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The Comparison Between Electromagnetic and Piezoelectric Vibrational Energy Harvesters Chi An Lu 1 , Yu Tang Hu 1 , Yu Chi Chang 1 , and Weileun Fang 1,2 1 Power Mechanical Engineering dept., 2 NEMS Inst., National Tsing Hua University, HsinChu, TAIWAN ABSTRACT In recent years, electronic components are starting to require low power consumption, combined with electronic components getting tinier and tinier, conventional batteries does not seem to be the ideal solution. The upcoming of MEMS energy harvesters is a possible answer to the problem, and this paper will attempt to determine if certain types of MEMS energy harvesters are up to the demand. We find that batch produced vibrational piezoelectric energy harvesters are applicable for low consumption devices, and manually assembled large electromagnetic energy harvesters can be considered for larger electronic devices. KeywordsEnergy harvestElectromagnetic energy harvesterPiezoelectric energy harvester IIntroduction MEMS based energy harvesters are similar to wireless battery chargers in the way that both do not require a transfer cable to provide power to an electronic component. However, unlike the limited life cycle of batteries, a significant advantage the energy harvester has is the possibility of allowing low power consumption components to theoretically be able to operate infinitely, which in turn allows continuous usage without worry of power depletion. The ability to operate components infinitely creates possibilities of several new concepts, among them are health monitoring devices [1] , where energy harvesters eliminates the need to replace the battery every now and then. And another is reconnaissance cyborg insects [2] , with energy harvesters providing power to the sensors and transmitters, it allows highly cost-effective surveillance in harsh conditions over extended periods of time. In recent years, we have seen the rising of wearable devices and the concept: Internet of Things (IoT), as well as the rapid evolution of technology. We observed that the overall design of electronic components leans towards lowering the power consumption, a trend that gives MEMS energy harvesters a chance to shine and perform. In general, the most common seen types of MEMS energy harvesters are as follows: Photoelectric, thermoelectric, electromagnetic, piezoelectric, and electrostatic [3] . Amongst photoelectric harvesters, solar harvesters are the most effective. Thermoelectric type designs generate electricity by using temperature differences, whereas the latter three mentioned takes in kinetic energy and transforms it into electrical energy.

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College class essay. Selection of a few publications, examine their faults and possibilities.

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  • The Comparison Between Electromagnetic and Piezoelectric

    Vibrational Energy Harvesters

    Chi An Lu1 , Yu Tang Hu1 , Yu Chi Chang1 , and Weileun Fang1,2

    1Power Mechanical Engineering dept., 2NEMS Inst., National Tsing Hua University, HsinChu, TAIWAN

    ABSTRACT

    In recent years, electronic components are starting to require low power

    consumption, combined with electronic components getting tinier and tinier,

    conventional batteries does not seem to be the ideal solution. The upcoming of

    MEMS energy harvesters is a possible answer to the problem, and this paper

    will attempt to determine if certain types of MEMS energy harvesters are up to

    the demand. We find that batch produced vibrational piezoelectric energy

    harvesters are applicable for low consumption devices, and manually

    assembled large electromagnetic energy harvesters can be considered for larger

    electronic devices.

    KeywordsEnergy harvestElectromagnetic energy harvester

    Piezoelectric energy harvester

    IIntroduction

    MEMS based energy harvesters are similar to

    wireless battery chargers in the way that both do not

    require a transfer cable to provide power to an electronic

    component. However, unlike the limited life cycle of

    batteries, a significant advantage the energy harvester has

    is the possibility of allowing low power consumption

    components to theoretically be able to operate infinitely,

    which in turn allows continuous usage without worry of

    power depletion.

    The ability to operate components infinitely creates

    possibilities of several new concepts, among them are

    health monitoring devices [1], where energy harvesters

    eliminates the need to replace the battery every now and

    then. And another is reconnaissance cyborg insects [2],

    with energy harvesters providing power to the sensors

    and transmitters, it allows highly cost-effective

    surveillance in harsh conditions over extended periods of

    time.

    In recent years, we have seen the rising of wearable

    devices and the concept: Internet of Things (IoT), as well

    as the rapid evolution of technology. We observed that

    the overall design of electronic components leans

    towards lowering the power consumption, a trend that

    gives MEMS energy harvesters a chance to shine and

    perform.

