Model amplifier in RF systems

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). 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 SimRF™ environment.

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

**Source of amplifier gain**Specify the source parameter of the amplifier gain as:

`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`

— Linear voltage gain term of the polynomial VCVS is calculated from the specified data source options:for the maximal value of

*S*_{21}.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 polynomial you specify. 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}*a*_{0}+*a*_{1}*V*+_{in}*a*_{2}*V*_{in}^{2}+ ... +*a*_{9}*V*_{in}^{9}

where*a*_{1}represents the linear gain term, and higher-order terms are modeled according to [2].For example, the vector

`[`

specifies the relation,`a`

_{0},`a`

_{1},`a`

_{2}]`a`

_{3}*V*=_{o}*a*_{0}+*a*_{1}*V*+_{1}*a*_{2}*V*_{1}^{2}+*a*_{3}*V*_{1}^{3}. Trailing zeroes are omitted. If*a*_{3}= 0, then`[`

defines the same polynomial as,`a`

_{0},`a`

_{1}]`a`

_{2}`[`

. The default value of this parameter is [0,1], corresponding to the linear relation,`a`

_{0},`a`

_{1}, 0]`a`

_{2}*V*=_{o}*V*._{i}The default value of this parameter is

`Available power gain`

.

**Available power gain**When you set the

**Source of amplifier gain**parameter to`Available power gain`

, you can specify the available power gain of the amplifier. Specify the units from the corresponding drop-down list.The default value of this parameter is

`0`

`dB`

.**Open circuit voltage gain**When you set the

**Source of amplifier gain**to`Open circuit voltage gain`

, you can specify the open circuit voltage gain of the amplifier. Specify the units from the corresponding drop-down list.The default value of this parameter is

`0`

`dB`

.**Input impedance (ohms)**When you set the

**Source of amplifier gain**to`Available power gain`

,`Open circuit voltage gain`

, or`Polynomial coefficients`

, you can specify the scalar input impedance of the amplifier.The default value of this parameter is

`50`

ohms.**Output impedance (ohms)**When you set the

**Source of amplifier gain**to`Available power gain`

,`Open circuit voltage gain`

, or`Polynomial coefficients`

, you can specify the scalar output impedance of the amplifier.The default value of this parameter is

`50`

ohms.**Data source**When you set

**Source of amplifier gain**to`Data source`

, you can specify the data source as either`Data file`

or`Network-parameters`

or`Rational model`

.`Data file`

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

. The block ignores noise and nonlinearity data in imported files.`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. The example, Model an RF Filter Using S-Parameter Data, shows how to use the RF Toolbox™_{k}`rationalfit`

function to create an`rfmodel.rational`

object. This object has the properties`C`

,`A`

, and`D`

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

**Noise figure (dB)**Specify the noise figure of the amplifier. The default value of this parameter is

`0`

dB, which implies that no noise is added to the system by this block.You can model noise in a SimRF model with a Noise, Resistor, Amplifier, or Mixer block. To do so, in the Configuration block dialog box, verify that the

**Simulate noise**check box is selected (default).**Ground and hide negative terminals**Select this option to internally ground and hide the negative terminals. Clear this 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**Specify either an

`Even and odd order`

or`Odd order`

polynomial nonlinearity. The default value is`Even and 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 preceding figure shows the graphical definition of the nonlinear amplifier parameters.

**Intercept points convention**Specify either an

`Input`

-referred or`Output`

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

`Output`

.**IP2**When

**Nonlinear polynomial type**is`Even and odd order`

, specify the second-order intercept point of the amplifier.The default value is

`inf`

`dBm`

, which corresponds to an unspecified point.**IP3**Specify the third-order intercept point of the amplifier. The default value is

`inf`

`dBm`

, which corresponds to an unspecified point.**1-dB gain compression power**When

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

, specify the 1-dB gain compression point. The 1-dB gain compression point must be less than the output saturation power.The default value is

`inf`

`dBm`

, which corresponds to an unspecified point.**Output saturation power**When

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

, specify the output saturation power. 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.The default value is

`inf`

`dBm`

, which corresponds to an unspecified point in the polynomial model.**Gain compression at saturation**When

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

, specify the gain compression at saturation. This parameter cannot be set unless**Output saturation power**is specified.The default value is

`inf`

`dBm`

.

Setting **Source of amplifier gain** to ```
Data
source
```

activates the **Modeling** Tab.

**Modeling options**SimRF provides two different ways to model S-parameters:

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

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`

.

`Time domain`

**Fitting options**The fitting options are

`Share all poles`

,`Share poles by columns`

, or`Fit individually`

.For the Amplifier block, the default value is

`Fit individually`

. For the S-parameters block and Transmission Line block, the default value is`Share all poles`

.**Relative error desired (dB)**Enter the desired relative error in decibels (dB). The default value is

`-40`

.**Rational fitting results**Shows values of

**Number of independent fits**,**Number of required poles**, and**Relative error achieved (dB)**.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`

**Automatically estimate impulse response duration**Select

**Automatically estimate impulse response duration**to calculate impulse response duration automatically. Clear the selection to specify impulse response duration.When using

`Frequency domain`

, the**Plot**in`Visualization`

tab plots the data defined in the`Data Source`

.

Setting **Source of amplifier gain** to ```
Data
source
```

activates the Visualization tab.

**Source of frequency data**Frequency data source. 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.For the Amplifier and S-parameters blocks, the default value is

`Extracted from source data`

. For the Transmission Line block, the default value is`User-specified`

.**Plot type**Specify the type of plot that you want to produce with your data. The

**Plot type**parameter provides the following options:`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.

The default value is

`X-Y plane`

.**Parameter #**Specify the S-parameters to plot. From the

**Parameter1**and**Parameter2**drop-down lists, select the S-parameters that you want to plot. If you specify two parameters, the block plots both parameters in a single window.The default value for

**Parameter1**is`S11`

. For the Amplifier and S-parameters blocks, the default value for**Parameter2**is`None`

. For the Transmission Line block, the default value for**Parameter2**is`S22`

.**Format #**For

*X-Y*plots, format the units of the parameters to plot from the**Format1**and**Format2**drop-down lists. For polar plots and Smith charts, the formats are set automatically.The default value is

`Magnitude (decibels)`

.**Y-axis scale**Scale for the

*Y*-axis.The default value is

`Linear`

.**X-axis scale**Scale for the

*X*-axis.The default value is

`Linear`

.

Circuit Envelope Simulation to Amplify Signals

The example, Validating IP2/IP3 Using Complex Signals, verifies the nonlinear modeling capabilities of the amplifier block.

The example, Impact of an RF Receiver on Communication System Performance, performs quantitative noise analysis of the noise from an RF cascade.

The example, Create a Low-IF Receiver Model, uses an amplifier in an IF receiver with specified gain and noise figure.

[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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