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Introduction to Miniature Antenna and Diversity Combining Techniques

Multipath, shadowing and fading effects are major challenges in the reliable operation of terrestrial wireless communication channels. Signals from transmitter to receiver bounce from various objects and from the ground, and add in the receiver antenna in a way that can be destructive to signal strength and therefore to communication quality and throughput. In addition, effects like shadowing, scattering and diffraction add to the complexity of the propagation in the channel. These effects have been a major concern in the design of various wireless networks and cellular standards (GSM, CDMA, 802.11, etc.). Overall signal reliability is especially acute in the design of miniature sensor radio systems, with their ultra limited power sources (small batteries) and operation in highly fading channels, when running close to ground level, in medical facilities, buildings, or even in-vivo.

The principle of space diversity uses multiple antennas (at least two), distributed in space with their signals processed, either independently or in concert. The “redundancy” built into such systems improves significantly both reception quality and reliability.

Of the various techniques available to combat multipath (spread spectrum has been heavily utilized in the last 10 years, either direct sequence, CDMA, or frequency hop configurations, 802.11), antenna directivity and diversity is the most powerful but also the most complicated and least economical, because of the extra hardware (and power) associated with the use of more than a single antenna. This technology, which has been used mainly in large installations, such as cellular base stations, is now emerging as a viable economical solution even in handheld devices. Array processing was previously complex and expensive, but with the advent of simpler processing algorithms, low power integrated radio ASICs and exponentially growing DSP engines, the limitations are gradually being mitigated.

Space diversity requires a certain “spatial separation” between the distributed elements, otherwise their signal will be correlated and the application offers no advantage. However, diversity can also be in polarization (left hand/right hand circular or vertical/horizontal, for example), which allows proximity between elements. Generally, cross-correlation below 0.5 is required. Since that separation is in the order of ?/3 to ?/2 (for vertical or horizontal polarization), physical separation in handheld devices at higher frequency platforms is very realistic. It is therefore possible in cell phones, WLAN terminals and in miniature network sensors operating at the higher ISM bands.

This article has been written from the standpoint of miniature (< 1 cubic inch, including the battery) radio-sensor technology, which is also only now emerging. It highlights briefly the alternatives, the modeling and the processing of miniature antennas, and reviews miniature antenna diversity and combining techniques.

Equations will be introduced for miniature antenna parameter calculations, performance limits will be reviewed and the focus will be on the performance of various small antennas and the advantages of antenna array processing, specifically antenna combining. The terminology and terms will be highlighted. Some simulation results will be provided, and technological and business opportunities and challenges will be pointed out.

Terrestrial wireless communications suffer from multipath, shadowing and fading effects. The electro-magnetic signals, which usually have a direct path from transmitter to receiver antenna, are also accompanied by other signals being reflected from the ground and from various objects in the neighborhood. These signals (hence multipath), or vectors, add in the receiver, mostly canceling and causing the deteriorating effects of channel fading.

The transmission of data from miniature radio designs is especially difficult because of the overall demand for low power and miniature antenna dimensions. These radios are usually designed to cover short (and sometimes very short) range, hence the term short range devices (SRD). The antennas of interest in such systems, with overall geometry usually smaller than 10 percent of a wavelength (/10), but sometimes with even much smaller restrictions, have low transmission efficiency and cover limited bandwidths. Such antennas obviously have no directivity. Various types of miniature antennas have been developed and used, though the amount of literature is quite limited. These are either air coils, wire loops, F-shaped or printed on PCB to save space. 2,3

In the past, such applications were mostly confined to military, security, eavesdropping and law enforcement applications, but not any more. The applications for miniature radio sensors are now growing exponentially in the commercial, homeland security, medical and military markets.

A miniature antenna is mostly a resonant structure that acts as a transformer, and that translates circuit voltages and currents into a radiated field, or the reverse. Antennas are passive components, reciprocal, and a bit cryptic for most people.

Fig. 1 Antenna radiation patterns.

The antenna gain is actually its directivity at the maximum point, as shown in Figure 1 . The radiation pattern is compared to the ideal (isotropic) pattern (there is actually no omni-directional solution to Maxwell equations) and the gain is defined as the extra punch beyond omni, and sometimes measured in dBi (the i for isotropic transmission). The omni-directional antenna is one that transmits all its power equally in all directions. Its power density at range R from the radiator is given by

P t = transmitted power

Note that the total volume in both patterns is similar (???P(R, ?, ?) = total power, is fixed); only one is “bigger” in its radiated direction. This is where the gain (or directivity) is measured.

Now, the antenna cannot deliver all the power, and there is a certain loss associated with this (passive) device. Satcom dishes have efficiencies in the 80 percent range.

In miniature antennas, the efficiency is very small, that is, their radiation pattern can be “omni-directional,” but with significant loss. Losses of 10 to 30 dB are not uncommon, and depend on antenna size relative to wavelength (?) and geometry. In many cases, simple rules determine such critical parameters.

In antenna measurements (once the design is completed, it is taken to a range and measured to show its performance), it is common to measure the field strength. Remember that the conversion from field strength to power is obtained according to

E = field strength in V/m

D = distance

For the popular FCC Part 15 standard, D = 3m, the power as a function of field strength is shown in Figure 2 . Note also that the power density is given by E 2 /(2 • 377).

Fig. 2 Power vs. field strength.

Generally speaking, miniature antennas are elements running at or close to resonance. For simplicity, it is assumed that the antenna can be presented as a parallel resonance circuit, with the inductor L, the radiating element (see Figure 3 ).

Fig. 3 Miniature antenna model.

The capacitor C resonates the coil, which radiates, and the resistors R s , shown here in series but which can be represented as a parallel element with the transformation R p = R s (1+Q 2 ), determine the resonator (antenna) quality factor Q. If the radio operates at an angular frequency wo, then for a parallel resonance circuit

For example: A 900 MHz antenna, made of a 30 nH coil and 1 pF capacitor, has a Q of 40. Therefore

The impedance of the circuit, resonating at 900 MHz, is shown in Figure 4 .

Fig. 4 Antenna circuit impedance resonating at 900 MHz.

The resistor value represents two elements, one dissipating power (mostly heat, due to coil resistance, skin effect and insulator dissipation) and the other part radiating. It is the radiating component that is sought and maximized.

Q is defined as the ratio of the stored-to-dissipated energy. Dissipation occurs for various reasons, including skin effect, dielectric losses, heat dissipation in the coil environment, insulating and shielding. The skin depth in copper is approximately 2.3 mm at 900 MHz and is proportional to 1/?f.

If R = R d + R rad (dissipation and radiation resistance), then for a given current I v through the antenna, the radiated power is given by

For miniature antennas, R rad is usually very small compared to R d . The other interesting point is that in the parallel resonance circuit model, the current through the coil is Q times that of the circuit. Therefore, if the antenna runs at resonance, and if the drive current is I d , then the radiated power is given by

It becomes immediately obvious that tuning or resonating the antenna is of utmost importance. Certain chips have adaptive mechanisms to perform that function. For printed coils on FR-4, up to 1000 MHz, the Q does not exceed 40 to 50. Air coils can have (unloaded) Qs up to 150. Remember that since the inductance is affected by the self-resonance of the antenna F c , as in

one should not operate above 40 percent of F c .

