1

Synchronous Inductor Switched Energy ExtractionCircuits for Triboelectric Nanogenerator

Madhav Pathak, Student Member, IEEE, and Ratnesh Kumar, Fellow, IEEE

This work has been submitted to the IEEE for possible publication. Copyright may be transferred without notice, after which this version may no longer beaccessible.

Abstract—Triboelectric nanogenerator (TENG), a class ofmechanical to electrical energy transducers, has emerged as apromising solution to self-power Internet of Things (IoT) sensors,wearable electronics, etc. The use of synchronous switched energyextraction circuits (EECs) as an interface between TENG andbattery load can deliver multi-fold energy gain over simpleminded Full Wave Rectification (FWR). This paper presents adetailed analysis of Parallel and Series Synchronous SwitchedHarvesting on Inductor (P-SSHI and S-SSHI) EECs to derivethe energy delivered to the battery load and compare it with thestandard FWR (a 3rd circuit) in a common analytical framework,under both realistic conditions, and also ideal conditions. Further,the optimal value of battery load to maximize output and upperbound beyond which charging is not feasible are derived for allthe three considered circuits. These closed-form results derivedwith general TENG electrical parameters and first-order circuitnon-idealities shed light on the physics of the modeling and guidethe choice and design of EECs for any given TENG. The derivedanalytical results are verified against PSpice based simulationresults as well as the experimentally measured values.

Index Terms—energy harvesting, triboelectric nanogenerator,switched circuits, internet of things

I. INTRODUCTION: MOTIVATION AND OBJECTIVES

ONE of the major challenges faced by today’s ever-expanding field of mobile electronics, Internet of Things

(IoT), implantables, and wearable electronics is limited on-board battery lifetime. Placing a high capacity battery presentsthe demerits of increased size, weight, maintenance, and cost.Hence, recent years have seen a tremendous interest in inte-grating a miniaturized energy harvester to increase the batterylife by scavenging the ambient energy [1]. Many potentialsources of energy are available in the environment, suchas mechanical, solar, thermal, and chemical [2]–[5]. Amongthese, tapping the mechanical energy in the form of ambientvibration, human body motion, airflow, ocean currents, etc.,is almost always possible. Hence, mechanical to electricalenergy transducers have received significant attention bothacademically and commercially [6].

Recently, a new class of mechanical to electrical en-ergy transducers termed triboelectric nanogenerators (TENGs)based on the conjugation of friction-induced electrificationwith electrostatic induction as its working principle have beendeveloped [7]. A major advantage of TENG is almost all ma-terials have triboelectric properties, offering the flexibility ofdesign, fabrication, and operation mode to suit the application[8]. TENG based on low-cost paper, stretchable interwoventhreads, printed circuit board (PCB), and environmentally

This work was supported in part by U.S. National Science Foundationunder grants NSF-CCF-1331390, NSF-ECCS-1509420, NSF-PFI-1602089,and NSF-CSSI-2004766.

The authors are with the Department of Electrical and ComputerEngineering, Iowa State University, Ames, IA, 50011 USA (e-mail:mpathak@iastate.edu; rkumar@iastate.edu).

degradable materials are some of the many examples, demon-strating the versatility of TENG [9]–[12]. TENGs have beenemployed in terms of application, ranging from harnessingheartbeat vibration for implantables to ocean wave motionsfor large scale energy harvesting [13], [14].

There remain engineering and technical challenges, e.g.,integrating TENG with electronic devices for practical appli-cations, optimal design of transducer, and energy extraction:A critical issue arises from the fact that TENG’s output har-nessing energy from environment with fluctuating movementis non-D.C. and random. Hence, it needs to be “rectified”to a stable positive form to be able to charge an on-boardbattery or capacitor. Also, TENGs are capacitive in naturewith high inherent impedance, which might be fixed or non-linearly varying based on the mode of TENG [15]. Hence,directly charging battery or capacitor with TENG will ingeneral, lead to a poor charging efficiency due to a severeimpedance mismatch. Thus, an interface circuit referred to asEnergy Extraction Circuit (EEC) is required between a TENGand energy storage (battery or capacitor).

Full Wave Rectifier (FWR) is one of the simplest EECin terms of implementation [16], [17]. However, it has beendemonstrated in the literature that higher per-cycle energyoutput can be achieved by more complex EEC architecturessuch as switched circuits [18]. Our previous work introducedsynchronous switched inductor circuits as EECs for TENG,which involve switching at the TENG voltage output extremato obtain manifold gain over the FWR output. Wherein, Par-allel Synchronous Switched Harvesting on Inductor (P-SSHI),and Series Synchronous Switched Harvesting on Inductor (S-SSHI) EECs for TENG transducers were introduced for thefirst time to best of our knowledge [19]. This work extendsit by providing a full mathematical derivation, a completesimulation and includes additional results on hardware imple-mentation and validation with the following contributions:

• The closed-form equations for the per-cycle energy output(Ecycle) of both the P-SSHI and S-SSHI circuits at agiven battery load are derived for the first time. In addi-tion, the upper limit on battery load, optimal battery load,and corresponding maximum Ecycle for both the SSHIcircuits are also derived. Effect of TENG parameters(determined by construction and operation of the givenTENG) and circuit non-idealities on the Ecycle have beencaptured in our models to guide the design of these EECs.

• Incorporation of the following critical non-idealities inthe analytical model to study their adverse effect onthe output energy (Ecycle) and also to provide a moreaccurate model for both the SSHI circuits:

– Leakage charge through any off switch over a cycle

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and also due to other sources such as ringing tran-sients of oscillators at switch toggle times;

– Limited quality factor of the resonator circuits de-termined by parasitic resistance of inductor and theon-state resistance of switches;

– On-state voltage drop of diodes.• Experimental implementation of FWR and both the SSHI

circuits using self-propelled electronic switches with asimple control circuit comprising just one active compo-nent (a comparator).

• Validation of the presented analytical models by wayof close match with those experimentally measured andPSpice simulated Ecycle at different battery loads.

• Comparison of P-SSHI, S-SSHI, and the standard FWRcircuit in a common framework to bring forward theirrespective pros and cons.

It is important to note that while these EECs have beenexplored previously for piezoelectric transducers [20]–[22],their models and hence analysis are entirely different in thecase of triboelectric transducers as discussed ahead, mainlyowing to the fact that while the piezoelectric capacitor appearsin parallel to the load, the triboelectric capacitor appears inseries. Also, while the capacitance remains constant in theformer, it can be time-varying in the latter.

A. Related WorksA variety of EEC architectures have been presented in litera-

ture [18]. A Half Wave Rectifier with a diode parallel to TENGwas used to increase the energy output compared to FWRat an optimized load battery voltage. Further improvementwas achieved by employing Bennet’s voltage doubler circuit[23]. A transformer with optimal turns ratio can be used forimpedance matching; however, the transformer is efficient onlyin the designed narrow frequency band [24]. Synchronousswitched EECs include the approach by [25] and [26] of usinga logic controlled switch to extract energy from a capacitor,being charged by a FWR circuit at an optimal instant, namelyat an optimal capacitor voltage determined from TENG pa-rameters. TENGs are characterized by high voltage and lowtransferred charge (or current). To address this condition, [27]presented a mechanically triggered extrema-seeking series-parallel switched capacitor scheme that reduces output voltageand increases charge in corresponding proportion. Also, amechanically triggered parallel switch to short the TENGat the extrema was used in [17] to improve the efficiencyand increase saturation voltage for capacitor load. Anotherapproach is using a synchronous serial switch to extract energyfrom the TENG capacitor at the extrema. This extracted energycan then be transferred to the DC load with high efficiencyby using a buck converter as shown by [28] or using coupledinductors (flyback converter) as demonstrated by [29] and [30].Another example of a switched EEC is the use of MaximumPower Point Tracking (MPPT) for TENG executed using dual-input buck converter over a compact integrated circuit (IC)[31].

[32] recently described the P-SSHI circuit’s implementationas an IC. Our work provides for the first time, the analyticalmodels for P-SSHI and S-SSHI circuits, that can help guide

the EEC design, such as determining optimal load voltage tomaximize energy extraction. [33] designed the P-SSHI circuitfor a TENG paired with a parallel capacitor that provides anadditional degree of controlling the variation between max tomin capacitance ratio. In contrast, our work deals with bothP-SSHI and S-SSHI circuits in a fully generalized setting andalso provides closed-form Ecycle equations. [34] demonstratedP-SSHI and S-SSHI circuits for a resistive load, one that doesnot need rectification, using mechanical switches. In contrast,our work studies both the SSHI circuits for varying batteryloads commonly encountered in the practical IoT applications;uses convenient automated electronic switches for physicalimplementation, and demonstrates the desired match betweenthe experimental, simulated, and the derived analytical Ecycleresults.

