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Antenna Theory and Matching
Hello and welcome to the antenna theory and matching presentation. My name is Farrukh Inam. I am an applications engineer at Texas Instruments. In this presentation, we will cover antenna basics, antenna parameters, radio range and communications link example, and an example that goes through the procedure of matching an antenna. An antenna is an element which converts guided electromagnetic waves from transmission line to spherical waves in free space or vice versa. This matches the transmission line impedance to that of free space for maximum radiated power. An important design consideration is matching the antenna to the transmission line and RF source. The quality of match is specified in terms of voltage standing wave ratio, or S11. Standing waves are produced when RF power is not completely delivered to the antenna. In high power RF systems, this might even cause arching or discharge in transmission lines. Resistive/dielectric losses are also undesirable, because they decrease the efficiency of the antenna. Radiation occurs when the charge is accelerated or decelerated in a conductor. Stationary charges mean there is zero current, so therefore there is no radiation. If a charge is moving with a uniform velocity, no radiation occurs. If charge is accelerated due to electromagnetic field or due to discontinuities such as termination, bend, curvature, then radiation occurs. Some of commonly used antennas are listed below. There are a PCB antennas, whip antennas, chip antennas, wire or helical antennas. Their respective performance is also listed here. Antenna radiation regions. The space surrounding the antenna is usually divided in three regions as functions of dimensions and wavelength of operation. Typically, we are only interested in far-field region of the antenna for all practical purposes. In this region, the electric and magnetic fields are perpendicular to each other, electric and magnetic field amplitude drops as 1/r, where r is the distance from the radiating element. For example, a 2 foot diameter dish operating at 10 gigahertz would have the start of the far-field region at about 24 meters. Isotropic radiator. An isotropic radiator is one that radiates uniformly in all directions. The radiated power goes through a sphere in all directions with same intensity. The power and energy bearing electromagnetic waves are used to transport information signals through a wireless medium. Poynting vector is a quantity used to describe power in an electromagnetic wave. A non-isotropic source does not have same radiation intensity in all direction. A non-isotropic antenna concentrates power in a desired direction more than any other. Hence, the term "directivity" is associated with non-isotropic radiated sources. Directivity is the antenna's ability to focus electromagnetic radiation when transmitting or receiving maximally. An antenna that radiates more or less equally in any orthogonal plane is called an omnidirectional antenna, whereas an isotropic radiator is just a hypothetical lossless antenna radiating in all directions. Directivity is the ratio of radiation intensity of an antenna with respect to an isotropic radiator. In general an antenna with 6 dBi specification of directivity means that the intensity is 6 dB more in the maximum directional of radiation compared to the isotropic antenna. What is the power density of a 2-watt non-isotropic source at 2 kilometers if the directivity is 50 in the maximum beam direction? And what is the directivity in dBi? So this example kind of clarifies the concept of a non-isotropic radiator. Antenna gain. Gain of an antenna is closely related to directivity and efficiency of the antenna. Usually antenna gain is a relative quantity which is measured with respect to a reference radiator. Relative gain is expressed as the ratio of power gain in a given direction to the power gain of a reference antenna. The expressions for gain are shown below. An antenna with a 90% efficiency and a directivity 120 would have a gain of about 20.3 dBi. Gain of an antenna is often proportional to its effective area and inversely proportional to operating wavelength. The effective area is related to physical area by the expressions below. Radiation patterns described the relative strength of the radiated or received field in various directions from the antenna at a constant distance. Although electromagnetic radiation takes place in three dimensions, the patterns documented are a two-dimensional slice of a three-dimensional pattern in the horizontal or vertical planes. In [INAUDIBLE] antenna theory, it's convenient to divide electric and magnetic fields surrounding an infinitesimal current carrying element. Once the field magnitudes due to these elements are found, then fields of finite sized antennas can be computed by integrating for all elements present. Thus the simple current carrying element becomes a building block for larger systems. This line of reasoning shows that the radiation field components from a current elements are tangential the spherical surface and the Poynting vector is perpendicular to the surface indicating a radial flow power of the current element. The average power in watt per meters squared is one half the product of these fields. The total power