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Antenna Fundamental

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Antenna Fundamental Antenna for EMC Prof. Tzong-Lin Wu EMC Lab. Department of Electrical Engineering National Taiwan University Introduction 1. Overview 2. Steps in evaluation of radiated fields 3. Ideal Dipole (Hertzian Dipole) 4. Antenna parameters 5. Dipole and Monopole 6. Small Loop Antenna 7. Antenna Arrays 8. Examples of Antenna 9. Antennas in communication systems How antenna radiate: a single accelerated charged particle • The static electric field originates at charge and is directed radially away from charge. • At point A, the charge begins to be accelerated until reaching point B. • The distance between the circles is that distance light would travel in time △t, and △r=rb – ra = △t * c • Charge moves slowly compared to the speed of the light, ∴ △r >> △z and two circles are concentric. • The electric field lines in the △r region are joined together because of required continuity of electrical lines in the absence of charges. • This disturbance expands outward and has a transverse component Et , which is the radiated field. • If charges are accelerated back and forth (i.e., oscillate), a regular disturbance is created and radiation is continuous. • This disturbance is directly analogous to a transient wave created by a stone dropped into a calm lake. How antenna radiate : Evolution of a dipole antenna from an open- circuited transmission line • Open-circuited transmission line 1. The currents are in opposite directions on the two wires and behaves as a standing wave pattern with a zero current magnitude at the ends and every half wavelength from the end. 2. The conductors guide the waves and the power resides in the region surrounding the conductors as manifested by the electric and magnetic fields. 3. Electric fields originate from or terminate on charges and perpendicular to the wires. 4. Magnetic fields encircle the wires. • Bending outward to form a dipole 1. The currents are no longer opposite but are both upwardly directed. 2. The bounded fields are exposed to the space. 3. The currents on the dipole are approximately sinusoidal. 4. The situation on the Fig. is the peak current condition. As time proceeds and current oscillation occur, the disturbed fields are radiated. How antenna radiate : Time dynamics of the fields for a dipole antenna Closed loop • At t = 0, peak charges buildup occurs (positive on the upper half and negative on the lower half). current I = 0. • At t = T/4, +/- charges are neutralized and I is maximum. • Because there are no longer charges for the termination of electric fields, they form closed loop near the dipole. • At t = T/2, peak charges buildup again, but upper half is negative and lower half is positive. I = 0. • Notice the definition of λ/2 at t = T/2. Overview of antenna Overview of antenna Antenna Concept (I) Antenna Concept (II) Steps in evaluation of radiation fields : Solution of Maxwell equations for radiation problems) Magnetic vector potential 1 H 0 H A Electric scalar potential E jH (E jA) 0 E jA H jE J A ( A) 2 A j( jA ) J E If we set A j (Lorenz condition) Vector wave equation 2 A 2 A J Solution is e jR A zzz J dv ' v' 4R Steps in evaluation of radiation fields (Far Fields) 1. Find A jr e ' Far field A Jej rˆ r dvn 4r v' jr e ' Z-directed sources A zˆ J ej rˆ r dv' z 4r v' jr e ' Z-directed line sources A zˆ I() z' ejz cos dv ' 4r v' Steps in evaluation of radiation fields (Far Fields) 2. Find E Far field E jω A Transverse to the propagation ˆ ˆ direction r E jω( Aθφ θ A φ) Z-directed sources ˆ E jωsinθ A θz 3. Find H 1 Far field (Plane wave) H rˆ E 1 Z-directed source HE Far-Field Conditions Parallel ray approximation for far-field calculations R r rˆ r ' 2D2 r Far Field conditions D is the length of rD line source r Far-Field and Near-field Conditions The ideal dipole (Hertzian dipole) : definition Ideal dipole: a uniform amplitude current that is electrically small with △z <<λ z /2 e jR A zˆ I dz' z /2 4 R ∵R～r for small dipole e jr A I z zˆ 4r The ideal dipole (Hertzian dipole): E and H field jr 1I z 1 e HHj A(1 ) sin ˆ 4j r r I z11 e jr 1 Ej[1 ] sin ˆ EH 2 j 4j r ( r ) r I z11 e jr [ jr ] cos ˆ 2r r2 r Far field condition : βr >> 1 I z e jr Hj sin ˆ 4 r E I z e jr 120 377 Ej sin ˆ H 4 r The ideal dipole (Hertzian dipole): radiated power Power flowing density : (Unit : w/m*m) 1 1Iz sin2 S E H ()2 rˆ 2 2 4 r 2 Total radiated power (Unit : W) z P S ds ( I z )2 40 2 ( ) 2 I 2 12 Antenna Parameters: radiation pattern E The field pattern with its maximum value is 1 F(,) E ,max For Hertzian dipole F(θ)=sinθ Antenna Parameters: power pattern PF(,)(,) 2 It is worth noting that the field patter and power pattern are the same in decibles. PF(,)(,) dB dB Power pattern parameters Antenna Parameters: Directivity Directivity: The ratio of the radiation intensity in a certain direction to the average radiation intensity. 