Antenna for EMC

Home , Antenna factor, Biconical antenna, Null (physics)

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

1 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.

2 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

3 Overview of antenna

Antenna Concept (I)

4 Antenna Concept (II)

Steps in evaluation of radiation fields : Solution of Maxwell equations for radiation problems)

Magnetic vector potential 1 ∇⋅H =0 HA=∇× Electric scalar potential μ ∇×EjH =− ωμ ∇×()EjA +ω =0 EjA+=−∇ωφ ∇×HjEJ =ωε + ∇×∇×AAAjjAJ =∇() ∇⋅ −∇2 =ωμε ( − ω −∇ φ ) + μ ρ ∇⋅E = If we set ∇⋅Aj = − ωμεφ ε (Lorenz condition) Vector wave equation ∇+22AAJωμε =− μ

Solution is e − jRβ AJ= zzz μ dv ' v' 4πR

5 Steps in evaluation of radiation fields (Far Fields)

1. Find A − jrβ e ' Far field A = μ ∫∫∫ Jejrrβ ˆ⋅ dvn 4π r v'

− jrβ e ' Z-directed sources A = zJedvˆμ jrrβ ˆ⋅ ' ∫∫∫ z 4π r v'

− jrβ e ' Z-directed line sources Az= ˆμ ∫∫∫ Ize()'cos'jzβθ⋅ dv 4π r v'

Steps in evaluation of radiation fields (Far Fields)

2. Find E Far field E =−jAω Transverse to the propagation ˆ ˆ direction r EjAA=−ω(θφ θ + φ) Z-directed sources ˆ E = jAωsinθ θz 3. Find H 1 Far field (Plane wave) H = rEˆ× η

1 Z-directed source HE= φ η θ

6 Far-Field Conditions

Parallel ray approximation for far-field calculations R = rrr−⋅ˆ '

2D2 r > λ Far Field conditions D is the length of rD>> line source r >> λ

Far-Field and Near-field Conditions

7 The ideal dipole (Hertzian dipole) : definition

Ideal dipole: a uniform amplitude current that is electrically small with △z <<λ

Δz /2 e− jRβ A = zIˆμ ∫ dz' −Δz /2 4π R ∵R～r for small dipole e− jrβ A =ΔμIz zˆ 4π r

The ideal dipole (Hertzian dipole): E and H field

1 IzΔ 1 e− jrβ HA=∇× Hj=+β (1 ) sin θφˆ μ 4πβjr r

IzΔ 11 e− jrβ 1 Ej= ωμθθ[1+− ] sin ˆ + E =∇×H 2 jωε 4()πββjrrr IzΔ 11 e− jrβ ηθ [− jr ] cos ˆ 2πβrrr2 Far field condition : βr >> 1 IzΔ e− jrβ Hj= ωμθφsin ˆ 4π r E ωμ μ IzΔ e− jrβ θ == ===ηπ120 377 Ej= β sinθθˆ Hφ βε 4π r

8 The ideal dipole (Hertziandipole): radiated power

Power flowing density : (Unit : w/m*m) 11 IzΔ sin2 θ SEH=×=∗ ()2ωμβ rˆ 224π r 2

Total radiated power (Unit : W)

ωμβ Δz P =⋅=Sds()40() Iz Δ=2222π I ∫∫ 12π λ

Antenna Parameters: radiation pattern E The field pattern with its maximum value is 1 F(,)θφ = θ Eθ ,max

For Hertzian dipole F(θ)=sinθ

9 Antenna Parameters: power pattern

PF(,)θφ = (,)θ φ 2

It is worth noting that the field patter and power pattern are the same in decibles. PF(,)θφ= (,) θφ 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 × Hr )⋅ ˆ UUr(,)θφ (,)/ θφ 2 D(,)θφ ==22 UUrPrave(,)θφ ave (,)/ θφ /4 π

Radiation intensity: the power radiated in a given direction per unit solid angle 1 UEHrr(,)θφ =×⋅ Re(∗ ) 2 ˆ 2

Average radiation intensity: 1 UUdP(,)θ φθφπ=Ω= (,) /4 ave 4π ∫∫

10 Antenna Parameters: Directivity

When directivity is quoted as a single number without reference to a direction, maximum directivity is usually intended.

