micromachines

Article Driving Design with Rising Gradient and Sawtooth of Electrowetting Displays for Ultra-Low Power Consumption

Wei Li 1,2, Li Wang 2,3,*, Taiyuan Zhang 1,2, Shufa Lai 1,2, Linwei Liu 1,2, Wenyao He 1,2, Guofu Zhou 1,2,3 and Zichuan Yi 2,4

1 Guangdong Provincial Key Laboratory of Optical Information Materials and Technology & Institute of Electronic Paper Displays, South China Academy of Advanced Optoelectronics, South China Normal University, Guangzhou 510006, China; [email protected] (W.L.); [email protected] (T.Z.); [email protected] (S.L.); [email protected] (L.L.); [email protected] (W.H.); [email protected] (G.Z.) 2 Shenzhen Guohua Optoelectronics Tech. Co., Ltd., Shenzhen 518110, China; [email protected] 3 Academy of Shenzhen Guohua Optoelectronics, Shenzhen 518110, China 4 College of Electron and Information, University of Electronic Science and Technology of China, Zhongshan Institute, Zhongshan 528402, China * Correspondence: [email protected] or [email protected]; Tel.: +86-0755-29415855

 Received: 26 November 2019; Accepted: 20 January 2020; Published: 28 January 2020 

Abstract: As a kind of paper-like display technology, power consumption is a very important index for electrowetting displays (EWDs). In this paper, the influence of driving on power consumption of the EWDs is analyzed, and a driving waveform with rising gradient and sawtooth wave is designed to reduce the power consumption. There are three stages in the proposed driving waveform. In the initial stage, the driving voltage is raised linearly from the threshold to the maximum value to reduce the invalid power consumption. At the same time, the oil breakup can be prohibited. And then, a section of sawtooth wave is added for suppressing oil backflow. Finally, there is a section of resetting wave to eliminate the influence of charge leakage. Experimental results show that the power consumption of the ultra-low power driving waveform is 1.85 mW, which is about 38.13% lower than that of the conventional used (2.99 mW), when the aperture ratio is 65%.

Keywords: driving waveform; power consumption; electrowetting display; aperture ratio; response speed

1. Introduction The electrowetting display (EWD) is a kind of reflective display technology, which has the advantages of video updating rate, high contrast ratio and low power consumption. Its working mechanism is to manipulate the interfacial tension of the polar liquid in a pixel by applying electric field, to achieve the control of optical switch and gray scale display [1]. The EWD technology has been proposed by G. Beni in 1981 at the first time [2]. In 2003, Robert A. Hayes realized high quality EWD [1], and then, a three-color EWD with vertical stack structure was proposed in 2010 [3]. In order to improve the display quality of EWDs, interface materials, pixel structures, fluidic motion mechanism and the relationship between electro-optical performances and applied voltage have been studied [4–7]. At the same time, the influence of driving waveforms on the performance of EWDs have been also studied. A decoupling driving waveform has been proposed to diminish the induced voltage stress [8]. However, the response time of the EWD is as long as 30 ms which cannot be used to display video. Then, a driving waveform was proposed for realizing the display of multi gray

