Model amplifier in RF systems

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

Use the Amplifier block to model a linear or
nonlinear amplifier, with or without noise. Defining the amplifier
gain using a data source also defines input data visualization and
modeling. Use the **Main** tab parameters to specify
amplifier gain and noise using data sheet values, standard `s2p`

files,
S-parameters, or circuit envelope polynomial coefficients.

The amplifier is implemented as a polynomial, voltage-controlled voltage source (VCVS) except
when the amplifier gain is obtained from a `Data source`

. The
VCVS includes nonlinearities that are described using parameters listed in the
**Nonlinearity** tab. To model linear amplification, the amplifier
implements the relation *V*_{out} =
a_{1}**V*_{in} between the input and output voltages. The input voltage is *V*_{i}(*t*) =
*A*_{i}(*t*)e^{jωt}, and the output voltage is *V*_{o}(*t*) =
*A*_{o}(*t*)e^{jωt} at each carrier *w* = 2π*f* in the RF
Blockset™ environment.

In case the amplifier gain is obtained from a data source, amplifier implementation is based on S-parameter data.

Nonlinear amplification is modeled as a polynomial (with the saturation power computed automatically). It also produces additional intermodulation frequencies.

`Source of amplifier gain`

— Source parameter of the amplifier gain`Available power gain`

(default) | `Open circuit voltage gain`

| `Data source`

| `Polynomial coefficients`

Source parameter of the amplifier gain, specified as one of the following:

`Available power gain`

—**Available power gain**parameter is used to calculate the linear voltage gain term of the polynomial VCVS,*a*_{1}. This calculation assumes a matched load termination for the amplifier.`Open circuit voltage gain`

—**Open circuit voltage gain**parameter is used as the linear voltage gain term of the polynomial VCVS,*a*_{1}.`Data source`

—When using the data source option,

*S*_{11}and*S*_{22}, are used as the input and output impedances. The data sources are specified using either`Data file`

or`Network-parameters`

or`Rational model`

, depending on the value of`Data source`

.`Polynomial coefficients`

— The block implements a nonlinear voltage gain according to the specified polynomial coefficients

`Available power gain`

— Available power gain0

`dB`

(default) | scalar Available power gain of amplifier, specified as a scalar in dB. Specify the units from the corresponding drop-down list.

To enable this parameter, choose ```
Available power
gain
```

in the **Source of amplifier gain** tab.

`Open circuit voltage gain`

— Open circuit voltage gain0

`dB`

(default) | scalar Open circuit voltage of amplifier, specified as a scalar in dB. Specify the units from the corresponding drop-down list.

To enable this parameter, choose ```
Open circuit voltage
gain
```

in the **Source of amplifier gain** tab.

`Data source`

— Data source`Data File`

(default) | `Network-parameters`

| `Rational Model`

Data source, specified as one of the following:

`Data file`

— Name of a Touchstone file with the extension`.s2p`

.`Network-parameters`

— Provide**Network parameter**data such as`S-parameters`

,`Y-parameters`

, and`Z-parameters`

with corresponding**Frequency**and**Reference impedance (ohms)**for the amplifier.`Rational model`

— Provide values for**Residues**,**Poles**, and**Direct feedthrough**parameters which correspond to the equation for a rational model$$F(s)=\left({\displaystyle \sum _{k=1}^{n}\frac{{C}_{k}}{s-{A}_{k}}+D}\right)\begin{array}{cc},& s=j2\pi f\end{array}$$

In this rational model equation, each

*C*is the residue of the pole_{k}*A*. If_{k}*C*is complex, a corresponding complex conjugate pole and residue must also be enumerated. This object has the properties_{k}`C`

,`A`

, and`D`

. You can use these properties to specify the**Residues**,**Poles**, and**Direct feedthrough**parameters.

When the amplifier is nonlinear, the nonlinearity applies only to the S21 term of the scattering parameters representing the 2-port element. In this case, S21 is frequency-independent with its constant value being either the maximal value of S21, or the S21 value at an Operation frequency specified by the user. The other scattering parameters, S11, S12, and S22 remain the same as in the linear case.

To enable this parameter, select `Data source`

in **Source
of amplifier gain** tab.

`Polynomial coefficients`

— Polynomial coefficients`[0 1]`

(default) | vectorOrder of polynomial, specified as a vector.

