Networks for Electrically Small Wire Loop Antennas for Mobile Communications ,Broadcast Applications

Small wire loop antennas have been in use since the Second World War when these antennas, which have the property of rejecting local electrical interference to focus on far field signals, were first used for military communications in the theatre of war. Since then, mobile communications and broadcasting have evolved and there has been a trend towards miniaturisation as well as the evolution of novel applications of radio technology.

Small wire loop antennas with loop circumference that is much smaller then the wavelengths of interest are today used for mobile communication equipment, broadcasting as well as in equipment for body area network applications and for body implants in medicine. It is relatively easy to etch these antennas on circuit boards and to improve their performance by using ferrite cores. The matching circuits that are used to match small wire loop antennas to radio equipment are relatively simple, using few components and the antennas can be easily used in designs of rugged radio equipment that is capable of providing superior performance in noisy environments. Although more sophisticated antenna designs based on smart antenna concepts are evolving, small loop antennas are still being widely used because of their simplicity. In this dissertation, an attempt has been made to look at the theory and analysis of small loop antennas. Matching techniques and networks for the antennas are considered and measurement methods for the characterisation of these antennas are examined. Techniques for enhancing the accuracy of antenna measurements in anechoic chambers and GTEM cells that have been presented in recent technical literature are briefly described and an attempt has been made to present typical performance curves including radiation patterns. It is hoped that this dissertation will provide a reasonable introduction to small wire loop antennas.

1.1 Introduction

In a radio system, the radiation and the reception of electromagnetic energy is of fundamental importance to the proper functioning of the radio equipment. An antenna is the structure that couples the radio device to free space and this device is designed to radiate and receive electromagnetic waves. Well designed antennas will have the capability to improve the signal-to-noise ratio as well as the link quality and reliability. Since the introduction of cellular communications in the 1970s, the demand for small and portable wireless radio equipment has seen a substantial increase with a trend existing towards the miniaturisation of the wireless radio devices and components including the antenna. The Advanced Wireless Phone System or the AMPS which was introduced in 1983 uses the 824 – 894 MHz frequency band with analogue FM modulation and FDMA. A total of 832 frequencies were assigned to a carrier and these were split into 790 voice and 42 data channels, with the voice frequency channels being 30 kHz wide in order to provide a performance comparable to that of the wired telephone. Transmit and receive frequencies in each channel had a separation of 45 MHz so as to avoid transmit and receive interference. An enhanced digital cellular system was introduced in 1991 which used digital cellular and TDMA in the 824 – 894 MHz band. This digital system was enhanced in 1993 to the IS-95 digital system which had a channel bandwidth of 1.25 MHz and used the QPSK/BPSK modulation scheme. An example of the present day Personal Communication Services or PCS is the DCS – 1900 which uses the 1850 – 1990 MHz band with TDMA and a 200 kHz channel spacing with eight time slots and provides paging, caller ID and email services in addition to voice and data communications. There are more then 60 million mobile customers today and the mobile radio equipment is required to have multimedia or voice, data video signal capabilities. The mobile digital equipment of today is highly and the equipment is supported by satellite, fixed ground networks, optical fibre, fixed radio links as well as connectivity to gateways for fixed networks. Hence, along with there being pressures to enhance the design of the mobile radio equipment, there is also a pressure to provide better antennas for such equipment. Loop antennas are made by bending a conductor into the shape of a loop or a closed curve such as a circle or a square with terminals being provided by using a gap in the closed conductor. Loop antennas may be electrically small or electrically large. Electrically small loop antennas have a loop circumference which is very small as compared to the wavelength of the radiation that is of interest, while an electrically large antenna has its circumference close to the operating wavelength. The shape of the loop becomes irrelevant when considering the far-field radiation patterns of the small-loop antenna. The antenna performance of the small-loop antennas can be enhanced by filing the core with ferrite which helps in increasing the radiation resistance. Loop antennas are very popular as receiving antennas with many such single loop designs being used for pagers and other mobile communications equipment, while multi-turn loop antennas are used for AM broadcast receivers. An electrically small loop antenna is, however, never resonant and a device is usually required to match the impedance of the antenna to the feed line. Gains of -2dB to 3dB and bandwidths of 10% are commonly associated with small loop antennas. Small and large loop antennas exhibit different radiation patterns as shown in the figure below.

