Fundamentals and design principles of RF, antenna (Part 2)
Keywords:half-wave dipole antenna? PCB? interface?
By Matthew Loy and Iboun Sylla
Texas Instruments Inc.
Antennas connect RF signals in an electrical circuit, such as between a PCB and an electromagnetic wave propagating in the transmission media between the transmitter and the receiver of a wireless link.
The second installment of the 3-part series discusses common antennas including half-wave dipole, quarter wave monopole, transversal mode helical, and small loop antennas.
The half-wave dipole antenna (Figure 6) is the basis of many other antennas and is also used as a reference antenna for the measurement of antenna gain and radiated power density.
At the frequency of resonance, i.e., at the frequency at which the length of the dipole equals a half-wavelength, we have a minimum voltage and a maximum current at the terminations in the center of the antenna, so the impedance is minimal. Therefore, we can compare the half-wave dipole antenna with a series RLC resonant circuit as given in Figure 2. For a lossless half-wave dipole antenna, the series resistance of the equivalent resonant circuit equals the radiation resistance, generally between 60? and 73?, depending on the ratio of its length to the diameter.
The bandwidth of the resonant circuit (or the antenna) is determined by the L-to-C ratio. A wire with a larger diameter means a larger capacitance and a smaller inductance, which gives a larger bandwidth for a given series resistance. That's why antennas made for measurement purposes have a particularly large wire diameter.
As opposed to the (only hypothetical) isotropic radiator, real antennas such as the half-wave dipole have a more or less distinct directional radiation characteristic. The radiation pattern of an antenna is the normalized polar plot of the radiated power density, measured at a constant distance from the antenna in a horizontal or vertical plane.
Figure 7 shows the radiation pattern of a half-wave dipole antenna.
Since the dipole is symmetrical around its axis, the three-dimensional radiation pattern rotates around the wire axis.
The isotropic gain of a half-wave dipole antenna is 2.15dB. Therefore, in the direction perpendicular to the wire axis, the radiated power density is 2.15dB larger than that of the isotropic radiator. There is no radiation in the wire axis. The half-wave dipole produces linear polarization with the electrical field vector in line with, or in other words parallel to, the wire axis.
Because the half-wave dipole is often used as a reference antenna for measurements, sometimes the gain of an antenna is referenced to the radiated power density of a half-wave dipole instead of an isotropic radiator. Also the effective radiated power (ERP), which is the power delivered to an ideal dipole that gives the same radiation density as the device under test, is used instead of the EIRP. The relations G_{dipole} = G_{isotropic} - 2.15dB and ERP = EIRP - 2.15dB can be applied.
Figure 6: Half-wave dipole antenna |
The half-wave dipole needs a differential feed because both of its terminations have the same impedance to ground. This can be convenient if the transmitter output or the receiver input have differential ports. A balun will be used along with the half-wave dipole in case of single-ended transmitters or receivers, or if an antenna switch is used. For external ready-manufactured half-wave dipoles, the balun is visually built-in to the antenna and provides a single-ended interface.
The half-wave dipole is an electrical antenna. This means that it is easily detuned by materials with a dielectric constant larger than 1 within its reactive near field. If, for instance, the housing of a device is in the reactive near field, the housing has to be present when the antenna is matched. The human body has a large dielectric constant of approximately 75. As a result, if an electrical antenna is worn on the body or held in the hand, it can be strongly detuned.
Figure 7: Radiation pattern of a half-wave dipole antenna |
If the antenna is built as two traces on a PCB, the dielectric constant of the PCB material has to be considered. The electrical field in the reactive near field region spreads out partially into the PCB material, partially into the surrounding air. This gives an effective dielectric constant e_{eff} between that of the air and the PCB material:
Where h is the thickness of the PCB material, w is the trace width of the dipole arms. The required length of the half-wave dipole is then:
Underneath the dipole and within the reactive near field, no ground plane is allowed.
Monopole structure
In many cases, the half-wave dipole is just too large. Also, the needed differential feed is often a disadvantage. If we replace one branch of the dipole antenna by an infinitely large ground plane, due to the effect of mirroring, the radiation pattern above the ground plane remains unaffected. This new structure is called a monopole antenna.
Figure 8: Building up the quarter-wave monopole |
Because all the radiated power is now concentrated in the half-space above the ground plane, the gain of the monopole is 3dB larger than the gain of the dipole.
Often a large ground plane is not feasible. The Marconi antenna replaces the (not realizable) infinitely large ground plane by several open-ended /4-Stubs, called the counterpoise.
A further reduction to only one stub gives a structure that looks like a bent dipole antenna. When designing a monopole antenna, the radiator should go as long as possible perpendicular to the ground stub or the ground plane. Bends close to the feeding point reduce the radiation resistance and the efficiency of the antenna.
The ideal quarter-wave monopole has a linear polarization with the vector of the electrical field in the wire axis. If the ground plane becomes unsymmetrical, the direction of polarization will be tilted towards the larger part of the ground plane, but still remains linear.
The radiation resistance of an ideal quarter-wave monopole is half of that of a dipole; depending on the ratio of length to diameter of the radiator between 30? and 36.5?.
Like the half-wave dipole, the quarter-wave monopole is an electrical antenna. It is influenced by the dielectric constant of the material in the reactive near field. The same formulas for the effective dielectric constant and the required length as for the half-wave dipole hold for the quarter-wave monopole.
