Antenna Regions

„ MtitiMotivation Antenna Regions „ Definitions

„ Examples Qin Yu „ Conclusion [email protected] Lucent Technologies, Inc.

Motivation Motivation

„ Far field / near field determination integral „ FCC CFR 47 , Part 15. 31(f), clearly states: to EMC measurements 1. At frequencies at or above 30 MHz, measurements may be performed at a distance other than what is specified „ Rules and Standards determine in which provided: measurements are not made in the near field except where it can be shown that near field antenna region measurements are to be measurements are appropriate due to the characteristics made of the device; 2. At frequencies below 30 MHz, measurements may be „ Aperture antenna regions are determined performed at a distance closer than specified in the differently than wire antenna regions regulations; however, an attempt should be made to avoid making measurement in the near field.

978-1-4244-1699-8/08/$25.00 ©2008 IEEE Motivation Definitions

„ Since the radiation pattern does not change in the far „ Far field and near field boundaries are not field, radiated emissions from EUT measured in a far field region have a better correlation with other test data. fixed. They depend on: For example: „ Radiation frequency. In an EMC radiated emission ⎧d ⎫ „ Sizes of the transmitting and receiving measurement, when the formula, 20log⎨ 1 ⎬ antennas. is used to adjust the radiated emission ⎩d2 ⎭ „ Type of antenna. limit specified at d1 to what the value would be at d2, both d1 and d2 must be „ Accuracy that an application requires. in the far field. „ Shield or antenna design application.

Definitions Definitions

Radiating Near -Field Region „ Terms used defining near and far field:

Far Field Region „ Electrically Large Antenna — D > λ, where D is the λ Region Boundaries: largest dimension of the antenna and is the −λ/2π wavelength. −5λ/2π d D „ Electrically Small Antenna — D<< λ. D D −(d+D)2/λ (d>.4D) Magnetic Loop „ For wire antennas, D is the length of the wire. Receiving Antenna R −50D2/λ Dipole −3λ „ For aperture antennas, D is the diagonal dimension −2D2/λ of the aperture. D Aperture „ Receiving antennas, similar dimensions are referred Reactive Near-Field Region to as d. Transmitting Antenna Definitions Definitions

„ Three radiation zones, consist of the reactive near field, „ Field regions may have two or three designations radiati ng near fi eld , and f ar fi eld . 3 „ For the two region designation, there is the far and „ Reactive near field- 1/r terms dominate in field near field equations. (Derivation later in Definitions.) 3 2 „ Near field- 1/r and 1/r terms dominate „ Reactive fields dominate over radiative fields

„ Other names for near field include, Fresnel Zone, „ Other names: Quasistatic or Static field, Quasistatic Field „ Using Huygens’ Principle, where each point on a radiat or i s consid ered t o b e a source o f sp her ica l „ Far field – 1/r terms dominate and the pattern in the waves, this region has spherical wavefronts far field is independent of the distance to the antenna „ No radial energy flow- energy is mostly stored. „ Other names for far field include, Fraunhoffer Zone „ Radial field components not zero. and Radiation Zone

Definitions Definitions

2 „ Radiating near field: 1/r terms dominate in field „ Far field or Fraunhoffer Region: 1/r terms dominate in equations. (D er ivati on l at er i n D efi niti ons.) field equations. (Derivation later in Definitions.) „ Radiation fields dominate and distance from „ Field distribution pattern in independent of distance antenna determines angular field distribution. to antenna. „ Other names: Induction Field, Transition Region, Fresnel Region. „ Using Huygens’ Principle, where each point on a radiator is considered to be a source of spherical „ Using Huygens’ Principle, where each point on a radiator is considered to be a source of spherical waves, this reggpion has planar wavefronts. waves, this region has spherical wavefronts. „ Energy is radiated.

„ Radial energy flow exists. „ Radial field components zero.

„ η Radial field components not zero. „ Wave impedance in free space, o=377Ohms Definitions Definitions:Plane Wave Incident on Aperture

„ Free Space impedance graph, important to shield Sinc Function (Sin(x)/x) didesigners. E-Fie ld Di st rib uti on Uniform E-Field λ π. E-Field Distribution „ Far field exists past 5 /2 . Depends on Distance λ 5 λ = 2.387 = 11.937 to Aperture λ 1 1 =15 η . 1 2 π 2 π o .β . 2 j r ()j .β .r Z E()r 1 1 500 j .β .r Z E()r

Z ()r η . 1 H o 1 j .β .r Z H()r 1 1 377 11. .β . 2 j r ()j .β .r Near-Field Radiation Incident Pattern 0 01020 Plane Wave Front Far-Field Radiation r Pattern

