applied sciences Article Considerations for the Design and Implementation of Ambient RF Signal Rectifiers in the 2.45 GHz WiFi Band Joan J. Garcia-Garcia Grupo de Aplicaciones Electro-Magnéticas Industriales (GAEMI), Departament d’Enginyeria Electrònica, Universitat Autonòma de Barcelona (UAB), Cerdanyola del Vallés, 08193 Barcelona, Spain; joan.garcia@uab.cat Abstract: Ambient RF energy harvesting (RF-EH) is a particular case of wireless power transfer (WPT), which is characterized by ultra-low power operation. This work points out theoretical and practical aspects that should be considered in the design of RF rectifiers for ambient RF energy harvesting systems. The most common RF rectifier circuits are compared and discussed using simulations and experimental data. The efficiency is analyzed in terms of the input power and load resistance. It is demonstrated that the most efficient RF rectifier in ultra-low power conditions is the simple diode capacitor structure. As an illustrative example, an RF rectifier has been fabricated by designing an impedance-matching network to operate into the WIFI band. The fabricated prototype shows a measured 12% efficiency working at 2.47 GHz with around −30 dBm ambient input power, which is higher than the reported efficiencies in the literature. The fabricated energy harvesting system delivers power between 25.6 nW and 129.6 nW to a resistive 10 kΩ load. The obtained results are applicable to ambient RF up to 6 GHz. Keywords: RF-DC conversion efficiency; RF ambient energy harvesting; RF energy scavenging; ultra-low RF power rectifier Citation: Garcia-Garcia, J.J. Considerations for the Design and 1. Introduction Implementation of Ambient RF Wireless Power Transfers (WPTs) have been a recurrent topic in the last decades Signal Rectifiers in the 2.45 GHz WiFi generating numerous practical and commercial applications [1,2]. WPT typically ranges Band. Appl. Sci. 2022, 12, 7884. between 20 dBm and −30 dBm. Ambient RF-EH is situated in the ultra-low power extreme https://doi.org/10.3390/app12157884 of this range, operating around and even below −30 dBm [3–7]. The possibility of feeding Academic Editor: Mengying Xie low-power devices by scavenging ambient RF energy is attractive for powering autonomous sensors [8] and IoTs general applications [9], especially in urban environments. More Received: 8 July 2022 specifically, ambient RF harvesting has been recently evaluated for feeding Low Power Accepted: 4 August 2022 Wide Area Networks (LPWANs) [3,10], wireless underground sensor networks (UWC) [11], Published: 5 August 2022 or batteryless sensors [12]. As a consequence of the low power level, ambient RF-EH Publisher’s Note: MDPI stays neutral systems tend to operate in broadband or multiband configurations to enhance the system’s with regard to jurisdictional claims in performance [12–15]. The impedance matching between the antenna and the rectifier published maps and institutional affil- constitutes an important challenge in the case of multiband or broadband applications; iations. however, there are promising approaches based on metamaterials [15]. The efficiency of an RF-EH system (ηRF ) can be expressed as the product of the RF-EH constituent functional block efficiencies, as shown in Equation (1): Copyright: © 2022 by the author. ηRF = ηant ·ηrec ·ηEMS ·ηsto (1) Licensee MDPI, Basel, Switzerland. This article is an open access article where ηant denotes antenna efficiency, ηrec denotes rectifier efficiency, ηEMS denotes energy distributed under the terms and management system efficiency, and ηsto denotes efficiency of the storage element. Hrec is de- conditions of the Creative Commons fined as the ratio between the effective input power delivered to the rectifier by the antenna Attribution (CC BY) license (https:// (Pin ) and the power (PR L ) delivered to the load resistor (R L ), as shown in Equation (2). creativecommons.org/licenses/by/ PR L 4.0/). ηrec = (2) Pin Appl. Sci. 2022, 12, 7884. https://doi.org/10.3390/app12157884 https://www.mdpi.com/journal/applsci 𝑃 =𝑃 (1 − |𝑆 | ) (3) If the antenna and the rectifier are not matched, a portion of the power delivered by In a perfect match condition, 𝑃 = 𝑃 and the efficiency defined in Equation (2) is the antenna to the rectifier is reflected in such a way that the effective power delivered to an intrinsicthe rectifier property independent rectifier (𝑃 ) is a fraction of the nominal power from the impedances. delivered by Many the antennaRF rectifier circuits at the rectifier can be found Appl. Sci. 2022, 12,input in the literature operating (𝑃 ). The relation between 𝑃 portREVIEW x FOR PEER in a wide range of frequencies, and 𝑃 and the reflection S-parameter loads, and 2 of (𝑆 input 11 ) Appl. Sci. 2022, 12, 7884 power conditions. is provided Inby [16–18], Equationauthors (3). utilize a simple diode with an output capacitor 2 of 11 in parallel with the load resistance. A four𝑃 diode-bridge = 𝑃 (1 − |𝑆 rectifier | ) is used in [15,19–21]. (3) In other cases, N-stage scalable Dickson or Greinacher 𝜂 architectures = are used. These circuits (2) In a perfect match condition, 𝑃 = 𝑃 and the efficiency defined in Equation (2) is combine rectification an intrinsic and the output voltages thatfrom are proportional to the stagedelivered number (N). If the antenna andrectifier property theIfrectifierantennaare independent and not matched, the rectifier are notthe impedances. amatched, portion of the a portion Many of power RF rectifier the power delivered circuits by by Dickson and cantheGreinacher be rectifier the found in the architectures antenna to the rectifier literature operating are is identical reflected in suchfor a N way = 1 that and the are effectiveused power in [22–24]. delivered to Sec- the antenna to is reflected the rectifier in such (𝑃 ) is a fraction ainnominal waya wide that range the of