Magnetically coupled resonators analysis simulations and experimental determination [306802]

RAPORT DE CERCETARE

DETERMINAREA PARAMETRILOR S AI REZONATOARELOR CUPLATE MAGNETIC PRIN SIMULĂRI SI DETERMINĂRI EXPERIMENTALE

Coordonator Științific: PhD. Student: [anonimizat]. Mihai IORDACHE MSc. Eng. Maria – Lavinia IORDACHE

București – 2015

Index figuri

Figure 1.2 Schema de principiu utilizată pentru transmiterea fără fir a energie prin cuplaj magnetic rezonant [Sample et al., 2011] 1-8

Figure 1.4 Sistemul de încărcare fără fir pentru baterii la un vehicul electric 1-9

Figure 1.6Efficiency of power transmission in the near field and far field 2-14

Figure 3.1Simplified representation of a two-port system [Agilent Technologies, 2005] 2-22

Figure 3.3Momentum – planar electromagnetic simulation 4-31

Figure 3.4 Simplified diagram of the impedances of the rectification circuit 4-32

Figure 3.5LSSP simulation results: Real part of the input impedance (left); Imaginary part of the input impedance (right) 4-32

Figure 4.1Full 3 Element Array Model ADS Schematic 4-33

Figure 4.2[anonimizat] 4-34

Figure 4.3 Circuit de simulation comportant un filtre d’entrée dimensionné à l’aide de l’outil automatique de synthèse de filtre cette caractéristique 4-36

Figure 4.4Circuit de simulation utilisé pour le dimensionnement du filtre d’entrée 4-37

Index tabele

Table 5.1 4-127

INTRODUCERE

Transferul de energie fără fir a fost subiectul cercetării de peste un secol. Motivațiile pentru această cercetare au venit într-o [anonimizat]. Revenirea in zona cuplajului rezonant, a dat naștere la diferite abordări ale aplicațiilor și integrării transferului de energie electrică fără contacte. [anonimizat], și descrie unele principii primare din spatele acestei cercetări.

[anonimizat] (Fig.1.2) permite transferul de energie in câmp apropiat. Frecvențele de lucru sunt relativ mici (de ordinul a câțiva MHz), de aceea transmițătorul si receptorul sunt chiar voluminoași [Karalis et al., 2008, Cannon et al., 2009, Valtchev et al. 2009]. Eficienta transferului de energie se poate efectua utilizând două sau mai multe obiecte rezonante la aceeași frecvență. [anonimizat], cuplajul rezonant este mult mai eficace [Karalis et al., 2008]. Îmbunătățirea se datorează utilizării regimului de cuplare puternic a [anonimizat] a transferului de energie.

Figure 1.2 Schema de principiu utilizată pentru transmiterea fără fir a energie prin cuplaj magnetic rezonant [Sample et al., 2011]

Structura de transmisie este formată dintr-o singură spiră și o bobină. [anonimizat], care se comportă în același fel ca și un circuit oscilant RLC. [anonimizat]. [anonimizat], Q (Figura1.3).

Figură 2.3. Circuitul echivalent a unui sistem de transmisie a energiei prin cuplaj magnetic rezonant [Sample et al., 2011]

Transferul radiatiant

Energia poate fi, de asemenea, transmisă de la distanță prin intermediul unui câmp de radiație de înaltă frecvență. Această metodă folosește unde electromagnetice cu o frecvență mare care depășește în general 1 GHz, transfer de energie făcându-se în câmp îndepărtat. După cum este prezentat in subcapitolul 1.1, transferul de putere, fără fir pe distanțe de cațiva kilometri este deja realizat cu o eficacitate superioara de 70 %, dar numărul de aplicații viabile la acest nivel de putere este foarte limitat, deoarece normele sanitare de protectie a persoanelor necesita impunerea dimensionării antenelor.

Această tehnică este deseori utilizată pentru a transmite energia la cipuri UHF RFID 1.

Figure 1.4 Sistemul de încărcare fără fir pentru baterii la un vehicul electric

[WiTricity Corporation]

Comparând aplicațiile de proximitate RFID, care utilizează o frecvență de 13,56 MHz sau inferioară [Hwang și Lin, 2009], dispozitivele RFID UHF pot fi alimentate pe o distanță de câțiva metri prin intermediul undelor electromagnetice de înaltă frecvență [Lee și Lee, 2009, Mandal și Sarpeshkar 2007, Yao și colab., 2009]. Acest concept poate fi aplicat, de asemenea, pentru a alimenta circuitele electronice de joasa tensiune, cum ar fi senzorii industriali sau rețele de senzori. Aceste dispozitive pot fi alimentate fie prin energia recuperată de la fasciculul de microunde [Ashry et al., 2009], sau de la baterii care pot fi reîncărcate de la distanță.[Essel et al., 2009].

EXTRAGEREA PARAMETRILOR REZONATOARELOR CUPLATE MAGNETIC

Propagarea undelor electromagnetice în spațiu liber

O unda electromagnetica este format din două componente (electrică și magnetică), care oscilează în fază, în planuri perpendiculare, una față de celălalt, și față de direcția de propagare. Componentele și se supun următoarele relații:

În cazul unei antene de emisie izotopică, și într-un anumit punct din spațiu puterea este distribuită uniform pe suprafața unei sfere de rază R (R fiind distanța dintre antena de transmisie și punctul de observație). Densitatea de putere în orice punct de pe suprafața sferei este dată de relația:

Pentru a determina puterea captată de o antenă plasata in acel punct, trebuie sa se țină seama de câștigurile antenei transmițător și al antenei receptor. Balanța transmisiei între emițător și receptor este dată de ecuația Friis,[]:

unde:

Pr puterea receptată;

Pt puterea transmisă;

Gr caștigul antenei de recepție;

Gt caștigul antenei de transmisie;

Ar deschiderea antenei de recepție;

At deschiderea antenei de transmisie;

lungimea de undă utilizată.

Această ecuație este valabilă pentru transmisie ideală fără traiecte multple. Această ecuație trebuie să fie completată pentru a lua în considerare pierderile în antene, pierderi cauzate de traiectrele multiple și incompatibilitatea polarozației dată de relația.