Figure 1.1 Small and Large Loop Antennas

Figure 1.2 Typical Radiation Patterns for Small and Large Loop Antennas

The small loop antenna is also attractive for mobile communications because it is possible to incorporate such antennas on chips through the process of micromachining and this can assist with good reliable designs for mobile communications equipment. Square – loop antennas are especially important because they can be constructed on the edges of a chip which may have active components in the middle. The frequencies for which this is possible include the 24 GHz ISM or the Industrial, Scientific and Medical band as well as the 60 GHz WLAN or the Wireless Local Area Network band. Although such an approach will reduce the radiation resistance of the antenna, due to the presence of ground planes within the antenna geometry, workable designs are still quite possible using this approach. Representative dimensions for such a micro-machined antenna that has been etched on a silicon wafer can be 3000 micro-meter for length and breadth with a loop – wire width of 120 micro-meters and a trench width of 360 micro-meters. Mechanical stability of a silicon wafer may require the placement of more then one bridge on the silicon wafer when fabricating the on-chip antenna as shown below. Hence, electrically small loop antennas have a considerable potential for applications in mobile and handheld devices of the future.

Figure 1.3 Small Loop Antenna on a Wafer

In spite of the new developments related to the small wire loop antennas, these antennas are not a new type of antenna and have been around for quite a while. In the Second World War, the German Army used small-loop antennas for battlefield communication equipment. Because the radiation field associated with an antenna is a space integral of antenna current over distance, small antennas with large currents are capable of producing the same field intensity as large antennas with relatively small currents. A small circumference for the small-wire loop antenna will result in a small radiation resistance which is purely inductive. A series-resonant circuit may be constructed by adding a capacitive element to the small-loop antenna. Because such an addition will nullify the effects of the reactance, leaving only a small resistance to oppose the flow of currents in the small-loop antenna, therefore, large currents can be made to flow in the antenna which can result in relatively large fields from small structures. In small-loop antennas, the currents around the loop are nearly in phase and the loop antenna can be treated as a magnetic dipole. This places a limit on the antenna circumference to about one quarter of the wavelength at the highest frequency of operation. As the frequency of operation increases, it becomes harder to match the radio equipment to the antenna because the impedance at the feed-point becomes extremely reactive and rather large. Hence, matching the small-loop antenna to the radio equipment becomes a challenge. However, at the higher frequencies, the small-wire loop provides gain and radiation patterns that are very similar to a half-wavelength dipole which is much bigger and more difficult to construct as well as requiring far greater effort to maintain. At lower frequencies, the efficiency of the small-wire loops deteriorates substantially and there is a requirement for constantly tuning the antenna. Hence, apart from mobile civilian radio equipment, small – wire loops are used extensively for high frequency military communications over a theatre. The armies of Norway, China and Russia use small-wire loops extensively.

Small-loops are, therefore, important when it comes to antenna design for rugged and highly mobile radio equipment. These antennas are relatively insensitive to near field electric sources such as sparks which may have been created by electrical machinery and hence they are attractive for reception in noisy environments for reception from distant sources. Small loop antennas respond far better to the H-fields as compared to the E-fields and because the emission from close interference sources is mostly of the E-field type, therefore the small-loop antenna remains relatively insensitive to these interferences. In this dissertation, an attempt has been made to analyse the small-wire loop and investigate the matching networks that are required for such antennas. Both practical experiments as well as theoretical investigations have been considered along with inputs from the latest published research related to the small-loop antennas. In the next section, the theory behind the small-loop wire antennas is discussed.

2.1 Background Theory

In this section, it will be appropriate to analyse and discuss the limitations of the small-loop wire antennas prior to continuing with experimental investigations. In order to simplify the analysis, it may be assumed that a rectangular loop, with a circumference that is much smaller then the wavelength lies on the xy-plane. The current that is distributed across the loop can be safely assumed to be in phase because the wire is purely resistive. The four arms of the rectangular loop can then be considered to be elemental dipoles that are contributing to the field of the antenna. The following equations may be written for the field of the small-loop which has been shown in the diagram drawn below.