Definitions: Finite Length Antenna Definitions: Finite Length Antenna

„ For the field of an antenna of finite length, where D>λ: „ For the field of an antenna of finite length „ First, find vector potential A, μ G G e − jκR „ = Then, find the E and H vectors from A. A(x, y, z) π I e (x', y', z') dl ' ∫c (x, y, z) Observation Point 4 R G ω G G If receiving antenna has finite size- = − − 1 ∇ ∇ • E A j A j ( A) R this must be taken into account. ωμε r θ G 1 θG y R = (x − x')2 + (y − y')2 + (z − z')2 H = ∇ × A o A μ = x2 + y2 + (z − z')2 θ Using binomial expansion, R is written as a series: x = 2 + 2 + 2 = θ 1 z'2 1 z′3 θ Let r x y z and z r cos R = r − z'cos + ( sin 2 ) + ( cos sin 2 θ ) +" r 2 r 2 2 Definitions: Finite Length Antenna Definitions: Finite Length Antenna

„ Provided r » z’,then the higher order terms become less „ Then the most significant term neglected in the significant. Some approximations on R can be made. phase is the third term. It can be found that The approximation of R in the phase needs to be more when θ =π/2, the third term reaches the accurate than the amplitude of R. maximum and the fourth term is zero. „ For amplitude, let R = r. κ „ ∴ the maximum error of the third term is: „ For phase, let R = r - z’cosθ . κ z ' 2 − j R − j r ⋅ jz 'cos θ ∴ e = e e 2 r R r

Definitions: Finite Length Antenna Definitions: Finite Length Antenna

„ It has been shown by many studies that for most practical „ ∴ For an antenna whose maximum dimension is antennas, with overall lengths greater than a wavelength D, the far field approximation is valid provided λ π o (D> ), a maximum total phase error of /8 rad (22.5 ) can the observations are made at a distance be considered negligible and has little effect on the overall far field radiation κcharacteristics in pattern calculations or 2 D 2 ≤ r ≤ ∞ predictions λ ()z ' 2 π ∴ ≤ 2D2 r < , 2 r 8 „ When λ the maximum phase error by 2 D 2 ≅ θ π o ⇒ r ≥ using R r - z’cos is greater than /8 rad (22.5 ). λ Definitions: Finite Length Antenna θDefinitions: Finite Length Antenna

th „ ∴In order to maintain the maximum phase error „ The 4 term becomes maximum when, less than π/8 rad (22.5o), the 3rd term in R needs to − κ D be kept, that is, θ = tan 1(± 2) and z'= . 2 1 ⎛ z'2 ⎞ θ R ≈ r − z'cos + ⎜ sin 2 θ ⎟. z'3 θ π ⎛ D3 ⎞ π ⎜ ⎟ ∴4thEq.term (4) ⇒ cos sin2 = ⎜ ⎟ ≤ . r ⎝ 2 ⎠ 2 ⎜ 2 ⎟ 2r 12 3 ⎝ λr ⎠ 8 „ The most significant term inθ R being ignored is θ D3 the 4th term: ⎡ 1 ⎛ z'3 ⎞⎤ π ⇒ r ≥ 0.62 . ⎜ cos sin 2 ⎟ ≤ . λ ⎢ 2 ⎜ ⎟⎥ max ⎣ r ⎝ 2 ⎠⎦ 8

Definitions: Finite Length Antenna Definitions:θ Infinitesimal Dipole φ φ D 3 ≤ < 2 D 2 „ Therefore, when 0 . 62 λ r λ , this „ The fields of an infinitesimal dipole are: = = = region is designated as radiating near field or H r κH 0, E 0, Fresnel region. 2 θ κ j I l sin ⎡ 1 1 ⎤ − 3 = πo + ∗ j r < < D H ⎢ 2 ⎥ e , „ When 0 r 0 . 62 λ , this region is θ 4 ⎣ r j( r) ⎦ κκ κ designated as reactive near field region. 3 κ I l cosθ ⎡ 1 1 ⎤ − κ E = o θ + ∗ e j r , „ Thus, for an antenna where D> λ: r πωεπωε ⎢ κ 2 κ 3 ⎥ 2 o ⎣( r) j( r) ⎦ 3 κ ⎧Reactive near-field: 0 < r < [0.62 D ], 3 ⎡ ⎤ − κ ⎪ = I ol sin 1 + κ1 − 1 ∗ j r E ⎢ 2 3 ⎥ e . ⎪ []3 ≤ < 2 4 r j( r) (κr) ⎨Radiating near-field: 0.62 D λ r 2D , o ⎣ ⎦ ⎪ Far-field: 2D2 λ ≤ r < ∞. λ ⎩⎪ λ Definitions: Infinitesimal Dipole Definitions: Infinitesimal Dipole