For an N turn air loop coil, with a diameter 2r, and a total length l, the inductance is given by

where all dimensions are in mm and the inductance is in nH, as shown in Figure 5 for l = 6 mm and N = 3.

Fig. 5 Air coil inductance vs. coil radius.

Fig. 6 Effect of the coil self-resonance on the inductance value.

The effect of self resonance on the inductance is shown in Figure 6 . In this model, F c is 1 GHz for a 50 nH inductor. For printed loops with a diameter R, the inductance is given approximately by

r = linear function of the line width

Radiation Resistance

For miniature antennas, R rad is given approximately by

A = area of the coil

N = number of turns

A simulation run is shown in Figure 7 , where R r (R rad given in dB–?, while the radius of the coil, r, is given in mm), for a 900 MHz design (the wavelength is a foot in free air). For r = 5 mm, the radiation resistance of the coil at 900 MHz is approximately 0.005 ?. The efficiency of such a system can now be calculated.

Fig. 7 Radiation resistance of a 900 MHz air coil.

It is assumed that the antenna system has a loaded Q of 30. The coil has a value of ~30 nH, which has an impedance of j130 ?.

Assume that 3V are developed on the antenna. The resistor R has a value of 3900 ?, and the current through the circuit (assuming resonance) is 3/3900 = 0.76 mA. The power dissipated in the resonator is 0.76 2 × 3900 ~2.25 mW = 3.5 dBm. The current through the coil is Q times higher than in the resistor, ~23 mA, and the radiated power P rad ~0.023 2 Rrad = –26 dBm. Obviously, the radiation efficiency of this small antenna is very small (~0.1 percent).

Alternatively, the radiation resistance of a printed loop, on a PCB, with a diameter of 30 mm (inductance in the order of 75 nH), with a line thickness of 1 mm, at 900 MHz, is in the order of 0.3 ? and 0.018 ? at 434 MHz. This antenna Q (no ground plane below the antenna printed line) is approximately 40.

Radiation Pattern

These antennas, being much smaller than a wavelength, have no directivity and can provide no protection from multipath by spatial filtering. A typical radiation pattern is shown in Figure 8 . It is similar to the radiation pattern of an infinitesimal dipole. The maximum radiation for an air coil is in the coil’s axis plane and the null is perpendicular to that plane.

Fig. 8 Radiation pattern of a miniature air coil.

Antenna Diversity and Combining

To mitigate some of the multipath effects, more than a single antenna will be utilized. The basic assumption is that the propagated wave will fade in and out of some of the elements but will be strong enough in others. The combiners then process the array to produce a “good enough” or “optimal” solution.

There are basically three methods for the application of antenna combining for diversity. The principal idea is to use more than one receive antenna, create spatial diversity and somehow combine the RF signals from the various receiving elements such that continuous signal reception shall improve significantly. The three methods are:

• Switch selection — use of a switch to choose an antenna with sufficient power. This is sometimes also referred to as switch diversity, since only one antenna is active in the active received path.
• Regular combining — the signals from various antennas are combined.
• Maximum ratio combining — an optimum, adaptive process is applied, to combine the received signals coherently and optimize the array SNR output.

Of course, there are various combinations of the three, based on requirements, size, power and cost. Many patents and intellectual properties (IP) have been generated in the last few years in this area.

Simple Antenna Combining — Switch Selection

A simple antenna diversity scheme is shown in Figure 9 . The system starts with an arbitrary choice, and the switch selects an alternative antenna when the existing power is below a certain level, or, initially, the system can measure the better one and start there. Generally, there is a single receiving path, so the algorithms are rather simple.

Fig. 9 Simple antenna diversity connected to a transceiver.

The detection algorithm can be based on checking the received signal strength indicator antenna (RSSI) and switching to the alternative antenna when the signal is degrading. The system is simple but effective as an alternative exists when the signal fades out. Note that when switching from antenna to antenna, certain transients and disturbances will occur, especially if it occurs in the middle of a packet or message file.

Adding Combiner

This method employs two (or N, depending on the number of elements) receiving paths that eventually add all signals. As some are fading, others rise, so an improvement is obtained in the overall signal’s availability. There are various nuances to this method, especially with the use of limiters in various areas of the design, as well as enhancement of the stronger signals. However, it will basically provide “strong signal” dominance and is reasonably close to optimum. Certain processing is possible in the individual paths (as has been mentioned already) but, overall, the system will provide dominance to the stronger channels, especially in FM systems, due to capture effect.

Of course, in the case when signals are either in anti-phase and close in amplitude, they can cancel, but statistically and practically, it is almost irrelevant. Figure 10 shows a block diagram of an adding combiner.

Fig. 10 Adding combiner.

MRC — Optimal Antenna Combining

A more complex operation and an optimum solution can be obtained by processing the array in parallel and combining the result such that better coverage and better SNR are achieved all the time, because the process will enhance the “better” elements dynamically. Such a system shall provide information on relative signal strength and phasing and shall require certain digital signal processing (DSP) in the antenna array processing. An application of such a system is shown in Figure 11 for a personal digital assistant (PDA).

Fig. 11 Antenna combining in a PDA at 2.45 GHz (courtesy of Avaak).

The quarter is there to show size perspective.

As was mentioned already, a certain geometrical separation must be provided, such that a level of “orthogonality” exists between the elements. For example, in the 2.5 GHz ISM band, the separation must be in the order of at least 4" to 5". A certain de-correlation between antennas can be achieved by geometrical alignment, polarization, or slightly changing their field patterns. The array will then be processed as a matrix of signals arriving with various phases and amplitudes according to a certain metric, and required to achieve an optimum (either SNR or interference rejection) performance. For example, in the case of antenna combining, an algorithm should be chosen that collects the signals such that the received SNR be maximized.

Therefore, there is an array of signals, a ie j?i , a i and ? i , representing the individual (and dynamic) amplitude and phase of the ith element. Without going through much mathematics, it is intuitive that these signals be added coherently (that is all of them must be rotated to the same phase and then added) and the stronger signal be emphasized while de-emphasizing the weaker one.

One such method optimizes the array performance (assuming that each element has the same noise level) and is called maximum ratio combining (MRC). The technique exercises an optimal (and coherent) solution to antenna combining, which allows more than one antenna to act in concert as an integrated “super antenna,” which adapts its gain (and directivity) to the direction of the “incoming antenna.”

Optimum antenna combining adaptively scales the various antennas such that the overall SNR is maximized. A block diagram of the concept is shown in Figure 12 .

Fig. 12 Closed loop maximum ratio combiner.

A simplified DSP procedure can be applied, either open or closed loop. Today, all processing will be done at baseband, using DSP and therefore improving performance and lowering the specifications of various components (such as bandpass filter group delay and amplitude response).

The beauty of the feedback array lies in the fact that once running, it optimizes the estimate of each element’s amplitude and phase. Similar open loop configurations can be applied too, with similar performance.