    In general, the most common seen types of MEMS

    energy harvesters are as follows: Photoelectric,

    thermoelectric, electromagnetic, piezoelectric, and

    electrostatic [3]. Amongst photoelectric harvesters, solar

    harvesters are the most effective. Thermoelectric type

    designs generate electricity by using temperature

    differences, whereas the latter three mentioned takes in

    kinetic energy and transforms it into electrical energy.

  • Considering most wearable devices are meant to be

    used indoors, and not all devices are in direct contact

    with our skin, we shall select the most commonplace

    kinetic energy as the harvesting energy and chose

    electromagnetic and piezoelectric harvester devices as

    the focus points of this review.

    1.1 Electromagnetic Energy Harvesters

    According to D.P. Arnold [5], we can deduce the

    scale law of electromagnetic devices. The scaling

    relationship between power P, length L and acceleration

    a0 as follows:

    { P 50

    2

    P 702 0

    (1)

    Arnolds paper divides energy harvesters into two

    categories, rotational and vibrational devices, since (1)

    has an acceleration factor embedded within, it makes

    rotational type harvesters difficult to analyze; as for

    vibrational harvesters, power scales down with length at

    a magnitude between 10-5 ~ 10-7.

    Power density graphs for the two harvesters are

    shown in Fig.1 and Fig.2. These figures contains datas of

    electromagnetic harvesters before 2007 [5], where it can

    observed that the scale law is not completely applicable.

    Our guess is that the given specifications does not reflect

    the best possible performance of the harvesters, which

    might be a result of lack of advanced technology for

    optimization, but it would seem certain that power

    density will decrease at a faster rate as the scale goes

    even lower.

    Fig.1 Summary of rotational generator (a) power density

    (W/cm3) and (b) normalized power density

    (W/cm3*krpm ) versus size. The data shows no

    significant trend with device size.[5]

    Fig.2 Summary of oscillatory generator (a) power

    density and (b) normalized power density (W/cm3*g2)

    versus size. Two reference lines are shown on (b),

    indicating the theoretical scaling trend of normalized

    power density with L2 and L4 [5]

    Other than the two presented above, other

    electromagnetic harvesters designs include the Rolling

    Rod Microgenerator [6] and the Linear Vibration

    Harvester [7], but both designs face the problem of

    stiction which occurs during operation, which is why we

    only select no-contact vibration design types of

    harvesters for our review.

    1.2 Piezoelectric Energy Harvesters

    Based on the piezoelectric harvester review done by

    H. S. Kim, Joo-Hyong Kim and Jaehwan Kim [8], the

    review lists the attributes of all kinds of piezoelectric

    materials, the point of our interest amongst the database

    is the conversion coefficient, which induces the energy

    conversion efficiency to grow 4 times the original value

    when the coefficient doubles in value. As we can see

    from Fig.3, piezoelectric membrane thickness is not a

    contributing factor to conversion efficiency, indicating

    the usage of membranes as the energy absorber is an

    acceptable design for piezoelectric materials. Although

    the effect of volume decrease on power density is not

    mentioned in the review, we believe that the ability to

    use membrane structure is an important factor to take

    into consideration, especially when integrating MEMS

    fabricating processes.

    Piezoelectric harvest methods are divided into

    impulse and vibration modes, impulse harvesters will

    encounter stiction problems due to repeated contact

    between structures. To get a clean comparison with all

  • our selected harvesters performing on an even footing,

    we choose to take impulse harvesters out of the list,

    which leaves vibration harvesters for piezoelectric

    energy harvesters.

    Fig.4 categorizes electrostatic, electromagnetic,

    piezoelectric energy harvesters and their respective

    power densities, where we find a relative low power

    density for electromagnetic harvesting, which as

    mentioned previously might be a problem with lack of

    optimization. So we searched for some of the more

    recent electromagnetic harvesters and piezoelectric

    harvesters listed below, in hopes that technology has

    advanced enough to get fully optimized energy

    harvesters.

    Fig.3 Energy conversion efficiency of a piezoelectric

    PVDF nanogenerator[8]

    Fig.4 Comparison of the energy density for the three

    types of mechanical to electrical energy converters[8]

    IIPaper Survey & Discussion

    For this section, we will show both electromagnetic

    and piezoelectric energy harvester designs in the past few

    years, and present their differences in fabrication

    process, design specifications and performance.