frequencies, effective power loads, and input antenna atdelivered to ond or higher-order power conditions. Dickson rectifiers In [16–18], canof be authors the found utilize power a simple delivered in [23–25] diode with by theGreinacher and an output the rectifier structures capacitor in the rectifier (Pin ) is a fraction input portof (𝑃the ).nominal The relationpower betweendelivered 𝑃 and 𝑃 by andthe antenna the reflection at the rectifier S-parameter (𝑆 ) in [26–28]. parallel A first withorder isthe Dickson–Greinacher load by provided resistance. Equation (3). A fourfull-wavediode-bridge variation rectifier is can usedbe infound in [27,29– [15,19–21]. In input port (Pnom other ). cases, The relation N-stage between scalable Pnom and Dickson or Pin and the Greinacher reflectionare architectures S-parameter used. These (S11 ) is circuits 31]. Table 1 summarizes the efficiencies, input power, 𝑃 = 𝑃 (1 and− |𝑆load| ) resistance in some of (3) these provided by combine Equation (3). rectification and output voltages that are proportional to the stage number (N). examples operating at 2.45 GHz. In all cases, the rectifier and antenna impedance have Dickson and Greinacher In a perfect match condition,−𝑃identical in = Pnom (1are Parchitectures |S=11𝑃|2 ) and fortheN efficiency = 1 and are defined usedin in Equation [22–24]. (2) is (3) Sec- been matched in such ond or higher-order ana way intrinsic that the rectifier efficiencies property independent of the from different the impedances. Dickson rectifiers can be found in [23–25] and Greinacher structures rectifiers are Many RF rectifier comparable. circuits can be found in the literature operating in a wide range of frequencies, loads, and input In a perfect Despite matchAcondition, theinefficiency [26–28]. variations first order inIn= Pshown Pnom Dickson–Greinacherin Tableand the inefficiency 1,full-wavemost cases, defined variation the can in found choice Equation of the (2) is rectifier power conditions. [16–18], authors utilize a simple diode with anbe in [27,29– output capacitor in anisintrinsic rectifier barely justified.31]. Table property parallel independent 1 summarizes with thetheload frominput efficiencies, resistance. the A four impedances. power, and load diode-bridge Many RF rectifier resistance rectifier is used in[15,19–21]. in some of circuits these In can be The found in the literature examples rectification other operating cases, is a passive at N-stage operating 2.45highly scalable GHz. aDickson inInnonlinear wide all cases, or Greinacher range the architectures of frequencies, rectifier process that and are used. antenna disperses loads, These impedance the and powercircuits input have of the been matched combine in such rectification a way thatandtheoutput voltages that efficiencies of are different the proportional to the stage rectifiers are number comparable. (N). power inputconditions. signal over In the[16–18], Dickson and Greinacher architectures are identical for N = 1 and are used in [22–24]. Sec- in harmonic authors spectrum utilize of a the simple input diode signal’s with an frequencies. output capacitor Section 2 of this parallel Despite the efficiency variations shown in Table 1, in most cases, the choice of the rectifier study with the load is dedicated toresistance. theoretically ond or higher-order A fouranalyzing Dickson diode-bridge thecaneffects rectifiers rectifier be found of this in [23–25]is power used indispersion and Greinacher[15,19–21]. structuresinIn the is barely justified.in [26–28]. A first order Dickson–Greinacher full-wave variation can be found in [27,29– other cases, N-stage rectifier’s efficiency. scalable In Dickson or Greinacher architectures are used. These circuits 31].Section The rectification a3, Table 1issummarizes harmonic passive highly the balance nonlinear efficiencies, input simulations process power, and thatload are dispersesusedthe resistance into compare power some of thethe of these combine 𝑃input effect ofrectification and 𝑅 and signal in output the theefficiency examples over voltages operating harmonic of that atspectrum 2.45 GHz. are the rectifiers In of all theproportional cases, input included the to inthe rectifier frequencies. signal’s and stage Table antenna 1. number At the impedance Section ofend 2have (N).of this Dickson and Greinacher beenarchitectures matched in such a are way that the efficiencies identical for of the N = different 1 and rectifiers are are comparable. used in [22–24]. Section 3, study simulated results is dedicated are corroborated to theoretically analyzing with experimental the effects of this power Despite the efficiency variations shown in Table 1, in most cases, the choice of the rectifier measurements dispersion in of thethe Second three or higher-order rectifier’s rectifiers Dickson withefficiency. higher Inrectifiers Section 3,can is barelyefficiencies justified. in be found harmonic ultra-low balance in [23–25] power simulations and are conditions. Greinacher used Section structures to compare 4 shows thethe [26–28]. Aeffect in fabrication first of and order 𝑃 Dickson–Greinacher andThe characterization 𝑅 rectification in theofefficiency an ofhighly the power full-wave is aultra-low passive rectifiers variation nonlinear RFincluded process canthatin rectifier be Table found disperses operating 1. in the At the end [27,29–31]. powerin ofthe of the WIFI Table 1 summarizes Section 3, simulated input signalresults over theare corroborated harmonic spectrum ofwith experimental the input measurements signal’s frequencies. Section 2 of of thisthe band, pointing outthe three rectifiers some efficiencies, study withisissues dedicated higher to input power, toconsider theoretically efficiencies in andimplementation the analyzing in ultra-low load resistance process. the effects power of this power conditions. in some This dispersion Section