Aceasta este o formă mult mai realistă a ecuației Friis, care ia în considerare parametri suplimentari, cum ar fi randamentele celor două antene (și ), la intrarea coeficienților de reflexie de a intrarea celor două antene (S22 și S11). Termenul ia în considerare neadaptarea datorită polarizării, care este în mod obișnuit determinată de antenele care au polarizări diferite sau de antene cu aceeași polarizare dar sunt aliniate greșit. Termenul α este folosit pentru a lua în considerare mai multe căi, prin care unda transmisă poate suferi modificăti înainte de a ajunge la antena de recepție. Acest termen este exprimat astfel:

Acest termen ia în considerare coeficientul de reflexie Γn a fiecăruia dintre obstacole și lungimea Dn a fiecărui căi de propagare. Această formulă este foarte dificil de utilizat în practică, pentru că presupune o cunoaștere perfectă a mediului de propagare a undei. Ea este cel mai bine implementată în software CAD pentru simulari electromagnetice complex 3D (Comsol, CST).

Ecuația Friis nu poate fi folosită pentru a calcula puterea receptată in cămp apropiat deoarece presupune că unda este plană. Acesta este cazul în câmp indepartat, dar în câmpul apropiat undele sferice exista. Prin urmare, este mai bine să folosiți parametrul τ pentru a calcula puterea sau randamentul transmiterii undei. [Brown, 1974]:

Distingem două cazuri (câmp apropiat și de câmp îndeparte), evolușia eficienței transmiterii energie, calculată folosind coeficientul τ, este prezentată în figura 2.1. Ecuația Friis este scrisă ca o funcție de τ cu .Tendința arată că, în teorie, este posibil să se obțină randamente de transmisie care tind spre 100%, atunci când τ > 2. Aceasta rezultă, conform ecuației (2.7), prin deschideri mari ale antenelor emițătoare și receptoare în raport cu produsul de lungimea de undă și cu distanța de transmisie.

Fig. 2.1. Bilanțul legăturii între două antene in comunicație.

Putere recupera de la antena de recepție de la unda incidentă, este o imagine a energiei transportate prin undă. Densitate de putere activă transportată de undă este dată de vectorul Poynting, care este produsul vectorial al câmpurilor electrice și magnetice și având aceeași direcție ca și direcția de propagare a undei:

Media densității de putere pe o perioadă este explimată în [W/m²] si magnitudinea vectorului Poynting este scrisă astfel:

Figure 2.2. Randamentul puterii transmise în câmpul apropiat – albastru și câmpul îndepărtat – verde.

În figura 2.2. sunt prezentate variațiile randamentelor corespunzătoare campului apropiat si, respectiv îndepărtat, in functie de τ.

Descrierea Diagramei Smith – Chart

Existența undelor reflectate este semnul sigur al ne adaptãrii liniei: Ori sarcina liniei diferã de cea nominalã (impedanța caracteristicã Zo). ori pe linie existã neuniformitãți. În mod obișnuit propagarea pe liniile lungi se studiazã în regim sinusoidal, iar concluziile se extind apoi la orice fel de semnal. Evident cã pe linie tensiunile celor douã unde (directã și reflectatã) se compun, dar datoritã diferențelor între drumurile parcurse, defazajul între cele douã componente se modificã în continuu de-a lungul liniei. În locurile în care cele douã componente sunt în fazã vom avea un maximum de tensiune (un “ventru”), iar în acele locuri în care sunt in antifazã vom avea un minim (de tensiune). Fenomenul este cunoscut sub denumirea de “unde staționare”. Maximele si minimele de tensiune sunt intercalate, iar distanța intre douã maxime (sau minime) vecine este de jumãtate de lungime de undã (λ/2) (pe linia respectivã). Raportul de unde staționare (cunoscutul “SWR”) este raportul între tensiunea într-un maxim și cea în minimul vecin. 3 Și curenții celor douã componente care circulã pe linie (directã și reflectatã se combinã în același mod ca și tensiunile. Așa cã vom avea maxime (ventre) și minime de curent. Rețineți însã cã totdeauna în dreptul unui maxim de curent vom avea un minim de tensiune, iar în dreptul unui minim de curent avem un maxim de tensiune. Coeficientul de reflexie (în tensiune) “Γ” hotãrãște cât de ample sunt aceste maxime și minime. El este definit ca raportul:

În care VREF și VDIR sunt tensiunile în undã reflectatã, respectiv în undã directã într-un punct dat de pe linie. De remarcat cã fiind raportul înte douã mãrimi vectoriale (exprimate prin numere complexe), “Γ” este el însași un numãr complex (deci are o parte realã și una imaginarã sau un modul și o fazã: Pe toatã lungimea unei linii fãrã pierderi modulul coeficientului de reflexie ([Γ]) este constant, dar faza variazã (cãci depinde de diferența de drum a celor douã unde. Relața matematicã între impedanța de sarcinã Zs și impedanța caracteristicã a liniei Zo dicteazã valoarea coeficientului de reflexie (complex) de la capãtul din spre sarcinã:

(2)

Pe traseul spre capãtul liniei conectat la generator faza sa se modificã continuu în funcție de diferența de drum între cele douã unde. Mãsurând raportul de unde staționare S=SWR cu ajutorul cunoscutului “reflectometru” nu putem cunoaște decât modulul coeficientului de reflexie [Γ], cãci:

(3)

Cunoscând eficacitatea reprezentãrilor grafice în înțelegerea fenomenelor fizice, sã încercãm sã folosim în acest scop cunoscutul sistem “cartezian” de reprezentare graficã a unei funcții (pe care l-am învãțat la școalã): Ne propunem sã reprezentãm grafic o figurã care sã conținã toate valorile impedanței de sarcinã care pe un fider cu impedanța caracteristicã “Zo” produc un raport de unde staționare S=SWE=5. (Cu alte cuvinte ”locul geometric” al sarcinilor care produc SWR=5.)

Douã valori sunt foarte cunoscute: sarcinile pur rezistive Rm =Zo/S =50/5 =10 Ohmi și RM =S.Zo =5×50 =250 Ohmi (vezi fig. 1).

