealed an extremely low startup requirement of vRES ≤ 89 mV for the capacitive harvester. Finally, the system can tolerate a frequency variation of 150 Hz before the steady-state voltage drops to 2/3 of its peak value. ACKNOWLEDGMENT This paper is based in part on [10]. The authors would like to thank both Professor Alex Slocum and Alexis Weber for their assistance in designing and fabricating the spring steel variable capacitor. We are also indebted to Professor Charles Sodini, who helped us work out the clock energy injection issues associated with ground-referenced gate drives. Finally, Professor Dave Perreault provided us with invaluable suggestions on the diode selection as well as alternative energy flyback techniques.
(22) R EFERENCES
An efficiency that removes the losses of the MOSFET and diodes can also be calculated. This value corresponds to the deliverable power given lossless power electronics. Because the MOSFET on-resistance, RDS,ON , is approximately a constant when operated as a switch, the average conduction loss, hPFET,COND i, is related to the root-mean-square current, iRMS . Using typical parameter values from the 2N7002 nchannel MOSFET datasheet, hPFET,COND i ≈ i2RMS × RDS,ON = 0.36 nW .
(23)
The value of iRMS = 14 µA comes from HSPICE simulation
[1] “Materials by Design: Piezoelectric Materials,” http://www.mse.cornell.edu/courses/engri111/piezo.htm, 1996. [2] G. K. Ottman, H. F. Hofmann, A. C. Bhatt, and G. A. Lesieutre, “Adaptive Piezoelectric Energy Harvesting Circuit for Wireless Remote Power Supply,” IEEE Transactions on Power Electronics, vol. 17, no. 5, pp. 669–676, September 2002. [3] S. Roundy, B. Otis, Y.-H. Chee, J. M. Rabaey, and P. Wright, “A 1.9GHz RF Transmit Beacon using Environmentally Scavenged Energy,” in International Symposium on Low Power Electronics and Design, 2003. [4] G. K. Ottman, H. F. Hofmann, and G. A. Lesieutre, “Optimized Piezoelectric Energy Harvesting Circuit Using Step-Down Converter in Discontinuous Conduction Mode,” IEEE Transactions on Power Electronics, vol. 18, no. 2, pp. 696–703, March 2003.
IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS—I: FUNDAMENTAL THEORY AND APPLICATIONS
[5] P. Glynne-Jones, M. Tudor, S. Beeby, and N. White, “An Electromagnetic, Vibration-Powered Generator for Intelligent Sensor Systems,” Sensors and Actuators A, vol. 110, no. 1-3, pp. 344–349, February 2004. [6] C. Williams and R. Yates, “Analysis of a Micro-electric Generator for Microsystems,” in 8th International Conference on Solid-State Sensors and Actuators, vol. 1, June 1995, pp. 369–372. [7] P. Miao, A. S. Holmes, E. M. Yeatman, and T. C. Green, “MicroMachined Variable Capacitors for Power Generation,” March 2003, unpublished. [8] J. O. Mur-Miranda, “MEMS-Enabled Electrostatic Vibration-to-Electric Energy Conversion,” Ph.D. dissertation, Massachusetts Institute of Technology, 2003. [9] M. Miyazaki, H. Tanaka, G. Ono, T. Nagano, N. Ohkubo, T. Kawahara, and K. Yano, “Electric-Energy Generation Using Variable-Capacitive Resonator for Power-Free LSI: Efficiency Analysis and Fundamental Experiment,” in ISPLED 2003, August 2003, pp. 193–198. [10] B. C. Yen, “Vibration-to-Electric Energy Conversion Using a Mechanically-Varied Capacitor,” Master’s thesis, Massachusetts Institute of Technology, 2005. [11] T. Sterken, K. Baert, R. Puers, G. Borghs, and R. Mertens, “A New Power MEMS Component with Variable Capacitance,” in Pan Pacific Microelectronics Symposium, February 2003, pp. 27–34. [12] S. Roundy, P. K. Wright, and J. Rabaey, “A Study of Low Level Vibrations as a Power Source for Wireless Sensor Nodes,” Computer Communications, vol. 26, no. 11, pp. 1131–1144, July 2003. [13] D. P. Arnold, F. Cros, I. Zana, D. R. Veazie, and M. G. Allen, “Electroplated Metal Microstructures Embedded in Fusion-Bonded Silicon: Conductors and Magnetic Materials,” Journal of Microelectromechanical Systems, vol. 13, no. 5, October 2004. [14] K. H. Rosen, Discrete Mathematics and Its Applications, 4th ed. McGraw-Hill, New York, 1999.
8
Bernard C. Yen (S’05) received the B.S. degree in electrical engineering from the University of California, Berkeley, in 2003, and the S.M. degree in electrical engineering from the Massachusetts Institute of Technology (MIT), Cambridge, in 2005. He is currently working toward the Ph.D. degree in electrical engineering at MIT. His research interests include vibration-to-electric energy harvesting, power electronics, micro-electromechanical systems, and analog circuit design.
Jeffrey H. Lang (S’78–M’79–SM’95–F’98) received the S.B., S.M., and Ph.D. degrees in electrical engineering from the Massachusetts Institute of Technology (MIT), Cambridge, in 1975, 1977, and 1980, respectively. Currently, he is a Professor of Electrical Engineering at MIT and has been a faculty member since 1980. His research and teaching interests focus on the analysis, design, and control of electromechanical systems with an emphasis on rotating machinery, microsensors and actuators, and flexible structures. He has written over 180 papers and holds 11 patents in the areas of electromechanics, power electronics and applied control, and has been awarded four best paper prizes from various IEEE societies. Prof. Lang is a former Hertz Foundation Fellowand a former Associate Editor of Sensors and Actuators.