B. Comments about Analysis MethodologyFor the different EECs (FWR, P-SSHI, S-SSHI), we derive

the per-cycle energy delivered to a battery load rather theinstantaneous output power since the vibration frequency canvary, affecting the power but not the per-cycle energy. Abattery load is selected for analysis (as opposed to a resistiveor capacitive load) since most frequently, there is an onboardbattery for IoT, wearables and, other mobile electronic devices,and the harvester’s role is to supplement their energy andextend the lifetime. The use of battery load as opposed toresistive load introduces additional complexity of rectificationthat our EECs also incorporate. The analytical derivationsadditionally include the computation of the optimal value ofthe battery load to maximize output and upper bound beyondwhich the charging becomes infeasible, providing additionalinsights into the 3 EECs.

Our analytical derivations and experimental verification areprovided for the most generalized case: “Contact-Separation”mode TENGs, in which the internal capacitance varies withtime, so that the ratio of maximum to minimum TENGcapacitances β ≥ 1. This general class also includes Lat-eral Sliding and Single Electrode Contact mode TENGs. Incontrast, the Sliding Freestanding and Contact Freestandingmode TENGs, having fixed internal capacitance (β = 1)[15], are a special case and can be derived by equating themaximum and minimum capacitances (CT,max and CT,min)of our framework.

Both the SSHI circuits operate with an external inductor,connected briefly at the TENG operation extremes to form aLC oscillator along with the TENG capacitor. For accuratemodeling, we carefully consider the quality factor of thisoscillator emanating from the non-idealities: parasitic seriesresistance of inductor (RL) as well as the on-state resistance(Ron) of the switch. Additionally, the leakage charge (QL)through the off switches and during the oscillator ringingtransients over an operation cycle is also included in ourmathematical modeling. Further, the diode’s on-state voltagedrop (VD) is the third analytically modeled non-ideality in oursetup.

II. TENG CIRCUIT MODEL

Here we summarize a 1st-order lumped circuit model forContact-Separation mode TENG [35]. Fig. 1(a) shows the

3

structure of TENG used for experimental validation of thecircuit analysis in this study. It consists of a parallel plate

x(t)

Vibration Plate

Electrode 2

(b)

VT

-

+

+

-VOC

+

-VC

CT

TENG

T

Q-σA

SubstrateElectrode 1

Dielectric

Substrate

td

(a)

Surface Triboelectric Charge

σA-QCT

CT

Fig. 1: (a) TENG cross section; (b) Equivalent circuit modelvariable capacitor with horizontal Aluminum plate electrodes(in orange). The top electrode attached to a vibrating platformcan move vertically, making contact and separation with thefixed bottom electrode with a dielectric (Teflon) layer laidover its upper face. The plates have an area A and develop acharge with density σ when the two triboelectrics, Aluminumon top vs. Teflon on the bottom, come into repeated contact.Due to Aluminium vs. Teflon’s triboelectric properties, the topplate is positively charged while the bottom plate is negativelycharged. It can be reasonably assumed that the triboelectriccharges (-σA) generated on the bottom plate’s dielectric layerare evenly distributed, close to the upper surface. Whenconnected to a circuit, the two plates of the TENG willdraw/supply charge from/to the circuit due to the electricfield of the triboelectric charges. Letting QCT (t) denote thecorresponding charge drawn on the bottom electrode of theTENG at time t, the total charge on the bottom structure attime t is (QCT (t)−σA), and by charge conservation, the topplate will have (σA−QC(t)) charge at time t.

Using Gauss law of electrostatics, under infinite parallelplate approximation (no fringing field), the electric fields inthe dielectric and air regions of the structure are given by:

Ed =QCT (t)

ε0εdA; Ea =

QCT (t)− σAε0A

, (1)

where ε0 is the electrical permittivity of air, and εd is therelative dielectric constant of the Teflon dielectric layer. De-noting the thicknesses of the dielectric and air-gap as td, x(t)respectively, the voltage across the two electrodes of TENGcan be calculated using the Poisson’s equation, as below:

VT (t) = −∫ td

0

Eddx−∫ x(t)+td

td

Eadx (2)

Inserting (1) in (2), the voltage across TENG can be writtenas:

VT (t) =σx(t)

ε0−QCT (t)(x(t) + td

εd)

ε0A(3)

From (3), we can arrive at the lumped element circuit modelof the “contact-separation mode TENG” shown in Fig. 1(b):

VT (t) = Voc(t)−QCT (t)

CT (t)= Voc(t)− VCT (t), with (4)

Voc(t) :=σx(t)

ε0(5)

CT (t) :=ε0A

x(t) + deff; deff :=

tdεd. (6)

It is clear from (4)-(6) that TENG capacitance CT (t) andvoltage V (t) change as the air-gap x(t) varies.

For the analysis purposes, we take x(t) to be varying withperiod T , with minimum value 0 (when the top plate is fullydown) and maximum value xmax (when the top plate is fullyup). Then at each integer multiple of the period (t = nT ),the two plates are in contact (x(t) = 0), whereas at thecorresponding half-period later (t = (n+ 1

2 )T ), the two platesare maximally separated (x(t) = xmax). Accordingly, thereare two extreme states of the TENG operation:• State I: t = nT, x(t) = 0, CT (t) = CT,max :=

ε0Adeff

, Voc(t) = 0;

• State II: t = (n+ 12 )T, x(t) = xmax, CT (t) = CT,min :=

ε0Axnax+deff

, Voc(t) = Voc,max := σxmaxε0

.

The voltage and capacitor values at these extreme states,namely, maximum open circuit voltage (Voc,max), minimumTENG capacitance (CT,min), and maximum TENG capaci-tance (CT,max) constitute the TENG parameters that influencethe energy output of the EECs. A convenient useful term insubsequent analysis is the ratio of the capacitances at the twoextremes: β :=

CT,maxCT,min

.III. ANALYSIS OF ENERGY EXTRACTION CIRCUITS

For each of the three circuits, the general approach to derivethe per-cycle energy delivered to the battery load (Ecycle) isto track the TENG voltage at States I and II of the circuitoperation. Since the capacitances at States I and II (CT,min andCT,max) are known, the corresponding charge on the TENGcapacitor (QCT ) can then be found using the TENG equation(4). By law of conservation of charge, the change in the TENGcapacitor charge over a cycle determines the charge flowingthrough the battery load and hence the delivered per-cycleenergy is simply a value scaled by the battery value. Thus, thefollowing analysis and results are purely dependent on the twoextrema states mentioned above and independent of the TENGmotion path to get to those two extrema. In other words, for agiven extraction circuit, Ecycle is dependent on the separationat maxima (xmax and the corresponding Voc,max) and not onthe path, x(t).

A. Full wave rectifierFor a FWR, its battery charging process can be understood

by following the voltage waveform shown in Fig. 3.

D1 D3

D2 D4

Io

Voc

CTVCTVCT +

- +

-TENG

VBLVTVT

Fig. 2: Full Wave Rectifier (FWR) CircuitThe system starts at State I, and initially, the TENG ca-

pacitor has zero charge and the TENG open-circuit voltageis also zero. As the two plates separate, the open-circuitvoltage increases (linearly with separation, see (5)). Thebattery charging commences at the time when the TENGopen-circuit voltage exceeds the battery voltage by two diodedrops (Voc(t) ≥ VBL + 2VD), and from that point on, theTENG voltage remains clamped to that same value, whilethe TENG capacitor accumulates charge equivalent to the

4

Io

Voc

VT

0

Voc,max

VBL+2VD

0

-(VBL+2VD)

State IState II State IState II

t

t

t

0

Fig. 3: Typical open circuit voltage: Voc(t), FWR circuitTENG voltage: VT (t) and output current: Io(t).

difference Voc(t) − (VBL + 2VD) until State II is reached.This completes the first half cycle. As the second half cyclebegins, Voc starts to drop, causing the overall TENG voltageto fall below the threshold VBL + 2VD and the conductionstops. Battery no longer charges, and capacitor retains itscharge to the level at State II, until the time when a dualsituation arises, namely, the absolute TENG voltage reaches∣∣VT (t)

∣∣ ≥ VBL+2VD and gets clamped at that value till State Iis reached, thus completing one full cycle (Refer Fig. 3).