U 4π D ==m U 2 ave ∫∫ Fd(,)θφ Ω

Directivity of Hertzian dipole 1 IzΔ U (,)θ φωμβθ= ( )22 sin 24π 1 IzΔ ∴U = ()2ωμβ m 24π 1 IzΔ UP(,)θ φπ== /4 ( )2 βωμ ave 34π 3 ∴DdB==10log1.5 = 1.75 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 4(,)πU θφ G(,)θφ = 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

∴GeD= r

11 Antenna Parameters: antenna impedance, radiation efficiency

• Input impedance

Z AA= RjX+ A

RA: Dissipation = Radiation + Ohmic loss XA: Power stored near the antenna

1122 PPP=+ = RI + R I in ohmic22 r A ohmic A • Efficiency

PPRr er == = PPPin+ ohmic R A

• For Ideal dipole Pz2 ωμβ Δ RIz==()80() Δ=222π r 2 I 2 12π λ 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.

12 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

Δz R = 80π 22 ( ) r λ Δz R = 20π 22 ( ) r λ

Antenna Parameters: How to increase the radiation resistance (efficiency) of the short dipole

2. Transmission line loaded antenna

Looks like uniform distribution if △z<

Image theory

3. Inverted-L antenna or Inverted-F antenna

13 Antenna Parameters: effective aperture

a. The effective aperture of an antenna, Ae ,is the ratio of power received in its load

impedance, PRav , to the power density of the incident wave, S ,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 =−RjX wave and the antenna. L rad * (2)matched load. (ie. Z L = Z ant )

Eˆ Suppose the incident wave is arriving at an θ ˆ Z in =+RjXrad angle θ Zˆ =+R jX (1)the open-circuit voltage produced at the in rad

Zˆ =−R jX terminals of the antenna is L rad Voc ˆ Vdloc = Eθ sinθ

14 (2)power density in the incident wave 2 1 Eθ Sav = 2 η0 (3)∵ the load is matched

2222 VEdloc θ sin θ ∴== the received power PR 88RRrad rad 2 112 ⎛⎞V ( ∵ I R=⎜⎟oc R ) 22⎜⎟rad ⎝⎠2Rrad (4)radiation resistance for Hertzian dipole 2 2 ⎛⎞dl R = 80π ⎜⎟ rad ⎜⎟ ⎝⎠λ0 2 2 E λ 2 ∴=P θ 0 sin θ R 640π 2 P ⎛⎞2 λ2 2 λ 0 (5) ∴==AD()θ ,φθθφR 1.5 sin⎜⎟0 =() , em S ⎜⎟4π 4π av ⎝⎠

d. For general antennas, the above relation hold. 4π ⇒=DA()θφ ,2 em () θφ , for lossless antenna. λ0 4π ⇒=GA()θφ ,2 em () θφ , for lossy antenna. λ0

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.

15 Antenna Factor Vrec

Received a. Antenna factor is a common way to E characterize the reception properties of inc Zrec 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:

RjXrad +

Einc AF = (incident field) (received voltage) Vrec V Z V rec rec μV oc Expressed as dB⇒= AFdB dB − dBμ V m Antenna Spetrum analyzer

c.The antenna factor is usually furnished by the manufacture of the antenna. d. Ex: please find the antenna factor at 100MHz for following measurement data. (1)the field intensity of antenna surface is 60dBuV/m (2)The specturm Analyzer measures 40dBuV (3)coaxial loss=4.5dB/100ft Vrec

Specturm

sol: V ant 30ft Analyzer

μV 3 AF=−+⋅ 60dB (40 dBμ V 4.5 dB ) dB m 10 =18.65dB

16 2 E f. Sav = η0

ZL =50Ω

PSA=⋅ Pout out av e E λ 2 V 2 =⋅⋅=SG 0 r av r V r 4π ZL 2 EE2 2 λ00Vr 4πη ∴⋅⋅=⇒GAFr . . == 2 ηπ0 4 ZLrLrVZG λ

The Friss transmission equation

a. The coupling of two antennas. d

θTT,φ θRR,φ

Pt PR

GTTT()θ ,φ GRRR(θ ,φ )

AeT()θ T,φ T AeR()θ R,φ R

17 b. Friss transmission equation: (1) The power density at the receiving antenna of distance d. P SG= T (θφ , ) av4π d 2 T T T

(2) and by the definition of effective asperture, the received power PR

PSARaveRRR= ()θφ ,

PR GATTT(,)θφ eRRR() θφ , ∴= 2 PdT 4π (3) and we know 4π GA()θφ ,= () θφ , RRRλ 2 eRRR