If there are N elements and the general output of the array is

(Wi are complex numbers) and the Wi solution that maximizes SNR is sought, using the Schwartz inequality, it is easy to show that the optimum result is achieved for the case

(where ? o is an arbitrary phase, or it can be the phase of the strongest signal, depending on the processing method).

In most applications, MRC is not used so much for pure antenna gain, but is used to improve coverage as fading effects degrade the reception of some elements but not all. Dynamically, the “center of gravity” will move from element to element.

A transient simulation is shown in Figure 13 . Green is the stronger signal, red is the weaker signal and blue is the combined signal. No noise is showing.

Fig. 13 Simulation of the combining process.

Figure 14 shows a simulation run for the SNR out improvement for antenna 1 with an SNR of 10 dB and antenna 2 with an SNR varying from –10 to 10 dB. For equal signal levels (in this case SNR in is 10 dB), the SNR out will improve by 10 log(N), in this case from 10 to 13 dB. However, as was noticed already, this is not the reason to apply the technique.

Fig. 14 Two antenna’s SNR.

Needless to say, combinations of the various techniques can be applied to save power. For example, if the signal is strong, connectivity to a single antenna can be maintained, until fading effects are sensed. Then extra antennas and processing can be added. Details of such strategies will not be described here.

Other Options

There are other options for applying antenna diversity, including polarization-sense diversity and element pattern control. Their practicality, however, depends on the size of the antenna (relative to wavelength).

Other Applications

If, for example, two elements are used (for simplicity), and a 1,2 and ? 1,2 are estimated accurately, then a matrix will be easily built, that will optimally cancel an interfering signal. With N elements, N-1 interferers can be cancelled. The phase of the arriving signals can also be estimated with excellent accuracy, and the direction of the emitter (transmitter) provided for location awareness.

A general processor block diagram for a general adaptive array is shown in Figure 15 . The important point here is that a rather small antenna system can achieve what otherwise will require much more space, which is a precious resource in many miniature radio systems emerging now. These systems will then use few radiating elements in combination with DSP, to generate features that can enhance the quality and utility of the overall network of nodes and enable efficiency in communication throughput, interference rejection, directivity, location awareness and overall system performance with low size, low power and reasonable computing power (silicon), hence improved economics and affordability.

Fig. 15 General adaptive array.

There has been a large volume of work done in the last few years on the networking of large sensor arrays; it is time to also address their electromagnetic aspects. These processing systems, sometimes referred to as MIMO (multiple input, multiple output) arrays, will play a growing role in systems ranging from WiFi to radio sensor networks as density and spectral utility crowds the airwaves and requires extra spatial intelligence and knowledge of location, interference and improved capacity.

Multipath and fading effects are dominating phenomena in wireless communications. Their effect on signal communications quality is of the greatest importance in terrestrial radio communications. Effects of these phenomena can be most effectively mitigated by space diversification and specifically antenna combining.

Few methods, from the simple to the more complex, have been demonstrated for the application of space diversity via antenna combining. The application of the various methods depends on the complexity, power and cost levels available in every system.

The theory of antenna combining is quite well understood, and economical solutions have started to appear in the market, specifically for 802.11 links as well as cell phones. The application of antenna combining in miniature sensor networks and their hubs is also becoming a reality with applications ranging from signal enhancement to localization and spatial filtering. n

• Smart Antenna Design, Ansoft Corp.
• “Small Loop Antenna,” Application Note nAN-400-3, Nordic Corp.
• C.A. Balanis, Antenna Theory, Analysis and Design , John Wiley & Sons Inc., 1997.
• L. Besser and R. Gilmore, Practical RF Circuit Design for Modern Wireless Systems, Volume I: Passive Circuits and Systems , Artech House Inc., Norwood, MA, 2003.
• E. Joy, Georgia Tech – CEI, Antenna Seminar Notes, 2003.
• J.D. Kraus, Antennas , McGraw-Hill, New York, NY, 1950.
• Krauss, Bostian and Raab, Solid State Radio Engineering , John Wiley & Sons Inc., 1980.
• “Antenna Selection in Multi-carrier Communications,” Intel Technology Journal , May 2003.
• B.G. Goldberg, “Miniature Radio-sensor Antenna Primer,” Avaak Inc. White Paper.
• C.K Ko and R.D. Murch, “A Diversity Antenna for External Mounting of Wireless Handsets,” IEEE Transactions on Antenna and Propagation , May 2001.

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Home > Books > Progress in Compact Antennas

Miniature Antenna with Frequency Agility

Submitted: 11 September 2013 Published: 10 September 2014

DOI: 10.5772/58838

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Progress in Compact Antennas

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Author Information

• University of Limoges, Xlim Laboratory, France

T. Monediere

*Address all correspondence to:

1. Introduction

The need of both mobility and communication leads to the integration of antennas in miniature devices so far non-connected (particularly in medical areas). The dedicated volume for the antenna, including its ground plane, has to be kept at its acceptable minimum, involving low bandwidth. Moreover, due to their poor impedance bandwidth, small antennas tend to be very sensitive to the environment. Indeed, they are directly affected by their immediate surroundings, which disturb their working band, their radiation and their performances [ 1 ]. To counter the low bandwidth of the antenna and to adapt it to variable conditions and surroundings, it can integrate active components.

Thus, active components become highly suitable for the development of modern wireless communications. Indeed, they allow the miniaturization, shifting the antenna working frequency to be matched over a wide bandwidth by covering only the user channel and the adaptation of antennas to variable operating conditions and surroundings. It is in this framework that authors will propose in this chapter to detail the integration of active components in antennas to be more compact, smart and integrated.

The first part will address an overview of the most common used techniques for compact antennas to become active. In this goal, active antennas state-of-the-art will be presented:

The first sub-section will present antennas integrating tunable components such as varactor diodes, MicroElectroMechanical systems (MEMS), Positive Intrinsic Negative (PIN) diode and Field Effect Transistor (FET).

The second sub-section will focus on active antennas using tunable materials properties, i.e. ferroelectric materials and liquid crystal.

A second part will show relevant parameters for active antennas studies. It will exhibit both challenges and how to integrate active components in order to maximize the antenna performances and efficiency. This part will be supported by concrete examples. Therefore, depending on their intended applications, readers will be prepared to find the best trade-offs between the agility method, the miniaturization and antenna performances.

The last part will be dedicated to present limitations of actual and most common solutions proposed for active and compact antennas. In this framework, new approaches will be detailed to overcome these physical limitations.

2. Overview of compact active antennas

Very small size antennas are needed for future dense wireless network deployment, for example in WBAN (Wireless Body Area Network) where the size is limited to dimensions much smaller (hearing aid, implants) than wavelength (λ 0 =12.2 cm at 2.45GHz) or for the DVB-H (Digital Video Broadcasting – Handheld) application, where the miniaturization aspect is even more critical because it is a low frequency standard (λ 0 =60 cm at 470 MHz). Therefore, the antenna has to be carefully optimized with trading off fundamental size limitations with its characteristics (especially bandwidth and efficiency). In addition, the environment of miniature antennas will be highly variable resulting in large antenna impedance and propagation channel changes. Several challenges have to be addressed. One of them is the adaptive antenna technology for compensating both low bandwidths and detuning effects.

