|Antenna Gain, Polarization, and Propagation|
Written By Dan Dobkin with an introduction by Louis Sirico
This article is from one of the most in-depth technical references I've ever read. It is Chapter 3: Radio Basics for UHF RFID from the book “The RF in RFID: Passive UHF RFID in Practice” written by Daniel M Dobkin printed with permission from Newnes, a division of Elsevier. Copyright 2008. You can order a copy of the book here: The RF in RFID: Passive UHF RFID in Practice.
|I had the pleasure of working with Dan for over a year in contributing content for the RFID Essentials suite of e-learning courses developed by RFID Revolution and he created the YouTag Virtual workshops, which you can find more information about here. I also had the pleasure of interviewing Dr. Dobkin for the premier episode of The RFID Network Cable TV Series where he explained how improbable it is to track a passive RFID tag from satellite. The video is below and is very funny regardless of your technical level. Anyone that spends more than a few minutes with Dan will quickly realize he knows a lot about the RF in RFID. Dan also has a PhD in Physics from Stanford. After reading this chapter, you will understand why we consider Dan a subject matter expert and trusted adviser in our community.|
We have been able to conclude that using an isotropic antenna, an RFID reader might achieve a read range of a few meters with 1 watt of output power. This configuration might be fine if RFID tags of interest are equally likely to be located in any direction with respect to the reader. However, such a circumstance is itself rather improbable. In the vast majority of cases, the reader antenna is placed at the edge of some region of interest, and the tags are to be located more or less centrally within this region, at some fairly well-defined angular relationship with the reader antenna. The power that is then being radiated in other directions is wasted (or worse, is reading tags outside the region of interest and confusing rather than enlightening the user). We could make better use of the transmitted power if we could cause the antenna to radiate preferentially along the directions in which tags are most likely to be found.
Fortunately, this is entirely possible to achieve. An antenna that performs this trick is known as a directional antenna. The operation of such an antenna is often depicted by showing an antenna radiation pattern; an example of such a pattern is depicted in Figure 3.24. For any direction d relative to the center of the antenna, the distance to the pattern surface represents the relative power density radiated by the antenna in that direction. The radiation pattern is an intuitively appealing method to represent the way a directional antenna concentrates its radiated power in a beam propagating in a particular direction.
The ratio of the radiation intensity in any direction d to the intensity averaged over all directions is the directive gain of the antenna in that direction. The directive gain along the direction in which that quantity is maximized is known as the directivity of the antenna, and the directivity multiplied by the radiation efficiency is the power gain of the antenna (very often just referred to as the gain, G). In the direction of maximum radiated power density, we get G times more power than we would have obtained from an isotropic antenna of the type discussed in connection with Figures 3.21"3.23.
A note of caution is appropriate in considering the terminology we have just introduced. Antennas are passive devices and have no gain, in the sense that they can only radiate the power that is put into them, no more. The term antenna gain refers to the fact that, for a receiving antenna fortunate enough to be located along the direction of maximum power density, the received power is increased relative to that of an isotropic antenna just as if the output power of the directive antenna had been increased (isotropically) by a factor of G.
Of course, this has not actually happened; the radiated power has just been rearranged, and receiving antennas located in less fortunate directions receive much less power than would have been the case with an isotropic radiator.
The higher the gain of a directional antenna the more narrowly focused is the energy radiated from it. We can express the relationship mathematically by making the approximation that all the energy radiated by the antenna is uniformly distributed across a beam with some solid angle Ωbeam, and no energy is radiated elsewhere. In this case, the directivity of the antenna must be equal to the ratio of the beam solid angle to the total area of the unit sphere (4π), so we find that the solid angle is inversely proportional to the directivity (Figure 3.25). If the antenna radiates most of the energy it receives (which is usually the case for antennas with high directivity), the gain and directivity are about the same, so the size of the beam is inversely proportional to the gain. The beam angle is roughly the square root of the beam solid angle when the beam is reasonably symmetric.
Pseudo-3D depictions of the radiation pattern are helpful to visualize complex geometries, but are difficult to obtain quantitative information from when printed. It is traditional to extract slices of the true radiation pattern in planes that pass through symmetry axes of the antenna.
These may be labeled as altitude and azimuth, or sometimes E-plane and H-plane patterns (the notation refers to the planes in which the electric and magnetic fields are located and needn't concern us here). An example of such a pattern diagram for a real commercial directional antenna usable for RFID readers is shown in Figure 3.26.
This particular antenna used is known as a panel or patch antenna because it is constructed of a metal patch suspended over a metal ground plane, though the user cannot see these details unless they have the courage to slice up the nice-looking plastic casing. This particular pattern is plotted on a logarithmic radial scale, but linear scales are also used. By simply finding the locations at which the gain is reduced by 3 dB from the maximum value in the center of the beam, we can extract the 3 dB beamwidth, as has been done in this figure. Since 72° ≈ 1.25 radians, we can estimate the beam solid angle to be about (1.25)2 = 1.6 steradians, so the antenna gain must be roughly G ≈ 4π/1.6 ≈ 8, or 9 dB. (The actual gain of this antenna as reported on the data sheet is about 8.5 dB, so our simple calculation has produced a quite acceptably accurate result. However, the gain is also influenced by the power in the sidelobes and deviations of a couple of dB from this simple formula are not uncommon.) Practical, usable commercial antennas can provide us with quite substantial gains relative to an isotropic antenna.
