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Research ArticleQuad-Band 3DRectennaArray for Ambient RF EnergyHarvesting

Fatima Khalid Warda Saeed Nosherwan Shoaib Muhammad U Khan and Hammad M Cheema

Research Institute for Microwave and Millimeter-Wave Studies (RIMMS)National University of Sciences and Technology (NUST) Islamabad Pakistan

Correspondence should be addressed to Nosherwan Shoaib nosherwanshoaibseecsedupk

Received 19 January 2020 Revised 23 March 2020 Accepted 8 April 2020 Published 15 May 2020

Academic Editor Herve Aubert

Copyright copy 2020 Fatima Khalid et al-is is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

-is paper presents a quad-band 3D mountable rectenna module for ambient energy harvesting With the aim of powering upInternet of -ings (IoT) nodes in practical ambient environments a hybrid approach of combining power both at RF and DC isadopted using 98MHz FM band GSM900 (Global System for Mobile Communications) GSM1800 and Wi-Fi 24 GHz band Adual polarized cross-dipole antenna featuring asymmetric slots as well as central ring structure enables multiband response andimproved matching at the higher three frequency bands whereas a loaded monopole wire antenna is used at the lower FM bandFour identical multiband antennas are placed in a 3D cubic arrangement that houses a 4-to-1 power combiner and matchingcircuits on the inside and the FM antenna on the top In order to maintain stable rectenna output at varying input power levels andload resistances a novel transmission line based matching network using closed form equations is proposed Integrated in form ofa 10times10times10 cm3 cube using standard FR4 substrate the rectenna generates a peak output voltage of 238V at minus10 dBm inputpower -e RF to DC conversion efficiency is 7028 417 3337 and 2769 at 98MHz 09GHz 18GHz and 24 GHzrespectively at minus6 dBm -e rectenna also exhibits a measured conversion efficiency of 313 at minus15 dBm for multitone inputs inambient environment -e promising results in both indoor and outdoor settings are suitable to power low power IoT devices

1 Introduction

Recent advancements in the field of Internet of -ings (IoT)have triggered the ldquosmartrdquo wave be it homes offices fac-tories automobiles manufacturing transportation logisticshealthcare agriculture and environment Billions of In-ternet enabled IoT nodes deployed across the globe gathermonitor and exchange data thereby providing actionableinformation to the end-users Efficient powering of thesenodes is a major challenge as many a time they cannot beconnected to the grid due to their operating environmentsand spatial distribution Batteries that are currently used topower sensor nodes need constant maintenance are dis-posal and are difficult to deploy and replace in remote andinaccessible areas Hence charging of batteries wirelessly ordesigning completely battery free systems has become keyresearch challenges

Energy harvesting offers an interesting solution forpowering IoT devices by utilizing energy available in the

natural environment Technologies like solar thermal pi-ezoelectric and Radio Frequency (RF) energy harvestinghave become potential alternatives to enable self-sustain-ability in sensor nodes RF energy harvesting offers a numberof advantages over others due to its constant availabilitysmaller size and independence from environmental andmechanical constraints Energy gathered from the radiofrequency band (3000Hzndash300GHz) can be utilized tooperate low power electronic devices however large scaledeployment of RF energy harvesting systems has remainedelusive to date

A large body of published works is available on RFenergy harvesting Applications such as prototype aerialvehicles [1] remote sensing nodes [2] and medical implants[3] have been demonstrated using RF energy harvestingalbeit using large dedicated and controlled power sources-is not only increases the expense of the overall system butalso limits the applications of energy harvesting On thecontrary harvesting energy from ambient sources can truly

HindawiInternational Journal of Antennas and PropagationVolume 2020 Article ID 7169846 23 pageshttpsdoiorg10115520207169846

realize the concept of ldquoenergy on the gordquo and is expected toreduce system costs as well as improve portability howeverit poses serious design challenges

-e basic driver for harvesting energy is a rectenna thatcomprises an antenna and a rectifier An impedancematching network is added before the rectifier to ensuremaximum power transfer between the antenna and load-eoverall RF-DC conversion efficiency is the key parameter toevaluate the performance of a rectenna A number of single-band multiband and broadband rectennas have beenpublished in literature Some single-band rectennas haveachieved high conversion efficiencies in access of 60however they have a narrowband response and operate athigh input power levels (eg 0 dBm [4] 5 dBm [5] 10 dBm[6]) 15 dBm [7] 18 dBm [8] and 20 dBm [9]) -e averagesignal strength of EM waves in the environment is aroundminus15 to minus30 dBm making these designs unsuitable for am-bient energy harvesting -erefore multiband and broad-band rectennas are preferred so that more energy can beharvested For instance [10] proposes a cross-dipole an-tenna that can harvest energy from six bands including DTVand most of the communication bands however it does notutilize the FM band Similarly [11] uses a differentially fedslot antenna with a reflector to enhance gain and harvestenergy from three bands A codesigned rectenna whicheliminates the need of a matching network by modifying thereceiving dipole antenna is presented in [12] whereas [13]proposes a stacked quad-band rectenna with an efficiency ofup to 84 A rectenna with embedded harmonic filter toreject higher order harmonics generated by the nonlinearrectifier is presented in [14] Design of multiband andbroadband rectennas is challenging due to the dependenceof input and load impedance on multiple frequencies and astable design for all frequencies and input power levels isextremely challenging to achieve Most of the above reporteddesigns exhibit high efficiencies for a narrow range of inputpower and gather energy from a single direction only

FM frequency band is also a potential harvesting sourcedue to its wide availability lower path loss and simplercircuit design -ere are very few published designs thatharvest energy from this band References [15 16] haveproposed rectennas operating in the FM band using a loopantenna with diameter (081λ) and a whip antenna re-spectively Reference [17] demonstrated a wideband FMrectenna harvesting from nearly 23 of the available FMband However the total size of the antenna is nearly1 times 059m2 which is quite large to be of any use in small IoTapplications Use of FM band in energy harvesting is limiteddue to the large antenna size miniaturizing which degradesits performance in terms of gathering usable amount ofenergy from environment -us harvesting from this bandhas not become mainstream

A major challenge in the design of a multiband rectennais the impedance matching network As the rectifier is in-herently a nonlinear device its input impedance is a functionof frequency input power level and load impedance Hencedesigning an impedance matching network having goodperformance at varying frequencies and input power is veryimportant Most of the existing multiband rectennas use

lumped element matching which is lossy and cannot beimplemented at higher frequencies Few transmission line(TL) based matching designs have also been reported inliterature For instance [18] proposes dual band rectifierusing transmission lines operating at 142 dBm input powerReferences [19 20] propose quad-band rectifier designsoperating at an input power range of minus12 dBm to 12 dBmand minus5 dBm respectively All these designs are operating onpower levels that are higher than the ambient power levelswhereas for ambient energy harvesting power levels areexpected to vary depending upon time and locationMoreover the matching network in [18] is designed for142 dBm power level only-erefore a matching network isrequired whose initial parameter values can be calculatedusing much simpler closed form equations and then thesevalues can be optimized to cover the entire range of ambientpower levels Moreover the proposed triband matchingnetwork is an extension of the dual band matching networkreported in [21] which could only be used for two frequencybands

In this paper a three-dimensional (3D) multiband rec-tenna with a novel impedance matching network is pre-sented -e rectenna uses four multiband antennas coveringGSM900 GSM1800 and 24GHz with combined RF outputfed to the rectifier -e matching network has been designedusing closed form equations for input power levels as low asminus30 dBm A separate FM rectenna has been designed at98MHz and integrated with the multiband rectenna usingDC combination of the rectifier outputs -e simulatedconversion efficiency of the triband and FM rectifier is up to77 and 80 respectively at minus6 dBm input power To thebest of the authorrsquos knowledge the proposed design is thefirst to harvest energy from FM (98MHz) GSM900GSM1800 and 24GHz (Wi-Fi) bands simultaneously

-e paper is organized as follows Section 2 introducesthe proposed concept of energy harvesting at a system levelSection 3 discusses the survey of ambient RF energy in testenvironment -e antenna design for multiband and FMenergy harvesting is discussed in Section 4 Sections 5 and 6discuss the design of the multiband rectifier and matchingnetwork respectively Experimental results of rectenna in-cluding indoor and outdoor measurements are presented inSection 7 followed by the conclusions in Section 8

2 System Level Concept

Multiple rectenna array architectures have been studied inliterature that aim to enhance harvested energy Arrayrectennas use either RF combination of the antenna outputsor DC combination of multiple rectifier outputs-e formershown in Figure 1(a) increases the power by combining thereceived RF power before rectification In this case rectifiersrequire larger breakdown diodes to handle more power [22]-e second configuration shown in Figure 1(b) combines therectified DC output voltage of all antennas but reduces theefficiency of the system [23] Figure 1(c) shows a hybridconfiguration of an array rectenna in which both the RFcombination of incoming signals and the DC combinationof rectified signals are shown for a greater voltage output

2 International Journal of Antennas and Propagation

-e proposed rectenna is modelled as a cube withmultiband cross-dipole antennas on four sides and FMmonopole antenna acting as the hanging structure at the top-e cubic shape is chosen to enable housing of multipleprinted circuit boards (PCBs) in a compact form factor aswell as to scavenge available energy from all directionsBased on the cubic rectenna design a hybrid array topologythat utilizes both RF and DC combinations depicted inFigure 1(c) is used -e energy received by the multibandantennas is combined and transferred to the matched rec-tifier housed within the cube Separate rectifiers are used formultiband and FM antennas and the DC output of both isrecombined Figure 2 shows the internal components of thecubic rectenna -e hybrid array topology from Figure 1(c)was selected in order to demonstrate the proof of conceptdesign of a rectenna system that utilizes multiple signalcombinations and covers a wide frequency spectrum

In order to achieve higher DC power at the output anovel concept of an RF energy harvesting (EH) tree isproposed -e proposed cubic rectenna module will act as

Receivingantenna

RFcombination

Multibandimpedancematchingnetwork

Cstorage Load

(a)

Receivingantenna

Cstorage Load

Impedancematchingnetwork

DCcombination

(b)

Multibandantenna


Single bandimpedancematchingnetwork

CstorageLoad

DCcombination

RFcombination

Singleband

antenna

(c)

Figure 1 Rectenna array topologies (a) Multiple antennas with RF combination and single multiband rectifier (b) Multiple antennas withseparate rectifiers and DC combination (c) Proposed hybrid topology

FM band monopoleantenna RF

combinationunit

Multibanddipole

antennasRectifier +matchingnetwork

Figure 2 3D cube rectenna structure

International Journal of Antennas and Propagation 3

the integral unit of the EH tree -e larger part of therectenna ie the FM antenna can be easily integrated withthe supposed branches of the tree while the multibandantennas will act as leaves (see Figure 3) -e harvestedvoltage can be transferred to the centre of the tree throughthe FM antenna-e design also introduces two levels of DCcombination (1) the combination of DC power from FMand multiband rectennas (as shown in Figure 1(c)) and (2)the combination of DC power from multiple rectennamodules on the tree structure -is concept of energyharvesting can be extended to include any frequency in-cluding the AM band at the lower end and higher frequencybands -e FM AM and broadcasting bands are potentialenergy sources but their use is limited due to the largeantenna size at these frequencies-e tree structure providesan ideal way to make use of such large antennas into anenergy harvesting system -e design approach is similar toexisting prototypes of EH trees which utilize solar and windenergy as a way towards green and sustainable power sources[24 25] -e design emulates the process of photosynthesiswhich can be seen as naturersquos energy harvesting mechanismwhereby fuel is created and transferred from the leaves to therest of the tree-e goal of the system is to harvest maximumamount of energy from the environment while the structureitself should be blended in the topography appearingpractically invisible

3 Ambient RF Energy Survey

Analysis of ambient energy density in an area is a complextask as it depends on distance from RF sources theirtransmit powers quantity and distribution of these sourcesas well as terrain Accurate estimation of power densityrequires either exact path loss models acquired from ex-perimental measurements or analytical modelling -is iswhy no general solution of ambient energy density calcu-lation exists -erefore power measurements in multiplelocations of the desired area and subsequent averaging of theresults are the most viable solution and have been adopted inthis work -e ambient RF field measurements conducted inthis work are a continuation of the tests performed in [26]

31 Methodology and Test Setup -e ambient RF mea-surements were carried out at multiple locations at theuniversity campus which lies in a semiurban environmentFigure 4 shows the general testing setup whereas the floorplans of the indoor and outdoor measurement sites mea-surement locations and distribution of RF sources likenearest communication towers and Wi-Fi routers areshown in Figure 5 -e indoor measurement points werechosen to be in different parts of the building like labs andlounge Outdoor measurement was carried out at differentpoints in the grounds surrounding the campus as well as onthe campus terrace Together all the measurement pointswere located within a radius of nearly 1 km Although anumber of cellular and broadcasting sources were present inthe broader vicinity the closest cellular tower lies about03 km away and the closest FM source is nearly 62 km away

from the measurement area as mapped out in Figure 5Multiple Wi-Fi sources are also present inside the building-e equipment used for ambient energy measurement in-cluded a portable spectrum analyzer and a set of broadbandomnidirectional whip antennas with a frequency range offewMHz to 27GHz were usedWithmeasured data for eachlocation the average power density for each frequency bandwas calculated -e antenna power factor and cable losseswere deembedded from the measurements Multiple mea-surement trials were conducted spreading over several daysto ensure data repeatability Since ambient RF power is notconstant and changes with time of day and presence of activedevices in vicinity the standard deviation of the collecteddata from the mean is also calculated

-e results of the RF field survey are shown in Figure 6whereas Table 1 summarizes the indoor vs outdoor availablepower levels from different sources along with standardfrequency ranges -e uplink and downlink bands are

FMantenna

DCcombination

Singlerectennamodule

Figure 3 Conceptual diagram of energy harvesting system

Measurementantenna

Portablespectrumanalyzer

Figure 4 Measurement setup


denoted by UTx and DTx respectively and the poweravailable in the environment is found by

Wi AePT (1)

where Wi and PT are the power density of incident wave andthe power delivered to the spectrum analyzer respectivelyand Ae is the effective antenna aperture -e peak availablepower values are recorded between minus60 dBm and minus10 dBmwith average ambient values between minus15 and minus30 dBm

32 Results and Discussion From the RF survey FMbroadcasting GSM900 GSM1800 3G and Wi-Fi wereidentified as potentially useful ambient RF energy sourcesGSM900 shows maximum peak power whereas FM andbroadcasting sources appear to be heavily dependent online-of-sight and Wi-Fi is very dependent on user trafficGSM900 shows higher power level in the uplink whileGSM1800 and 3G show greater power in the downlink -e

outdoor measurements show higher levels of GSM900 andbroadcasting signals due to close proximity to a base stationand a near line-of-sight from a TV transmitter Mobilecommunication sources show much less power indoorswhereas Wi-Fi sources show relatively constant power inboth indoor and outdoor measurements as there are nu-merous sources present around campus -e energy avail-able in cellular communication bands and the Wi-Fi bandshows the greatest amount of deviation depending upontime -is can be attributed to dynamic user traffic FM andbroadcasting energy sources show comparatively lowerdeviation

Wi-Fi sources have low transmit power and are usuallyfound indoors -is makes them more suited for energyharvesting for devices used inside homes and buildings likewearable electronics and domestic sensing devices On theother hand mobile communication and broadcastingsources can be used to power sensors in outdoor environ-ment due to higher transmit power of base stations and theiromnipresence across the globe -e results also confirm theneed of multiband antennas to meet practical requirements

On the basis of the above analysis the FM GSM900GSM1800 and Wi-Fi bands have been exploited for theproposed rectenna design 3G band shows promising am-bient energy availability which will be incorporated in ourrectenna as a future work

4 Antenna Design

41MultibandDualLPAntenna To harvest energy from theGSM900 GSM1800 and 24GHz Wi-Fi band a multibandantenna consisting of a modified cross-dipole antenna isdesigned -e cross-dipole antenna is selected based on itswide bandwidth bidirectional radiation pattern and duallinearly polarized (LP) characteristics -e antenna is madeon an FR4 substrate with relative permittivity of 43 and athickness of 16mm -e size of the PCB is selected as100times100mm2 which is 03λ0 times 03λ0 at the lowest

Cellulartower

(nearest)

03 km

62 km

Lounge

Lab Lab

HallCorridor

Office Office OfficeLab

FM source(nearest)

Outdoor grounds

Outdoor terrace

Measurement point

Wi-Fi source

Figure 5 Floor plans of testing site with nearest energy harvesting sources (distances are not realistic and have been scaled down to fitimage)

OutdoorsIndoors

FM

GSM900

GSM1800

3G

Wi-FiBroad casting

minus70

minus60

minus50

minus40

minus30

minus20

minus10

0

Am

bien

t pow

er (d

Bm)

05 1 15 2 25 30Frequency (GHz)

Figure 6 Peak ambient power vs frequency in a semiurbanenvironment


operating frequency of 900MHz-e radius and angle of thebowtie shape are selected as 50mm and 80deg respectivelyTwo pairs of cross dipoles are orthogonally printed on eachside of the PCB -e antenna is probe fed by a 50Ω coaxialcable -e inner conductor of the coaxial cable is fed to thetop side metal and the outer conductor is connected to thebottom side-e dipole antenna has a balanced topology andtypically requires a balun to connect to a coaxial cableHowever in this case the bandwidth is limited and theantenna is being matched to a 50Ω impedance so omitting abalun structure does not affect the overall antenna perfor-mance -is has also been done to maintain the simplicityand ease of integration of the cubic rectenna structure -esame feeding structure has been employed in a number ofother antenna designs without the use of a balun in cross-dipole to coaxial transition ([10 27ndash29])

A simplified cross-dipole is designed for an arbitraryfrequency lying between 900MHz and 24GHz -e pro-posed cross-dipole resonates at 16GHz with a widebandwidth of nearly 800MHz In order to cover more bandsat higher frequencies (up to 24GHz) the cross-dipole ismodified by adding a number of slots of different dimen-sions Figure 7 shows the modified dipole arm with arbitrarynumber of slots -is converts each arm of the cross-dipoleinto a number of bent dipoles defined by a circular part(Ln + Wnsec(θn)) and a radial edge (Rn) where θn is theangle of the dipole arm -e total length of each bent dipolearm can be estimated as

Ln + Wnsec θt( 1113857 + Rn λn

4 (2)

where θt is the angle of the cross dipole and λn is thewavelength of the nth frequency obtained using suspendedstrip-line model [30] -e parameter Ln is the arc length andcan be calculated by Ln Rnθn -e overall bandwidth canbe increased by increasing the width (centre angle) of thecross-dipole whereas the bandwidth of each individual bandcan be fine-tuned by adjusting the slot width

-e design iterations of the antenna are shown in Fig-ure 8 Table 2 shows the optimized dimensions of slots addedto dipole arm to make the antenna resonate at specificfrequencies -e simulated S11 of the multiple stages of theantenna design is shown in Figure 9 It can be seen thatincreasing the number of slots introduces a multiband re-sponse however matching of the antenna is degraded To

Table 1 Peak ambient power level survey

Frequency bandrange (MHz)

Peak available powerpower density

Standard deviation (σ)Indoor OutdoorPT Wi PT Wi

(dBm) (μWm2) (dBm) (μWm2)

FM(88ndash108) minus45 00095 minus2956 0332 2098

Broadcasting(150ndash600) minus54 000497 minus2758 218 5659

GSM900UTx(860ndash915)

minus2841 345 minus8991 300 1848

DTx(925ndash960) minus375 591 minus1987 290 1116


minus601 0091 minus433 437 7385


3GUTx(1920ndash1980)

minus51547 082 minus3107 919 1026


Wi-Fi(2390ndash2490) minus424 107 minus4775 315 1043

W1

L1

L2R2 R1W2

WnRn

θn

Ln

Figure 7 Slotted dipole arm


overcome this a printed vacant quarter ring is added to thestructure

-e vacant ring is significantly able to improve theantenna performance It helps in the matching of the an-tenna in its operating bands -e matching performance isgreatly dependent on the dimensions of this feeding ring To

achieve a good matching at all frequencies of interest thewidth and radius of the ring are optimized using parametricanalysis to 4mm and 16mm respectively Figure 10 showsthe final antenna design along with its dimensions Figure 11shows the simulated and measured S11 of the proposedmultiband antenna Addition of the vacant ring improvesthe matching performance of the antenna which covers thefollowing bands GSM900 (720MHz to 940MHz) GSM-1800 (1650MHz to 1760MHz) and Wi-Fi (2334GHz to243GHz) -e individual multiband antenna has a peakgain of 16 24 and 53 dBi at 09 173 and 24GHzrespectively