The most commonly cited performance criterion is the achievable frequency tuning range (TR) defined as:

T R ( % ) = 2 ( f max − f min ) f max + f min .100 where f max and f min are respectively the upper and the lower antenna operating frequency. The frequency tuning can either be continuous or discrete. The continuous frequency tuning is able to continuously cover each channel of a same standard while the discrete frequency tuning can only switch between different standards. This part will present the most common methods to target frequency tunable antennas design.

2.1. Integration of active components

2.1.1. varactor diodes.

For continuous frequency tuning, the integration of varactor diodes within an antenna is the most common approach [ 2 - 5 ]. P. Bhartia et al. were the first to publish antenna integrating varactor diodes [ 6 ]. Indeed, they presented a microstrip patch antenna with varactor diodes at the edges of the structure, as illustrated Figure 1 . Both rectangular and circular tunable patches were studied, results reveal that 22% and 30% of bandwidth can respectively be achieved by varying the DC-bias-voltage between 0V and 30V.

Patch antenna integrating varactor diodes [ 28 ]

Slot antennas are also good candidates for the frequency agility [ 7 - 9 ]. N. Behdad and K. Sarabandi presented in [ 9 ] a dual band reconfigurable slot antenna. The schematic of its proposed dual-band slot antenna is shown in Figure 2 . Matching is performed by choosing appropriately the location of the microstrip feed and the length of the open circuited line.

Dual reconfigurable slot antenna [ 9 ]

Figure 3 shows the simulated and measured dual-band responses of the antenna where by applying the appropriate combination of bias voltages (V 1 and V 2 ) the frequency of the first band is kept fixed and that of the second band is tuned. Similarly, as shown in Figure 3 , it is possible to keep the frequency of the second band stationary and sweep the frequency of the first band.

Measured |S 11 | parameters for different combination of bias voltages [ 9 ]

Another example show a 3D Inverted F Antenna [ 10 ] designed to cover the entire DVB-H band going from 470 MHz to 862 MHz. To be integrated in a mobile handheld device, the antenna allocated volume had to be very compact. A good trade-off between small sizes and the impedance bandwidth was to choose a structure based on the IFA design. Indeed, the radiating monopole of this kind of structure can be folded all around a material to become more compact (see Figure 4 ).

Inverted F Antenna design (a). Antenna top view (b) [ 10 ]

However, the more compact the antenna is, the lowest the bandwidth is becoming. To counter this issue, it has been proved that using a magneto-dielectric material rather than a dielectric one allows enhancing the input impedance bandwidth. Basing on this antenna design, the idea was to integrate a varactor diode to tune the impedance matching all over the DVB-H band (see Figure 5 ).

Design integrating both magneto-dielectric material and a varactor diode [ 10 ]

A prototype of the tunable antenna has been realized ( Figure 6 ) and measured. For the diode polarization, a DC bias Tee is optimized with SMD components and measured on the DVB-H band ( Figure 6 ). After being validated, it is integrated upstream from the antenna structure as shown Figure 6 . In order to improve the quality and the reliability of wireless links, the final mobile device is integrating two antennas (see Figure 6 ) for diversity operations.

DC bias Tee with SMD components and its integration upstream from the antenna (a), integration of two antennas in the tablet dedicated to the DVB-H reception (b) [ 10 ]

Figure 7 presents respectively the variation of the input impedances and |S 11 | parameters of the antenna versus frequency for different values of the varactor diode bias voltages.

Measured input impedances (a) and |S 11 | parameters (b) for several DC bias voltages [ 10 ]

Therefore, the antenna working band is continuously tuned all over the whole DVB-H band. In the worst case, i.e. for a 2V DC bias voltage, the antenna is matched with |S 11 | <-6dB in a bandwidth which is covering more than one channel of the DVB-H band at-6 dB (largely suitable for the DVB-H standard).

2.1.2. Positive Intrinsic Negative (PIN) diodes

PIN diodes are using as switches:

The ON state of the diode can be modelled by a zero resistance, i.e. a continuous metal strip across the slot where the diode is integrated.

The OFF state of the diode can be modelled as an infinite resistance. The radiating length after the diode is not seen from RF point of view. The effective length of the antenna, and hence its operating frequency, is changing compared with the ON state case.

Selected antenna’s types for integrating PIN diodes are often slot antennas or printed antennas (e.g. printed monopole, Inverted F Antenna, …). J-M. Laheurte presented in [ 11 ] a slot antenna including pin diodes for multi-frequency operation within a frequency octave.

Switchable slot antenna including eight pin diodes [ 11 ]

As shown Figure 8 , this antenna integrates eight PIN diodes and according to their ON or OFF states combination, the antenna can operate at different and discrete frequency bands (see Figure 9 ). Instantaneous impedance bandwidths are between 8% and 21% depending on the diodes’ states combination.

Measured |S 11 | parameters for different states of diodes: all diodes OFF (i), diodes 1, 8 ON (ii), diodes 1, 2, 7, 8 ON (iii) and diodes 1, 2, 3, 6, 7, 8 ON (iv) [ 11 ]

Eventually, this antenna presents somewhat large dimensions since its main size is higher than à λ 0 /2 at 2.8 GHz. The literature presents smaller antennas integrating PIN diodes since their main size are lower than à λ 0 /2 at the working frequency [ 12 ].

Peroulis et al. [ 13 ] presented a tunable single-fed S-shaped slot loaded with a series of four PIN diodes. The effective length modification allows this antenna to operate in one of four selectable frequency bands between 530 and 890 MHz.

Before directly studying the tunable slot antenna, both single S-shaped slot antenna and PIN diodes were separately presented and studied. By this way, the issue related to the design of a suitable PIN switch has been grasped before integrate it and show its effects on the antenna performances. Indeed, to implement the electronic reconfigurability, the ideal shunt switches must be replaced by real PIN diodes. Therefore, the RF equivalent circuit of the diode has been studied (see Figure 10 ) for both the ON and OFF states. The reactive components C p and L p are modeling the packaging effect, while the others come from the electric properties of the diode junction in the ON and OFF positions. Then, the switch bias network was presented as an inductor of 470 nH and three 10 pF capacitors ( Figure 10 ).

RF equivalent circuit of the PIN diode (a) and the switch bias network (b) [ 13 ]

Finally, a reconfigurable slot antenna design ( Figure 11 ) is presented in this paper. Four switches are used in order to tune the antenna over a range of 540–950 MHz. The integration of the fours PIN diodes allows choosing the operating frequency of the antenna ( Figure 11 ).

Reconfigurable slot antenna (a) and its measured |S 11 | parameters (b) [ 13 ]

2.1.3. MicroElectroMechanical systems (MEMS)

MEMS components can allow:

Continuous frequency tuning when they are used as a variable capacitance.

Discrete frequency tuning, when they are used as switches.