Table 1 gives the length of half-wave dipoles and quarter-wave monopoles in free space and on a PCB for commonly used short-range frequencies. For the PCB antennas, a PCB thickness of h = 1.5mm and a trace width of w = 1mm has been assumed; the PCB material is FR4 with _{r} = 4.2. This gives an effective dielectric constant of _{r} = 2.97.
It has to be mentioned that parasitic components, such as capacitance to ground, inductance introduced by bends in the antenna as well as the influence of the package, alter the antenna impedance. For monopole antennas, the ground plane is sometimes smaller than a quarter-wave length or not perpendicular to the radiator. In practice, the exact length of the dipole or the monopole has therefore to be determined by measuring the feed impedance with a vector network analyzer.
Sometimes the available space limits the length of an antenna. The antenna is made as long as the geometry permits, which can be smaller than one quarter wavelength. A monopole shorter than a quarter-wave length can be considered as a quarter-wave monopole, which is used at a frequency lower than the frequency of resonance.
Loaded stub antenna
According to the equivalent schematic given in Figure 2, the input impedance at the frequency of operation will then be a series connection of a resistor and a capacitor. The series capacitance can be resonated out by a series inductor. A monopole antenna shorter than l/4 with a series inductor is also referred to as a loaded stub antenna.
The radiation resistance of a loaded stub decreases with decreasing length. The smaller radiation resistance and the larger L-to-C ratio increase the quality factor and make the bandwidth smaller than for a quarter-wave monopole. Approximations for the radiation resistance of a monopole antenna are:
At the frequency of operation (i.e., resonance), the impedance of the short stub will be that of a small resistor (radiation resistance plus loss resistance) with a series capacitor. From the Smith Chart in Figure 9 we can see that matching to a 50? source can be achieved by a series inductor and a parallel capacitor.
Figure 9: Matching of a short loaded stub antenna |
Figure 10 shows an example of a loaded stub PCB antenna with matching components.
Figure 10: Loaded stub PCB antenna with matching components |
The series inductor and the parallel capacitor transform the antenna impedance to 50?, the input impedance of the filter (FIL1).
For dipole or monopole antennas, the component values for the series inductor and the parallel capacitor (CP) have to be determined by measuring the feed impedance at point A in Figure 10 (with L_{S} = 0? resistor and C_{P} left unpopulated) with a vector network analyzer.
Once this is determined, we can use a Smith Chart to assist in matching the antenna to 50? using L_{S} and C_{P}.
Derivatives of the monopole are the inverted-L and inverted-F antennas as shown in Figure 11.
Figure 11: Inverted-L antenna and Inverted-F antenna |
In the inverted-L antenna, the monopole does not run perpendicularly to the ground plane over its whole length but is bent parallel to the ground plane after some distance. This helps to save space, but decreases the radiation resistance because the radiator comes closer to the ground plane. An additional matching circuit is needed to match the low-feed impedance to the usual transmission line impedance of 50?.
If we proceed from the feed point of the inverted-L antenna to the end, we notice that the voltage increases (while the current decreases) from a maximum voltage value at the feeding point to almost zero at the end. This means, that the antenna impedance has its minimum if we feed the antenna as shown in Figure 11a) and increases if we move the feeding point towards the end. The inverted-F antenna in Figure 11b is an inverted-L antenna with a feeding tap that gives larger antenna impedance. If the antenna is tapped at the right location, no additional matching circuit is required.
The structure of inverted-F antennas and, in particular, the location of the tap, is usually determined by electromagnetic simulations.
Helical antennas
Another option to reduce the size of a monopole is to coil it up into a helix as shown in Figure 12.
Figure 12: Helix antenna on a ground plane |
When the coil circumference and the spacing between adjacent turns are comparable to the wavelength, the antenna radiates a circular polarized beam in the axis of the helix. These antennas are called axial mode helicals.
In small short-range applications, the helix diameter and the spacing between turns are much smaller than a wavelength. So, the result is a normal mode helical antenna. The radiation pattern of a normal mode helix is similar to that of a monopole; the maximum radiation occurs perpendicular to the helix axis. Due to the shape and the size of the ground plane, radiation patterns of practical antennas can show deviations from this idealized form. The radiation from a normal mode helix is elliptically polarized. Usually the component having the electrical field vector parallel to the antenna axis is stronger than the component which is parallel to the ground plane.
The exact calculation of transversal mode helical antennas is not as simple as for dipole and monopole antennas. Usually they are designed empirically: start with a wire that is half a wavelength long, wind it up into a helix, and measure the antenna impedance using a vector network analyzer. Then, cut it back until nearly real input impedance at the frequency of operation is obtained. Real input impedance means that the antenna is in resonance. Fine-tuning of the frequency of resonance is possible by compressing or stretching the helix.
Even if the antenna is in resonance, it will not be matched to 50? yet. The input impedance will be the sum of the radiation and loss resistances, usually smaller than 50?. For the design of the needed additional matching circuit, we can use the Smith Chart as described above.
Chu's and Wheeler's limit on the bandwidth for a given dimension also holds for helix antennas. A small transversal mode helix, therefore, has tight bandwidth and is sensitive to tolerances of the matching components.
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