-e antenna exhibits dual linear polarization due to theorthogonal arrangement of the dipoles -is allows theantenna to receive energy from diversely polarized sourcesFigure 12 shows the surface current distribution at thefrequencies of interest It can be seen that the current flowsthrough the longest bent dipole at lowest frequency and viceversa Figure 13 shows the 2D radiation patterns of theindividual antenna while Figure 14 shows the simulated 3Dradiation patterns -e radiation patterns are of thestandalone antenna -e patterns are similar in the lowerfrequency band-e difference arises at the higher frequencyand is mainly attributed to the measurement equipmentAlso higher order modes are excited at the higher frequencyresulting in more lobes in the radiation patterns of theantenna

Table 2 Parameters of the proposed slotted cross-dipole antenna

Resonant operating frequency Rn Wn θn Ln Rnθn Ln + Wnsec(θ) + Rn λn4(MHz) (mm) (mm) (deg) (mm) (mm) (mm)

875 43 4 65 4878 8575 85711730 33 2 50 2879 4368 41672100 30 2 45 2356 3544 35712400 15 2 40 1047 2808 3125

Antenna dimensionsWa Ra θa Rr Wr

(mm) (mm) (deg) (mm) (mm)100 50 80 4 16

S 11

(dB)

Cross dipoleStep 1Step 2

Step 3Step 4

minus14

minus12

minus10

minus8

minus6

minus4

minus2

0

1 15 2 25 305Frequency (GHz)

Figure 9 -e simulated S11 of the proposed antenna versus fre-quency for different design steps

Bow-tie crossdipole

Step 1 Step 2

Step 4Final design Step 3

Top metal

Botttom metal

Figure 8 Antenna design iterations introduction of slots for multiband response and vacant quarter ring to improve matching


42 FM Band Antenna Design An inductively loadedmonopole antenna at 98MHz is designed for energyharvesting in FM band In order to minimize the size ofotherwise large FM antenna an inductively loaded coil isadded to the monopole reducing the antenna size andimproving performance -e loading coil placement on themonopole rather than the feed point also provides greaterradiation efficiency -e exact location of loading point istypically based on bandwidth and size requirement

Loading nearer to the feed (at 33 or 66) provides betterradiation performance However loading near the endresults in antenna size reduction [31] -e antenna hasa 10times10 cm2 reflector at the bottom to enhance gainFigure 15 shows the design of the proposed antenna alongwith dimensions

-e loading point for the monopole can be denoted asthe ratio of lowermonopole length and the total length of theantenna

Top metal

Botttom metal

WaWr

Ra

Rr

θa

(a)

Top metal

Coaxial cable

Conducting pinBotttom metal

Substrate

(b)

Figure 10 Proposed antenna design (a) Front view (b) Side view

SimulatedMeasured

S 11

(dB)

minus50

minus40

minus30

minus20

minus10

0

10


Figure 11 Simulated and measured S11 of the proposed antenna versus frequency

(a) (b) (c)

Figure 12 Current distribution of the antenna (a) 875MHz (b) 1730MHz (c) 2400MHz


minus16

minus12

minus8

minus4

0

60

300

330

300

270

120

150

180210

240

90

minus16

minus12

minus8

minus4

0

60

300

330

300

270

120

150

180

210

240

90

SimulatedMeasured

(a)

minus16

minus12

minus8

minus4

0

60

300

330

300

270

120

150180

210

240

90

minus16

minus12

minus8

minus4

0

60

300

330

300

270

120

150180

210

240

90

SimulatedMeasured

(b)

minus16

minus12

minus8

minus4

0

60

300

330

300

270

120

150180

210

240

90

minus16

minus12

minus8

minus4

0

60

120

30

150

0

180

30

150

60

120

90 90

SimulatedMeasured

(c)

Figure 13 Comparison between the simulated and measured 2D radiation patterns for XZ plane (left) and XY plane (right) at (a) 900 (b)1730 and (c) 2400MHz


m LML

LT

(3)

-e required resonance is achieved at m 067 with thesize reduced to 55 cm (018λ0) in case of loading as opposedto nearly 160 cm when no loading coil is used Figure 16shows the simulated and measured S11 while gain of 176 dBiis obtained from the antenna

RF combination of the multiband antennas has beendone using a 1 times 4 Wilkinson power combiner covering afrequency range of 05 to 3 GHz -e 4-way combiner hasbeen designed using three 2-way combiners Each com-biner consists of three semi-circular transmission linesections of different widths to give a wideband response atthe frequency range of interest -e transmission lineimpedances and resistor values for each section are shownin Table 3 It is fabricated on FR4 substrate with thicknessof 16mm and relative permittivity of 43 -e insertionloss isolation return loss and phase of the combiner atinput and output ports are shown in Figure 17 where port 1

is the output port with combined RF power and ports 2 to 5are input ports -e ports of the combiner are designed inan orthogonal arrangement so that they can be easilyinserted in the energy harvesting cube with connections tofour antennas on the side (Figures 18(a) and 18(b)) -edrawback of the proposed power combiner is the degra-dation in output voltage of the rectenna due to phasedifferences in incoming signals In an ambient environ-ment the power level and phase of available signals arecompletely unpredictable and random in nature thusmaking the design of an efficient power combiner con-siderably difficult -e rectenna performance in the worstcase scenario (ie completely out of phase incoming sig-nals) was simulated and the output voltage was noted to belower than that in other cases However in real scenariosthe ambient power is rarely completely out of phase andshows slight phase differences In this work the proposedcombiner is utilized due to its superior performance overother combiner designs simplicity of design and ease of

Y

XZ875MHz 1730MHz 2400MHz

Figure 14 3D radiation patterns of antenna

Rc

LG

LC

LT

LMT

LS

LML

Figure 15 Side view of proposed loaded monopole antenna(LT 55 LML 37 LMT 11 LC 7 LS 1 LG 5 RC 2)

SimulatedMeasured

minus30

minus25

minus20

minus15

minus10

minus5

0

S 11 (

dB)

95 100 105 11090Frequency (GHz)

Figure 16 Simulated and measured S11 of loaded monopoleantenna

Table 3 Power combiner parameters

Parameter Z1 Z2 Z3 R1 R2 R3

Value (Ω) 9333 7816 6418 120 220 470


integration with the antennas and rectifier -e multibandand FM antennas are integrated to form a 3D harvestingnode of the proposed harvesting system-e end product isa 10times10 times10 cm3 cube with a 55 cm hanging FM antennaon top It can also be seen from Figure 18(c) that the top

side of the cube acts as a reflector of the FM antenna -iscubic arrangement of multiband antennas helps increaseindividual antenna gains to 234 25 and 63 dBi at 09 18and 24 GHz respectively and makes the rectenna virtuallyomnidirectional

S11 simulatedS11 measuredS22 simulated

S22 measuredS12 simulatedS12 measured

minus60

minus50

minus40

minus30

minus20

minus10

0M

agni

tude

(dB)

1 15 2 2505Frequency (GHz)

(a)

S23 measuredS23 measured

S24 simulatedS24 measured

minus80

minus60

minus40

minus20

0

Mag

nitu

de (d

B)


(b)

Arg (S51 S41S31 S21)

minus200

minus100

0

100

200

Phas

e (de

g)


(c)

Figure 17 Simulated and measured S parameters of the power combiner (a) Insertion loss and return loss at input and output ports (b)Isolation between adjacent and opposite input ports (c) Transmission phase

P1 P5

P4

P3

P2

R1R2

R3

Z1Z2Z3

(a) (b)

FMmonopoleantenna

Multibandantenna

cube

(c)

Figure 18 Integration of antennas to form one harvesting node (a) Power combiner (b) Combiner with multiband antennas (c) Proposed3D rectenna module


A number of structures (adjacent antennas opposingantennas triangular and cubic arrangement) were analysedfor the final form of the energy harvesting node -e cubicstructure was selected due to better gain and radiationcharacteristics and ease of integration of inner components-e analysis of radiation characteristics of the antennas inthe vicinity of each other has also been done At 09 and173GHz the energy harvesting cube shows an overall gainincrease from 16 to 3 dBi at 09GHz and from 24 to 472 dBiat 173GHz respectively Similarly at 24GHz the gainmarginally decreases from 53 to 49 dBi Due to the size andplacement of the antennas the overall gain and efficiency donot alter much after the cubic structure is employed -eobtained radiation efficiency of the antenna system is around90 80 and 70 in GSM900 GSM1800 andWi-Fi bandsrespectively -e choice of antenna or type of antenna ar-rangement does not have a significant effect on the con-version efficiency as it is measured using the RF power inputto the rectifier -e antenna arrangement only determinesthe level of this input RF power

5 Rectifier Design

-e three commonly used rectifier topologies for rectennainclude single series diode voltage doubler and the Grei-nacher rectifiers A single diode is preferred when inputpower levels are very low whereas the Greinacher rectifier isused for applications involving higher power handling -eambient power levels range from low to medium intensity-erefore the voltage doubler topology is chosen due itshigh power handling capability low input voltage require-ment (depending on diode) and doubled output DC voltage-e voltage doubler has been constructed using SkyworksSMS7630 diodes and 100 nF Murata GRM188 series ca-pacitors -e SMS7630 has a low threshold voltage andexhibits high sensitivity at low input power levels thusmaking it ideal for power harvesting applications A loadresistance of 10 kΩ is chosen as it represents the typicalresistance value of IoT sensors -e rectifier circuit is sim-ulated in an electronic design automation software namelyAdvanced Design System (ADS) to accurately model theparasitics arising due to the capacitors Figure 19 shows thesimulated complex input impedance of the voltage doublerfor multiple power levels (minus30 dBm to 0 dBm) at 10 kΩ Itcan be observed that the real and imaginary parts of theinput impedance decrease with an increase in operatingfrequency and increase with an increase in the input powerlevels

6 Matching Network Design

-e multiband impedance matching network is requiredbetween antennas and rectifier circuit for four frequencybands (0098 09 18 and 24GHz) and is designed througha combination of a Triband matching network for 09 18and 24 GHz and a separate matching circuit for 98MHz

61 Triband Matching Network -e triband matchingnetwork is required to match the complex rectifier

impedance at 09 18 and 24GHz to 50Ω antenna resis-tance It is a combination of a Dual Band ImpedanceTransformer (DBIT) and a Dual-to-Triband ImpedanceTransformer (DTBT) as shown in Figure 20 [32]-e formertransforms the Frequency Dependent Complex Load(FDCL) impedance at the first two frequency bands of09GHz and 18GHz to 50Ωwhile the DTBTtransforms thecomplex DBIT input impedance at the third frequency bandof 24 GHz

611 Dual Band Impedance Matching Network With anaim to derive a closed form solution the schematic of DBITis shown in Figure 21 where ZL1 Ra + jXa andZL2 Rb + jXb Stage I transforms the complex load im-pedance at f1 and f2 to pair of complex conjugate im-pedances ldquoZL2rdquo such that ZL2 | f1 (ZL2 | f2)

lowast-e two series transmission lines of stage II transform

ZL2 impedance to Z0 resistance at the first two frequencybands -e characteristic impedance and length of stage Itransmission line are obtained using the following set ofequations [21]

ndash30dBmndash20dBm

ndash10dBm0dBm

0

50

100

150

200

250

300

350

Real

(Zin

)

1 12 14 16 18 2 22 24 2608Frequency (GHz)

(a)


ndash10dBm0dBm

minus700

minus600

minus500

minus400

minus300

minus200

Img

(Zin

)

1 12 14 16 18 2 22 24 2608Frequency (GHz)

(b)

Figure 19 Input impedance of the voltage doubler rectifier versusfrequency and input power levels for 10 kΩ load (a) Real part (b)Imaginary part


Zs

RaRb + XaXb +Xa + Xb

Rb minus Ra

RaXb minus RbXa( 1113857

1113971

l3 n 1113937 +arctan Z3 Ra minus Rb( 1113857( 1113857 RaXb minus RbXa( 1113857( 1113857

(m + 1)βa

(4)

-e input impedance of stage II is found using thefollowing transmission line equations

Z0 Zin Z1ZL1 + jZ1 tan βal1( 1113857

Z1 + jZL1 tan βal1( 1113857 (5)

ZL1 Z2ZL2 + jZ2 tan βbl2( 1113857

Z2 + jZL2f3 tan βbl2( 1113857 (6)

whereas the TL parameters for stage II are obtained using thefollowing equations

l l1 l2 1113937

βa + βb

(7)

Z41 + bZ

31 + cZ

21 + dZ1 + e 0 (8)

where

b 2aR0XL2

R0 minus RL2

c R0RL2 X2

L2 minus R0 minus RL2( 11138572

1113872 1113873 minus X2L2R

20 1 + a2( 1113857

2

a2RL2 RL2 minus R0( 1113857

d 2aR3

0XL2

RL2 minus R0

e R30 R2

L2 + X2L2 minus R0RL2( 1113857

R0 minus RL2

(9)

From (8) the value of Z1 is obtained which can be usedto find the value of Z2 using (6) -e calculated values of theTL parameters are shown in Figure 22

612 Dual-To-Triband Impedance Matching Network Inorder to match the third frequency band the circuit shownin Figure 23 is used as dual-to-triband impedance trans-former (DTBT) It consists of Open-Circuit-Short-Circuit(OCSC) stubs along with a series transmission line having

characteristic impedance Z0 which is the same as the sys-temrsquos characteristic impedance

-e DTBTdoes not affect the impedance matching thatis already achieved at the first two frequency bandsthrough the DBIT Initially only the series TL and OCSC-1stubs are considered -e input impedance of the DBIT atthe third frequency band is found using the followingequations [33]

Zin1f3 Z1ZL1 + jZ1 tan υβal1( 1113857

Z1 + jZL1 tan υβal1( 1113857 G1 + jB1 (10)

where

υ f3

f1

ZL1 Z2ZL2f3 + jZ2 tan βbl2( 1113857

Z2 + jZL2f3 tan βbl2( 1113857

ZL2f3 Z3ZL3 + jZ3 tan υβal3( 1113857

Z3 + jZL3 tan υβal3( 1113857

(11)

-e ZL3 represents the rectifierrsquos input impedance and βc

is the propagation constant at the third frequency Since onlyOCSC-1 is used therefore B1 B2 and the value of B3 canbe computed using (10) and (12) thus obtaining the values ofcharacteristic impedances of OCSC-1 stubs

B3 1 minus Z0B2 tan υθ( 1113857 Z0B2 + tan υθ( 1113857 minus Z2

0G21 tan υθ

Z0 1 minus Z0B2 tan υθ( 11138572

+ Z0G1 tan υθ( 11138572

1113960 1113961

(12)

-e electrical length ldquoθrdquo of the series transmission linecan be found using (13) which can be used to find thecharacteristic impedances of the OCSC stubs using (14)

tan υθ Z0B2 plusmn

Z0B2( 11138572

+ 1 minus Z0G1( 1113857 Z20B

22 + Z2

0B22( 1113857 minus Z0G1

1113969

Z20B

22 + Z2

0B22 minus Z0G1( 1113857

(13)

Ya B3

tan υθ1 minus tan2θ1 cot υθ1 (14)

From the calculated value of Za Zb can be found using(15) and (16)

Z0

Zin ZL1

Stage II Stage I

ZL2

ZL1 f1ZL2 f2

Z1 Z2 Z3l1 l2 l3

Figure 21 Block diagram of the Dual Band Impedance Trans-former (DBIT)

Triband matching network

AntennaRectifier

+load

Compleximpedance

50 Ωantenna

impedance

Dual to tribandimpedancetransformer

Dual bandimpedance

matching network

Figure 20 Block diagram of the Triband Impedance MatchingNetwork (TIMN)


θ1 (1 + s) 1113937

1 + r (15)

Za Zbtan2θ1 (16)

If the calculated characteristic impedances are outsidethe physically realizable range of 30Ω to 130Ω the designprocedure has to be repeated by incorporating OCSC-2 stubswith an assumed ofZc-e corresponding value ofZd can befound using (17) as follows

Zc Zdtan2θ1 (17)

-e overall design procedure can be summarized asfollows

(1) -e transmission line parameters of DBIT are de-termined by finding the complex load impedances atthe first two frequency bands

(2) -e input impedance (Zin1f3) of DBITat the thirdfrequency band is determined using equations orsimulations

Yin4 = 1Z0 f11Z0 f21Z0 f3

Yin3 = 1Z0 f11Z0 f2

G2 + jB3 f3

Yin2 = 1Z0 f11Z0 f2

G1 + jB2 f3

Yin1 = 1Z0 f11Z0 f2

G1 + jB1 f3

Zaθ1

θZb

Z0

Z0

θ1

Zdθ1

Zc

θ1

OCSC-2OCSC-1

Figure 23 Block diagram of the Dual-to-Triband Impedance Transformer (DTBT)

DTBT DBIT421mm3462mm

043mm3767mm

216mm2395mm

092mm2158mm

103mm379mm

1618mm864mm

321mm2069mm

114mm

Z0

C1

C2

D2

D1

3538mm

10kΩRF source

Rectifier

(a)

(b)

Figure 22 Schematic and prototype of the proposed Triband rectifier (PCB size 7times 75 cm2)


(3) -is value (ie Zin1f3) is used to calculate theelectrical length of the series TL followed by thecalculation of electrical length and characteristicimpedance values of the OCSC-1 and OCSC-2 stubs

-e calculations are initially carried out for complexload impedances corresponding to 0 dBm input power levelobtained from Figure 19 and subsequently the design isoptimized in ADS to achieve triband matching at multiplepower levels ie minus30 to 0 dBm -e schematic and pro-totype of the matching network along with the parametersare shown in Figure 22 -e proposed network uses closedform equations unlike reported works that rely solely onoptimization tools After cosimulation of the network andrectifier the design is fabricated on a 0762mm thickRogers RO4350B substrate with εr 348 -e S11 ismeasured using Agilent Technologies E8362B PNA SeriesNetwork Analyzer and shown in Figure 24 -e proposedtriband matching network covers the GSM-900(870ndash900MHz) GSM-1800 (1700ndash1730MHz) and Wi-Fi(2360ndash2390MHz) band for multiple power levels -eslight shift in the measured results can be attributed tounknown parasitics of the SMD capacitors and diodes -eRF-DC conversion efficiency of the rectifier is calculatedusing the following equation

ηRFminusDC PDC

Pin (18)

where PDC is the output electrical power while Pin is theinput RF power to the rectifier Figure 25 shows thetriband rectifier efficiency -e higher efficiency isachieved at 09 GHz as compared to 18 GHz and 24 GHz-is is expected due to increased PCB losses at higherfrequencies It can be seen that the rectifier has the highestefficiency around the input power level of minus6 dBm Amaximum efficiency of 77 at 09 GHz 74 at 18 GHzand 54 at 24 GHz is obtained at this power level Al-though multitone input could not be provided due toequipment limitation the simulated result for multitoneinput is shown It can be observed that the efficiency formultitone input is higher than the individual single toneinputs

62 FM Rectifier Design -e matching network for the FMrectifier is a lumped LC circuit optimized to achieve aminus10 dB bandwidth over the FM band with a centre fre-quency of 98MHz -e selected values of the inductor andcapacitor for the LC circuit are 500 nH and 39 pFrespectively

Figure 26 shows the schematic and prototype of the FMrectifier fabricated on Rogers RO4350B while Figure 27presents the S11 for multiple power levels Better match-ing is achieved for higher power with a maximum band-width of 10MHz at minus20 dBm

-e simulated and measured efficiency values at 98MHzare shown in Figure 28 which highlights a good correlationA maximum efficiency of 80 is achieved at 98MHz forminus6 dBm power level

