Basic Wireless Communication for Microcontrollers

Chapter 4 - Design Project 3: 900MHz Automatic Error-Correcting Data Link

Advanced Antennas

     In the first design project, we covered the basics of antennas. It should be clear to you now that antennas have only two performance factors to consider: efficiency, or how much power is lost to resistive losses in the antenna system, and directivity, or how the antenna selectively directs or accepts power from some angles and not others. We already discussed antenna efficiency in the section on Basic Antennas In this section, we will cover a few ideas on how to make directive antennas and also how to make small antennas which are efficient enough for some applications.

Directive Antennas

     While all antennas are directive to some degree, there are many types of antenna which are specifically designed to radiate or receive in certain directions. These are called beam antennas when they are designed to radiate a narrow beam of RF in one direction. The major types are active arrays, passive arrays (Yagi antennas), and aperture radiators.

Active Arrays

     Active arrays consist of two or more antennas of any type(called elements of the array), all of which are fed (that is, they are all attached to the transmitter or receiver). While transmitting, the radiation from each antenna interferes with the radiation from the other elements to produce greater radiation in some directions than in others. The interference is due to the E and B fields adding when in phase and canceling when out of phase. The phase is determined by the relative positions of the antennas (i.e., it takes different amounts of time for the wave from different elements to propagate to the same point) and also from phase differences between the signals feeding each element (due to different lengths of transmission line or other phase shifting devices). A similar thing happens in the receiving mode where the voltage from each element differs in phase from that from the other elements and either adds or cancels depending on the reception angle. Active arrays are common in radar, cellular communications, and in broadcasting stations which want to transmit only to certain areas and not omnidirectionally.

Passive Arrays and Yagi Antennas

     An alternative to active arrays are passive arrays, of which the most common kind is the Yagi (or more completely Yagi-Uda antenna) (see figure 1). In a passive array, only one element (the driven element) is connected to the transmitter or receiver. The fact that the other elements are placed well within the near field of the driven element means that current is induced in them by the driven element and the situation is similar to one in which all are driven. The process of the radiation from the driven element being affected by the other elements is actually diffraction, as opposed to interference in the active array case. Because only one element needs to be driven, passive arrays are much simpler to construct than active arrays. Passive arrays, like active arrays, can also produce very narrow beam widths, sending radiation into a beam only a few degrees wide.

Figure 1 - A Yagi-Uda antenna, which is an example of a passive array.


     The drawback to passive arrays is that their analysis is a very complex problem, due to the need to compute how much coupling there is among the elements and then their collective radiation pattern on top of that. In contrast, the analysis of active arrays can be carried out in a cookbook fashion, and almost any pattern can be easily synthesized. As a result, passive arrays are designed using standard tables or computer software, combined with testing which usually reveals some discrepancies. Passive arrays are used in situations where some difference between the desired pattern and the actual one is tolerable, the desired pattern is simple and never needs to change (a single beam in one direction), and simplicity and low-cost are major factors. Active arrays are used in cases where the pattern needs to be changed electronically (by changing the phasing) or needs to conform well to a complex specification (such as having several maxima and a few deep nulls).
     Yagi antennas, the most common type of passive array, consist of a driven element, a reflector, and one or more director elements, as shown in figure 1. The measurements shown are for a 432MHz 6-element Yagi. The radiation pattern consists of a main lobe (a lobe is a range of angles where there is significant radiation) along the direction from the driven element to the directors, and several unintended sidelobes. As the number of directors is increased, the main lobe increases in magnitude, narrows in angle, and the sidelobes increase in number but the ratio of sidelobe magnitude to main lobe magnitude decreases. For more info on Yagis, see Appendix 4.

Aperture Radiators

     A third type of directive antenna, used at UHF and higher frequencies, is the aperture radiator. A common type of aperture radiator is the parabolic dish antenna. Aperture radiators operate similar to the way optics do for light. A dish antenna has a small source or feed antenna at the focus of the dish. Any radiation incident on the dish from straight ahead gets reflected by the dish and focused on the feed. The reverse happens during transmission.
     When using waveguide type transmission line, an aperture radiator can be as simple as an open end of a waveguide, although usually the end of the waveguide is shaped to provide the correct impedance termination (match the impedance of free space to that of the waveguide) and generate a certain radiation pattern. The result is usually a rectangular or circular horn, but can take many forms.
     In any case, aperture radiators have an effective area which is a large fraction (50 to 80% usually) of the physical aperture area (the frontal area seen as you look straight at the antenna). The fraction is called aperture efficiency (and has nothing to do with power loss, just with how "efficiently" you use the size of the antenna to your advantage) and is never more than 1. It is increased by ensuring that the E field is close to uniform over the aperture. At VHF and lower frequencies, dishes and other aperture radiators, which would have better performance than simple dipoles or Yagis, become prohibitively large, which is why it is rare to see such antenna types below 400MHz, and they are common above 1GHz.