The order of the polynomial must be less than or equal to 9. The
coefficients are ordered in ascending powers. If a vector has 10
coefficients,
`[`

, the
polynomial it represents is:`a`

_{0},`a`

_{1},`a`

_{2},
... `a`

_{9}]

*V _{out}* =

where

For example, the vector
`[`

specifies the relation `a`

_{0},`a`

_{1},`a`

_{2},`a`

_{3}]*V _{out}* =

`[``a`

_{0},`a`

_{1},`a`

_{2}]

defines the same polynomial as
`[``a`

_{0},`a`

_{1},`a`

_{2},
0]

. The default value of this parameter is [0,1],
corresponding to the linear relation
To enable this parameter, select ```
Polynomial
coefficients
```

in **Source of amplifier
gain** tab.

`Network parameter type`

— Network parameter type`S-parameters`

(default) | `Y-parameters`

| `Z-parameters`

Network parameter type, specified as `S-parameters`

, `Y-parameters`

,
or `Z-parameters`

.

To enable this parameter, first select `Data source`

in **Source
of amplifier gain** tab. Then, select `Network-parameters`

in
the **Data source** tab.

`Input impedance (Ohm)`

— Input impedance`50`

(default) | scalar Input impedance of amplifier, specified as a scalar.

To enable this parameter, select ```
Available power
gain
```

, `Open circuit voltage gain`

,
or `Polynomial coefficients`

in **Source
of amplifier gain** tab.

`Output impedance (Ohm)`

— Output impedance`50`

(default) | scalar Output impedance of amplifier, specified as a scalar.

To enable this parameter, select ```
Available power
gain
```

, `Open circuit voltage gain`

,
or `Polynomial coefficients`

in **Source
of amplifier gain** tab.

`Data file`

— Name of network parameter data file`simrfV2_unitygain.s2p`

(default) | character vectorName of network parameter data file, specified as a character vector.

To enable this parameter, first select `Data source`

in **Source
of amplifier gain** tab. Then, select `Data file`

in **Data
source**.

`Frequency (dB)`

— Frequency of network parameters`1e9 Hz`

(default) | scalar | `Hz`

| `kHz`

| `MHz`

| `GHz`

Frequency of network parameters, specified as a scalar in Hz.

To enable this parameter, first select `Data source`

in **Source
of amplifier gain** tab. Then, select `Network-parameters`

in **Data
source**.

`Reference Impedance(Ohm)`

— Reference impedance of network parameters`50`

(default) | scalar Reference impedance of network parameters, specified as a scalar.

To enable this parameter, first select `Data source`

in **Source
of amplifier gain** tab. Then, select `Network-parameters`

in **Data
source**.

`Residues`

— Residues in order of rational model`0`

(default) | vectorResidues in order of rational model, specified as a vector.

To enable this parameter, first select `Data source`

in **Source
of amplifier gain** tab. Then, select ```
Rational
model
```

in **Data source**.

`Poles`

— Residues in order of rational model`0`

(default) | vectorPoles in order of rational model, specified as a vector.

To enable this parameter, first select `Data source`

in **Source
of amplifier gain** tab. Then, select ```
Rational
model
```

in **Data source**.

`Direct feedthrough`

— Direct feedthrough `{0 0:1 0}`

(default) | array of vectorsDirect feedthrough, specified as an array vector.

To enable this parameter, first select `Data source`

in **Source
of amplifier gain** tab. Then, select ```
Rational
model
```

in **Data source**.

`Specify operation frequency`

— Specify operation frequency`on`

(default) | `off`

Select this option to specify operation frequency.

By default, this option is not selected.

To enable this parameter, first you should specify nonlinear
`Polynomial coefficients`

in
**Source of amplifier gain**. Then select
`Piece-wise linear`

or`Colored`

in **Noise
distribution** in the Noise pane.

`Operation frequency`

— Operation frequency`0`

(default) | scalar | vectorOperation frequency, specified as a scalar or vector in Hz.

To enable this parameter, first you should select **Specify
operation frequency**.

`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.