63TribandandFMRectifier Integration In order to harvestenergy simultaneously from four frequency bands a DCcombination of FM rectenna and triband rectenna wasdesigned Both rectennas use a single rectifier each makingthe complete design employ two rectifiers -e RF power ofthe four triband antennas is combined and fed to onerectifier while the FM antenna is connected to a separaterectifier -e DC combination of both rectifiers is shown inFigure 29(a) Figure 29(b) shows the fabricated prototypeof the integrated quad-band rectifier design after DCcombination -e substrate used is the same as that fortriband rectifier designed earlier -e S11 of the integratedmultiband rectifier is shown in Figure 30 -ere is a shift inthe FM frequency response as compared to standalone FMrectifier response shown in Figure 27 because of the ad-ditional capacitance which is introduced due to the sol-dering of matching network lumped components -e bigshift in the measured triband response compared to thesimulated results can be accounted for by the solderinglosses and high frequency losses in the capacitors that werea part of the voltage doubler circuit Besides this theparasitic capacitance between the PCB traces has alsocaused the measured results to shift left Figure 31 showsthe simulated and measured efficiency of the integratedquad-band rectifier at frequencies of interest and multitoneinput -e DC connection has a negative effect which canbe attributed to the DC combination of two dissimilarrectenna units having different output powers and effi-ciencies Due to this the triband rectenna cannot operate atits optimum efficiency For this reason there is a reductionof around 10 in the FM efficiency and nearly 40 deg-radation in the simulated multitone efficiency A possiblesolution to increase the total efficiency of the integratedrectifier could be to improve the individual efficiency of thetriband rectenna at all the frequency bands so that both theFM and triband rectifiers can achieve optimum operation-is can be done through layout optimization of the rec-tifier design which is also a future work of our researchgroup

0ndash5

ndash10ndash15ndash20ndash25ndash30

S 11 (

dB)

ndash35ndash40


16 18 2 22 24

Simu 0dBmSimu minus10dBmSimu minus20dBmSimu minus30dBm

Meas 0dBmMeas minus10dBmMeas minus20dBmMeas minus30dBm

Figure 24 Simulated and measured S11 of triband rectifier for10 kΩ load


7 Rectenna Measurements

-e integrated rectifier is connected to corresponding an-tennas (Figure 32) A typical lab at ground level and 24m2

area was chosen as the indoor test environment-e outdoortesting was done on an open terrace at a height of 9m -erectenna was measured with single multiband antenna aswell as with integrated multiband and FM antennas in bothindoor and outdoor settings

80

70

60

50

40

30

20

10

Input power level to rectifier (dBm)

RF-D

C co

nver

sion

effic

ienc

y (

)

0ndash40 ndash35 ndash30 ndash25 ndash20 ndash15 ndash10 ndash5 0

Simu 875MHzMeas 875MHzSimu 1730MHzMeas 1730MHz

Simu 2400MHzMeas 2400MHzSimu 875 + 1730 + 2400MHz

Figure 25 RF-DC conversion efficiency of the triband rectifier for 10 kΩ load

RF source

Matchingnetwork

Voltage doubler circuitwith load

Z0 D1

D2C1

C2

500nH10kΩ

39pF

(a) (b)

Figure 26 Schematic and prototype of FM rectifier (PCB size 35times 25 cm2)

S 11 (

dB)



minus35

minus30

minus25

minus20

minus15

minus10

minus5

0

90 92 94 96 98 100 102 104 106 10888Frequency (MHz)

Figure 27 Simulated and measured S11 of FM rectifier for 10 kΩload

SimulatedMeasured

0

20

40

60

80

100

RF-D

C co

nver

sion

effic

ienc

y (

)

minus35 minus30 minus25 minus20 minus15 minus10 minus5 0minus40Input power level to rectifier (dBm)

Figure 28 RF-DC conversion efficiency of FM rectifier at 98MHzfor 10 kΩ load


Tribandrectenna

Z0

C1

C2

D2

D1

421mm3462mm

043mm3767mm

216mm2395mm

092mm2158mm

103mm379mm

1618mm864mm

500nH

321mm2069mm

114mm3538mm

Z0FMrectenna

39pF

C1

C2

D2

D1

+

ndash

10kΩ

Vdc

DCcombination

(a)

(b)

Figure 29 Proposed multiband rectifier (a) Schematic (b) Prototype (PCB size 7 times 75 cm2)

minus40

minus35

minus30

minus25

minus20

minus15

minus10

minus5

0

S 11 (

dB)

90 92 94 96 98 100 102 104 106 10888Frequency (MHz)



(a)

minus35

minus30

minus25

minus20

minus15

minus10

minus5

0

5

S 11 (

dB)

1 12 14 16 18 2 22 2408Frequency (GHz)



(b)

Figure 30 Simulated and measured S11 of the integrated multiband rectifier for 10 kΩ load (a) FM band (b) Triband


Simu 98MHzMeas 98MHzSimu 875MHzMeas 875MHzSimu 1800MHz

Meas 1800MHzSimu 2400MHzMeas 2400MHzSimu98 + 875 + 1800 + 2400

0

10

20

30

40

50

60

70

80

RF-D

C co

nver

sion

effici

ency

()


Figure 31 RF-DC conversion efficiency of the integrated multiband rectifier for 10 kΩ load

(a) (b)

(c)

Figure 32 Dedicated testing setup for the rectenna at minus10 dBm input power using (a) single multiband antenna element (b) singlemultiband antenna element combined with FM rectenna and (c) two multiband antenna elements (all measurements have been conductedwith multitone sources)


71 Dedicated Source Testing A sim65 dBi log periodic an-tenna (LPDA) with a frequency range of 10MHzndash3GHz isused as transmit antenna It is connected to RampS SME06signal generator to transmit varying powers at the desiredfrequencies -e rectenna module is placed in the far-field ofthe transmitting antenna

-e multiband antenna is initially connected to the RampSFS300 spectrum analyzer and the received RF power isnoted -e distance between the proposed antenna and thesource antenna is varied to calibrate input power levelsbetween minus40 and 0 dBm Note that this power level refers tothe power input to the rectifier Next the spectrum analyzeris replaced with direct connection of the proposed antennato the rectifier circuit -e distance of the rectenna modulefrom the source antenna is again varied to measure har-vested voltage at different input power levels -e DC outputvoltage across the load resistance at different power levels ismeasured using a digital multimeter-emeasured values ofRF-DC conversion efficiency are found using (18) where theoutput DC power PDC is found from the measured DCvoltage using

PDC(dBm) 10logV2

DCRL

times 1031113888 1113889 (19)

-e energy harvested by the rectenna using a singleantenna is shown in Figure 32(a) A Peak voltage of0926 V is harvested at an input power level of minus10 dBmMultiple RF sources have been used to generate signals ofrequired frequencies (900 1730 and 2400MHz) atminus10 dBm Figure 32(b) shows the test setup of the mul-tiband and FM rectenna using a dedicated source It canbe seen that the harvested voltage is considerably in-creased due to the addition of the FM band at a similarinput power -is is because of the high efficiency of themultiband rectifier at FM frequencies Figure 32(c) showsthe test setup of the two multiband rectennas using adedicated source Due to the nonavailability of four signalgenerators testing is carried out using only two multibandantennas of the proposed cube structure One multitonesource is placed in front of each antenna to establish anambient environment with signal incident from all sides-e output rectified voltage is 238 V which is more thandouble the voltage produced by rectenna using a singlemultiband antenna (Figure 32(a)) -is proves that use offour antennas will roughly quadruple the voltage outputSimilarly the FM antenna connected with the cubic rec-tenna will add to the output voltage -eoretically themeasured voltage should increase by a factor of 4 afterdoubling the number of antennas However due to theinherent losses of the power combiner and efficiencylimitation of the rectifier a lesser value (238 V) ispractically achieved It needs to be noted that all theresults of harvested output voltage with dedicated sourcesare obtained while keeping the level of input power level atminus10 dBm at all frequencies of interest -is has been doneto maintain uniformity in measurements and due tolimitations of signal source to achieve higher signal level-e constant power level was ensured by periodically

changing the distance between the rectenna and thesource antenna to achieve minus10 dBm power at the input tothe rectifier

72AmbientTesting Rectenna testing is also carried out ina semiurban university campus -e testing site is ap-proximately 300m from the nearest cellular tower and 5mfrom the nearest Wi-Fi source -e measured ambientpower levels vary around minus60 dBm to minus15 dBm for therelevant frequency bands with an average power level ofminus15 dBm using the proposed antenna Figure 33(a) showsthe test setup of the proposed rectenna in the presence ofambient RF sources -e output voltage from the rectennawith a single antenna is recorded to be 92mV Ambientrectenna testing for the 3D cube structure is also carriedout with and without the FM rectenna -e measurementsetup for the cube with multiband antennas only is shownin Figure 33(b) An output voltage of 123mV is obtainedwhich is higher as compared to that of the single mul-tiband antenna Figures 33(c) and 33(d) show the ambienttesting setup for complete cubic rectenna including theFM rectenna -e output voltage obtained after deem-bedding the RF cable used for FM antenna is 315mVwhich is higher than the preceding cases It is observedthat the FM input significantly increases the harvestedvoltage even though the ambient power available in theFM band is lower than the communication bands asdiscussed in Section 3 -is increase in output voltage canbe attributed to the high efficiency of FM rectifier asshown in Figure 31

-e average available power in the environment mea-sured using the proposed antenna is nearly minus15 dBm -eDC power harvested by the antenna is calculated to beminus20035 dBm using (19) where the DC voltage and loadresistance are taken as 315mV and 10 kΩ respectivelyUsing (18) the overall conversion efficiency of the rectennafor ambient measurements is found as 313 at minus15 dBm-is is the multitone efficiency and is therefore higher thanindividual efficiencies at each frequency band except the FMband -e results are in accordance with the simulated ef-ficiency values of quad-band rectifier as shown in Figure 31-e degradation in overall efficiency is accounted by thelosses incurred due to DC combination of two dissimilarrectennas

73 Comparative Performance Analysis A comparison ofthe proposed rectifier to the existing topologies is presentedin Figure 34 -e proposed triband rectifier is at least 10more efficient than the designs reported in [10 11 13 36]while there is a 40 improvement in the rectifierrsquos efficiencyat 24GHz as compared to [20]

A tabular comparison between the proposed rectennaand some recent rectenna designs is given in Table 4 It canbe seen that the proposed design is the only one thatharvests energy from the FM band along with GSM900GSM1800 and Wi-Fi bands It not only miniaturizes theFM element but also integrates it into the overall struc-ture In addition a hybrid combination of outputs and


two antennas results in an output voltage as high as 238 Vat an input power level of minus10 dBm in dedicated mode-erectenna also shows 315mV harvested voltage in ambientsettings with an average available power of minus15 dBm in theenvironment Although this voltage is not enough topower conventional IoT devices the integration ofboosting circuits and power management units with the

rectenna module can greatly enhance the harvestedvoltage -e demonstration of powering an IoT sensorusing the proposed rectenna in ambient settings is en-visaged as a future extension to this work Integration ofmultiple 3D mountable rectenna modules makes theproposed design a good candidate for energy harvestingfor IoT applications

minus40 minus35 minus30 minus25 minus20 minus15 minus10 minus5 00

10

20

30

40

50

60

70

80


RFminusD

C co

nver

sion

effici

ency

()

875MHz1730MHz2400MHz

Voltage doublerSingle series diodeGrenaicher topology

[19](09GHz)

[11](2GHz)

[13](09GHz)

[13]( 18 24GHz)

[36]

[14](185GHz)

[14](0915GHz)

[20] (17GHz)[20] (24GHz)

Figure 34 Comparison of conversion efficiency of proposed rectifier with existing topologies

(a) (b) (c)

(d)

Figure 33 Ambient environment testing setup for the rectenna using (a) single multiband antenna element (b) proposed cube rectennawithout FM antenna (c) proposed cube rectenna (open) and (d) proposed cube rectenna (closed)


8 Conclusions

A novel multiband 3D rectenna is proposed for RF energyharvesting using a modified cross-dipole antenna and atransmission line based triband matching networkdesigned for multiple power levels and frequency bandsusing closed form equations -e rectenna achieves amaximum measured efficiency of 70 with minus6 dBm inputpower at 98MHz whereas the ambient rectenna mea-surements show a maximum achieved efficiency of 313 atmultitone inputs It exhibits a comparable RF-DC con-version efficiency and a higher output DC voltage com-pared to recent published designs Moreover the design ofthe receiving antenna and the triband impedance matchingnetwork is based on closed form equations making it ge-neric in nature and extendable to any desired frequencyrange -e 3D cubic structure enhances antenna gain andenables the rectenna to harvest greater amount of energyfrom all directions -is is the first published rectennadesign that is capable of harvesting energy from the FMband along with GSM900 GSM1800 andWi-Fi bands -eintegration of multiple 3D mountable rectenna modulesmakes it suitable for powering IoT sensors in practicalscenarios

Data Availability

-e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

-e authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

-is work was funded through Higher Education Com-mission (HEC) National Research Program for Universities(NRPU) Grant Program Project no 9971 titled ldquoRF EnergyHarvesting for Internet of -ings (IoT) Applicationsrdquo

References

[1] W Brown ldquoExperiments involving a microwave beam topower and position a helicopterrdquo IEEE Transactions onAerospace and Electronic Systems vol AES-5 no 5pp 692ndash702 1969

[2] F Congedo G Monti L Tarricone and V Bella ldquoA 245-GHz vivaldi rectenna for the remote activation of an enddevice radio noderdquo IEEE Sensors Journal vol 13 no 9pp 3454ndash3461 Sep 2013

[3] B J DeLong A Kiourti and J L Volakis ldquoA radiating near-field patch rectenna for wireless power transfer to medicalimplants at 24 GHzrdquo IEEE Journal of Electromagnetics RFand Microwaves in Medicine and Biology vol 2 no 1pp 64ndash69 2018

[4] B Strassner and K Kai Chang ldquo58-GHz circularly polarizeddual-rhombic-loop traveling-wave rectifying antenna for lowpower-density wireless power transmission applicationsrdquo

Table 4 Comparison of the proposed rectenna with related designs

Ref(year)

Frequency(GHz)

Randompolarizationreceivingcapability

Type of matchingnetwork used

Inputpowerlevel(dBm)

Maximum RF-DC conversionefficiency ()

Maximumconversionefficiency at

multitone input()

Maximumharvested DCoutput voltage

(V)

[10](2016)

Six-band 055075 09 185

215 245Dual CP Lumped matching

for each band minus30 to minus5 67 at minus5 dBm 80 at minus5 dBm 0663 atminus15 dBm

[11](2018)

Triple-band 2124ndash248 33ndash38 LP Differential

matching minus20 to 0 53 at minus13 dBm Not available Not available

[12](2017)

Broadband09ndash11 and18ndash25

Dual LP Not used minus25 to 0 60 at 0 dBm Not available Not available

[13](2015)

Four-band 0918 21 24 Dual LP Lumped matching

for each band minus20 to 6 84 at 58 dBm 84 at 58 dBm 09 at minus15 dBm

[34](2018)

Triband 09 18and 21 Linear

Optimizationbased TLmatching

minus35 tominus10 56 at minus10 dBm 55 at minus10 dBm 075 at minus10 dBm

[35](2017)



minus30 to 10 40 at minus10 dBm 81 with minus30 dBmper tone

06 at500 μWm2

[15](2013)

FM band819ndash847 Linear Lumped element

matching NA NA Single tone input 172 at minus20 dBm

[16](2017) FM band 88ndash108 Linear Lumped element

matching minus35 to 10 74 at 5 dBm Single tone input 0619 at142 dBm


matching minus20 to 10 56 at 0 dBm Single tone input 15 at 0 dBm

ltiswork(2019)

Four-band0098 09 18

24Dual LP

Closed formequation based TL

matchingminus30 to 0 69 at minus6 dBm 40 at minus10 dBm 238 at minus10 dBm


IEEE Transactions on Microwave lteory and Techniquesvol 51 no 5 pp 1548ndash1553 2003

[5] Q Awais Y Jin H T Chattha M Jamil H Qiang andB A Khawaja ldquoA compact rectenna system with high con-version efficiency for wireless energy harvestingrdquo IEEE Accessvol 6 pp 35 857ndash35 866 2018

[6] Y-J Ren and K Chang ldquo58-GHz circularly polarized dual-diode rectenna and rectenna array for microwave powertransmissionrdquo IEEE Transactions on Microwave lteory andTechniques vol 54 no 4 pp 1495ndash1502 2006

[7] Y Yang L Li J Li et al ldquoA circularly polarized rectenna arraybased on substrate integrated waveguide structure withharmonic suppressionrdquo IEEE Antennas and Wireless Prop-agation Letters vol 17 no 4 pp 684ndash688 2018

[8] Y Yang J Li L Li et al ldquoA 58 GHz circularly polarizedrectenna with harmonic suppression and rectenna array forwireless power transferrdquo IEEE Antennas and Wireless Prop-agation Letters vol 17 no 7 pp 1276ndash1280 2018

[9] X Li L Yang and L Huang ldquoNovel design of 245-GHzrectenna element and array for wireless power transmissionrdquoIEEE Access vol 7 pp 28356ndash28362 2019

[10] C Song Y Huang P Carter et al ldquoA novel six-band dualcp rectenna using improved impedance matching tech-nique for ambient rf energy harvestingrdquo IEEE Transactionson Antennas and Propagation vol 64 no 7 pp 3160ndash31712016

[11] S Chandravanshi S S Sarma and M J Akhtar ldquoDesign oftriple band differential rectenna for RF energy harvestingrdquoIEEE Transactions on Antennas and Propagation vol 66no 6 pp 2716ndash2726 2018

[12] C Song Y Huang J Zhou et al ldquoMatching networkelimination in broadband rectennas for high-efficiencywireless power transfer and energy harvestingrdquo IEEETransactions on Industrial Electronics vol 64 no 5pp 3950ndash3961 2017

[13] V Kuhn C Lahuec F Seguin and C Person ldquoA multi-bandstacked rf energy harvester with RF-to-DC efficiency up to84rdquo IEEE Transactions on Microwave lteory and Tech-niques vol 63 no 5 pp 1768ndash1778 2015

[14] C Song Y Huang J Zhou J Zhang S Yuan and P CarterldquoA high-efficiency broadband rectenna for ambient wirelessenergy harvestingrdquo IEEE Transactions on Antennas andPropagation vol 63 no 8 pp 3486ndash3495 2015

[15] A Noguchi and H Arai ldquoSmall loop rectenna for rf energyharvestingrdquo in Proceedings of the 2013 Asia-Pacific MicrowaveConference Proceedings (APMC) pp 86ndash88 IEEE SeoulSouth Korea November 2013

[16] Mutee-Ur-Rehman M I Qureshi W Ahmad andW T Khan ldquoRadio frequency energy harvesting from am-bient fm signals for making battery-less sensor nodes forwireless sensor networksrdquo in Proceedings of the 2017 IEEEAsia Pacific Microwave Conference (APMC) pp 487ndash490Kuala Lumpur Malaysia November 2017

[17] E M Jung Y Cui T-H Lin et al ldquoA wideband quasi-isotropic kilometer-range fm energy harvester for perpetualIoTrdquo IEEE Microwave and Wireless Components Lettersvol 30 no 2 pp 201ndash204 2020

[18] J Liu X Y Zhang and C-L Yang ldquoAnalysis and design ofdual-band rectifier using novel matching networkrdquo IEEETransactions on Circuits and Systems II Express Briefs vol 65no 4 pp 431ndash435 2018

[19] J-J Lu X-X Yang H Mei and C Tan ldquoA four-band rectifierwith adaptive power for electromagnetic energy harvestingrdquo

IEEE Microwave and Wireless Components Letters vol 26no 10 pp 819ndash821 2016

[20] C-Y Hsu S-C Lin and Z-M Tsai ldquoQuadband rectifierusing resonant matching networks for enhanced harvestingcapabilityrdquo IEEE Microwave and Wireless Components Let-ters vol 27 no 7 pp 669ndash671 2017

[21] X Liu Y Liu S Li F Wu and Y Wu ldquoA three-section dual-band transformer for frequency-dependent complex loadimpedancerdquo IEEE Microwave and Wireless ComponentsLetters vol 19 no 10 pp 611ndash613 2009