Small, Efficient Antennas

     As you might guess or remember from our earlier antenna discussion, it is very difficult to make small (much less than a wavelength in all dimensions) antennas work efficiently. Some times we can put up with this (as we did with the receiver in the second design project), especially for receivers in simple, very short range links. When it comes to transmitters, FCC regulations for unlicensed transmitters with FCC approval usually limit radiated field strength and not output power, so using an inefficient antenna is OK since we can just output more power and lose most of it in the antenna's resistive losses. For homebuilt unlicensed transmitters, though, FCC regulations often limit the total power used by the device, so inefficient antennas can be a real problem. In cases where only limited power is available or we have to try to maximize the performance of the link while still keeping the antennas small, we have to apply a few tricks.
     One thing which may not be obvious is that when we talk about small antennas, we almost necessarily mean ones which are not designed to be very directive. While some limited directivity can be achieved using ground planes, shielding, or loops, most directive antenna designs require that the antenna's dimensions be comparable to a wavelength.

Antenna Loading

     For an omnidirectional antenna, it would be ideal, in terms of efficiency, to choose either a half wave dipole or a quarter wave monopole over a ground plane. If this is possible given the size constraints, then this discussion is moot and this simple antenna type should be used.
     In cases where the antenna must be shortened significantly, reactive elements (inductors and capacitors) can be added to make the best use of the length allowed, although the result will always be less efficient than the simple dipole or monopole. Since a straight wire antenna (above a ground plane) which is much shorter than a quarter wavelength appears as a small resistor in series with a tiny capacitor, and we want to achieve an optimal match between this and the resistive receiver or transmitter, we need to add some inductance to create a conjugate match, or in an alternative but equivalent view, to cancel the capacitance.
     This inductor is usually added either at the base or at the middle of the antenna wire. Placing the inductor at the middle will cause the current distribution to be nearly uniform from the base to where the inductor (called a loading coil) is placed, and then taper off like a normal short wire antenna current distribution from there until the end. This is better than placing it at the base because there will be a higher antenna current over more of the antenna's length, resulting in a higher radiation resistance and greater efficiency. The disadvantages of placing the coil up higher than the base are that a larger inductance is needed for resonance (the capacitance between the ground plane and the smaller piece of wire on top of the inductor is smaller than for the whole piece of wire, thus the capacitive reactance is greater) and it is mechanically more difficult, in many cases, to mount the coil higher up.
     Another method of increasing the radiation resistance of a monopole antenna is to add a capacitive hat on top. A capacitive hat is any piece of conductive material specifically designed to have the highest capacitance value possible, between it and the ground plane below. This has the same effect, to make the current distribution more uniform and increase the radiation resistance, but it also reduces the capacitive reactance at the same time.
     The difficulty in using this procedure for very short antennas is that the loading coil has losses and large capacitive hats can be difficult to support mechanically and protect from damage. There is also a limit to how high the radiation resistance can be raised, and therefore, also a practical limit on efficiency.
     When doing a design for a loaded antenna (with loading coil, capacitive hat, or both), it is best to use several methods at once. First, you would look up previous designs for such antennas to get ideas and basic design rules. Secondly, you would (ideally) use a NEC computer program to analyze the performance of the planned configuration. Thirdly, you would test the antenna's impedance using either an SWR meter or field strength measurements (with a field strength meter or a receiver at some distance). You would often end up trimming the antenna's measurements or number of coil turns to optimize it.
     As a rough rule of thumb, the capacitance of a vertical wire of 1 millimeter diameter above a ground plane much larger than the antenna is about 7.2pF per meter for lengths much shorter than a wavelength (less than 1/10th of a wavelength). This may be useful as an even rougher approximation for antennas closer to 1/4 wave (resonance).
     A final note about loaded antennas is that they usually exhibit a very narrow usable bandwidth and for very short antennas, the inductor and capacitive hat specifications can be very critical to the performance of the antenna, so much so that each individual one that was manufactured would have to be tweaked. This makes such designs much more practical for hobbyists than for commercial operations. The narrow bandwidth is due to the antenna Q being very high, because of the high ratio between component reactance and Rrad.