1) Per-Cycle Energy Output: The energy delivered to theload battery in each cycle denoted Ecycle, is the product ofthe battery voltage (VBL) and the total charge flowing throughit in that cycle (∆Qcycle). From the charge conservation, thistotal charge flowing through the battery equals the change inthe TENG capacitor charge in the two half-cycles, ∆Qcycle =|∆QI→IICT

|+ |∆QII→ICT|.

By using (4), the voltage and the charge on the TENGcapacitor at the two states, denoted V IT , Q

ICT, V IIT , QIICT , can

be written as follows:

V IT = − QICTCT,max

= −(VBL + 2VD)

⇒ QICT = CT,max(VBL + 2VD) (7)

V IIT = Voc,max −QIICTCT,min

= (VBL + 2VD)

⇒ QIICT = CT,min(Voc,max − VBL − 2VD) (8)

It follows that,∣∣∣∆QI→II ∣∣∣ = |QICT −QIICT |

= CT,minVoc,max − (CT,min + CT,max)(VBL + 2VD)

=∣∣∣∆QII→I ∣∣∣ =

∣∣∣QIICT −QICT ∣∣∣ .Since this same change in charge flows through the loadbattery in the respective half-cycles, the energy that the batterygains during one cycle is given by twice this change in chargetimes the battery voltage:Ecycle = 2VBLCT,min[Voc,max− (1 + β)(VBL + 2VD)]. (9)

2) Optimal Battery Load: From (9), Ecycle is a quadraticfunction of VBL, and it can be maximized with respect to VBLby differentiating (9) and setting it to zero, to yield the optimalbattery load V ∗BL and the optimal per-cycle energy, E∗cycle:

V ∗BL =Voc,max2(1 + β)

− VD

E∗cycle =CT,minV

2oc,max

2(1 + β)

− 2CT,minVD(Voc,max − (1 + β)VD).

3) Upper Bound to Battery Voltage: In order for the loadbattery to charge, certain conditions must hold. In particular,for the charging in the first half cycle to commence, themaximum achievable voltage must exceed the upper thresholdvoltage needed for charging:

Voc,max ≥ VBL + 2VD.

Similarly, for the charging in the second half cycle to occur,the minimum achievable voltage must fall below the lowerthreshold voltage required for charging:

− V ICT ≤ −(VBL + 2VD).

Combining the two cases, it follows that for charging in bothhalf-cycles, the following should hold:

minVoc,max, V ICT ≥ VBL + 2VD. (10)

Once the first half-cycle completes, the capacitor acquires avoltage of Voc,max − (VBL + 2VD), and in the extreme case(corresponding to the upper bound battery load, where theconduction will occur just at the end of the second half-cycle,i.e., at State I), the conduction ceases until State I, preservingthe capacitor charge at:

QICT = QIICT = CT,min[Voc,max − (VBL + 2VD)].

So,V ICT =

QICTCT,max

=QIICTCT,max

=CT,min[Voc,max − (VBL + 2VD)]

CT,max

=[Voc,max − (VBL + 2VD)]

β< Voc,max. (11)

Now since V ICT < Voc,max, (10) simplifies to:

V ICT ≥ VBL + 2VD

⇔ [Voc,max − (VBL + 2VD)]

β≥ VBL + 2VD

⇔ VBL ≤Voc,maxβ + 1

− 2VD. (12)

The last condition provides an upper bound to the load batteryvoltage for it to charge in the FWR extraction circuit. Asexpected of a quadratic function, it is double the optimalbattery value.

B. Parallel Synchronous Switched Harvesting on InductorP-SSHI circuit is shown in Fig. 4. Compared to FWR, it

has an added parallel path with a switch and an inductor.The parallel switch S is closed at States I and II for half the

D1 D3

D2 D4

Io

-VBL

S

L

RS

Voc

CTVCTVCT

+

-TENG

VTVT+

Fig. 4: Parallel Synchronous Switched Harvesting on Inductor(P-SSHI) Circuit

LCT resonator time period, which flips TENG voltage polarityas apparent from the waveform plot in Fig. 5. This instantinversion increases the load charging duration (compared tothe FWR circuit) in the following half-cycle. The voltage

5

VBL+2VD

-(VBL+2VD)

0

VBL+2VD

-(VBL+2VD)

0

0

0

Case 1: VBL < VBL,t

Case 2: VBL > VBL,t

State II

VT

I0

VT

I0

t

State I State II State I

t

t

t

VTI-VTI- VT

II+VTII+

VTI+

VTI+ VT

II-VTII-

VTI-VTI-

VTII+VTII+

VTI+

VTI+

VTII-VTII-

Fig. 5: Typical P-SSHI circuit TENG voltage: VT (t) andOutput current: Io(t) for higher and lower load battery range.

inversion is imperfect owing to the limited quality factor ofthe resonator LCT circuit being limited by the presence ofswitch on-state resistance (Ron) and the inductor parasiticresistance (RL). Together those are modeled as RS in thefollowing derivation of the per-cycle energy output (Ecycle).During the switch off states, the charging occurs similar to theFWR circuit with one difference. The TENG capacitor chargepartly leaks through the parallel path of S − L − Rs due tothe finite off-state resistance (Roff ) of the switch. Since theTENG voltage polarity and value, which dictate the extent ofcharge leakage, in the first half-cycle (separation of plates) andthe second half-cycle (retraction of plates) are asymmetric, thecorresponding leakage terms are also different, denoted QILand QIL respectively in the following derivation.

1) P-SSHI circuit analysis at States I and II: For the sakeof analytical convenience, we introduce four sets of notationfor the pre and post switching TENG voltage (VT (t)), TENGcapacitor charge (QCT (t)) and its voltage (VCT (t)) at StatesI and II:• State I- (V I−T , QI−CT , V

I−CT

)T Ion−−→State I+ (V I+T , QI+CT , V

I+CT

)

•State II- (V II−T , QII−CT , VII−CT

)T IIon−−→State II+(V II+T , QII+CT

, V II+CT).

Here, T Ion and T IIon denote the switching periods at States Iand II respectively, and equal the corresponding half the LCTresonator cycle time period. Those are designed to be smallcompared to the vibration cycle period (T ); hence we canapproximate the TENG capacitance CT (t) and open circuitvoltage Voc(t) to be constant over the switching period.

At State II, the P-SSHI circuit can be simplified to that inFig. 6(b). We analyze it first to obtain the relation betweenpre and post switching TENG voltages and charges. The

Voc,max

+

-

L

RS

+

-

(a)

L

RS

(b)

CT,maxVCTVCT

+

-TENG

VTVTCT,min

VCTVCT+

-TENG

VTVT

Fig. 6: Simplified P-SSHI circuits at States (a) I and (b) II

differential equation for this resonator loop obtained usingKVL is given by:

d2VCT (t)

dt+RSL

dVCT (t)

dt+

VCT (t)

LCT,min− Voc,maxLCT,min

= 0.

This can be solved for TENG capacitor voltage VCT (t) withinitial condition as VCT (0) = V II−CT

to obtain:

VCT (t) =e−RSt

2L (V II−CT− Voc,max)(cos(ωIId t)

+RS

2LωIIdsin(ωIId t)) + Voc,max,

where ωIId is the resonance frequency given by,

ωIId :=

√1

LCT,min−R2S

4L2. (13)

Switch is kept “on” for half the resonant time period (T IIon =πωIId

). Hence,

V II+CT= VCT (

π

ωIId) = −αIIV II−CT

+ (1 + αII)Voc,max, (14)

with

αII := e−πRS2ωIIdL = e

−π2QIIf , and QIIf :=

ωIId L

RS. (15)

Here, QIIf is the series resonator quality factor at State II, and0 < αII < 1 is its “normalized” form.

The TENG voltage at the end of switching period (V II+T )can then be obtained from (14) and the TENG equation (4):

V II+T = Voc,max − V II+CT= −αIIV II−T . (16)

Thus, the normalized quality factor, αII captures the reductionin the voltage swing (flip) at State II due to the circuit’sseries parasitic resistance (RS). On the other hand, duringthe switching at State I, the P-SSHI circuit is simplified toas shown in Fig. 6(a). Following the same process as above,we obtain:

V I+T = −V I+CT = −αIV I−T , where (17)

αI := e−πRS2ωIdL = e

−π2QIf ;QIf :=

ωIdLRS

; (18)

ωId :=√

1LCT,max

− R2S

4L2 . (19)

Note that the resonance frequency (19) and the normalizedquality factor (18) have changed from that in State II, since theTENG capacitor value has changed to CT,min from CT,max.