[22] U Olgun C-C Chi-Chih Chen and J L Volakis ldquoInves-tigation of rectenna array configurations for enhanced rfpower harvestingrdquo IEEE Antennas and Wireless PropagationLetters vol 10 pp 262ndash265 2011

[23] T Matsunaga E Nishiyama and I Toyoda ldquo58-GHzstacked differential rectenna suitable for large-scale rec-tenna arrays with dc connectionrdquo IEEE Transactions onAntennas and Propagation vol 63 no 12 pp 5944ndash59492015

[24] Spotloght solar ldquosolar energy treesrdquo httpsspotlightsolarcomsolar-energy-trees-projects

[25] New world wind ldquothe wind treerdquo httpsnewworldwindcomenwind-tree

[26] F Khalid M U Khan N Shoaib W Saeed andH M Cheema ldquoMultiband antenna design for ambient en-ergy harvesting based on rf field investigationrdquo in Proceedingsof the 2018 IEEE International Symposium on Antennas andPropagation amp USNCURSI National Radio Science Meetingpp 673-674 Boston MA USA July 2018

[27] H H Tran and I Park ldquoWideband circularly polarized cavity-backed asymmetric crossed bowtie dipole antennardquo IEEEAntennas and Wireless Propagation Letters vol 15 pp 358ndash361 2016

[28] T K Nguyen H H Tran and N Nguyen-Trong ldquoA wide-band dual-cavity-backed circularly polarized crossed dipoleantennardquo IEEE Antennas and Wireless Propagation Lettersvol 16 pp 3135ndash3138 2017

[29] S X Ta H Choo I Park and R W Ziolkowski ldquoMulti-bandwide-beam circularly polarized crossed asymmetricallybarbed dipole antennas for gps applicationsrdquo IEEE Trans-actions on Antennas and Propagation vol 61 no 11pp 5771ndash5775 2013

[30] M-T Wu and M-L Chuang ldquoApplication of transmission-line model to dual-band stepped monopole antenna de-signingrdquo IEEE Antennas and Wireless Propagation Lettersvol 10 pp 1449ndash1452 2011

[31] R C Hansen ldquoOptimum inductive loading of short whipantennasrdquo IEEE Transactions on Vehicular Technologyvol 24 no 2 pp 21ndash29 1975

[32] W Saeed N Shoaib H M Cheema M U Khan andF Khalid ldquoTriband impedance transformer for frequencydependent complex loadrdquo in Proceedings of the 18th Inter-national Symposium on Antenna Technology and AppliedElectromagnetics (ANTEM) pp 1ndash3 Waterloo ON CanadaAugust 2018

[33] M A Maktoomi M S Hashmi A P Yadav and V KumarldquoA generic tri-band matching networkrdquo IEEE Microwaveand Wireless Components Letters vol 26 no 5 pp 316ndash3182016

[34] A Bakytbekov T Q Nguyen C Huynh K N Salama andA Shamim ldquoFully printed 3d cube-shaped multiband fractalrectenna for ambient rf energy harvestingrdquo Nano Energyvol 53 pp 587ndash595 2018


[35] S Shen C-Y Chiu and R D Murch ldquoA dual-port triple-band l-probe microstrip patch rectenna for ambient rf energyharvestingrdquo IEEE Antennas and Wireless Propagation Lettersvol 16 pp 3071ndash3074 2017

[36] M Pinuela P D Mitcheson and S Lucyszyn ldquoAmbient RFenergy harvesting in urban and semi-urban environmentsrdquoIEEE Transactions on Microwave lteory and Techniquesvol 61 no 7 pp 2715ndash2726 2013


realize the concept of ldquoenergy on the gordquo and is expected toreduce system costs as well as improve portability howeverit poses serious design challenges

-e basic driver for harvesting energy is a rectenna thatcomprises an antenna and a rectifier An impedancematching network is added before the rectifier to ensuremaximum power transfer between the antenna and load-eoverall RF-DC conversion efficiency is the key parameter toevaluate the performance of a rectenna A number of single-band multiband and broadband rectennas have beenpublished in literature Some single-band rectennas haveachieved high conversion efficiencies in access of 60however they have a narrowband response and operate athigh input power levels (eg 0 dBm [4] 5 dBm [5] 10 dBm[6]) 15 dBm [7] 18 dBm [8] and 20 dBm [9]) -e averagesignal strength of EM waves in the environment is aroundminus15 to minus30 dBm making these designs unsuitable for am-bient energy harvesting -erefore multiband and broad-band rectennas are preferred so that more energy can beharvested For instance [10] proposes a cross-dipole an-tenna that can harvest energy from six bands including DTVand most of the communication bands however it does notutilize the FM band Similarly [11] uses a differentially fedslot antenna with a reflector to enhance gain and harvestenergy from three bands A codesigned rectenna whicheliminates the need of a matching network by modifying thereceiving dipole antenna is presented in [12] whereas [13]proposes a stacked quad-band rectenna with an efficiency ofup to 84 A rectenna with embedded harmonic filter toreject higher order harmonics generated by the nonlinearrectifier is presented in [14] Design of multiband andbroadband rectennas is challenging due to the dependenceof input and load impedance on multiple frequencies and astable design for all frequencies and input power levels isextremely challenging to achieve Most of the above reporteddesigns exhibit high efficiencies for a narrow range of inputpower and gather energy from a single direction only

FM frequency band is also a potential harvesting sourcedue to its wide availability lower path loss and simplercircuit design -ere are very few published designs thatharvest energy from this band References [15 16] haveproposed rectennas operating in the FM band using a loopantenna with diameter (081λ) and a whip antenna re-spectively Reference [17] demonstrated a wideband FMrectenna harvesting from nearly 23 of the available FMband However the total size of the antenna is nearly1 times 059m2 which is quite large to be of any use in small IoTapplications Use of FM band in energy harvesting is limiteddue to the large antenna size miniaturizing which degradesits performance in terms of gathering usable amount ofenergy from environment -us harvesting from this bandhas not become mainstream

A major challenge in the design of a multiband rectennais the impedance matching network As the rectifier is in-herently a nonlinear device its input impedance is a functionof frequency input power level and load impedance Hencedesigning an impedance matching network having goodperformance at varying frequencies and input power is veryimportant Most of the existing multiband rectennas use

lumped element matching which is lossy and cannot beimplemented at higher frequencies Few transmission line(TL) based matching designs have also been reported inliterature For instance [18] proposes dual band rectifierusing transmission lines operating at 142 dBm input powerReferences [19 20] propose quad-band rectifier designsoperating at an input power range of minus12 dBm to 12 dBmand minus5 dBm respectively All these designs are operating onpower levels that are higher than the ambient power levelswhereas for ambient energy harvesting power levels areexpected to vary depending upon time and locationMoreover the matching network in [18] is designed for142 dBm power level only-erefore a matching network isrequired whose initial parameter values can be calculatedusing much simpler closed form equations and then thesevalues can be optimized to cover the entire range of ambientpower levels Moreover the proposed triband matchingnetwork is an extension of the dual band matching networkreported in [21] which could only be used for two frequencybands

In this paper a three-dimensional (3D) multiband rec-tenna with a novel impedance matching network is pre-sented -e rectenna uses four multiband antennas coveringGSM900 GSM1800 and 24GHz with combined RF outputfed to the rectifier -e matching network has been designedusing closed form equations for input power levels as low asminus30 dBm A separate FM rectenna has been designed at98MHz and integrated with the multiband rectenna usingDC combination of the rectifier outputs -e simulatedconversion efficiency of the triband and FM rectifier is up to77 and 80 respectively at minus6 dBm input power To thebest of the authorrsquos knowledge the proposed design is thefirst to harvest energy from FM (98MHz) GSM900GSM1800 and 24GHz (Wi-Fi) bands simultaneously

-e paper is organized as follows Section 2 introducesthe proposed concept of energy harvesting at a system levelSection 3 discusses the survey of ambient RF energy in testenvironment -e antenna design for multiband and FMenergy harvesting is discussed in Section 4 Sections 5 and 6discuss the design of the multiband rectifier and matchingnetwork respectively Experimental results of rectenna in-cluding indoor and outdoor measurements are presented inSection 7 followed by the conclusions in Section 8

2 System Level Concept

Multiple rectenna array architectures have been studied inliterature that aim to enhance harvested energy Arrayrectennas use either RF combination of the antenna outputsor DC combination of multiple rectifier outputs-e formershown in Figure 1(a) increases the power by combining thereceived RF power before rectification In this case rectifiersrequire larger breakdown diodes to handle more power [22]-e second configuration shown in Figure 1(b) combines therectified DC output voltage of all antennas but reduces theefficiency of the system [23] Figure 1(c) shows a hybridconfiguration of an array rectenna in which both the RFcombination of incoming signals and the DC combinationof rectified signals are shown for a greater voltage output




Receivingantenna

RFcombination


Cstorage Load

(a)

Receivingantenna

Cstorage Load


DCcombination

(b)

Multibandantenna



CstorageLoad

DCcombination

RFcombination

Singleband

antenna

(c)



combinationunit

Multibanddipole










FMantenna

DCcombination



Measurementantenna





Wi AePT (1)






4 Antenna Design


Cellulartower

(nearest)

03 km

62 km

Lounge

Lab Lab

HallCorridor


FM source(nearest)

Outdoor grounds

Outdoor terrace

Measurement point

Wi-Fi source


OutdoorsIndoors

FM

GSM900

GSM1800

3G

Wi-FiBroad casting

minus70

minus60

minus50

minus40

minus30

minus20

minus10

0

Am

bien

t pow

er (d

Bm)







4 (2)











minus2841 345 minus8991 300 1848



minus601 0091 minus433 437 7385



minus51547 082 minus3107 919 1026



W1

L1

L2R2 R1W2

WnRn

θn

Ln









875 43 4 65 4878 8575 85711730 33 2 50 2879 4368 41672100 30 2 45 2356 3544 35712400 15 2 40 1047 2808 3125


(mm) (mm) (deg) (mm) (mm)100 50 80 4 16

S 11

(dB)


Step 3Step 4

minus14

minus12

minus10

minus8

minus6

minus4

minus2

0



Bow-tie crossdipole

Step 1 Step 2


Top metal

Botttom metal






Top metal

Botttom metal

WaWr

Ra

Rr

θa

(a)

Top metal

Coaxial cable


Substrate

(b)


SimulatedMeasured

S 11

(dB)

minus50

minus40

minus30

minus20

minus10

0

10



(a) (b) (c)



minus16

minus12

minus8

minus4

0

60

300

330

300

270

120

150

180210

240

90

minus16

minus12

minus8

minus4

0

60

300

330

300

270

120

150

180

210

240

90

SimulatedMeasured

(a)

minus16

minus12

minus8

minus4

0

60

300

330

300

270

120

150180

210

240

90

minus16

minus12

minus8

minus4

0

60

300

330

300

270

120

150180

210

240

90

SimulatedMeasured

(b)

minus16

minus12

minus8

minus4

0

60

300

330

300

270

120

150180

210

240

90

minus16

minus12

minus8

minus4

0

60

120

30

150

0

180

30

150

60

120

90 90

SimulatedMeasured

(c)



m LML

LT

(3)




Y



Rc

LG

LC

LT

LMT

LS

LML


SimulatedMeasured

minus30

minus25

minus20

minus15

minus10

minus5

0

S 11 (

dB)

95 100 105 11090Frequency (GHz)




Value (Ω) 9333 7816 6418 120 220 470






minus60

minus50

minus40

minus30

minus20

minus10

0M

agni

tude

(dB)


(a)



minus80

minus60

minus40

minus20

0

Mag

nitu

de (d

B)


(b)

Arg (S51 S41S31 S21)

minus200

minus100

0

100

200

Phas

e (de

g)


(c)


P1 P5

P4

P3

P2

R1R2

R3

Z1Z2Z3

(a) (b)

FMmonopoleantenna

Multibandantenna

cube

(c)




5 Rectifier Design










ndash10dBm0dBm

0

50

100

150

200

250

300

350

Real

(Zin

)

1 12 14 16 18 2 22 24 2608Frequency (GHz)

(a)


ndash10dBm0dBm

minus700

minus600

minus500

minus400

minus300

minus200

Img

(Zin

)

1 12 14 16 18 2 22 24 2608Frequency (GHz)

(b)



Zs


Rb minus Ra


1113971


(m + 1)βa

(4)



Z1 + jZL1 tan βal1( 1113857 (5)

ZL1 Z2ZL2 + jZ2 tan βbl2( 1113857

Z2 + jZL2f3 tan βbl2( 1113857 (6)


l l1 l2 1113937

βa + βb

(7)

Z41 + bZ

31 + cZ

21 + dZ1 + e 0 (8)

where

b 2aR0XL2

R0 minus RL2

c R0RL2 X2


1113872 1113873 minus X2L2R

20 1 + a2( 1113857

2


d 2aR3

0XL2

RL2 minus R0

e R30 R2

L2 + X2L2 minus R0RL2( 1113857

R0 minus RL2

(9)






Z1 + jZL1 tan υβal1( 1113857 G1 + jB1 (10)

where

υ f3

f1


Z2 + jZL2f3 tan βbl2( 1113857


Z3 + jZL3 tan υβal3( 1113857

(11)




0G21 tan υθ


+ Z0G1 tan υθ( 11138572

1113960 1113961

(12)



Z0B2( 11138572

+ 1 minus Z0G1( 1113857 Z20B

22 + Z2

0B22( 1113857 minus Z0G1

1113969

Z20B

22 + Z2

0B22 minus Z0G1( 1113857

(13)

Ya B3



Z0

Zin ZL1

Stage II Stage I

ZL2

ZL1 f1ZL2 f2

Z1 Z2 Z3l1 l2 l3



AntennaRectifier

+load

Compleximpedance

50 Ωantenna

impedance


Dual bandimpedance

matching network



θ1 (1 + s) 1113937

1 + r (15)

Za Zbtan2θ1 (16)


Zc Zdtan2θ1 (17)




Yin4 = 1Z0 f11Z0 f21Z0 f3

Yin3 = 1Z0 f11Z0 f2

G2 + jB3 f3

Yin2 = 1Z0 f11Z0 f2

G1 + jB2 f3

Yin1 = 1Z0 f11Z0 f2

G1 + jB1 f3

Zaθ1

θZb

Z0

Z0

θ1

Zdθ1

Zc

θ1

OCSC-2OCSC-1



043mm3767mm

216mm2395mm

092mm2158mm

103mm379mm

1618mm864mm

321mm2069mm

114mm

Z0

C1

C2

D2

D1

3538mm

10kΩRF source

Rectifier

(a)

(b)





ηRFminusDC PDC

Pin (18)






0ndash5


S 11 (

dB)

ndash35ndash40


16 18 2 22 24








80

70

60

50

40

30

20

10


RF-D

C co

nver

sion

effic

ienc

y (

)





RF source

Matchingnetwork


Z0 D1

D2C1

C2

500nH10kΩ

39pF

(a) (b)


S 11 (

dB)



minus35

minus30

minus25

minus20

minus15

minus10

minus5

0

90 92 94 96 98 100 102 104 106 10888Frequency (MHz)


SimulatedMeasured

0

20

40

60

80

100

RF-D

C co

nver

sion

effic

ienc

y (

)




Tribandrectenna

Z0

C1

C2

D2

D1

421mm3462mm

043mm3767mm

216mm2395mm

092mm2158mm

103mm379mm

1618mm864mm

500nH

321mm2069mm

114mm3538mm

Z0FMrectenna

39pF

C1

C2

D2

D1

+

ndash

10kΩ

Vdc

DCcombination

(a)

(b)


minus40

minus35

minus30

minus25

minus20

minus15

minus10

minus5

0

S 11 (

dB)

90 92 94 96 98 100 102 104 106 10888Frequency (MHz)



(a)

minus35

minus30

minus25

minus20

minus15

minus10

minus5

0

5

S 11 (

dB)

1 12 14 16 18 2 22 2408Frequency (GHz)



(b)





0

10

20

30

40

50

60

70

80

RF-D

C co

nver

sion

effici

ency

()



(a) (b)

(c)





PDC(dBm) 10logV2

DCRL

times 1031113888 1113889 (19)











10

20

30

40

50

60

70

80


RFminusD

C co

nver

sion

effici

ency

()



[19](09GHz)

[11](2GHz)

[13](09GHz)

[13]( 18 24GHz)

[36]

[14](185GHz)

[14](0915GHz)

[20] (17GHz)[20] (24GHz)


(a) (b) (c)

(d)



8 Conclusions


Data Availability




Acknowledgments


References






Ref(year)

Frequency(GHz)






multitone input()


(V)

[10](2016)

Six-band 055075 09 185



[11](2018)



[12](2017)



[13](2015)



[34](2018)




[35](2017)




06 at500 μWm2

[15](2013)







ltiswork(2019)

Four-band0098 09 18

24Dual LP










































Receivingantenna

RFcombination


Cstorage Load

(a)

Receivingantenna

Cstorage Load


DCcombination

(b)

Multibandantenna



CstorageLoad

DCcombination

RFcombination

Singleband

antenna

(c)



combinationunit

Multibanddipole










FMantenna

DCcombination



Measurementantenna





Wi AePT (1)






4 Antenna Design


Cellulartower

(nearest)

03 km

62 km

Lounge

Lab Lab

HallCorridor


FM source(nearest)

Outdoor grounds

Outdoor terrace

Measurement point

Wi-Fi source


OutdoorsIndoors

FM

GSM900

GSM1800

3G

Wi-FiBroad casting

minus70

minus60

minus50

minus40

minus30

minus20

minus10

0

Am

bien

t pow

er (d

Bm)







4 (2)











minus2841 345 minus8991 300 1848



minus601 0091 minus433 437 7385



minus51547 082 minus3107 919 1026



W1

L1

L2R2 R1W2

WnRn

θn

Ln









875 43 4 65 4878 8575 85711730 33 2 50 2879 4368 41672100 30 2 45 2356 3544 35712400 15 2 40 1047 2808 3125


(mm) (mm) (deg) (mm) (mm)100 50 80 4 16

S 11

(dB)


Step 3Step 4

minus14

minus12

minus10

minus8

minus6

minus4

minus2

0



Bow-tie crossdipole

Step 1 Step 2


Top metal

Botttom metal






Top metal

Botttom metal

WaWr

Ra

Rr

θa

(a)

Top metal

Coaxial cable


Substrate

(b)


SimulatedMeasured

S 11

(dB)

minus50

minus40

minus30

minus20

minus10

0

10



(a) (b) (c)



minus16

minus12

minus8

minus4

0

60

300

330

300

270

120

150

180210

240

90

minus16

minus12

minus8

minus4

0

60

300

330

300

270

120

150

180

210

240

90

SimulatedMeasured

(a)

minus16

minus12

minus8

minus4

0

60

300

330

300

270

120

150180

210

240

90

minus16

minus12

minus8

minus4

0

60

300

330

300

270

120

150180

210

240

90

SimulatedMeasured

(b)

minus16

minus12

minus8

minus4

0

60

300

330

300

270

120

150180

210

240

90

minus16

minus12

minus8

minus4

0

60

120

30

150

0

180

30

150

60

120

90 90

SimulatedMeasured

(c)



m LML

LT

(3)




Y



Rc

LG

LC

LT

LMT

LS

LML


SimulatedMeasured

minus30

minus25

minus20

minus15

minus10

minus5

0

S 11 (

dB)

95 100 105 11090Frequency (GHz)




Value (Ω) 9333 7816 6418 120 220 470






minus60

minus50

minus40

minus30

minus20

minus10

0M

agni

tude

(dB)


(a)



minus80

minus60

minus40

minus20

0

Mag

nitu

de (d

B)


(b)

Arg (S51 S41S31 S21)

minus200

minus100

0

100

200

Phas

e (de

g)


(c)


P1 P5

P4

P3

P2

R1R2

R3

Z1Z2Z3

(a) (b)

FMmonopoleantenna

Multibandantenna

cube

(c)




5 Rectifier Design










ndash10dBm0dBm

0

50

100

150

200

250

300

350

Real

(Zin

)

1 12 14 16 18 2 22 24 2608Frequency (GHz)

(a)


ndash10dBm0dBm

minus700

minus600

minus500

minus400

minus300

minus200

Img

(Zin

)

