Basic Principles of Electrically Small Antennas

Home , Antenna types, Radiation resistance

By Gary Breed Editorial Director

lectrically small With wavelengths in the 200 to 600 meter This tutorial looks at electri- antennas have range, these antennas far exceed the λ/10 cri- cally small antennas, which Ebeen an important terion. Antennas for FM and television broad- have always been, and will part of communications cast reception are sometimes reduced in size continue to be, an impor- engineering since the for convenience and portability. tant part of radio communi- beginning. Whether they The ubiquitous 315 or 433 MHz wireless cations, especially in are small compared to remote control and telemetry systems for key- portable applications the extremely long wave- less entry, garage door openers, wireless door- lengths used at the low- bells and remote-reading thermometers rarely est radio frequencies, or intended to save have “full-size” resonant antennas, since a space in GHz-range wireless devices, the basic wavelength is around 1 meter. A λ/4 monopole principles are the same. This tutorial will would be 17 cm long, and requires a similarly- review those principles, with primary atten- sized counterpoise. tion to describing the performance tradeoffs of The developing RFID market demands low small size. cost and small size. A 3 cm square RFID tag will have an antenna that is considered elec- Definition of “Electrically Small” trically small at any frequency below about 1 There are various rules of thumb for con- GHz. Handheld RFID readers will allow some- sidering an antenna to be electrically small. what larger antennas, but will still fit the λ/10 The most common definition is that the criterion at many of the commonly used fre- largest dimension of the antenna is no more quencies. than one-tenth of a wavelength. Thus, a dipole Finally, of course, are wireless phones, with a length of λ/10, a loop with a diameter of which now have integrated GPS, Bluetooth™ λ/10, or a patch with a diagonal dimension of and other radio systems. Only the largest form λ/10 would be considered electrically small [1]. factors can support antennas that are large This definition makes no distinction enough to be outside the electrically small def- among the various methods used to construct inition. electrically small antennas. In fact, most work on these antennas involves selecting topolo- Small Antenna Types gies suitable for specific applications, and the The most common structures used in elec- development of integral or external matching trically small antennas are the short dipole (or networks. equivalent monopole and ground place), the small loop, and the dielectrically-loaded patch. Common Applications Each of these has many variations to fit the Most readers will be familiar with several mechanical constraints of specific applica- common uses of small antennas. Loop anten- tions, but these three are an appropriate basis nas and short monopoles (whip) for medium- for understanding the issues involved in effi- wave (AM broadcast) reception are common in ciency, impedance matching and radiation home and vehicle entertainment systems. patterns. We will examine the topic using the

50 High Frequency Electronics High Frequency Design SMALL ANTENNAS classic dipole and loop as examples. are similar to the λ/10 short dipole. For more information on electrically λ/10 Current distribution is nearly small patch antennas, readers are uniform on a small loop and does not directed to Reference [2]. reveal much about its behavior.