of these 4 shows in thethework examples operating points out fabrication some practicalat 2.45 GHz. rectifier’s In and theoretical efficiency. all In cases,issues Section 3,the rectifier that should harmonic balance and antenna berectifier considered simulations are impedance used when to compare have designing the and characterization of an ultra-low power RF operating in the WIFI been matched in such aeffect way 𝑃 and ofthat the 𝑅 efficiencies in the efficiency of ofthe the rectifiers different included in Tableare rectifiers 1. At the end of comparable. an ultra-low band,power RF pointing rectifier out 3,some Section for ambient issues simulated areRF to consider results harvesting in the with corroborated systems. implementation process. This experimental measurements of thework Despite the efficiency points out some variations threepractical shown and higher rectifiers with in Table theoretical 1, issues efficiencies in most that should in ultra-low cases, power the choice beconditions. considered of when Section the rectifier designing 4 shows the is Table barely1.justified. an ultra-low Examples fabrication power RF of common and characterization rectifier RF-Rectifier forCircuits ambient of an ultra-low RF operating power harvesting @ 2.45 RFGHz.rectifier operating in the WIFI systems. band, pointing out some issues to consider in the implementation process. This work pointsRF-Rectifier Table 1. Examples Tableof 1. common Ref. Examples ofout some practical common and theoretical 𝑷𝒊𝒏 RF-Rectifier Circuits 𝑹operating Circuits 𝑳 issues@that Eff. should 2.45 operating 2.45be @ GHz. considered when designing GHz. an ultra-low power RF rectifier for ambient RF harvesting systems. [16]Ref. Ref.1 μW cm 𝑷𝒊𝒏 5.1RkΩ𝑹𝑳 Eff. 45% Eff. Simple diode- Table 1. ExamplesPofincommon L RF-Rectifier Circuits operating @ 2.45 GHz. [17][16] [16] −6.6 1 μW dBm 1 µW cm 6 −2cm 5.1 kΩ kΩ 5.1 kΩ 48% 45% 45% capacitor recti- Simple diode- Ref. 𝑷 𝑹 Eff. Simple diode-capacitor [17] −6.6 dBm 𝒊𝒏 6 kΩ 𝑳 48% 𝑷𝒊𝒏 𝑹𝑳 capacitor [17] recti- − 6.6 [16] dBm 1 μW6 cm kΩ 5.1 48% kΩ 45% fier rectifier [18]Simple diode- −15 dBm [17] 1.7dBm −6.6 kΩ 6 kΩ28 % 48% 𝑷𝒊𝒏 𝑹𝑳 fier [18] [18] capacitor −15 dBm recti- 1.7 kΩ 28%28 % −15 dBm 1.7 kΩ 𝑷𝒊𝒏 𝑹𝑳 1.7 kΩ [15][15] [15] −30 dBm −30 dBm 32 kΩ fier −30 dBm 32 kΩ [18] −15 dBm 8.8% 32 kΩ 8.8%8.8% 𝑷𝒊𝒏 28 % [19] −9.2 dBm 10 kΩ 32 68% kΩ 8.8% 𝑷𝒊𝒏 Four-diodeFour-diode [19] [19] − 9.2 [15] dBm −30 −9.2 dBm 10 10 kΩ 68% dBm kΩ 68% 𝑷 𝒊𝒏 Four-diode Bridge [19] −9.2 dBm 10 kΩ 68% Bridge Bridge Four-diode [20][20] −7.6 [20] dBm −7.6 −7.6 dBm [20] dBm500 500 Ω 500 Ω −7.6 dBm Ω 58% 58% 500 Ω 58%58% 𝑹𝑳 𝑹𝑳 Bridge 𝑹𝑳 [21][21] [21]17 17 dBmdBm [21] 350 17 dBm 17 350 350 Ω Ω35050% Ω dBm Ω 50%50% 50% Appl. Sci. 2022, 12, x FOR PEER REVIEW 2 kΩ 3 of 11 [22][22] [22]−20 −20 dBm −20 dBm 22 kΩ dBm kΩ2 kΩ 5% [22] 5%5%20% 𝑷 −20 dBm 5% [23] −15 dBm 50 Ω Appl.Sci. Appl. Sci.2022, 2022,12, 12,xxFOR FORPEER PEERREVIEW REVIEW Dickson-Greinacher [23] Dickson-Grein- −15 dBm 50 Ω 50 Ω 20% 𝑷𝒊𝒏 𝒊𝒏 33 of of 11 11 N = 1 [23][23] Dickson-Grein- acher N −15 = 1 −15 dBmdBm 50 Ω 20% 20% 𝑷𝒊𝒏 Dickson-Grein- [24] −201 dBm 1 kΩ acher N = 1 [24] −20 dBm kΩ 17% 17% 𝑹𝑳 acher N = 1 [23][24] −5 −20 dBm dBm 50 1kΩ kΩ 17% 70% 𝑹𝑳 𝑷𝒊𝒏 [24][23] [25] −20 − [23] [23] dBm 5 dBm 5 dBm −5−5 dBm dBm 1 50 kΩ kΩ 5 kΩ50 50 kΩ kΩ 17% 70% 70% 70% 59% 𝑷𝑷𝒊𝒏 𝑹𝑳 Dickson N ≥ 2 dBm5 kΩ 55kΩ [25]5 dBm 55dBm kΩ 59% 59% 59% 𝒊𝒏 Dickson NN[25] Dickson N ≥ 2Dickson ≥≥22 [25] [24] −20 dBm 1 kΩ 5% [24] [24] [24] −20 dBm dBm 1 kΩ −20 dBm1 kΩ 1 kΩ 5% 5% −20 5% [26] [26]13 dBm 20 kΩ 20kΩ 37.5% kΩ37.5% [26] [26]13 dBm1313dBm dBm20 kΩ20 37.5% 37.5% Greinacher [27] Greinacher Greinacher [27] [27] −5 dBm−5dBm −5 dBm 5 kΩ 5 kΩ 10% 5kΩ 10% N≥ Greinacher N ≥ 22 NN≥≥22[27] −5 dBm 5 kΩ 10% 10% 𝑹 𝑹𝑹𝑳𝑳 𝑳 𝑷𝑷 [28] [28]−7.5 dBm 300 Ω 300 Ω 9% 𝑷𝒊𝒏 𝒊𝒏 [28] −7.5dBm300 Ω300 Ω 9% 9% dBm 9% −7.5 𝒊𝒏 [28] −7.5 dBm [29] [29] [29]9 9dBm [29] dBm dBm6.76.7 99dBm 6.7kΩ kΩ kΩ6.7 kΩ 68% 68%68% 68% Full-WaveFull-Wave Full-Wave [27] [27]−20 dBm [27] dBm1.2 1.2 −20dBm −20 1.2kΩ kΩ kΩ 6%6% 6% [27] −20 dBm 1.2 kΩ 6% 𝑹𝑹𝑳𝑹 Full-Wave DicksonDickson DicksonDickson Varia- Varia- Varia- [30] −27.5 dBm 14.7 14.7 kΩ kΩ 𝑷𝑷𝑷𝒊𝒏𝒊𝒏 𝑳 Variation [30] −27.5 dBm 14.7 kΩ [30] −27.5 dBm 5%5% 𝒊𝒏 5% 𝑳 tion [30] −27.5 dBm 14.7 kΩ 5% tion tion [31] [31] −20dBm −20 dBm 99kΩ kΩ 12% 12% [31] [31] −−20 dBm 20 dBm 9 kΩ 9 kΩ 12% 12% 2.2.Theoretical TheoreticalLimitations Limitationsof ofthe theRectifier’s Rectifier’sEfficiency Efficiency The2.rectification TheoreticalThe The Limitations is passive of arectification rectification the Rectifier’s highly process process nonlinear Efficiency is aa nonlinear is nonlinear process processthat process withsome with disperses the power some characteristics characteristics of that limit that the limit input signal Theover rectification the the efficiency, the harmonic efficiency, process especially is spectrum especially whena nonlinear when operating of the at operating process at input high with some highfrequency. frequency. signal’s Thecharacteristics inputpower frequencies. The input powerSectionthat wave wave limit signal 2 of signal this study ofthe of theRF theisefficiency, dedicated RF rectifier especially rectifier to can when can bedescribed be theoretically described operating using using analyzing linear at high linear the combinations frequency. combinations effects ofThe of of this the input the wave power wave power complex varia- wavevaria- complex dispersion signal in ble ble 𝑎𝑎 of the efficiency. defined defined RF rectifier In in in canSectionEquation Equation be described (4): (4): using linear combinations of theare wave complex varia- the rectifier’s 3, harmonic balance simulations used to compare of 𝑎Pin defined the effectble and R LininEquation (4): the efficiency of𝑎𝑎the ==rectifiers (( ++ 𝑍𝑍 𝐼𝐼̅ ̅ )) included in Table 1. At the (4) end (4) of Section 