Micromachines 2020, 11, 145; doi:10.3390/mi11020145 www.mdpi.com/journal/micromachines Micromachines 2020, 11, 145 2 of 13 scales according to the characteristics of EWDs, square wave with high is used for reducing flicker, a reset process is added to eliminate the influence of charge leakage [9]. However, the high frequency will lead to high power consumption. At the same time, a method was proposed to reduce oil breakupMicromachines by 2020 adding, 11, x a voltage rising gradient in the driving waveform [10]. However,2 theof 14 rising gradient can increase the response time of EWDs. Recently, a dynamic and asymmetric driving gray scales according to the characteristics of EWDs, square wave with high frequency is used for waveform was proposed to achieve more gray levels with limited voltage levels [11]. Although the reducing flicker, a reset process is added to eliminate the influence of charge leakage [9]. However, powerthe consumptionhigh frequency haswill beenlead to decreased high power by cons restrictingumption. At the the maximum same time, voltage a method of was the proposed dynamic and asymmetricto reduce driving oil breakup waveform, by adding the a voltage maximum rising aperture gradientratio in the cannot driving be waveform achieved [10]. due However, to the limitation the of therising maximum gradient voltage. can increase the response time of EWDs. Recently, a dynamic and asymmetric driving waveformIn this paper, was accordingproposed to achieve EWD’s equivalentmore gray levels circuit with model, limited the voltage power consumptionlevels [11]. Although of conventional the drivingpower waveforms consumption is calculated has been anddecreased measured. by restri Then,cting the the relationship maximum voltage between of thethe drivingdynamicwaveform and andasymmetric the power driving consumption waveform, is studiedthe maximum based aperture on the ratio experimental cannot be achieved data. A due driving to the limitation waveform for ultra-lowof the powermaximum consumption voltage. is proposed by reducing the driving voltage and shortening the effective In this paper, according to EWD’s equivalent circuit model, the power consumption of driving time in each frame. With the same display effect, the proposed driving waveform can achieve conventional driving waveforms is calculated and measured. Then, the relationship between the lower power consumption than conventional waveforms. driving waveform and the power consumption is studied based on the experimental data. A driving waveform for ultra-low power consumption is proposed by reducing the driving voltage and 2. Principle of EWDs shortening the effective driving time in each frame. With the same display effect, the proposed drivingGray scale waveform is realized can achieve in EWDs lower by applyingpower consumption an external than voltage conven totional control waveforms. the movement of colored oil. Its essence is an optical switch, which has excellent gray scale display characteristics [12]. As shown in Figure2. Principle1a, the of colored EWDs oil in the pixel spreads naturally and covers the whole pixel when no external voltage isGray applied, scale andis realized the color in ofEWDs the oilby isapplying displayed; an external the colored voltage oil isto pushedcontrol tothe a movement corner in theof pixel whencolored the external oil. Its essence voltage is is an applied, optical switch, and the which color has of excellent the substrate gray scale is displayed, display characteristics as shown in [12]. Figure 1b. FigureAs1 shownc is the in top Figure view 1a, ofthe oil colored spreading. oil in the Figure pixel 1spreadsd is the naturally top view and of covers oil contracting. the whole pixel The when di ff erent degreesno external of oil contraction voltage is applied, represent and dithefferent color opticalof the oil states, is displayed; which arethe characterizedcolored oil is pushed by the to aperture a corner in the pixel when the external voltage is applied, and the color of the substrate is displayed, ratio. The aperture ratio is the proportion of the opening area in the whole pixel. The formula is as shown in Figure 1b. Figure 1c is the top view of oil spreading. Figure 1d is the top view of oil defined as follows [5]: contracting. The different degrees of oil contract ion represent! different optical states, which are Soil( V) characterized by the aperture ratio.WA The( V )aperture= 1 ratio is the proportion100% of the opening area in the (1) whole pixel. The formula is defined as follows [5]:− Spix ×

In Equation (1), WA( V) represents the aperture ratio, Soil( V) and Spix represent the surface area 𝑆(𝑉) of oil in a single pixel and the𝑊 surface(V) = 1 area − of the whole 100% pixel respectively, V represents the(1) voltage 𝑆 applied to the EWD, and the area of pixel wall is ignored in calculating the aperture ratio. The pixel wall is a transparent grid structure which can divide the EWD into several pixels. In Equation (1), 𝑊(𝑉) represents the aperture ratio, 𝑆(𝑉) and 𝑆 represent the surface areaThe of pixel oil structurein a single of pixel the EWDand the is shownsurface inarea Figure of the2a, whole which pixel is mainly respectively, composed 𝑉 represents of glass substrate, the ITOvoltage (Indium applied Tin Oxides) to the guideEWD, and electrode, the area hydrophobic of pixel wall insulationis ignored layer,in calculating pixel wall, the aperture color oil, ratio. and polar liquidThe [13 pixel]. The wall three-dimensional is a transparent grid structure structure of which an EWD can divide pixel the is shown EWD into in Figureseveral2 pixels.b.

(a) (b)

Figure 1. Cont. Micromachines 2020, 11, x 3 of 14

Micromachines 2020, 11, x 3 of 14

Micromachines 2020, 11, 145 3 of 13 150( ×a )150 um 150 (×b )150 um

150 × 150 um 150 × 150 um

(c) (d) Figure 1. Principle of the electrowetting display (EWD). (a) Without applied voltage, the color of oil is displayed in a(c pixel.) (b) With applied voltage, the color of substrate (isd )displayed. (c) The top view when the pixel is turned off. (d) The top view when the pixel is turned on. FigureFigure 1. Principle 1. Principle of of the the electrowetting electrowetting display display (EWD). ( (aa)) Without Without applied applied voltage, voltage, the the color color of oil of oil is displayedis displayedThe in apixel pixel.in a pixel.structure (b) ( Withb) With of applied theapplied EWD voltage, voltage, is shown thethe color in Figureof of substrate substrate 2a, whichis displayed. is displayed. is mainly (c) The ( ccomposed) top The view top viewof glass whenwhensubstrate, the pixelthe pixel ITO is turnedis (Indiumturned off off..( Tind ()d ) TheOxides) The top top view viewguide when when electrode, the the pixel pixel hydrophobic is isturned turned on. on. insulation layer, pixel wall, color oil, and polar liquid [13]. The three-dimensional structure of an EWD pixel is shown in Figure 2b. The pixel structure of the EWD is shown in Figure 2a, which is mainly composed of glass substrate, ITO (Indium Tin Oxides) guide electrode, hydrophobic insulation layer, pixel wall, color oil, and polar liquid [13]. The three-dimensional structure of an EWD pixelTop is plate shown in Figure 2b. NaCl solution Colored oil Top plate Pixel wall NaCl solution Hydrophobic insulator Colored oil ITO Pixel wall White substrate Hydrophobic insulator (a) ITO White substrate

