ΤΗΛ412 Ανάλυση & Σχεδίαση (Σύνθεση) Τηλεπικοινωνιακών Διατάξεων. Διαλέξεις 8-9. Άγγελος Μπλέτσας ΗΜΜΥ Πολυτεχνείου Κρήτης, Φθινόπωρο 2014

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1 ΤΗΛ412 Ανάλυση & Σχεδίαση (Σύνθεση) Τηλεπικοινωνιακών Διατάξεων Διαλέξεις 8-9 Άγγελος Μπλέτσας ΗΜΜΥ Πολυτεχνείου Κρήτης, Φθινόπωρο

2 Διαλέξεις 8-9 Κεραίες (Από την οπτική γωνία του µηχανικού!) Εξισώσεις Helmholtz & Maxwell (&vector calculus). Far Field Coupling. Antenna Characteristics: VSWR, RL, Efficiency, Gain, Bandwidth, HPBW, Polarization. Rough Estimation in High-Gain Antennas. Polarization Mismatch 2

3 Για την σηµερινή διάλεξη έχει χρησιµοποιηθεί υλικό κυρίως από το βιβλίο Kai Chang, RF and Microwave Wireless Systems, Wiley Series in Microwave and Optical Engineering, John Wiley & Sons,

4 Βασική ερώτηση µαθήµατος ή? 4

5 Κεραίες GHz 5

6 Ορισµός Ø Κεραία = διεπαφή (i.e. interface) µεταξύ κυµάτων/ σηµάτων. Ø Kεραία συντονισµός Ø Κεραία = µέγιστη ακτινοβολία. Ø Κυµατοδηγός = ελάχιστη ακτινοβολία. Ø Χαρακτηρισµός: γεωµετρία, κέρδος, λωβός, εύρος ζώνης. 6

7 Ισοτροπικός Ακτινοβολητής και Επίπεδα Κύµατα Ø Θεωρητικό (και µόνο) εργαλείο. Ø Μέτωπο κύµατος σφαιρικό. Ø Πυκνότητα ισχύος: Pt P d = 4πR 2 Ø Μεγάλο R => επίπεδο κύµα (όχι σφαιρικό) Ø Η/Μ πεδίο: Εξίσωση Κύµατος (Helmholtz). 7

8 Θυµάστε τις εξισώσεις του Maxwell? Div: Ροή διανυσµατικού πεδίου ανά µονάδα όγκου Curl: Κυκλοφορία διανυσµατικού πεδίου ανά µονάδα επιφάνειας 8

9 Basic E/M Units Ø charge density ρ (Coulomb/m 3 ), current density J (Ampere/m 2 ) Ø permittivity ε: Farad/m Ø Electric Field E: Volt/m Ø permeability µ: Henry/m Ø Magnetic Field H: Ampere/m Ø Magnetic flux density B=magnetic flux/surface=µ Η: Tesla Ø Magnetic flux Φ: Weber = Henry Ampere Ø Electric Displacement D=ε E: Coulomb/m 2 9

10 Θυµάστε διανυσµατική ανάλυση? 10

11 Τίτλος Θυµάστε διανυσµατική ανάλυση? Laplacian Ø.. curl No(ce that 11

12 Θυµάστε διανυσµατική ανάλυση? 12

13 Θυµάστε διανυσµατική ανάλυση? Τα παρακάτω δείχνουν το Intuition... (curl (rotation)= vector circulation per unit area, div=vector flux per unit of volume, grad=direction of rate of change) Curl Div Grad 13

14 Divergence of A at a point: net outward flux of A per unit volume, when the volume around the point of interest tends to zero. 14

15 Divergence Theorem (aka Gauss Theorem): volume integral of of div of vector A = flux of A through bounding surface of that volume. 15

16 Curl of A at a point: vector, with magnitude = the maximum net circulation of vector A per unit area around that point, as the area tends to zero, direction = normal to area, when area is oriented such that circulation is maximized. Circulation of A in closed path c = line integral of A over c. 16