3, simulated results̅ ̅ are corroborated where 𝑉𝑉 and where and 𝐼𝐼 are arethe 𝑎 = ( with thevoltage voltageand andcurrent currentcomplex 𝑍 𝐼̅ ) + experimental complexvariables variablesat atthe measurements of the therectifier rectifierinput inputport, port, (4) and 𝑍𝑍 isisthe and therectifier rectifierinput inputimpedance impedance(in(ingeneral generalaacomplex complexnumber). number).The Therectifier rectifierin- in- and 𝐼 ̅ complex where 𝑉put-power put-power are the voltage complex variableand variable cancurrent can complex be obtained be obtained variables from the from at thefollowing the 𝑎𝑎 variable variable rectifier followinginput port, Equation Equation and 𝑍 (5). is the rectifier input impedance (in general a complex number). The rectifier in- (5). put-power complex variable can be obtained from the ∗ 𝑎 variable following Equation 𝑃𝑃 == 𝑎𝑎 𝑎𝑎∗ (5) (5) (5). Appl. Sci. 2022, 12, 7884 3 of 11 three rectifiers with higher efficiencies in ultra-low power conditions. Section 4 shows the fabrication and characterization of an ultra-low power RF rectifier operating in the WIFI band, pointing out some issues to consider in the implementation process. This work points out some practical and theoretical issues that should be considered when designing an ultra-low power RF rectifier for ambient RF harvesting systems. 2. Theoretical Limitations of the Rectifier’s Efficiency The rectification process is a nonlinear process with some characteristics that limit the efficiency, especially when operating at high frequency. The input power wave signal of the RF rectifier can be described using linear combinations of the wave complex variable ain defined in Equation (4): 1 V in √ ain = (√ + Zrec I in ) (4) 2 Zrec where V in and I in are the voltage and current complex variables at the rectifier input port, and Zrec is the rectifier input impedance (in general a complex number). The rectifier input-power complex variable can be obtained from the ain variable following Equation (5). 1 Pin = a a∗ (5) 2 in in The input power (Pin ) is obtained by averaging the corresponding temporal expression of Pin over a period. It can be shown that only the DC, ωo , and the harmonics contribute to the Pin averaged value. The power dispersion over the harmonic spectrum in the rectifica- tion process is described by the Fourier series of the rectifier wave. Equations (6) and (7) show the Fourier series of a half- ( f hrw ) and full-rectified ( f f rw ) waves of a sinusoidal signal with amplitude A and angular frequency ωo . A A 2A ∞ cos(2nωo t) f hrw = π + sin(ωo t) − 2 π ∑ n =1 4n2 − 1 (6) 2A 4A ∞ cos(2nωo t) f f rw = π − π ∑ n =1 4n2 − 1 (7) The DC power component directly delivers a fraction of the input power to the load. The rest of the input power is spitted in the harmonic signal spectrum. Impedance matching networks are designed to guarantee that the input wave at the operating frequency is not reflected. However, RF systems are not matched for all frequencies, and harmonic components different from the matched wave will be mainly reflected when S11 ≤ −3 dB. The numerical evaluation of the DC and the fundamental frequency points out a 67% limit for the half-wave rectifier and a 64% for the full-wave rectifier in a matched system operating at the fundamental frequency (see Table 2). Therefore, in the case of a perfect impedance matching at the input signal frequency, a similar performance is expected for the half-wave and full-wave rectifier (67% and 64%, respectively). Depending on the return loses at the second harmonic, these efficiencies can be increased up to 82% in the case of the half-wave rectifier and up to 94% in the case of the full-wave rectifier. This maximum efficiency values are degraded by the loses in the lumped elements at low input power and by the diode breakdown voltage VBr at high input power [4], as observed in Figures 2–4 in the following section. In the case of high input power, the maximum DC power across the diode is limited by the reverse breakdown voltage in such a manner that VDC diode max = V2Br . Consequently, the maximum DC power that a rectifier V2 can deliver to the load is given by PDCMAX = 4RBrL . This limitation of the output power produces a quick efficiency drop, as Pin grows beyond some specific value that may vary depending on the rectifier’s architecture [32]. 𝜋 𝜋 𝜋 𝜋 𝐴 1 67% 64% 𝑓 = 0.35 -- -- 2 √2𝜋 2𝐴 2 4𝐴 4 2𝑓 = 0.15 15% = 0.30 30% 3𝜋 3√2𝜋 3𝜋 3√2𝜋 3𝑓 -- -- -- -- -- -- Appl. Sci. 2022, 12, 7884 2 4 4 of 11 2𝐴 4𝐴 4𝑓 = 0.03 3% = 0.0 6% 15𝜋 15√2𝜋 15𝜋 15√2𝜋 ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ Table 2. Harmonic coefficients of the full- and half-rectifier waves and the associate power. Therefore, in the case of a perfect impedance matching at the input signal frequency, Half-Wave a similar Rectifier (fishrw performance ) expected Full-Wave for the half-wave and Rectifier full-wave (ffrw rectifier ) and 64%, (67% Frequential Fourierrespectively). OutputDepending Power on the Power Input return loses atFourier the second harmonic, these efficiencies Output Power can Input Power Component be increased Coefficient up to 82% in the Coefficient case of the half-wave Percentage rectifier and Coefficient up to 94% inPercentage Coefficient the case of DC A the full-wave 1 rectifier. 2A 2 This = 0.32 efficiency values are degraded by the loses=in0.64 maximum the lumped elements π π π π 67% 64% fo A at low input1 power and by the diode breakdown– voltage V at high – input power [4], as √ = 0.35 2 observed in2πFigures 2–4 in the following section. In the case of high input power, the max- 2 fo 2A imum DC power 2 across the diode 15% is limited by 4A the reverse breakdown 4 voltage in30% such a √ = 0.15 √ = 0.30 3 2πV 3π manner that = 3π . Consequently, the maximum DC power that a rectifier 3 2π 3 fo – – – can deliver to the load is given by P = . –This limitation of– the output power – pro- 2A 2 4A 4 4 fo √ efficiency duces a quick = 0.03 drop,3% as 𝑃 grows beyond some specific √ =value 6% vary 0.0 that may 15π 15 2π 15π 15 2π depending on the rectifier’s architecture [32]. .. .. .. .. .. .. .. . . . . . . . 