Up to now we've concentrated on considering the antenna's behaviour when transmitting power. However, from the reciprocal property mentioned earlier we can expect the same antenna, when used to receive signals, to collect G times as much power as we'd get using an antenna whose sensitivity is omnidirectional. The gain value is therefore appropriate whether we're using the antenna to transmit or receive. An alternative way to describe the behaviour of a receiving antenna is in terms of the power, W, it picks up when placed in a plane uniform field of power density, E2/Z0 , where E is the rms electric field and Z0 is the impedance of free space. We can link the power density falling on the antenna and the power it collects by an expression of the form
This expression can be used to define the antenna's Effective Area, Ae. For some high frequency and ‘optical’ antennas is essentially equal to the actual area of the antenna which the incident field is striking. Other antenna's, for example a dipole, don't have a physical area we can identify in this way. Although we won't prove it here, it can be shown that the effective area and beam angle of an antenna can be linked by the expression
where lambda is the radiation's free space wavelength. Combining the two equations above we can therefore say that
The above expressions mean that, once we know the radiation wavelength we only need to know one of the three quantities; the gain, the antenna solid angle, or the effective area, and we can work out the others. In effect, these three quantities are three ways to tell us the same thing about an antenna.
6.3 Radiation resistance and antenna impedance.
Up until now we've treated the the antenna as a sort of lossless power transformer. To complete our understanding of antenna basics we need to consider the electrical properties of an antenna. Figure 6.5a shows a simple transmitter system. Power from a source is sent along some form of transmission line (i.e. a waveguide, pair of wires, light fibre, or whatever is a convenient way to carry the signal from place to place) to the antenna. The antenna then radiates power in a directional manner we can describe using its power pattern.
So far as the signal source or generator is concerned, the system looks like the circuit shown in 6.5b. The generator doesn't know anything about the details of the antenna or its power pattern. So far as it is concerned, the antenna/transmission line combination just looks like some sort of load impedance.
An ideal antenna would simply accept all the power sent to it from a source and radiate it away into space. So far as the generator is concerned, this behaviour is indistinguishable from what happens if it's output is connected to a load impedance which matches its own output impedance, Zg.
A real antenna won't radiate all the power it receives. Some will be dissipated in antenna losses and simply warm it up a bit. Some power may ‘bounce’ off the antenna and be reflected back to the generator. These three effects, radiation, loss, and reflection, can be represented by three impedances as illustrated in figure 6.5b. RR is the antenna's Radiation Resistance value; it represents the antenna properties which allow power to radiate away. R is the Loss Resistance; it represents the ways power is dissipated, warming up the antenna. X is the antenna reactance; this represents any ways the antenna can store energy, returning it to the generator after a delay.
This reactive behaviour is a bit like the way a capacitor or inductor can store electrical energy and release it later. For an ideal antenna we would therefore arrange that
Zg = RR , R = 0 , and X = 0
This would ensure that all the power the generator can produce is radiated into space. A value of R greater than zero means that some power is ‘wasted’ warming the antenna. Since we can't expect to completely avoid dissipation losses, in practice we have to settle for attempting to ensure that the loss resistance is as small as possible. All being well, we can usually get a zero reactance — although this may be difficult to arrange sometimes!
Content and pages maintained by: Jim Lesurf (jcgl@st-and.ac.uk)
using HTMLEdit3 on a StrongARM powered RISCOS machine.
University of St. Andrews, St Andrews, Fife KY16 9SS, Scotland.