being radiated is the surface integral of the Poynting vector over the surrounding surface. And in this case, for an infinitesimally small current carrying element, the surrounding space is a sphere. The radiation resistance is due to power radiated. The total power input to an antenna will be decreased by the losses. And consequently, the total resistance of the antenna is made up of the radiation resistance plus the resistance to the other [? power ?] losses. For a high efficiency, the value of radiation resistance should be large with respect to the loss resistance. One of the simplest antennas and frequently used is the half-wave long thin wire dipole. The current at the end of the antenna has to be 0, since there is nowhere for it to go. A sinusoidal distribution exists for a thin wire, and the figure below shows the central wire as reference. And the current along the antenna is given by this expression. Choosing a point P far away, the radius vectors r0 and r1 can considered parallel. The RMS fields, electric, and magnetic fields are given by the expressions below. They are orthogonal to each other. So one is orientated in a pi direction, and the electric field is orientated in theta direction. The Poynting vector using the RMS values is given by the expression below. In order for a transmitter and a receiver antenna to have a link, they must have seen same polarization. Polarization of a plane wave shows how the instantaneous electric or magnetic field is oriented at a given point in space. Polarization mismatch will cause signal loss. There are three types of polarization-- linear, vertical or horizontal, if electric and magnetic field vector are always oriented along the same straight line every incidence of time; circular, if electric and magnetic field vector at a point traces out a circular path as a function of time; elliptical, if electric and magnetic field vectors at that point traces out an elliptical path as a function of time. To summarize thus far, the radiation resistance of an antenna is due to the power it radiates. And thus, the concept of this radiation resistance can be used to model antenna as a circuit element. Here we see circuit models of a transmitter antenna and a receiving antenna. The antenna of interest in this presentation is the transmitter antenna, where the transmitter or the RF generator is connected via a transmission line to the antenna. And we see that the total antenna impedance is the sum of the radiation resistance, the loss resistance of the antenna, and the antenna reactance. When setting up a radio link, the maximum range between a transmitter and receiver is often desired. Realistic range estimation can made by employing a two-ray Friis model for RF propagation, which takes into account typical building construction materials. Maximum range can be influenced by antenna performance and its location; the output power of transmitters and the receiver sensitivity; the unwanted RF jammers present in the RF environment; the operating frequency of the radio link; the radio configuration; and the building material between the transmitter and the receivers. For transmitter and receiver antennas that are matched for polarization and reflection, and aligned for maximum directional radiation and reception, the ratio of receiver power to transmitter power is given by the following expression. This expression is based on a simplified two-ray model of propagation. By solving the Friis formula for the maximum range and replacing the received power with minimum detectable signal, we can get the expression for the maximum range. And the important thing to note over here is that the range depends on the frequency of the RX signal and is inversely proportional to it. We have on our website an Excel sheet along with an application note that one can use to estimate RF length range. In the Excel sheet, you can change various parameters that affect the communication link and get a realistic range expectation. In this screenshot for example, we have the location and the height of the antenna above the ground, the frequency of operation, the antenna position, transmitted power, various interference levels in the environment, and various building materials that can be used inside the Excel sheet to estimate your realistic range estimation of the RF length. Antenna matching. Only inductors or capacitors should be used for matching purposes. Matching circuits, distributed or lumped, have losses due to limited quality factor. If an antenna has a reasonable initial resonance, the improvement obtained from the matching circuit will compensate for the loss it introduces. The block diagram shows a typical matching scenario. The matching circuit is placed between the generator and the antenna. The matching circuit transforms the impedance of the antenna and conjugately match that of the generator. The matching circuit can be of any topology. And we will consider L-matching a natural topology in our example today. Antenna matching consideration. Input impedance is the impedance presented by the antenna at its terminal. Maximum power is transferred to the antenna during conjugate match. Transceivers and their transmission lines are typically designed for 50 ohm impedances. If the antenna has an impedance different from 50 ohm, then there is a mismatch and an impedance