3. Parametric Analysis of RF Rectifier Circuits Efficiency As it has been 3. Parametric commented, Analysis the choice of RF Rectifier of anEfficiency Circuits architecture for the RF rectification is barely justified in many examples that can be found in the literature. In the case of the As it has been commented, the choice of an architecture for the RF rectification is design of a rectifier for ambient RF that is destinated to operate in ultra-low power condi- barely justified in many examples that can be found in the literature. In the case of tions, the most important parameter is the efficiency. To determine the best rectifier for the design of a rectifier for ambient RF that is destinated to operate in ultra-low power this specific conditions, Table 1 rectifiers have been simulated using ADS-harmonic bal- conditions, the most important parameter is the efficiency. To determine the best rectifier ance foranalyses to evaluate this specific and compare conditions, the efficiencies. Table 1 rectifiers have been Each rectifier circuit simulated has a partic- using ADS-harmonic ular input impedance that reflects a fraction of the injected power balance analyses to evaluate and compare the efficiencies. Each rectifier circuit (𝑃 ). The intrinsic has a efficiency defined in Equation (2) is referred to the effective power delivered to particular input impedance that reflects a fraction of the injected power (Pnom ). The intrinsic the load (𝑃 efficiency ). Therefore, it is ainmagnitude defined Equation independent (2) is referredfrom theeffective to the input impedance that canto power delivered bethe com- load pared between different rectifiers. Figure 1 shows the harmonic-balance (Pin ). Therefore, it is a magnitude independent from the input impedance that can be simulation setup used to evaluate compared the intrinsic between differentrectifier efficiency rectifiers. Figureof1 different shows the rectifiers. harmonic-balance simulation setup used to evaluate the intrinsic rectifier efficiency of different rectifiers. Figure 1. Simulation setup to evaluate the intrinsic efficiency ηrec of the different rectifiers included in Table 1, using harmonic balance analysis with a 50 Ω single-tone source operating at 2.45 GHz. The different rectifier circuits have been simulated using identical elements. The SMS- 7630 Schottky diode model has been chosen because of its low forward voltage (ranging from 60 to 120 mV at 0.1 mA [33]). The rectifier output capacitors have been fixed to the standard value of 4.7 µF in all cases for the simulations. The analysis of the efficiency as a bidimensional function on Pin and R L points out the existence of different combinations that optimize the efficiency. Figure 2 shows, as example, the simulated ηrec ( Pin , R L ) for the N = 2 Dickson rectifier circuit. As it can be observed, there are multiple Pin and R L combinations producing the maximum efficiency (close to 70%). It is also observed that for the expected ambient RF power (Pin ≤ −30 dBm), the maximum DC conversion efficiencies are lower than 30%, which are higher than 10% only in the range of 1 kΩ < R L < 300 kΩ. The efficiency mapping in Figure 2 offers a good overview of the efficiency general behavior but renders the comparison between rectifiers difficult. tions that optimize the efficiency. Figure 2 shows, as example, the simulated 𝜂 (𝑃 , 𝑅 ) for the N = 2 Dickson rectifier circuit. As it can be observed, there are multiple 𝑃 and 𝑅 combinations producing the maximum efficiency (close to 70%). It is also observed that for the expected ambient RF power (𝑃 ≤ −30 dBm), the maximum DC conversion effi- ciencies are lower than 30%, which are higher than 10% only in the range of 1 kΩ < 𝑅 < Appl. Sci. 2022, 12, 7884 300 kΩ. The efficiency mapping in Figure 2 offers a good overview of the efficiency gen- 5 of 11 eral behavior but renders the comparison between rectifiers difficult. Representation Figure2.2.Representation Figure of of thethe simulated simulated intrinsic intrinsic efficiency efficiency function function (𝑃( P, 𝑅 𝜂 ηrec in , )Rfor L ) for N =N = 2 Dickson 2 Dick- son RFRF rectifier rectifier operatingatat2.45 operating 2.45GHz. GHz. Figure Figure 3a3a shows shows intrinsic intrinsic efficiencies efficiencies as aas a function function of nominal of the the nominalpower power (𝑃 )(Pfornom ) for 𝑅R =L =1010kΩ,kΩ, andand a curve a curve for for eacheach different different rectifier rectifier canobserved. can be be observed. However, However, since since the the inputimpedance input impedance of of eacheach rectifier rectifier is different, is different, the curves the curves in Figure in Figure 3a are3anot arecomparable. not comparable. Figure Figure3b3bshows shows thethe samesame data plotted data plottedas aasfunction of 𝑃of enabling a function Pin enablingthe comparison. the comparison.It It can canbebeobserved observedthat, in Figure that, 3b, only in Figure 3b, four onlydifferent traces are four different appreciated, traces because Nbecause are appreciated, = 2N Dickson, N = 2 Greinacher, = 2 Dickson, and the full N = 2 Greinacher, wave and thevariation full wave rectifier efficiencies variation areefficiencies rectifier degener- are ated in this representation. It can be observed that the more degenerated in this representation. It can be observed that the more complex complex circuits (N = 2 andcircuits full wave variation) offer better efficiencies at higher input power (𝑃 (N = 2 and full wave variation) offer better efficiencies at higher input power (PinHow- > 0 dBm). > 0 dBm). ever, for low for However, andlow ultra-low input power and ultra-low (𝑃 ≤ input −30 dBm), power (Pin ≤the− best 30 efficiencies dBm), the correspond best efficiencies Appl. Sci. 2022, 12, x FOR PEER REVIEW 6 of 11 tocorrespond the simple diode-capacitor rectifier, N = 1 Dickson-Greinacher to the simple diode-capacitor rectifier, N = 1 Dickson-Greinacher rectifier, and four-bridge rectifier, and rectifier. four-bridge rectifier. Figure Figure 3. 