(a) Top plate NaCl solution Colored oil Top plate Pixel wall NaCl solution Hydrophobic insulator Colored oil ITO Pixel wall White Substrate Hydrophobic insulator

ITO (b) White Substrate Figure 2. FigureStructure 2. Structure of the EWD. of the (EWD.a) Pixel (a) structurePixel structure of the of EWD.the EWD. (b) ( Three-dimensionalb) Three-dimensional structure structure of an an EWD panel.EWD panel.

In orderIn to order display to display different different grayscales gray scales in EWDs, in EWDs it is, it necessary is necessary to to apply apply a a voltage voltage sequencesequence for for driving thedriving pixel, the the pixel, voltage the voltage sequence sequence is called is called as driving as driving waveform waveform [14 [14].]. The The driving driving waveformwaveform is is designed as PWM (pulse width modulation) or AM (amplitude modulation) for displaying different designed as PWM (pulse width modulation) or AM (amplitude modulation) for displaying different gray scales accurately in EWDs [15]. The driving waveform affects the display effect of the EWD gray scales accurately in EWDs [15]. The driving waveform affects the display effect of the EWD seriously. Figure 3 shows the conventional driving waveforms [9,10]. seriously. Figure3 shows the conventional driving waveforms [9,10]. Micromachines 2020, 11, 145 4 of 13 Micromachines 2020, 11, x 4 of 14

40 35 30 25 20 15 Voltage (V) Voltage 10 5 0 0 5 10 15 20 25 30 35 Time (ms)

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40 35 30 25 20 15 Voltage (V) Voltage 10 5 0 0 5 10 15 20 25 30 35 Time (ms)

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FigureFigure 3. Conventional 3. Conventional driving driving waveforms. waveforms. (a )(a Square) Square Wave. Wave. (b ()b Trapezoidal) Trapezoidal Wave. Wave. ( c()c Sawtooth) Sawtooth Wave. Wave. MicromachinesMicromachines2020 2020, 11,, 145 11, x 5 of5 13of 14

3. Driving Waveform Design for Low Power Consumption 3. Driving Waveform Design for Low Power Consumption 3.1. Power Consumption Analysis 3.1. Power Consumption Analysis As a capacitive device, the equivalent circuit model of an EWD pixel can be defined as a R-C As a capacitive device, the equivalent circuit model of an EWD pixel can be defined as a R-C (Resistance-Capacitance) circuit, as shown in Figure 4 [16]. In Figure 4a, 𝐶 represents the (Resistance-Capacitance) circuit, as shown in Figure4[ 16]. In Figure4a, Cp represents the capacitance capacitance of the pixel unit, 𝑅 represents the resistance of the pixel unit, 𝑅 represents the of theexternal pixel unit,resistance,Rp represents and the E the is resistancethe driving of voltage. the pixel Each unit, pixelRE representsunit can be the represented external resistance, by a resistor andconnected the E is the in driving parallel voltage. with a Eachcapacitor. pixel All unit pixel can beunits represented are connected by a resistor in series connected or parallel in parallel to form a withwhole. a capacitor. And then, All pixel the unitswhole are units connected are connected in series orin parallel series with to form an aexternal whole. Andresistance. then, the This whole is the unitscomplete are connected equivalent in series circuit with model an external of the EWD. resistance. Figure This 4 b is is the the complete simplified equivalent equivalent circuit circuit model model of the EWD. Figure4b is the simplified equivalent circuit model of an EWD pixel. CS represents the of an EWD pixel. 𝐶 represents the capacitance of an EWD pixel, 𝑅 represents the resistance of an capacitanceEWD pixel. of an EWD pixel, RS represents the resistance of an EWD pixel.

(a) (b)

FigureFigure 4. The 4. The equivalent equivalent circuit circuit models mo ofdels an EWDof an pixel.EWD ( apixel.) Complete (a) Complete equivalent equivalent circuit model.circuit model. (b) Simplified(b) Simplified equivalent equivalent circuit model.circuit model.

So,So, the the power power consumption consumption of the of the simplified simplified equivalent equivalent circuit circuit can can beshown be shown as Equation as Equation (2). (2).