`Nonlinear polynomial type`

— Type of nonlinearity`Even and odd order`

(default) | `Odd order`

Type of nonlinearity, specified as ```
Even and odd
order
```

or `Odd order`

.

When you select

`Even and odd order`

, the amplifier can produce second- and third-order intermodulation frequencies in addition to a linear term.When you select

`Odd order`

, the amplifier generates only odd order intermodulation frequencies.The linear gain determines the linear

*a*_{1}term. The block calculates the remaining terms from the specified parameters. These parameters are**IP3**,**1-dB gain compression power**,**Output saturation power**, and**Gain compression at saturation**. The number of constraints you specify determines the order of the model. The figure shows the graphical definition of the nonlinear amplifier parameters.

`Intercept points convention`

— Intercept points convention`Output`

(default) | `Input`

Intercept points convention, specified a `Input`

-referred,
or `Output`

-referred convention. Use this
specification for the intercept points, 1-dB gain compression power,
and saturation power.

`IP2`

— Second-order intercept point`inf`

`dBm`

(default) | scalar | `W`

| `mW`

| `dBW`

| `dBm`

Second-order intercept point, specified as a scalar.

To set this parameter, select `Even and odd order`

in **Nonlinear
polynomial type**.

`IP3`

— Third-order intercept point`inf`

`dBm`

(default) | scalar | `W`

| `mW`

| `dBW`

| `dBm`

Third-order intercept point, specified as a scalar.

`1-dB gain compression power`

— 1-dB gain compression power`inf dBm`

(default) | scalar | `W`

| `mW`

| `dBW`

| `dBm`

1-dB gain compression power, specified as a scalar.

To set this parameter, select `Odd order`

in **Nonlinear
polynomial type**.

`Output saturation power`

— Output saturation power`inf dBm`

(default) | scalar | `W`

| `mW`

| `dBW`

| `dBm`

Output saturation power, specified as scalar. The block uses this value to calculate the voltage saturation point used in the nonlinear model. In this case, the first derivative of the polynomial is zero, and the second derivative is negative.

To set this parameter, select `Odd order`

in **Nonlinear
polynomial type**.

`Gain compression at saturation`

— Gain compression at saturation`inf dBm`

(default) | scalar | `W`

| `mW`

| `dBW`

| `dBm`

Gain compression at saturation, specified as scalar.

When **Nonlinear polynomial type** is ```
Odd
order
```

, specify the gain compression at saturation.

To set this parameter, first select `Odd order`

in **Nonlinear
polynomial type**. Then, change the default value of **Output
saturation power**

`Specify operation frequency`

— Specify operation frequency`on`

(default) | `off`

Select this option to specify operation frequency.

By default, this option is not selected.

To enable this parameter, the data source must be nonlinear or the noise should be colored.

`Operation frequency`

— Operation frequency`0`

(default) | scalar | vectorOperation frequency, specified as a scalar or vector in Hz.

To enable this parameter, first you should select **Specify
operation frequency**.

`Simulate noise`

— Simulate thermal noise`on`

(default) | `off`

Select this parameter, to simulate noise as specified in block parameters or on file.

If the noise is specified in an `.s2p`

file, then it is
used for simulation.

`Noise type`

— Noise type`Noise figure`

(default) | `Spot noise data`

Noise type, specified as `Noise figure`

or
`Spot noise data`

.

`Noise distribution`

— Noise distribution`White`

(default) | `Piece-wise linear`

| `Colored`

Noise distribution, specified as:

`White`

, spectral density is a single non-negative value. The power value of the noise depends on the bandwidth of the carrier and the bandwidth depends on the time step. This is an uncorrelated noise source.`Piece-wise linear`

, spectral density is a vector of values [p_{i}]. For each carrier, the noise source behaves like a white uncorrelated noise. The power of the noise source is carrier-dependent.`Colored`

, depends on both carrier and bandwidth. This is a correlated noise source.

`Noise figure (dB)`

— Noise figure0 (default) | scalar

Noise figure, specified as a scalar in decibels.

`Frequencies`

— Frequency data`0`

`Hz`

(default) | scalar | vectorFrequency data, specified as a scalar or vector in hertz.

To set this parameter, first select ```
Piece-wise
linear
```

or `Colored`

in
**Noise distribution**.

`Minimum noise figure (dB)`

— Minimum noise figure`0`

(default) | scalar | vectorMinimum noise figure, specified as a scalar or vector in decibels.

To set this parameter, first select ```
Spot noise
data
```

in **Noise type**.

`Optim reflection coefficient`

— Optim reflection coefficient`0`

(default) | scalar | vectorOptim reflection coefficient, specified as a scalar or a vector.

To set this parameter, first select ```
Spot noise
data
```

in **Noise type**.

`Equivalent normalized noise resistance`

— Equivalent normalized noise resistance`0`

(default) | scalar | vectorEquivalent normalized noise resistance, specified as a scalar or vector.

To set this parameter, first select ```
Spot noise
data
```

in **Noise type**.

`Automatically estimate impulse response duration`

— Automatically estimate impulse response duration`on`

(default) | `off`

Select this parameter to automatically calculate impulse response for
frequency dependent noises. Clear this parameter to manually specify the
impulse response duration using **Impulse response
duration**. You cannot specify impulse response when amplifier
is nonlinear, as in this case noise is simulated as white-noise.

To set this parameter, first select `Colored`

in **Noise distribution**.