E. Erdil presents in [ 14 ] a reconfigurable microstrip patch antenna integrating RF MEMS capacitor for continuously tuning the resonant frequency (see Figure 12 ). The reconfigurability of the operating frequency is obtained by loading one of the radiating edges of the microstrip patch antenna with a CPW stub on which RF MEMS bridge type capacitors are periodically placed.

Frequency tunable microstrip patch antenna integrating MEMS capacitors [ 14 ]

When a DC voltage is applied, the height of the MEMS bridges on the stub is varying, and thus the loading capacitance is also changing. Therefore, as showed Figure 13 the matching frequency around 16.05 GHz shifts down to 15.75 GHz as the actuation voltage is increased from 0 to 11.9 V, where the height of the capacitive gap changes from 1.5 μm to 1.4 μm.

|S 11 |parameters for different actuation voltages and simulation results [ 14 ]

Discrete frequency tuning can be illustrated with a reconfigurable annular slot antenna with a monolithic integration of MEMS actuators presented by B.A. Cetiner in [ 15 ]. The architecture and a photograph of the microstrip-fed reconfigurable antenna annular slot are shown in Figure 14 . The antenna has two concentric circular slots. According to MEMS switch S 1 state, they can be individually excited in order to achieve frequency reconfigurability. S 2 and S 3 switches enable the metallic annular ring, which stays between the outer and inner slots, to be shorted to RF ground.

Microstrip feeding line integrating a single-arm MEMS switch (a) and the annular slot integrating two double-arm MEMS actuators [ 15 ]

The measured |S 11 | parameters ( Figure 15 ) show that when MEMS switches are activated (down-state) by applying DC bias voltages, the antenna working band is around 5.2 GHz. Vice-versa, when MEMS switches are in the up-state, the antenna is working at 2.4 GHz.

Measured and simulated |S 11 |parameters for MEMS switches activated (5.2 GHz) and deactivated (2.4 GHz) [ 15 ]

2.1.4. Field Effect Transistor

Continuous frequency tuning can be achieved by using Field Effect Transistor. In [ 16 ], S. Kawasaki presents a slot antenna loaded with two one-port reactive FET. The electrically length of the slot is changing according to the voltage bias applying on the FET. The measured |S 11 | parameters (see Figure 16) show a 10% frequency tuning range for a gate tuning voltage (V gs ) going from 0V to-0.6V while the drain voltage (V ds ) is tuned from 0V to 0.4V.

Measured |S 11 |parameters for both gate and drain tuning voltages [ 16 ]

2.2. Agile antennas using tunable materials

Changing the material characteristics in a part of antenna designs also promise the ability to tune them in frequency. The application of a static electric field can be used to change the relative permittivity of a ferroelectric material or a liquid crystal, respectively a static magnetic field can changed the relative permeability of a ferrite. In case of printed antennas, these changes modify the effective electrical length of antennas, and then resulting in shifts of their operating frequencies.

2.2.1. Ferroelectric materials

Lead-based perovskite ceramics such as PbZr x Ti 1−x O 3 (PZT) have been the leaders, for the past 50 years, on ferroelectric material research [ 17 ] for electronic devices, sensors, actuators, and medical ultrasonic transducers, owing to their good dielectric properties over a wide temperature range. Due to health care and environmental regulations, restriction of hazardous substances as lead has been required [ 18 ]. Since the last 10 years, many efforts have been mainly devoted in the field of microwave applications to Ba x Sr 1-x TiO 3 (BST) material which is one of the most attractive materials [ 19 ] because it presents high dielectric constant, relatively low dielectric loss, interesting tunability and small temperature dependence. In fact, in BST, the Curie temperature (Tc) which defines the ferroelectric/paraelectric transition is tuned by controlling the Ba/Sr ratio. More recently some other ferroelectric ceramics such as the tantalate niobate oxide KTa x Nb 1−x O 3 (KTN) or the sodium bismuth titanate Na 0.5 Bi 0.5 TiO 3 (BNT) and its solid solutions BNT-BT are emerging.

Two different methods exist to polarize a ferroelectric material with a static electric field. A better tunability is obtained when the static electric field is perpendicular to the two electrodes. For antenna application point of view, antenna designs integrating ferroelectric materials have to move toward this kind of polarization in order to have a better reconfigurability. However, many efforts have to be devoted from realization and also simulation point of views. Therefore, compact antenna community exhibits only few papers of this kind of antennas.

V. K. Palukuru et al. [ 20 ] present a tunable antenna using an integrated ferroelectric-thick film made of BST material. The antenna is depicted in Figure 17 . It exhibits a folded slot antenna loading with a BST thin film varactor. In order to tune the dielectric permittivity of the BST film, a DC bias voltage is applied thanks to a bias-T component, which was attached to the Vector Network Analyzer. The BST varactor is placed over the radiating slot: the upper electrode (0.2 mm 0.2 mm) is part of the antenna’s metallization and the lower electrode is the antenna’s ground plane. In order to reduce the capacitance of the varactor, a slight horizontal offset is used between the electrodes. Therefore, the electric field for biasing the material is both in the vertical and the horizontal directions.

Folded slot antenna with the BST varactor (a), side cross-section (b) and top view (c) of the BST varactor [ 20 ]

The |S 11 | parameters ( Figure 18 ) show that a frequency tunability of 3.5% can be obtained with a change of the bias voltage from 0V to 200V.

Measured |S 11 |parameters for different DC-bias voltages [ 20 ]

H. Jiang presents a coplanar waveguide (CPW) square-ring slot antenna as showed Figure 19 [ 21 ]. Nine shunt ferroelectric BST thin film varactors are integrated with the CPW antenna structure achieving both antenna miniaturization and reconfiguration.

Coplanar waveguide square-ring slot antenna integrating BST material [ 21 ]

Figure 20 shows the measured |S 11 |parameter with DC bias voltages from 0 V to 7 V. Therefore the antenna working band is continuously tuned from 5.28 GHz up to 5.77 GHz.

Measured |S 11 |parameters for different DC-bias voltages [ 21 ]

2.2.2. Liquid crystal

Another technological approach for designing an agile antenna is the use of liquid crystal as a tunable dielectric. Indeed, the characterizations of liquid crystals [ 22 - 24 ] have shown that they are promising tunable materials for microwave applications, especially for operating frequencies above 10 GHz. The material features low dielectric loss and continuous tunability with low bias power consumption. The literature show that some microwave applications are using liquid crystals, e.g. for polarization agile antenna [ 25 ], tunable patch antennas [ 26 ], reflectarrays [ 27 - 28 ], filters [ 29 ], resonators [ 30 ] and variable delay lines [ 31 - 33 ].

In this framework, L. Liu presents in [ 34 ] a tunable patch antenna using a liquid crystal. Its operating frequency is around 5 GHz with a tuning range around 4% in measurement. The Figure 21 presents the antenna geometry composed of three layers of Taconic substrate. The liquid crystal is injected in the middle layer just under the microstrip patch and between the ground plane and patch top hat. A DC bias voltage was applied between the patch and ground across the liquid crystal using a bias tee at the feed input.

