Antenna
Model antenna or antenna array accounting for incident power wave (RX) and radiated power wave (TX)
Since R2020b
Libraries:
RF Blockset /
Circuit Envelope /
Elements
Description
Model an antenna or antenna array using the Antenna block. Use this block to:
Convert a Simulink^{®} input of an incident power wave vector into RF Blockset™ voltage signal at the antenna or antenna array ports.
Convert current at RF Blockset antenna or antenna array ports 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 overwhich the Antenna block creates the radiated power wave. For more information, see Radiated Wave and Incident Wave.
The Antenna block mask icons are dynamic: The icons show the current state
of the noise parameter, indicate if you have specified an antennaarray
object
in the Antenna object
parameter, and update the number of ports based on the number of elements in the
antennaarray
object. This table shows how the block icons vary based on the
state of the Simulate noise
and Antenna object
parameters.
Antenna object  Simulate noise: on  Simulate noise: off 

Antenna Catalog Objects 


Antenna Array Catalog Objects 


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.
Set the Antenna_TX and Antenna_RX blocks to be isotropic radiators with the following parameters:
The following values are set upon loading the model:
R
=100
[m]FreqCarrier
=5.0
[GHz]Gt
=Gr
=7.9988
[dBi]Zin_t
=Zin_r
=56.2947  4.2629i
[Ohm]
where the antenna gains and impedances were calculated beforehand from dipoles backed by circular reflectors.
With Antenna Toolbox™, it is possible to design the antenna using the Antenna Designer app invoked directly from the block. To do so, change the choice of Source of the antenna model to Antenna Designer and press the Create antenna button. Within the Antenna Designer
app, create a new antenna, choose Dipole from the Antenna Gallery , Circular from the Backing Structure Gallery
in the app toolstrip and select Accept. Note that the design frequency was prepopulated with the RF system frequency of 5 GHz.
Select the Impedance button in the app toolstrip to analyze the structure and select the Update Block button to update the block with the chosen antenna. Note that the Antenna block requires that the designed antenna be analyzed for at least one frequency in the Antenna Designer app before updating and using it in the block.
In the Antenna_TX block mask parameter dialog box, change the default Direction of departure to 0
degrees in azimuth and 90
degrees in elevation:
Repeat the above steps to design Antenna_RX. However, the receiving antenna needs to be rotated to face the transmitting antenna. To do so, in the Antenna Properties panel of the Antenna Designer app, set Tilt to 180
degrees. Again, select the Impedance button and then press the Update Block button to update the block. In the Antenna_RX block mask parameter dialog box, change the Direction of arrival to 180
degrees in azimuth and 90
degrees in elevation. – 90degree elevation is chosen since the radiated signal that was transmitted in the positive z direction in the coordinate system of the transmitter, is now arriving from the negative z direction in the coordinate system of the receiver. Azimuth is set to 180 degrees to align vector fields of the transmitter and receiver antennas.
Run the model again, and note that the output power remained almost exactly the same. This is since the original gain and impedance values used for the isotropically radiating antenna in the beginning were calculated from the same antennas and spatial settings. However, it is now possible to change the antenna properties and observe the effect on the output power in the model. For example: Select the 'Edit Antenna' button in the Antenna_TX block mask parameter dialog box to reopen the Antenna Designer app. In the Antenna Properties panel of the Antenna Designer app, change Tilt to 30
degrees and the TiltAxis to [0 1 0]
. Select the Impedance button and then press the Update Block button to update the block. Rerun the model to observe reduction of 2.5 dB in the output received power due to the mismatch in antenna orientation.
Use Measured Antenna Object in Antenna Block
Since R2023b
This example shows how to use measuredAntenna
object in the Antenna block to model a measured antenna or array characterized by means of its Sparameters and frequency dependent farfield radiation pattern including both polarization components. The measuredAntenna
object lets you replace the physical antennas from the antenna catalog with measured field data of the antenna. This example extracts data from a linear array to create a measuredAntenna
object using hcreate_mAnt
helper function.
