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Model antenna accounting for incident power wave (RX) and radiated power wave (TX)

**Library:**RF Blockset / Circuit Envelope / Elements

Model an antenna using the Antenna block:

Convert a Simulink

^{®}input of an incident power wave vector into an RF Blockset™ voltage at the antenna ports.Convert current at an RF Blockset antenna port to a Simulink output of a radiated power wave vector.

Introduce antenna impedance into an RF system.

By default, the antenna block is an isotropic radiator producing a Simulink output signal. For an isotropic radiator, specify the gain and impedance of the
antenna in the block parameters. The **Radiated carrier frequencies**
parameter is a set of carrier frequencies over-which the Antenna block creates
the radiated power wave. For more information, see Radiated Wave and Incident Wave.

`RX`

— Received signalscalar | vector | matrix |

Receiving signal, specified as a scalar, vector matrix, or an array of size
*m*-by-*n*-by-2.

**Data Types: **`double`

`TX`

— Transmitted signalscalar | vector | matrix |

Transmitting signal, specified as a scalar, vector, matrix, or an array of size
*m*-by-*n*-by-2

**Data Types: **`double`

`Source of antenna model`

— Antenna model`Isotropic radiator`

(default) | `Antenna Designer`

| `Antenna object`

Antenna model, specified as one of the following:

`Isotropic radiator`

`Antenna Designer`

`Antenna object`

**Note**

To use `Antenna Designer`

and ```
Antenna
object
```

options you will need Antenna Toolbox™.

`Create Antenna`

— Open Antenna Toolbox button

Open the **Antenna Designer** app from the Antenna Toolbox to create an antenna.

To enable this parameter, set the **Source of antenna model**
to `Antenna Designer`

.

`Antenna object`

— Antenna element input from workspace`antenna`

objectAntenna element input from the workspace, specified as a single port antenna element created using the Antenna Toolbox. Analyze the antenna object in the workspace for at least one frequency before using it in the block.

To enable this parameter, set **Source of antenna model** to
`Antenna object`

.

`Antenna Gain`

— Antenna gain`0`

`dBi`

(default) | real scalar or vector | positive scalar or vectorAntenna gain, specified as real scalar or vector if you set units to
`dBi`

or positive scalar or vector if you set units are
`None`

. If the antenna gain is a vector, the vector length must be
equal to the vector length of **Incident carrier frequencies** and
**Radiated carrier frequencies**.

To enable this parameter, set **Source of antenna model** to
`Isotropic radiator`

and check **Input incident
wave** or **Output radiated wave** or both

`Impedance (Ohm)`

— Input impedance`50`

(default) | complex-valued scalar or vectorInput impedance, specified as a complex-valued scalar or vector in ohms. If the
impedance is a vector, the vector length must be equal to the length of
**Incident carrier frequencies** and **Radiated carrier
frequencies**.

To enable this parameter, set **Source of antenna model** to
`Isotropic radiator`

.

**Data Types: **`double`

**Complex Number Support: **Yes

`Input incident wave`

— Input incident wave for simulating receiving antenna`'off'`

(default) | `'on'`

Select this parameter if you want to simulate a receiving antenna.

`Output radiated wave`

— Output radiated wave for transmitting antenna`'on'`

(default) | `'off'`

Select this parameter if you want a simulate a transmitting antenna.

`Incident carrier frequencies`

— Carrier frequencies for receiving signal`2.1`

`GHz`

(default) | nonnegative scalar or row vectorCarrier frequencies for a receiving signal, specified as a nonnegative scalar in
hertz or a row vector with each element unit in hertz. If the value of
**Antenna gain** or **Impedance** is a vector,
then the values of **Incident carrier frequencies** and
**Radiated carrier frequencies** must be identical.

To enable this parameter, select **Input incident
wave**.

`Radiated carrier frequencies`

— Carrier frequencies for transmitting signal`2.1`

`GHz`

(default) | nonnegative scalar or row vectorCarrier frequencies for a transmitting signal, specified as a nonnegative scalar
in hertz or a row vector with each element unit in hertz. If the value of
**Antenna gain** or **Impedance** is a vector,
then the values of **Incident carrier frequencies** and
**Radiated carrier frequencies** must be identical.

To enable this parameter, select **Output radiated
wave**.

`Direction of departure`

— Azimuth and elevation angles towards which output signal power wave radiates`[0 0]`

`deg`

(default) | finite real row vectorAzimuth and elevation angles towards which the output signal power wave radiates, specified as a finite real row vector of length two with each element unit in degrees or radians.

To enable this parameter, set **Source of antenna model** to
`Antenna Designer`

or ```
Antenna
object
```

and select **Output radiated
wave**.