`Impulse response duration`

— Impulse response duration`1e-10`

`s`

(default) | scalarImpulse response duration used to simulate frequency dependent noise, specified as a scalar in seconds. You cannot specify impulse response if the amplifier is nonlinear.

To set this parameter, first clear **Automatically estimate
impulse response duration**.

`Modeling options`

— Model S-parameters`Time-domain (rationalfit)`

(default) | `Frequency-domain`

Model S-parameters, specified as:

Time-domain (rationalfit) technique creates an analytical rational model that approximates the whole range of the data. When modeling using

`Time domain`

, the**Plot**in`Visualization`

tab plots the data defined in`Data Source`

and the values in the`rationalfit`

function.Frequency-domain 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.

For the Amplifier and S-parameters blocks, the default value is

`Time domain (rationalfit)`

. For the Transmission Line block, the default value is`Frequency domain`

.

To set this parameter, first select `Data source`

in **Source
of amplifier gain**. This selection activates the **Modeling** Tab
which contains **Modeling options**

`Fitting options`

— Rationalfit fitting options`Fit individually`

(default) | `Share poles by column`

| `Share all poles`

Rationalfit fitting options, specified as `Fit individually`

, ```
Share
poles by column
```

, or `Share all poles`

.

**Rational fitting results** shows values of **Number
of independent fits**, **Number of required poles**,
and **Relative error achieved (dB)**.

To set this parameter, select `Time domain (rationalfit)`

in **Modeling
options**.

`Relative error desired (dB)`

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

(default) | scalarRelative error acceptable for the rational fit, specified as a scalar.

To set this parameter, select `Time domain (rationalfit)`

in **Modeling
options**.

`Automatically estimate impulse response duration`

— Automatically calculate impulse response`on`

| `off`

Select this parameter to automatically calculate impulse response.
Clear this parameter to manually specify the impulse response duration
using **Impulse response duration**.

To set this parameter, select `Frequency domain`

in **Modeling
options**.

`Impulse response duration`

— Impulse response duration`1e-10`

(default) | scalarImpulse response duration, specified as a scalar.

To set this parameter, first select `Frequency domain`

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

.

`Use only S-parameter magnitude with appropriate delay`

— Use only S-parameter magnitude with appropriate delay`off`

(default) | `on`

Select this parameter to s-parameter phase and delay the impulse response by half its length. This parameter is applicable only for S-parameter data modeled in time domain. You can use this to shape spectral content with filter effects by specifying only magnitude.

This parameter introduces an artificial delay to the system.

`Source of frequency data`

— Frequency data source`Extracted from data source`

(default) | `User-defined`

Frequency data source, specified as:

When **Source of frequency data** is ```
Extracted
from data source
```

, the **Data source** must
be set to `Data file`

. Verify that the specified **Data
file** contains frequency data.

When **Source of frequency data** is `User-specified`

,
specify a vector of frequencies in the **Frequency data** parameter.
Also, specify units from the corresponding drop-down list.

To set this parameter, first select `Data source`

in **Source
of amplifier gain**. This selection activates the **Visualization** Tab
which contains **Source of frequency data**

`Frequency data`

— Frequency data range`[1e9:1e6:3e9]`

(default) | vector | `Hz`

| `kHz`

| `MHz`

| `GHz`

Frequency data range, specified as a vector

`Plot type`

— Type of data plot`X-Y plane`

(default) | `Polar plane`

| `Z Smith chart`

| `Y Smith chart`

| `ZY Smith chart`

Type of data plot that you want to produce with your data specified as one of the following:

`X-Y plane`

— Generate a Cartesian plot of your data versus frequency. To create linear, semilog, or log-log plots, set the**Y-axis scale**and**X-axis scale**accordingly.`Polar plane`

— Generate a polar plot of your data. The block plots only the range of data corresponding to the specified frequencies.`Z smith chart`

,`Y smith chart`

, and`ZY smith chart`

— Generate a Smith^{®}chart. The block plots only the range of data corresponding to the specified frequencies.

`Parameter 1`

— Type of S-Parameters to plot`S11`

(default) | `S12`

| `S21`

| `S22`

| `NF`

Type of S-Parameters to plot, specified as `S11`

, `S12`

,
`S21`

, or `S22`

. When noise is
spectral `NF`

plotting is possible.

`Parameter 2`

— Type of S-Parameters to plot`None`

(default) | `S11`

| `S12`

| `S21`

| `S22`

| `NF`

`S11`

, `S12`

,
`S21`

, or `S22`

. When noise is
spectral `NF`

plotting is possible.

`Format1`

— Plot format`Magnitude (decibels)`

(default) | `Angle(degrees)`

| `Real`

| `Imaginary`

Plot format, specified as `Magnitude (decibels)`

, `Angle(degrees)`

, `Real`

,
or `Imaginary`

.