1 12 14 16 18 2 22 24 2608Frequency (GHz)

(b)



Zs


Rb minus Ra


1113971


(m + 1)βa

(4)



Z1 + jZL1 tan βal1( 1113857 (5)

ZL1 Z2ZL2 + jZ2 tan βbl2( 1113857

Z2 + jZL2f3 tan βbl2( 1113857 (6)


l l1 l2 1113937

βa + βb

(7)

Z41 + bZ

31 + cZ

21 + dZ1 + e 0 (8)

where

b 2aR0XL2

R0 minus RL2

c R0RL2 X2


1113872 1113873 minus X2L2R

20 1 + a2( 1113857

2


d 2aR3

0XL2

RL2 minus R0

e R30 R2

L2 + X2L2 minus R0RL2( 1113857

R0 minus RL2

(9)






Z1 + jZL1 tan υβal1( 1113857 G1 + jB1 (10)

where

υ f3

f1


Z2 + jZL2f3 tan βbl2( 1113857


Z3 + jZL3 tan υβal3( 1113857

(11)




0G21 tan υθ


+ Z0G1 tan υθ( 11138572

1113960 1113961

(12)



Z0B2( 11138572

+ 1 minus Z0G1( 1113857 Z20B

22 + Z2

0B22( 1113857 minus Z0G1

1113969

Z20B

22 + Z2

0B22 minus Z0G1( 1113857

(13)

Ya B3



Z0

Zin ZL1

Stage II Stage I

ZL2

ZL1 f1ZL2 f2

Z1 Z2 Z3l1 l2 l3



AntennaRectifier

+load

Compleximpedance

50 Ωantenna

impedance


Dual bandimpedance

matching network



θ1 (1 + s) 1113937

1 + r (15)

Za Zbtan2θ1 (16)


Zc Zdtan2θ1 (17)




Yin4 = 1Z0 f11Z0 f21Z0 f3

Yin3 = 1Z0 f11Z0 f2

G2 + jB3 f3

Yin2 = 1Z0 f11Z0 f2

G1 + jB2 f3

Yin1 = 1Z0 f11Z0 f2

G1 + jB1 f3

Zaθ1

θZb

Z0

Z0

θ1

Zdθ1

Zc

θ1

OCSC-2OCSC-1



043mm3767mm

216mm2395mm

092mm2158mm

103mm379mm

1618mm864mm

321mm2069mm

114mm

Z0

C1

C2

D2

D1

3538mm

10kΩRF source

Rectifier

(a)

(b)





ηRFminusDC PDC

Pin (18)






0ndash5


S 11 (

dB)

ndash35ndash40


16 18 2 22 24








80

70

60

50

40

30

20

10


RF-D

C co

nver

sion

effic

ienc

y (

)





RF source

Matchingnetwork


Z0 D1

D2C1

C2

500nH10kΩ

39pF

(a) (b)


S 11 (

dB)



minus35

minus30

minus25

minus20

minus15

minus10

minus5

0

90 92 94 96 98 100 102 104 106 10888Frequency (MHz)


SimulatedMeasured

0

20

40

60

80

100

RF-D

C co

nver

sion

effic

ienc

y (

)




Tribandrectenna

Z0

C1

C2

D2

D1

421mm3462mm

043mm3767mm

216mm2395mm

092mm2158mm

103mm379mm

1618mm864mm

500nH

321mm2069mm

114mm3538mm

Z0FMrectenna

39pF

C1

C2

D2

D1

+

ndash

10kΩ

Vdc

DCcombination

(a)

(b)


minus40

minus35

minus30

minus25

minus20

minus15

minus10

minus5

0

S 11 (

dB)

90 92 94 96 98 100 102 104 106 10888Frequency (MHz)



(a)

minus35

minus30

minus25

minus20

minus15

minus10

minus5

0

5

S 11 (

dB)

1 12 14 16 18 2 22 2408Frequency (GHz)



(b)





0

10

20

30

40

50

60

70

80

RF-D

C co

nver

sion

effici

ency

()



(a) (b)

(c)





PDC(dBm) 10logV2

DCRL

times 1031113888 1113889 (19)











10

20

30

40

50

60

70

80


RFminusD

C co

nver

sion

effici

ency

()



[19](09GHz)

[11](2GHz)

[13](09GHz)

[13]( 18 24GHz)

[36]

[14](185GHz)

[14](0915GHz)

[20] (17GHz)[20] (24GHz)


(a) (b) (c)

(d)



8 Conclusions


Data Availability




Acknowledgments


References






Ref(year)

Frequency(GHz)






multitone input()


(V)

[10](2016)

Six-band 055075 09 185



[11](2018)



[12](2017)



[13](2015)



[34](2018)




[35](2017)




06 at500 μWm2

[15](2013)







ltiswork(2019)

Four-band0098 09 18

24Dual LP














































FMantenna

DCcombination



Measurementantenna





Wi AePT (1)






4 Antenna Design


Cellulartower

(nearest)

03 km

62 km

Lounge

Lab Lab

HallCorridor


FM source(nearest)

Outdoor grounds

Outdoor terrace

Measurement point

Wi-Fi source


OutdoorsIndoors

FM

GSM900

GSM1800

3G

Wi-FiBroad casting

minus70

minus60

minus50

minus40

minus30

minus20

minus10

0

Am

bien

t pow

er (d

Bm)







4 (2)











minus2841 345 minus8991 300 1848



minus601 0091 minus433 437 7385



minus51547 082 minus3107 919 1026



W1

L1

L2R2 R1W2

WnRn

θn

Ln









875 43 4 65 4878 8575 85711730 33 2 50 2879 4368 41672100 30 2 45 2356 3544 35712400 15 2 40 1047 2808 3125


(mm) (mm) (deg) (mm) (mm)100 50 80 4 16

S 11

(dB)


Step 3Step 4

minus14

minus12

minus10

minus8

minus6

minus4

minus2

0



Bow-tie crossdipole

Step 1 Step 2


Top metal

Botttom metal






Top metal

Botttom metal

WaWr

Ra

Rr

θa

(a)

Top metal

Coaxial cable


Substrate

(b)


SimulatedMeasured

S 11

(dB)

minus50

minus40

minus30

minus20

minus10

0

10



(a) (b) (c)



minus16

minus12

minus8

minus4

0

60

300

330

300

270

120

150

180210

240

90

minus16

minus12

minus8

minus4

0

60

300

330

300

270

120

150

180

210

240

90

SimulatedMeasured

(a)

minus16

minus12

minus8

minus4

0

60

300

330

300

270

120

150180

210

240

90

minus16

minus12

minus8

minus4

0

60

300

330

300

270

120

150180

210

240

90

SimulatedMeasured

(b)

minus16

minus12

minus8

minus4

0

60

300

330

300

270

120

150180

210

240

90

minus16

minus12

minus8

minus4

0

60

120

30

150

0

180

30

150

60

120

90 90

SimulatedMeasured

(c)



m LML

LT

(3)




Y



Rc

LG

LC

LT

LMT

LS

LML


SimulatedMeasured

minus30

minus25

minus20

minus15

minus10

minus5

0

S 11 (

dB)

95 100 105 11090Frequency (GHz)




Value (Ω) 9333 7816 6418 120 220 470






minus60

minus50

minus40

minus30

minus20

minus10

0M

agni

tude

(dB)


(a)



minus80

minus60

minus40

minus20

0

Mag

nitu

de (d

B)


(b)

Arg (S51 S41S31 S21)

minus200

minus100

0

100

200

Phas

e (de

g)


(c)


P1 P5

P4

P3

P2

R1R2

R3

Z1Z2Z3

(a) (b)

FMmonopoleantenna

Multibandantenna

cube

(c)




5 Rectifier Design










ndash10dBm0dBm

0

50

100

150

200

250

300

350

Real

(Zin

)

1 12 14 16 18 2 22 24 2608Frequency (GHz)

(a)


ndash10dBm0dBm

minus700

minus600

minus500

minus400

minus300

minus200

Img

(Zin

)

1 12 14 16 18 2 22 24 2608Frequency (GHz)

(b)



Zs


Rb minus Ra


1113971


(m + 1)βa

(4)



Z1 + jZL1 tan βal1( 1113857 (5)

ZL1 Z2ZL2 + jZ2 tan βbl2( 1113857

Z2 + jZL2f3 tan βbl2( 1113857 (6)


l l1 l2 1113937

βa + βb

(7)

Z41 + bZ

31 + cZ

21 + dZ1 + e 0 (8)

where

b 2aR0XL2

R0 minus RL2

c R0RL2 X2


1113872 1113873 minus X2L2R

20 1 + a2( 1113857

2


d 2aR3

0XL2

RL2 minus R0

e R30 R2

L2 + X2L2 minus R0RL2( 1113857

R0 minus RL2

(9)






Z1 + jZL1 tan υβal1( 1113857 G1 + jB1 (10)

where

υ f3

f1


Z2 + jZL2f3 tan βbl2( 1113857


Z3 + jZL3 tan υβal3( 1113857

(11)




0G21 tan υθ


+ Z0G1 tan υθ( 11138572

1113960 1113961

(12)



Z0B2( 11138572

+ 1 minus Z0G1( 1113857 Z20B

22 + Z2

0B22( 1113857 minus Z0G1

1113969

Z20B

22 + Z2

0B22 minus Z0G1( 1113857

(13)

Ya B3



Z0

Zin ZL1

Stage II Stage I

ZL2

ZL1 f1ZL2 f2

Z1 Z2 Z3l1 l2 l3



AntennaRectifier

+load

Compleximpedance

50 Ωantenna

impedance


Dual bandimpedance

matching network



θ1 (1 + s) 1113937

1 + r (15)

Za Zbtan2θ1 (16)


Zc Zdtan2θ1 (17)




Yin4 = 1Z0 f11Z0 f21Z0 f3

Yin3 = 1Z0 f11Z0 f2

G2 + jB3 f3

Yin2 = 1Z0 f11Z0 f2

G1 + jB2 f3

Yin1 = 1Z0 f11Z0 f2

G1 + jB1 f3

Zaθ1

θZb

Z0

Z0

θ1

Zdθ1

Zc

θ1

OCSC-2OCSC-1



043mm3767mm

216mm2395mm

092mm2158mm

103mm379mm

1618mm864mm

321mm2069mm

114mm

Z0

C1

C2

D2

D1

3538mm

10kΩRF source

Rectifier

(a)

(b)





ηRFminusDC PDC

Pin (18)






0ndash5


S 11 (

dB)

ndash35ndash40


16 18 2 22 24








80

70

60

50

40

30

20

10


RF-D

C co

nver

sion

effic

ienc

y (

)





RF source

Matchingnetwork


Z0 D1

D2C1

C2

500nH10kΩ

39pF

(a) (b)


S 11 (

dB)



minus35

minus30

minus25

minus20

minus15

minus10

minus5

0

90 92 94 96 98 100 102 104 106 10888Frequency (MHz)


SimulatedMeasured

0

20

40

60

80

100

RF-D

C co

nver

sion

effic

ienc

y (

)




Tribandrectenna

Z0

C1

C2

D2

D1

421mm3462mm

043mm3767mm

216mm2395mm

092mm2158mm

103mm379mm

1618mm864mm

500nH

321mm2069mm

114mm3538mm

Z0FMrectenna

39pF

C1

C2

D2

D1

+

ndash

10kΩ

Vdc

DCcombination

(a)

(b)


minus40

minus35

minus30

minus25

minus20

minus15

minus10

minus5

0

S 11 (

dB)

90 92 94 96 98 100 102 104 106 10888Frequency (MHz)



(a)

minus35

minus30

minus25

minus20

minus15

minus10

minus5

0

5

S 11 (

dB)

1 12 14 16 18 2 22 2408Frequency (GHz)



(b)





0

10

20

30

40

50

60

70

80

RF-D

C co

nver

sion

effici

ency

()



(a) (b)

(c)





PDC(dBm) 10logV2

DCRL

times 1031113888 1113889 (19)











10

20

30

40

50

60

70

80


RFminusD

C co

nver

sion

effici

ency

()



[19](09GHz)

[11](2GHz)

[13](09GHz)

[13]( 18 24GHz)

[36]

[14](185GHz)

[14](0915GHz)

[20] (17GHz)[20] (24GHz)


(a) (b) (c)

(d)



8 Conclusions


Data Availability




Acknowledgments


References






Ref(year)

Frequency(GHz)






multitone input()


(V)

[10](2016)

Six-band 055075 09 185



[11](2018)



[12](2017)



[13](2015)



[34](2018)




[35](2017)




06 at500 μWm2

[15](2013)







ltiswork(2019)

Four-band0098 09 18

24Dual LP









































Wi AePT (1)






4 Antenna Design


Cellulartower

(nearest)

03 km

62 km

Lounge

Lab Lab

HallCorridor


FM source(nearest)

Outdoor grounds

Outdoor terrace

Measurement point

Wi-Fi source


OutdoorsIndoors

FM

GSM900

GSM1800

3G

Wi-FiBroad casting

minus70

minus60

minus50

minus40

minus30

minus20

minus10

0

Am

bien

t pow

er (d

Bm)







4 (2)











minus2841 345 minus8991 300 1848



minus601 0091 minus433 437 7385



minus51547 082 minus3107 919 1026



W1

L1

L2R2 R1W2

WnRn

θn

Ln









875 43 4 65 4878 8575 85711730 33 2 50 2879 4368 41672100 30 2 45 2356 3544 35712400 15 2 40 1047 2808 3125


(mm) (mm) (deg) (mm) (mm)100 50 80 4 16

S 11

(dB)


Step 3Step 4

minus14

minus12

minus10

minus8

minus6

minus4

minus2

0



Bow-tie crossdipole

Step 1 Step 2


Top metal

Botttom metal






Top metal

Botttom metal

WaWr

Ra

Rr

θa

(a)

Top metal

Coaxial cable


Substrate

(b)


SimulatedMeasured

S 11

(dB)

minus50

minus40

minus30

minus20

minus10

0

10



(a) (b) (c)



minus16

minus12

minus8

minus4

0

60

300

330

300

270

120

150

180210

240

90

minus16

minus12

minus8

minus4

0

60

300

330

300

270

120

150

180

210

240

90

SimulatedMeasured

(a)

minus16

minus12

minus8

minus4

0

60

300

330

300

270

120

150180

210

240

90

minus16

minus12

minus8

minus4

0

60

300

330

300

270

120

150180

210

240

90

SimulatedMeasured

(b)

minus16

minus12

minus8

minus4

0

60

300

330

300

270

120

150180

210

240

90

minus16

minus12

minus8

minus4

0

60

120

30

150

0

180

30

150

60

120

90 90

SimulatedMeasured

(c)



m LML

LT

(3)




Y



Rc

LG

LC

LT

LMT

LS

LML


SimulatedMeasured

minus30

minus25

minus20

minus15

minus10

minus5

0

S 11 (

dB)

95 100 105 11090Frequency (GHz)




Value (Ω) 9333 7816 6418 120 220 470






minus60

minus50

minus40

minus30

minus20

minus10

0M

agni

tude

(dB)


(a)



minus80

minus60

minus40

minus20

0

Mag

nitu

de (d

B)


(b)

Arg (S51 S41S31 S21)

minus200

minus100

0

100

200

Phas

e (de

g)


(c)


P1 P5

P4

P3

P2

R1R2

R3

Z1Z2Z3

(a) (b)

FMmonopoleantenna

Multibandantenna

cube

(c)




5 Rectifier Design










ndash10dBm0dBm

0

50

100

150

200

250

300

350

Real

(Zin

)

1 12 14 16 18 2 22 24 2608Frequency (GHz)

(a)


ndash10dBm0dBm

minus700

minus600

minus500

minus400

minus300

minus200

Img

(Zin

)

1 12 14 16 18 2 22 24 2608Frequency (GHz)

(b)



Zs


Rb minus Ra


1113971


(m + 1)βa

(4)



Z1 + jZL1 tan βal1( 1113857 (5)

ZL1 Z2ZL2 + jZ2 tan βbl2( 1113857

Z2 + jZL2f3 tan βbl2( 1113857 (6)


l l1 l2 1113937

βa + βb

(7)

Z41 + bZ

31 + cZ

21 + dZ1 + e 0 (8)

where

b 2aR0XL2

R0 minus RL2

c R0RL2 X2


1113872 1113873 minus X2L2R

20 1 + a2( 1113857

2


d 2aR3

0XL2

RL2 minus R0

e R30 R2

L2 + X2L2 minus R0RL2( 1113857

R0 minus RL2

(9)






Z1 + jZL1 tan υβal1( 1113857 G1 + jB1 (10)

where

υ f3

f1


Z2 + jZL2f3 tan βbl2( 1113857


Z3 + jZL3 tan υβal3( 1113857

(11)




0G21 tan υθ


+ Z0G1 tan υθ( 11138572

1113960 1113961

(12)



Z0B2( 11138572

+ 1 minus Z0G1( 1113857 Z20B

22 + Z2

0B22( 1113857 minus Z0G1

1113969

Z20B

22 + Z2

0B22 minus Z0G1( 1113857

(13)

Ya B3



Z0

Zin ZL1

Stage II Stage I

ZL2

ZL1 f1ZL2 f2

Z1 Z2 Z3l1 l2 l3



AntennaRectifier

+load

Compleximpedance

50 Ωantenna

impedance


Dual bandimpedance

matching network



θ1 (1 + s) 1113937

1 + r (15)

Za Zbtan2θ1 (16)


Zc Zdtan2θ1 (17)




Yin4 = 1Z0 f11Z0 f21Z0 f3

Yin3 = 1Z0 f11Z0 f2

G2 + jB3 f3

Yin2 = 1Z0 f11Z0 f2

G1 + jB2 f3

Yin1 = 1Z0 f11Z0 f2

G1 + jB1 f3

Zaθ1

θZb

Z0

Z0

θ1

Zdθ1

Zc

θ1

OCSC-2OCSC-1



043mm3767mm

216mm2395mm

092mm2158mm

103mm379mm

1618mm864mm

321mm2069mm

114mm

Z0

C1

C2

D2

D1

3538mm

10kΩRF source

Rectifier

(a)

(b)





ηRFminusDC PDC

Pin (18)






0ndash5


S 11 (

dB)

ndash35ndash40


16 18 2 22 24








80

70

60

50

40

30

20

10


RF-D

C co

nver

sion

effic

ienc

y (

)





RF source

Matchingnetwork


Z0 D1

D2C1

C2

500nH10kΩ

39pF

(a) (b)


S 11 (

dB)



minus35

minus30

minus25

minus20

minus15

minus10

minus5

0

90 92 94 96 98 100 102 104 106 10888Frequency (MHz)


SimulatedMeasured

0

20

40

60

80

100

RF-D

C co

nver

sion

effic

ienc

y (

)




Tribandrectenna

Z0

C1

C2

D2

D1

421mm3462mm

043mm3767mm

216mm2395mm

092mm2158mm

103mm379mm

1618mm864mm

500nH

321mm2069mm

114mm3538mm

Z0FMrectenna

39pF

C1

C2

D2

D1

+

ndash

10kΩ

Vdc

DCcombination

(a)

(b)


minus40

minus35

minus30

minus25

minus20

minus15

minus10

minus5

0

S 11 (

dB)

90 92 94 96 98 100 102 104 106 10888Frequency (MHz)



(a)

minus35

minus30

minus25

minus20

minus15

minus10

minus5

0

5

S 11 (

dB)

1 12 14 16 18 2 22 2408Frequency (GHz)



(b)





0

10

20

30

40

50

60

70

80

RF-D

C co

nver

sion

effici

ency

()



(a) (b)

(c)





PDC(dBm) 10logV2

DCRL

times 1031113888 1113889 (19)











10

20

30

40

50

60

70

80


RFminusD

C co

nver

sion

effici

ency

()



[19](09GHz)

[11](2GHz)

[13](09GHz)

[13]( 18 24GHz)

[36]

[14](185GHz)

[14](0915GHz)

[20] (17GHz)[20] (24GHz)


(a) (b) (c)

(d)



8 Conclusions


Data Availability




Acknowledgments


References






Ref(year)

Frequency(GHz)






multitone input()


(V)

[10](2016)

Six-band 055075 09 185



[11](2018)