2) Per-Cycle Energy Output: Equations (16) and (17) re-lated the post-switching TENG voltages to their pre-switchingvalues at the States II and I, respectively. Next we derivethe values for the pre-switching TENG voltages at the twoStates, to complete the characterization. This also allows us tothen characterize the per-cycle energy output. As noted in thewaveform plot (Fig. 5), similar to the FWR circuit, the TENGvoltage is clamped at VBL + 2VD during the charging phasein the first half-cycle until the time State II is reached, whichis when a charge reversal due to the switch closure occurs (forT IIon duration). Thus,

V II−T = Voc,max −QII−CT

CT,min= VBL + 2VD

⇒ QII−CT = CT,min(Voc,max − VBL − 2VD). (20)

Post switching at State II, using (16),

6

V II+T = Voc,max −QII+CT

CT,min= −αII(VBL + 2VD)

⇒ QII+CT= CT,min(Voc,max + αII(VBL + 2VD)). (21)

In the second half-cycle, there are two possibilities, ei-ther the TENG voltage reaches the lower threshold voltage,−(2VD + VBL) for charging of load to occur (Fig. 5 Case 1)or the battery load is high enough to resist any current flowupto subsequent State I (Fig. 5 Case 2). It is necessary todifferentiate the two cases in order to obtain energy output,Ecycle which is different for the two cases.

The “transition” load value, VBL,t separating these twocases can be derived from the limiting case of no conductionin the second half cycle and TENG Voltage at State I (V I−T )just reaching the lower threshold, −(VBL,t + 2VD), i.e.,

V I−T = −QI−CTCT,max

= −(VBL,t + 2VD). (22)

Under the condition of no current flow through load in thesecond-half cycle, considering leakage, QI−CT = QII+CT

−∣∣QIIL ∣∣.

Then, inserting the value of QII+CTfrom (21) into (22), and

invoking the definition of β, we arrive at:

VBL,t =Voc,maxβ − αII

− 2VD −∣∣QIIL ∣∣

(β − αII)CT,min. (23)

Case 1: VBL < VBl,t: Here, TENG conducts in the sec-ond half-cycle, and hence, the TENG voltage is clamped to−(VBL + 2VD) until reaching State I. Hence,

V I−T = −QI−CTCT,max

= −(VBL + 2VD)

⇒ QI−CT = CT,max(VBL + 2VD). (24)

Post switching at State I, using (17),

V I+T = −QI+CTCT,max

= αI(VBL + 2VD)

⇒ QI+CT = −αICT,max(VBL + 2VD). (25)

Current flows through the load barring the switching periodsat States I and II. As before, the per-cycle energy delivered tothe load (Ecycle) is the battery load (VBL) times the chargeflowing through it (∆Qcycle). The absolute difference betweenthe TENG capacitor charge at State I after switching (QI+CT )and the TENG capacitor charge at State II before switching(QII−CT ) obtained using (25) and (20) respectively less theswitch leakage charge between the above two states (QIL) givesthe total charge flowing through the load in the first half cycle,∣∣∣∆QI+→II−∣∣∣ :=

∣∣∣QII−CT −QI+CT ∣∣∣−∣∣∣QIL∣∣∣= CT,min(Voc,max + (αIβ − 1)(VBL + 2VD))−

∣∣∣QIL∣∣∣ .Similarly, using (24) and (21) and taking into considerationthe switch leakage charge between the States II+ and I- (QIIL ),the charge flowing through the load in the second half cycleis given by,∣∣∣∆QII+→I−∣∣∣ :=

∣∣∣QI−CT −QII+CT

∣∣∣−∣∣∣QIIL ∣∣∣= CT,min(Voc,max + (αII − β)(VBL + 2VD))−

∣∣∣QIIL ∣∣∣ .

Hence, ∆Qcycle :=∣∣∆QI+→II−∣∣+∣∣∆QII+→I−∣∣ and for this

case, E1cycle = VBL∆Qcycle, implies:

E1cycle = VBLCT,min[2Voc,max − [(1− αI)β (26)

+(1− αII)](VBL + 2VD)]− VBL(∣∣∣QIL∣∣∣+

∣∣∣QIIL ∣∣∣).Case 2: VBL ≥ VBL,t: Here, no conduction occurs throughload in the second half cycle, implying QI−CT = QII+CT

−∣∣QIIL ∣∣.

So,

V I−T = −QI−CTCT,max

= −Voc,max + αII(VBL + 2VD)

β+

∣∣QIIL ∣∣CT,max

Post switching at State I, using (17),

V I+T = −QI+CTCT,max

=αI

β(Voc,max + αII(VBL + 2VD))−

αI∣∣QIIL ∣∣

CT,max

⇒ QI+CT = −αICT,min(Voc,max + αII(VBL + 2VD))

+αI∣∣∣QIIL ∣∣∣ . (27)

From (20) and (27) and considering the leakage charge, QILwe find the charge flowing through the load in the first halfcycle is given by,∣∣∣∆QI+→II−∣∣∣ =

∣∣∣QII−CT −QI+CT ∣∣∣−∣∣∣QIL∣∣∣= CT,min[(1 + αI)Voc,max − (1− αIαII)(VBL + 2VD)]

− αI∣∣∣QIIL ∣∣∣−∣∣∣QIL∣∣∣ .

Since in this case, ∆Qcycle =∣∣∆QI+→II−∣∣, we can obtain,

E2cycle = VBLCT,min[(1 + αI)Voc,max

−(1− αIαII)(VBL + 2VD)]

−VBL(∣∣∣QIL∣∣∣+ αI

∣∣∣QIIL ∣∣∣). (28)

3) Optimal Battery Load: We first show that the optimalcondition occurs in the case when, VBL ≥ VBL,t. Using (23):

VBL ≥ VBL,t =Voc,maxβ − αII

− 2VD −∣∣QIIL ∣∣

(β − αII)CT,min

⇔ (β − αII)(VBL + 2VD)− Voc,max +

∣∣QIIL ∣∣CT,min

≥ 0.

Also from (28) and (26),

E2cycle − E1

cycle = VBL(1− αI)

[CT,min((β − αII)(VBL + 2VD)− Voc,max) +∣∣∣QIIL ∣∣∣]

Employing the above inequality into the last equation, andnoting that VBL > 0 and 0 < αII < 1, it follows thatE2cycle − E1

cycle ≥ 0, implying that a larger per-cycle energyis harvested when VBL ≥ VBL,t. The optimal battery voltage(V ∗BL) and the maximized per-cycle energy (E∗cycle) can thenbe found by analyzing this case to yield:

7

V ∗BL =1

2(1− αIαII)[(1 + αI)Voc,max −

c

CT,min]− VD

E∗cycle =(1 + αI)2

4(1− αIαII)(CT,minV

2oc,max)

−CT,minVD[(1 + αI)Voc,max − (1− αIαII)VD]

+c

2(1− αIαII)

[c

2CT,min− (1 + αI)Voc,max

]+cVD; c =

∣∣∣QIL∣∣∣+ αI∣∣∣QIIL ∣∣∣ .

As detailed in Sec.V, the values of the non-ideality parameters(VD, αI /αII , and QIL/QIIL ) change significantly over theoperation range as the load battery varies, causing the currentsand voltages in the circuits to change. Hence, to estimate theoptimal battery load and corresponding optimal energy output,their averaged values over the entire load operating range areused in the above derived equations.

4) Upper bound to Battery Voltage: If the load VBL ishigher than Voc,max − 2VD − QIL

CT,min, there shall be transient

operation cycles before the steady-state charging commences.We introduce the notation VT,k to denote the TENG voltagein the kth cycle. Then starting from rest, i.e., V IT,1 = 0 and noconduction through the load in the first half-cycle, the TENGvoltage at State II is simply given by,

V II−T,1 = Voc,max − V IL ; V IL =

∣∣QIL∣∣CT,min

.

which is then followed by a voltage inversion due to theswitching action, implying,

V II+T,1 = −αII(Voc,max − V IL ).

Similarly, when no conduction occurs in the second half-cycle,

V I−T,2 = − (1 + αII)

βVoc,max +

αII

βV IL + V IIL ; V IIL =

∣∣QIIL ∣∣CT,max

.

The voltage is flipped again at the onset of the second vibrationcycle, implying,

⇒V I+T,2 =αI(1 + αII)

βVoc,max −

αIαII

βV IL − αIV IIL ;

⇒V II−T,2 = (1 + αI + αIαII)Voc,max − (1 + αIαII)V IL

−αIβV IIL ;

⇒V II−T,3 =[1 + αIαII + (αIαII)2+ αI1 + αIαII

]Voc,max − 1 + αIαII + (αIαII)2V IL−αI(1 + αIαII)βV IIL .