17 Curl Theorem (aka Stokes Theorem): the surface integral of curl of a vector over an open surface = the closed line integral of the vector over the bounding contour of of the surface.!! Question: what are the units of div( A), curl( A)? 17

18 Εξίσωση Κύµατος (Εξίσωση Helmholtz): Επίλυση k 0 E = = E 2π λ 0 0 e, k jk 0 0 = r, k 0 n 0, Maxwell Διαστάσεις σε Ωhm Λύση Helmholtz 18

19 Far Field Region Ø Region where plane-wave is a good approximation! Ø Practically, where antenna patterns are independent of distance. 19

20 Antenna Analysis (in one minute) Ø Solution through inhomogeneous Helmholtz equation. Ø Antenna with volume V and current J: Ø Current distribution from Antenna geometry. Ø Numerical methods. 20

21 Characteristics: Input VSWR & Impedance We prove these in next lecture! 0< Γ 2 <1, sign depends on book/context ± Return Loss Ø Γ 2 shows the percentage of power lost due to mismatch (reflection). Ø power coupled to antenna = (1- Γ 2 ) times the power delivered from source. Ø Typically, VSWR is less than 2:1. Ø Example: VSWR = 2:1 means that 11% of delivered tx power to antenna is lost! 21

22 Characteristics: Bandwidth Ø Various meanings, depending on context. Ø Most common: impedance bandwidth. Ø Impedance bandwidth: range of frequencies where VSWR below a threshold. Ø Other definitions based on gain, efficiency, patterns etc. Ø Operational bandwidth usually smaller. λ = f c ε r 22

23 Characteristics: Power Radiation Patterns Ø Remember: far-field electric characteristics are independent of distance. Ø Typically, plot power density (Poynting vector across a sphere,centered at the ant.) Ø Simpler approach: draw electric and/or magnetic field at cut planes where the field is maximized. Ø E-plane: E θ plane. Ø Cross-polarization component: E φ λ = f c ε r 23

24 Characteristics: Half-power Beamwidth and Side Lobe Level (SLL) Ø HPBW: the range in degrees such that the radiation drops to one-half. Ø SLL: the number of decibels below the main peak of the side peaks. 24

25 Characteristics: Directivity, Gain, Efficiency Note: P t = P rad Ø Gain and efficiency connect radiated power with ant input power. Ø For example: G P t /4πR 2 is radiated power density towards maximum radiation direction (Note: P t is total input power P t = P rad +P loss ). Ø Why don t we always maximize gain? 25

26 Characteristics: gain-bw tradeoff Ø Gain-beamwidth tradeoff: maximizing one, minimizes the other. Ø Gain-bandwidth tradeoff also exists (fundamental). Ø Thus, maximizing ant gain comes at the cost of reduced bandwidth and increased HPBW. 26

27 Characteristics: Rough Estimation of High-Gain Ant HPBW λ D 0 K1, G K θ θ Ø K 1 70 o, D ant dimension at the plane of interest. Ø K 2 30,000, θ 1, θ 2 are HPBW across the two orthogonal principal planes. 27

28 Characteristics: Effective Area, Polarization Ø Effective area proportional, but smaller, than physical area. Ø Friis Equation is derived through A e 4π G = Α e λ 2 Ø Polarization = direction of Electric Field as a function of time: straight line: linear polarization, circle: circular polarization (LH or RH), ellipse: eliptical polarization. 28

29 Polarization Example Ø linear Ø circular 29

30 Polarization Mismatch Ø reducing received power by 3-dB 30

31 Example: Dipole Open circuit? Ø G = 1.64 => 2.15 dbi Ø ERP: transmitted power referenced to dipole gain. Ø EIRP: transmitted power referenced to isotropic antenna. 31

32 Βασική ερώτηση µαθήµατος ή? 32

33 Κεραίες GHz 33

34 Questions? 34

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