Ground Plane Details

     In most "textbook" antenna examples with ground planes, the plane is assumed to be a perfectly conducting infinite sheet. To ensure that a real ground plane is a good approximation to this, it should ideally be much larger than both the antenna size and the wavelength involved. However, for small antennas (much less than a wavelength), good performance can be achieved with one which is just a good fraction of the size of the height of the antenna, and reducing the size of the ground plane has the primary effect of increasing the capacitive reactance of the antenna. For resonant antennas, the same rule, that the ground plane should be as big as the antenna (at least a 1/4 wave) generally works quite well, too, and yields an antenna which is very close in resonant frequency and impedance to the result obtained theoretically with an infinite ground plane.
     Since the earth is somewhat conductive, it can act as a ground plane, as discussed earlier. If you actually want to use it as such, it helps to place pieces of wire (called radials) inside or at least on top of the ground to make it a better approximation to a real ground plane. All of this is only practical if you are making a very large vertical antenna (say for frequencies below 50MHz). For VHF and above it is much easier and better to just make a conductive metal ground plane.
     In some antennas, radials alone (not in or in contact with the ground) are used instead of a ground plane. A very simple VHF/UHF antenna design consists of just one 1/4 wave piece of wire arranged vertically, with four 1/4 wave pieces of wire connected together and either going out horizontally at 90 deg to each other (making a cross) which gives an input impedance of around 36 ohms or bent down at a 45 degree angle, yields an impedance close to 50 ohms.
     One final note about ground planes: the antenna pattern of any antenna can be severely distorted if it is closer than a few wavelengths away from any large conductive object, including the earth. The impedance can also change. For this reason, it is best to place antennas at least several wavelengths away from other objects and the ground. This is not always possible (or necessary), but it is worth knowing that it can help with performance and predictability.

Helical Antennas

     What happens if you try to make an antenna out of just a coil of wire, such as a loading coil with a zero-length antenna attached, placed above a ground plane? You get a helical antenna. Helical antennas can operate in two modes. One is called the normal mode and is dominant when the size of the coil in all dimensions is much smaller than a wavelength (< 0.1 lambda). In this mode, the helix acts like a monopole and radiates a linearly polarized wave from its sides and has a minimum or null along the long direction. If the size of the turn radius and turn spacing gets comparable to a wavelength, then the helix produces circular polarization and acts as a beam antenna with maximum radiation along the long direction (endfire). This is called the axial mode.
     Normal mode helical antennas are usually not very efficient because they have a low radiation resistance. If their length becomes comparable to a wavelength (say, 1/8 wave) while their turn radius and spacing is still a lot smaller, they can become efficient antennas but their tuning can be critical. Some "rubber duck" antennas are actually helical antennas and operate in this mode. It is also worth noting that any inductor will act as a normal mode helical antenna, whether desired or not, and typically has a low Rrad. If care is used in design, though, a reasonably efficient, small size normal mode helical antenna (whether both sides are electrically connected as in an inductor or it is operated above a ground plane) can be designed. For more information, see Appendix 4

PCB Antennas

     Just as pieces of wire in free space can serve as antennas, so can traces on a printed circuit board. The main difference is that the effective dielectric constant of the medium surrounding the antenna is altered by the presence of the PCB material. Normal dipole antennas can be fabricated on PCBs, and I have even seen designs for microwave dish feeds using just traces on a PCB. For small, cheap UHF and VHF transmitters and receivers (such as garage door openers and keyfob transmitters for locking and unlocking car doors) various types of loop and spiral PCB trace antennas are common. These antennas can be very tricky to design, though, because their proximity to other components and the case in which the radio is housed can affect the impedance. Also, as mentioned above, the PCB material will alter the impedance from what one would expect from such an antenna in free space. It is always true, though, that some antenna is better than none and a PCB antenna may be a suitable choice for very short range links between tiny devices. For more information on designing PCB antennas, see Appendix 4

Exotic Types

     Recently, a few strange types of antennas have emerged which some people claim achieve much greater Rrad (and therefore greater efficiency) for the same dimensions as traditional types. Once such type is the fractal antenna. Fractals are patterns generated by starting with a basic shape (called the generator shape) and then following a set of simple steps to place copies of the generator shape at locations relative to the original. These steps are then repeated, recursively, ad infinitum. A true fractal cannot be represented because of the infinite number of steps involved. However, if the number of steps is held to a finite quantity, an approximation to the real fractal is achieved. A company, called Fractal Antennas, Inc. (http://www.fractenna.com) claims to be able to etch these patterns onto PCBs and get very high performance when using those traces as antennas. I don't know whether these claims are true, but I certainly cannot rule out the possibility that improvements in antenna efficiency cannot be made by using some pattern of traces on a PCB, or by any other method.