`Format2`

— Plot format`Magnitude (decibels)`

(default) | `Angle(degrees)`

| `Real`

| `Imaginary`

Plot format, specified as `Magnitude (decibels)`

, `Angle(degrees)`

, `Real`

,
or `Imaginary`

.

`Y-axis scale`

— Y-axis scale`Linear`

(default) | `Logarithmic`

Y-axis scale, specified as `Linear`

or `Logarithmic`

.

`X-axis scale`

— X-axis scale`Linear`

(default) | `Logarithmic`

X-axis scale, specified as `Linear`

or `Logarithmic`

.

`Plot`

— Plot specified databutton

Plot specified data using plot button.

Noise figure represents only a subset of the noise information (spot noise data) needed to fully describe the noise behavior of a two-port device. When only noise figure is specified, RF Blockset amplifier defines the spot noise parameters in the following manner:

$$\begin{array}{l}N{F}_{\mathrm{min}}=NF\text{\hspace{0.17em}}({F}_{\mathrm{min}}={10}^{NF/10})\\ \text{\hspace{1em}}{R}_{n}={Z}_{0}\frac{{F}_{\mathrm{min}}-1}{4},\text{\hspace{1em}}{Z}_{0}\in \text{R}\\ \text{\hspace{1em}}\text{\hspace{1em}}\text{\hspace{1em}}{Y}_{opt}=\frac{1}{{Z}_{0}}\end{array}$$

Amplifier exhibits specified noise figure when source impedance is matched to the reference impedance ($$Z={Z}_{0},\text{\hspace{0.17em}}{Z}_{0}\in \text{R}$$).

Noise in RF Blockset amplifiers are represented as two correlated noise sources at the input port of a noiseless two-port:

The noise sources variance and correlation are governed by an ABCD-correlation matrix:

that is determined by measurable quantities:

$$\begin{array}{l}{C}_{A}=2kT\left(\begin{array}{cc}{R}_{n}& \frac{N{F}_{\mathrm{min}}-1}{2}-{R}_{n}{Y}_{opt}^{*}\\ \frac{N{F}_{\mathrm{min}}-1}{2}-{R}_{n}{Y}_{opt}& {R}_{n}{\left|{Y}_{opt}\right|}^{2}\end{array}\right)\\ \end{array}$$

NF

_{min}- Minimum noise figureR

_{n}- Equivalent noise resistanceY

_{opt}- Optimal source admittancek - Boltzman's constant

T - Noise temperature in Kelvin

.

The above quantities are specified in the amplifier from the noise data section in
the `.s2p`

file or directly as masked parameters in the noise pane.
In both cases:

NF

_{min}is specified in decibelsR

_{n}is specified as equivalent normalized resistance, R_{N}(`R`

)._{n}= Z_{0}R_{N}Y

_{opt}is specified in terms of optimal reflection coefficient, Γ_{opt}(`Y`

)._{opt}= Y_{0}(1-Γ_{opt})/(1+Γ_{opt})

In the above, `Z`

is the reference impedance that is
real. If the _{0} =
1/Y_{0}**Source of amplifier gain** is ```
Data
source
```

, the reference impedance is specified in the
`.s2p`

file or in the amplifier mask. Other wise the reference
impedance is 50 ohms.

The noise factor, F, of the amplifier is affected by the noisy source impedance,
Z_{s}, and is determined from the ABCD-correlation
matrix:

$$\begin{array}{l}F=1+\frac{{z}^{+}{C}_{A}z}{2kT\mathrm{Re}\left\{{Z}_{S}\right\}}\\ z=\left(\begin{array}{l}1\\ {Z}_{S}^{*}\end{array}\right)\end{array}$$

The noise figure, NF, is obtained from the noise factor using, ```
NF =
10log(F)
```

.

[1] Gonzalez, Guillermo. “Microwave Transistor Amplifiers: Analysis and Design”, Englewood Cliffs, N.J.: Prentice-Hall, 1984.

[2] Grob, Siegfried and Juergen Lindner. “Polynomial
Model Derivation of Nonlinear Amplifiers, *Department of
Information Technology*, University of Ulm, Germany.

[3] Kundert, Ken. “Accurate and Rapid
Measurement of IP _{2} and IP _{3}”, *The
Designers Guide Community*, Version 1b, May 22, 2002. http://www.designers-guide.org/analysis/intercept-point.pdf.

[4] Pozar, David M. “Microwave Engineering”, Hoboken NJ: John Wiley & Sons, 2005.

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