Figure 2.1 Diagrams Illustrating the Geometry of the Small-Loop

Geometric relations can be established to a good approximation in relation to the small-loop as follows:

Substituting the above into the previous equations and simplifying results in the following equations:

In the above equations, is a small angle for the sin function and can be replaced by the angle itself for small values, resulting in the following simplification to the two equations:

Adding the two field components gives the overall result as follows:

If considering the spherical coordinate system, the following relationship holds with S being the area of the loop:

For a small-loop antenna, the impedance is inductive as compared to that of a dipole which is capacitive. For a loop parameter that is less then 0.3 wavelengths, the radiation resistance is given by the formula:

This radiation resistance can be increased, as is the case with AM receivers by winding the small-loop on a ferrite core. In such a situation, the following formula for the radiation resistance will hold:

For a ferrite core having at 1 MHz, . For a rectangular loop of wire of radius a, with sides’ l1, and l2 the following formula holds for the small-loop:

A wire radius a, which is much smaller as compared to the dimensions of the sides, the above formula reduces to:

For a circular small-loop of radius b, the following relationship holds.

The inductance associated with a rectangular loop is given by the formula.

While, the inductance of the circular loop is represented as

For a small-loop, the reduction in the radiation resistance is far more rapid with a reduction in frequency, being correlated with as compared to a short-dipole in which the reduction resistance decreases in relation to .

The efficiency of a small-loop antenna is given by the formula

Regardless of their construction, electrically small antennas have fundamental limitations which have been investigated by researchers. An approximate lower limit for the Q of an electrically small antenna has been derived and has been presented in literature as being

Where k is the wave number associated with the frequencies incident on the antenna. Q is defined in literature as being the ratio of the resistance to the reactance for a device and is given by the formula presented below, where X is the reactance or the stored energy associated with a circuit and R is the resistance associated with the circuit.

In literature, the radiation Q for an antenna has been defined as

Here, is the radian frequency, Prad is the radiated power, and W is the time-averaged, nonpropagating, stored electric or magnetic energy. Either electric or magnetic energy may be considered, depending on which is greater. The fundamental limit on the Q for an electrically small antenna is derived without regard to the geometry of the antenna or consideration of the current distribution in the antenna. When deriving the expression for the Q of an antenna, the antenna is considered as being surrounded by an imaginary sphere, that has a radius a. This is also the maximum dimension of the antenna that is under consideration. The fields outside of the imaginary sphere are analysed with a relation between the stored and propagated energy being established. The value of Q is minimized by this approach because any energy that is considered as being stored within the sphere is ignored as this would only have served to increase Q.

The radiation outside an imaginary sphere enclosing an antenna may be separated into a weighted sum of spherical wave functions which are known as the modes of free space. The spherical mode of radiation may be described over the radial length by a spherical Hankel function which is the spherical Bessel function, while a Legandre polynomial is used to weight the spherical mode over the spherical surface of the imaginary sphere. The complex power radiated through the sphere, assuming that the directivity is maximum for the equatorial plane with q = 90° is described by the following equation in which An is an arbitrary coefficient that describes the excitation of the nth spherical mode, while k is the wave number, a is the radius of the spherical shell, n is the mode number of TMn and hn represents the spherical Hankel function of the second kind. The formula given below is for odd modes of TMn with results for even n being left out because these modes do not result in omni-directional values.

An equivalent circuit for each mode may be derived by equating the complex power of each mode to the power of a second order equivalent circuit and expressions for the voltage as well as current can be expressed as follows.

In the above expression, differentiation with respect to ka is indicated by a prime. The input impedance of the circuit is represented as a ratio of the voltage to the current and the normalised radial wave impedance on the surface of the imaginary sphere can then be represented as:

Using the recurrence relationship for spherical Bessel functions, the equivalent circuit for the spherical TMn mode may be represented as shown below. The resistance and the reactance of the antenna may be equated to the values indicated in the equivalent circuit in order to derive an expression for Q for the antenna. The power dissipated in the real resistance of the equivalent circuit represents the radiated power while the energy stored in the reactive elements of the equivalent circuit represents the stored energy in the antenna.

Figure 2.2 Equivalent Circuit for a Small Loop Antenna in the TMn Spherical Mode

Using an approximation by assuming that an equivalent lumped RLC circuit can represent the equivalent circuit and behave the same for small variations in frequency, the following equations may be derived in relation to the equivalent circuit that has been presented.

The power dissipated by the electric circuit may be represented by the following equation.

The energy stored in the reactive components of the equivalent circuit that has been presented is given by the expression presented below.

The value of Q can be found from the ratio of the stored and dissipated energy in the equivalent circuit and is given by the expression shown below.