[12](2017)



[13](2015)



[34](2018)




[35](2017)




06 at500 μWm2

[15](2013)







ltiswork(2019)

Four-band0098 09 18

24Dual LP











































4 (2)











minus2841 345 minus8991 300 1848



minus601 0091 minus433 437 7385



minus51547 082 minus3107 919 1026



W1

L1

L2R2 R1W2

WnRn

θn

Ln









875 43 4 65 4878 8575 85711730 33 2 50 2879 4368 41672100 30 2 45 2356 3544 35712400 15 2 40 1047 2808 3125


(mm) (mm) (deg) (mm) (mm)100 50 80 4 16

S 11

(dB)


Step 3Step 4

minus14

minus12

minus10

minus8

minus6

minus4

minus2

0



Bow-tie crossdipole

Step 1 Step 2


Top metal

Botttom metal






Top metal

Botttom metal

WaWr

Ra

Rr

θa

(a)

Top metal

Coaxial cable


Substrate

(b)


SimulatedMeasured

S 11

(dB)

minus50

minus40

minus30

minus20

minus10

0

10



(a) (b) (c)



minus16

minus12

minus8

minus4

0

60

300

330

300

270

120

150

180210

240

90

minus16

minus12

minus8

minus4

0

60

300

330

300

270

120

150

180

210

240

90

SimulatedMeasured

(a)

minus16

minus12

minus8

minus4

0

60

300

330

300

270

120

150180

210

240

90

minus16

minus12

minus8

minus4

0

60

300

330

300

270

120

150180

210

240

90

SimulatedMeasured

(b)

minus16

minus12

minus8

minus4

0

60

300

330

300

270

120

150180

210

240

90

minus16

minus12

minus8

minus4

0

60

120

30

150

0

180

30

150

60

120

90 90

SimulatedMeasured

(c)



m LML

LT

(3)




Y



Rc

LG

LC

LT

LMT

LS

LML


SimulatedMeasured

minus30

minus25

minus20

minus15

minus10

minus5

0

S 11 (

dB)

95 100 105 11090Frequency (GHz)




Value (Ω) 9333 7816 6418 120 220 470






minus60

minus50

minus40

minus30

minus20

minus10

0M

agni

tude

(dB)


(a)



minus80

minus60

minus40

minus20

0

Mag

nitu

de (d

B)


(b)

Arg (S51 S41S31 S21)

minus200

minus100

0

100

200

Phas

e (de

g)


(c)


P1 P5

P4

P3

P2

R1R2

R3

Z1Z2Z3

(a) (b)

FMmonopoleantenna

Multibandantenna

cube

(c)




5 Rectifier Design










ndash10dBm0dBm

0

50

100

150

200

250

300

350

Real

(Zin

)

1 12 14 16 18 2 22 24 2608Frequency (GHz)

(a)


ndash10dBm0dBm

minus700

minus600

minus500

minus400

minus300

minus200

Img

(Zin

)

1 12 14 16 18 2 22 24 2608Frequency (GHz)

(b)



Zs


Rb minus Ra


1113971


(m + 1)βa

(4)



Z1 + jZL1 tan βal1( 1113857 (5)

ZL1 Z2ZL2 + jZ2 tan βbl2( 1113857

Z2 + jZL2f3 tan βbl2( 1113857 (6)


l l1 l2 1113937

βa + βb

(7)

Z41 + bZ

31 + cZ

21 + dZ1 + e 0 (8)

where

b 2aR0XL2

R0 minus RL2

c R0RL2 X2


1113872 1113873 minus X2L2R

20 1 + a2( 1113857

2


d 2aR3

0XL2

RL2 minus R0

e R30 R2

L2 + X2L2 minus R0RL2( 1113857

R0 minus RL2

(9)






Z1 + jZL1 tan υβal1( 1113857 G1 + jB1 (10)

where

υ f3

f1


Z2 + jZL2f3 tan βbl2( 1113857


Z3 + jZL3 tan υβal3( 1113857

(11)




0G21 tan υθ


+ Z0G1 tan υθ( 11138572

1113960 1113961

(12)



Z0B2( 11138572

+ 1 minus Z0G1( 1113857 Z20B

22 + Z2

0B22( 1113857 minus Z0G1

1113969

Z20B

22 + Z2

0B22 minus Z0G1( 1113857

(13)

Ya B3



Z0

Zin ZL1

Stage II Stage I

ZL2

ZL1 f1ZL2 f2

Z1 Z2 Z3l1 l2 l3



AntennaRectifier

+load

Compleximpedance

50 Ωantenna

impedance


Dual bandimpedance

matching network



θ1 (1 + s) 1113937

1 + r (15)

Za Zbtan2θ1 (16)


Zc Zdtan2θ1 (17)




Yin4 = 1Z0 f11Z0 f21Z0 f3

Yin3 = 1Z0 f11Z0 f2

G2 + jB3 f3

Yin2 = 1Z0 f11Z0 f2

G1 + jB2 f3

Yin1 = 1Z0 f11Z0 f2

G1 + jB1 f3

Zaθ1

θZb

Z0

Z0

θ1

Zdθ1

Zc

θ1

OCSC-2OCSC-1



043mm3767mm

216mm2395mm

092mm2158mm

103mm379mm

1618mm864mm

321mm2069mm

114mm

Z0

C1

C2

D2

D1

3538mm

10kΩRF source

Rectifier

(a)

(b)





ηRFminusDC PDC

Pin (18)






0ndash5


S 11 (

dB)

ndash35ndash40


16 18 2 22 24








80

70

60

50

40

30

20

10


RF-D

C co

nver

sion

effic

ienc

y (

)





RF source

Matchingnetwork


Z0 D1

D2C1

C2

500nH10kΩ

39pF

(a) (b)


S 11 (

dB)



minus35

minus30

minus25

minus20

minus15

minus10

minus5

0

90 92 94 96 98 100 102 104 106 10888Frequency (MHz)


SimulatedMeasured

0

20

40

60

80

100

RF-D

C co

nver

sion

effic

ienc

y (

)




Tribandrectenna

Z0

C1

C2

D2

D1

421mm3462mm

043mm3767mm

216mm2395mm

092mm2158mm

103mm379mm

1618mm864mm

500nH

321mm2069mm

114mm3538mm

Z0FMrectenna

39pF

C1

C2

D2

D1

+

ndash

10kΩ

Vdc

DCcombination

(a)

(b)


minus40

minus35

minus30

minus25

minus20

minus15

minus10

minus5

0

S 11 (

dB)

90 92 94 96 98 100 102 104 106 10888Frequency (MHz)



(a)

minus35

minus30

minus25

minus20

minus15

minus10

minus5

0

5

S 11 (

dB)

1 12 14 16 18 2 22 2408Frequency (GHz)



(b)





0

10

20

30

40

50

60

70

80

RF-D

C co

nver

sion

effici

ency

()



(a) (b)

(c)





PDC(dBm) 10logV2

DCRL

times 1031113888 1113889 (19)











10

20

30

40

50

60

70

80


RFminusD

C co

nver

sion

effici

ency

()



[19](09GHz)

[11](2GHz)

[13](09GHz)

[13]( 18 24GHz)

[36]

[14](185GHz)

[14](0915GHz)

[20] (17GHz)[20] (24GHz)


(a) (b) (c)

(d)



8 Conclusions


Data Availability




Acknowledgments


References






Ref(year)

Frequency(GHz)






multitone input()


(V)

[10](2016)

Six-band 055075 09 185



[11](2018)



[12](2017)



[13](2015)



[34](2018)




[35](2017)




06 at500 μWm2

[15](2013)







ltiswork(2019)

Four-band0098 09 18

24Dual LP














































875 43 4 65 4878 8575 85711730 33 2 50 2879 4368 41672100 30 2 45 2356 3544 35712400 15 2 40 1047 2808 3125


(mm) (mm) (deg) (mm) (mm)100 50 80 4 16

S 11

(dB)


Step 3Step 4

minus14

minus12

minus10

minus8

minus6

minus4

minus2

0



Bow-tie crossdipole

Step 1 Step 2


Top metal

Botttom metal






Top metal

Botttom metal

WaWr

Ra

Rr

θa

(a)

Top metal

Coaxial cable


Substrate

(b)


SimulatedMeasured

S 11

(dB)

minus50

minus40

minus30

minus20

minus10

0

10



(a) (b) (c)



minus16

minus12

minus8

minus4

0

60

300

330

300

270

120

150

180210

240

90

minus16

minus12

minus8

minus4

0

60

300

330

300

270

120

150

180

210

240

90

SimulatedMeasured

(a)

minus16

minus12

minus8

minus4

0

60

300

330

300

270

120

150180

210

240

90

minus16

minus12

minus8

minus4

0

60

300

330

300

270

120

150180

210

240

90

SimulatedMeasured

(b)

minus16

minus12

minus8

minus4

0

60

300

330

300

270

120

150180

210

240

90

minus16

minus12

minus8

minus4

0

60

120

30

150

0

180

30

150

60

120

90 90

SimulatedMeasured

(c)



m LML

LT

(3)




Y



Rc

LG

LC

LT

LMT

LS

LML


SimulatedMeasured

minus30

minus25

minus20

minus15

minus10

minus5

0

S 11 (

dB)

95 100 105 11090Frequency (GHz)




Value (Ω) 9333 7816 6418 120 220 470






minus60

minus50

minus40

minus30

minus20

minus10

0M

agni

tude

(dB)


(a)



minus80

minus60

minus40

minus20

0

Mag

nitu

de (d

B)


(b)

Arg (S51 S41S31 S21)

minus200

minus100

0

100

200

Phas

e (de

g)


(c)


P1 P5

P4

P3

P2

R1R2

R3

Z1Z2Z3

(a) (b)

FMmonopoleantenna

Multibandantenna

cube

(c)




5 Rectifier Design










ndash10dBm0dBm

0

50

100

150

200

250

300

350

Real

(Zin

)

1 12 14 16 18 2 22 24 2608Frequency (GHz)

(a)


ndash10dBm0dBm

minus700

minus600

minus500

minus400

minus300

minus200

Img

(Zin

)

1 12 14 16 18 2 22 24 2608Frequency (GHz)

(b)



Zs


Rb minus Ra


1113971


(m + 1)βa

(4)



Z1 + jZL1 tan βal1( 1113857 (5)

ZL1 Z2ZL2 + jZ2 tan βbl2( 1113857

Z2 + jZL2f3 tan βbl2( 1113857 (6)


l l1 l2 1113937

βa + βb

(7)

Z41 + bZ

31 + cZ

21 + dZ1 + e 0 (8)

where

b 2aR0XL2

R0 minus RL2

c R0RL2 X2


1113872 1113873 minus X2L2R

20 1 + a2( 1113857

2


d 2aR3

0XL2

RL2 minus R0

e R30 R2

L2 + X2L2 minus R0RL2( 1113857

R0 minus RL2

(9)






Z1 + jZL1 tan υβal1( 1113857 G1 + jB1 (10)

where

υ f3

f1


Z2 + jZL2f3 tan βbl2( 1113857


Z3 + jZL3 tan υβal3( 1113857

(11)




0G21 tan υθ


+ Z0G1 tan υθ( 11138572

1113960 1113961

(12)



Z0B2( 11138572

+ 1 minus Z0G1( 1113857 Z20B

22 + Z2

0B22( 1113857 minus Z0G1

1113969

Z20B

22 + Z2

0B22 minus Z0G1( 1113857

(13)

Ya B3



Z0

Zin ZL1

Stage II Stage I

ZL2

ZL1 f1ZL2 f2

Z1 Z2 Z3l1 l2 l3



AntennaRectifier

+load

Compleximpedance

50 Ωantenna

impedance


Dual bandimpedance

matching network



θ1 (1 + s) 1113937

1 + r (15)

Za Zbtan2θ1 (16)


Zc Zdtan2θ1 (17)




Yin4 = 1Z0 f11Z0 f21Z0 f3

Yin3 = 1Z0 f11Z0 f2

G2 + jB3 f3

Yin2 = 1Z0 f11Z0 f2

G1 + jB2 f3

Yin1 = 1Z0 f11Z0 f2

G1 + jB1 f3

Zaθ1

θZb

Z0

Z0

θ1

Zdθ1

Zc

θ1

OCSC-2OCSC-1



043mm3767mm

216mm2395mm

092mm2158mm

103mm379mm

1618mm864mm

321mm2069mm

114mm

Z0

C1

C2

D2

D1

3538mm

10kΩRF source

Rectifier

(a)

(b)





ηRFminusDC PDC

Pin (18)






0ndash5


S 11 (

dB)

ndash35ndash40


16 18 2 22 24








80

70

60

50

40

30

20

10


RF-D

C co

nver

sion

effic

ienc

y (

)





RF source

Matchingnetwork


Z0 D1

D2C1

C2

500nH10kΩ

39pF

(a) (b)


S 11 (

dB)



minus35

minus30

minus25

minus20

minus15

minus10

minus5

0

90 92 94 96 98 100 102 104 106 10888Frequency (MHz)


SimulatedMeasured

0

20

40

60

80

100

RF-D

C co

nver

sion

effic

ienc

y (

)




Tribandrectenna

Z0

C1

C2

D2

D1

421mm3462mm

043mm3767mm

216mm2395mm

092mm2158mm

103mm379mm

1618mm864mm

500nH

321mm2069mm

114mm3538mm

Z0FMrectenna

39pF

C1

C2

D2

D1

+

ndash

10kΩ

Vdc

DCcombination

(a)

(b)


minus40

minus35

minus30

minus25

minus20

minus15

minus10

minus5

0

S 11 (

dB)

90 92 94 96 98 100 102 104 106 10888Frequency (MHz)



(a)

minus35

minus30

minus25

minus20

minus15

minus10

minus5

0

5

S 11 (

dB)

1 12 14 16 18 2 22 2408Frequency (GHz)



(b)





0

10

20

30

40

50

60

70

80

RF-D

C co

nver

sion

effici

ency

()



(a) (b)

(c)





PDC(dBm) 10logV2

DCRL

times 1031113888 1113889 (19)











10

20

30

40

50

60

70

80


RFminusD

C co

nver

sion

effici

ency

()



[19](09GHz)

[11](2GHz)

[13](09GHz)

[13]( 18 24GHz)

[36]

[14](185GHz)

[14](0915GHz)

[20] (17GHz)[20] (24GHz)


(a) (b) (c)

(d)



8 Conclusions


Data Availability




Acknowledgments


References






Ref(year)

Frequency(GHz)






multitone input()


(V)

[10](2016)

Six-band 055075 09 185



[11](2018)



[12](2017)



[13](2015)



[34](2018)




[35](2017)




06 at500 μWm2

[15](2013)







ltiswork(2019)

Four-band0098 09 18

24Dual LP











































Top metal

Botttom metal

WaWr

Ra

Rr

θa

(a)

Top metal

Coaxial cable


Substrate

(b)


SimulatedMeasured

S 11

(dB)

minus50

minus40

minus30

minus20

minus10

0

10



(a) (b) (c)



minus16

minus12

minus8

minus4

0

60

300

330

300

270

120

150

180210

240

90

minus16

minus12

minus8

minus4

0

60

300

330

300

270

120

150

180

210

240

90

SimulatedMeasured

(a)

minus16

minus12

minus8

minus4

0

60

300

330

300

270

120

150180

210

240

90

minus16

minus12

minus8

minus4

0

60

300

330

300

270

120

150180

210

240

90

SimulatedMeasured

(b)

minus16

minus12

minus8

minus4

0

60

300

330

300

270

120

150180

210

240

90

minus16

minus12

minus8

minus4

0

60

120

30

150

0

180

30

150

60

120

90 90

SimulatedMeasured

(c)



m LML

LT

(3)




Y



Rc

LG

LC

LT

LMT

LS

LML


SimulatedMeasured

minus30

minus25

minus20

minus15

minus10

minus5

0

S 11 (

dB)

95 100 105 11090Frequency (GHz)




Value (Ω) 9333 7816 6418 120 220 470






minus60

minus50

minus40

minus30

minus20

minus10

0M

agni

tude

(dB)


(a)



minus80

minus60

minus40

minus20

0

Mag

nitu

de (d

B)


(b)

Arg (S51 S41S31 S21)

minus200

minus100

0

100

200

Phas

e (de

g)


(c)


P1 P5

P4

P3

P2

R1R2

R3

Z1Z2Z3

(a) (b)

FMmonopoleantenna

Multibandantenna

cube

(c)




5 Rectifier Design










ndash10dBm0dBm

0

50

100

150

200

250

300

350

Real

(Zin

)

1 12 14 16 18 2 22 24 2608Frequency (GHz)

(a)


ndash10dBm0dBm

minus700

minus600

minus500

minus400

minus300

minus200

Img

(Zin

)

1 12 14 16 18 2 22 24 2608Frequency (GHz)

(b)



Zs


Rb minus Ra


1113971


(m + 1)βa

(4)



Z1 + jZL1 tan βal1( 1113857 (5)

ZL1 Z2ZL2 + jZ2 tan βbl2( 1113857

Z2 + jZL2f3 tan βbl2( 1113857 (6)


l l1 l2 1113937

βa + βb

(7)

Z41 + bZ

31 + cZ

21 + dZ1 + e 0 (8)

where

b 2aR0XL2

R0 minus RL2

c R0RL2 X2


1113872 1113873 minus X2L2R

20 1 + a2( 1113857

2


d 2aR3

0XL2

RL2 minus R0

e R30 R2

L2 + X2L2 minus R0RL2( 1113857

R0 minus RL2

(9)






Z1 + jZL1 tan υβal1( 1113857 G1 + jB1 (10)

where

υ f3

f1


Z2 + jZL2f3 tan βbl2( 1113857


Z3 + jZL3 tan υβal3( 1113857

(11)




0G21 tan υθ


+ Z0G1 tan υθ( 11138572

1113960 1113961

(12)



Z0B2( 11138572

+ 1 minus Z0G1( 1113857 Z20B

22 + Z2

0B22( 1113857 minus Z0G1

1113969

Z20B

22 + Z2

0B22 minus Z0G1( 1113857

(13)

Ya B3



Z0

Zin ZL1

Stage II Stage I

ZL2

ZL1 f1ZL2 f2

Z1 Z2 Z3l1 l2 l3



AntennaRectifier

+load

Compleximpedance

50 Ωantenna

impedance


Dual bandimpedance

matching network



θ1 (1 + s) 1113937

1 + r (15)

Za Zbtan2θ1 (16)


Zc Zdtan2θ1 (17)




Yin4 = 1Z0 f11Z0 f21Z0 f3

Yin3 = 1Z0 f11Z0 f2

G2 + jB3 f3

Yin2 = 1Z0 f11Z0 f2

G1 + jB2 f3

Yin1 = 1Z0 f11Z0 f2

G1 + jB1 f3

Zaθ1

θZb

Z0

Z0

θ1

Zdθ1

Zc

θ1

OCSC-2OCSC-1



043mm3767mm

216mm2395mm

092mm2158mm

103mm379mm

1618mm864mm

321mm2069mm

114mm

Z0

C1

C2

D2

D1

3538mm

10kΩRF source

Rectifier

(a)

(b)





ηRFminusDC PDC

Pin (18)






0ndash5


S 11 (

dB)

ndash35ndash40


16 18 2 22 24








80

70

60

50

40

30

20

10


RF-D

C co

nver

sion

effic

ienc

y (

)





RF source

Matchingnetwork


Z0 D1

D2C1

C2

500nH10kΩ

39pF

(a) (b)


S 11 (

dB)



minus35

minus30

minus25

minus20

minus15

minus10

minus5

0

90 92 94 96 98 100 102 104 106 10888Frequency (MHz)


SimulatedMeasured

0

20

40

60

80

100

RF-D

C co

nver

sion

effic

ienc

y (

)




Tribandrectenna

Z0

C1

C2

D2

D1

421mm3462mm

043mm3767mm

216mm2395mm

092mm2158mm

103mm379mm

1618mm864mm

500nH

321mm2069mm

114mm3538mm

Z0FMrectenna

39pF

C1

C2

D2

D1

+

ndash

10kΩ

Vdc

DCcombination

(a)

(b)


minus40

minus35

minus30

minus25

minus20

minus15

minus10

minus5

0

S 11 (

dB)

