Designing dual-band internal antennas

As cellular telephones have evolved over the years, so have their components, particularly the antennas. The first cellular telephones were big, heavy, and clumsy but worked well using large, coax-fed, half-wavelength antennas. As cellular-phone handsets became smaller, so did the antennas. By using the phone's case as the RF counterpoise, which is half of the antenna that corresponds to a semi-infinite ground plane, a much shorter quarter-wavelength antenna replaced the half-wavelength antenna (see sidebar "Antenna terminology"). Next came the retractable antenna and the nonretractable, stubby antenna, as consumers demanded smaller, more convenient models. Because cell-phone users today prefer even smaller and sleeker phones, handset designers are incorporating "invisible," or internal, antennas.

As the continuing cellular-infrastructure buildup eases demand on the communications-link margin—more cell towers mean a better signal—service providers are willing to surrender 2 or 3 dB of communications-link margin to offer distinctively designed, highly compact phones that rely solely on internal antennas. As a result, cell-phone designers are learning how to design internal antennas with optimum performance subject to the competing demands of physics and styling.

Multiband operation is a necessary feature for nearly every cellular phone. The design of an effective single-band internal antenna is not trivial, and designing a multiband internal antenna is even more demanding. Many of the fundamental design issues conflict with each other (see sidebar "Factors to consider in internal-antenna design").

Figure 1 illustrates a dual-band internal antenna in its elementary form. This simple model can help you understand many design issues. The antenna has two distinct elements: the low band and the high band. The longer low-band element resonates at the lower frequency, or the first Eigenmode. The physical length of this element roughly corresponds to a quarter wavelength, as modified by local dielectric effects and the parasitic shunt capacitance of the high-band element, which is generally a high impedance across the same inductive ground tab.

The high-band element resonates at the higher frequency, which is usually less than three times the low-band frequency (the third Eigenmode). The load on the high-band resonant impedance is the low-band element's shunt parasitic load across the inductive ground tab. At this frequency, the low-band element's impedance must be higher than the impedance of the high-band element.

Placing the feedpoint close to the single ground tab creates the RF transformer. This transformer converts the generally low impedance of the antenna, which is 10Ω or less, to a more useful value of 50Ω, without using external components. This impedance conversion is a modern example of the classic "gamma match." Although some designs differ, the feedpoint is typically on the high-band side of the ground strap.

These elements are not independently tunable. Each unused element represents a parasitic load on the used element, and the tuning of one element has a noticeable effect on the other.

You must carefully consider size and shape constraints of the phone when modifying the layout of the RF transformer. The antenna designer will often test several sizes of and ways of spacing the elements before achieving a 50Ω match of both the high- and low-band elements. A volume of 7 cc or more is usually necessary to implement a dual-band internal antenna with a height of approximately 7 mm above the ground plane.

In some cases, you can use an external matching circuit to widen, or "broadband," the electrical performance of the low-band element. This matching circuit typically incorporates a highpass design so that the matching circuit is transparent to the high-band element. Such a circuit serves to reduce the lowest operating frequency of the antenna—a welcome benefit when there are severe restrictions on antenna volume.

Sometimes, antenna designers attempt to use parasitic elements to create a four-pole response to increase antenna bandwidth for a given space constraint. It is more productive to maintain the antenna as a two-pole structure and, if necessary, to introduce additional poles with an electrical matching circuit.

This reasoning is twofold. First, it requires just as much space to create a parasitic element as it does to create a radiating element. Because the parasitic element is unloaded, it robs the radiating element of the surface area and the corresponding radiation resistance the element might have otherwise had, thereby compromising overall antenna efficiency. Second, the current distribution of the driven and parasitic element varies widely over the bandwidth of the final structure. These electrical currents often support each other but at other times cancel each other. When you use a network analyzer to examine four-pole structures, they appear to be broadband. However, performing a swept-gain test on the same element often reveals frequencies for which antenna gain degrades sharply.

An internal antenna cannot match the performance of a well-designed fixed, retractable, or stubby antenna. This fact becomes clear when you examine efficiency or average gain. Even the most optimal internal-antenna design generally does not exceed 70% efficiency in free-space testing, and a practical design is typically less than 50% efficient. A well-matched retractable antenna often exceeds 90% antenna efficiency. The following rules will help designers to attain the best possible performance with dual-band internal antennas.