Relațiile (2) și (3) ne aratã cã impedanțele care au aceiași parte rezistivã, iar pãrțile reactive au acelaș modul, dar sunt de semne contrare – produc același SWR [N2]. Deci locul geometric pe care-l cãutãm este poziționat simetric fațã de axa rezistențelor. Ca sã evitãm considerații matematice mai complicate, credeți-ne pe cuvânt cã toate impedanțele de sarcinã care provoacã același SWR se gãsesc pe un cerc, al cãrui diametru este segmentul cuprins între valorile Rm și RM, așa cum este prezentat în fig. 1. (De altfel ecuația (2) este ecuația unui cerc.) Surprizã: Toate valorile posibile ale impedanței de intrare “Zi” în aceastã linie (cu SWR=5 și Zo dat) se gãsesc pe acest cerc. Dacã fixãm pe cerc poziția impedanței de sarcinã Zs =Rs-jXs, putem afla impedanța de intrare în linie Zi “rotindu-ne” pe cerc în sensul acelor de ceasornic (denumit “sensul spre generator”) cu un arc de cerc proporțional cu lungimea electricã a liniei [N3]. Unul din punctele slabe ale reprezentãrii noastre este acela cã este foarte greu sã gradãm aceste cercuri de SWR constant în fracțiuni de lungimi de undã de-a lungul liniei (ca sã aflãm impedanța de intrare), deoarece aceste gradații depind puternic de valoarea raportului de undã staționarã “S=SWR”. În plus uneori reprezentarea Cartezianã “clasicã” este incomodã: În cazul nostru pe aceiași reprezentare trebuie sã putem citi comod și Rm= 10 Ohmi și RM= 500 Ohmi. Inainte de apariția diagramei Smith, pentru ameliorarea situației s-a folosit “reprezentarea Cartezianã normatã” (fig. 2), în care pe cele douã axe sunt reprezentate numere reprezentând rapoartele R* =R/Zn și X* =X/Zn, unde “Zn” este “impedanța de normare”. Este totdeauna profitabil ca impedanța de normare sã fie aceiași cu impedanța caracteristicã a liniei (Zn=Zo). (În acest material mãrimile normate (care sunt simple numere) sunt marcate cu asterisc (*) în partea superioarã).

În fig. 2 se poate observa câștigul principal în reprezentarea Cartezianã normatã: Evantaiul de curbe care pornesc din punctul R* =1 de pe axa realã împarte toate cercurile de SWR constant în diviziuni ale lunginii de undã pe linie. Așa dar acum se poate calcula impedanța de intrare în linie când se cunoaște sarcina (“rotația spre generator”) sau impedanța de sarcinã când se cunoaște impedanța de intare (“rotația spre sarcinã”). Din pãcate nici în aceastã reprezentare graficã cercurile de SWR constant nu au același centru. De asemeni valoarea SWR pentru fiecare cerc trebuie calculatã pornind de la intersecțiile cu axa rezistențelor (corespunzãtoare valorilor “Rm” și “RM” din fig.1). Soluția idealã este diagrama cercului sau diagrama Smith, în care pornind de la reprezentarea Cartezianã normatã (fig.2) se aplicã celor douã axe perpendiculare (R* și X* ) o transformare matematicã (numitã de specialiști “o transformare conformã), astfel cã:

Verticalele din sistemul Cartezian, care reprezintã liniile de R* constant(fig. 2) devin cercurile de R* constant ca în fig. 3. Acestea se înscriu într-un cerc mai mare (care delimiteazã de fapt diagrama Smith denumitã în continuare “diagrama”) și sunt tangente în extremitatea dreaptã a acesteia (notatã cu “infinit”). De remarcat cã cercul de R* =1 trece chiar prin centrul diagramei. Cât privește familia de drepte paralele orizontale care în sistemul Cartezian (fig. 2) reprezintã curbele de X* constant, acestea se transformã în arce aparținând unor cercuri ortogonale celor de R* constant, așa cum se poate observa în fig. 4.

Fascicolul de arce din partea de sus a diagramei reprezintã reactanțele inductive, iar cele din partea inferioarã (notate cu minus) pe 7 cele capacitive. Arcul de reactanțã zero este chiar diametrul orizontal al diagramei și se mai denumește și “axa rezistențelor pure”, sau “diametrul principal”. Diagrama Smith complectã ce conține toate impedanțele cu valori care sunt de luat în seamã pe o linie cu Zo= Zn este reprezentatã în fig. 5 [N4]. Unul dintre marile avantaje ale acestei reprezentãri constã în faptul cã locul geometric al tuturor impedanțelor ce produc un SWR dat este tot un cerc, dar toate aceste cercuri au centrul în centrul diagramei. Alt avantaj constã în aceia cã raza acestor cercuri este calibrabilã în toate mãrimile care apreciazã adaptarea:coeficient de reflexie “[Γ]”, pierderi de reflexie “RL”, SWR, etc. În acest scop pe planșa care conține diagrama Smith (de obicei în partea sa inferioarã) sunt prezentate mai multe scale rectilinii Cu alte cuvinte pentru orice impedanțã marcatã cu un punct pe diagramã, se ia în compas distanța de la acel punct la centrul diagramei (raza cercului de SWR constant). Acest segment se plaseazã pe una din scalele rectilinii menționate și se citesc pe rând toate valorile ce caracterizeazã adaptarea: coeficient de reflexie “[Γ]”, pierderi de reflexie “RL”, SWR, etc. Mai mult decât atât, dacã prin punctul ce reprezintã impedanța respectivã se duce o razã pânã la exteriorul diagramei, așa ca sã intersecteze o scalã circularã gradatã în grade (hexazecimale) pe care se poate citi faza coeficientului de reflexie “Γ”. Scala respectivã este inscripționatã în domeniul +/- 180 grade, cu zero in extremitatea dreaptã a axei rezistențelor pure (diametrul orizontal al diagramei). De obicei este cea mai apropiatã de centrul diagramei, deoarece tot pe exterior sunt plasate și douã scale circulare gradate în fracțiuni de lungime de undã pe linie (necasare stabilirii “rotațiilor” impedanței) Amândouã au “zero-ul” în extremitatea stângã a diametrului orizontal al diagramei și se întind pe o jumãtate de lungime de undã (0,5λ), dar una este gradatã crescãtor în sensul acelor de ceasornic (sensul “spre generator”), iar alta în sens invers (sensul “spre sarcinã”) Așa dar diagrama Smith reprezintã un dublu sistem de reprezentare graficã: Unul (mai deosebit) pentru reprezentarea impedanțelor (normate) și o reprezentare polarã a coeficientului de reflexie “Γ” (valoare complexã) care corespunde unei impedanțe date. Așa cum a fost prezentatã pânã acum (fig. 5) este adesea denumitã diagrama “Z”, sau “diagrama Smith pentru impedanțe”, dar existã și o diagramã Smith pentru cazul când se lucreazã cu admitanțe (diagrama “Y”).