3. Simulated Simulated rectifierefficiency rectifier efficiencyfor forthe thesix sixcircuits circuitsininTable Table11as asaafunction function of Pnom in of 𝑃 in (a) (a)and andas asaafunction functionof ofP𝑃 in inin (b). (b). InIn ultra-low ultra-low poweroperation power conditions(𝑃(Pin≤≤−30 operationconditions −30dBm), dBm),it it cancan bebe observed observed that that the the best best efficiency efficiency is is around around 12% 12% and and corresponds corresponds toto thethe simple simple diode-capacitor diode-capacitor rectifier.The rectifier. The second-best performance is obtained with the first order N = 1 Dickson–Greinacher second-best performance is obtained with the first order N = 1 Dickson–Greinacher recti- rectifier (around 8%) and finally the four-diode rectifier with less than 4% efficiency. fier (around 8%) and finally the four-diode rectifier with less than 4% efficiency. Figure 4 shows the intrinsic efficiency η ( P , R ) for R = 100 Ω (Figure 4a) and Figure 4 shows the intrinsic efficiency 𝜂 rec(𝑃 in, 𝑅 )L for 𝑅 L= 100 Ω (Figure 4a) and for R L = 100 kΩ (Figure 4b). In both cases, the load is far from the optimum values for 𝑅 = 100 kΩ (Figure 4b). In both cases, the load is far from the optimum values (around 10 kΩ), and maximum efficiencies are lower than 50%. In the case of low load impedances (𝑅 ∼ 100 Ω), the best efficiencies correspond to the four-diode bridge recti- fier for 𝑃 ≥ 0 dBm. However, under high load-resistance conditions (𝑅 ∼ 100 kΩ), the best performance corresponds to both the second-order Dickson and Greinacher rectifiers Figure 3. Simulated rectifier efficiency for the six circuits in Table 1 as a function of 𝑃 i as a function of 𝑃 in (b). In ultra-low power operation conditions (𝑃 ≤ −30 dBm), it can be observed best efficiency is around 12% and corresponds to the simple diode-capacitor rectif Appl. Sci. 2022, 12, 7884 6 of 11 second-best performance is obtained with the first order N = 1 Dickson–Greinach fier (around 8%) and finally the four-diode rectifier with less than 4% efficiency. Figure 4 shows the intrinsic efficiency 𝜂 (𝑃 , 𝑅 ) for 𝑅 = 100 Ω (Figure for 𝑅 = 100 kΩ (Figure 4b). In both cases, the load is far from the optimum (around 10 kΩ), and maximum efficiencies are lower than 50%. In the case of low load (around 10 kΩ), and maximum efficiencies are lower than 50%. In the case of lo impedances (R L ∼ 100 Ω), the best efficiencies correspond to the four-diode bridge rectifier impedances (𝑅 ∼ 100 Ω), the best efficiencies correspond to the four-diode bridg for Pin ≥ 0 dBm. However, under high load-resistance conditions (R L ∼ 100 kΩ), fier for 𝑃 ≥ 0 dBm. However, under high load-resistance the best conditions (𝑅 ∼ 100 performance corresponds best performance corresponds to both the second-order Dickson andand to both the second-order Dickson and Greinacher rectifiers Greinacher r are achieved in the range −20 andofare dBm ≤ achieved in the ≤ 15ofdBm. Pin range In both −20 dBm ≤ 𝑃 cases, the conversion ≤ 15 dBm. In both cases, the con efficiency under ultra-low powerunder efficiency ≤ −30 dBm (Pin ultra-low ) is(𝑃lower power ≤ −30 than dBm)2%is for lower = 100 R Lthan 2% forΩ 𝑅 = 10 and 5% for R L = 100 kΩ. for 𝑅 in 5% Even = 100 the kΩ. extreme Even inloads described the extreme loadsin described Figure 4,inthe simple Figure 4, the simple diode-capacitor rectifier capacitor (Rect. Simple) efficiency rectifier is notefficiency (Rect. Simple) below the other is not rectifiers. below the other rectifiers. Appl. Sci. 2022, 12, x FOR PEER REVIEW 7 of 11 (a) (b) loaded with 𝑅 = 8.9 kΩ. The four-diode bridge rectifier is the less efficient rectifier show- ( PinFigure , R= 4. Simulated 𝜂 Ω (𝑃 ,𝑅 ) R for 𝑅 = 100 Ω(b). (a) and 𝑅 = 100 kΩ (b). Figure ing 4. Simulated a maximum ηrecfor of 4.3% 𝑅 L ) 5for = 100 kΩ.R LThe better (a) and performance L = 100 kΩdiode-capacitor of the rec- tifier at ultra-low input power is attributable to its simpler structure that minimizes losses due toResults parasiticinimpedances Figures 3 and 4Results in the discard in the constituent Figures 3 and 4 discard the utilization of Dickson and Greinach utilization elements. of Dickson and Greinacher high-order rectifiers at ultra-low orderFigure power. rectifiers 5 at ultra-low shows the power. Figure simulated 5 showsas efficiency the a simulated efficiency function of the as a f Simulated results in Figure 5 have been corroborated with experimental measure- load resistance for the threeof the load bestthat resistance rectifiers for the identified three best rectifiers in Figures 4 andidentified 5. As in Figures observed, 4 and the 5. As ob ments using an experimental setup reproduces the simulation setup Figure 1. A vec- the maximum efficiency of 12.8% corresponds to the simple diode-capacitor maximum tor analyzer efficiency with zero of span 12.8% has corresponds been used as to theΩsimple a 50 diode-capacitor input source at 2.45 GHz, rectifier with loaded loaded with 𝑅 = 4.5 kΩ. The second-best efficiency corresponds to the first-ord 𝑃with=R L = −30 4.5The dBm. kΩ.sameThevector second-best analyzer efficiency measures the 𝑆 corresponds parameterto the first-order needed to evalu- son–Greinacher rectifier, which is considerably lower, showing an efficiency of 7.8 Dickson– Greinacher ate rectifier, which the power delivered is considerably to the rectifier (𝑃 ) according lower, showing(3). to Equation anTheefficiency rectifiersof 7.8% when under loaded test been R have with L = 8.9 by fabricated kΩ.minimizing The four-diode connectionbridge pathsrectifier using aisFR4the PCB less prototype efficient rectifier board. showing Theaoutput maximum DC voltage of 4.3% has for R been L = measured 5 kΩ. The with better a N6781A performanceSMU in of a thefour-wire diode-capacitor voltage rectifiermeasurement at ultra-lowconfiguration input powerby is averaging attributable thetooutput voltage. its simpler 𝑅 values structure thathave minimizes been generated with a standard resistor decade losses due to parasitic impedances in the constituent elements. box. Figure Figure5. 