Antenna measurement techniques refers to the testing of antennas to ensure that the antenna meets specifications or simply to characterize it. Typical parameters of antennas are gain, bandwidth, radiation pattern, beamwidth, polarization, and impedance.

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The antenna pattern is the response of the antenna to a plane wave incident from a given direction or the relative power density of the wave transmitted by the antenna in a given direction. For a reciprocal antenna, these two patterns are identical. A multitude of antenna pattern measurement techniques have been developed. The first technique developed was the far-field range, where the antenna under test (AUT) is placed in the far-field of a range antenna. Due to the size required to create a far-field range for large antennas, near-field techniques were developed, which allow the measurement of the field on a surface close to the antenna (typically 3 to 10 times its wavelength). This measurement is then predicted to be the same at infinity. A third common method is the compact range, which uses a reflector to create a field near the AUT that looks approximately like a plane-wave.

The far-field range was the original antenna measurement technique, and the simplest; it consists of placing the antenna under test (AUT) a long distance away from the instrumentation antenna. Generally, the far-field distance or Fraunhofer distance, ${\displaystyle \ D_{\mathsf {Frnh}}\ ,}$ is considered to be

${\displaystyle D_{\mathsf {Frnh}}={\frac {\ 2d^{2}\ }{\lambda }}\ ,}$

where ${\displaystyle \ d\ }$ is the widest diameter of the antenna in any direction, and ${\displaystyle \ \lambda \ }$ is the wavelength of the radio wave.^[1] Separating the AUT and the standard receiving antenna by this distance reduces the detectable phase variation across the AUT enough to obtain a reasonably accurate estimate of the antenna pattern in the far distance.

The IEEE antenna measurement standard (document i.d. IEEE-Std-149-1979), suggests set-up for measurement and various techniques for both far-field ranges and ground-bounce ranges (discussed below).

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The formula for electromagnetic radiation dispersion and information propagation is:

${\displaystyle \ D^{2}={\frac {P}{\ S\ }}\ \propto \ 3{\mathsf {\ dB}}\ ,}$

where D represents distance, P power and S speed.

The equation means that double the communication distance requires four times the power. It also means double power allows double communication speed (bit rate). Double power is approximately 3 dB increase (or exactly 10×log₁₀(2) ≈ 3.0103000 ). Of course, in the real world there are all sorts of other phenomena which complicate the estimated delivered power, such as Fresnel canceling, path loss, background noise, etc.

Except for polarization, the SWR is the most easily measured of the parameters above. Impedance can be measured with specialized equipment, as it relates to the complex SWR. Measuring radiation pattern requires a sophisticated setup including significant clear space (enough to put the sensor into the antenna's far field, or an anechoic chamber designed for antenna measurements), careful study of experiment geometry, and specialized measurement equipment that rotates the antenna during the measurements.

The electrical field created by an electric charge ${\displaystyle \scriptstyle {q}}$ is

${\displaystyle {\vec {E}}={-q \over 4\pi \varepsilon _{\circ }}\left[{{\vec {e}}_{r'} \over r'^{2}}+{r' \over c}{d\ \over dt}\left({{\vec {e}}_{r'} \over r'^{2}}\right)+{1 \over c^{2}}{d^{2}\ \over dt^{2}}\left({\vec {e}}_{r'}\right)\right]\,}$

where:

• ${\displaystyle \scriptstyle {c}}$ is the speed of light in vacuum.
• ${\displaystyle \scriptstyle {\varepsilon _{\circ }}}$ is the permittivity of free space.
• ${\displaystyle \scriptstyle {r'}}$ is the distance from the observation point (the place where ${\displaystyle \scriptstyle {\vec {E}}}$ is evaluated) to the point where the charge was ${\displaystyle \scriptstyle {r' \over c}}$ seconds before the time when the measure is done.
• ${\displaystyle \textstyle {{\vec {e}}_{r'}}}$ is the unit vector directed from the observation point (the place where ${\displaystyle \scriptstyle {\vec {E}}}$ is evaluated) to the point where the charge was ${\displaystyle \scriptstyle {r' \over c}}$ seconds before the time when the measure is done.