`Direction of arrival`

— Azimuth and elevation angles from which input signal power wave arrives`[180 0]`

`deg`

(default) | finite real row vectorAzimuth and elevation angles towards which the input signal power wave arrives, specified as a finite real row vector of length two with each element unit in degrees or radians.

To enable this parameter, set **Source of antenna model** to
`Antenna Designer`

or ```
Antenna
object
```

and select **Input incident wave**.

`Simulate noise`

— Simulate thermal noise`'on'`

(default) | `'off'`

Select this parameter to simulate thermal noise in the antenna due to the real
part of the impedance see at the antenna terminals. You must select **Simulate
noise** in the Configuration block also.

`Ground and hide negative terminals`

— Ground RF circuit terminals`'on'`

(default) | `'off'`

Select this option to ground and hide the negative terminals. Clear this parameter to expose the negative terminals. By exposing these terminals, you can connect them to other parts of your model.

By default, this option is selected.

`Modeling options`

— Model frequency-dependent antenna parameters`Time-domain (rationalfit)`

(default) | `Frequency-domain`

Model frequency-dependent antenna parameters, specified as:

`Time-domain (rationalfit)`

— This technique creates an analytical rational model that approximates the whole range of the data.`Frequency-domain`

— This technique computes the baseband impulse response for each carrier frequency independently. This technique is based on convolution. There is an option to specify the duration of the impulse response. For more information, see Compare Time and Frequency Domain Simulation Options for S-parameters.

The frequency-dependent parameters are:

Antenna impedance — The input impedance at the antenna terminals. This is used in RF system simulation.

Normalized vector effective length — A property used that ties between the current flowing at the antenna terminals and the radiated far-field at a given direction. Due to reciprocity, the effective length also ties between the incident field and the induced open-circuit voltage on the antenna terminals.

To set source **Source of antenna model** of
`Antenna Designer`

or ```
Antenna
object
```

to activate the **Modeling** Tab that
contains the **Modeling options** parameters.

`Relative error desired (dB)`

— Relative error acceptable for the rational fit`-40`

(default) | scalarRelative error acceptable for the rational fit, specified as a scalar. Applies to time-domain modeling of both antenna impedance and normalized vector effective length. The corresponding rational fitting results for each property are displayed on the block mask.

To set **Modeling options** to ```
Time domain
(rationalfit)
```

in .

`Automatically estimate impulse response duration`

— Automatically calculate impulse response`'on'`

| `'off'`

Select this parameter to automatically calculate the impulse response duration.
Clear this parameter to manually specify the impulse response duration using
**Impulse response duration**. Applies to frequency-domain modeling
of both antenna impedance and normalized vector effective length.

To set this parameter, select `Frequency domain`

in
**Modeling options**.

`Impulse response duration`

— Impulse response duration`1e-10`

`s`

(default) | scalarImpulse response duration, specified as a scalar. Applies to frequency-domain modeling of both antenna impedance and normalized vector effective length.

To set this parameter, first select `Frequency domain`

in **Modeling options**. Then, clear ```
Automatically
estimate impulse response duration
```

.

The antenna block produces a Simulink signal representing a normalized power wave similar to power waves in circuits. Since an antenna radiates two independent field components in the far field, the signal is extended into the third dimension:

$$\begin{array}{l}TX\left(:,:,1\right)=T{X}_{\theta}=\frac{{E}_{\theta}}{\sqrt{{\eta}_{0}}}\xb7\sqrt{4\pi}\xb7R\xb7{e}^{j\gamma R}\\ TX\left(:,:,2\right)=T{X}_{\phi}=\frac{{E}_{\varphi}}{\sqrt{{\eta}_{0}}}\xb7\sqrt{4\pi}\xb7R\xb7{e}^{j\gamma R}\end{array}$$

where

and*E*_{θ}

are the electric field components radiated from the antenna and measured at a far-field location in the direction of departure.*E*_{φ}

is the free-space intrinsic impedance*η*_{0}

is the distance to the far-field measurement location.*R*$$\gamma =\frac{j\omega}{c}$$ where

*ω*is the angular frequency and

is the speed of light in free space.*c*

The above definition makes the transmit (TX) signal independent of the
distance

. The total power carried by this
normalized radiated power wave is the equivalent isotropically radiated power wave (EIRP) of
the transmitter in the direction of departure:*R*

$${\Vert TX\Vert}^{2}={\left|T{X}_{\theta}\right|}^{2}+{\left|T{X}_{\varphi}\right|}^{2}=EIRP={P}_{t}{G}_{t}$$

where total

is the input power at the antenna terminals*P*_{t}

is transmitter antenna gain at the direction of departure.*G*_{t}

The EIRP is a commonly used concept in communication systems. This value represents the amount of power radiated from an isotropic antenna such that the same power density is obtained in the direction of departure.