Following the above reasoning, the maximum TENG voltagein the kth cycle (at State II) can be written as a sum ofgeometric series with common ratio αIαII , i.e.,

V II−T,k =

[1− (αIαII)k

1− αIαII+ αI

1− (αIαII)k−1

1− αIαII

]Voc,max

−1− (αIαII)k

1− αIαIIV IL −

1− (αIαII)k−1

1− αIαII(αIβV IIL ).

Thus, through the switching at the extremes, the TENG voltagewill continue to build up until it reaches VBL + 2VD, post to

which charging commences and the energy output equation(Ecycle) derived in (28) yields the per-cycle harvested energy.

An upper bound to the battery voltage can be derived fromthe extreme case where no charging occurs even as k → ∞,and with αIαII < 1, we get,

VBL ≤ limk→∞

V II−T,k − 2VD=(1 + αI)Voc,max − V IL − αIβV IIL

1− αIαII−2VD.

C. Series Synchronous Switched Harvesting on InductorWhile TENGs generally have high open circuit voltage

(Voc,max), in the earlier discussed circuits, the maximumTENG voltage (VT ) gets clamped to a value limited by thebattery load voltage. In contrast, a serial switch can allowthe voltage buildup irrespective of the battery load, as in thepresented case of the S-SSHI circuit. It consists of a serial

D1 D3

D2 D4

Io

-

VBL

S L RS

Voc

CTVCTVCT

+

-TENG

VTVT

+

Fig. 7: Series Synchronous Switched Harvesting on Inductor(S-SSHI) Circuit

switch connecting TENG with the battery load via an inductorL (Fig. 7). The TENG operates in an open circuit condition(barring the leakage current) except when the switch is closedat States I and II for half the LCT resonator cycle to flip theTENG voltage polarity and in that process charges the battery(Fig. 8). For the battery to be charged, the battery voltage mustbe below a critical value (derived below in Section III-C5).Fig. 8 contrasts the two cases, one where this condition issatisfied (top two plots, where the TENG voltage builds upand the battery charging current are shown) versus wherethe condition is not satisfied (bottom plot, where the TENGvoltage does not build up and no battery charging currentflows).

VBL+2VD

0

0

0

Case 1: VBL < VBL,c

Case 2: VBL > VBL,c

VT

I0

VT

t

t

t

VT,ssII-VT,ssII-

VT,ssI-VT,ssI-

Voc,max-VLIVoc,max-VLI

Voc,max-VLIVoc,max-VLI

Fig. 8: (Top) Typical S-SSHI circuit TENG voltage: VT (t)and Output current: Io(t) for below critical battery load and(Bottom) TENG voltage: VT (t) for above critical battery load.

1) S-SSHI circuit analysis at States I II: We first analyzethe simplified S-SSHI circuit at State II, as in Fig. 9(b), toobtain the relation between and pre and post switched TENGvoltages. The initial voltage of the TENG capacitor before the

8

D1

D4

L RSD2

D3

+

-L RS

Voc,max

CT,minVCTVCT

+

TENG

VTVTCT,max

VCTVCT+

-TENG

VTVT

-

VBLVBL

VBLVBL+

-

(a) (b)

Fig. 9: Simplified S-SSHI circuits at States (a) I and (b) II

switching at Stage II is still denoted as V II−CT. Using KVL

around the loop, we arrive at the differential equation below,d2VCT (t)

dt+RSL

dVCT (t)

dt+VCT (t)

LCT,min=Voc,max − VBL − 2VD

LCT,min.

(29)As in the case of the P-SSHI circuit, the switch is closed forhalf the LCT resonator cycle. Accordingly, solving the abovedifferential equation and performing the analysis as in SectionIII-B1, the TENG capacitor voltage after the switching (V II+CT

)is given by,V II+CT

= −αIIV II−CT+ (1 + αII)(Voc,max − VBL − 2VD).

Using the TENG equation (4),V II+T = −αIIV II−T + (1 + αII)(VBL + 2VD). (30)

On the other hand, at State I, the S-SSHI circuit is simplifiedto that in Fig. 9(a), with pre and post switching TENG voltagesrelated by (obtained by solving an equation of the type (29)with Voc,max replaced by Voc,min = 0 so that VCT = −VT ,and CT,min replaced by CT,max),

V I+T = −αIV I−T − (1 + αI)(VBL + 2VD). (31)

Here, αII and αI are the same as those defined earlier in (15)and (18), respectively.

2) Switching among States: Transient Phase: The previoussubsection discussed the S-SSHI circuit when the switch isclosed at States I and II and derived the relations among thepre-switching and post-switching TENG voltages at both thosestates. Next we derive the pre-switching TENG voltages atthe two states to complete the characterization of the TENGvoltages. Unlike P-SSHI, the S-SSHI circuit has a transientphase and either the TENG voltage settles to a steady-statevalue higher than or equal to Voc,max, or a value less thanVBL + 2VD (refer Fig. 8), depending on whether the batteryvoltage is below or above a critical value. We model the TENGvoltage transients to derive the steady-state values at States Iand II. As before, we let the VT,k denote the TENG voltagein the kth cycle.

With no current flow other than leakage between States Iand II with switch S open, QII−CT ,k = QI+CT ,k −

∣∣QIL∣∣. Hence,

V II−T,k = Voc,max −QII−CT ,kCT,min

= Voc,max + βV I+T,k − VIL . (32)

Using the above equation and the relation in (30), the post-switching TENG voltage at State II is given by,

V II+T,k = Voc,max −QII+CT ,k

CT,min=− αII(βV I+T,k + Voc,max − V IL )

+ (1 + αII)(VBL + 2VD).

With only leakage current up to reaching State I of thesubsequent (k + 1)th cycle (QI−T,k+1 = QII+T,k −

∣∣QIIL ∣∣) andfrom above equation, it follows,

V I−T,k+1 = −QI−CT ,k+1

CT,max= −αIIV I+T,k +

αIIV ILβ

+ V IIL

− (1 + αII)

β(Voc,max − VBL − 2VD).

Using (31), we arrive at the desired relation,V I+T,k+1 = c1V

I+T,k + c2, where

c1 := αIαII ;

c2 := −[1 + αI +αI(1 + αII)

β](VBL + 2VD)

+αI(1 + αII)

βVoc,max −

αIαIIV ILβ

− αIV IIL .

(33)

Above is a recursive relation, which can be solved to obtainthe relation between V I+T,k+1 and V I+T,1 :

V I+T,k = ck−11 V I+T,1 + ck−21 c2 + ....+ c2.

Taking the TENG operation to start from rest, i.e., V I+T,1 = 0,the above equates to a sum of geometric series with (k − 1)terms and common ratio, c1 = αIαII < 1, and the first termas c2. It follows that,

V I+T,k =1− ck−11

1− c1c2. (34)

This provides a closed-form solution for the post-switchingTENG voltage at State I of the kth cycle. Also using (32),

V II−T,k = Voc,max + β1− ck−11

1− c1c2 − V IL . (35)

From above equation it is clear that when c2 > 0, the TENGvoltage builds up over time (increases with respect to k) as inFig. 8 Case 1, and otherwise when c2 < 0, it diminishes overtime as in Fig. 8 Case 2. The latter case leads to no charging inthe steady-state. No transient cycles are present for the specialcase of c2 = 0.

3) Per-Cycle Energy Output in Steady-State: In the steady-state, from (34), the post-switching voltage and charge onTENG at State I can simply be written as:

V I+T,ss =c2

1− c1= −

QI+CT ,ssCT,max

⇒ QI+CT ,ss = −CT,maxc2

1− c1. (36)

Using this, along with the relations (32)-(33), we obtain theTENG capacitor charge values in the steady-state as:

QII−CT ,ss = QI+CT ,ss −∣∣∣QIL∣∣∣ ; (37)

QII+CT ,ss= CT,min[

αIIβc21− c1

(38)

+ (1 + αII)(Voc,max − VBL − 2VD)]− αII∣∣∣QIL∣∣∣ ;

QI−CT ,ss = QII+CT ,ss−∣∣∣QIIL ∣∣∣ . (39)

The change in TENG capacitor charge during the two switch-ing periods flows through the load. S-SSHI being a seriescircuit, the leakage charge flows through the load too. So thecharge flowing through the load in one cycle equals,

∆Qcycle=∣∣∣∆QI−→I+∣∣∣+

∣∣∣∆QII−→II+∣∣∣+|QL|

=∣∣∣QI+T,ss −QI−T,ss∣∣∣+

∣∣∣QII−T,ss −QII+T,ss

∣∣∣+∣∣∣QIL∣∣∣+

∣∣∣QIIL ∣∣∣ .