PR λ0 2 ∴=GGTTT (θφ , ) ⋅ R() θφ RR , ⋅ ( ) PdT 4π (4) In terms of dB

⎛ PR ⎞ 10log⎜⎟=+−GGTdB,, RdB 20log f − 20log d + 147.6 ⎝⎠PT

c. Note : Friss transmission equation is valid under two assumptions: (1) the receiving antenna must be matched to its load impedance and the polarization of the incoming wave. (2) two antenna should be in the far field 2 ie . . d > 20 /λo ( for surface antennas )

d > 3λo ( for wire antennas )

18 Half-wave Dipole Antenna:

λ Iz( )=− I sin[β ( z )] m 4

− jrβ e 'jzβθ' cos ' Ejθ = ωμsin θ Izedz ( ) 4π r ∫ cos[(π / 2)cosθ ] F()θ = 2I e− jrβ cos[(π / 2)cosθ ] = jωμm sin θ sinθ βθr sin2

Input impedance = 73+ j42.5Ω

If the length is slightly reduced to achieve resonance, the input impedance is about 73 + 0Ω

Half-wave Dipole Antenna: performance comparison between some dipoles

19 Dipole Antenna: length v.s. directivity

In-phase and enhancement in the far-field Out-of-phase and Cancellation in the far field

Type Directivity HP width Short dipole 1.5 78° A λ/2 dipole 1.64 47° Directivity is dropped A λ dipole 2.41 32° longer ↓

Dipole Antenna: length v.s. radiation resistance

Input resistance is near infinity because the input current is zero at the feeding point.

20 Monopole 1. Radiation resistance is half 2. Directivity is double

1 VAdipole, VA, mono 2 1 ZZA== = A, dipole IIA,, mono A dipole 2

DDmono= 2 dipole

EMI due to Common-mode current can be explained by The theory of monopole antenna.

Small loop antenna:

S is the area of the loop μIe− jrβ Aj= sinθφˆ 4π r Ie− jrβ ES=ηβ2 sin θφˆ 4π r 1 Ie− jrβ HrE=×=−ˆ ηβθθ2 S sin ˆ ηπ4 r

The fields depend only on the magnetic moment (IS) and not the loop shape. S RPI==2 /222 20(β S ) ≅ 31200( ) 2 Ω r λ 2 The radiation resistance can be increased by using multiple turns (N) NS R =Ω31200( )2 r λ 2

21 Small loop antenna:

• The small loop antenna is very popular in receiving antenna.

• Single turn small loop antennas are used in pagers.

• Multi-turn small loops are popular in AM broadcast receiver.

• Small loop antennas are also used in direction-finding receivers and for EMI field strength probes.

Yagi-Uda Antenna

Array Antenna can be used to increase directivity. Array feed networks are considerably simplified if only a few elements are fed directly. Such array is referred to as a parasitic array. A parasitic linear array of parallel dipole is called a Yagi-Uda antenna. Uda antennas are very popular because of their simplicity and relatively high gain.

22 Yagi-Uda Antenna: Principles of operation

If a parasitic element is positioned very close to the driver element, it is excited with roughly equal amplitude.

EEincident= driver

EEEparasitic=− incident =− driver

Because the tangential E field on a good conductor should be zero.

From array theory, we know that the closely spaced, equal amplitude, opposite phase elements will have end-fire patterns. Why null here?

Yagi-Uda Antenna: Principles of operation

The simplistic beauty of Yagi is revealed by lengthening the parasite The dual end-fire beam is changed to a more desirable single end-fire beam.

The H-plane pattern is obtained by the numerical method.

Such a parasite is called a reflector because it appears to reflect radiation from the driver.

0.49λ 0.4781λ

23 Yagi-Uda Antenna: Principles of operation

If the parasite is shorter than the driver, but now placed on the other side of the driver, the patter effect is similar to that when using a reflector in the sense that main beam enhancement is in the same direction.

This parasite is then referred to as a director since it appears to direct radiation in the direction from the driver toward the director.

Spacing = 0.04λ

0.4781λ 0.45λ

Yagi-Uda Antenna: Principles of operation

The single endfire beam can be further enhanced with a reflector and a director on opposite Sides of a driver.

The maximum directivity obtained from three-element Yagi is about 9dBi or 7dBd.

24 Yagi-Uda Antenna: Principles of operation

Optimum reflector spacing SR (for maximum directivity) is between 0.15 and 0.25 wavelengths.

Director-to-director spacings are typically 0.2 to 0.35 wavelengths, with the larger spacings being more common for long arrays and closer spacings for shorter arrays.

