# ` Measuring Gain `

 Antennas (Home) Antenna Measurements Back: Measurement of Antenna Radiation Patterns

On the previous page on measuring radiation patterns, we saw how the radiation pattern of an antenna can be measured. This is actually the "relative" radiation pattern, in that we don't know what the peak value of the gain actually is (we're just measuring the received power, so in a sense can figure out how directive an antenna is and the shape of the radiation pattern). In this page, we will focus on measuring the peak gain of an antenna - this information tells us how much power we can hope to receive from a given plane wave.

We can measure the peak gain using the Friis Transmission Equation and a "gain standard" antenna. A gain standard antenna is a test antenna with an accurately known gain and polarization (typically linear). The most popular types of gain standard antennas are the thin half-wave dipole antenna (peak gain of 2.15 dB) and the pyramidal horn antenna (where the peak gain can be accurately calculated and is typically in the range of 15-25 dB). Consider the test setup shown in Figure 1. In this scenario, a gain standard antenna is used in the place of the test antenna, with the source antenna transmitting a fixed amount of power (PT). The gains of both of these antennas are accurately known.

Figure 1. Record the received power from a gain standard antenna.

From the Friis transmission equation, we know that the power received (PR) is given by:

If we replace the gain standard antenna with our test antenna (as shown in Figure 2), then the only thing that changes in the above equation is GR - the gain of the receive antenna. The separation between the source and test antennas is fixed, and the frequency will be held constant as well.

Figure 2. Record the received power with the test antenna (same source antenna).

Let the received power from the test antenna be PR2. If the gain of the test antenna is higher than the gain of the "gain standard" antenna, then the received power will increase. Using our measurements, we can easily calculate the gain of the test antenna. Let Gg be the gain of the "gain standard" antenna, PR be the power received with the gain antenna under test, and PR2 be the power received with the test antenna. Then the gain of the test antenna (GT) is (in linear units):

The above equation uses linear units (non-dB). If the gain is to be specified in decibels, (power received still in Watts), then the equation becomes:

And that is all that needs done to determine the gain for an antenna in a particular direction.

### Efficiency and Directivity

Recall that the directivity can be calculated from the measured radiation pattern without regard to what the gain is. Typically this can be performed by approximated the integral as a finite sum, which is pretty simple.

Recall that the efficiency of an antenna is simply the ratio of the peak gain to the peak directivity:

Hence, once we have measured the radiation pattern and the gain, the efficiency follows directly from these.

In the next section, we'll look at measuring the phase of an antenna's radiation pattern.

Next: Antenna Measurements 3 - Phase Measurements

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