Broadband Antennas

     All of the antennas discussed so far have been designed to operate at only one frequency. There are certainly cases, though, where an RF link might need to operate on a wide variety of frequencies without changing antennas. Antenna bandwidth was mentioned above, and it was noted that loaded antennas have particularly narrow bandwidths due to high Q. A typical resonant straight wire antenna (dipole or monopole) has a Q from 5 to 10, meaning that the half-power bandwidth would be from 1/5th to 1/10 of its center frequency (so, for example, a 1/4 wave vertical operating at 100 MHz could be used from about 93 to 107 MHz). This is actually somewhat liberal because many types of transmitter cannot tolerate the degree of mismatch where half of the power is reflected, so the real value is somewhere around 1/15th of its center frequency.
     We have not mentioned, however, that straight wire antennas (and many antenna types) have multiple resonant points, each with different characteristics in terms of Q and impedance (although, by definition, the reactance is zero and the impedance purely resistive at each point). A regular center-fed half wave dipole (or monopole over a ground plane) is resonant at every third harmonic of its design frequency (so one designed for 100MHz would also resonate at 300,500,700 MHz, etc.). Depending on application, these resonances may or may not be usable due to their somewhat different impedance than the primary resonance. If you are using a 1/2 wave dipole and feed it off-center at 1/8 wave from the end (1/4 of the length of the 1/2 wave dipole), it will have resonances at most of both the even and odd harmonics. Once again, though, they differ in bandwidth and resonant impedance from each other and from the primary resonance.
     When several straight wire antennas (such as monopoles or dipoles) of different resonant lengths are connected in parallel, the one which is resonant at a particular frequency will always have the lowest impedance, since impedance increases for such antennas as you go farther away from resonance. The parallel combination, therefore, will essentially have several independent resonances, one at the resonant frequencies of each antenna. This is somewhat of a simplification since it is only completely true when the antennas are not close together in space and when their resonant frequencies are widely spaced. Still, this can work as a practical solution.
     There are also antenna types which are inherently broadband due to their geometry. All of the antennas discussed so far have some length associated with them. The resonant frequency depends on this length. What would happen if you could make an antenna which had no specific length associated with it? You might think it would be resonant at all frequencies. As it turns out, you would be right if you thought so. No such antenna can actually be built because it would have to either be infinite in size or in number of components. However, antennas which approximately fit this requirement can be built. Logarithmic spirals and log periodic antennas are two examples. They are described not in terms of length but, in the first case, diameter increase per angle change and in the second case, the ratio of lengths of several dipole elements connected in a series-parallel arrangement.

Radiation Angle and Vertical Length

     While we treat 1/4 wave vertical monopoles as omnidirectional antennas, they really are not optimized for transmitting to receivers in the horizontal plane. A large fraction of the power radiated by a 1/4 wave vertical goes upward into the sky. The pattern looks like a donut sliced in half horizontally, meaning that there is a null around the exact vertical direction, but almost as much power goes up at a 45 degree angle as does horizontally. One way of solving this is to use a longer monopole. With a monopole of about 5/8 wave long, the pattern changes to have a higher gain in the horizontal plane. A 5/8 wave long monopole is not resonant and exhibits a capacitive reactance, but only a moderate amount of inductance is needed to cancel it (about 165 ohms) and the resistive part of the impedance is close to 50 ohms, so it is easy to achieve an efficient match.