9

Hence, the per-cycle energy output equals, VBL∆Qcycle. Us-ing (36-39) and inserting value of c1 and c2 from (33),

Ecycle =

[2(1 + αI)(1 + αII)

(1− αIαII)

]CT,minVBL (40)

×[Voc,max − (1 + β)(VBL + 2VD)

]− 2VBL

(1− αIαII)c3;

c3 = (αII(1 + 2αI)− 1)∣∣∣QIL∣∣∣+ αI(1 + αII)

∣∣∣QIIL ∣∣∣ .The number of transient cycles required to attain the steady-state depends on the product of the two normalized qualityfactors c1 = αIαII (or equivalently their geometric mean). Asystem with a lower quality factor shall reach the steady-statequicker but with a lower per-cycle energy output for a givenload.

4) Optimal Battery Load: Ecycle found in (40) is quadraticin VBL, which can be optimized to attain the optimal batteryload (V ∗BL) and maximized per-cycle energy (E∗cycle):

V ∗BL =Voc,max2(1 + β)

− VD

− c32CT,min(1 + β)(1 + αI)(1 + αII)

E∗cycle =

[2CT,min(1 + αI)(1 + αII)

(1− αIαII)

]

×

[V 2oc,max

4(1 + β)− Voc,maxVD + (1 + β)V 2

D

]

− c3(1− αIαII)

[Voc,maxβ + 1

− 2VD

− c32CT,min(1 + β)(1 + αI)(1 + αII)

]5) Upper bound to Battery Voltage: As discussed earlier,

condition for S-SSHI circuit to reach a non-zero steady-state(so battery can be charged in steady-state) is:

c2 ≥ 0

⇔ VBL ≤Voc,max

1 + (1+αI)βαI(1+αII)

− αIαIIV IL(1 + αI)(1 + β)

− V IIL

1 + 1αI

+ (1+αII)β

− 2VD. (41)

The above condition sets an upper bound to the battery voltagefor a sustained S-SSHI charging.D. Comparative Analysis

In the above sections, we derived the closed-form results foreach of the three considered circuits’ per-cycle energy output.Here, we compare their optimal output in a common analyticalframework. For the sake of simplicity, we relax the analysisconditions by using ideal diodes and switches, i.e., take thevalues of diode voltage drop (VD), leakage (QIL/Q

IIL ), and

switch-on resistance (Ron) as zero. For further convenience,we define:

Eref = CT,minV2oc,max.

This allows easy tabulation of optimal per-cycle energy output(E∗cycle), optimal battery load (V ∗BL), and maximum gain over

FWR circuit (E∗cycle

E∗FWR,cycle

) as in Table I.

TABLE I: Optimal energy output, optimal battery load, andmaximum gain over FWR (under VD=0; QIL=QIIL =0)

Circuit V ∗BL

Voc,max

E∗cycle

Eref

E∗cycle

E∗FWR,cycle

FWR 12(1+β)

12(1+β)

1

P-SSHI (1+αI )

2(1−αIαII )(1+αI )2

4(1−αIαII )(1+αI )2(1+β)

2(1−αIαII )

S-SSHI 12(1+β)

(1+αI )(1+αII )

2(1−αIαII )(1+β)(1+αI )(1+αII )

(1−αIαII )

Using Table I values and taking the approximations,

ωId ≈

√1

LpCT,maxand ωIId ≈

√1

LpCT,min,

QIIf =ωIId L

RL≈√βQIf and lnαII ≈ lnαII√

β,

we study the effect of quality factor on the optimal gains ofP-SSHI and S-SSHI circuits over FWR as in Fig. 10.

Optimal Gain

Optimal Load

Ecy

cle/

EF

WR

,cy

cle

**

Ecy

cle/

EF

WR

,cy

cle

**

VB

L/V

oc,

ma

x*

VB

L/V

oc,

ma

x*

Quality factor: QI (αI)f

Quality factor: QI (αI)f

P-SSHI | β=2.5

P-SSHI | β=2.5

P-SSHI | β=1 S-SSHI | β=1 S-SSHI | β=2.5

S-SSHI | β=2.5

S-SSHI/P-SSHI | β=1

Fig. 10: Top/Bottom: Comparison of optimal energy gain(resp., battery load) of the P-SSHI and S-SSHI circuits overFWR (resp., over Voc,max) against the inductor quality factor.• The optimal gains of P-SSHI and S-SSHI circuit are

increasing with inductor quality factor (Fig. 10(Top)).• For β = 1, the optimum gains turn out to be the same for

both P-SSHI and S-SSHI circuits, and it improves withincreasing β for both circuits (Fig. 10(Top)).

• For any β > 1, the optimal gain of P-SSHI is higherthan S-SSHI (Fig. 10(Top)), but this is achieved foroptimal battery load several times the maximum opencircuit voltage (Voc,max) depending on the quality factor(Fig. 10(Bottom)). TENGs typically have high Voc,max(in tens to hundreds of volts), and hence implementing aP-SSHI circuit at optimal load shall be challenging.

• In contrast, optimal load for S-SSHI circuit is in-dependent of quality factor and lower than Voc,max(Fig. 10(Bottom)).

Further, the effect of battery load on the energy output isstudied in section V.

IV. EXPERIMENTAL IMPLEMENTATIONA. Experimental Setup

TENG with a contact area of 113.8 cm2 is built as shownin the schematic of Fig. 1 using Al foil as the electrodes and

10

E4

V’T

V’DT

VC

0

0

0

State II State I

V’TV’T

VB

-VB

VC

Differentiator Comparator

V’DT

(a)

(b)

(c)

Cd

Rd

V’oc

C’TV’CTV’CT

- +

-AUX-TENG

E3

+

EEC

TENGAUX -TENG

StepperMotor

t

t

t

D1 D3

D2 D4Voc

CT

VCTVCT

- +

-TENG

VBL

L

N1 P1

VC

(e)

E1

E2

+VT

VBL

L

VC

D1 D3

D2 D4

D5 D6

(d)

N1 P1Voc

CT

VCTVCT

- +

-TENG

E1

E2

+VT

SubstrateElectrode 1

DielectricElectrode 2

Substrate

Vibration Plate

E4

E3

Fig. 11: (a) Experimental Setup; Inset: Cross section view of a contact-separation TENG with Aux-TENG (b) Control circuit forP-SSHI and S-SSHI circuits (c) Control circuit waveforms (d) P-SSHI circuit implementation (e) S-SSHI circuit implementation

Teflon of thickness 127 µm as the dielectric. The bottom plateis fixed while the top plate is driven in a vertical contact-separation mode using a programmed stepper motor at 10 Hzfrequency and maximum separation (xmax) of 1.2 mm. Thesetup picture is shown in Fig. 11(a).B. TENG Characterization

The key electrical parameters to characterize TENG aremaximum open circuit voltage (Voc,max), minimum and max-imum TENG capacitance (CT,min and CT,max).

1) TENG Capacitance: We follow the method describedin [23], [36] to measure the dynamic variation of the TENGCapacitance (CT (t)) and extract the minimum and maximumvalue (CT,min and CT,max). The details of the method arerepeated in the Appendix A along with the plot of measuredCT (t).

2) TENG maximum open circuit voltage: We use the stan-dard FWR circuit to measure Voc,max. In the section III-A3,the upper bound on the load battery voltage is derived forthe FWR circuit. Instead of a battery, if a capacitor (of anycapacitance) is charged using a FWR circuit, its voltage willsaturate at the same value (Vsat), which by (12) satisfies:

Voc,max = (β + 1)(Vsat + 2VD).By charging a capacitor, Vsat was measured as 54.4V . Atsaturation, negligible current flows through the FWR circuit,and hence diode voltage drop (VD) can be neglected, yieldingVoc,max as 188.77V . The measured TENG parameters aresummarized in Table II.

TABLE II: Measured TENG Parameters

Maximum open circuit voltage: Voc,max 188.77 V

Minimum TENG capacitance: CT,min 97.28 pF

Maximum TENG capacitance: CT,max 239.80 pF

TENG capacitance ratio: β 2.47

C. Implementation of Energy Extraction CircuitsSynchronous switched circuits (P-SSHI and S-SSHI) de-

scribed above are implemented using the MOSFET as switchesand operated through dedicated control circuits. The controlcircuit’s function is to detect States I and II during the TENGoperation and issue the required gate pulse to the MOSFET

switches. The switching control circuit receives input froman “auxiliary” TENG (with contact area 1/8th to that ofthe main TENG) that is implemented on the same fixedbottom and moving upper plates as the main TENG to operatein parallel (Fig. 11(a)). This isolation of auxiliary TENG(from the main TENG) allows non-interfering operation of thecontrol circuit independent of the TENG voltage waveformand prevents charge leakage (and subsequent performancedegradation) from the main TENG into the control circuit.The energy consumed by the control circuit can be deducedseparately and is given in Table III. Off-the-shelf componentsused for the implementation are listed in Appendix B.