5. ADS-harmonic ADS-harmonic balance simulated balance (blue, red, simulated andred, (blue, blackand lines) and lines) black measured and(blue, red, and measured (blue, red, black dots) efficiencies for simple diode-capacitor rectifier, four-diode Bridge rectifier, and the first- and black dots) efficiencies for simple diode-capacitor rectifier, four-diode Bridge rectifier, and the order Dickson–Greinacher rectifier circuits. 𝑃 = −30 dBm. The optimal efficiencies and 𝑅 values first-order for Dickson–Greinacher each rectifier are labelled. rectifier circuits. Pin = −30 dBm. The optimal efficiencies and R L values for each rectifier are labelled. Experimental measurements show a good agreement with the simulated results. The above analysis shows that the diode capacitor circuit is the most efficient rectifier operat- ing at −30 dBm, achieving efficiencies higher than 10% for loads between 1 kΩ and 10 kΩ. 4. Ambient RF Energy Harvesting Prototype Performance in Real Conditions Appl. Sci. 2022, 12, 7884 7 of 11 Simulated results in Figure 5 have been corroborated with experimental measure- ments using an experimental setup that reproduces the simulation setup Figure 1. A vector analyzer with zero span has been used as a 50 Ω input source at 2.45 GHz, with Pnom =−30 dBm. The same vector analyzer measures the S11 parameter needed to evaluate the power delivered to the rectifier (Pin ) according to Equation (3). The rectifiers under test have been fabricated by minimizing connection paths using a FR4 PCB prototype board. The output DC voltage has been measured with a N6781A SMU in a four-wire voltage measurement configuration by averaging the output voltage. R L values have been generated with a standard resistor decade box. Experimental measurements show a good agreement with the simulated results. The above analysis shows that the diode capacitor circuit is the most efficient rectifier operating at −30 dBm, achieving efficiencies higher than 10% for loads between 1 kΩ and 10 kΩ. 4. Ambient RF Energy Harvesting Prototype Performance in Real Conditions Numerical and experimental data discussed in the previous sections show that the most efficient RF rectifier for Pin = −30 dBm is the simple diode-capacitor circuit when 1 kΩ ≤ R L ≤ 10 kΩ. The implementation of an ambient RF energy harvester is conditioned Appl. Sci. 2022, 12, x FOR PEER REVIEW by practical issues related with the impedance-matching network that should be considered. Theoretically, a lumped C-L impedance network can be used to match the diode-capacitor rectifier with the standard 50 Ω antenna. However, tolerances and parasitic capacitances and inductances of the lumped elements complicate the fabrication of the prototype. All these effects account can the be compensated measured input byimpedance tuning the constituent elements of the of the fabricated impedance diode-capacitor re matching network. nal values of the impedance matching network have been tuned to optimiz Figure 6 shows the picture of the implemented prototype of an RF rectifier. The tion. Figure matching 7 shows network the has been measurements initially of athe designed by using fabricated ADS SmithRF diode-capacitor chart, taking into r account the measured input impedance of the fabricated diode-capacitor type finally matched at 2.47 GHz for -30 dBm input power. The impedance- rectifier. The final values of the impedance matching network have been tuned to optimize the adaptation. work is a C-L network with C = 0.1 pF and L = 6 nH, as shown Figure 7a’s in Figure 7 shows the measurements of a fabricated RF diode-capacitor rectifier prototype shows the measured finally matched at 2.47 GHzinput for −30impedance of the dBm input power. Thematched rectifiernetwork impedance-matching (𝑍 ) at the is a C-L network with C = 0.1 pF and L = 6 nH, as shown Figure 7a’s inset. Figure 7b shows quency. the measured input impedance of the matched rectifier (Zrec ) at the operating frequency. Figure 6. Implemented prototype of an ambient RF energy harvesting system composed by the Figure 6. Implemented input antenna prototype port, the C-L impedance of an network, ambient a thru RFtheenergy connector, harvesting diode-capacitor system rectifier, and a comp put antenna connector to theport, the C-L load resistor. impedance Fabrications network, have been a thru performed usingconnector, the following:the diode-capacitor SMS-7630 [33] connector to the load resistor. Fabrications have been performed using the following diode, capacitors from the HiQ-CBR Series, Case Size 0402 Radio Frequency and Microwave Ceramic Capacitor diode, Kit from Kemet, capacitors fromandthe the HiQ-CBR inductors from the High Series, Frequency Case Inductor Size 0402 Designer Radio Kit EIA and Frequency 0402 from Johanson Technology. ramic Capacitor Kit from Kemet, and the inductors from the High Frequency Induct EIA 0402 from Johanson Technology. Figure 6. Implemented prototype of an ambient RF energy harvesting system composed by put antenna port, the C-L impedance network, a thru connector, the diode-capacitor rectifier connector to the load resistor. Fabrications have been performed using the following: SMS-76 diode, capacitors from the HiQ-CBR Series, Case Size 0402 Radio Frequency and Microwa ramic Capacitor Kit from Kemet, and the inductors from the High Frequency Inductor Desig Appl. Sci. 2022, 12, 7884 EIA 0402 from Johanson Technology. 