Aceasta se obține plecând de la diagrama “Z” prin dublu “flip” (orizontal și vertical) și aratã ca în fig.6. Aici dupã cum se vede cercurile de conductivitate constantã (G=1/R) sunt tangente la diagramã în extremitatea stângã a diametrului principal (care întocmai ca la diagrama “Z” reprezintã regimul de scurtcircuit: Admitanțã infinitã, corespunzãtor impedanței nule). Aceasta Inseamnã cã cele douã diagrame pot fi suprapuse. Dar în acest caz este necesar sã se utilizeze douã culori diferite pentru a evita confuziile. Cât privește arcele de susceptanțã constanta (B=1/X),acestea aratã ca în fig.7. Important: Utilizatorul trebuie sã-și inchipuie permanent cã peste diagrama impedanțelor (diagrama “Z”) este suprapusã o a douã diagramã Smith pe care sunt reprezentate admitanțele (diagrama Y) și care este imaginea “în oglindã” a acesteia așa cum se vede în fig.6 cu cercurile de conductibilitate constantã “G” și arcele de susceptanțã constantã “B".

Utilizatorul avizat se poate prevala de o proprietate deosebit de utilã a diagramei Smith: Admitanța corespunzãtoare unei impedanțe Z se poate citi pe aceeași diagramã “Z”, dar într-un punct simetric fațã de centrul diagramei. Nu trebuie sã uitați însã cã susceptanțele inductive au semnul minus (ca în fig. 7).

Exemplu simplu: dacã Z* =5+j0, simetricul acestui punct fațã de centrul diagramei se gãsește pe axa rezistențelor la “0,2”. Dar Y =1/Z* =0,2+j0. Este ușor de presupus cã ar urma întrebarea: La ce ne folosește sã trecem când pe diagrama Y, când pe diagrama Z? Circuitele de adaptare sunt în general rețele în scarã, conținând exclusiv reactanțe conectate în brațele serie sau în cele paralel. Când unei anumite impedanțe i se adaugã în serie o reactanțã, punctul “Z” respectiv se deplaseazã pe cercul de R* constant în sensul corespunzãtor, așa cum rezultã din fig,8

Când reactanța ce se adaugã este într-un braț paralel,atunci trebuie operat pe diagrama “Y” prin deplasarea corespunzãtoare pe cercul de conductibilitate “G” constantã (ca în fig. 9). Chiar dacã diagrama Smith nu se mai folosește pentru calcule (dispunându-se de programe dedicate acestui scop) înțelegerea procedurei resprctive permite (celui avizat) sã rãspundã la clasicele întrebãri: “ce s-ar întâmpla dacã….”, sau “ce ar trebui fãcut ca sã….”.

Procedurile prezentate sumar în figurile 8 și 9 ne permit sã analizãm (sau sã proiectãm) principalele tipuri de circuite de adaptare care sunt rețele reactive în scarã . Deplasãrile pe cercurile de “R” sau de “G” constant care corespund adãugãrii unor reactanțe într-un braț serie (respectiv paralel) în rețeaua de adaptare se încep de la sarcinã (impedanța de intrare înh fider “Zi”) și se continuã pâna se ajunge în centrul diagramei (adaptarea perfectã).

S-Parameter

In the case of linear circuit elements or non-linear elements but function with small signals so as to consider the linear, one can characterize a system or a network only through the measured parameters to the input-output ports system without having to worry about the exact content of this one. Once identified parameters, it is possible to predict the exact behavior of this system to any external stimuli, still without knowing its constitution [Hewlett Packard, 1996].

Figure 3.1Simplified representation of a two-port system [Agilent Technologies, 2005]

The S-parameter simulation is a type of simulation small signals usually used to characterize RF components to determine liability or small signals characteristic of a device under conditions of polarization or precise temperature. The non-linear components are linearized around the operating point. The resulting linear circuit is analyzed as a multi-port network. Each port is sequentially excited by small signals and the response is measured and converted to S parameters

La Figure 3.1 gives the representation of a wave in a two-port system, with [Srivastava and Gupta, 2006]:

a1 signal returning to the Port 1;

b1 output signal from the Port 1;

a2 signal returning to Port 2;

b2 signal leaving the Port 2.

The S parameters for this type of system are defined as:

b1 = a1 ·S11+a2 ·S12 (4.3)

b2 = a1 ·S21+a2 ·S22 (4.4)

In these relationships, the represent terms:

S11 reflection coefficient of the Port 1;

S22 reflection coefficient of the Port 2;

S21 transmission coefficient of 1 to 2;

S12 transmission coefficient of 2 to 1.

S – parameters are defined relative to a characteristic impedance which is generally 50

Large Signal S Parameter (LSSP)

Unlike the simulation parameters S, which is basically a simulation for small signal linear or linearized circuits around an operating point, the LSSP simulation uses a method type Harmonic Balance dedicated to non-linear circuits. Since the Harmonic Balance simulation is a simulation "large signal", its solutions include nonlinear effects, which means that the S parameters "large signal" change with the power levels. Like the S-parameters "small signal" S-parameters "large-signal" is defined as the quotient between the incident waves and reflected waves [Agilent Technologies, 2004b]:

(4.5)

The incident and reflected waves are defined as:

(4.6)

(4.7)

with:

Vi, Vj Fourier coefficients of the voltages at the ports i and j at the fundamental frequency;

Ii, Ij Fourier coefficients currents to the ports i and j to the fundamental frequency;

Z0i, Z0j Reference impedances at ports i and j;

R0i, R0j Real parts of Z0i and Z0j.

Port 2 is loaded with an impedance equal to its complex conjugate impedance.

A power signal P1 set by the user is applied to port 1 through a source whose impedance equals the complex conjugate impedance of this port.

Using Harmonic Balance simulation, currents and voltages at ports 1 and 2 are calculated. This information is used for parameter calculation S11 and S21.

Port 1 is loaded with an impedance equal to its complex conjugate impedance.

A power signal P2 = | S21 | 2 · P1 is applied to port 2 through a source whose impedance equals the complex conjugate impedance of this port.

Using Harmonic Balance simulation, currents and voltages at ports 1 and 2 are calculated.

This information is used for parameter calculation S12 and S22. To compare with the simulation parameters S, the LSSP simulation takes into account the nonlinear phenomena, such as the compression gain or changes in incident power. It is therefore preferred when it comes to simulate nonlinear circuits whose behavior is highly dependent on levels of forward power, as is the case of rectennas.

Conclusion

Work around wireless power transmission systems are driven by the accelerated development of mobile electronic devices (smartphones, tablets, wireless sensors). These devices integrate more and more features and the ability to power the wireless would bring great benefit to enable them to limit the battery space..

