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The *port* of an antenna is the physical
location where the RF source is connected. From a network theory perspective,
the antenna has a single port. In Antenna
Toolbox™, a red dot on
the antenna figure represents the feed point. A half-wavelength dipole
is shown with its feed point:

All antennas are excited by a voltage of `1V`

at
the port. The various terminal port parameters are as follows:

*Input impedance* is the ratio of voltage
to current at the port. Antenna impedance is calculated as the ratio
of the phasor voltage, which is `1V`

at a phase angle
of `0 deg`

, to the phasor current at the port. The
impedance equation is:

$$Z=V/I=R+jX$$

`V`

is the antenna excitation voltage`I`

is the current`R`

is the antenna resistance in ohms`X`

is the antenna reactance in ohms

Antenna input impedance is a frequency-dependent quantity. The plot shows the input impedance of a dipole antenna over the frequency band 20–120 MHz. The resistance and reactance traces vary with frequency. The variation can be qualitatively described in terms of resonances.

d = dipole; impedance(d,20e6:1e6:120e6)

Use `impedance`

to calculate
the input impedance of any antennas in Antenna
Toolbox.

The *resonant frequency* of the antenna is
the frequency at which the reactance of the antenna is equal to zero.

The plot shows two resonance points of a dipole antenna.

In the plot, the reactance values are negative, or capacitive, before the resonance. These values are positive or inductive after the resonance. This type of resonance is called series resonance. You can model this type of resonance using a series RLC circuit. If the impedance curve goes from positive reactance to negative reactance, it is called parallel resonance. You can model this type of resonance using a parallel RLC circuit.

The* reflection coefficient*, or `S_1_1`

,
of the antenna describes a relative fraction of the incident RF power
that is reflected back due to the impedance mismatch. Impedance mismatch
is the difference between the input impedance of the antenna and the
characteristic impedance of the transmission line (or the generator
impedance when the transmission line is not present). The characteristic
impedance is the reference impedance.

S = sparameters(d,20e6:1e6:120e6,72) rfplot(S)

The reflection coefficient also gives the operating bandwidth of the antenna. Antenna bandwidth is usually the frequency band over which the magnitude of the reflection coefficient is below –10 dB.

Use `sparameters`

to calculate
the value of `S`

for any
antenna in the Antenna
Toolbox._{11}

The *return loss* of an antenna is a measure
of the effectiveness of power delivery from a transmission line or
coaxial cable to a load such as an antenna. The return loss can also
be defined as the difference in dB between the power sent toward the
antenna and the power reflected back from it. The higher the power
ratio, the better matching between load and line. Return loss equation
is:

$$RL=-20{\mathrm{log}}_{10}\left|{S}_{11}\right|$$

`RL`

is the return loss`S`

is the reflection coefficient, or power reflected from the antenna._{11}

For passive devices, the return loss is a positive nondissipative term representing the reduction in amplitude of the reflected wave in comparison to the incident wave. In active devices, a negative return loss is possible.

d = dipole; returnLoss(d,20e6:1e6:120e6,72)

Return loss plots also give the operating bandwidth of the antenna.
Antenna bandwidth is the frequency band over which the magnitude of
return loss is greater than 10 dB. Use the `returnLoss`

function
to calculate the return loss of any antenna in the Antenna
Toolbox library.

The *voltage standing wave ratio* (VSWR)
of an antenna is another measure of impedance matching between transmission
line and antenna. The standing wave is generated because of the impedance
mismatch at the port. VSWR equation is:

$$VSWR=\frac{1+\left|{S}_{11}\right|}{1-\left|{S}_{11}\right|}$$

`S`

is the reflection coefficient._{11}

d = dipole; vswr(d,20e6:1e6:120e6,72) axis([20 120 1 20])

VSWR is scalar and contains
no phase information. The value of VSWR lies between `1`

and
infinity. Antenna bandwidth is usually the frequency band over which
the VSWR is less than approximately 2.

Use `vswr`

to calculate
the voltage standing wave ratio for any antenna in Antenna
Toolbox.

*Bandwidth* describes the range of frequencies
over which the antenna can properly radiate or receive energy. It
is a fundamental antenna parameter. Often, the desired bandwidth is
one of the parameters used to determine which antenna to use. Antenna
bandwidth is usually the frequency band over which the magnitude of
the reflection coefficient is below -10 dB, or the magnitude of the
return loss is greater than 10 dB, or the VSWR is less than approximately
2. All these criteria are equivalent. You can control the bandwidth
using proper antenna design.

[1] Balanis, C.A. *Antenna Theory: Analysis and
Design*.3rd Ed. New York: Wiley, 2005.

[2] Stutzman, Warren L., and Thiele, Gary A. *Antenna
Theory and Design*. 3rd Ed. New York: Wiley, 2013.

[3] Bird, T.S. “Definition and Misuse of Return Loss.” *IEEE
Antennas and Propagation Magazine*. Vol. 51, Issue 2, April
2009, pp. 166–167.

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