matching circuit is required. In conjugate match, half of the power is dissipated in heat. Generator resistance and the other half that makes to the antenna, part of it is radiated through the radiation resistance of the antenna, and the rest it dissipated in the loss resistance of the antenna. Return loss is a way of expressing mismatch. It is a logarithmic ratio measured in dB that compares the power reflected by the antenna to the power that is fed into the antenna. The quality of match is specified most often in terms of voltage standing wave ratio or S11 under matched conditions. The expression is shown below. The antenna VSWR changes according to the environment around the antenna. And therefore, matching conditions can change accordingly. This change in VSWR, if large enough, can disrupt the noise figure of the front end of a receiving system. The influence of antenna VSWR on the nose figure is given by the expression below. Rho is the voltage standard wave ratio of the antenna in this expression. And F is the noise factor. The bandwidth of an antenna refers to the radio frequency over which the antenna can operate with acceptable voltage standing wave ratio. Typical bandwidth of operation when VSWR is less than 2 to the ratio 1 is acceptable. This translates to a return loss of about 9.5 dB. L-matching networks can be used to match any impedance that falls anywhere on this [INAUDIBLE] chart. Here we see various scenarios of impedances that can be matched by the respective circuit topology consisting of inductors and/or capacitors. This L-matching network topology provides a very narrow band match. The analytic expressions for L-match are shown here. By using these equations, we can calculate theoretical values of the components that are required to match the given impedance of the antenna. And in the lab, with actual measurements on the network analyzer, we can tweak these component values to bring the match to a perfect state. In many low power [INAUDIBLE] applications, antenna matching is usually done on small PCBs. In this example, we will match a compact PCB helical antenna at 868 megahertz to a 50 ohm source. First step is to calibrate the network analyzer. We can simply calibrate just one port of the network analyzers, since we only require S11 parameter to calculate the antenna input impedance. Next, we prepare the board for mounting a semi-rigid coaxial cable. In figure 1, we have placed a holder for the matching network shown in yellow box. This is where the L-match will be placed. And the orientation of the layout will be determined by the measured antenna impedance. In the same figure, we have also shown the pad where the conductor of the semi-rigid coaxial cable will be soldered onto. In figure 2, we have soldered the semi-rigid cable onto the PCB and extended the open circuit port of the vector network analyzer up to the point where the antenna feed begins. At this point a 0-ohm resistor can be used to connect the antenna to the coaxial feed. However, for the VNA port extension, this resistor has to be disconnected. Here in the figure, we finally place the 0-ohm resistor and measure the S11 the unmatched antenna. This value turns out to be 15.4 minus j70.4 ohm at 868 megahertz. And in the corresponding VSWR, it's 9.8. After measuring the impedance shown on previous slide, you can then use the analytic solutions equations 9 to 12 to obtain theoretical values of the matching components. The resulting plots are shown. And we see a nice match at 868 megahertz. The component values obtained in this manner are not realistic. Therefore, real values close to theoretical ones are chosen, and circuit is simulated again. Finally, after a few iterative lab measurements, we finalize the component values as shown. Here we see the difference between the theoretical and the final measured result. A few important considerations for antenna are the following. If using an antenna from a TI reference design, be sure to copy the design exactly as drawn and check if the stack-up in the reference design matches your stack-up. Changes in feed line length of the antenna will change the input impedance. Any metal in close proximity, plastic enclosure, or human body will change the antenna input impedance and resonance frequency. And this must be taken into account for matching purposes. For multiple antenna on the same board, use antenna polarization and directivity to isolate the radiation patterns. For chip antennas, verify that the spacing from the orientation with respect to the ground is correct as specified in the datasheets. After matching the antenna on the PCB, the final step is to obtain a three-dimensional radiation pattern of the antenna in a RF anechoic chamber. This way, the efficiency of the antenna can be measured, and a good visualization of its performance can be made. An antenna evaluation kit is available from TI which has different antenna covering various frequency ranges. This kit, along with associated application notes, serves as a good reference for antenna evaluation. This concludes the presentation on antenna basics and matching. Thank you.
Details
Date:
July 31, 2018
Antenna basics
Antenna parameters
Radio range and communication link
Antenna matching example
PDFs for download
antennabasicsmatching.pptx
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