Rule 1—Minimize parasitics: You obtain maximum bandwidth when group delay is at a minimum. As in any resonant circuit, minimizing group delay requires minimizing parasitics at the feedpoint. You must keep the parasitic inductance represented by the ground tab and the feedpoint as low as possible by making these structures as wide and as short as possible. Conversely, you must minimize the parasitic capacitance at the open end of each element by keeping the high-voltage end of each element as far as possible from the counterpoise (ground plane). Similarly, it is often counterproductive to meander the element.

Although you position the feedpoint of the element to represent a load of 50Ω to the circuit, this load is not representative of the antenna's actual impedance. In fact, the radiation impedance of the element as viewed from the ground tab is only a few ohms. Only the transformer effect of the gamma match presents the usable impedance to the feedpoint.

Therefore, the ground tab is the most critical part of the design with respect to reducing parasitic inductance. Due to the low impedance of the antenna at this point, a small amount of series inductance here can combine with the transformer effect of the gamma match to magnify undesirable parasitic effects and substantially degrade antenna performance. Likewise, the means by which the ground tab connects to the counterpoise must provide a consistently low-impedance connection of much less than 1Ω.

Addressing parasitic inductance is a priority for low-impedance circuits, and, similarly, addressing parasitic capacitance is a priority for high-impedance circuits. Both issues are present in varying degrees in antenna design. You can reduce parasitic capacitance on the high-voltage end of the element by keeping this end of the element as far from the ground plane as possible and by minimizing exposure to lossy dielectrics. Dielectric losses—if dielectrics are present—are dominant at this part of the antenna but are insignificant at the grounded end. Likewise, using dielectric loading to reduce the physical length of the first Eigenmode is effective only at the high-voltage end of the antenna.

Generally, cellular-phone internal-antenna design requires determined efforts to reduce the element to a size that fits inside typically cluttered and irregular phone housing. Only two techniques are available: You either meander the element or use a dielectric between the element and the counterpoise to reduce the physical length of the Eigenmode. Often, both techniques are necessary.

If you meander the element, keep the high-voltage end of the element as far as possible from the low-voltage end and make as few meanders as possible. Meandering rarely provides adequate size reduction, and it always introduces unwanted parasitics.

Rule 2—Minimize dielectric loading: Dielectric loading always has a negative impact on antenna performance. Using dielectrics to reduce the physical size of the antenna reduces antenna efficiency and gain. Although it appears that you can reduce the size while maintaining bandwidth, the corresponding dielectric losses introduced are no different in principle from placing a resistor across the feedpoint.

Small antennas typically exhibit a large input reactance, a small radiation resistance, and—when you tune the antenna to resonance—a small bandwidth of operation. A measure of the small bandwidth and high input reactance is the Q of the antenna, defined as follows:

where

As this equation shows, the Q of the antenna comes from two independent sources: radiation resistance and internal losses. In well-designed internal antennas, internal losses typically equal radiation resistance. As the volume of the antenna becomes smaller, or if you introduce dielectrics, internal losses become predominant.

To see more clearly how this works, it is helpful to review the singular work of LJ Chu, HA Wheeler, and RF Harrington. Chu established the equation for the maximum Q of small antennas in 1948 using a partial-fraction expansion of the wave impedance of all spherical modes that exist outside the smallest circumscribing sphere surrounding the antenna (Reference 1). From this work, he was able to obtain an equivalent two-pole ladder network from which you could find Q using conventional circuit analysis. Harrington and Wheeler later expanded Chu's work (references 2 and 3).

The Chu-Harrington Limits provide specific relationships that define the maximum available bandwidth for a small two-pole antenna. You cannot exceed these limits even by using dielectric loading to reduce the physical length of the low-band and high-band Eigenmodes. Dielectric losses, and not radiation resistance, predominantly determine the bandwidth of small antennas that use dielectrics. Fundamentally, all small-aperture antennas of the same efficiency must have similar gains. The gain differences that occur in practice are always due to efficiency losses.