For a practical situation in which most antennas will have ka to be very much less then 1, the above equation may be reduced to a simplified form as shown below. This expression provides a value for the lower limit of Q for an electrically small antenna regardless of its construction or shape.

A more exacting result has been presented by researchers in published literature as follows.

Because a limit has been placed on the value of Q for the electrically small antennas, therefore there is also a limit on the bandwidth for the electrically small antennas as indicated by the formula shown below which is a very fundamental relation of circuit analysis and filter theory.

The variation of Q for the electrically small antenna with a variation in ka is shown below in graphical form.

Figure 2.3 Illustrating the Minimal Limit on the Value of Q for Electrically Small Antennas

It can, therefore, be summarised that electrically small antennas have high input reactance and a low input resistance with a high value of Q and a low bandwidth. Thus it is possible to use electrically small antennas for highly selective narrowband tuning applications in radio direction finders as an example. It can also be shown that apart from a fundamental limitation on Q, electrically small antennas also have a limitation on their radiation efficiency. For an electrically small antenna with a radiation resistance of Rr and an ohmic or copper resistance of Rohmic, the radiation resistance of the antenna may be defined as:

Radiation efficiency of antennas measures the ability of an antenna to deliver a percentage of the radiation received from space to the receiver. Contrary to the belief which had existed in the past, an electrically small antenna cannot deliver infinite amounts of energy which is picked up from the free space. However, there is a fundamental limit for the efficiency of electrically small antennas as can be seen from the following analysis.

The radiation power factor p is a quantity which is defined as the reciprocal of Q, which is equivalent to the impedance bandwidth. An electrically small antenna can be thought of as a reactance consisting of a capacitor, an inductor or a combination of these circuit elements. A dipole antenna behaves similar to a capacitor, while an electrically small loop antenna behaves like an inductor and these antennas can be represented as a combination of lumped resistive and reactive components as shown below. The electrically small loop antenna is represented as a combination of reactive and resistive elements while a dipole is presented as a shunt capacitance and a susceptance.

Figure 2.4 Equivalent Circuit of an Electrically Small Loop Antenna

Figure 2.5 Equivalent Circuit of a Small Dipole Antenna

From the above circuits, the radiation power factors of the electrically small loop and dipole antennas can be presented by the following equations respectively.

The radiation power factor expression may be re-written in terms of the radiation power factor and the loss power factors as follows:

In the above equation, the loss power factor or ploss, is important for small amounts of radiated powers, as is the case with small antennas. The radiated power and hence the radiation power factor is affected by the effective volume of an antenna, which is the physical volume of the antenna with an addition to allow for the near field effects. With these considerations in mind, it can be shown that for different radiation efficiencies, the lower limit on Q, the lower bound for radiation is related to ka, the dimensions of the electrically small antenna as shown in the curves below. These curves indicate that for the electrically small antennas, there are limitations associated with performance of the antenna that are related to the size of the antenna.

When analyzing electrically small antennas in practical situations for use in radio equipment, many other considerations such as currents that can flow in the antenna conductor, issues related to a ground plane, effects of the casing of the radio equipment as well as effects of the human body on antennas operating near the human body, as is the case with most mobile and handheld equipment, will have to be considered for accurate analysis. However, the theoretical background that has been presented is sufficient to understand the basic functioning of the electrically small loop antennas.

From the theory that has been presented, it will be obvious that electrically small loop antennas have a very low electrical impedance and therefore the techniques that are required to match these antennas to the radio equipment by making the impedance of the radio equipment the same as the impedance of the antenna become important for maximum power transfer of the radiated power to the equipment and from the equipment into the free space.

Figure 2.6 Limitations on Q for Electrically Small Antennas for different Antenna Efficiencies

In addition to ensuring that maximum power is transferred from the antenna to the radio equipment, matching networks ensure that maximum sensitivity can be obtained from the attached antenna.

Figure 2.7 Variations of Radiation Resistance, Loss Resistance and Efficiency of a 30MHz Small Loop

Small loop antennas can be etched onto the printed circuit boards of mobile communications equipment such as phones or pagers and for an area A, the radiation resistance of the antenna may be given by the equation which is presented below:

For a loop parameter of length P and trace width w, which is the similar to the loop conductor diameter and for a magnetic permeability of µ = 400π nH / meter, frequency f and copper conductivity of σ = 5.8 × 107 ohms / meter, the dissipative resistance of the small wire loop is given by the formula:

Inductance of the loop antenna is presented by the following formula in terms of the parameter P of the loop, the wire diameter or trace width w and the magnetic permeability μ as follows:

These formulas are nothing new and are special cases of the formulas which have already been derived when considering the analysis of the electrically small loop antennas. Thus, for a 25mm by 32 mm rectangular loop, the radiation resistance comes to 0.025 ohm, the loss resistance comes to 0.3 ohm and the inductance of the loop antenna comes to 95 nH for a frequency of 315 MHz. Calculations may be easily performed for other frequencies that are associated with mobile communications and broadcasting.