90 92 94 96 98 100 102 104 106 10888Frequency (MHz)



(a)

minus35

minus30

minus25

minus20

minus15

minus10

minus5

0

5

S 11 (

dB)

1 12 14 16 18 2 22 2408Frequency (GHz)



(b)





0

10

20

30

40

50

60

70

80

RF-D

C co

nver

sion

effici

ency

()



(a) (b)

(c)





PDC(dBm) 10logV2

DCRL

times 1031113888 1113889 (19)











10

20

30

40

50

60

70

80


RFminusD

C co

nver

sion

effici

ency

()



[19](09GHz)

[11](2GHz)

[13](09GHz)

[13]( 18 24GHz)

[36]

[14](185GHz)

[14](0915GHz)

[20] (17GHz)[20] (24GHz)


(a) (b) (c)

(d)



8 Conclusions


Data Availability




Acknowledgments


References






Ref(year)

Frequency(GHz)






multitone input()


(V)

[10](2016)

Six-band 055075 09 185



[11](2018)



[12](2017)



[13](2015)



[34](2018)




[35](2017)




06 at500 μWm2

[15](2013)







ltiswork(2019)

Four-band0098 09 18

24Dual LP








































minus16

minus12

minus8

minus4

0

60

300

330

300

270

120

150

180210

240

90

minus16

minus12

minus8

minus4

0

60

300

330

300

270

120

150

180

210

240

90

SimulatedMeasured

(a)

minus16

minus12

minus8

minus4

0

60

300

330

300

270

120

150180

210

240

90

minus16

minus12

minus8

minus4

0

60

300

330

300

270

120

150180

210

240

90

SimulatedMeasured

(b)

minus16

minus12

minus8

minus4

0

60

300

330

300

270

120

150180

210

240

90

minus16

minus12

minus8

minus4

0

60

120

30

150

0

180

30

150

60

120

90 90

SimulatedMeasured

(c)



m LML

LT

(3)




Y



Rc

LG

LC

LT

LMT

LS

LML


SimulatedMeasured

minus30

minus25

minus20

minus15

minus10

minus5

0

S 11 (

dB)

95 100 105 11090Frequency (GHz)




Value (Ω) 9333 7816 6418 120 220 470






minus60

minus50

minus40

minus30

minus20

minus10

0M

agni

tude

(dB)


(a)



minus80

minus60

minus40

minus20

0

Mag

nitu

de (d

B)


(b)

Arg (S51 S41S31 S21)

minus200

minus100

0

100

200

Phas

e (de

g)


(c)


P1 P5

P4

P3

P2

R1R2

R3

Z1Z2Z3

(a) (b)

FMmonopoleantenna

Multibandantenna

cube

(c)




5 Rectifier Design










ndash10dBm0dBm

0

50

100

150

200

250

300

350

Real

(Zin

)

1 12 14 16 18 2 22 24 2608Frequency (GHz)

(a)


ndash10dBm0dBm

minus700

minus600

minus500

minus400

minus300

minus200

Img

(Zin

)

1 12 14 16 18 2 22 24 2608Frequency (GHz)

(b)



Zs


Rb minus Ra


1113971


(m + 1)βa

(4)



Z1 + jZL1 tan βal1( 1113857 (5)

ZL1 Z2ZL2 + jZ2 tan βbl2( 1113857

Z2 + jZL2f3 tan βbl2( 1113857 (6)


l l1 l2 1113937

βa + βb

(7)

Z41 + bZ

31 + cZ

21 + dZ1 + e 0 (8)

where

b 2aR0XL2

R0 minus RL2

c R0RL2 X2


1113872 1113873 minus X2L2R

20 1 + a2( 1113857

2


d 2aR3

0XL2

RL2 minus R0

e R30 R2

L2 + X2L2 minus R0RL2( 1113857

R0 minus RL2

(9)






Z1 + jZL1 tan υβal1( 1113857 G1 + jB1 (10)

where

υ f3

f1


Z2 + jZL2f3 tan βbl2( 1113857


Z3 + jZL3 tan υβal3( 1113857

(11)




0G21 tan υθ


+ Z0G1 tan υθ( 11138572

1113960 1113961

(12)



Z0B2( 11138572

+ 1 minus Z0G1( 1113857 Z20B

22 + Z2

0B22( 1113857 minus Z0G1

1113969

Z20B

22 + Z2

0B22 minus Z0G1( 1113857

(13)

Ya B3



Z0

Zin ZL1

Stage II Stage I

ZL2

ZL1 f1ZL2 f2

Z1 Z2 Z3l1 l2 l3



AntennaRectifier

+load

Compleximpedance

50 Ωantenna

impedance


Dual bandimpedance

matching network



θ1 (1 + s) 1113937

1 + r (15)

Za Zbtan2θ1 (16)


Zc Zdtan2θ1 (17)




Yin4 = 1Z0 f11Z0 f21Z0 f3

Yin3 = 1Z0 f11Z0 f2

G2 + jB3 f3

Yin2 = 1Z0 f11Z0 f2

G1 + jB2 f3

Yin1 = 1Z0 f11Z0 f2

G1 + jB1 f3

Zaθ1

θZb

Z0

Z0

θ1

Zdθ1

Zc

θ1

OCSC-2OCSC-1



043mm3767mm

216mm2395mm

092mm2158mm

103mm379mm

1618mm864mm

321mm2069mm

114mm

Z0

C1

C2

D2

D1

3538mm

10kΩRF source

Rectifier

(a)

(b)





ηRFminusDC PDC

Pin (18)






0ndash5


S 11 (

dB)

ndash35ndash40


16 18 2 22 24








80

70

60

50

40

30

20

10


RF-D

C co

nver

sion

effic

ienc

y (

)





RF source

Matchingnetwork


Z0 D1

D2C1

C2

500nH10kΩ

39pF

(a) (b)


S 11 (

dB)



minus35

minus30

minus25

minus20

minus15

minus10

minus5

0

90 92 94 96 98 100 102 104 106 10888Frequency (MHz)


SimulatedMeasured

0

20

40

60

80

100

RF-D

C co

nver

sion

effic

ienc

y (

)




Tribandrectenna

Z0

C1

C2

D2

D1

421mm3462mm

043mm3767mm

216mm2395mm

092mm2158mm

103mm379mm

1618mm864mm

500nH

321mm2069mm

114mm3538mm

Z0FMrectenna

39pF

C1

C2

D2

D1

+

ndash

10kΩ

Vdc

DCcombination

(a)

(b)


minus40

minus35

minus30

minus25

minus20

minus15

minus10

minus5

0

S 11 (

dB)

90 92 94 96 98 100 102 104 106 10888Frequency (MHz)



(a)

minus35

minus30

minus25

minus20

minus15

minus10

minus5

0

5

S 11 (

dB)

1 12 14 16 18 2 22 2408Frequency (GHz)



(b)





0

10

20

30

40

50

60

70

80

RF-D

C co

nver

sion

effici

ency

()



(a) (b)

(c)





PDC(dBm) 10logV2

DCRL

times 1031113888 1113889 (19)











10

20

30

40

50

60

70

80


RFminusD

C co

nver

sion

effici

ency

()



[19](09GHz)

[11](2GHz)

[13](09GHz)

[13]( 18 24GHz)

[36]

[14](185GHz)

[14](0915GHz)

[20] (17GHz)[20] (24GHz)


(a) (b) (c)

(d)



8 Conclusions


Data Availability




Acknowledgments


References






Ref(year)

Frequency(GHz)






multitone input()


(V)

[10](2016)

Six-band 055075 09 185



[11](2018)



[12](2017)



[13](2015)



[34](2018)




[35](2017)




06 at500 μWm2

[15](2013)







ltiswork(2019)

Four-band0098 09 18

24Dual LP








































m LML

LT

(3)




Y



Rc

LG

LC

LT

LMT

LS

LML


SimulatedMeasured

minus30

minus25

minus20

minus15

minus10

minus5

0

S 11 (

dB)

95 100 105 11090Frequency (GHz)




Value (Ω) 9333 7816 6418 120 220 470






minus60

minus50

minus40

minus30

minus20

minus10

0M

agni

tude

(dB)


(a)



minus80

minus60

minus40

minus20

0

Mag

nitu

de (d

B)


(b)

Arg (S51 S41S31 S21)

minus200

minus100

0

100

200

Phas

e (de

g)


(c)


P1 P5

P4

P3

P2

R1R2

R3

Z1Z2Z3

(a) (b)

FMmonopoleantenna

Multibandantenna

cube

(c)




5 Rectifier Design










ndash10dBm0dBm

0

50

100

150

200

250

300

350

Real

(Zin

)

1 12 14 16 18 2 22 24 2608Frequency (GHz)

(a)


ndash10dBm0dBm

minus700

minus600

minus500

minus400

minus300

minus200

Img

(Zin

)

1 12 14 16 18 2 22 24 2608Frequency (GHz)

(b)



Zs


Rb minus Ra


1113971


(m + 1)βa

(4)



Z1 + jZL1 tan βal1( 1113857 (5)

ZL1 Z2ZL2 + jZ2 tan βbl2( 1113857

Z2 + jZL2f3 tan βbl2( 1113857 (6)


l l1 l2 1113937

βa + βb

(7)

Z41 + bZ

31 + cZ

21 + dZ1 + e 0 (8)

where

b 2aR0XL2

R0 minus RL2

c R0RL2 X2


1113872 1113873 minus X2L2R

20 1 + a2( 1113857

2


d 2aR3

0XL2

RL2 minus R0

e R30 R2

L2 + X2L2 minus R0RL2( 1113857

R0 minus RL2

(9)






Z1 + jZL1 tan υβal1( 1113857 G1 + jB1 (10)

where

υ f3

f1


Z2 + jZL2f3 tan βbl2( 1113857


Z3 + jZL3 tan υβal3( 1113857

(11)




0G21 tan υθ


+ Z0G1 tan υθ( 11138572

1113960 1113961

(12)



Z0B2( 11138572

+ 1 minus Z0G1( 1113857 Z20B

22 + Z2

0B22( 1113857 minus Z0G1

1113969

Z20B

22 + Z2

0B22 minus Z0G1( 1113857

(13)

Ya B3



Z0

Zin ZL1

Stage II Stage I

ZL2

ZL1 f1ZL2 f2

Z1 Z2 Z3l1 l2 l3



AntennaRectifier

+load

Compleximpedance

50 Ωantenna

impedance


Dual bandimpedance

matching network



θ1 (1 + s) 1113937

1 + r (15)

Za Zbtan2θ1 (16)


Zc Zdtan2θ1 (17)




Yin4 = 1Z0 f11Z0 f21Z0 f3

Yin3 = 1Z0 f11Z0 f2

G2 + jB3 f3

Yin2 = 1Z0 f11Z0 f2

G1 + jB2 f3

Yin1 = 1Z0 f11Z0 f2

G1 + jB1 f3

Zaθ1

θZb

Z0

Z0

θ1

Zdθ1

Zc

θ1

OCSC-2OCSC-1



043mm3767mm

216mm2395mm

092mm2158mm

103mm379mm

1618mm864mm

321mm2069mm

114mm

Z0

C1

C2

D2

D1

3538mm

10kΩRF source

Rectifier

(a)

(b)





ηRFminusDC PDC

Pin (18)






0ndash5


S 11 (

dB)

ndash35ndash40


16 18 2 22 24








80

70

60

50

40

30

20

10


RF-D

C co

nver

sion

effic

ienc

y (

)





RF source

Matchingnetwork


Z0 D1

D2C1

C2

500nH10kΩ

39pF

(a) (b)


S 11 (

dB)



minus35

minus30

minus25

minus20

minus15

minus10

minus5

0

90 92 94 96 98 100 102 104 106 10888Frequency (MHz)


SimulatedMeasured

0

20

40

60

80

100

RF-D

C co

nver

sion

effic

ienc

y (

)




Tribandrectenna

Z0

C1

C2

D2

D1

421mm3462mm

043mm3767mm

216mm2395mm

092mm2158mm

103mm379mm

1618mm864mm

500nH

321mm2069mm

114mm3538mm

Z0FMrectenna

39pF

C1

C2

D2

D1

+

ndash

10kΩ

Vdc

DCcombination

(a)

(b)


minus40

minus35

minus30

minus25

minus20

minus15

minus10

minus5

0

S 11 (

dB)

90 92 94 96 98 100 102 104 106 10888Frequency (MHz)



(a)

minus35

minus30

minus25

minus20

minus15

minus10

minus5

0

5

S 11 (

dB)

1 12 14 16 18 2 22 2408Frequency (GHz)



(b)





0

10

20

30

40

50

60

70

80

RF-D

C co

nver

sion

effici

ency

()



(a) (b)

(c)





PDC(dBm) 10logV2

DCRL

times 1031113888 1113889 (19)











10

20

30

40

50

60

70

80


RFminusD

C co

nver

sion

effici

ency

()



[19](09GHz)

[11](2GHz)

[13](09GHz)

[13]( 18 24GHz)

[36]

[14](185GHz)

[14](0915GHz)

[20] (17GHz)[20] (24GHz)


(a) (b) (c)

(d)



8 Conclusions


Data Availability




Acknowledgments


References






Ref(year)

Frequency(GHz)






multitone input()


(V)

[10](2016)

Six-band 055075 09 185



[11](2018)



[12](2017)



[13](2015)



[34](2018)




[35](2017)




06 at500 μWm2

[15](2013)







ltiswork(2019)

Four-band0098 09 18

24Dual LP












































minus60

minus50

minus40

minus30

minus20

minus10

0M

agni

tude

(dB)


(a)



minus80

minus60

minus40

minus20

0

Mag

nitu

de (d

B)


(b)

Arg (S51 S41S31 S21)

minus200

minus100

0

100

200

Phas

e (de

g)


(c)


P1 P5

P4

P3

P2

R1R2

R3

Z1Z2Z3

(a) (b)

FMmonopoleantenna

Multibandantenna

cube

(c)




5 Rectifier Design










ndash10dBm0dBm

0

50

100

150

200

250

300

350

Real

(Zin

)

1 12 14 16 18 2 22 24 2608Frequency (GHz)

(a)


ndash10dBm0dBm

minus700

minus600

minus500

minus400

minus300

minus200

Img

(Zin

)

1 12 14 16 18 2 22 24 2608Frequency (GHz)

(b)



Zs


Rb minus Ra


1113971


(m + 1)βa

(4)



Z1 + jZL1 tan βal1( 1113857 (5)

ZL1 Z2ZL2 + jZ2 tan βbl2( 1113857

Z2 + jZL2f3 tan βbl2( 1113857 (6)


l l1 l2 1113937

βa + βb

(7)

Z41 + bZ

31 + cZ

21 + dZ1 + e 0 (8)

where

b 2aR0XL2

R0 minus RL2

c R0RL2 X2


1113872 1113873 minus X2L2R

20 1 + a2( 1113857

2


d 2aR3

0XL2

RL2 minus R0

e R30 R2

L2 + X2L2 minus R0RL2( 1113857

R0 minus RL2

(9)






Z1 + jZL1 tan υβal1( 1113857 G1 + jB1 (10)

where

υ f3

f1


Z2 + jZL2f3 tan βbl2( 1113857


Z3 + jZL3 tan υβal3( 1113857

(11)




0G21 tan υθ


+ Z0G1 tan υθ( 11138572

1113960 1113961

(12)



Z0B2( 11138572

+ 1 minus Z0G1( 1113857 Z20B

22 + Z2

0B22( 1113857 minus Z0G1

1113969

Z20B

22 + Z2

0B22 minus Z0G1( 1113857

(13)

Ya B3



Z0

Zin ZL1

Stage II Stage I

ZL2

ZL1 f1ZL2 f2

Z1 Z2 Z3l1 l2 l3



AntennaRectifier

+load

Compleximpedance

50 Ωantenna

impedance


Dual bandimpedance

matching network



θ1 (1 + s) 1113937

1 + r (15)

Za Zbtan2θ1 (16)


Zc Zdtan2θ1 (17)




Yin4 = 1Z0 f11Z0 f21Z0 f3

Yin3 = 1Z0 f11Z0 f2

G2 + jB3 f3

Yin2 = 1Z0 f11Z0 f2

G1 + jB2 f3

Yin1 = 1Z0 f11Z0 f2

G1 + jB1 f3

Zaθ1

θZb

Z0

Z0

θ1

Zdθ1

Zc

θ1

OCSC-2OCSC-1



043mm3767mm

216mm2395mm

092mm2158mm

103mm379mm

1618mm864mm

321mm2069mm

114mm

Z0

C1

C2

D2

D1

3538mm

10kΩRF source

Rectifier

(a)

(b)





ηRFminusDC PDC

Pin (18)






0ndash5


S 11 (

dB)

ndash35ndash40


16 18 2 22 24








80

70

60

50

40

30

20

10


RF-D

C co

nver

sion

effic

ienc

y (

)





RF source

Matchingnetwork


Z0 D1

D2C1

C2

500nH10kΩ

39pF

(a) (b)


S 11 (

dB)



minus35

minus30

minus25

minus20

minus15

minus10

minus5

0

90 92 94 96 98 100 102 104 106 10888Frequency (MHz)


SimulatedMeasured

0

20

40

60

80

100

RF-D

C co

nver

sion

effic

ienc

y (

)




Tribandrectenna

Z0

C1

C2

D2

D1

421mm3462mm

043mm3767mm

216mm2395mm

092mm2158mm

103mm379mm

1618mm864mm

500nH

321mm2069mm

114mm3538mm

Z0FMrectenna

39pF

C1

C2

D2

D1

+

ndash

10kΩ

Vdc

DCcombination

(a)

(b)


minus40

minus35

minus30

minus25

minus20

minus15

minus10

minus5

0

S 11 (

dB)

90 92 94 96 98 100 102 104 106 10888Frequency (MHz)



(a)

minus35

minus30

minus25

minus20

minus15

minus10

minus5

0

5

S 11 (

dB)

1 12 14 16 18 2 22 2408Frequency (GHz)



(b)





0

10

20

30

40

50

60

70

80

RF-D

C co

nver

sion

effici

ency

()



(a) (b)

(c)





PDC(dBm) 10logV2

DCRL

times 1031113888 1113889 (19)











10

20

30

40

50

60

70

80


RFminusD

C co

nver

sion

effici

ency

()



[19](09GHz)

[11](2GHz)

[13](09GHz)

[13]( 18 24GHz)

[36]

[14](185GHz)

[14](0915GHz)

[20] (17GHz)[20] (24GHz)


(a) (b) (c)

(d)



8 Conclusions


Data Availability




Acknowledgments


References






Ref(year)

Frequency(GHz)






multitone input()


(V)

[10](2016)

Six-band 055075 09 185



[11](2018)



[12](2017)



[13](2015)



[34](2018)




[35](2017)




06 at500 μWm2

[15](2013)







ltiswork(2019)

Four-band0098 09 18

24Dual LP









































5 Rectifier Design










ndash10dBm0dBm

0

50

100

150

200

250

300

350

Real

(Zin

)

1 12 14 16 18 2 22 24 2608Frequency (GHz)

(a)


ndash10dBm0dBm

minus700

minus600

minus500

minus400

minus300

minus200

Img

(Zin

)

1 12 14 16 18 2 22 24 2608Frequency (GHz)

(b)



Zs


Rb minus Ra


1113971


(m + 1)βa

(4)



Z1 + jZL1 tan βal1( 1113857 (5)

ZL1 Z2ZL2 + jZ2 tan βbl2( 1113857

Z2 + jZL2f3 tan βbl2( 1113857 (6)


l l1 l2 1113937

βa + βb

(7)

Z41 + bZ

31 + cZ

21 + dZ1 + e 0 (8)

where

b 2aR0XL2

R0 minus RL2

c R0RL2 X2


1113872 1113873 minus X2L2R

20 1 + a2( 1113857

2


d 2aR3

0XL2

RL2 minus R0

e R30 R2

L2 + X2L2 minus R0RL2( 1113857

R0 minus RL2

(9)






Z1 + jZL1 tan υβal1( 1113857 G1 + jB1 (10)

where

υ f3

f1


Z2 + jZL2f3 tan βbl2( 1113857


Z3 + jZL3 tan υβal3( 1113857

(11)