2 W 𝑈 U t U2t 𝑡R P =𝑊 =𝑅 =𝑈 𝑡 (2)(2) 𝑃= T= T= TR 𝑇 𝑇 𝑇𝑅 In Equation (2), P represents the power consumption of the EWD, W represents the electric energy consumedIn inEquation a unit time (2), T𝑃, Urepresentsrepresents the the power driving consumption voltage, t represents of the EWD, the eff ective𝑊 represents driving timethe electric in a unitenergy time T ,consumed and R represents in a unit the time impedance 𝑇, 𝑈 ofrepresents the EWD. the Because driving of thevoltage, following 𝑡 represents theoretical the analysis effective anddriving experimental time in verification, a unit time the𝑇, and impedance 𝑅 represents of the the EWD impedance used in this of the paper EWD. is basically Because unchanged of the following at thetheoretical frequency ofanalysis 60 Hz. and experimental verification, the impedance of the EWD used in this paper is basicallyAccording unchanged to the circuit at model,the frequency an EWD of pixel 60 Hz. is an R-C series parallel circuit, as shown in Figure5. There are two breakAccording to the fcircuit1 and fmodel,2 in R-C an series EWD parallel pixel is circuit an R-C [17 series,18], as parallel shown circuit, in Equations as shown (3) and in Figure (4). 5. There are two break frequencies 𝑓1 and 𝑓2 in R-C series parallel circuit [17,18], as shown in 1 Equations (3) and (4). f 1 = (3) 2πR2CE 1 𝑓1 = 1 (3) f 2 = 2𝜋𝑅𝐶  (4) 2πC R1R2 E R1+R2 In the Equations (3) and (4), f 1 and f 2 are the1 break frequencies, C is the capacitance, R and R 𝑓2 = E 1 2 are series resistance and parallel resistance respectively.𝑅𝑅 (4) 2𝜋𝐶 𝑅 + 𝑅 When the frequency is lower than f 1, CE is equivalent to an open circuit, and the total impedance of the circuit is R1 + R2. When the frequency is higher than f 2, CE is equivalent as a short circuit, In the Equations (3) and (4), 𝑓1 and 𝑓2 are the break frequencies, 𝐶 is the capacitance, 𝑅 and the total impedance of the circuit is R1. When the frequency is higher than f 1 and lower than f 2, and 𝑅 are series resistance and parallel resistance respectively. the total impedance of the circuit can be changed between R1 + R2 and R1. When the frequency is lower than 𝑓1, 𝐶 is equivalent to an open circuit, and the total impedance of the circuit is 𝑅 +𝑅. When the frequency is higher than 𝑓2, 𝐶 is equivalent as a short Micromachines 2020, 11, x 6 of 14

circuit, and the total impedance of the circuit is 𝑅. When the frequency is higher than 𝑓1 and lower Micromachines 2020, 11, 145 6 of 13 than 𝑓2, the total impedance of the circuit can be changed between 𝑅 +𝑅 and 𝑅.

(a) (b)

FigureFigure 5.5. TheThe impedance-frequency impedance-frequency characteristics characteristics of the of R-C the series-parallel R-C series-parallel circuit. circuit. (a) R-C (a )series- R-C series-parallelparallel circuit. circuit. (b) The (b )relationship The relationship between between the impedance the impedance and the and break the break frequency. frequency.

ItIt can can be be seen seen fromfrom thethe FigureFigure5 b5b that that the the impedance impedance remains remains unchanged unchanged at at a a fixed fixed frequency. frequency. TheThe impedance impedance of of the the EWD EWD used used in in this this paper paper is is 170.43 170.43 k kΩΩmeasured measured by by the the TH2828 TH2828 Precision Precision LCR LCR MeterMeter (Tonghui, (Tonghui, Changzhou, Changzhou, China) China) at at the the frequency frequency of of 60 60 Hz. Hz. AccordingAccording toto thethe aboveabove analysis,analysis, thethe drivingdriving powerpower ofof thethe EWDEWD isis mainlymainly determineddetermined byby thethe drivingdriving voltage voltageU 𝑈and and the the eff effectiveective driving driving time timet, which𝑡, which can can be be expressed expressed as as the the Equation Equation (5). (5).