Reactance can be used to create resistive impedance matches for small-loop antennas. By adding a series or parallel reactance to a resistor, the value of the resistance can be increased or decreased over a frequency range. A series or parallel reactance network can be added to the series resistance in order to create a match as illustrated in the diagrams below.

Figure 2.8 Series or Parallel Addition of Impedance to an Antenna Figure

2.9 Matching Network for an Antenna

The admittances of the antenna and the radio circuit can be equated as follows:

Equating the real and imaginary parts gives the following:

Substituting QS = XS/RS, in the above equation gives the following expression:

The series resistance and reactance for a given parallel resistance and reactance can be determined from the following:

The following expressions can be derived from the above equation:

The above expressions can also be written in terms of QP =RP/XP

The matching network for the small-loop antenna effectively converts the small resistance of the electrically small loop into a larger resistance RL that can be driven by the power amplifier. The antenna resistance and the resistance of the radio device are known, therefore, Q and the total series reactance can be found using the following equations:

From here X1can be calculated. The parallel part of the matching network X2 can be calculated as being equal and opposite to the value of the XP from the expression presented below:

In practical terms, the above discussion about matching networks for electrically small wire-loop antennas means that one form of a matching network for electrically small loop antennas consists of two capacitors as shown below:

Figure 2.10 Split Capacitor Matching Network with Bias Inductor

Using the expressions which have been previously presented for the matching networks, the values of capacitances for the matching network can be determined for various frequencies. As an example, the values of C1= 2.82 pF, C2= 63 pF and L1= 36 nH are obtained for a frequency of 315 MHz.

The expressions which may be derived for capacitors C1 and C2 by considering the broadband conductance which is to be seen by looking into the capacitor tapping network are as follows:

From these equations, it may be inferred that the capacitor C2 is to shunt most of the current to the ground because it dominates the input conductance. This ability to shunt currents to the ground assists with the ability to reject second or higher order harmonics in the matching network. Capacitors C1 and C2 must be well controlled in order to meet the resonance and input impedance requirements for the network and the antenna. For electrically small antennas on printed circuit boards, parasitic radiation effects from bond wires and traces on the circuit board can dominate performance. For harmonics, the input conductance of the tapping network may be approximated by the following formula:

A measure of the rejection of the harmonic power as compared to the power in the fundamental frequencies for the small loop antenna is given by the following relationship:

For most small loop antennas, the harmonic rejection performance with a capacitive matching network is sufficiently good to comply with the regulatory requirements of bodies such as the FCC and small loop antennas are extensively used as built in antennas for mobile radio equipment.

Another matching network that has been described in literature for electrically-small loop antennas consists of an additional low-pass filter stage being added to the capacitive circuit which has been previously described. This is shown in the diagram presented below.

Figure 2.11 Capacitive Matching Networks in Combination with a Low-Pass Filter to Enhance Harmonic Rejection

The actual value of Q for practical electrically small loop antennas is lower as compared with what is calculated by the theoretical calculations and there is also a need to have reduced levels of lower harmonics emanating from an antenna because of requirements that may exist in relation to regulations for frequency channel allocations. Hence, there can be a need for an improved matching network with an ability to reject harmonics. The best way to design the network containing the low pass filter elements for harmonic rejection is by referring to filter design tables or a CAD simulation program such as Ansoft Designer or the analysis program Aplac from Aplac technologies and further fine tuning the elements by experimental observations

Another important matching method for small loop antennas which has been described in published literature is the transformer approach to matching the small loop antenna. This approach is also quite common because there is a minimal part requirement associated with this matching technique. This approach involves the placement of a small secondary loop near the main small loop antenna, which in fact shares one of the sides of the main small loop antenna as shown in the figure below:

Figure 2.12 Transformer Approach to Loop Matching the Small Loop Antenna

A tuning capacitor is still included in the main small loop and there is a tendency to consider the two loops as either tapped inductors with no mutual coupling or auto-transformer with a mutual coupling between the loops. Published literature has, however, criticised the concept of the two small loops being thought of as an auto-transformer and it is stated that errors are introduced in analysis as a result of this thinking. It can be shown by considering the coupling between loops and using Ampere’s Law as well as other fundamental relations of electromagnetism, that:

This expression may be used to determine the size of the secondary loop that may be used to match a small loop antenna to radio device with an output resistance. The output resistance can be equated to ZIN, in order to calculate a value of Rs which can then be used to determine the size of the secondary loop. The dimensions of the primary small loop antenna should be made as large as possible, while trying to minimize the size of the secondary loop. The harmonic rejection performance of the transformer matched loop is described by the following equation.

The performance of the tapped capacitor matching network is superior when compared to the transformer method, because the second and third harmonic rejection performance figures are better for the tapped capacitor matching networks. However, the transformer method is used because it is simpler to attach a secondary loop on a PCB when designing a radio device and there is no need to worry about stability of capacitors or breakdown of these components. The efficiencies presented by both the tapped capacitor and the transformer methods present about the same figures and these figures are significantly better then those for the unmatched transformer. Small loops can also be used with differential drivers and a perfect geometric balance is not required in order to maintain a balance in the loop or the loop drivers. It is necessary to be careful when designing small loop antennas and their matching networks on printed circuit boards and to consider the impact of power line leakage which can result in poor harmonic performance.

After having discussed the theoretical aspects of electrically small loop antennas and their matching networks, it is appropriate to consider how measurements can be made on these antennas in order to determine radiation patterns and other parameters associated with the antennas. This is done in the next section which deals with the testing and measurements on small loop antennas.

3.1 Work Done & Results

For electrically small antennas, there is far less directivity and the measurements associated with an antenna are important from all angles for the Antenna under Test, AUT. Radiation patterns for an antenna describe the relative strength of the fields associated with radiation from the antenna at a constant distance, in all directions. The radiation pattern also describes the reception properties of the antenna and these are three dimensional. However, because it is difficult to display three dimensional results and also time consuming to take the associated measurements for the three dimensional case, it is usually considered sufficient to take measurements for a slice of the three dimensional space. These measurements are presented in polar or rectangular formats. Near field measurements are also possible as compared to the far field measurements, but for electrically small antennas the near field measurements will require far more effort as compared to the far field measurements and the results for the near field measurements are not all that important for most applications. Measurements involving antennas are conducted in anechoic chambers so that interference from fields radiated by other objects do not corrupt the experimental results. The anechoic chamber consists of walls that are covered with radio-frequency absorbing material and there are no conducting surfaces present, with the result that a highly homogeneous field environment exists in the chamber and variations are lower then 0.5 dB for a wide frequency range and in the better anechoic chambers, the field variations can be as low as 0.1 dB. A field variation of 0.5 dB is necessary for compliance with antenna calibration standards and measurement techniques must allow for these. For a relatively simple experiment without the automatic test equipment that is to be found in sophisticated anechoic chambers or Gigahertz Transverse Electromagnetic Mode Cells, additional equipment that is required includes an Agilent E4400B Signal Generator with an operating frequency of 250 kHz - 1GHz or similar with high frequency sweep and an Agilent ESA-L1500A Spectrum Analyzer: 9 kHz - 1.5 GHz or an instrument with a higher frequency performance capability. In order to perform measurements on the small loop antenna, the signal distortion associated with the setup has to be determined so that this may be compensated for in all measurements to determine antenna characteristics. The signal distortion can be found by connecting the signal generator to the spectrum analyzer and passing a sinusoidal signal at the frequency of interest, e.g. in the 900 MHz band and tracing as well as storing this signal on the spectrum analyzer. Typical settings for the signal generator for a measurement of 900MHz may have an amplitude: -20dBm, modulation: off and RF: on. The settings for the spectrum analyzer may be centre frequency f = 900MHz, Span: 20 kHz and Amplitude: -20dBm. The spectrum analyser can be set to a span of perhaps 0 Hz with a 20 second sweep time. Further calibration is made possible by connecting standard testing antennas of 900 MHz ,which may be dipole antennas, to the signal generator and the spectrum analyzer and storing the received signal on the spectrum analyzer for a separation between antennas exceeding ten wavelengths. This step is then repeated using the electrically small loop attached to the spectrum analyzer and it provides a clean sinusoidal signal measurement for signal received over cable and antennas. The set up of the test gear is shown below.