Tunable patch antenna using a liquid crystal [ 34 ]

The Figure 22 shows the measured return losses for the patch antenna for three states of liquid crystal bias: 0V, 5V and 10V. The 0V state reveals that the used liquid crystal without DC bias presents somewhat high losses around 0.12 for the loss tangent. Thus a 4% frequency tuning can be achieved with relatively poor radiation efficiencies, i.e. 14% at least (at 0V) to 40% (at 10V).

Measured |S 11 |parameters for different DC-bias voltages [ 34 ]

2.2.3. Ferrite materials

Frequency-tuned ferrite-based antennas are rarely presented in the literature. In [ 35 ] and [ 36 ], authors study patch antennas on ferrite substrates ( Figure 23 ) whereas A. Petosa presents in [ 37 ] a ferrite resonator antenna. In this latter, biasing of the ferrite with a static magnetic field is achieved using a permanent magnet. The magnet was located under the ferrite antenna beneath the ground plane. For a parallel magnetic-bias orientation, the resonance frequency can be tuned on 8% of bandwidth. That scales to 9% for a perpendicular magnetic-bias orientation.

Patch antenna on a ferrite substrate [ 37 ]

All results presented in the literature and investigated the properties of ferrite-based microstrip antennas indicate that factors including non-uniform bias fields and the multiple modal field distributions excited in a bulk ferrite substrate may preclude their use in practical applications.

Now that an overview of the most common used techniques for compact antennas to become active has been presented, the next part will address both challenges and how to integrate active components in order to maximize the antenna performances and efficiency.

3. Relevant parameter for frequency agile antenna studies – New approach for wireless applications.

3.1. how to integrate an active component – challenges.

To implement the reconfigurability in an antenna, the knowledge of the active component or the tunable material is essential. Even in case of commercial components, as varactor or PIN diodes, users and particularly the microwave community do not have enough parameters and information at RF frequencies. Some papers detail the integration of the RF equivalent circuit of the used component [ 10 ],[ 13 ].

The varactor diodes integrated in an antenna for frequency reconfigurability is the most popular way. Thus, this section will focus on varactor diodes issues. However, arguments can be extended to other frequency tuning methods.

In [ 10 ], the paper completes the lack of information related to most of varactor diode datasheets. Indeed, constructor only provide characteristics at low frequencies and do not give enough parameters for antenna application point of view, such as capacitance values, serial resistance and accepted power at RF frequencies. The chosen varactor in this paper has been characterized according to antenna designer criteria and its electromagnetic model has been deduced. This example is chosen in the framework of this chapter.

To correctly explain this example, the next subsection will investigate the place where the varactor can be integrated. Following the presentation of the varactor diode manufacturer’s datasheet, a complete characterization meeting antenna designer’s criteria will be explained. That will lead to the determination of the varactor diode S parameters. With the knowledge of the latter, two methods will be explained and described to reach an accurate antenna simulation and realization:

The electromagnetic equivalent circuit of the varactor diode can be deduced from the S parameters thanks to Agilent ADS.

The S parameters of the varactor diode can be directly injected in the electromagnetic simulator CST Microwave Studio ® and the antenna performances deduced thanks to a co-simulation.

3.1.1. Varactor diode area in an antenna

The varactor diode is a tunable capacitor which loads the antenna in order to artificially increase its electrical length. To be the most efficient, it must be placed where the electrical field is maximum. Take a folded Inverted F Antenna for example presented Figure 24 . The maximum of the electrical field is at the end of the radiating element (see Figure 24 ). To be integrated at this place and joined the ground plane at the same time, the varactor diode can be soldered between the ribbon and the ground. In most cases, DC-block capacitors have to be added for the varactor’s DC-bias not to be shunt.

Inverted F Antenna Measured (a) and the total electric field on the radiating element (b)

3.1.2. Varactor diode datasheet

In [ 10 ], the chosen GaAs hyperabrupt varactor diode MGV125-22 (Aeroflex Metelics) [ 38 ] has a capacity range between 0.2 pF and 2 pF for 0 to 22 Volts tuning voltage as shown Figure 25 . However, these values are given as a rough line and the datasheet does not give enough parameters for high frequencies antenna application’s point of view. Indeed, the values for junction capacitance C j ( Figure 25 ) and the quality factor Q are supplied by the manufacturer and are almost always specified at a low frequency. The Figure 25 shows the widely used varactor diode model with L p and C p the values of the package inductance and capacitance.

Manufacturer’s capacitance value (extracted at 1MHz) versus the DC bias voltage (a) and the Varactor diode model (b)

In the MGV125-22 case, junction capacitance values are specified at 1 MHz and the Q factor equals 3000 at 50 MHz for a DC bias voltage of –4 Volts. Q is defined by Q=1/(ωC j R s ). This formula can be used to calculate the series resistance R s of the varactor model at the measured frequency, its value is assumed to be constant with reverse voltage. Thus, at 50 MHz R s =1.06Ω. It is important to note that R s impacts directly the antenna total efficiency. A too high value (from 3Ω) is basically penalizing for antenna performances. This enhances the need to assess its value at microwave frequencies. For this purpose, the hyperabrupt varactor diode has to be characterized close to operating conditions (here between 470 MHz and 862 MHz).

3.1.3. Varactor diode characterization

First method: Electromagnetic model

The varactor diode is soldered on a 50 Ω impedance microstrip line as shown Figure 26 . A dedicated TRL (Through-Reflect-Line) calibration kit is manufactured ( Figure 26 ) in order to de-embed both connectors and lines. Thus S parameters of the single varactor diode can be deduced. Considering the varactor diode model previously presented in Figure 26 , C j , L p , C p and R s values can be deduced for each voltage and for a constant injected power of-10 dBm. Therefore, model component values are adjusted (see Figure 26 ) in order their S parameters to correspond with the measured ones. The Figure 26 shows the comparison between S parameters of the determined electromagnetic model (Agilent ADS) and the measured ones for 2 Volts and 10 Volts DC bias voltages.

Characterization of the varactor diode (a) and the Comparison between the electromagnetic model and the measurement on S 11 parameter on the [400 MHz – 1 GHz] frequency band (b)

These results are given as an example and the same work has been done for varactor reverse bias voltages varying from 2V to 22V with a 2V step. As expected, the corresponding electromagnetic model presents constant values according to the DC bias voltage ( Figure 27 ): L p =3.821nH, C p =0.08pF and R s =1.8Ω. The C j value presented in Figure 27 decreases as a function of DC bias voltage value.

Electromagnetic model with the capacitance values C j versus the DC bias voltage (b)

Second method: Co-simulation

Another way is to directly insert the S parameters touchstone file of the varactor diode in the antenna electromagnetic simulation as illustrated in Figure 28 .

Co-simulation of the antenna including measured S parameters of the diode

Thanks to the previous TRL calibration, only the varactor diode S parameters are inserted in the simulator. By this way, both antenna and varactor diode are combined and the S parameters of the global device can be directly simulated. An example (presented paragraph 3.3) will confirm that the two previous methods exhibit similar antenna performances.