    2.1 Vibrational Electromagnetic Energy Harvesters

    2.1.1 S. P. Beeby et al. [9]

    This team uses photolithography to define the shape

    of the stainless steel cantilever beam, and manually

    attaches the permanent magnet onto the beam as well as

    the copper coil onto the stationary platform, Fig.5. The

    sole MEMS fabricating process ends once the cantilever

    beam is complete, and the paper focuses on effect of

    number of coils has on electromagnetic harvesting,

    shown in TABLE 2. Since the coil is stationary, its

    effects on oscillating frequency is minimal to a few Hzs.

    Something worthy of note is that in the three coil

    numbers presented, generated energy all lands around 45

    W, showing that generated power ceases to increase

    after a certain number of coils. This type of vibrational

    energy harvesting mostly use diodes to filter the

    alternating electric current, since there will always be a

    voltage drop after passing a diode [17], a higher generated

    voltage means less energy loss, so a larger number of

    coils for electromagnetic energy harvesters is optimal.

    Fig.5 Micro cantilever generator[9]

  • Harvester specifications are shown in TABLE 3.

    From the fabrication perspective, this design cannot put

    the batch production of MEMS to use, but the

    performance at low frequency and low acceleration

    achieves 300W/cm3 output energy, which is acceptable

    to put into commercial use for wearable devices.

    2.1.2 Qian Zhang et al. [10]

    This design defines an array pattern before

    electroplating copper to form a coil, then uses ICP for

    backside dry etching to form a cavity for the magnet

    array. Finally, the magnets are assembled onto the

    component as the stationary end, distance between beam

    and magnet is approx. 100m, as shown in Fig.6. As was

    mentioned during lectures, not fully supported structures

    suffer from residual stress; and to obtain a low natural

    frequency, the beam must be long in length. From the

    specifications of this design, the beam shows minimal

    bending, meaning that the beam must be rather thick,

    which can only be achieved with bulk micromachining.

    The authors of this paper made a large scale model

    in addition to the MEMS scale model. The models are

    tested on a shaker providing vertical vibration, and

    measurement is done with a Laser Doppler Displacement

    Meter to find the natural frequency, the component specs

    are shown in TABLE 3.

    Fig.6 Brief fabrication process of the micro-electromagnetic energy harvester with magnet and coil arrays[10]

    TABLE 3. The comparison between four electromagnetic energy harvester.

    Volume

    (cm3)

    Power

    (W)

    Power

    Density(W/cm3)

    Natural

    Frequency (Hz)

    Voltage

    (mV)

    Acceleration (g)

    S. P. Beeby et

    al.[9]

    0.15 46 307 52 428

    (Vrms)

    0.06

    Qian Zhang et

    al.[10]

    0.09 2.6 28.9 290 30

    (Vp-p)

    4

    Qian Zhang et

    al.[10]

    26 26,300 10,120 65 28,800 12

    K. Tao et al.[11] 0.02 ----- ----- 365 0.0209 1

    The result is that in comparison with the MEMS

    fabrication processed model, the manually assembled

    large model has a much higher power rating, which

    supports Arnolds assumptions of scale down effects. But

    the big advantage this design has over the design by S.P.

    Beeby et al. is the lack of the final assembly process,

    which is crucial for mass production.

  • 2.1.3 K. Tao et al [11]

    This team uses LIGA process to make the copper

    coil, macromolecule coating is coated afterwards as an

    insulation layer, copper and nickel is then electroplated

    as structure layer. And finally, integrates magnetic

    macromolecule composites to the component, and a lift-

    off process to remove the sacrificial layer, the process is

    as shown in Fig.7. The most significant aspect of this

    energy harvester is the fact that it is produced using only

    MEMS fabrication processes, easily achieving batch

    production.

    Fig.7 Process flow for fabrication of fully-integrated

    energy harvesters[11]

    Measurement of this harvester is done on a shaker

    as well, shown in TABLE 3. The paper does not provide

    the power rating nor power density, but we could use

    Power equation (2)[17] to estimate, giving us a power

    density graded in degrees of nanoWatt/cm3.

    Power = 2 (2)

    The energy output of this design is significantly

    smaller than the first two presented, but the possibility of

    batch production taken into consideration gives this

    design a slight edge if the manufacturing department.