2 „ So when κr = 1, that is , r = λ/2π, the 1/ r, 1/r and „ Thus, for an infinitesimal dipole or for an 3 1/r terms in equations for Hφ, Er and Eθ are equal; electrically small antenna: λ π κ 2 3 „ For r < /2 , that is, r < 1, the 1/r and 1/r r « λ/2π, reactive near-field region, terms in equations for H , E and E are larger than φ r θ ≅λ π the 1/r term. When r « λ/2π, the 1/r3 terms begin r /2 , transition region, to dominate. r » λ/2π, far-field region.

„ For r > λ/2π, that is, κr > 1, the 1/r term is larger „ The λ/2π boundary is derived from the than the 1/r2 and 1/r3 terms; when r » λ/2π, the infinitesimal dipole, but it also applies to small 1/r2 and 1/r3 terms in equations for H , E and E φ r θ dipole antennas. become negligible and the 1/r term dominates. ≅ ≠ ≠ =>Er 0, Eθ 0, and HΦ 0.

Example 1 Example 1

„ EMCO 3160 -09 Pyramid Horn antenna has a „ EMCO 3160 -09 Pyramid Horn antenna has a working frequency range of 18-26GHz. working frequency range of 18-26GHz. „ Diagonal dimension D = 4.36cm. At 18GHz, λ = „ Aperture size is 3.5cm x 2.6cm. 1.7cm and at 26GHz, λ = 1.1cm. „ Diagonal dimension D = 4.36cm. „ 3λ = 5.1cm to 3.3cm „ At 18GHz, λ = 1.7cm and at 26GHz, λ = 1.1cm. „ (5λ)/2π = .812cm to .525cm „ D > λ – electrically large, but not physically large. 2 „ (50D )/λ = 5.59m to 8.64m 2 „ Note: Most aperture antennas are electrically large „ (2D )/λ = 22.36cm to 34.56cm antennas. „ λ/2π = .271cm to .175cm Example 2 Example 2

„ EMCO 3301B Rod antenna has a working „ EMCO 3301B Rod antenna has a working frequency range of 30Hz-50MHz. frequency range of 30Hz-50MHz. „ D = 1.1m. At 30Hz, λ = 107m and at 50MHz, λ = „ D = 1.1m. 6m „ At 30Hz, λ = 107m and at 50MHz, λ = 6m „ 3λ = 321m to 18m „ D << λ – electrically small, but not physically „ (5λ)/2π = 85.14m to 4.77m small. 2 „ (50D )/λ = .565m to 10.08m (Not a precision „ Note: Most rod antennas and many wire antennas antenna!!) are electrically small antennas. 2 „ (2D )/λ = .023m to .403m (Not electrically large!) „ λ/2π = 17.03m to .955m

Example 3 Example 3

„ EMCO 3115 Double Ridged Waveguide antenna has a „ EMCO 3115 Double Ridged Waveguide antenna has a wide frequency range of 1GHz-18GHz. wide frequency range of 1GHz-18GHz. „ Aperture dimensions are 14cm x 24cm, so the diagonal „ Diagonal, D = 28cm. effective aperture size, is less D = 28cm. De, than D. „ For an aperture antenna, its effective aperture is not necessarily the same as its physical size. F(GHz) λ(cm) (2D2)/λ(m) F(GHz) λ(cm) (2D2)/λ(m) „ For a broadband app,gerture antenna, gain is sacrificed to 3 10 1571.57 11 272.7 5755.75 create a broad frequency range. De, effective aperture 5 6.0 2.61 13 2.3 6.79 size, is less than D. Sometimes De is given. 2 λ „ Since De

„ EMCO 3115 Double Ridggged Waveguide antenna has a „ Far field and near field boundaries are not wide frequency range of 1GHz-18GHz. fixed. They depend on: „ In order to avoid mutual coupling between Tx antenna and EUT, a few wavelengths of separation are needed. „ Radiation frequency. „ Sizes of the transmitting and receiving 3λ λ/2π 3λ λ/2π F(GHz) (cm) (mm) F(GHz) (cm) (mm) antennas. 3 30 15. 9 11 8188.18 434.3 „ Type of antenna. 5 18 9.5 13 6.92 3.6 „ Accuracy that an application requires. 7 12.9 6.8 15 6.00 3.1 „ Shield or antenna design application. 9 10 5.3 18 5.00 2.6