## Port Analysis

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

*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:

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

where:

`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.

### Resonance

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.

### Reflection Coefficient

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}

### Return Loss

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:

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

where:

`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.

### Voltage Standing Wave Ratio

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:

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

where:

`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

*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.

## References

[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.