Several energy wireless transmission techniques exist and the choice of a method over another is based on the specifics of the intended application. Under the RWU project, or there are severe constraints on the dimensions of the transmitter and receiver, as well as the need to perform clock over a distance of several meters, the choice of the microwave transfer is required. The energy levels involved are very low, because of the health standards to protect the people, hence the need for highly sensitive reception and rectennas be able to close the power switch with a low level of input voltage. The detailed design of these structures rectenna very sensitive and full alarm system will be detailed later .

SIMULATION OF THE MAGNETICALLY COUPLED RESONATORS, USE ADVANCED DESIGN SISTEM SOFTWARE (ADS)

Agilent EEsof EDA is the leading supplier of Electronic Design Automation (EDA) software for communications product design. High-frequency, high-speed, device modeling, signal-processing and RF circuit design engineers create better products faster using design flows built on our system, component, and physics-level design tools. We offer complete design integration for products such as cellular phones, wireless networks, radar, satellite communications systems and high-speed digital wireline designs. Applications include electronic system level (ESL), high-speed digital, RF-Mixed signal, device modeling, RF and Microwave design for commercial wireless, aerospace, and defense markets. Our software is compatible with and is used to design Agilent’s own test and measurement equipment.

Advanced Design System (ADS) is the world’s leading electronic design automation (EDA) software

For RF, microwave, and high speed digital applications. In a powerful and easyto- use interface, ADS pioneers the most innovative and commercially successful technologies, such as X-parameters* and 3D EM simulators, used by leading companies in the wireless communication and networking and aerospace and defense industries. For WiMAX,™ LTE, multi-gigabit per second data links, radar, and satellite applications, ADS provides full, standards-based design and verification with Wireless Libraries and circuitsystem- EM co-simulation in an integrated platform.

Complete Design Flow

Create robust designs with first pass success and high yield Innovative and industry-leading simulation technologies

Figure 1

S-parameter linear frequency-domain simulator

Harmonic balance nonlinear frequencydomain simulator

Circuit envelope hybrid time-/frequencydomain nonlinear simulator

Transient/convolution time-domain simulator

Momentum 3D planar EM simulator

Finite Element full 3D EM simulator

X-parameter generator simulator

Signal Integrity Channel simulator

Agilent Ptolemy system simulator

Post processing with Data Display

Figure 2

A powerful Data Display capability allows you to learn about your design’s performance by post-processing and analyzing the data without re-running simulation. Countless built-in functions simplify the process. For added flexibility, you can even write your own functions.

Optimizing your design

Figure 3

Once your initial design is done, ADS optimizers can further improve its nominal performance. The ADS optimization cockpit provides an interactive environment with multiple optimization variables, interactive tuning and progress controls. Using it, you can achieve optimal performance while gaining design insight into the optimized variables versus the goals.

Making your designs more robust

Figure 4

ADS features unique and easy-to-use statistical tools to pinpoint problems during design. Yield sensitivity histograms help identify the most sensitive design components and how best to set their specifications to improve manufacturing yield.

Easy layout in your foundry’s specific process

Figure 5

ADS offers a full-featured tool for generating production-ready RF layouts. With the largest number of fully endorsed foundry design kits, ADS helps you layout your design in your foundry’s specific process. The MMIC Toolbar and layout command line editor, available in all enhanced foundry PDKs, ensures layout editing commands are easily accessible and provide a full suite of layout verification tools.

Catch errors early with ADS desktop DRC and LVS

Figure 6

ADS Desktop design rule check (DRC) enables you to determine whether your physical layout satisfies foundry design rules. Use ADS Desktop layout vs. schematic (LVS) to verify no discrepancies exist between the layout and schematic, to identify missing components and easily find and correct connections in your schematic or layout. ADS also supports DRC/LVS with Calibre and Assura directly from the ADS cockpit.

Integrated Electro-Thermal Solver

Figure 7

ADS provides a full 3-D thermal solver that is tightly integrated with the ADS layout environment and circuit simulators. Simply add the Electro-Thermal controller to the ADS schematic, start a circuit simulation and the integrated thermal solver will run in the background. No more manual export of IC layouts to stand-alone thermal solvers; no more manual import of temperature data into the circuit simulators.

Innovative multi-technology capability

Figure 8

ADS capabilities enable tradeoffs to be made interactively on the IC, laminate, packaging, and printed circuit boards being designed or co-designed together. Circuits designed in multiple technologies can be combined and simulated at both the circuit and full 3D EM level.

CONVERSION CIRCUIT DESIGN

Momentum

Momentum is a planar electromagnetic simulation engine used for the analysis of passive circuits. It uses the Method of Moments (MoM) [Gibson, 2008] to simulate complex EM effects including interconnections, couplings and parasitic elements. The Method of Moments is a numerical method for solving linear partial differential equations formulated as an integral form [Harrington, 1993]. Because this method requires the calculation of values at the edges rather than the entire space, it is much more efficient in terms of computing time that 3D numerical methods. The principle is to create a mesh characterized the surface.

Figure 3.3Momentum – planar electromagnetic simulation

Design circuit

Due to the presence of the diodes, the circuitry rectenna have a nonlinear behavior. That is why it is not practical to design the sub-parts of a rectenna, such as input and output filters, independently of each to the others. Indeed, the input impedance of a diode loaded by a load output and a specific filter is changed if the input filter changes. To illustrate this phenomenon, we compared two input filter design methods starting from a mono-diode rectenna series with an LC output filter, as shown in Figure 1.8.

The equivalent circuit seen is as the mounting of Figure 1.9. The rectifier circuit can be approximated by a characteristic impedance Z0 which acts as load for the transmiter. The peculiarity of this charge is its highly nonlinear behavior due mainly to the presence of diodes used to make rectification. The level of non-linearity certainly depends on the level of power delivered by because of the behavior of antenna diodes. We recall that the power transfer from the antenna to the rest of rectification circuit is optimal when the characteristic impedance of the antenna is the same as the combined impedance of the load, that is to say

Figure 3.4 Simplified diagram of the impedances of the rectification circuit

One can observe that the circuit has a highly capacitive behavior with an real part of 50Ω for a frequency of 300 kHz. The target is to size a simple structure of the input filter to achieve 50Ω impedance matching between the antenna and the rest of the rectification circuit.