TABLE III: Control Circuit Power ConsumptionCircuit Avg. Current Supply Voltage (2VB) PowerP-SSHI 257 nA 4 V 1.03 uWS-SSHI 590 nA 7 V 4.13 uW

1) FWR Circuit: Implementation of the FWR circuit thatcontains no synchronized switches is straightforward, asshown in Fig. 2. Fig. 12(a) shows the measured TENG voltage(VT ) and load current (Io) for the battery load (VBL) of 15V.

2) P-SSHI Circuit: P-SSHI circuit is implemented as shownin Fig. 11(d). Its synchronized switching control circuit con-sists of a RC differentiator followed by a zero-crossing com-parator (Fig. 11(b)). Value of RC differentiator is chosen toprovide high output impedance to the Aux-TENG (“auxiliary”TENG); hence it operates in near open circuit condition (V ′T ).The differentiated signal (V ′DT ) is zero at the extrema: StatesI and II, which triggers the state change of the comparator(VC) (Fig. 11(c)). The NMOS switch is turned on at State IIand PMOS at State I due to state change in gate signal (VC).The switch turn-off is automatic since the current directionreversal at the end of half the LCT oscillation time-period isblocked by the corresponding diode D5 (or D6). The controlcircuit is powered by ±2V external source. Fig. 12(b) showsthe measured TENG voltage (VT ), control signal (VC), andload current (Io) for the battery load (VBL) of 15V. Note theinstants of voltage inversion at States I and II compared to theFWR circuit TENG voltage (Fig. 12(a)).

11

FWR

Time (s)

P-SSHI

Time (s)(a) (b)

S-SSHI

Time(s)(c)

VT (V)

Io (x10uA)VC (V)

VT (V)

Io (x10uA)VC (x10V)

VT (V)

Io (x10mA)

Fig. 12: Measured TENG Voltage (VT ), load current (Io) and (if) control voltage (VC) waveforms at 15V battery load of the(a) FWR, (b) P-SSHI, and (c) S-SSHI circuits.

Time (us)Time (us)

Io (mA)VC (V)

Fig. 13: Zoomed in measured load current (Io) and controlvoltage (VC) waveforms during switching at State I.

3) S-SSHI Circuit: Here, the same control circuit as usedfor the P-SSHI circuit is used (Fig. 11(b)) and is powered by±3.5V supply. Fig. 11(e) shows the implementation of the S-SSHI circuit. The circuit operation is the same as the P-SSHIcircuit explained above, with the inductor, NMOS and PMOSswitches in series connection with the TENG compared toparallel as in the case of the P-SSHI circuit. Fig. 12(a) showsthe measured steady-state TENG voltage (VT ), control signal(VC), and load current (Io) for the battery load VBL = 15V .Note the TENG voltage at State II reaches almost twice themaximum open circuit voltage of the TENG (Voc,max) due tothe transient buildup via voltage inversions. Fig. 13 shows thezoomed in view of the Io and VC during the switching at StateI. The load current (Io) is a half sinusoid since the switch is onfor half the LCT oscillation time period. The post-switchingringing transients observed in Io can be attributed to the strayparasitics of the circuit.

V. ENERGY RESULTS AND DISCUSSION

The experimentally measured, simulated, and analyticallyobtained per-cycle energy output (Ecycle) at different loadbattery values (VBL) for each of the three considered energyextraction circuits (EECs) are co-plotted in Fig. 14. Experi-mental results were obtained using the implemented TENGwith parameters listed in Table II. For simulation, the TENGcircuit model described in Sec. II was implemented in a PSpicetool using the same measured parameters of Table II and op-eration frequency of 10 Hz. The circuits were built using thePSpice models of the off-the-shelf components (diodes, MOS-FETs, and comparator) used in experimental implementationavailable from the vendor websites. The commercial inductorused in the P-SSHI/S-SSHI circuits was modeled as a seriesL-RL for simulation with frequency dependent inductance andresistance values obtained experimentally using the RLC meterat the respective L-CT resonance frequencies of States I andII: ωId and ωIId (refer Appendix C for details). While for theanalytical results, measured TENG parameters (Table II) and

the non-ideality parameters estimated from the manufacturerprovided PSpice models and the simulation of those models atmultiple operating points were used in the equations derived inSec. III. The parameter values of the considered non-idealities:Diode voltage drop (VD), Leakage charges (QIL and QIIL ),and the normalized quality factors (αI and αII ), that changesignificantly over the operating range of the battery load, aretabulated for each circuit in Appendix D Tables VI-VIII andwere estimated at each 2V increment of battery load usingtheir PSpice model simulations.

A. FWR CircuitReferring to Fig. 14(a), Ecycle shows the parabolic behavior

to the change in VBL with peak at 26.7V , as expected fromthe analytical derivation of (9). A close match between theanalytical, simulated, and measured values is achieved.

B. P-SSHI CircuitThe Ecycle for the P-SSHI circuit strictly increases with

VBL in the considered range of 0 − 35V (Fig. 14(b)). Asexpected from the analysis (28), the response is parabolicin nature with a peak obtained at battery load several timesthe maximum open circuit voltage (Voc,max). Extrapolationof the analytical curve (inset Fig. 14(b)) indeed confirms thesame with the peak around 400V , keeping in mind that theextrapolation is based on the used non-ideality parameters atlower operating voltages.

C. S-SSHI CircuitFor the S-SSHI circuit, the parabolic response gives the

peak Ecycle at around 26V (Fig. 14(c)). For an ideal circuit,the peak is expected at the same voltage as the FWR circuit(refer Table I), but the leakage and diode drop shifts thepeak lower. S-SSHI circuit has a high steady-state voltage ofalmost 400V (Fig. 12(c)), which requires the use of high-ratedMOSFETs (refer Appendix B for details) accompanied withsignificant leakage charge (refer cols 5 and 6 in Table VIII ofAppendix D). Hence, leakage charge becomes the dominantnon-ideality affecting the S-SSHI circuit’s performance. Also,stray parasitics such as inductor and MOSFET’s parallelcapacitance give rise to post-switching ringing transients ascan be seen in the measured circuit current (Fig. 13). Suchringing leads to a post-switching additional loss of TENGcharge, and so an immediate decrease (in absolute terms) in thepost switching voltage (refer Fig. 12(c)), resulting in reducedEcycle. This additional loss in the TENG charge is also cap-tured in the analytical results through the added leakage chargeterm QL. Any additional remaining discrepancy between theexperimental and the analytical results may be attributed to

12

AnalyticalSimulatedAnalyticalSimulatedMeasured

AnalyticalSimulatedMeasured

AnalyticalSimulatedMeasured

Ecycle (uJ) FWR

Battery Load (V)

Ecycle (uJ) P-SSHI

Battery Load (V)

AnalyticalSimulatedAnalyticalSimulatedMeasured

AnalyticalSimulatedMeasured

(a) (b)

Battery Load (V)

Ecycle (uJ) S-SSHI

Battery Load (V)(c)

AnalyticalSimulatedAnalyticalSimulatedMeasured

AnalyticalSimulatedMeasured

Voc,maxEcy

cle

(uJ)

Fig. 14: Analytical, simulated and measured per-cycle energy plot for (a) FWR, (b) P-SSHI; Inset: Extrapolated P-SSHIanalytical plot, and (c) S-SSHI circuits against the battery load.

Ec

ycl

e (

uJ)

Battery Load (V)

Circuit R2

FWRP-SSHI

S-SSHI

0.99690.9980

0.9860

Circuit R2

FWRP-SSHI

S-SSHI

0.99690.9980

0.9860 S-SSHI

P-SSHI FWR

Fig. 15: Comparison of measured per-cycle energy output forFWR, P-SSHI, and S-SSHI circuit against the battery load.

the unaccounted factors such as practical delay in the controlcircuit that leads to switching past the extrema (States I and II);measurement errors in the TENG parameters of Table II; theTENG’s own parasitic resistance (due to imperfect connectionto the electrode, connection wires); etc.D. Overall Comparison

Fig. 15 plots the measured Ecycle for all the consideredcircuits. At lower battery loads, the P-SSHI circuit has outputalmost equal to the FWR circuit as expected: The MOSFETswitches fail to turn “on” since the battery load equals the drainto source voltage (Vds) of the MOSFETs, that turns the P-SSHIcircuit of Fig. 11(d) to simply the FWR circuit of Fig. 2. TheS-SSHI circuit has the highest output in the considered loadrange. The two switched inductor circuits require overheadpower for the control circuit (Table III), meaning their netoutput and gain over FWR is lower. For example, in ourimplementation, the P-SSHI control circuit requires 1.03 µW .Hence, the operation at 10Hz extracts net positive energy forbattery load greater than 3.2V and has increased gain overFWR circuit post battery load of 16.75V .