0G21 tan υθ


+ Z0G1 tan υθ( 11138572

1113960 1113961

(12)



Z0B2( 11138572

+ 1 minus Z0G1( 1113857 Z20B

22 + Z2

0B22( 1113857 minus Z0G1

1113969

Z20B

22 + Z2

0B22 minus Z0G1( 1113857

(13)

Ya B3



Z0

Zin ZL1

Stage II Stage I

ZL2

ZL1 f1ZL2 f2

Z1 Z2 Z3l1 l2 l3



AntennaRectifier

+load

Compleximpedance

50 Ωantenna

impedance


Dual bandimpedance

matching network



θ1 (1 + s) 1113937

1 + r (15)

Za Zbtan2θ1 (16)


Zc Zdtan2θ1 (17)




Yin4 = 1Z0 f11Z0 f21Z0 f3

Yin3 = 1Z0 f11Z0 f2

G2 + jB3 f3

Yin2 = 1Z0 f11Z0 f2

G1 + jB2 f3

Yin1 = 1Z0 f11Z0 f2

G1 + jB1 f3

Zaθ1

θZb

Z0

Z0

θ1

Zdθ1

Zc

θ1

OCSC-2OCSC-1



043mm3767mm

216mm2395mm

092mm2158mm

103mm379mm

1618mm864mm

321mm2069mm

114mm

Z0

C1

C2

D2

D1

3538mm

10kΩRF source

Rectifier

(a)

(b)





ηRFminusDC PDC

Pin (18)






0ndash5


S 11 (

dB)

ndash35ndash40


16 18 2 22 24








80

70

60

50

40

30

20

10


RF-D

C co

nver

sion

effic

ienc

y (

)





RF source

Matchingnetwork


Z0 D1

D2C1

C2

500nH10kΩ

39pF

(a) (b)


S 11 (

dB)



minus35

minus30

minus25

minus20

minus15

minus10

minus5

0

90 92 94 96 98 100 102 104 106 10888Frequency (MHz)


SimulatedMeasured

0

20

40

60

80

100

RF-D

C co

nver

sion

effic

ienc

y (

)




Tribandrectenna

Z0

C1

C2

D2

D1

421mm3462mm

043mm3767mm

216mm2395mm

092mm2158mm

103mm379mm

1618mm864mm

500nH

321mm2069mm

114mm3538mm

Z0FMrectenna

39pF

C1

C2

D2

D1

+

ndash

10kΩ

Vdc

DCcombination

(a)

(b)


minus40

minus35

minus30

minus25

minus20

minus15

minus10

minus5

0

S 11 (

dB)

90 92 94 96 98 100 102 104 106 10888Frequency (MHz)



(a)

minus35

minus30

minus25

minus20

minus15

minus10

minus5

0

5

S 11 (

dB)

1 12 14 16 18 2 22 2408Frequency (GHz)



(b)





0

10

20

30

40

50

60

70

80

RF-D

C co

nver

sion

effici

ency

()



(a) (b)

(c)





PDC(dBm) 10logV2

DCRL

times 1031113888 1113889 (19)











10

20

30

40

50

60

70

80


RFminusD

C co

nver

sion

effici

ency

()



[19](09GHz)

[11](2GHz)

[13](09GHz)

[13]( 18 24GHz)

[36]

[14](185GHz)

[14](0915GHz)

[20] (17GHz)[20] (24GHz)


(a) (b) (c)

(d)



8 Conclusions


Data Availability




Acknowledgments


References






Ref(year)

Frequency(GHz)






multitone input()


(V)

[10](2016)

Six-band 055075 09 185



[11](2018)



[12](2017)



[13](2015)



[34](2018)




[35](2017)




06 at500 μWm2

[15](2013)







ltiswork(2019)

Four-band0098 09 18

24Dual LP








































Zs


Rb minus Ra


1113971


(m + 1)βa

(4)



Z1 + jZL1 tan βal1( 1113857 (5)

ZL1 Z2ZL2 + jZ2 tan βbl2( 1113857

Z2 + jZL2f3 tan βbl2( 1113857 (6)


l l1 l2 1113937

βa + βb

(7)

Z41 + bZ

31 + cZ

21 + dZ1 + e 0 (8)

where

b 2aR0XL2

R0 minus RL2

c R0RL2 X2


1113872 1113873 minus X2L2R

20 1 + a2( 1113857

2


d 2aR3

0XL2

RL2 minus R0

e R30 R2

L2 + X2L2 minus R0RL2( 1113857

R0 minus RL2

(9)






Z1 + jZL1 tan υβal1( 1113857 G1 + jB1 (10)

where

υ f3

f1


Z2 + jZL2f3 tan βbl2( 1113857


Z3 + jZL3 tan υβal3( 1113857

(11)




0G21 tan υθ


+ Z0G1 tan υθ( 11138572

1113960 1113961

(12)



Z0B2( 11138572

+ 1 minus Z0G1( 1113857 Z20B

22 + Z2

0B22( 1113857 minus Z0G1

1113969

Z20B

22 + Z2

0B22 minus Z0G1( 1113857

(13)

Ya B3



Z0

Zin ZL1

Stage II Stage I

ZL2

ZL1 f1ZL2 f2

Z1 Z2 Z3l1 l2 l3



AntennaRectifier

+load

Compleximpedance

50 Ωantenna

impedance


Dual bandimpedance

matching network



θ1 (1 + s) 1113937

1 + r (15)

Za Zbtan2θ1 (16)


Zc Zdtan2θ1 (17)




Yin4 = 1Z0 f11Z0 f21Z0 f3

Yin3 = 1Z0 f11Z0 f2

G2 + jB3 f3

Yin2 = 1Z0 f11Z0 f2

G1 + jB2 f3

Yin1 = 1Z0 f11Z0 f2

G1 + jB1 f3

Zaθ1

θZb

Z0

Z0

θ1

Zdθ1

Zc

θ1

OCSC-2OCSC-1



043mm3767mm

216mm2395mm

092mm2158mm

103mm379mm

1618mm864mm

321mm2069mm

114mm

Z0

C1

C2

D2

D1

3538mm

10kΩRF source

Rectifier

(a)

(b)





ηRFminusDC PDC

Pin (18)






0ndash5


S 11 (

dB)

ndash35ndash40


16 18 2 22 24








80

70

60

50

40

30

20

10


RF-D

C co

nver

sion

effic

ienc

y (

)





RF source

Matchingnetwork


Z0 D1

D2C1

C2

500nH10kΩ

39pF

(a) (b)


S 11 (

dB)



minus35

minus30

minus25

minus20

minus15

minus10

minus5

0

90 92 94 96 98 100 102 104 106 10888Frequency (MHz)


SimulatedMeasured

0

20

40

60

80

100

RF-D

C co

nver

sion

effic

ienc

y (

)




Tribandrectenna

Z0

C1

C2

D2

D1

421mm3462mm

043mm3767mm

216mm2395mm

092mm2158mm

103mm379mm

1618mm864mm

500nH

321mm2069mm

114mm3538mm

Z0FMrectenna

39pF

C1

C2

D2

D1

+

ndash

10kΩ

Vdc

DCcombination

(a)

(b)


minus40

minus35

minus30

minus25

minus20

minus15

minus10

minus5

0

S 11 (

dB)

90 92 94 96 98 100 102 104 106 10888Frequency (MHz)



(a)

minus35

minus30

minus25

minus20

minus15

minus10

minus5

0

5

S 11 (

dB)

1 12 14 16 18 2 22 2408Frequency (GHz)



(b)





0

10

20

30

40

50

60

70

80

RF-D

C co

nver

sion

effici

ency

()



(a) (b)

(c)





PDC(dBm) 10logV2

DCRL

times 1031113888 1113889 (19)











10

20

30

40

50

60

70

80


RFminusD

C co

nver

sion

effici

ency

()



[19](09GHz)

[11](2GHz)

[13](09GHz)

[13]( 18 24GHz)

[36]

[14](185GHz)

[14](0915GHz)

[20] (17GHz)[20] (24GHz)


(a) (b) (c)

(d)



8 Conclusions


Data Availability




Acknowledgments


References






Ref(year)

Frequency(GHz)






multitone input()


(V)

[10](2016)

Six-band 055075 09 185



[11](2018)



[12](2017)



[13](2015)



[34](2018)




[35](2017)




06 at500 μWm2

[15](2013)







ltiswork(2019)

Four-band0098 09 18

24Dual LP








































θ1 (1 + s) 1113937

1 + r (15)

Za Zbtan2θ1 (16)


Zc Zdtan2θ1 (17)




Yin4 = 1Z0 f11Z0 f21Z0 f3

Yin3 = 1Z0 f11Z0 f2

G2 + jB3 f3

Yin2 = 1Z0 f11Z0 f2

G1 + jB2 f3

Yin1 = 1Z0 f11Z0 f2

G1 + jB1 f3

Zaθ1

θZb

Z0

Z0

θ1

Zdθ1

Zc

θ1

OCSC-2OCSC-1



043mm3767mm

216mm2395mm

092mm2158mm

103mm379mm

1618mm864mm

321mm2069mm

114mm

Z0

C1

C2

D2

D1

3538mm

10kΩRF source

Rectifier

(a)

(b)





ηRFminusDC PDC

Pin (18)






0ndash5


S 11 (

dB)

ndash35ndash40


16 18 2 22 24








80

70

60

50

40

30

20

10


RF-D

C co

nver

sion

effic

ienc

y (

)





RF source

Matchingnetwork


Z0 D1

D2C1

C2

500nH10kΩ

39pF

(a) (b)


S 11 (

dB)



minus35

minus30

minus25

minus20

minus15

minus10

minus5

0

90 92 94 96 98 100 102 104 106 10888Frequency (MHz)


SimulatedMeasured

0

20

40

60

80

100

RF-D

C co

nver

sion

effic

ienc

y (

)




Tribandrectenna

Z0

C1

C2

D2

D1

421mm3462mm

043mm3767mm

216mm2395mm

092mm2158mm

103mm379mm

1618mm864mm

500nH

321mm2069mm

114mm3538mm

Z0FMrectenna

39pF

C1

C2

D2

D1

+

ndash

10kΩ

Vdc

DCcombination

(a)

(b)


minus40

minus35

minus30

minus25

minus20

minus15

minus10

minus5

0

S 11 (

dB)

90 92 94 96 98 100 102 104 106 10888Frequency (MHz)



(a)

minus35

minus30

minus25

minus20

minus15

minus10

minus5

0

5

S 11 (

dB)

1 12 14 16 18 2 22 2408Frequency (GHz)



(b)





0

10

20

30

40

50

60

70

80

RF-D

C co

nver

sion

effici

ency

()



(a) (b)

(c)





PDC(dBm) 10logV2

DCRL

times 1031113888 1113889 (19)











10

20

30

40

50

60

70

80


RFminusD

C co

nver

sion

effici

ency

()



[19](09GHz)

[11](2GHz)

[13](09GHz)

[13]( 18 24GHz)

[36]

[14](185GHz)

[14](0915GHz)

[20] (17GHz)[20] (24GHz)


(a) (b) (c)

(d)



8 Conclusions


Data Availability




Acknowledgments


References






Ref(year)

Frequency(GHz)






multitone input()


(V)

[10](2016)

Six-band 055075 09 185



[11](2018)



[12](2017)



[13](2015)



[34](2018)




[35](2017)




06 at500 μWm2

[15](2013)







ltiswork(2019)

Four-band0098 09 18

24Dual LP










































ηRFminusDC PDC

Pin (18)






0ndash5


S 11 (

dB)

ndash35ndash40


16 18 2 22 24








80

70

60

50

40

30

20

10


RF-D

C co

nver

sion

effic

ienc

y (

)





RF source

Matchingnetwork


Z0 D1

D2C1

C2

500nH10kΩ

39pF

(a) (b)


S 11 (

dB)



minus35

minus30

minus25

minus20

minus15

minus10

minus5

0

90 92 94 96 98 100 102 104 106 10888Frequency (MHz)


SimulatedMeasured

0

20

40

60

80

100

RF-D

C co

nver

sion

effic

ienc

y (

)




Tribandrectenna

Z0

C1

C2

D2

D1

421mm3462mm

043mm3767mm

216mm2395mm

092mm2158mm

103mm379mm

1618mm864mm

500nH

321mm2069mm

114mm3538mm

Z0FMrectenna

39pF

C1

C2

D2

D1

+

ndash

10kΩ

Vdc

DCcombination

(a)

(b)


minus40

minus35

minus30

minus25

minus20

minus15

minus10

minus5

0

S 11 (

dB)

90 92 94 96 98 100 102 104 106 10888Frequency (MHz)



(a)

minus35

minus30

minus25

minus20

minus15

minus10

minus5

0

5

S 11 (

dB)

1 12 14 16 18 2 22 2408Frequency (GHz)



(b)





0

10

20

30

40

50

60

70

80

RF-D

C co

nver

sion

effici

ency

()



(a) (b)

(c)





PDC(dBm) 10logV2

DCRL

times 1031113888 1113889 (19)











10

20

30

40

50

60

70

80


RFminusD

C co

nver

sion

effici

ency

()



[19](09GHz)

[11](2GHz)

[13](09GHz)

[13]( 18 24GHz)

[36]

[14](185GHz)

[14](0915GHz)

[20] (17GHz)[20] (24GHz)


(a) (b) (c)

(d)



8 Conclusions


Data Availability




Acknowledgments


References






Ref(year)

Frequency(GHz)






multitone input()


(V)

[10](2016)

Six-band 055075 09 185



[11](2018)



[12](2017)



[13](2015)



[34](2018)




[35](2017)




06 at500 μWm2

[15](2013)







ltiswork(2019)

Four-band0098 09 18

24Dual LP











































80

70

60

50

40

30

20

10


RF-D

C co

nver

sion

effic

ienc

y (

)





RF source

Matchingnetwork


Z0 D1

D2C1

C2

500nH10kΩ

39pF

(a) (b)


S 11 (

dB)



minus35

minus30

minus25

minus20

minus15

minus10

minus5

0

90 92 94 96 98 100 102 104 106 10888Frequency (MHz)


SimulatedMeasured

0

20

40

60

80

100

RF-D

C co

nver

sion

effic

ienc

y (

)




Tribandrectenna

Z0

C1

C2

D2

D1

421mm3462mm

043mm3767mm

216mm2395mm

092mm2158mm

103mm379mm

1618mm864mm

500nH

321mm2069mm

114mm3538mm

Z0FMrectenna

39pF

C1

C2

D2

D1

+

ndash

10kΩ

Vdc

DCcombination

(a)

(b)


minus40

minus35

minus30

minus25

minus20

minus15

minus10

minus5

0

S 11 (

dB)

90 92 94 96 98 100 102 104 106 10888Frequency (MHz)



(a)

minus35

minus30

minus25

minus20

minus15

minus10

minus5

0

5

S 11 (

dB)

1 12 14 16 18 2 22 2408Frequency (GHz)



(b)





0

10

20

30

40

50

60

70

80

RF-D

C co

nver

sion

effici

ency

()



(a) (b)

(c)





PDC(dBm) 10logV2

DCRL

times 1031113888 1113889 (19)











10

20

30

40

50

60

70

80


RFminusD

C co

nver

sion

effici

ency

()



[19](09GHz)

[11](2GHz)

[13](09GHz)

[13]( 18 24GHz)

[36]

[14](185GHz)

[14](0915GHz)

[20] (17GHz)[20] (24GHz)


(a) (b) (c)

(d)



8 Conclusions


Data Availability




Acknowledgments


References






Ref(year)

Frequency(GHz)






multitone input()


(V)

[10](2016)

Six-band 055075 09 185



[11](2018)



[12](2017)



[13](2015)



[34](2018)




[35](2017)




06 at500 μWm2

[15](2013)







ltiswork(2019)

Four-band0098 09 18

24Dual LP








































Tribandrectenna

Z0

C1

C2

D2

D1

421mm3462mm

043mm3767mm

216mm2395mm

092mm2158mm

103mm379mm

1618mm864mm

500nH

321mm2069mm

114mm3538mm

Z0FMrectenna

39pF

C1

C2

D2

D1

+

ndash

10kΩ

Vdc

DCcombination

(a)

(b)


minus40

minus35

minus30

minus25

minus20

minus15

minus10

minus5

0

S 11 (

dB)

90 92 94 96 98 100 102 104 106 10888Frequency (MHz)



(a)

minus35

minus30

minus25

minus20

minus15

minus10

minus5

0

5

S 11 (

dB)

1 12 14 16 18 2 22 2408Frequency (GHz)



(b)





0

10

20

30

40

50

60

70

80

RF-D

C co

nver

sion

effici

ency

()



(a) (b)

(c)





PDC(dBm) 10logV2

DCRL

times 1031113888 1113889 (19)











10

20

30

40

50

60

70

80


RFminusD

C co

nver

sion

effici

ency

()



[19](09GHz)

[11](2GHz)

[13](09GHz)

[13]( 18 24GHz)

[36]

[14](185GHz)

[14](0915GHz)

[20] (17GHz)[20] (24GHz)


(a) (b) (c)

(d)



8 Conclusions


Data Availability




Acknowledgments


References






Ref(year)

Frequency(GHz)






multitone input()


(V)

[10](2016)

Six-band 055075 09 185



[11](2018)



[12](2017)



[13](2015)



[34](2018)




[35](2017)




06 at500 μWm2

[15](2013)







ltiswork(2019)

Four-band0098 09 18

24Dual LP










































0

10

20

30

40

50

60

70

80

RF-D

C co

nver

sion

effici

ency

()



(a) (b)

(c)





PDC(dBm) 10logV2

DCRL

times 1031113888 1113889 (19)











10

20

30

40

50

60

70

80


RFminusD

C co

nver

sion

effici

ency

()



[19](09GHz)

[11](2GHz)

[13](09GHz)

[13]( 18 24GHz)

[36]

[14](185GHz)

[14](0915GHz)

[20] (17GHz)[20] (24GHz)


(a) (b) (c)

(d)



8 Conclusions


Data Availability




Acknowledgments


References






Ref(year)

Frequency(GHz)






multitone input()


(V)

[10](2016)

Six-band 055075 09 185



[11](2018)



[12](2017)



[13](2015)



[34](2018)




[35](2017)




06 at500 μWm2

[15](2013)







ltiswork(2019)

Four-band0098 09 18

24Dual LP










































PDC(dBm) 10logV2

DCRL

times 1031113888 1113889 (19)











10

20

30

40

50

60

70

80


RFminusD

C co

nver

sion

effici

ency

()



[19](09GHz)

[11](2GHz)

[13](09GHz)

[13]( 18 24GHz)

[36]

[14](185GHz)

[14](0915GHz)

[20] (17GHz)[20] (24GHz)


(a) (b) (c)

(d)



8 Conclusions


Data Availability




Acknowledgments


References






Ref(year)

Frequency(GHz)






multitone input()


(V)

[10](2016)

Six-band 055075 09 185



[11](2018)



[12](2017)



[13](2015)



[34](2018)




[35](2017)




06 at500 μWm2

[15](2013)







ltiswork(2019)

Four-band0098 09 18

24Dual LP











































10

20

30

40

50

60

70

80


RFminusD

C co

nver

sion

effici

ency

()



[19](09GHz)

[11](2GHz)

[13](09GHz)

[13]( 18 24GHz)

[36]

[14](185GHz)

[14](0915GHz)

[20] (17GHz)[20] (24GHz)


(a) (b) (c)

(d)



8 Conclusions


Data Availability




Acknowledgments


References






Ref(year)

Frequency(GHz)






multitone input()


(V)

[10](2016)

Six-band 055075 09 185



[11](2018)



[12](2017)



[13](2015)



[34](2018)




[35](2017)




06 at500 μWm2

[15](2013)







ltiswork(2019)

Four-band0098 09 18

24Dual LP








































8 Conclusions


Data Availability




Acknowledgments


References






Ref(year)

Frequency(GHz)






multitone input()


(V)

[10](2016)

Six-band 055075 09 185



[11](2018)



[12](2017)



[13](2015)



[34](2018)




[35](2017)




06 at500 μWm2

[15](2013)







ltiswork(2019)

Four-band0098 09 18

24Dual LP








































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