To do this, we will first use automatic synthesis tool filters included in ADS. This tool allows to synthesize a filter of order 2 that allows for adaptation between charges:

Z1 = R1+ j ·X1 (4.10)

Z2 = R2+ j ·X2 (4.11)

Figure 3.5LSSP simulation results: Real part of the input impedance (left); Imaginary part of the input impedance (right)

Circuit Simulation to analisess the spiral inductivities (Advanced Design System)

Advanced Design System®is a multi-use RF circuit analysis tool. Its primary use in this design process is as an optimization toolkit. As described before in Section 4.1, the 3D EM Simulator allows the user to extract the interactions between elements by way of an S-parameter matrix. This matrix gives insight to the return loss due to an amalgamation of reflections that we see from the coupling elements, ground reflections, and ohmic dissipation. With this information, the matching input impedance can be calculated in order to give the maximum power transfer at a given frequency.

The network will be simulated from lossless lumped element models. Figure 2-23 shows the full network schematic for a 4 port network (this is from the phased array). The ports have a 50Ω impedance, as well as the input impedance to the S-parameter block. The S-parameter block is an unmodified imported matrix from the 3D MoM Simulator, which is used to hold the EM signature of the couplers (L2) in Figure 2-23. The matrix block is grounded with the same reference as the networks, which represents the semi-infinite ground plane that will be placed under the coupler during design construction. This is important as it shows that the inductive coupling between the half-loops (matrix block) are part of a total network, illustrated in Figure 2-23.

Figure 4.1Full 3 Element Array Model ADS Schematic

Each reactive component to the network was given a practical constraint to limit the optimization time and to give reasonable reactance values for prototyping. There are a variety of optimization techniques that are available for this particular software. The general goal for the optimizer is acquiring an impedance match for the S-parameter matrix. The solution to this goal can be most efficiently isolated by using a gradient descent. The issue, however, with the gradient descent method is a "zig-zag" fashion in which it acquires a final solution to a contour's steepest descent. In this case it might be a better idea to isolate a solution, and then use a different technique to optimize in order to nullify the processing bottleneck.

A particular area of interest for the optimization is the frequency at which the maximum coupling occurs between terminal 1 and terminal 2 in Figure 2-23. This frequency is intrinsic to the resonant network, described in Section 3.3 for the lossless case. However, when the inductive coupling between the half-loops is integrated via S-parameter matrix, spurious losses have been added to the model of the resonant network, as well as an impedance that is dispersive which varies with differing half-loop structures (such as a phased array). This dispersive impedance causes a shift in the optimal frequency that should be used for optimization. Due to this variability, the process of optimization was repeated for a range of frequencies, which pinpoints an optimal frequency for the structure to couple. Once the solution for a single frequency was achieved, this result was compared to the optimization solutions to frequencies in a certain range. From the maximum coupling solutions a single frequency was determined for the most efficient coupling. An example of this output is displayed in Figure 2-24. For each structure this process must be repeated in order to secure optimal results.

Figure 4.2Meshing for the Finite Ground Plane, Single Feed Case

LSSP simulation results: Real part of the input impedance (left); Imaginary part of the input impedance (right)

The adjustment is made at a single point frequency that must be filled. In this case of application, the frequency point is 300 kHz – 10 MHz and the two impedances are given by:

Z1 = 50 Ω

The filter synthesis tool also gives the theoretical characteristics of adaptation between the two ports Z1 and Z2. The curves are shown in Figure 4.9. The value of the S11 parameter reaches a minimum of about -30 dB at 30 MHz, which means a very good impedance matching. The Smith chart confirms that the impedance of the circuit with the filter passes through the point impedance.

A second method of design of the input filter is to use global optimization tool circuit. To do this, we choose an input filter having the same configuration as the filter obtained by the filter synthesis tool (Figure 4.8). The values of the components L and C are variables and we set limits of variations in component values. We chose to vary between 0.1 C and 100 pF and L 1 to 20 nH.

Once the two filters have been designed for two different ways described above, the two circuits are simulated together with a LSSP simulation to take into account non-linearities. Figure 4.10 shows the results of the optimization of the two circuits as a function of frequency.

Once the two filters have been designed for two different ways described above, the two circuits are simulated together with a LSSP simulation to take into account non-linearities. Figure 4.10 shows the results of the optimization of the two circuits as a function of frequency.

The circuit with the filter obtained through the optimization procedure is centered in frequency at 300 kHz. In contrast, the circuit with the synthesized filter is automatically shifted in frequency to 300 MHz. This finding and the fact that the filter synthesis tool uses the S Parameter simulation engine, which is a simulation "small signal" and ignores the non-linear behavior of the circuit. The circuit without the filter to a certain impedance at -15 dBm incident power and the filter is sized to

Figure 4.3 Circuit de simulation comportant un filtre d’entrée dimensionné à l’aide de l’outil automatique de synthèse de filtre cette caractéristique

But the fact of introducing the filter into the circuit actually changes the power injected into the diode and thus the input impedance of the rectifying circuit changes. The result is that the assembly is adapted to a different frequency.

In contrast, in the case of the filter obtained by optimization, this optimization is done through simulation LSSP thus take into account the non-linear characteristic of the circuit. The result of the rétrosimulation line with expectations.

The obvious conclusion is that the overall circuit optimization method is preferred over individual design of each component or part of each sub. This method is the one used later, and the results will be verified by time or Harmonic Balance simulations.

Analiza in Advanced Design System (ADS) a bobinelor in spiral si a rezonatoarelor cuplate magnetic ce le utilizeaza in transmiterea wireless a energiei electromagnetice

Figure 4.4Circuit de simulation utilisé pour le dimensionnement du filtre d’entrée

The first case analisat with 1 inductance

Subtrate design of one inductance

Momentum design one inductance with 1 mm distance betwin spirals

Simulare frecvente intre 300kHz si 30 MHz

Mesh 1 bobina distanta 1 mm intre spire

Results S-Parameters for ADS Momentum

Results S-Parameters for ADS Momentum – Smith Chart

3D calculation of far field

4.4.1.1. Frequenci plan – 300 kHz – 10MHz

O singura bobina distanta 1 mm intre spire

Simulare frecvente intre 10MHz – 100 MHz

II – 10MHz – 100MHz

1 singura bobina distanta 1 mm intre spire

Simulare frecvente intre 100MHz – 250 MHz

III – 100MHz – 250MHz

.5.1.1. 1 singura bobina distanta 1 mm intre spire

Simulare frecvente intre 250MHz – 500 MHz

IV – 250MHz – 500MHz

1.5.1.1. 1 singura bobina distanta 1 mm intre spire

Simulare frecvente intre 500MHz – 1 GHz

V – 500MHz – 1GHz

1.5.1.1. 1 singura bobina distanta 1 mm intre spire

Simulare frecvente intre 10kHz – 60 MHz

V – 10kHz – 60 MHz

Table 5.1

Tabel 4.1

Momentum

Pentru 2 bobine suprapuse

Prototyping Results

The implementation of these networks into a prototype required careful design and consideration for many spurious effects of surroundings. All efforts were directed at reducing the loss in the networks, in order to achieve the large Q values expected from simulating lossless elements. This chapter will describe the process of construction, and results measured from the near field coupling prototype.