The "prime" in this formula appears because the electromagnetic signal travels at the speed of light. Signals are observed as coming from the point where they were emitted and not from the point where the emitter is at the time of observation. The stars that we see in the sky are no longer where we see them. We will see their current position years in the future; some of the stars that we see today no longer exist.

The first term in the formula is just the electrostatic field with retarded time.

The second term is as though nature were trying to allow for the fact that the effect is retarded (Feynman).

The third term is the only term that accounts for the far field of antennas.

The two first terms are proportional to ${\displaystyle \textstyle {1 \over r^{2}}}$. Only the third is proportional to ${\displaystyle \textstyle {1 \over r}}$.

Near the antenna, all the terms are important. However, if the distance is large enough, the first two terms become negligible and only the third remains:

${\displaystyle {\vec {E}}={-q \over 4\pi \varepsilon c_{\circ }^{2}}{d^{2}\ \over dt^{2}}\left({\vec {e}}_{r'}\right)=-q10^{-7}{d^{2}\ \over dt^{2}}\left({\vec {e}}_{r'}\right)\,}$

If the charge q is in sinusoidal motion with amplitude ${\displaystyle \scriptstyle {\ell _{\circ }}}$ and pulsation ${\displaystyle \scriptstyle {\omega }}$ the power radiated by the charge is:

${\displaystyle P={q^{2}\omega ^{4}\ell _{\circ }^{2} \over 12\pi \varepsilon _{\circ }c^{3}}}$ watts.

Note that the radiated power is proportional to the fourth power of the frequency. It is far easier to radiate at high frequencies than at low frequencies. If the motion of charges is due to currents, it can be shown that the (small) electrical field radiated by a small length ${\displaystyle \scriptstyle {d\ell }}$ of a conductor carrying a time varying current ${\displaystyle \scriptstyle {I}}$ is

${\displaystyle dE_{\theta }(t+\textstyle {r \over c})=\displaystyle {-d\ell \sin \theta \over 4\pi \varepsilon _{\circ }c^{2}r}{dI \over dt}\,}$

The left side of this equation is the electrical field of the electromagnetic wave radiated by a small length of conductor. The index ${\displaystyle \scriptstyle {\theta }}$ reminds that the field is perpendicular to the line to the source. The ${\displaystyle \scriptstyle {t+{r \over c}}}$ reminds that this is the field observed ${\displaystyle \scriptstyle {r \over c}}$ seconds after the evaluation on the current derivative. The angle ${\displaystyle \scriptstyle {\theta }}$ is the angle between the direction of the current and the direction to the point where the field is measured.

The electrical field and the radiated power are maximal in the plane perpendicular to the current element. They are zero in the direction of the current.

Only time-varying currents radiate electromagnetic power.

If the current is sinusoidal, it can be written in complex form, in the same way used for impedances. Only the real part is physically meaningful:

${\displaystyle I=I_{\circ }e^{j\omega t}}$

where:

• ${\displaystyle \scriptstyle {I_{\circ }}}$ is the amplitude of the current.
• ${\displaystyle \scriptstyle {\omega =2\pi f}}$ is the angular frequency.
• ${\displaystyle \scriptstyle {j={\sqrt {-1}}}}$

The (small) electric field of the electromagnetic wave radiated by an element of current is:

${\displaystyle dE_{\theta }(t+\textstyle {r \over c})=\displaystyle {-d\ell j\omega \over 4\pi \varepsilon _{\circ }c^{2}}{\sin \theta \over r}e^{j\omega t}\,}$

And for the time ${\displaystyle \textstyle {t}\,}$:

${\displaystyle dE_{\theta }(t)={-d\ell j\omega \over 4\pi \varepsilon _{\circ }c^{2}}{\sin \theta \over r}e^{j\left(\omega t-{\omega \over c}r\right)}\,}$

The electric field of the electromagnetic wave radiated by an antenna formed by wires is the sum of all the electric fields radiated by all the small elements of current. This addition is complicated by the fact that the direction and phase of each of the electric fields are, in general, different.