8 of 11 Figure Figure 7. Measured 7. simulated and Measured Sand 11 parameter 𝑆 and simulated(a) parameter impedance(a) and impedance in the in the Smith Chart (b)Smith of a Chart ( fabricated RF-rectifier prototype matched at 2.45 GHz for -30 dBm input power. Fabrication has Fabricati fabricated RF-rectifier prototype matched at 2.45 GHz for -30 dBm input power. been done using:been done using: [33], CSMS-7630 [33], 𝐶 =𝐶 +𝐶 being 𝐶 = 2.2 pF, 𝐶 = 6.8 mF; 𝑅 = SMS-7630 Load = CRF + Csto being CRF = 2.2 pF, Csto = 6.8 mF; R L = 10 kΩ and 𝐶 = 0.1 pF and Cm = 0.1 pF using a CBR04C108B1GAC RF-capacitor and Lm = 6and using a CBR04C108B1GAC RF-capacitor nH 𝐿L-07C12NJV6S = 6 nH L-07C12NJV6S RF- RF induction for the matching circuit. Simulated 𝑆 only have sense below the series resona autoinduction for the matching circuit. Simulated S11 only have sense below the series resonant quency of the RF inductor used (3.5 GHz). frequency of the RF inductor used (3.5 GHz). Figure 8 overlaps Figure the8 measured overlaps theS11measured parameter S11of parameter of the and the fabricated fabricated andRF matched matched R Appl. Sci. 2022, 12, x FOR PEER REVIEW tifier prototype with the power max-hold measurement of the ambient RF spectr9 rectifier prototype with the power max-hold measurement of the ambient RF spectrum in our laboratory. As observed, the matching frequency coincides with one of the active of the our laboratory. As observed, the matching frequency coincides with one channels of thechannels of the WIFI band. WIFI The band. The efficiencies efficiencies shown shown in Figure in Figure 5 indicate that5only indicate 10% that of only 1 −of −30 dBm (1 μW) input power would be delivered to a 10 kΩ 30 dBm (1 µW) input power would be delivered to a 10 kΩ load, producing a maximum a max load, producing 32 mV voltage and supplying 33.2 μA to the load. However, it must be considered of 32 mV voltage and supplying 33.2 µA to the load. However, it must be considered that the ambient RF signals are constantly oscillating depending on the wireless traffic. the ambient RF signals are constantly oscillating depending on the wireless traffic. As a resultofof result these these fluctuations, fluctuations, theeffective the real real effective outputdelivered output power power delivered to the load to willthe be load w lowerthan lower than that that indicated indicated by Figure by Figure 5 efficiencies. 5 efficiencies. Figure 8. Max-hold ambient RF power spectrum measurement, between 2.35 GHz and 2.55 GHz (in black and Figure 8. Max-hold S11 of the RF left-scale);ambient RF power rectifier spectrum with 6.8 mFmeasurement, and 10 kΩ load between in the output 2.35(inGHz red and and 2.55 GH black and left-scale); S11 of the RF rectifier with 6.8 mF and 10 kΩ load in the output (in red right scale). right scale). As observed in Figure 9, the output voltage oscillates between 16 mV and 36 corresponding to 25.6 nW and 129.6 nW. In the low voltage region, the harvesting sy black and left-scale); S11 of the RF rectifier with 6.8 mF and 10 kΩ load in the output (in r right scale). Appl. Sci. 2022, 12, 7884 As observed in Figure 9, the output voltage oscillates between 169 ofmV 11 and 3 corresponding to 25.6 nW and 129.6 nW. In the low voltage region, the harvesting s can supply 2.5 μA, which should be enough to power ultra-low commercial powe sors. However, forina Figure As observed proper power 9, the outputfunction, several voltage oscillates systems between 16 mVshould and 36 be mV combin corresponding to 25.6 nW and 129.6 nW. In the low voltage region, the harvesting system achieve the minimum voltage requirements. can supply 2.5 µA, which should be enough to power ultra-low commercial power sensors. However, for a proper power function, several systems should be combined to achieve the minimum voltage requirements. Figure 9. Measured output voltage in the 10 kΩ output resistance produced by the ambient RF energy Figure harvesting.output 9. Measured The red line indicates voltage in the 10 kΩand the voltage powerresistance output level corresponding producedto a − by30the dBmambient input power. The blue lines indicate the maximum and minimum voltage and power supplied by the ergy harvesting. The red line indicates the voltage and power level corresponding to a −3 RF harvesting system. input power. The blue lines indicate the maximum and minimum voltage and power supp 5. harvesting the RF Conclusionssystem. The efficiency of the most common RF rectifier circuits has been compared side-by-side using simulations and experimental data. It has been shown that the simple diode-capacitor RF rectifier is the most efficient choice when operating in ultra-low input-power conditions. The fabricated prototype has shown to be suitable for powering ultra-low power sensors in the standby stage using the ambient RF energy. There are two clear methods for improving the RF energy harvested by the described prototype: first, designing a broadband matching network that takes advantage of the energy in all the communication band, and the second possibility is to combine several rectifiers in a power network to increase the output voltage and the final stored charge. Funding: This research has been founded by the Grupo de Aplicaciones Electro-Magnéticas In- dustriales (GAEMI) of the Departament d’Enginyeria Electrònica of the Universitat Autònoma de Barcelona. Institutional Review Board Statement: Not applicable. Informed Consent Statement: Not applicable. Data Availability Statement: Not applicable. Conflicts of Interest: The author declares no conflict of interest. Appl. Sci. 2022, 12, 7884 10 of 11 References 1. Cansiz, M.; Altinel, D.; Kurt, G.K. 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