The director length is typically 10 to 20% shorter than their resonant length. satuation The addition of directors up to 5 or 6 provides a significant increase in gain.

Yagi-Uda Antenna: Principles of operation

The main effect of the reflector is on the driving point impedance at the feeding point and on the back lobe of The array.

Pattern shape, and therefore gain, are mostly controlled by The director elements.

25 Broadband Measurement Antennas a.FCC prefers to use tuned half-wave dipoles. For measurement of radiated emission from 30MHz~1GH, it is time consuming because its length must be physically adjusted to provide λ /2 at each frequency. b. Broadband measurement antennas for EMC. 1.Input / output impedence is fairly constant over the frequency band. 2.The pattern is fairly constant over the frequency band. two commonly used antenna 1.biconical antenna -- 30MHz~200MHz 2.log-periodic antenna -- 200MHz~1GHz

The Biconical Antenna a. Infinite biconical antenna z 1. half angle θh . ^ 2.feed point with small gap. Eθ b. In the free space , the symmetry ^ θ Hφ h ^^^ θ suggests: HHa = φ φ + ^^^ EEa = θ - θ ▽×=HjEJforJ ωε + , = 0

(1/rHjE sinθθθ )∂∂ / (sinφ ) = ωεr = 0 .....(1)

(-1/rrrHjE )∂∂ / (φθ ) =ωε .....(2)

26 c. by the Faraday’s and Ampere’s law

^ − jrβ0 HHφ = ( 0 /sinθ ) er / from (1) => ∂∂= Hφ sinθθ / 0 ^ − jrβ0 and EHθ = (βωεθ00 / 0 sin ) er / from (2) and TEM mode type ^^ => EHθφ = η0 so , we may uniquely define voltage between two points on the cores as was the case in tx lines.

θθ ^ hh d. Vr ( )== - Edl - (ηθθ He− jrβ0 / r sin )* rd ∫∫00 θπθ=−hh θπθ =−

θh == -ηθθηθHe−−jrββ00 d /sin 2 He jr ln (cot( / 2)) 00∫ 00 h πθ− h

^^2π - jrβ0 by Ampere's law => Ir ( ) =⋅⋅= HΦ r sinθφ d 2 π He ∫ 0 Φ=0 e. Input impedence : ( at r = 0) ^^^ ZVrIrin == ( ) / ( ) (ηπ / )ln(cot( θ / 2)) = 120ln(cot( θ / 2)) r=0 0 hh ^^ Usually , the half angle is choosen such that ZZin= C

27 f. for infinite biconnical antenna ^ Rrad = Zin πθ- 2 2π h ^ proof => PSdsErdd == / 2ηθθφ⋅ 2 sin rad ∫∫∫S av θ 0 0 θθ= h πθ- h 2 == πηHd2 * θ /sin θ 2 πη H *ln(cot( θ /2)) 00∫ 0 0 h θθ= h 2 = (1/2)(2πηπθH00 ) ( / *ln(cot(h /2))) ^^^ 22 == (1/2)(IR )rad (1/2)( IZ ) in

^ f. note : (1) Zin is independent of frequency ( flat response) for infinite core (2) but , practice antenna is finite length , so ^ ' Zin = R + jX→ some storage energy will apear g. EMC biconical antenna

-+ -+

With wire element

28 Log-Periodic Dipole Array (LPDA) Antenna

Scale factor R τ = n+1 < 1 Rn

Spacing factor

d σ = n 2Ln

Why is the LPDA constructed as below?

Log-Periodic Dipole Array (LPDA) Antenna

It is convenient to view the LPDA operation as being similar to that of a Yagi-Uda antenna.

The longer dipole behind the most active dipole behaves as a reflector and the adjacent shorter dipole in front acts as a director.

The radiation is then off of the apex.

29 Antenna Arrays: • Hertzian dipole, small loop, half dipole, and monopole are all omnidirectional because of symmetry of the structure.

• Two or more omni-directional antennas can change the pattern (create null or maximum). Better both for communication and EMI considerations.

• This can be achieved by phasing the currents to the antennas and separated them sufficiently such that the fields will add constructively and destructively to result in the null/maximum patterns.