Ground Plane/Connector Assembly

The ground plane was required to have a surface that easily bonds with solder flux in order to solder any sort of SMA connector or coupling device to it. It was concluded that brass, instead of copper, would provide a surface that would strengthen the solder connects between all devices. A 2ft by 4ft sheet of brass, with a thickness of 1mm. The metallic sheet can be seen in Figure 4-69. In order to ensure that this planar thickness is applicable for the frequencies under consideration, the skin depth for the minimum frequency must be calculated. Skin depth, or the depth above which surface current flows in the conductor. The skin depth can be mathematically defined by 𝛿=􀶨2𝜔𝜇𝜎

where 𝜎 is the conductivity of the metal. For brass it is known that 𝜎=2.56∗107 𝑆𝑚. The skin depth of

FIGURE 4.9 – Inductors prototipe build on 3D Printer LPKF Laser & Electronics

FIGURE 4.9 – The tools used to calibrate performed measuring device and the used coil

FIGURE 4.9 – Measurements made for a frequency between 300 kHz – 10 MHz

FIGURE 4.9 – Measurements made for a frequency between 10 MHz – 100 MHz

FIGURE 4.9 – Measurements made for a frequency between 100 MHz – 250 MHz

FIGURE 4.9 – Measurements made for a frequency between 250 MHz – 500 MHz

FIGURE 4.9 – Measurements made for a frequency between 500 MHz – 1 GHz

FIGURE 4.9 – Laboratory where have been made the measurements

Figure 4-68 Brass Ground Plane with SMA Connections copper is, at 10MHz maximum, is 3.1∗10−5𝑚 which is well within the thickness of the sheet.

Connections on the ground plane were made in two areas. On one side of the plane there is a connection for the resonant networks, and this takes the form of an SMA 3.5mm connection. An approximate 3mm diameter hole was drilled at different points in the sheet corresponding to different distances between transmitter and receiver. The distances were 200mm, 300mm, and 500mm from the original transmitter placement. The hole for the SMA connector was constructed to be wide enough for the dielectric to fit through the sheet and become visible on the opposite side. The additional space insured that the coupling structure soldered to the tip of the SMA pin would have additional room between it and ground to avoid shorting the element. Once the connectors were fit through the holes, the ground plane of the SMA was soldered onto the ground plane. Figure 4-70 illustrates three SMA connectors soldered to the ground plane (this arrangement would eventually be used for the three element axially directed array). Each element was placed apart with a distance determined by the width of the SMA connector individual grounds. This distance was 13mm, and was a nominal spacing reflected in simulation and numerical analysis. This is the extent of connections on the network side of the ground plane. On the opposite side the SMA pins were soldered to the various structures that were under test (either a wire or strip loop). As in simulation, a side of the element was soldered to the pin while the other end of the half-loop structure was soldered directly onto the ground plane. This maneuver required the user to heat the brass sheet in the area of soldering considerably before attempting to lead the solder onto the element from the sheet for a strong connection. Figure 4-70 displays the coupler structure side of the metallic sheet for the various structures under consideration. 72

Figure 4-69 SMA Connection Separation and Prototype Structural Variations 73

Resonant Network Assembly

The resonant networks under prototyping will be modeled by a simple RLC tank circuit, where R is described as any loss mechanism in the circuit (no physical resistors were used). To understand an idea of the complexity of the loss within the circuit, observe Figure 2-21 in Section 2.4. These networks are connected to the elements via the 3.5mm threaded female SMA connection on the "underside" of the brass metallic ground plane.

The resonant network is built upon an FR4 dielectric board. The underside of the board is a copper sheet and will provide the ground for the network. The connection port of the resonant network (opposite the excitation port) was tightly fastened to a male to male barrel connector in order to give the board, in which the resonant network was placed, a small offset above the ground plane for tuning purposes. This distance allows for connections to be made under the FR4 board and above the brass ground plane. The excitation port utilized a 90o male to male 3.5mm SMA connector in order to create an easier connection for VNA cables.

Variable Capacitor

The primary method of tuning the networks was the variable shunt capacitor placed in series with coupling element. These capacitors ranged from 2-22pF in product specifications. They are designed as plate capacitors that adjust the amount of surface area between two plates as the plates are slid across each other. This design leads to a somewhat linear (should be 2nd order given area) capacitance to turn ratio. Figure 4-71 shows the two different variable capacitors used for prototyping of the resonant networks. Both of the variable capacitors are tuned using a flathead adjustment on the center column of rotation. This tuning screwdriver must have a dielectric tip in order to negate the effects of the electrical length of the screwdriver on the overall performance of the network. It is imperative that the center rotational column is placed on the ground side of the shunt capacitor or the effect of tuning the capacitor, regardless of flathead type, will affect the coupling of the network.

Figure 4-70 Comparison of Variable Capacitors

Inductor Design and Implementation

The primary method for storing magnetic energy in the circuit was the series inductor. As with all elements in this design, the minimization of loss was an important factor in determining the overall Q of the network. There are a variety of structural inductor designs that can be implemented for the frequency range under prototype testing. Since the primary objective of this element is to provide an inductive reactance without loss, an air core inductor was used. Ferromagnetic and dielectric core inductors tend to show higher loss characteristics. Furthermore, any magnetic core material will saturate with a strong applied B field and would thus be inappropriate for any high power applications.

There are several different structural types of air core inductors. These “types” are organized according to the geometry in which the conductor is shaped. “Coil” inductors are structures in which the wire is curved around a central axis of rotation, in a pattern similar to a helix. These air-core coil inductors can take a variety of forms, such as toroidal, helical, and circular. Toroidal inductors have a circular axis of rotation, and are typically used in conjunction with a core material. The helical and circular coil inductors have a linear axis of rotation, and are generally used for inductive coupling purposes. For prototyping purposes, the toroidal inductor was not considered in the design process given its typical uses, and difficulty of construction. Both the helical and circular inductors were designed and tested in the prototype resonant networks. A third variety of inductor was also used for the prototype resonant networks: the spiral inductor. The gap capacitance for the spiral inductor is highly reduced given the proximity of the conducting wire loops to each other, with reference to a helical or circular inductor. The Archimedean spiral was used as it gives a linear spacing between adjacent loops.