    2.2 Vibrational Piezoelectric Energy Harvesters

    2.2.1 D. Shen et al. [12]

    This team proposed in 2008 Journal of

    Micromechanics and Microengineering, to use silicon

    and piezoelectric materials for a cantilever beam and a

    pure silicon vibrating mass together forming the

    harvesting device. The beam length and silicon mass is

    tweaked to operate at a lower frequency. Fabrication

    process is shown in Fig.8, thermal oxide is first grown on

    silicon wafer before depositing electrical layer and

    piezoelectric PZT layer. A lift-off process difines the

    electrode pattern, and double-side dry etching forms the

    beam and mass. The main fabrication processes used are

    thermal growth, sputtering, lift-off, and dry etching, all

    of which were mentioned during lectures, indicating a

    high probability to be batch produced.

    Fig.8 Fabrication flow chart: (a) multilayer

    deposition; (b) top electrode patterning by liftoff (mask

    1); (c) bottom electrode opening via RIE (mask 2); (d)

    cantilever patterning by RIE (mask3); (e) proof mass

    patterning and cantilever release via backside RIE

    (mask4).[12]

    Measurements are done using the same methods as

  • electromagnetic energy harvesters using a shaker to

    determine the natural frequency. The additional testing in

    this paper is changing acceleration magnitudes to

    simulate different energy input, calculate the damping

    ratio of the beam, and record the output power and

    voltage under different loadings (RLoad). We therefore

    choose the maximum power output in this paper as a

    comparison basis, listed in TABLE 4.

    2.2.2 E. E. Aktakka et al. [13]

    Aktakkas team bonds PZT bulk materials onto SOI

    wafer and applies mechanical thinning to get a

    piezoelectric membrane. Parylene is used as the

    insulation layer, and the electrodes are patterned via

    sputtering. Double-sided dry etching is used to create the

    cantilever beam, and a Transient Liquid Phase (TPL)

    bonding completes the fabrication process.

    Fig.9 Process steps of thinned-PZT on SOI process

    The fabrication processes involved is a lot more

    complicated than the previous design by Shens team,

    and is likely to have a lower yield. The main point of

    selecting this paper is for discussion of the effects of

    packaging. Since PZT is affected by residual stress,

    which in turn changes piezoelectric performances, this

    paper offers insight into System in Packaging (SIP).[13]

    The authors of this paper made two types of energy

    harvesting devices using different materials, silicon and

    tungsten, as the vibrating mass. Measurement on a

    shaker gets the data shown in TABLE 4. In comparison

    with the previous harvester at Fn = 462 Hz, 1.5g; and this

    design at Fn = 415 Hz, 1.5g; the power density for this

    energy harvester is only half of the previous Shen et al.

    design, which we predict to be a result of too many

    fabrication procedures causing accumulation of residual

    stress.

    2.2.3 R. Elfrink et al. [14]

    Elfrink et al. purposes using vacuum packaging to

    decrease aerial dampening and achieve better power

    density. The fabrication process is shown in Fig.10. The

    team made 11 different components and took them all to

    a shaker for measurement, the results are in Fig.11. We

    can see that power density increases significantly by

    100~200 times with vacuum packaging.

    Fig.10 Wafer-scale vacuum package process flow. a. The

    piezoelectric capacitor is formed by consecutive

    deposition, lithography and etching steps of the Pt

    bottom electrode, the AlN piezoelectric layer and the Al

    top electrode. The Si mass and beam are shaped by

    subsequent front- and backside etching. b. The cavities in

    the glass wafer are etched with HF and the contact holes

    are made with powder blasting. The SU-8 bonding layer

    is applied with a wafer scale roller-coating process. c.

  • The glass substrates are bonded to the Si device wafer in

    two consecutive wafer scale vacuum bonding steps. d.

    Single devices with the movable mass and beam in the

    vacuum cavity are obtained after dicing.[14]

    Fig.11 Resonance curves of packaged devices type 3 at

    0.1 g and 1.0 g at atmospheric pressure and at vacuum,

    showing a 200 and 140 fold increase in power.[14]

    We selected the best power density component and

    placed it into TABLE 4 to compare with the other two

    designs, where we find the selected component to be

    slightly weak in power density, but this might be due to

    different piezoelectric materials [8]. After reconfiguration

    [8] of each designs power rating, the Elfrink et al.

    harvester is approximated at 340 microWatt/cm3, around

    100 times the Shen et al. design, showing just how big an

    effect vacuum packaging has for vibrational piezoelectric

    energy harvesters.