Z T 1 1 P = U2(t)dt (5) 𝑃= 𝑈TR (𝑡) 𝑑𝑡 (5) 𝑇𝑅 0 where U(t) is the voltage of the driving waveform at time t. where 𝑈(𝑡) is the voltage of the driving waveform at time 𝑡. 3.2. Power Consumption Analysis of Conventional Driving Waveforms 3.2. Power Consumption Analysis of Conventional Driving Waveforms For conventional driving waveforms, such as square wave and trapezoidal wave, their expressions and powerFor conventional consumption driving expressions waveforms, can be derived. such as square wave and trapezoidal wave, their expressions and power consumption expressionsC can be derived. 1 T C Square wave is shown in Equation (6). 1 is the voltage constant from 0 to 2 , and 2 is the Square wave is shown1 in Equation (6). 𝐶 is the voltage constant from 0 to 𝑇, and 𝐶 is the voltage constant from 2 T to T.  voltage constant from 𝑇 to 𝑇.  1 C1, 0 t < 2 T U(t) =  ≤ (6) C , 1 T t < T 2 2 ≤ 1 Then, the power consumption expression𝐶 ,0≤𝑡< of Square Wave𝑇 can be obtained, as shown in Equation (7). 2 𝑈(𝑡) = (6) 1 1 Z 2 T Z T 1 𝐶, 2𝑇≤𝑡<𝑇1 2 P = C12 dt + C2 dt (7) TR TR 1 0 2 T

Then, the power consumption expression of Square Wave can be obtained, 1as shown in Equation Trapezoidal wave is shown in Equation (8). k is the slope between 0 and 4 T, C1 is the voltage (7). 1 1 1 constant from 4 T to 2 T, and C2 is the voltage constant from 2 T to T.  1 1  kt,1 0 t < T 𝑃= 𝐶𝑑𝑡 + 𝐶≤ 4𝑑𝑡 (7) 𝑇𝑅U(t) =  C , 𝑇𝑅1 T t< 1 T (8)  1 4 2  1 ≤ C2, 2 T t < T ≤ Trapezoidal wave is shown in Equation (8). 𝑘 is the slope between 0 and 𝑇, 𝐶 is the voltage Then, the power consumption expression of trapezoidal wave can be obtained, as shown in constant from 𝑇 to 𝑇, and 𝐶 is the voltage constant from 𝑇 to 𝑇. Equation (9). 1 1 Z 4 T Z 2 T Z T 1 2 1 2 1 2 P = (kt) dt + C1 dt + C2 dt (9) TR TR 1 TR 1 0 4 T 2 T Micromachines 2020, 11, x 7 of 14

1 ⎧𝑘𝑡, 0 ≤ 𝑡< 𝑇 ⎪ 4 1 1 𝑈(𝑡) = 𝐶 , 𝑇≤𝑡< 𝑇 (8) ⎨ 4 2 ⎪ 1 𝐶 , 𝑇≤𝑡<𝑇 ⎩ 2 Then, the power consumption expression of trapezoidal wave can be obtained, as shown in Equation (9).

Micromachines 2020, 11, 145 7 of 13 1 1 1 𝑃= (𝑘𝑡) 𝑑𝑡 + 𝐶 𝑑𝑡 + 𝐶𝑑𝑡 (9) 𝑇𝑅 𝑇𝑅 𝑇𝑅 1 Sawtooth wave is shown in Equation (10). k is the slope between 0 and 2 T, C1 is the voltage 1 constantSawtooth from waveT to Tis. shown in Equation (10). 𝑘 is the slope between 0 and 𝑇, 𝐶 is the voltage 2 ( kt, 0 t < 1 T constant from 𝑇 to 𝑇. U(t) = ≤ 2 (10) C , 1 T t < T 1 2 ≤ Then, the power consumption expression of Sawtooth1 Wave can be obtained, as shown in Equation (11). 𝑘𝑡, 0 ≤ 𝑡< 𝑇 1 2 𝑈(𝑡) = Z 2 T Z T (10) 1 1 2 1 2 P = (kt) dt + C1 dt (11) TR𝐶, 𝑇≤𝑡<𝑇TR 1 0 2 2 T

3.3. Driving Waveform Design Then, the power consumption expression of Sawtooth Wave can be obtained, as shown in EquationThe driving(11). waveform for low power consumption is a sequence of voltages. In order to design a perfect driving waveform, not only the frequency, amplitude and duty cycle of the waveform should be considered, but also the inherent defects of the EWD should be avoided by appropriate optimization 1 1 and adjustment. In the proposed𝑃= driving(𝑘𝑡) waveform, 𝑑𝑡 + the𝐶 frequency 𝑑𝑡 is set as 60 Hz [19], the voltage(11) can 𝑇𝑅 𝑇𝑅 be changed between 0 and 35 V, and the duty is set as 50%. Based on the square wave, the proposed driving waveform is shown in Figure6a, which consists of three stages. The first stage is a linear rising process. The driving voltage is changed from 10 V to 35 V in 5 ms 3.3.with Driving a linear Waveform gradient. Design The 10 V is the threshold voltage for driving the oil. The oil is in a balance state of natural spreading when no voltage is applied. In order to break this balance state, the threshold The driving waveform for low power consumption is a sequence of voltages. In order to design voltage needs to be applied. As shown in Figure6b, the static balance can be broken when the driving a perfect driving waveform, not only the frequency, amplitude and duty cycle of the waveform voltage is improved to 10 V. should be considered, but also the inherent defects of the EWD should be avoided by appropriate In addition, the rising gradient from 10 V to 35 V is added for reducing the effect of oil rupture on optimization and adjustment. In the proposed driving waveform, the frequency is set as 60 Hz [19], the aperture ratio [10]. At the same time, it can reduce the duration of the driving cycle. The aperture the voltage can be changed between 0 and 35 V, and the duty is set as 50%. Based on the square wave, ratio of different rising gradients is shown in Figure6c. The rising duration is designed as 5ms for the proposed driving waveform is shown in Figure 6a, which consists of three stages. reducing power consumption.