System Configuration
Define the carrier frequency in Hz and set it in these parameters:
Radiated carrier frequency parameter in the Transmit Antenna block
Incident carrier frequency parameter in the Receiver Antenna block
Carrier frequencies parameter in the Inport and Outport blocks
FreqCarrier = 5e9;
Define gain for the Gain block. This Gain block acts as a freespace pathloss channel.
lambdaCarrier = physconst('lightspeed')/FreqCarrier; %[m]
Define the input impedance of the low noise amplifier (LNA) in ohms.
Zin_r =71.3819  1j*2.1795;
Define the available input power in dBm for the two RF transmitter chains and assign the variables to Pin 1 and Pin 2 in the Constant block.
Pin1 = 30; Pin2 = 30;
Create a linear antenna array and extract data from it to create a measuredAntenna
object. The data extracted from the linear array is a substitute of realworld measured data that can be inputted by changing the hcreate_mAnt
helper function so as to read the embedded electric fields from data file.
dist = lambdaCarrier*0.5; d1 = design(dipole,FreqCarrier); antElems = [d1 copy(d1)]; la = linearArray('Element',antElems,'ElementSpacing',dist); la.TiltAxis = [0 1 0]; la.Tilt = 90; freqRange = (4.5:0.05:5.5)*1e9; [mAnt,R] = hcreate_mAnt(la,freqRange);
Compute impedances in ohms for PA and PA1 Amplifier blocks in the transmitter.
z = impedance(la,freqRange); z = z(freqRange==FreqCarrier,:); Zin_t1 = z(1); Zin_t2 = z(2);
Simulate Model
Open and simulate the measuredAnt.slx
model. Observe the output power at the receiver.
open_system("measuredAnt.slx") sim("measuredAnt.slx");
Extended Examples
Ports
Input
RX — Received signal
scalar  vector  matrix  mbynbyk
array
Received signal, specified as a scalar, vector, matrix, or an array of size mbynbyk. In the array:
m — Represents the frame size
n — Represents the number of interferers
k — Represents horizontal or vertical polarization. The value of the k must be 2.
Data Types: double
Output
TX — Transmitted signal
scalar  vector  matrix  mbynbyk
array
Transmitted signal, specified as a scalar, vector, matrix, or an array of size mbynbyk. IN the array:
m — Represents the frame size
n — Represents the number of interferers
k — Represents horizontal or vertical polarization. The value of the k must be 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 or array element input from workspace
antenna catalog object  antenna array catalog object  measuredAntenna
object  pcbstack
object
Antenna or array element input from the workspace, specified as one of these objects:
Antenna catalog — Use any one of the antenna objects from the Antenna Catalog (Antenna Toolbox).
Array catalog — Use any one of the array objects from the Array Catalog (Antenna Toolbox). You can specify an array with a maximum of 65 ports.
Measured antenna — Use
measuredAntenna
object to model a measured antenna or array characterized by its Sparameters and frequencydependent farfield radiation pattern that includes both the polarization components. You can model an array with a maximum of 65 ports. (since R2023b)PCB stack — Use
pcbStack
(Antenna Toolbox) object to model a singlefeed or multifeed PCB antenna.
Note
Analyze the antenna, array, or PCB stack objects in the workspace for at least one frequency before using them 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)  complexvalued scalar or vector
Input impedance, specified as a complexvalued 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 of length 1by2  finite real matrix of length mby2
Azimuth and elevation angles towards which the output signal power wave radiates, specified as a finite real row vector of length 1by2 or finite real matrix of length mby2 (since R2023a) with each element unit in degrees or radians. m is an integer between in the range [2, 100].
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 of length 1by2  finite real matrix of length mby2
Azimuth and elevation angles towards which the input signal power wave arrives, specified as a finite real row vector of length 1by2 or finite real matrix of length mby2 (since R2023a) with each element unit in degrees or radians. m is an integer between in the range [2, 100].
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.
