Antenna Factor

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Antenna Definitions

The Antenna Factor is used by RF or EMC antenna engineers to describe the required electric field strength that produces 1 Volt at the terminals of an antenna. Alternatively, the Antenna Factor concept specifies what the received voltage is in the presence of an electric field. It is defined mathematically as:

definition of antenna factor AF

Technically, the above definition is a little ambiguous. For instance, if the terminals of the antenna are short circuited, the received voltage is always zero, so the Antenna Factor is not defined. Hence, the Antenna Factor has an implied impedance associated with the antenna terminals, most commonly 50 Ohms. However, sometimes an "open circuit" antenna factor is discussed, which is the available voltage for an antenna with an open circuit (no receiver or load attached). The basic concept of antenna factor with a terminal (port, receiver or load) impedance is shown in Figure 1.

antenna factor depends on the load or impedance at the antenna's terminals

Figure 1. Graphical Illustration of Antenna Factor, with Antenna Terminated in a Load (which represents the Receiver).

In the above Figure, the E-field is shown as part of a propagating wave (which isn't neccessarily the case). The antenna receives the field at a voltage shows up at its terminals, the circles shown in Figure 1. The receiver impedance (or the load, or a measuring device such as a network analyzer) is shown connected to the antenna terminals. The ratio of the incident field strength to the output voltage is the Antenna Factor.

The above equation for the Antenna Factor assumes that the polarization of the E-field and the antenna are matched (no polarizatoin mismatch loss).

A relationship can be derived for the Antenna Factor in terms of the antenna's gain and the frequency of operation. Assuming that the antenna is receiving a propagating wave (as is the case if the antenna is receiving power in the far field of another antenna), we can derive this relationship. If the an incident field is part of a propagating wave, the power density S [in Watts/meter-squared (W/m^2)] of the wave is given by:

power density in watts per square meter

In the above, intrinsic impedance is the intrinsic impedance of free space. The amount of power available from the antenna can be determined using the antenna's effective aperture. Hence, the power captured from the plane wave is given by:

antenna factor equation derivation

In the above equation we have substituted in the formula for the effective aperture, f is the frequency of the plane wave, c is the speed of light and G is the gain of the antenna.

On the receiver side of the antenna, the power received depends on the impedance of the receiver (Zload) and the received voltage:

received power assuming an impedance for the receiver

Setting the preceding equations equal to each other, we can obtain the final result:

antenna factor for plane wave

If the load impedance is 50 Ohms, then the Antenna Factor can be written in a form that is commonly seen:

antenna factor for 50 ohm load

Its crucial to note that the preceding two relationships only hold for propagating plane waves (far field conditions), and are polarization matched to the fields. The impedance mismatch between the antenna and receiver is included in the Antenna Factor - only the available voltage is measured at the receiver.

In addition, since the gain of an antenna varies with direction, the antenna factor also varies as a function of the direction of the incoming fields towards the antenna. If no direction is specified, the direction that is meant is always the direction of maximum gain.

The antenna factor also sometimes comes in different varieties - near field and far-field conditions. Because near fields can behave differently than far fields (in general near fields are more reactive and complex to figure out), an antenna behaves differently in the presence of the two. Hence, sometimes an antenna has near and far field antenna factors specified.

Finally, although much less common, the Antenna Factor can also be defined in terms of the magnetic field:

magnetic antenna factor

This is simply the required magnetic field strength to produce a volt at the terminals of the antenna.

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