40 35 30 25 20 15

Voltage (V) Voltage 10 5 0 0 5 10 15 20 25 30 35 Time (ms)

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Figure 6. Cont. MicromachinesMicromachines 20202020, ,1111, ,x 145 8 8of of 14 13

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FigureFigure 6. 6. Design ofof thethe proposed proposed driving driving waveform. waveform. (a) ( Thea) The proposed proposed driving driving waveform waveform for low for power low powerconsumption. consumption. (b) The (b relationship) The relationship between between the voltage the andvoltage the aperture and the ratio. aperture (c) The ratio. relationship (c) The relationshipbetween the between rising duration the rising and theduration aperture and ratio. the (apertured) The relationship ratio. (d) betweenThe relationship minimum between driving minimumvoltage and driving Aperture voltage Ratio and in Aperture the sawtooth Ratio wave. in the sawtooth wave.

The first stage is a linear rising process. The driving voltage is changed from 10 V to 35 V in 5 ms with a linear gradient. The 10 V is the threshold voltage for driving the oil. The oil is in a balance Micromachines 2020, 11, 145 9 of 13

The second stage is a periodic change process. The driving voltage is changed between 31 V and 35 V in 3 ms, which is a sawtooth wave. The sawtooth wave can reduce the driving voltage for saving the power consumption and inhibit the oil backflow to a certain extent. The oil will backflow due to charge trapping when the same voltage is applied continuously [8]. The 31 V is the minimum driving voltage of the sawtooth wave. Although the lower driving voltage can reduce more power consumption, the lower driving voltage can reduce the aperture ratio. In order to obtain higher aperture ratio and lower power consumption, 31 V is selected as the minimum driving voltage for the sawtooth wave. The relationship between minimum driving voltage of the sawtooth wave and aperture ratio is shown in Figure6d, and a higher aperture ratio can be obtained at 31 V. In order to achieve a higher aperture ratio, a higher voltage is needed, but the oil will backflow when a constant voltage is applied to the EWD. And the sawtooth wave can inhibit the oil backflow to a certain extend. So, the aperture ratio will fluctuate locally under the driving of constant voltage and sawtooth wave. Further, for different EWDs, the minimum driving voltages of the sawtooth wave are different, which can be obtained by the same experimental method. The third stage is a resetting process. The driving voltage is held at 0 V for 8 ms to eliminate the influence of charge leakage [9]. According to the proposed driving waveform, its expression can be expressed as Equation (12). k1 5 5 1 is the slop, b1 is the intercept between 0 and 16 T, k2 is the slop, b2 is the intercept between 16 T and 2 T, 1 C represents the voltage constant from 2 T to T.   + 5 k1t b1, 0 t < 16 T  ≤ U(t) = k (t a) + b , 5 T t 1 T (12)  2 2 16 < 2  − ≤ C, 1 T t < T 2 ≤ Then, the power consumption expression of the proposed driving waveform can be expressed as Equation (13).

5 1 Z 16 T Z 2 T Z T 1 2 1 2 1 2 P = (k1t + b1) dt + [k2(t a) + b2] dt + C dt (13) R R 5 − R 1 0 16 T 2 T

4. Experimental Results and Discussion For the sake of evaluating the performance of the proposed driving waveform, an experimental platform is developed to measure the aperture ratio and the power consumption of EWDs, as shown in Figure7. This experimental platform includes a driving system, a measuring system, and an EWD panel. The driving system, which is used to input the driving waveform for driving the EWD, consists of a computer, a , and a high-voltage amplifier. The testing system is used to measure and record test results, including a microscope, a high-speed camera, a power meter, and a computer, and the EWD is the measured object. Its parameters are shown in the Table1. The experimental process can be divided into two steps. Firstly, the EWD is driven by the driving system. The driving waveform is edited by a computer with ArbexPress software, and it is sent to function generator by serial communication, and then, the driving voltage in the driving waveform can be output when it is amplified by the high-voltage amplifier for driving the EWD. Secondly, the experimental data is measured by the testing system. The high-speed camera captures the display state of the EWD in real time by the microscope and transmits testing data to the computer for calculating the aperture ratio. Meanwhile, the power meter measures and records the power consumption of the EWD panel in real time. During the experiment, the temperature is kept constant to avoid the influence of the external environment. The aperture ratio and power consumption of the EWD with different driving waveforms are measured by the above-mentioned experimental platform. The measurement results are shown in Figure8. Micromachines 2020, 11, 145 10 of 13 Micromachines 2020, 11, x 10 of 14

