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Satellite Communications  Antennas
 Short Wire Antennas
Authors: Darioush Agahi, William Domino
Conexant Systems Inc.
Newport Beach, CA
In the design of wireless portable devices, antenna efficiency is a variable that can have a great effect on overall system performance, and yet may not always receive the attention it deserves. As an example, RF engineers must frequently make critical tradeoffs in receiver design in order to improve sensitivity by mere fractions of a dB, but a poor antenna efficiency can easily cause a degradation of several dB. This pitfall can occur in systems such as GSM, where many tests are performed using a cable connection to the antenna port; a handset may easily pass such tests, only to be later hampered by its antenna in the field. This paper is targeted at the very important parameter of antenna efficiency, and a measurement technique that can be used to quantify it.
Antenna “efficiency” must be distinguished from antenna “gain”. Antenna gain is a directional quantity that refers to the signal strength that can be derived from an antenna relative to a reference dipole. Efficiency, on the other hand, quantifies the resistive loss of the antenna, in terms of the proportion of power that is actually radiated versus the power that is first delivered to it. It is not a directional quantity.
The Model
We model the antenna’s loss as a resistor placed in series with the radiation resistance, as shown in Figure 1. Since the model includes no reactances, there is an implicit assumption that the measurements must be taken at resonance. The equations to be derived later require this assumption.
Figure1 Model of Antenna Loss
The antenna efficiency (see appendix) is
h = (1)
Note that it is immaterial whether the antenna is matched to the source resistance R_{S}. While it is certainly desirable and necessary to match the antenna in actual use, the match is not part of the problem of finding the above resistance ratio. Therefore we need only relate the radiated power to that which is transferred forward at the point shown in Figure 1. What is needed, then, is a way to effectively separate the resistances R_{LOSS} and R_{RAD} by way of measurement, so that the efficiency can be calculated.
The Wheeler Cap
Wheeler [1] sets forth just such a method, where a hollow conductive sphere is placed over the antenna at the radius of transition between the antenna’s energystoring nearfield and its radiating farfield. This transition radius occurs at a distance of l/2p, and thus the sphere is referred to as the “radiansphere”. The role of the conductive sphere is to reflect all of the antenna’s radiation while causing minimal disturbance to the nearfield. In theory, a complete sphere is appropriate for reflecting the radiation of a small dipole, which is an approximation of an isotropic antenna, while in practice a monopole with a ground plane can be capped with a halfsphere. The halfspherical “Wheeler cap” is shown in Figure 2. For 900MHz, the cap’s radius is 5.3cm.
Figure 2 HalfSpherical Wheeler Cap
If all of the power radiated by the antenna is reflected back by the cap and not allowed to escape, then in our model this is the equivalent of setting R_{RAD} to zero. By making separate S_{11} measurements with the cap in place and with the cap removed, we gather enough information to find the resistances and the antenna’s efficiency.
The spherical or halfspherical cap is intended for physically small antennas; simple dipole or monopole antennas must therefore also be electrically short. Given the cap’s radius, it is not possible to fit a monopole of length l/4 under it. To test such an antenna we replace the halfspherical cap with a cylindrical cap, keeping the radius at l/2p. Such a cylindrical cap is shown in Figure 3.
Figure 3 Cylindrical Wheeler Cap
For an electrically short antenna (< l/10), the radiation resistance is typically small in comparison to the 50W source resistance of the measuring system. The radiation resistance of an ideal short monopole [2] is
R_{RAD MONO} = (2)
(3)
Cap off. The radiation resistance is that of the antenna radiating into free space, and the antenna reflection coefficient is measured and referred to as S_{11FS.} Then
(4)
h = (5)
h = (6)
The efficiency can therefore be found directly from the reflection coefficient magnitude measurements, without any need to actually determine R_{RAD }and R_{LOSS}. It should still be noted that the measurements must be made at resonance, because the loss model is based on vector S_{11} values that are allreal, even though only their magnitudes are needed in the above equations.
S_{11WC} = 0.966 S_{11FS} = 0.823
h = 79.3%
10log(79.3%) = 1.0 dB
Efficiency of ModerateLength Antennas: The ConstantLossResistor Method
h = (7)
(8)
Cap off. The radiation resistance is that of the antenna radiating into free space, and the antenna reflection coefficient is S_{11FS.} Then
(9)
(10)
(11)
h = (12)
h = (13)
S_{11WC} = 0.626 S_{11FS} = 0.325
h = 54.9% = 2.6dB
h = 32.0% = 4.9dB
Figure 4 Efficiency vs. R_{LOSS} for Antenna with 4W Radiation Resistance
Figure 5 Efficiency vs. R_{LOSS} for Antenna with 14W Radiation Resistance
Making the Measurements: Practical Considerations
Figure 6 Smith Chart Display of FreeSpace S_{11}
It is especially true that the free space measurement should be done at the actual resonance instead of the antenna’s nominal operating frequency F_{0}. This is because the antenna is normally loaded down when installed on the handset, and it is expected that there should be a small shift when it is removed and placed on a different ground plane. A rule of thumb that is normally used for the maximum limit of this shift is ± 10% of F_{0}. Detuning beyond this could impact the accuracy of the measurement, as it means the actualusage environment differs too much from the measuring setup.
Figure 7 Allowable Detuning for Measurement
R_{in} = R _{RAD} + R_{LOSS }(a1)
Pin = ½ R_{in}  I_{in} ^{2 }(a2)
Pin = ½ ( R _{RAD} + R_{LOSS})  I_{in} ^{2} = ½ R _{ RAD}  I_{in} ^{2 }+ ½ R_{LOSS}  I_{in} ^{2}
Or equivalently,
P_{RAD} = ½ R _{RAD}  I_{in} ^{2} (a3)
P_{LOSS} = ½ R_{LOSS}  I_{in} ^{2} (a4)
Using the efficiency equation and inserting (a3) and (a4) yields,
h = = =
After canceling similar terms, it yields,
h =
3)
R. H. Johnston, L. P. Ager, and J. G. McRory, “A new small antenna efficiency measurement method,”
IEEE 1996 Antennas and Propagation Society International Symposium, vol.1, pp. 176179