Not all antennas are highly directional. Though it turns out to be impossible to fabricate a truly isotropic antenna, one can come fairly close to this ideal. A very common example of a not-very-directional antenna is the dipole antenna (Figure 3.27). A dipole is constructed of two pieces of collinear wire driven by opposed voltages. Many RFID tag antennas are variants of a simple dipole. Dipole antennas do not radiate along their axes but radiate equally well in every direction perpendicular to the axis. Thus, the radiation pattern looks rather like a donut (or a bagel, depending on your nutritional inclinations). The gain of a typical dipole roughly half a wavelength long (16 cm at 900 MHz) is about 2.2 dB.
The gains we have been quoting so far are all measured with respect to an ideal (nonexistent) isotropic antenna and are often written as dBi to denote that reference state. In practice, gain is measured by comparing the received power of an antenna under test to a reference antenna, the latter often being a standard dipole antenna. Thus, it is easy to measure and report the gain of an antenna relative to a dipole, and this is sometimes done; such gains are usually written as "dBd." Since a dipole has 2.2 dBi of gain, gain referenced to a dipole is 2.2 dB less than gain referenced to an isotropic antenna: dBd = dBi -2.2.
Given the gain and transmit power of an antenna, we can calculate how much power we would need to put into an isotropic antenna to get the same peak power as we get in the main beam of a directional antenna (Figure 3.28). This power is called the effective isotropic radiated power (EIRP). The EIRP is larger than the actual power by the antenna gain, or in dBm:
EIRP is often either explicitly or implicitly used as a regulatory limitation on radio operations because it is the EIRP rather than the transmitted power, which determines the peak power density transmitted by a reader, and thus, the likelihood that it will interfere with other users of the same frequency bands. For example, FCC regulations in the United States allow an unlicensed transmitter to use up to 1 watt of power with an antenna with 6 dBi of gain; for each dB of additional antenna gain, the transmit power must be reduced by 1 dB. In effect, the FCC is requiring that the EIRP not exceed +36 dBm (30 dBm + 6 dBi).
A closely related quantity, the effective radiated power (ERP) is also used in similar contexts. However, this term is used rather more loosely: web references can be found in which it is defined in an identical fashion to EIRP, though the United States FCC defines ERP as being referenced to a half-wave dipole antenna. In this book, we will define ERP following the FCC definition:
where as the reader will recall, gain in dBd is defined relative to a standard dipole antenna rather than relative to an isotropic antenna. However, we shall generally encourage the use of EIRP rather than ERP since the former is unambiguously defined.
Recall that the purpose of this digression into antenna behavior was to see if we could improve the performance of our theoretical RFID reader by using a directional antenna. If we use a directional antenna to transmit the 1 watt of allowed power and the RFID tag of interest is located within the main beam of that antenna, we would expect the transmitted power density to be increased by the gain of the antenna. The result ought to be an increase in the read range. The argument is depicted graphically in Figure 3.29, for an antenna with 6 dBi of gain.
The forward-link-limited range has doubled, from 3 to 6 m, relative to that obtained in Figure 3.22. This is what we'd expect: we increased the signal power by a factor of 4, but power falls as the square of the distance, so this only provides us with a factor of 2 in range. At the same time, we've reduced our ability to see tags outside the main beam, presumably around 80 to100° wide here, which is usually desirable: by using a directional antenna we are able to (mostly) select the region in which tags can be read, and thus exclude tags that are not of interest.
What about the reverse link? In considering the action of an antenna as a receiver, we have heretofore asserted without detailed proof that the antenna collects energy from some effective aperture, and given a typical size. In fact, the size of the receiving aperture of any antenna is directly proportional to the gain of the antenna when used as a transmitter. This is a consequence of the principle of reciprocity, briefly alluded to previously, which for our purposes, we can state as: transmitting from antenna 1 and receiving with antenna 2 ought to give the same result as transmitting from antenna 2 and receiving with antenna 1. Since we have already cited the effective aperture for an isotropic antenna (equation (3.15)), we can write:
where the gain G is measured relative to an isotropic antenna, that is in dBi. Using this relationship, we can write a very general equation for the power received from a transmitting antenna TX by a receiving antenna RX if both gains and the distance between them are known:
The last form of the relationship is known as the Friis equation, a very convenient way to state the expected received power. Note that this equation does not imply, as is sometimes erroneously asserted, that waves fail to propagate as wavelength decreases; from the derivation it should be apparent that the factor of λ2 arises from the effective aperture of the receiving antenna and is not related at all to propagation in the intervening space.
With the Friis equation in hand, we can immediately draw the reverse-link diagram for a directional antenna: the received power is simply increased by the antenna gain, just as the transmit power was. The result is given graphically in Figure 3.30. The received power is the same as in the isotropic case, even though the tag is twice as far away because the power at the tag is the same in both cases, and the received power is decreased by 6 dB due to the larger distance but increased by 6 dB due to the receiver antenna gain.
We can also construct a mathematical statement of the same relationships using the Friis equation. We define the gain of the tag antenna Gtag and a backscatter transmission loss Tb (= 1/3 or '5 dB here). We then have:
As promised, in the most general case, the power received at the reader goes as the inverse fourth power of the (symmetric) distance. It is also proportional to the square of the antenna gains, so when reverse link power is important (e.g. when a semipassive tag, or an unpowered device like a surface-acoustic-wave (SAW) tag, is used) the antenna gain plays a very large role in achievable read range. We have previously treated the tag antennas as having a gain of 1 (0 dBi). Real tag antennas have some gain, but it is typically modest (around 2 dBi, since they are usually dipole-like), and since we don't always control the exact orientation of the tag antenna and may not be able to guarantee that the main beam of the tag antenna is pointed at the reader, it is prudent to count on minimal gain from the tag antenna.