The Chu-Harrington equation for the Q that stems from radiation resistance is as follows:

where k=wave number and a=radius of the sphere.

The model is a sphere that completely encloses the antenna under test. By computing the ratio of the radiating fields to the reactive fields (the evanescent mode) for the "ideal" antenna and then transferring this understanding into an equivalent two-port ladder network, you can compute Q. No practical antenna can achieve this ideal limit; a real antenna can only approach it.

For small values of ka, this equation reduces to an even simpler version:

In other words, for small antennas, bandwidth is proportional to the subtended volume in cubic wavelengths.

The corollary to this insight is that if you reduce the size of your antenna and the bandwidth does not drop by the cube of the subtended volume, then internal losses, and not radiation resistance, are dictating the bandwidth.

Designers often view antennas as simple two-pole structures and assume that the Q completely determines antenna bandwidth. However, filter theory demonstrates that a more complex electrical structure—a four-pole or Chebyshev structure, for example—will readily produce much more bandwidth.

You can design four-pole—or greater—structures using either parasitic antenna elements or by incorporating additional poles in the electrical matching circuit. The most reliable technique is to implement the poles in the matching circuit and avoid using parasitic elements.

Rule 3—Maximize element surface area: Most internal antennas are generally planar in structure and use a less-than- ideal counterpoise, making it difficult to apply the Chu-Harrington Limits with precision. However, widening both the low- and the high-band elements as much as possible can maximize the surface area of both conductive elements and reduce inherent parasitics. By doing so, you reduce group delay and optimize bandwidth.

A typical mobile antenna looks like neither a balanced dipole nor a monopole over a ground plane. In general, it looks like a monopole over an edge-fed small counterpoise, a configuration for which little theoretical work exists. The Chu-Harrington Limits, however, were developed for a balanced antenna. You must modify the insights of this important study to properly apply them to complex unbalanced electromagnetic structures. In applying these limits, it is best to rely on some standard principles.

Thick antennas produce a smaller group delay and therefore have wider bandwidths than do thin antennas. Thus, in a planar structure, wide traces produce a smaller group delay and smaller parasitics than thin traces.

A constant current along the length of the element represents the greatest possible usage of the element, because one portion of the element contributes to radiation just as well as any other. This ideal condition is nearly impossible to achieve because of the widely varying impedance along the Eigenmode.

The best way to approximate this ideal condition is to increase the surface area of the element in proportion to the voltage you expect on that local portion of the element. In principle, the optimum planar antenna shape is an isosceles triangle fed at the apex. Although it is unlikely that there will ever be enough space to implement this geometry in a cell-phone design, recognizing this principle can help you decide on an optimum shape for the antenna element.

Maximizing the element surface area is not contrary to minimizing parasitics. In practice, the high-voltage end of the element should be as wide as possible and as far from the counterpoise as packaging allows.

Rule 4—Maximize height above the ground plane: The Chu-Harrington Limits demonstrate that the radiation Q of an antenna varies in proportion to the subtended volume in cubic wavelengths. Any bandwidth exceeding this limit is due to efficiency losses, either from internal resistance losses or from lossy dielectrics. However, you can apply the Chu-Harrington Limits to a cellular phone only in general terms, because the phone handset represents half of the antenna, and the unbalanced nature of the overall radiating system bears little similarity to the original study.

In successful internal-antenna designs, the subtended volume of dual-band internal antennas is 8 to 12 cc for CDMA/PCS and 6 to 10 cc for GSM/DCS, and the spacing between the element and the counterpoise is 6 to 10 mm. Some designs use spacing as small as 5 mm but show substantial losses in efficiency and gain. Decreasing the height above the counterpoise by 5% should reduce the bandwidth of a typical internal antenna by 15 to 20%. Any internal antenna with good bandwidth and efficiency will have a generous space between the element and the ground plane.

Author Information

Leslie J Reading is chief technical officer of Galtronics (Phoenix), where he performs research and development on telemetry products, internal antennas, and microwave systems. He holds a BSEE from the US Naval Academy (Annapolis, MD) and an MSEE from the US Naval Postgraduate School. His hobbies include sailing, ham radio, history, and woodworking.