Antenna arrays z

d a. By using two or more omni-directional antennas to produce maxima and/or nulls in the resulting pattern. -d/2θ d/2 θ1 θ2 b. The far fields at point P due to each antenna are of the form: y r1 r r2 MIˆ ∠α Eeˆ = − jβ 0 r1 θ 1 x ψ r1 P MIˆ ∠0 Eeˆ = − jβ 0 r 2 θ 2 r 2

30 note:

1.II12=∠ 0 and II =∠α , we assume that the currents of the two antennas are equal in magnitude but with phase difference α . 2.Mˆ depends on the type of antennas used. ˆ ⎛⎞dl for Hertzian dipole: Mj= ηβ00⎜⎟ sin θ ⎝⎠4π ˆ for long dipole : MjF= εθ0 () . c. The total field at point P jjαα⎛⎞−−jrββ jr j α 01 02 ˆˆˆ ˆ22⎜⎟ee 2 EEEθθ=+=12 θ MIe⎜⎟ e + e rr ⎜⎟12 ⎝⎠ using for field approximation.

(1) rrr12≅≅ for distance term. dd (2) rr≅+ cosγθφ ≅+ r sin sin 1 22 dd rr≅− cosγ ≅− r sinθ sinφγ ,where cos = aa ⋅ = sinθ sinφ 2 22 ry

jα ⎡⎤⎛⎞⎛⎞⎛⎞ddαα ⎛⎞ ⎢⎥jjβθφβθφ⎜⎟sin sin−− ⎜⎟ sin sin − MIˆ − jrβ ⎜⎟⎜⎟002222 ∴=Eeeeˆ 2 0 ⎢⎥⎝⎠⎝⎠⎝⎠ + e ⎝⎠ θ r ⎢⎥ ⎢⎥ ⎣⎦ jα ⎡⎤− jrβ Ie0 ⎛⎞πα d =×− 2eM2 ⎢⎥ˆ cos⎜⎟ sinθφ sin ⎢⎥r ⎜⎟λ 2 ⎣⎦⎢⎥⎝⎠0 pattern of individual Farray()θφ , elements d. The principle of Pattern Multiplication: The resultant field is the product of the individual antenna element and

the array factor Farray ()θφ , . e. Some examples of the patternsof two-element array

31 (1) d=λ/2,α=0

I∠α I∠0 0 ⎛⎞πsinθ F(=90,)=cosarray θφ⎜⎟ ⎝⎠2 ψ X

(2) d=λ/2,α=π

d 0 ⎛⎞πsinθπ Farray (θφ =90 , )=cos⎜⎟− y ⎝⎠22

I∠α I∠0

(3) d=λ/4,α=π/2

d y πsinθπ ψ 0 ⎛⎞ F(=90,)=cosarray θφ⎜⎟− ⎝⎠44

32 Antenna Arrays:

• Two arbitrary omni-directional antennas

• Separate a distance d

• currents on two antennas are equal in amplitude and phase delay α

− jrβ0 jα /2 Ieπ d α EeMθ =×2[ ]cos(sinsin)θφ − r λ0 2

Pattern of Array pattern individual antenna

Microstrip Antenna and Resonance frequency

port3(1cm,9cm) port2(4cm,8cm)

port4(6cm,6cm) Y 10cm port1(5cm,4cm) (0,0) X 1.6mm

10cm

22 1 ⎛⎞mn ⎛⎞ fr =+⎜⎟ ⎜⎟ 2 με ⎝⎠ab ⎝⎠

33 Antenna Examples: Printed Dipole (at 2.12 GHz)

Source excitation 2D

Current distribution

34 Antenna Examples: Printed Dipole

Radiation Patterns Omni-directional

Gain: 2.1dB Efficiency : 99.1%

Antenna Examples: Microstrip Antenna with edge coupled (at 2.1GHz)

Current distribution

3cm x 4cm ε=2.2

35 Antenna Examples: Microstrip Antenna with edge coupled (at 2.1GHz)

Gain: 6.6dB Efficiency: 71.1%

Antenna Examples: Microstrip Antenna with inserted feed and edge coupled (at 2.1GHz)

Current distribution

36 Antenna Examples: Microstrip Antenna with inserted feed and edge coupled (at 2.1GHz)

Gain: 6.4dB Efficiency: 49.1%

Antenna Examples: Small Array (at 9.76 GHz)

Current distribution

X = 7.5mm Y = 3.75mm

37 Antenna Examples: Small Array (at 9.76 GHz)

Gain: 10.5dB

Antenna Examples: slot coupled microstrip antenna (at 2.213 GHz)

Current distribution

38 Antenna Examples: slot coupled microstrip antenna (at 2.213 GHz)

Gain: 7.1dB Efficiency: 55.3%

Antenna Examples: many others

Crossed slot coupled patch for dual polarization

Edge coupled patch with matching feed network