VI. CONCLUSIONThis work developed a mathematical analysis framework

for the synchronous switched energy extraction circuits: P-SSHI and S-SSHI along with the standard FWR circuit forTENG transducers and derived closed-form formulae for theirper-cycle energy output, optimum battery load value, and alsothe upper bound on battery voltage beyond which extraction isnot feasible. The modeling included the non-idealities of diodedrop, leakage current, and switch and inductor resistances. Thestrong match of analytical model results with simulation andmeasured ones shows that the analytical models can be used

to assess TENG EEC performance once the TENG parametershave been measured.

An ideally switched P-SSHI/S-SSHI circuit at optimal loadwas found to provide more than 100 fold gain over the FWRcircuit at their optimum values, depending on the inductorquality factor. The effect of load battery change on the per-cycle energy output was examined. All the circuits show aparabolic response, providing an optimal battery load and anupper bound.

Such comparison of energy extraction circuits brought for-ward their pros versus cons over each other. S-SSHI hassuperior energy output compared to other circuits but operatesover a smaller load range. While P-SSHI energy output canexceed that of S-SSHI, it is optimized at a load voltagevalue several times the TENG maximum open circuit voltage(Voc,max). Use of a DC/DC converter can make this feasible,but with added complexity and loss, and so P-SSHI shall bemore suited for TENG with low Voc,max. Also, for a TENGwith low Voc,max or high β, the low upper bound on the batteryload in the case of the S-SSHI circuit can be limiting. Insummary, the presented work offers design insights/tradeoffsfor TENG energy extraction circuits.

A possible direction of further research is to implementthe discussed circuit architectures by using “passive” controlcircuits. Development of integrated efficient DC/DC convertersto operate the P-SSHI and S-SSHI circuit at their optimalload for any given TENG and the on-board battery is anotherdirection. Further, implementing the EECs identified leakagethrough MOSFET switches as one of the major loss factors.So other switching technologies with high rated voltage andlow leakage, such as SiC (Silicon Carbide), can be explored.

APPENDIX

A. Dynamic measurement of TENG capacitanceAn AC voltage source with frequency fac several magni-

tudes higher than the TENG operation frequency f was con-nected to TENG (see Fig. 16). Using a high input impedancevoltage follower op-amp, Voltages VA and VB were observedon the two channels of oscilloscope. With VA as reference,it can be easily showed that, CT = 1

2πfacRM tan(θ), where

θ is the phase difference between the AC voltages VA andVB . Fig. 16 plot shows the measured CT (t), from which wedetermined, CT,max = 239.80pF and CT,min = 97.28pF .B. List of off-the-shelf components used

All MOSFETs were sourced from Diodes Inc. (diodes.com),inductor from Bourns Inc. (bourns.com), didoes from ON

13

Voc

CT

VCTVCT

- +

-TENG

VA VB

RM

+VT

fac f

Time (s)

CT

(t)

Fig. 16: Measurement setup for TENG capacitance (CT (t))and its plot

Semiconductors (onsemi.com), and TS881 used as comparatorin the control circuit from STMicroelctronics (st.com). PSpicemodels used were downloaded from vendor websites.

TABLE IV: List of discrete components usedCircuit FWR P-SSHI S-SSHIDiode 1N4148 1N4148 MUR160NMOS - DMN601K DMN60H080DSPMOS - DMP510DL DMP45H150DE

Inductor - RLB1014-104KL RLB1014-104KL

C. Inductor CharacterizationThe inductor is modeled as series L-RL for the simulation.

Both L and RL were measured using the RLC meter at theState I and State II resonance frequency (ωId and ωId) and aretabulated below. The nominal inductance for RLB1014-104KLused in P-SSHI/S-SSHI circuit was 100mH .

TABLE V: Inductor CharacterizationFrequency L(mH) RL(Ω)

ωId =227.02 kHz 80.91 296

ωIId =343.55 kHz 87.09 395.6

D. Non-ideality parametersTable VI lists the values of the diode voltage drops (VD),

averaged across all the diodes, for the FWR circuit, andwas obtained from manufacturer PSpice models and theirsimulation at the increments of 2V battery load (VBL).TABLE VI: FWR circuit’s average diode voltage drop atdifferent battery load

VBL(V ) VD(mV ) VBL(V ) VD(mV )2 239.190 24 239.0004 239.195 26 235.8956 239.170 28 236.8808 240.010 30 233.820

10 241.085 32 232.11012 241.715 34 231.19014 240.405 36 229.97516 240.890 38 228.43018 239.935 40 225.68020 239.660 42 222.92022 238.615 44 219.840

Table VII and Table VIII list the values of non-idealityparameters obtained from manufacturer PSpice models andthe simulation of those models at increments of 2V batteryload (VBL) for the P-SSHI and S-SSHI circuits, respectively.In both the tables, the diode voltage drop: VD averaged acrossall diodes is listed first. Next two columns list αI and αII , thenormalized resonator quality factor during switching at StatesI and II, respectively. In the last two columns, QIL and QIILlist the leakage charge during the first half-cycle and secondhalf-cycle, respectively.

TABLE VII: P-SSHI circuit’s non-ideality parameters at dif-ferent battery loadVBL(V ) VD(mV ) αI αII QIL(nC) QIIL (nC)

2 238.630 0.982685 0.992048 0.417454 0.3365434 238.610 0.964918 0.972427 0.471214 0.3557216 238.580 0.962172 0.963049 0.527053 0.3747578 238.530 0.958906 0.962619 0.573477 0.392414

10 238.480 0.956383 0.959136 0.618310 0.41048612 238.360 0.955017 0.960197 0.663186 0.42935714 238.565 0.954870 0.961392 0.705960 0.44755616 238.485 0.954431 0.960071 0.748835 0.46351318 238.375 0.954023 0.959017 0.787447 0.48036020 238.260 0.953624 0.958170 0.825341 0.49737422 238.115 0.953273 0.958331 0.866459 0.51653024 237.955 0.952561 0.958361 0.906872 0.53133626 237.780 0.952291 0.957609 0.937981 0.54939028 237.620 0.952431 0.957765 0.979318 0.56519430 237.420 0.951825 0.958160 1.012891 0.58242732 237.210 0.952550 0.957170 1.046312 0.59838834 236.970 0.951946 0.957555 1.075120 0.61660036 236.730 0.951743 0.957006 1.119814 0.63115638 236.480 0.951257 0.957007 1.169261 0.64724840 236.195 0.951298 0.956769 1.216217 0.66616642 235.915 0.951122 0.957339 1.270956 0.68982744 235.595 0.951433 0.956825 1.360819 0.712828

TABLE VIII: S-SSHI circuit’s non-ideality parameters at dif-ferent battery loadVBL(V ) VD(mV ) αI αII QIL(nC) QIIL (nC)

2 711.620 0.824141 0.973194 6.729874 16.0946714 711.205 0.827699 0.973968 6.644104 15.0833346 710.860 0.829109 0.973642 6.570467 13.6096668 710.585 0.827362 0.97366 6.515866 12.701908

10 710.065 0.831173 0.971093 6.434156 11.45303512 709.680 0.833499 0.969869 6.402619 10.41361214 708.965 0.838585 0.962589 6.410849 9.18269816 707.990 0.844684 0.964754 6.421081 8.23067318 707.440 0.851579 0.961934 6.453288 7.31540620 701.105 0.861117 0.961399 6.474542 6.54174722 705.045 0.872938 0.95959 6.571256 5.89658624 703.925 0.881601 0.958869 6.505392 5.27353926 703.040 0.895017 0.960909 6.471428 4.81009528 700.830 0.908616 0.954769 6.471593 4.28692430 699.540 0.924828 0.957486 6.472602 3.97476932 697.450 0.945902 0.957086 6.455887 3.52647234 692.645 0.960356 0.956701 6.499851 2.9052736 682.280 0.94225 0.94882 6.101366 1.89280238 673.480 0.943536 0.953631 5.625206 1.73811540 660.885 0.940743 0.948493 5.171155 1.47443542 647.110 0.940695 0.951682 4.715545 1.24259844 629.710 0.942761 0.950688 4.058914 1.021044

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