3.2. Limitations of currently varactor diode method – Power characterization

Figure 29 provides some information regarding the accepted power by the varactor diode: high injected power involves some varactor diode distortions.

Measured S parameters according to the injected power

This figure presents S parameters of the diode for only three values of injected power:-10 dBm, 0 dBm and 10 dBm. The non-linear distortion of the diode has been studied. It reveals that the varactor diode model well fits measurements for an injected RF power lower than-5 dBm. Beyond this injected power (see for 0 dBm), no varactor model can fit the measurement. Regarding antenna’s parameters, the following example will show that a large RF power (upper than-5 dBm) involves a mismatched antenna. As far as the DVB-H application, the system is only working in receiving mode, the diode distortion will never appear and the linear electromagnetic model can be used and integrated in the electromagnetic simulator. Indeed, for receiver devices, the antenna accepted power is far lower than – 5 dBm.

3.3. Example of a basic tunable DVB-H antenna

This subsection investigates an example to show the interest of the previous varactor diode characterization. This was briefly presented in [ 4 ], it is completed here by adding the first method (electromagnetic model) and the power characterization. A basic IFA prototype loaded by the same varactor diode (see Figure 30 ) has been manufactured.

Basic IFA prototype

It has been measured for a-10 dBm RF power and its performances compared with three simulations: with both presented methods and with the varactor diode’s datasheet ( Figure 31 ). |S 11 | parameters show that both investigated methods and measurement present a good agreement. Moreover, they are different from |S 11 | parameters determined with the varactor diode datasheet. That underlines the relevance of the varactor diode characterization. Regarding the antenna total efficiency, it equals 50 % in the real case whereas it reaches 60% when the varactor datasheet is used in electromagnetic simulations.

Power characterization is illustrated on Figure 31 . This figure reminds the measured |S 11 | parameter for a power of-10 dBm. For a 10 dBm injected power, the measured |S 11 | parameter is compared with the simulated one with the second method.

|S 11 | parameters for the different methods (a) and according to the injected power (b)

There is a good agreement between the measurement and the simulation. This figure shows that the non-linearity of the varactor diode disturbs the |S 11 | parameter of the antenna. Thus, this kind of varactor diode has to be used only for reception devices.

Therefore, this section has presented how to integrate and characterize a varactor diode. It reveals the importance of the diode characterization in a design flow dedicated to antenna structure.

3.4. Discussion and trade-offs between agility techniques and physical limitations

According to the aimed application, trade-offs are necessary to design a frequency tunable antenna.

For discrete frequency tuning, PIN diodes or MEMS switches can be planed.

For continuous frequency tuning, which is often aiming for compact antennas, varactor diodes, MEMS variable capacitor and tunable materials can be used.

However, previous paragraphs have revealed that varactor diodes are not usable for transmitter devices because of their non-linearity for considering power levels.

The RF characterization of ferroelectric films shows high power handling capability [ 39 ]. Good permittivity tunability may be obtained if both materials properties and variable capacitor sizes have been properly dimensioned. The conclusion is the same for MEMS variable capacitor.

Studies on both ferroelectric material and MEMS capacitor merit extended investigations because these solutions seem to be the best and most promising alternatives faced with varactor diodes.

Performing rigorous full-wave analysis of these new components is the new challenge to extract their accurate electromagnetic models. Antennas would be optimized by considering the real response of these components. These investigations would enable the co-development of antennas integrating components’ electromagnetic models.

4. Conclusion

To conclude, an overview of compact and frequency agile antenna has been presented and detailed in this chapter while mentioning a lot of literature references. A special part has been dedicated to the presentation of the most common method to achieve a frequency tuning: the use of varactor diodes. Their integration within an antenna to be the most efficient has been shown. The study exhibits varactor diodes characterization and also reveals their limitation. A summary of the presented methods according to the intended application has been presented. Eventually, some ideas on varator diodes alternatives have been proposed in order to make antenna tunability viable for transmitter devices.

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Chapter 9Miniature Antennas 1

9.1. introduction.

The surge in new technologies is enabling more and more features for compact mobile terminals to be presented. Numerous wireless communication standards are being developed, some concurrent, some complementary. For example, it is well known that standards in mobile telephony present a wide coverage and allow a high mobility, while standards in wireless local area networks, such as the IEEE 802.11 standards, enable much higher throughputs, but with poorer coverage and more reduced mobility. A terminal claiming to offer a large range of services with variable throughputs and dynamics should therefore integrate send/receive modules working with several intrinsically different characteristic standards. A common characteristic will, in the case of mobile terminals, always be bulk: with user acceptance assuming a practical and aesthetically pleasing object, then, this being the case, antennas must be as discreet as possible.

Furthermore, each communication standard has been allocated a band of defined working frequencies by the regulatory authorities. As we will see later, the width of the allocated spectrum will directly influence the bandwidth of the antenna and therefore its size. The standards also induce particular characteristics in the performance of the antenna, such as its matching level, the form of radiation created, field polarization, or even a multiplication of the number of antennas for the same standard, as is the ...

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Mar 30, 2019

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Antennas. Theory, characteristics, and implementations. Topics. Role of antennas Theory Antenna types Characteristics Radiation pattern – beamwidth, pattern solid angle Directivity, gain, effective area Bandwidth Friis’ transmission formula Implementations

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Antennas Theory, characteristics, and implementations

Topics Role of antennas Theory Antenna types Characteristics • Radiation pattern – beamwidth, pattern solid angle • Directivity, gain, effective area • Bandwidth Friis’ transmission formula Implementations • Dipole, monopole, and ground planes • Horn • Parabolic reflector • Arrays Terminology

The role of antennas Antennas serve four primary functions • Spatial filter directionally-dependent sensitivity • Polarization filter polarization-dependent sensitivity • Impedance transformer transition between free space and transmission line • Propagation mode adapter from free-space fields to guided waves (e.g., transmission line, waveguide)

Spatial filter Antennas have the property of being more sensitive in one direction than in another which provides the ability to spatially filter signals from its environment. Radiation pattern of directive antenna. Directive antenna.

Polarization filter Antennas have the property of being more sensitive to one polarization than another which provides the ability to filter signals based on its polarization. In this example, h is the antenna’s effective height whose units are expressed in meters.

Impedance transformer Intrinsic impedance of free-space, E/H Characteristic impedance of transmission line, V/I A typical value for Z0 is 50 . Clearly there is an impedance mismatch that must be addressed by the antenna.

Propagation mode adapter In free space the waves spherically expand following Huygens principle:each point of an advancingwave front is in fact thecenter of a fresh disturbanceand the source of a new train of waves. Within the sensor, the waves are guided within a transmission line or waveguide that restricts propagation to one axis.

Propagation mode adapter During both transmission and receive operations the antenna must provide the transition between these two propagation modes.

Antenna types Antennas come in a wide variety of sizes and shapes Helical antenna Horn antenna Parabolic reflector antenna

Theory Antennas include wire and aperture types. Wire types include dipoles, monopoles, loops, rods, stubs, helicies, Yagi-Udas, spirals. Aperture types include horns, reflectors, parabolic, lenses.

