Antenna

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

• Library:

• RF Blockset / Circuit Envelope / Elements

• 

Description

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.

Ports

Input

RX — Received signal

scalar | vector | matrix | m-by-n-by-2 array

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

Data Types: double

Output

TX — Transmitted signal

scalar | vector | matrix | m

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

Data Types: double

Parameters

Main

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 Antenna Designer app

button

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

Dependencies

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

Antenna object — Antenna element input from workspace

antenna object

Antenna 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.

Dependencies

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 vector

Antenna 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.

Dependencies

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 vector

Input 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.

Dependencies

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 vector

Carrier 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.

Dependencies

To enable this parameter, select Input incident wave.

Radiated carrier frequencies — Carrier frequencies for transmitting signal

2.1 GHz (default) | nonnegative scalar or row vector

Carrier 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.

Dependencies

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 vector

Azimuth 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.

Dependencies

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 vector

Azimuth 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.

Dependencies

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

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.

Dependencies

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) | scalar

Relative 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.

Dependencies

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.

Dependencies

To set this parameter, select Frequency domain in Modeling options.

Impulse response duration — Impulse response duration

1e-10s (default) | scalar

Impulse response duration, specified as a scalar. Applies to frequency-domain modeling of both antenna impedance and normalized vector effective length.

Dependencies

To set this parameter, first select Frequency domain in Modeling options. Then, clear Automatically estimate impulse response duration.

Model Examples

Simulation of RF Systems with Antenna Blocks

Use the antenna block to incorporate the effect of an antenna into an RF simulation. In this model, a single tone is fed to the transmitter and the power of the received signal at the output of the receiver is calculated.

More About

Radiated Wave

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:

$$\begin{array}{l}TX\left(:,:,1\right)=T{X}_{\theta }=\frac{E_{\theta }}{\sqrt{{\eta }_0}}·\sqrt{4\pi }·R·e^{j\gamma R}\\ TX\left(:,:,2\right)=T{X}_{\phi }=\frac{E_{\varphi }}{\sqrt{{\eta }_0}}·\sqrt{4\pi }·R·e^{j\gamma R}\end{array}$$

where

• Eθ and Eφ are the electric field components radiated from the antenna and measured at a far-field location in the direction of departure.

• η0 is the free-space intrinsic impedance

• R is the distance to the far-field measurement location.

• $$\gamma =\frac{j\omega }{c}$$ where ω is the angular frequency and c is the speed of light in free space.

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

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

where total

• Pt is the input power at the antenna terminals

• Gt is transmitter antenna gain at the direction of departure.

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:

• Zin is the input impedance of the antenna.

• Iin is the current at antenna terminals.

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.

Effect of Free Space Channel

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:

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

where

• λ is the wavelength modeled outside the antenna.

• R is the distance between the antennas

• Exponential term at the end of the equation represents the time delay occurring over the distance R.

• pl is free-space path loss.

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

Incident Wave

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:

$$\begin{array}{l}RX(:,:,1)=R{X}_{\theta }=T{X}_{\theta }·pl=\frac{E_{\theta }}{\sqrt{{\eta }_0}}·\frac{\lambda }{\sqrt{4\pi }}\\ RX(:,:,2)=R{X}_{\varphi }=T{X}_{\varphi }·pl=\frac{E_{\varphi }}{\sqrt{{\eta }_0}}·\frac{\lambda }{\sqrt{4\pi }}\end{array}$$

where

• TXθ and TXφ are signals from transmitting antenna.

• pl free-space channel transfer function.

• Eθ and Eφ are the electrical field components measured from transmitting antenna.

• η0 is the free-space intrinsic impedance.

• λ is the wavelength.

• 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 Gr is the receiver antenna gain at the direction of arrival.

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.

References

[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.