Design Considerations

     As you can see, there are many factors to consider in choosing an antenna for a particular application. First of all, there is a tradeoff between size and efficiency. There is also a tradeoff between size and directivity, in cases where directivity is desirable (such as when you can point the antenna accurately and you want some type of array, or when you want a lower radiation angle for a monopole). In applications with very lax requirements (such as transmitting across the room), just attaching random short lengths of wire or PCB trace to the transmitter and receiver may work just fine. In a case such as this, making the receiving antenna better could actually be worse by allowing it to better receive stray interfering signals. Even though these random antennas will be extremely inefficient and highly mismatched (perhaps radiating only 1% of the power generated by the transmitter), the short range, extra power generated by the transmitter, and a sensitive receiver easily make up for the antennas' shortcomings.
     In more demanding applications, such as communicating with a remote weather station a mile away from your house using a minimum of power, great care will be needed in antenna choice. You would at least need optimally matched omnidirectional antennas and some type of beam antenna (probably a Yagi) at least on one end would be a great help.
     One final thing to keep in mind is the issue of legality. The FCC regulations for unlicensed transmitters are often very restrictive. In most cases, they assume that the antennas to be used will be inefficient and mismatched, so they limit not transmitter output power but the maximum E field generated by the antenna at some given distance. In other cases, such as homebuilt transmitters in the 49MHz band, they limit the total input power to the transmitter. In many instances they also limit the maximum size of the transmitting antenna, which for lower frequencies eliminates the possibility of using a beam or other full-size antenna. It is annoying to be limited by more than what is physically possible, but it is a reality. Just consider this when selecting an antenna.

Our Design Choice

     Because we are using such a relatively high frequency in this project (916 MHz), there is no difficulty in making a resonant antenna which is acceptably small. We do not want to be concerned with pointing antennas at each other, and there are definite legal limits on the maximum transmitted E field strength at 3 meters, so beam antennas are not a good choice. Since we want an omnidirectional pattern, the logical choice is some type of vertical monopole, using one side of the PCB copper as a ground plane. A 5/8 wave would give potentially the best performance if we were sure that both ends of the link were roughly in the same plane. A 5/8 wave would also require some type of matching system to cancel the capacitive reactance. A 1/4 wave, strictly speaking, also needs a matching system (because it has an impedance of 36 ohms and the output impedance of our RF module is 50 ohms), but that is a very minor mismatch and the resulting network will be much less critical in its design and could even be left off entirely with only a few percent reduction in efficiency.
     For these reasons, we will use a 1/4 wave vertical monopole. Since we have to use a section of transmission line between the RF module and the antenna anyway, we will make a quarter-wave transformer out of it to accomplish the 36 ohm to 50 ohm match. This adds no complexity so it is worth doing. We will describe the transmission line in the next section on PCB layout, because we will be using microstrip line, which is just a trace on the PCB with exact dimensions. The antenna itself will just be a length of semi-rigid copper wire extending up from the PCB. The length of the wire, above the PCB, should be 234/916=0.255 feet or 3.07 inches. Three inches would be close enough. The ground plane around the antenna should be relatively free from components and be at least 3 inches (1/4 wave) in each direction. It will be placed on the bottom of the board so that the microstrip trace can be on the top, minimizing the interaction between the microstrip and whatever the unit might be sitting on.
     The final consideration is legality. We are limited to a power density of 50mV/meter at 3 meters distance. This works out to: Pdens=0.5*0.05^2/377=3.3uW per meter^2 at 3 meters away. Almost all of the power of a 1/4 wave vertical goes into the hemisphere above the PCB ground plane, so we can compute the total radiated power (assuming uniform power over the hemisphere) which would give 3.3uW/meter^2 at 3 meters away. The area of a 3 meter radius hemisphere is (4*pi*r^2)/2=2*pi*9=57 meter^2. This comes out to 3.3x10^-6 * 57 = 188uW. To be really safe, this should be reduced slightly to account for the small amount of gain that a 1/4 wave vertical exhibits (i.e., the radiation is not really uniform over the hemisphere). This would require reducing the power by about 2 dB (a factor of 1.25). We have totally neglected the system losses, though, and we have also neglected the small amount of power which will be radiated downward. For these reasons, we will consider 188uW to be a compliant level. In a situation where we were applying for FCC approval, we would actually test the antenna field strength to ensure both compliance and that we were radiating as much power as we are allowed. While our transceiver allows power adjustment via a resistor, the datasheet does not explain how much the power is reduced for a given resistor value, only that a short results in 15dB reduction (-15dBm) and an open yields 0dBm (1 mW or 1000uW). Since we are only testing two homebuilt devices and not marketing anything, it is probably OK to leave the resistor out and possibly exceed the legal limits, although you do so at your own risk and shorting the LVADJ pin would be legally the safest thing to do.

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