Zfeed = 1.96 –j1758 Ω The Short Dipole Impedance Matching Issues (a) Figure 1(a) shows a short dipole The input impedance of both the antenna. At 100 MHz, a λ/10 dipole short dipole and small loop has a Relative current with a 1 mm conductor diameter has small resistive component and a an impedance at the center feedpoint large reactive component. Of concern of 1.96 –j1758 ohms, as determined is the loss within the matching cir- by NEC2 numerical modeling [3]. cuitry. Even with relatively high Q, This low resistance and high capaci- (b) large-value reactive components will tive reactance illustrates that a large have significant resistance that con- impedance transformation will be tributes to system loss. required to match this antenna to a For example, Figure 3(a) shows an typical 50 ohm system. ideal, lossless matching network to The current distribution on a transform the 1.96 –j1758 ohms of short dipole is a portion of the cosine the short dipole to 50 ohms system current distribution seen on a half- Max. gain impedance. Mathematically, this pro- 1.77 dBi wave resonant dipole. In this case, vides a proper match, albeit narrow- the current distribution is nearly tri- band. angular (Figure 1(b)). This current However, ideal inductors do not distribution results in the free-space exist. A practical Q for an inductor is radiation pattern of Figure 1(c), in a between 50 and 200, depending on plane containing the antenna wire. construction and effects of coupling to (c) Note that the small size of this the surrounding environment. For a antenna does not greatly reduce the Figure 1 · Short dipole example: Q of 100, each inductor will have a efficiency. The maximum gain of 1.77 (a) dimensions and impedance; resistive loss of XL/Q, or 879/100 = dBi is only 0.37 dB less than a half- (b) current distribution, and (c) 8.79 ohms. Since there are two induc- wave dipole’s 2.14 dBi gain. However, radiation pattern and gain. tors, the total additional resistance in this is only part of the efficiency series with the antenna input is story. As will be shown later, the 17.58 ohms. Ignoring the smaller loss matching system is the primary con- from the capacitor, the finite Q of the tributor to reduced efficiency in elec- inductors results in a loss of trically small antennas. 20log[1.96/(17.58+1.96)] = 21 dB. Figure 3(b) shows a modified The Small Loop D = λ/10 matching network that accommo- Figure 2(a) shows a small circular (r = λ/20) dates the additional loss. The differ- loop, with a diameter of λ/10. The ent values demonstrate how an radiation resistance of a small loop empirically-derived matching net- can be calculated from [4]: work (e.g. determined by trial-and- error experimentation) can get 2 2 Rr = 31,171 (A/λ ) results that are far from calculated

Rr = 1.92 Ω network values that do not account where Rr is radiation resistance, the for losses. number 31,171 is 320π4, with A (loop Figure 2 · A small loop also has a The matching process is similar area) and λ (wavelength) in the same low radiation resistance. for the small loop, except that the units. matching involves a large value of XC Solving for a λ/10 diameter loop, instead of XL. Since capacitors have where A = π(λ/20)2, the radiation ductor (with skin effect), plus the much higher Q than inductors, it resistance is found to be 1.92 ohms. inductance of the loop, which will would seem that small loop matching The actual feedpoint impedance will have a result in range of 3.0 +j800 would have lower losses than an include the resistive loss of the con- ohms. The radiation pattern and gain equivalent dipole match. This is gen-

52 High Frequency Electronics 1.407 µH 1.407 µH 1.42 µH 1.42 µH Q = 100 Q = 100 151 pF 40 pF

50 Ω 50 Ω

(a) (b) Figure 3 · Short dipole matching: (a) ideal lossless components, and (b) values required for practical inductors with a Q of 100. erally true, but note that the loop to be aware that such an improve- example occupies an area much larg- ment can be obtained. er than the example dipole. A loop Hopefully, this tutorial raises the that is more comparable to the dipole awareness of loss and efficiency in its physical dimensions will be issues with small antennas. The next smaller and have a lower value of Rr, step is to learn some of the options which will increase matching net- for getting better performance for work losses. future product designs.

Mitigating the Loss Problem References Many technical papers and 1. D. Miron, Small Antenna patents describe alterations in the Design, Newnes 2006. structure of small antennas in ways 2. R. Garg, P. Bhartia, Inder Bahl that increase the radiation resistance and A. Ittipiboon, Microstrip Antenna and/or implement lower loss match- Design Handbook, Artech House ing technqiues. Loading—the addi- 2001. tion of capacitive or inductive ele- 3. As implemented in EZNEC+ by ments, both lumped and integral to Roy Lewallen, www.eznec.com. the antenna, is the most common 4. J. Kraus, Antennas, McGraw- group. Top hats, folded elements, 3- Hill 1950, Ch. 6, section 6-8. dimensional structures, dielectric foreshortening and other methods are commonly used to add electrical length to a small antenna, raising the radiation resistance. Often—perhaps too often—the inefficiency of a small antenna is just included in the link budget calcula- tions and overcome by increased system gain, transmit power or simply accepting reduced communication range. This may work for some applications, but all these consequences are detrimental to system performance, decreasing performance and shortening battery life. A useful reduction of losses in the antenna and matching network can be easy and cheap, but requires the designer