Figure 3.1 Calibration of Signal Generator and Spectrum Analyzer for Measurements on Small Loop Antennas

A simple method of measuring the bandwidth of the small loop antenna consists of using standard antennas attached to the signal generator as well as the spectrum analyzer and then the small loop antenna under test AUT to the spectrum analyzer and transmitting signals of various frequencies of interest around the centre frequency of the AUT. The two antennas should be placed at least ten wavelengths apart. The relative gain as a function of frequency can be plotted for the two test antennas and the small loop AUT. The effects of the test antennas attached to the signal generator and the spectrum analyzer are to be subtracted from the measured data for the small loop antenna by subtracting out the effect of the test antennas in dB from the measurements taken. This yields a bandwidth curve for the small loop AUT.

The radiation patterns of the small loop AUT may be measured by first connecting test antennas to the signal generator and the spectrum, analyzer and orienting both antennas at a distance of at least ten wavelengths. For horizontal radiation pattern, the two antennas should be oriented vertically and the received signal strengths should be measured in steps of 10 to 20 degrees with the measurements being repeated for the small loop AUT at the same point as they were performed with the two test antennas. This is the horizontal radiation pattern. For the vertical radiation pattern, the orientation of the placement of the antennas needs to be changed and measurements similar to those for the horizontal radiation pattern are taken. The effects of the test antennas can be subtracted out from the results for the small wire antennas. Polarisation may be measured by placing the transmit antenna parallel to the ground and rotating the receive antenna from horizontal to vertical with measurements being separated by 10 to 20 degrees. The received signal can then be plotted as a function of the polarization angle to give the polarization curves for the antennas. Dips in the measured results tend to indicate interference with signals due to ground and metallic conductors. Such dips will not be prominent in good anechoic chambers in which due consideration has been given to providing an interference free ambience and efforts have been made to allow for the effects of coaxial cables.

The method that has been described above can give reasonably good results for the radiation patterns and other parameters associated with small-loop antennas. With sophisticated test facilities being made available, more elaborate and exacting set-ups are possible which can automatically step measurements associated with antennas in space under computer control in sophisticated anechoic chamber facilities with efforts being made to take into consideration the effects of feed cables. These sophisticated techniques for measurements on small loop antennas which have been developed as a result of research in various labs and research centres have been described in a survey by Helsinki University of Technology’s Radio Research Laboratories. The methods that have been described in this published report present techniques for the minimisation of the dimensions for anechoic chambers in which measurements have to be made. Hence, the techniques presented are the best available for the reduction of measurement uncertainty in small loop antenna measurements. The distance between the measurement antenna and the AUT can range from 3 to5 meter and the AUT is placed at a distance of 1 – 3 meter from the floor, the ceiling and the walls, resulting in a chamber that can be fairly large and expensive. Attempts have been made to reduce the size of the dimensions for anechoic chamber to bring them within the dimension of a table, improving accessibility and reducing cost in the process. GTEM cells which are the result of such efforts are mini chambers dimensions of about 2m length which can be placed on a table and are very useful in antenna design and measurements because they can be relatively quickly used to test a small antenna during the design process. GTEM cells are immune from broadcast signal interference and require less signal amplification as compared to full sized anechoic chambers.

Their cross-polarisation performance is, however inferior to that of the anechoic chamber. In the GTEM cell, an expanded transmission line that is operating in the TEM mode is used to excite the cell by feeding radiation into it through its narrow end using a standard coaxial cable. The TEM mode of the frequency of operation for the cell is matched by a wideband termination at the wide end of the GTEM cell. Equipment that is suitable for tests in the GTEM cell is a tenth of the dimensions of the GTEM cell and hence, most small loop antennas can be adequately tested in such cells, with antenna gains being measured to an accuracy of +/- 1dB. The antenna under test is used as either a transmitter or a receiver. The network analyser connected to the antenna may be used to measure the received signal at the AUT, with an amplifier connected to the signal analyser providing the excitation. The GTEM cell does present some limitations related to the accuracy of measurements because of its small size and the influence of the metal cell walls on the antenna characteristics with differences of several dB being observed between measurements taken in a GTEM cell and a full anechoic chamber. Hence, GTEM cells are used for rapidly testing small antennas, but they cannot be used to replace full anechoic chambers which are capable of providing more accurate and reliable measurements especially at frequencies that are about 1GHz for mobile paging equipment. Software that is capable of correlating experimental results from a GTEM cell to an anechoic chamber is commercially available and may be used to enhance GTEM measurements. Antenna efficiencies can also be measured to an adequate degree of reliability using the GTEM cells.