(b)

（a） (c) (d)

(g) (f) (e)

FigureFigure 7. Experimental 7. Experimental platform platform of of the the driving driving waveformwaveform for for EWDs. EWDs. (a) (aA) computer A computer for driving for driving system.system. (b) Arbitrary (b) Arbitrary function function generator generator ATA-2022H ATA-2022H (Agitek, Xi’an, Xi’an, China). China). (c) (AFG-3052Cc) AFG-3052C (Agitek, (Agitek, Xi’an,Xi’an, China) China) high high voltage voltage amplifier. amplifier. (d ()d) Microscope. Microscope. ( (ee)) High High speed speed camera. camera. (f) (PCf) PCfor formeasuring measuring system.system. (g) An (g) EWDAn EWD panel. panel.

TableTable 1. Parameters 1. Parameters of of the the electrowetting electrowetting display display (EWD) (EWD) panel. panel.

Panel Oil PixelPixel Wall Pixel PixelWall HydrophobicHydrophobic DrivingDriving Panel Size Oil ColorResolution Pixel Pixel Size Size Size Color WallSize Size HeightWall Height LayerLayer Thickness Thickness voltageVoltage 10 1010 cm × 10 cm Cyan Cyan 200 × 200 150 150 × 150150 um um 1515 × 1515 um um 5.65.6 um um 1 um 1 um 0–35 0–35 V V × Micromachines 2020, 11, x × × × 11 of 14 The experimental process can be divided into two steps. Firstly, the EWD is driven by the driving system. The driving5 waveform is edited by a computer with ArbexPress software, and it is sent to function generator4 by serial communication, and then, the driving voltage in the driving waveform can be output when3 it is amplified by the high-voltage amplifier for driving the EWD. Secondly, the

experimental data2 is measured by the testing system. The high-speed camera captures the display state of the EWD in real time by the microscope and transmits testing data to the computer for Power (mW) 1 calculating the aperture ratio. Meanwhile, the power meter measures and records the power consumption of the0 EWD panel in real time. During the experiment, the temperature is kept constant to avoid the influence0 of the 1020304050607080 external environment. The aperture ratio and power consumptionAperture of Ratiothe EWD (%) with different driving waveforms are measured by the above-mentioned experimental platform. The measurement results are shown in Square Wave Trapezoid Wave Figure 8. Sawtooth Wave Proposed Wave 65% Standard Line 2mW Standard Line

Figure 8. The relationship between Aperture Ratio and Power Consumption. Figure 8. The relationship between Aperture Ratio and Power Consumption.

As can beAs seen can frombe seen Figure from 8Figure, with 8, the with same the aperturesame aperture ratio, ratio, the the power power consumption consumption of the proposed driving waveformproposed driving is lower waveform than thatis lower of thethan conventionalthat of the conventional driving driving waveforms waveforms for for the the EWD. EWD. As shown in Figure9As, the shown aperture in Figure ratio 9, the of aperture the proposed ratio of the driving proposed waveform driving waveform is larger is thanlarger thatthan ofthat conventional of driving waveformsconventional whendriving the waveforms power when consumption the power consumption is 2 mW. is 2 mW. More experiments are designed to further illustrate the characteristics of the proposed driving waveform. As shown65.93% in Figure 10a, with the59.44% increase of the aperture ratio,60.36% the influence of the voltage on it decreases gradually. And as can be seen from the Figure 10b, the driving frequency also have an effect on the aperture ratio. The aperture ratio increases with the increase of driving frequency, but there will be local fluctuation. Figure 10c shows the relationship between aperture ratio and power.

(a) (b) (c)

Figure 9. Aperture ratio with different driving waveforms under the same power consumption. (a) The proposed driving waveform. (b) Trapezoid driving waveform. (c) Square driving waveform.

More experiments are designed to further illustrate the characteristics of the proposed driving waveform. As shown in Figure 10a, with the increase of the aperture ratio, the influence of the voltage on it decreases gradually. And as can be seen from the Figure 10b, the driving frequency also have an effect on the aperture ratio. The aperture ratio increases with the increase of driving frequency, but there will be local fluctuation. Figure 10c shows the relationship between aperture ratio and power. Micromachines 2020, 11, x 11 of 14

5

4

3

2

Power (mW) 1

0 0 1020304050607080 Aperture Ratio (%)

Square Wave Trapezoid Wave Sawtooth Wave Proposed Wave 65% Standard Line 2mW Standard Line

Figure 8. The relationship between Aperture Ratio and Power Consumption.