    TABLE 4 The comparison between four piezoelectric energy harvester

    Volume

    (cm3)

    Power

    (W)

    Power

    Density(W/cm3)

    Natural

    Frequency (Hz)

    Voltage

    (mV)

    Acceleration (g)

    D. Shen et al.[12] 0.000625 2.15 3,272 462.5 150

    (Vp-p)

    2

    E. E. Aktakka et

    al.[13]

    0.1462 205 1,404 154 ----- 1.5

    E. E. Aktakka et

    al.[13]

    0.1462 160.8 1,099 415 ----- 1.5

    R. Elfrink et

    al.[14]

    2.5 85 340 325 ----- 1.75

    IIIConclusion

    We have now separately compared different

    vibrational electromagnetic energy harvesters and

    vibrational piezoelectric energy harvesters. For the

    electromagnetic devices, it is observed that as the

    manufacturing becomes MEMS based, the power density

    goes down. Since the three designs we choose have

    volume differences within an order, scale down effects

    can be neglected, and the main factors to power density

    drop are the two following reasons: One, multiple

    MEMS processes means lower yield, so the coil number

    is limited, and from the results of S. P. Beeby et al., coil

    amount could lower the output voltage and power

    density Two, the magnets are made using composites, the

    energy product is 2 to 3 orders weaker than bulk

    permanent magnets. Though MEMS production makes

    electromagnetic energy harvesters capable of batch

    producing, the problem remains when implementing

    magnetic materials into MEMS [16], and the rapid

    decrease of power rating due to scaling down is also an

    extremely negative factor.

    As for vibrational piezoelectric energy harvesters,

    we selected three cantilever beam vibration designs, and

  • observed a more stable power output from these

    cantilever piezoelectric energy harvesters. The main 4

    factors affecting output are: Natural frequency, decided

    by structure distortion; Residual stresses, resulting from

    multiple MEMS fabricating procedures and packaging

    procedure; Application of vacuum packing, which

    decreases the effect of aerial dampening and increases

    power density; Piezoelectric material, due to power

    rating being the piezoelectric converting coefficient

    squared, making PZT a much more suitable material

    rather than A1N

    At the end of our review, we draft a graph of Power

    density-Volume containing all the energy harvesters we

    selected, Fig.12.

    Fig.12 The comparison of power density between

    piezoelectric & electromagnetic energy harvester

    In conclusion, scale effects are neglect able for

    vibrational piezoelectric energy harvesters, and

    microscale piezoelectric harvesters have power densities

    2~3 orders higher than vibrational electromagnetic

    energy harvesters, plus the advantage of being

    compatible with existing MEMS fabricating

    technologies, if considering energy harvesting to power

    low consumption wearable devices, piezoelectric

    harvesters are much more suitable. Another aspect that

    Qian Zhang et al.[10] provides is observed at larger scales

    of >10cm3, where assembled electromagnetic energy

    harvesters have a power density than piezoelectric

    energy harvesters, so larger devices should consider

    using electromagnetic energy harvesters for power.

    IVAcknowledgement

    A thank you to Professor Fang, for introducing us

    to the world of MEMS, and providing us the knowledge

    to understand and delve further into micro processes. A

    deep gratitude to National Tsing Hua University for

    providing access to databases of publications around the

    world.

    IVReferences

    1. http://www.ctimes.com.tw/DispArt-

    tw.asp?O=HJYC592HWH8ARASTD0

    2. http://www.memsjournal.com/2010/07/mems-

    microbots-harness-insect-knowhow.html

    3. S. P. Beeby, M. J. Tudor, and N. M. White, Energy

    harvesting vibration sources for microsystems

    applications, Measurement Science and

    Technology, 17(12), R175-R196 (2006)

    4. P. D. Mitcheson, E. M. Yeatman, G. K. Rao, A. S.

    Holmes, and T. C. Green, Energy Harvesting From

    Human and Machine Motion for Wireless

    Electronic Devices, Proceedings of the IEEE,

    96(9), pp. 1457-1486 (2008)

    5. D. P. Arnold, Review of Microscale Magnetic

    Power Generation, IEEE Transactions on

    Magnetics, 43(11), pp. 3940 -3951 (2007)

    6. M. E. Kiziroglou, C. He, and E. M. Yeatman,

    Rolling Rod Electrostatic Microgenerator, IEEE

    Transactions on Industrial Electronics, 56(4), pp.

