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Model amplifier in RF systems
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 = 2πf in the SimRF™ environment.
Nonlinear amplification is modeled as a polynomial (with the saturation power computed automatically). It also produces additional intermodulation frequencies.
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, [a_{0},a_{1},a_{2}, ... a_{9}], the polynomial it represents is:
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 [a_{0},a_{1},a_{2},a_{3}] specifies the relation 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 [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 V_{o} = V_{i}.
The default value of this parameter is 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.
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.
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.
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.
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_{k} is the residue of the pole A_{k}. If C_{k} 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™ 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.
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).
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.
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.
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.
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.
Specify the third-order intercept point of the amplifier. The default value is inf dBm, which corresponds to an unspecified point.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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).
Scale for the Y-axis.
The default value is Linear.
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.