Modeling
Modeling options — Model frequencydependent antenna parameters
Time domain (rationalfit)
(default)  Frequency domain
Model frequencydependent 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 Sparameters.
The frequencydependent 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 farfield at a given direction. Due to reciprocity, the effective length also ties between the incident field and the induced opencircuit 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 enable this property, set Modeling options to
Time domain (rationalfit)
.
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 frequencydomain modeling of both antenna impedance and normalized vector effective length.
Dependencies
To set this parameter, set Modeling options to
Frequency domain
.
Impulse response duration — Impulse response duration
1e10
s
(default)  scalar
Impulse response duration, specified as a scalar. Applies to frequencydomain 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.
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:
$$\begin{array}{l}TX\left(:,:,1\right)=T{X}_{\theta}=\frac{{E}_{\theta}}{\sqrt{{\eta}_{0}}}\xb7\sqrt{4\pi}\xb7R\xb7{e}^{\gamma R}\\ TX\left(:,:,2\right)=T{X}_{\phi}=\frac{{E}_{\varphi}}{\sqrt{{\eta}_{0}}}\xb7\sqrt{4\pi}\xb7R\xb7{e}^{\gamma R}\end{array}$$
where
E_{θ}
andE_{φ}
are the electric field components radiated from the antenna and measured at a farfield location in the direction of departure.η_{0}
is the freespace intrinsic impedanceR
is the distance to the farfield 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:
$${\Vert TX\Vert}^{2}={\leftT{X}_{\theta}\right}^{2}+{\leftT{X}_{\varphi}\right}^{2}=EIRP={P}_{t}{G}_{t}$$
where total
P_{t}
is the input power at the antenna terminalsG_{t}
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:
Z_{in}
is the input impedance of the antenna.I_{in}
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 freespace channel the effect is given by the transfer function:
$$pl=\frac{\lambda}{4\pi R}\xb7{e}^{\gamma R}$$
where
λ is the wavelength modeled outside the antenna.
R
is the distance between the antennasExponential term at the end of the equation represents the time delay occurring over the distance
R
.pl
is freespace path loss.
You can model a freespace 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:
$$\begin{array}{l}RX(:,:,1)=R{X}_{\theta}=T{X}_{\theta}\xb7pl=\frac{{E}_{\theta}}{\sqrt{{\eta}_{0}}}\xb7\frac{\lambda}{\sqrt{4\pi}}\\ RX(:,:,2)=R{X}_{\varphi}=T{X}_{\varphi}\xb7pl=\frac{{E}_{\varphi}}{\sqrt{{\eta}_{0}}}\xb7\frac{\lambda}{\sqrt{4\pi}}\end{array}$$
where
TX_{θ}
andTX_{φ}
are signals from transmitting antenna.pl
freespace channel transfer function.E_{θ}
andE_{φ}
are the electrical field components measured from transmitting antenna.η_{0}
is the freespace 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, $${\Vert RX\Vert}^{2}={\leftR{X}_{\theta}\right}^{2}+{\leftR{X}_{\varphi}\right}^{2}$$ 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 G_{r}
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.
Version History
Introduced in R2020bR2023b: Model antenna using measuredAntenna
object
The Antenna block in the Circuit Envelope library now supports the
measuredAntenna
object. Specify this object to model a measured antenna
or array characterized by its Sparameters and frequencydependent farfield radiation
pattern that includes both the polarization components.
R2023a: Multiple directions of arrival and departure in Antenna block
You can now use the Antenna block to transmit and receive signals in multiple directions using the Direction of arrival and Direction of departure properties.
R2022a: Model transmit and receive antenna array
To model a transmit and receive antenna, specify an antenna array from the Array Catalog (Antenna Toolbox) in the Antenna object parameter.
R2021b: Antenna block icon updated
The Antenna block icon was updated in R2021b. The block icon is now dynamic and shows the current state of the noise parameter.
When you open a model created before R2021b containing an Antenna block, the software replaces the block icon with the R2021b version.
See Also
Amplifier  SParameters  Free Space Path Loss (Communications Toolbox)
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