Figure 3.2 A GTEM Cell for Small Loop Antenna Measurements

Some results for RF testing on a straight line are shown below for a typical electrically small antenna. The results also present measurements for 2nd harmonic signals and the dips are due to ground and other interference effects. Ideal response refers to results for testing in a good anechoic chamber.

Figure 3.3 Results of RF Measurements on a Straight Line for a Small Antenna

In order to measure the Q value of the small loop AUT, the antenna is connected to a signal generator which is set at the desired frequency and which is capacitive coupled. The output is set at -20 dBm with a sinusoidal signal output and the peak output power from the AUT is measured using the spectrum analyser. After this measurement, the signal generator output power is swept up and down until frequencies are reached when the output power from the AUT drops by -3 dB. For an antenna that is not perfectly tuned, there is a possibility of the power drifting up while attempting to sweep through the frequencies to locate the 3dB points for the AUT. Typical spectrum analyser plots for small loop antenna are shown in the figure below.

Figure 3.4 Spectrum Analyser Plot for the Measurement of Q for a Small Loop Antenna

In the above set of results, the 3 dB bandwidth is 18.45 MHz while the frequency associated with the peak power is 432.3 MHz. Q can be calculated by dividing the peak power frequency by the 3 dB bandwidth and for this set of results, the value of Q is found to be 23.4 for the AUT.

A calibrated network analyser such as the HP 8714C that has been calibrated using its calibration kit can be used to take measurements on a small wire loop. The network analyser can sweep from a frequency of 150 MHz to 950 MHz or higher frequencies. These measurements which can be plotted on a smith chart using the plotting facilities available on the network analyser and the measurements will indicate the resonance for the antenna being tested and the associated load impedance. A ferrite clamp that can be placed on the coaxial just beyond the feed point may be used to suppress the sheath currents that may be flowing on the outside. A resonant balun can interfere at frequencies that are included in the range of measurements on the network analyser and therefore it is appropriate that such an attempt to match the antenna not be used for the experiment. The use of a ferrite clamp can enhance the accuracy of the measurements with a small variation showing up on the plot that is the result of measurements. An even smoother plot from the network analyser can be obtained by using additional ferrite sleeves for shielding. The smooth curve from the network analyser measurements indicates that the interference from external fields has been minimised. Room and cable resonances can corrupt measurements and result in a Smith Chart plot which is indicative of these effects. A screen shot for such measurements after attempts have been made to shield for cable and other interference effects is shown below.

Figure 3.5 Smith Chart Plots for Measurements on a Loop Antenna using a Network Analyser

It is also possible to perform measurements on small loop antennas using radio transceiver, communications receivers, coaxial cable assemblies and inline attenuators instead of the arrangements involving signal generators and spectrum analysers. Reasonably good radiation pattern plots may be obtained by using this equipment. These measurements are also required to be taken in a shielded radio environment, but the equipment involved is far less expensive and can still provide reasonably good results. Radiation patterns associated with small loop antennas are presented below.

Figure 3.6 Vertical Radiation Patterns for a Small Loop

Figure 3.7 Horizontal Radiation Patterns for a Small Loop

4.1 Conclusion

Small loop antennas are widely used in mobile communications equipment such as pagers, mobile handsets, voice communications equipment and direction finding equipment for military as well as civilian applications. These antennas can be readily etched on printed circuit boards or constructed using lengths of wire. Analysis and measurement techniques for small loop antennas were presented in this dissertation. There are several methods which may be used to match the small loop antenna to radio equipment, the simplest of which involves the use of split capacitor circuits. Rugged transformer matching circuits may also be constructed by providing a secondary loop on a printed circuit. Harmonic rejection in the antenna circuit can be improved by using low – pass filters and such matching circuits may provide superior performance as compared to simple capacitor circuits. Small loop antennas tend to reject the interference of near field sources and hence, they are successfully used in locally noisy environments including mobile military vehicles. With ongoing efforts to design novel miniature radio equipment for a wide variety of applications, the significance of small loop antennas as structures for coupling radio devices to space is likely to continue to grow in the future.

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