ICT083 Antenna Design

Small Antennas

I. Theory

1. Small Antenna Theory

Antenna Volume:

- Antenan sphere: A sphere of radius a entirely encloses the antenna.

- Antenna cylinder: A cylinder of radius a and heigth b encloses the antenna.

Figure: Antenna sphere and antenna cylinder [Fujimoto (2013)].

Fujimoto (2013), Modern Small Antennas

Fundamental Limitations of Antennas [Hansen (1981)]

Small Antenna:

- Size boundary is not clearly defined.

- One that is operated below its natural resonance frequency.

- Dipole resonance: Half-wave dipole, a = 0.5 λ, ka = π

- Antenna smaller than 0.1 wavelength: a = 0.1 λ, ka = 0.2π = 0.63

- Has fundamental physical limits in gain and bandwith.

- Analyzed via spheical wave mode theory.

Feartures of Small Antennas

- Electrically small: ka < 1

- Low gain and narrow bandwidth

- Most antennas are a small antenna below 1 MHz.

- Small antennas are inevitable for small platforms: SoPs, ICs, implantable devices

Radian Sphere:

- Sphere with radius

- Antenna length or size in radian wavelength: Multiply by k or divide by λ/(2π)

- Boundary between the reactive near field and the radiationg near field.

1.1 Antenna Efficiency

Figure: Circuit representation of a small antenna

e : Antenna system efficiency including the matching network efficiency

R_r : Radiation resistance

R_L : Loss resistance

R_c : Conductor loss resistance

R_d : Dielectric loss resistance

R_m : Matching network resistance

: Input reflecton coefficient

1.2 Antenna Gain

D = 1.5 = 1.8 dBi : For all small antennas

G : Gain

e : Anenna sytem efficiency

D : Directivity

[Compston (2008)]

Figure: Maximum theoretical gain of small antennas [Shantz (2005)]

Figure: Small antenna gain [Compston (2008)]

1.3 Bandwidth

Chu limit: Fundamental limit (minimum Q) of small antennas. Chu (1948), Wheeler (1960), Harrington (1960)

Quality factor Q:

: R + jX, Series circuit representation of the antenna

: G + jB, Parallel circuit representation of the antenna

: Linear polarized antenna

Fractional bandwith:

|S₁₁| < –10 dB at

f₀ : Center frequency

B = 10% → Q = 5

Percent bandwidth:

Absolute bandwith:

Figure: Reflecton coefficient of an RLC series resonant circuit with various Q values [Ehrenborg (2019)]

1.4

Gain-bandwidth product GB:

1.4 Small Dipole Antennas

Figure: Small dipole antenna

b: Wire radius, much larger than skin depth

L: Dipole length

: Skin depth

: Radiation resistance

: Conductor loss

: Surface impedance

: Reactance

: Directivity

1.5 Small Loop Antennas

a: Loop radius

b: Wire radius, much larger than skin depth

: Skin depth

: Radiation resistance

A: Loop area (πa² for cirular loop, a² for square loop)

: Conductor loss

: Surface resistance

R_p / R₀ : Correction factor due to wire proximity effect. Neglect if c/b > 3

: Directivity

: Inductance, circular loop

: Inductance, square loop antenna with side a and wire radius b

Figure: Geometry of a multiturn helical loop antenna [Balanis]

Figure: Proximity effect correction factor of multiturn loop antennas [Smith]

1.6 Small antenna impedance modeling

- Small dipole

- Small loop

Bibliography

Balanis(2012), Small antennas ans Wheeler's radian sphere

Davis(2010), Fundamental limits on antenna size: a new limit

Shahpari(2018), Fundamental limitations for antenna radiation efficiency

Wheeler(1959), The radiansphere around a small antenna

2. Small Antenna Impedance Matching

2.1 Small antenna input impeance

Figure: Small antenna impedance matching

R : antenna input restance, R << Z₀

X : antenna input reactance, X >> Z₀

: Antenna feed line characteristic impedance

- Matching elements

1st element: Series connection

2nd element: Parallel connection

2.2 Impedance matching equations

: Antenna input impedance divided by 50 ohms.

: Characteristic admittance

Two solutions:

1st solution: [Antenna] + [Series L_1a or C_1a] + [Parallel C_2a]

2nd solution: [Antenna] + [Series L_1b or C_1b] + [Parallel L_2b]

The first matching element: Series connection

b: Negative or positive

The second matching element: Parallel connection

Computer program: exe code, source code

2.3 Small dipole and small loop antenna matching

- Small dipole anenna

- Small loop antenna

3. Active Matching of Small Antennas

4. Small Antenna Examples

4.1 Ferrite Loopstick Antenna

Figure: A ferrite loop stick antenna with inductance of 0.37 mHz at MW (550 - 1550 kHz) and 4.1 mm at LW (150 - 280 kHz). The anenna is 120 mm long with 9.5-mm diameter. The anenna is 6×10^-5 wavelength at 150 kHz [www.ebay.ie]

Ferrite loopstick antenna design references: Koshima (2016), CIA (1957)

4.2 Long Wave Receiving Loop Antenna

Figure: Left = A 2.2-m diameter (0.00091 wavelength at 137 kHz) loop antenna [DF3LP, 1988 in QSL]

Right = Tessun AN-100 AM broadcast receiving loop antenna of 224-mm diameter constructed with 28 turns of 21 gauage varnished magnet wire. It is tunable from 515 kHz to 1850 kHz. The antenna is 0.00038 wavelength at 515 kHz [Antique Radios].

4.3 Whip Antennas

Figure: A 136-174 MHz whip antenna on Motorola CP200D digital 16-channel walkie-talkie [Location Sound Corp]. The antenna size is 128 mm (0.058 wavelength at 136 MHz) including the device chassis.

4.4 식당 호출벨 안테나

Figure: 좌 = 식당용 무선호출벨, 447.8625 MHz (FM) 50×50×18 mm [엔티티웍스]. 우 = 무선호출벨용 루프 안테나 30×15 mm (0.045 파장) [blog.daum.net/dryer/12293237]

4.5 Ceramic Chip Antenna

Figure: Left = Ceramic chip antennas for 2.4 GHz (6.5×2.2×1.0 mm), 868 MHz (16×3×1.7 mm), and 916 MHz (16×3×1.7 mm) [Linx Technology]. For the 868-MHz antenna, the size is 0.046 wavelength. Right = A chip antenna used in a Bluetooth module [NKC Electonics]

Linx chip antenna datasheet (2.4 GHz, 868 MHz, 916 MHz models)

4.6 Headphone Antenna

Figure: The headphone wire can be used as antenna for AM/FM broadcast receivers. An LC-matching circuit is used. Static charges can easily accumulate on the headphone wire and the ESD diode (CM1213) is connected before the LC-matching circuit [Silicon Labs AN602].

Silicon Labs AN602, "Si4822/26/27/40/44 antenna, shematic, layout and design guideline"; Antenna interfacing for the AM/FM/SW receiver chip