Theory In wire-type antennas the radiation characteristics are determined by the current distribution which produces the local magnetic field. Yagi-Uda antenna Helical antenna

Theory – wire antenna example Some simplifying approximations can be made to take advantage the far-field conditions.

Theory – wire antenna example Once Eq and Ef are known, the radiation characteristics can be determined. Defining the directional function f (q, f) from

Theory – aperture antennas In aperture-type antennas the radiation characteristics are determined by the field distribution across the aperture. Horn antenna Parabolic reflector antenna

Theory – aperture antenna example The far-field radiation pattern can be found from the Fourier transform of the near-field pattern. Where Sr is the radial component of the power density, S0 is the maximum value of Sr, and Fn is the normalized version of the radiation pattern F(q, f)

Theory Reciprocity If an emf is applied to the terminals of antenna A and the current measured at the terminals of another antenna B, then an equal current (both in amplitude and phase) will be obtained at the terminals of antenna A if the same emf is applied to the terminals of antenna B. emf: electromotive force, i.e., voltage Result – the radiation pattern of an antenna is the same regardless of whether it is used to transmit or receive a signal.

Characteristics Radiation pattern Radiation pattern – variation of the field intensity of an antenna as an angular function with respect to the axis Three-dimensional representation of the radiation pattern of a dipole antenna

Characteristics Radiation pattern Spherical coordinate system

Characteristics Radiation pattern

Characteristics Beamwidth and beam solid angle The beam or pattern solid angle, p [steradians or sr] is defined as where d is the elemental solid angle given by

Characteristics Directivity, gain, effective area Directivity – the ratio of the radiation intensity in a given direction from the antenna to the radiation intensity averaged over all directions. [unitless] Maximum directivity, Do, found in the direction (, ) where Fn= 1 and or Given Do, D can be found

Characteristics Directivity, gain, effective area Gain – ratio of the power at the input of a loss-free isotropic antenna to the power supplied to the input of the given antenna to produce, in a given direction, the same field strength at the same distance Of the total power Pt supplied to the antenna, a part Po is radiated out into space and the remainder Pl is dissipated as heat in the antenna structure. The radiation efficiencyhl is defined as the ratio of PotoPt Therefore gain, G, is related to directivity, D, as And maximum gain, Go, is related to maximum directivity, Do, as

Characteristics Directivity, gain, effective area Effective area – the functional equivalent area from which an antenna directed toward the source of the received signal gathers or absorbs the energy of an incident electromagnetic wave It can be shown that the maximum directivity Do of an antenna is related to an effective area (or effective aperture) Aeff, by where Ap is the physical aperture of the antenna and ha = Aeff / Ap is the aperture efficiency (0 ≤ ha ≤ 1) Consequently [m2] For a rectangular aperture with dimensions lxandly in the x- and y-axes, and an aperture efficiency ha = 1, we get [rad] [rad]

Characteristics Directivity, gain, effective area Therefore the maximum gain and the effective area can be used interchangeably by assuming a value for the radiation efficiency (e.g., l = 1) Example: For a 30-cm x 10-cm aperture, f = 10 GHz ( = 3 cm)xz  0.1 radian or 5.7°, yz  0.3 radian or 17.2°G0  419 or 26 dBi (dBi: dB relative to an isotropic radiator)

Characteristics Bandwidth The antenna’s bandwidth is the range of operating frequencies over which the antenna meets the operational requirements, including: • Spatial properties (radiation characteristics) • Polarization properties • Impedance properties • Propagation mode properties Most antenna technologies can support operation over a frequency range that is 5 to 10% of the central frequency (e.g., 100 MHz bandwidth at 2 GHz) To achieve wideband operation requires specialized antenna technologies (e.g., Vivaldi, bowtie, spiral)

Friis’ transmission formula At a fixed distance R from the transmitting antenna, the power intercepted by the receiving antenna with effective aperture Ar is where Sr is the received power density (W/m2), and Gt is the peak gain of the transmitting antenna.

Friis’ transmission formula If the radiation efficiency of the receiving antenna is hr, then the power received at the receiving antenna’s output terminals is Therefore we can write which is known as Friis’ transmission formula

Friis’ transmission formula as Friis’ transmission formula can be rewritten to explicitly represent the free-space transmission loss, LFS which represents the propagation loss experienced in transmission between two lossless isotropic antennas.With this definition, the Friis formula becomes

Friis’ transmission formula Finally, a general form of the Friis’ transmission formula can be written that does not assume the antennas are oriented to achieve maximum power transfer where (t, t) is the direction of the receiving antenna in the transmitting antenna coordinates, and vice versa for (r, r). An additional term could be included to represent a polarization mismatch between the transmit and receive antennas.

Implementation Dipole, monopole, and ground planes Horns Parabolic reflectors Arrays

ImplementationDipole, monopole, and ground plane For a center-fed, half-wave dipole oriented parallel to the z axis (V/m) (W/m2) Tuned half-wave dipole antenna

Dipole antennas Versions of broadband dipole antennas

Dipole antennas

Monopole antenna q q Ground plane Radition pattern of vertical monopole above ground of (A) perfect and (B) average conductivity Mirroring principle creates image of monopole, transforming it into a dipole

Ground plane A ground plane will produce an image of nearby currents. The image will have a phase shift of 180° with respect to the original current. Therefore as the current element is placed close to the surface, the induced image current will effectively cancel the radiating fields from the current. The ground plane may be any conducting surface including a metal sheet, a water surface, or the ground (soil, pavement, rock). Horizontal current element Conducting surface(ground plane) Current element image

Implementation Horn antennas

Implementation Parabolic reflector antennas Circular aperture with uniform illumination. Aperture radius = a. Ap = p a2 where where J1( ) is the Bessel function of the first kind, zero order

Implementation Antenna arrays Antenna array composed of several similar radiating elements (e.g., dipoles or horns). Element spacing and the relative amplitudes and phases of the element excitation determine the array’s radiative properties. Linear array examples Two-dimensional array of microstrip patch antennas

Implementation Antenna arrays The far-field radiation characteristics Sr(, ) of an N-element array composed of identical radiating elements can be expressed as a product of two functions: Where Fa(, ) is the array factor, and Se(, ) is the power directional pattern of an individual element. This relationship is known as the pattern multiplication principle. The array factor, Fa(, ), is a range-dependent function and is therefore determined by the array’s geometry. The elemental pattern, Se(, ), depends on the range-independent far-field radiation pattern of the individual element. (Element-to-element coupling is ignored here.)

Implementation Antenna arrays In the array factor, Ai is the feeding coefficient representing the complex excitation of each individual element in terms of the amplitude, ai, and the phase factor, i, as and ri is the range to the distant observation point.

Implementation Antenna arrays For a linear array with equal spacing d between adjacent elements, which approximates to For this case, the array factor becomes Note that the e-jkR term which is common to all of the summation terms can be neglected as it evaluates to 1.

Implementation Antenna arrays By adjusting the amplitude and phase of each elements excitation, the beam characteristics can be modified.

Implementation Antenna arrays

Implementation Example: 2-element arrayIsotropic radiators

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