1 2 Re(E H ) rˆ U(,)(,)/ U r 2 D(,) 22 Uave( , ) U ave ( , ) / r P / 4 r Radiation intensity: the power radiated in a given direction per unit solid angle 1 U( , ) Re( E H ) r2 rˆ 2 Average radiation intensity: 1 U( , ) U ( , ) d P / 4 ave 4 Antenna Parameters: Directivity When directivity is quoted as a single number without reference to a direction, maximum directivity is usually intended. U 4 D m U 2 ave Fd(,) Directivity of Hertzian dipole 1 Iz U( , ) ( )22 sin 24 1 Iz U ()2 m 24 1 Iz UP( , ) / 4 ( )2 ave 34 3 D 10log1.5 1.75 dB 2 Antenna Parameters: Gain Gain : 4π times the ratio of radiation intensity in a given direction to The net power accepted by the antenna from the connected transmitter 4U ( , ) G(,) Pin • If all input power appeared as radiated power (Pin=P), Directivity = Gain. • In reality, some of the power is lost in the antenna absorbed by the antenna and nearby structures). • Radiation efficiency: P eerr,(0 1) Pin G er D Antenna Parameters: antenna impedance, radiation efficiency • Input impedance ZAAA R jX RA: Dissipation = Radiation + Ohmic loss XA: Power stored near the antenna 1122 PPPRIRI in ohmic22 r A ohmic A • Efficiency PPRr er PPPRin ohmic A • For Ideal dipole Pz2 R ( I z )2 80 2 ( ) 2 r 2 I 2 12 I A Rr is very small since △z << λ Antenna Parameters: ideal dipole is an ineffective radiator Example For radiator △z = 1cm, f0 = 300MHz (λ= 1m) → Rr = 79mΩ ∴ It needs 3.6A for 1W of radiated power. For radiator △z = 1cm, f0 = 1GHz (λ= 30cm) → Rr = 0.87Ω ∴ It needs 1.5A for 1W of radiated power. Antenna Parameters: How to increase the radiation resistance (efficiency) of the short dipole Practical short dipole with triangular-like current distribution 1. Capacitor-plate antenna: the top-plate supply the charge such that the current on the wire is constant z R 80 22 ( ) r z R 20 22 ( ) r Antenna Parameters: How to increase the radiation resistance (efficiency) of the short dipole 2. Transmission line loaded antenna Looks like uniform distribution if △z<<L Image theory 3. Inverted-L antenna or Inverted-F antenna Antenna Parameters: effective aperture a. The effective aperture of an antenna, Ae ,is the ratio of power received in its load impedance, PR , to the power density of the incident wave, S av ,when the polarization of the incident wave and the polarization of receiving antenna ard matched: PR 2 Ae in m Sav b. The maximum effective aperture Aem is the A e when the maximum power transferring to the load takes place, which means load impedance is the conjugate to the antenna impedance. c. Example: compute the Aem (maximum effective aperture) of a Hertzian dipole antenna. Ans: To solve Aem, two conditions should be kept in mind: (1)matched polarization for the incident θ Zˆ R jX wave and the antenna. L rad * (2)matched load. (ie. ZZ L ant ) Eˆ Suppose the incident wave is arriving at an ˆ Zin Rrad jX angle (1)the open-circuit voltage produced at the terminals of the antenna is Voc ˆ Voc = E dl sin (2)power density in the incident wave 2 1 E Sav 2 0 (3) the load is matched 2222 Voc E dl sin the received power PR 88RRrad rad 2 112 V ( I R=oc R ) 22rad 2Rrad (4)radiation resistance for Hertzian dipole 2 2 dl R 80 rad 0 2 2 E 2 P 0 sin R 640 2 P 2 2 2 0 (5) AD, R 1.5 sin 0 , em S 4 4 av d. For general antennas, the above relation hold. 4 DA, 2 em , for lossless antenna. 0 4 GA, 2 em , for lossy antenna. 0 The maximum effective aperture of an antenna used for reception is related to the directive gain in the direction of the incoming wave of that antenna when it is used for transmission. Antenna Factor Vrec Received a. Antenna factor is a common way to E characterize the reception properties of inc EMC antenna. b. Antenna factor is defined as the ratio of the incident electric field at the surface of the measurement antenna to the received voltage at the antenna terminals: Rrad jX Einc AF (incident field) (received voltage) V rec Vrec Zrec V Voc Expressed as dB AFdB dB dB V m Antenna Spectrum analyzer c.The antenna factor is usually furnished by the manufacture of the antenna.
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