In case of an isotropic radiator, you resolve the ambiguity in polarization by assuming that the antenna is radiating a single field component. You also assume that this field component is always aligned for full reception by a receiving antenna. Thus, the TX signal and the expected RX in a receiving antenna is two dimensional. Following the above definitions, the transmit signal for an isotropic radiator is:

$$TX(:,:)=\sqrt{{G}_{t}{R}_{e}\left\{{Z}_{in}\right\}}.{I}_{in}$$

where:

is the input impedance of the antenna.*Z*_{in}

is the current at antenna terminals.*I*_{in}

In all definitions of TX, the array elements are arranged in the first two dimensions in a manner similar to the of the output signal of an RF Blockset Outport block. If the signal is framed, the column size corresponds to the number of frame bits and the row size corresponds to the number of carrier frequencies. If the signal is not framed, then the column size corresponds to the number of carrier frequencies and the row size is one.

The effect of free space channel between the antennas is not captured by antenna block. You can model it externally using Simulink blocks. For a free-space channel the effect is given by the transfer function:

$$pl=\frac{\lambda}{4\pi R}\xb7{e}^{-j\gamma R}$$

where

*λ*is the wavelength modeled outside the antenna.

is the distance between the antennas*R*Exponential term at the end of the equation represents the time delay occurring over the distance

.*R*

is free-space path loss.*pl*

You can model a free-space channel using the Communications Toolbox™ Free Space Path Loss (Communications Toolbox). The effect of the power wave is described using the Friis equation. The Free Space Path Loss block operates for a single carrier frequency and is narrow band. for multiple carriers with narrow bands, the signal must be split and passed through multiple Free Space Path Loss blocks. with carrier frequencies specified in the Antenna block. When the Antenna blocks are not isotropic radiators, the output signal is a 3D array and needs to be split and reshaped before being send to the Free Space Path Loss

The antenna block can also accept a Simulink signal representing a normalized incident power wave. Since an antenna also receives two independent field components, the signal is extended in the third dimension:

$$\begin{array}{l}RX(:,:,1)=R{X}_{\theta}=T{X}_{\theta}\xb7pl=\frac{{E}_{\theta}}{\sqrt{{\eta}_{0}}}\xb7\frac{\lambda}{\sqrt{4\pi}}\\ RX(:,:,2)=R{X}_{\varphi}=T{X}_{\varphi}\xb7pl=\frac{{E}_{\varphi}}{\sqrt{{\eta}_{0}}}\xb7\frac{\lambda}{\sqrt{4\pi}}\end{array}$$

where

and*TX*_{θ}

are signals from transmitting antenna.*TX*_{φ}

free-space channel transfer function.*pl*

and*E*_{θ}

are the electrical field components measured from transmitting antenna.*E*_{φ}

is the free-space intrinsic impedance.*η*_{0}

is the wavelength.*λ*`RX`

is the incident power wave normalized such that is the power received by the isotropic antenna.

Using the above equations, the total power carried by the normalized incident power wave, $${\Vert RX\Vert}^{2}={\left|R{X}_{\theta}\right|}^{2}+{\left|R{X}_{\varphi}\right|}^{2}$$ is available power received by ideal isotropic receiving antenna. The available power received by a true antenna is:

$${P}_{r}={\Vert RX\Vert}^{2}{G}_{r}$$

where

is the receiver
antenna gain at the direction of arrival.*G _{r}*

In case the receiving antenna is an isotropic radiator, you can resolve the ambiguity in polarization by assuming that the antenna is receiving a single field component that it is aligned for full reception. Thus, the RX signal is expected to be two dimensional. In all definitions of the RX signal, the array elements are arranged in the first two dimensions in a manner similar to that of the input signal of an RF Blockset Inport block.

[1] Stutzman, Warren L., and Gary A.
Thiele. *Antenna Theory and Design*. 3rd ed. Hoboken, NJ:
Wiley, 2013

[2] Farr, Everett G. “Characterizing
Antennas in the Time and Frequency Domains [Education Corner].” *IEEE Antennas and
Propagation Magazine* 60, no. 1 (February 2018): 106–10.
https://doi.org/10.1109/MAP.2017.2774200.

Amplifier | S-Parameters | Free Space Path Loss (Communications Toolbox)

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