    1101-1108 (2008)

    7. X. Jiang, Y. Li, and J. Li, Design of a Novel Linear

    Permanent Magnet Vibration Energy Harvester,

    IEEE/ASME International Conference on Advanced

    Intelligent Mechatronics (AIM), pp. 1090-1095

    (2013)

    8. H. S. Kim, J. H. Kim, and J. Kim, A Review of

    Piezoelectric Energy Harvesting Based on

    Vibration, International Journal of Precision

    Engineering and Manufacturing, 12(6), pp. 1129-

    1141 (2011)

    9. S. P. Beeby, R. N. Torah, M. J. Tudor, P. Glynne-

    Jones, T. O'Donnell, C. R. Saha, and S. Roy, A

    D. Shen et al. [12]

    E. E. Aktakka et al.[13]

    S. P. Beeby et al.[9]

    Qian Zhang et al.[10] K. Tao et al. [11]

    Power Density(W/cm3)

    Volume(cm3)

    http://www.ctimes.com.tw/DispArt-tw.asp?O=HJYC592HWH8ARASTD0http://www.ctimes.com.tw/DispArt-tw.asp?O=HJYC592HWH8ARASTD0http://www.memsjournal.com/2010/07/mems-microbots-harness-insect-knowhow.htmlhttp://www.memsjournal.com/2010/07/mems-microbots-harness-insect-knowhow.html

  • micro electromagnetic generator for vibration

    energy harvesting, Journal of Micromechanics and

    Microengineering, 17(7), pp. 1257-1265 (2007)

    10. Q. Zhang, and E .S. Kim, Vibration Energy

    Harvesting Based on Magnet and Coil Arrays for

    Watt-Level Handheld Power Source, Proceedings

    of the IEEE, 102(11), pp. 1747-1761 (2014)

    11. K. Tao, G. Ding, P. Wang, Z. Yang, and Y. Wang,

    Fully integrated micro electromagnetic vibration

    energy harvesters with micro-patterning of bonded

    magnets, IEEE 25th International Conference on

    Micro Electro Mechanical Systems (MEMS), pp.

    1237-1240 (2012)

    12. D. Shen, J. H. Park, J. Ajitsaria, S. Y. Choe, H. C.

    Wikle III and D. J. Kim, The design, fabrication

    and evaluation of a MEMS PZT cantilever with an

    integrated Si proof mass for vibration energy

    harvesting, Journal of Micromechanics and

    Microengineering, 18(5), 055017, pp. 1-7 (2008)

    13. E. E. Aktakka, R. L. Peterson, and K. Najafi,

    Thinned-PZT on SOI process and design

    optimization for piezoelectric inertial energy

    harvesting, 16th International Solid-State Sensors,

    Actuators and Microsystems Conference

    (TRANSDUCERS), pp. 1649-1652 (2011)

    14. R. Elfrink, V. Pop, D. Hohlfeld, T. M. Kamel, S.

    Matova, C. de Nooijer, M. Jambunathan, M.

    Goedbloed,, L. Caballero, M. Renaud, J. Penders

    and R. van Schaijk, First autonomous wireless

    sensor node powered by a vacuum-packaged

    piezoelectric MEMS energy harvester, IEEE

    International Electron Devices Meeting (IEDM), pp.

    1-4 (2009)

    15. T. K. Chung, C. M. Wang, P. C. Yeh, T. W. Liu, C.

    Y. Tseng, and C. C. Chen, A Three-Axial

    Frequency-Tunable Piezoelectric Energy Harvester

    Using a Magnetic-Force Configuration, IEEE

    Sensors Journal, 14(9), pp. 3152-3163 (2014)

    16. D. P. Arnold, and N. Wang, Permanent Magnets for

    MEMS, Journal of Microelectromechanical

    Systems, 18(6), pp. 1255-1266 (2009)

    17. Donald A. Neamen., Microelectronics Circuit

    Analysis and Design, 4th Ed., McGraw-Hill

    Education, New York, (2010).