As can be seen from Figure 8, with the same aperture ratio, the power consumption of the proposed driving waveform is lower than that of the conventional driving waveforms for the EWD. MicromachinesAs shown2020 in, 11 Figure, 145 9, the aperture ratio of the proposed driving waveform is larger than that of11 of 13 conventional driving waveforms when the power consumption is 2 mW.

65.93% 59.44% 60.36%

(a) (b) (c)

FigureFigure 9. Aperture 9. Aperture ratio ratio with with di differentfferent driving driving waveformswaveforms under under the the same same power power consumption. consumption. (a) (a) The proposedThe proposed driving driving waveform. waveform. (b (b)) Trapezoid Trapezoid drivingdriving waveform. waveform. (c) ( cSquare) Square driving driving waveform. waveform. Micromachines 2020, 11, x 12 of 14 More experiments are designed to further illustrate the characteristics of the proposed driving waveform. As shown in Figure80 10a, with the increase of the aperture ratio, the influence of the voltage on it decreases gradually.70 And as can be seen from the Figure 10b, the driving frequency also have an effect on the aperture60 ratio. The aperture ratio increases with the increase of driving frequency, but there will be local fluctuation.50 Figure 10c shows the relationship between aperture ratio and power. 40 30 20

Aperture Ratio(%) 10 0 0 10203040 Voltage (V)

(a)

70 68 66 64 62 60 Aperture Ratio(%) 58 0 20 40 60 80 100 120 140 Frequency (Hz)

(b) 2.5

2

1.5

1 Power (mW) 0.5

0 0 1020304050607080 Aperture Ratio (%)

(c)

Figure 10.FigureCharacteristics 10. Characteristics of the of proposed the proposed driving driving waveform. waveform. ( (aa) )The The relationship relationship between between voltage voltage and and aperture ratio. (b) The relationship between frequency and aperture ratio. (c) The relationship aperture ratio. (b) The relationship between frequency and aperture ratio. (c) The relationship between between aperture ratio and power. aperture ratio and power. Similarly, the structural parameters of the EWD can affect its power consumption and aperture ratio. However, the shape of the proposed driving waveform cannot be affected, nor will it affect the result in that the proposed driving waveform has lower power consumption than the conventional square wave under the same aperture ratio.

Micromachines 2020, 11, 145 12 of 13

Similarly, the structural parameters of the EWD can affect its power consumption and aperture ratio. However, the shape of the proposed driving waveform cannot be affected, nor will it affect the result in that the proposed driving waveform has lower power consumption than the conventional square wave under the same aperture ratio.

5. Conclusions In this paper, the power consumption of the driving waveform for EWDs is analyzed, and the relationship between the driving waveform and the power consumption is obtained. Then, a new driving waveform with a rising gradient and a sawtooth wave is proposed. The rising gradient can prohibit the oil breakup effectively. The section of sawtooth wave can inhibit the backflow of the oil. Experimental results show that the proposed driving waveform has a lower power consumption and higher aperture ratio than conventional waveforms. When the aperture ratio is 65%, the power consumption of the proposed driving waveform is about 38.13% lower than that of the conventionally used square wave. In addition, the proposed driving waveform can provide a new way for the optimization of the EWD driving system.

Author Contributions: W.L. and Z.Y. designed this project. W.L. and L.W. carried out most of the experiments and data analysis. T.Z., S.L., L.L. and W.H. performed part of the experiments and for help discussion during manuscript preparation. L.W. and Z.Y. contributed to the data analysis and correction. G.Z. gave suggestions on the project management and conducted helpful discussion on the experimental results. All authors have read and agree to the published version of the manuscript. Funding: This research was funded by National Key R&D Program of China (No. 2016YFB0401502), the Key Research Platforms and Research Projects in Universities and Colleges of Guangdong Provincial Department of Education (No. 2018KQNCX334), Zhongshan Innovative Research Team Program (No. 180809162197886), Zhongshan Institute high-level talent scientific research startup fund project (No. 416YKQ04), National Key R&D Program of China (No. 2018YFB0407100-02, No. 2018YFB1801302), Key-Area Research and Development Program of GuangDong Province (2019B010924005), Program for Chang Jiang Scholars and Innovative Research Teams in Universities (No. IRT_17R40), Science and Technology Program of Guangzhou (No. 2019050001), Guangdong Provincial Key Laboratory of Optical Information Materials and Technology (No. 2017B030301007), MOE International Laboratory for Optical Information Technologies and the 111 Project. Conflicts of Interest: The authors declare no conflict of interest.

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