Each of the inductors’ loss characteristics were tested by soldering each end of the inductor to two ports on the FR4 test board. Figure 4-72 shows examples of how each of these appeared during testing. 75

Figure 4-71 Coil Inductor Variations

All of the aforementioned coils were tested for loss characteristics. This was observed by measuring the S12 for each of the inductors in series, and measuring the Q from the first harmonic. It is important to note that given the amount of wire required to make the inductors, the resonance of the inductor may have occurred within the frequency range under consideration (10-250MHz). This was undesirable considering an increase in radiation resistance would subsequently increase the loss in the network. Figure 4-73 shows a comparison of the three types of inductors and their S12. In the figure "coil" refers to the helical coil while "compressed coil" refers to the circular coil. All inductors were created with the same length of wire (1.2m) in order to normalize the effect of the inductors' antenna properties. 76 050100150200250300-30-25-20-15-10-50Frequency (MHz)S12 (dB)Differing Inductor Structure Q's Archimedian SpiralCoilCompressed Coil

Figure 4-72 Comparison of S12for Differing Coils

From observing the reverse voltage gain of each of the structures it is apparent that the circular coil structure has a lower Q, with a capacitive characteristic over much of the HF/VHF range. The capacitive characteristic is most likely correlated to the distance between subsequent loops of the coil. For the circular case, these loops are touching each other (held together by dielectric tape). This is an undesirable characteristic as it leads to more loss in the network. The spiral and helical coils both had somewhat similar characteristics with the helical coil providing the highest Q, around 26. By this comparison it was determined that the helical coil was the optimal choice for to implement on the prototype.

Connections/Isolation/Tuning

The networks were directly connected to the coupling elements through the ground plane via a straight male to male 3.5mm SMA connector. These connectors were configured for multiple element arrays to align with each individual element's SMA connector so no stress was placed on adjacent connectors from bending or torsion of any kind. All connects were firmly tightened using a torque wrench intended for use with the VNA that was used for all measurements. Under these conditions the resonant networks were held firmly parallel with the ground plane approximately 3.5cm above the ground plane. Figure 4-74 displays the full networks connected for the 3 element axial directed array. This particular prototyping utilized the three inductors, as presented in Chapter 4. It can be seen that there is a brass sheet standing in the center of the two networks lying normal to the ground plane surface. This purpose of this sheet is to increase isolation between the network inductors. Figure 4-75 compares the coupling between this array and the simulated version of this array. As can be seen from the prototyping, there is a small amount of coupling that occurs around 150MHz, and a larger coupling that occurs just after 250MHz. These two 77 050100150200250-140-120-100-80-60-40-200Frequency (MHz)S12(dB)Comparison between Prototype Axial Directed Array and Simulated Array PrototypeSimulationMax Coupling = -6.8dB105105.2105.4105.6105.8106106.2106.4106.6106.8107-16-15-14-13-12-11-10-9-8-7-6Frequency (MHz)S12 (dB)Coupling for Phased Array

peaks are examples of the inductors in the resonant networks coupling rather than the coupling elements themselves coupling. The strongest peak, however, represents the resonant coupling between the elements and networks combined. For the axially directed array this occurred the strongest at 105.85MHz, around 10MHz higher than prediction in simulation. Figure 4-75 (right) shows an expansion of the frequency range around maximum coupling for the axially directed array.

Figure 4-73 Full Setup for Resonant Tuning

Figure 4-74 (left) Comparison between Simulation and Prototype for Axially Directed Array (3 Element) (right) Expanded View of Prototype Coupling under Resonance

This process was also duplicated for the single feed case, and for the strip-loop cases. Figure 4-76 compares the prototyping frequency sweep with that of the simulation for the single feed case.

This primary structure that was configured as the optimal candidate for maximum coupling was the strip-loop. In order to properly prototype this structure, the inductive coupling between the two loops must be similar, to provide integrity for the simulation to measurement. Figure 4-77 displays the inductive coupling between the prototype strip loop and the simulation. Figure 4-78 displays the resonant coupling comparison for the strip-loop structure. All of the array prototypes had relatively the same 78 050100150200250-90-80-70-60-50-40-30-20-100Frequency (MHz)S12 (dB) SimulationMeasured

maximum coupling between them. This result directly relates the efficiency of the network as a whole to the loss associated with each resonant network. It can be assumed that the load of resonant network (the coupler) has some Q value, called Qc. It can also be assumed that the resonant network has an unloaded Q as well, which can be called Qr. If the coupler is connected to the resonant network, the total Q, Ql is 1𝑄𝑙=1𝑄𝑐+1𝑄𝑟

which results in the majority of the loss stemming from the resonant networks, if all prototype structures tend toward the same maximum coupling. This, in effect, taking into account the derivation for coupling, eliminates the ability to differentiate which structure/network combination forms the strongest coupling. Of course, by reducing the loss in the resonant network, the effects of the couplers will become more apparent, and thus the ability to test specific resonant structures would be available.

Figure 4-75 Comparison of Prototype and Simulation Coupling for the Single Feed Case 79

Experimenta determinations using the realised models

Experimentals Graphic

Analised Cases

Comparations results between experimental and simulations cases

Conclusions

Cette partie contient des résultats de simulation et expérimentaux issus de la procédure de conception

de structures de rectennas dédiées aux faibles niveaux de puissance RF incidente, spécifiques à l’application de réveil à distance par ondes électromagnétiques. Le niveau de puissance incidente préconisé par le CdC technique (-15 dBm), nous a obligé à réaliser des optimisations globales des circuits, ayant comme objectif a maximisation du niveau de tension de sortie. Plusieurs topologies de rectennas ont été comparées en simulation et en mesure. Un nouveau degré de liberté, constitué par l’impédance de l’antenne réceptrice a été introduit dans le processus de conception. Ceci nous a permis d’obtenir un gain de 100 % en termes de niveau de tension DC et donc une portée du système

de réveil potentiellement doublée.

Les résultats expérimentaux sont conformes aux simulations, en raison notamment de l’utilisation de la co-simulation HB-Momentum qui tient compte aussi bien des non-linéarités des circuits que des interactions électromagnétiques et les composants parasites introduits par les interconnections et les éléments distribués.

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On-line databases access to documentation:

[1] http://www.keysight.com/en/pc-1297113/advanced-design-system-ads?cc=US&lc=eng

[2] http://www.maplesoft.com/documentation_center/

Tabelul 5.1 – Parametii electrici ai mașinii studiate

Table 5.1