The gain in any given direction and the impedance at a given frequency are the same when the antenna is used in transmission or in reception.

The electric field of an electromagnetic wave induces a small voltage in each small segment in all electric conductors. The induced voltage depends on the electrical field and the conductor length. The voltage depends also on the relative orientation of the segment and the electrical field.

Each small voltage induces a current and these currents circulate through a small part of the antenna impedance. The result of all those currents and tensions is far from immediate. However, using the reciprocity theorem, it is possible to prove that the Thévenin equivalent circuit of a receiving antenna is:

${\displaystyle V_{a}={{\sqrt {R_{a}\ G_{a}\ }}\lambda \cos \psi \over 2{\sqrt {\pi Z_{\circ }}}}E_{b}}$

• ${\displaystyle \scriptstyle {V_{a}}}$ is the Thévenin equivalent circuit tension.
• ${\displaystyle \scriptstyle {Z_{a}}}$ is the Thévenin equivalent circuit impedance and is the same as the antenna impedance.
• ${\displaystyle \scriptstyle {R_{a}}}$ is the series resistive part of the antenna impedance ${\displaystyle \scriptstyle {Z_{a}}\,}$.
• ${\displaystyle \scriptstyle {G_{a}}}$ is the directive gain of the antenna (the same as in emission) in the direction of arrival of electromagnetic waves.
• ${\displaystyle \scriptstyle {\lambda }}$ is the wavelength.
• ${\displaystyle \scriptstyle {E_{b}}}$ is the magnitude of the electrical field of the incoming electromagnetic wave.
• ${\displaystyle \scriptstyle {\psi }}$ is the angle of misalignment of the electrical field of the incoming wave with the antenna. For a dipole antenna, the maximum induced voltage is obtained when the electrical field is parallel to the dipole. If this is not the case and they are misaligned by an angle ${\displaystyle \scriptstyle {\psi }}$, the induced voltage will be multiplied by ${\displaystyle \scriptstyle {\cos \psi }}$.
• ${\displaystyle \scriptstyle {Z_{\circ }={\sqrt {\mu _{\circ } \over \varepsilon _{\circ }}}=376.730313461\ \Omega }}$ is a universal constant called vacuum impedance or impedance of free space.

The equivalent circuit and the formula at right are valid for any type of antenna. It can be as well a dipole antenna, a loop antenna, a parabolic antenna, or an antenna array.

From this formula, it is easy to prove the following definitions:

Antenna effective length${\displaystyle =\displaystyle {{\sqrt {R_{a}G_{a}}}\lambda \cos \psi \over {\sqrt {\pi Z_{\circ }}}}\,}$

is the length which, multiplied by the electrical field of the received wave, give the voltage of the Thévenin equivalent antenna circuit.

Maximum available power${\displaystyle =\displaystyle {{G_{a}\lambda ^{2} \over 4\pi Z_{\circ }}E_{b}^{2}}\,}$

is the maximum power that an antenna can extract from the incoming electromagnetic wave.

Cross section or effective capture surface${\displaystyle =\displaystyle {{G_{a} \over 4\pi }\lambda ^{2}}\,}$

is the surface which multiplied by the power per unit surface of the incoming wave, gives the maximum available power.

The maximum power that an antenna can extract from the electromagnetic field depends only on the gain of the antenna and the squared wavelength ${\displaystyle \scriptstyle {\lambda }}$. It does not depend on the antenna dimensions.

Using the equivalent circuit, it can be shown that the maximum power is absorbed by the antenna when it is terminated with a load matched to the antenna input impedance. This also implies that under matched conditions, the amount of power re-radiated by the receiving antenna is equal to that absorbed.

• Antenna modeling
• Free space
• Impedance of free space
• Near and far field