Model amplifier in RF systems
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,
Sparameters, or circuit envelope polynomial coefficients.
The amplifier is implemented as a polynomial, voltagecontrolled 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 = 2πf in the RF Blockset™ environment.
In case the amplifier gain is obtained from a data source, amplifier implementation is based on Sparameter data.
Nonlinear amplification is modeled as a polynomial (with the saturation power computed automatically). It also produces additional intermodulation frequencies.
Amplifier block mask icons are dynamic and show the current state of the applied noise parameter. This table shows you how the icons on this block vary based on the state of the Noise figure (dB) parameter on the block.
Noise Figure (dB): 10  Noise Figure (dB): 0 



Source of amplifier gain
— Source parameter of the amplifier gainAvailable 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 Networkparameters
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 gaindB
(default)  scalar Available power gain of amplifier, specified as a scalar in dB. Specify the units from the corresponding dropdown list.
To enable this parameter, choose Available power
gain
in the Source of amplifier
gain tab.
Open circuit voltage gain
— Open circuit voltage gaindB
(default)  scalar Open circuit voltage of amplifier, specified as a scalar in dB. Specify the units from the corresponding dropdown list.
To enable this parameter, choose Open circuit voltage
gain
in the Source of amplifier
gain tab.
Data source
— Data sourceData File
(default)  Networkparameters
 Rational Model
Data source, specified as one of the following:
Data file
— Name of a
Touchstone file with the extension.s2p
.
Networkparameters
—
Provide Network parameter data such as
Sparameters
,
Yparameters
, and
Zparameters
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. This object has the properties
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 2port element. In this case, S21 is frequencyindependent 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} = 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 higherorder terms are modeled according to [1].
For example, the vector
[
specifies the relation V_{out} = a_{0} + a_{1}V_{1} + a_{2}V_{1}^{2} + a_{3}V_{1}^{3}. Trailing zeroes are omitted. So,
a
_{0},a
_{1},a
_{2},a
_{3}][
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
V_{out} =
V_{in}.a
_{0},a
_{1},a
_{2},
0]
To enable this parameter, select Polynomial
coefficients
in Source of amplifier
gain tab.
Network parameter type
— Network parameter typeSparameters
(default)  Yparameters
 Zparameters
Network parameter type, specified as Sparameters
,
Yparameters
, or
Zparameters
.
To enable this parameter, first select Data
source
in Source of amplifier
gain tab. Then, select
Networkparameters
in the
Data source tab.
Input impedance (Ohm)
— Input impedance50
(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 impedance50
(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 filesimrfV2_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 parameters1e9 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
Networkparameters
in Data
source.
Reference Impedance(Ohm)
— Reference impedance of network parameters50
(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
Networkparameters
in Data
source.
Residues
— Residues in order of rational model0
(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 model0
(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 frequencyon
(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
Piecewise linear
orColored
in Noise
distribution in the Noise pane.
Operation frequency
— Operation frequency0
(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 terminalson
(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 nonlinearityEven 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 thirdorder
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, 1dB 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 conventionOutput
(default)  Input
Intercept points convention, specified a
Input
referred, or
Output
referred convention. Use this
specification for the intercept points, 1dB gain compression power, and
saturation power.
IP2
— Secondorder intercept pointinf
dBm
(default)  scalar  W
 mW
 dBW
 dBm
Secondorder intercept point, specified as a scalar.
To set this parameter, select Even and odd
order
in Nonlinear polynomial
type.
IP3
— Thirdorder intercept pointinf
dBm
(default)  scalar  W
 mW
 dBW
 dBm
Thirdorder intercept point, specified as a scalar.
1dB gain compression power
— 1dB gain compression powerinf dBm
(default)  scalar  W
 mW
 dBW
 dBm
1dB gain compression power, specified as a scalar.
To set this parameter, select Odd order
in Nonlinear polynomial type.
Output saturation power
— Output saturation powerinf 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 saturationinf 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 frequencyon
(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 frequency0
(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 noiseon
(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 typeNoise figure
(default)  Spot noise data
Noise type, specified as Noise figure
or
Spot noise data
.
Noise distribution
— Noise distributionWhite
(default)  Piecewise linear
 Colored
Noise distribution, specified as:
White
, spectral density is a
single nonnegative 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.
Piecewise 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
carrierdependent.
Colored
, depends on both
carrier and bandwidth. This is a correlated noise
source.
Noise figure (dB)
— Noise figureNoise figure, specified as a scalar in decibels.
Frequencies
— Frequency data0
Hz
(default)  scalar  vectorFrequency data, specified as a scalar or vector in hertz.
To set this parameter, first select Piecewise
linear
or Colored
in
Noise distribution.
Minimum noise figure (dB)
— Minimum noise figure0
(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.
Optimal reflection coefficient
— Optimal reflection coefficient0
(default)  scalar  vectorOptimal 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 resistance0
(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 durationon
(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 whitenoise.
To set this parameter, first select
Colored
in Noise
distribution.
Impulse response duration
— Impulse response duration1e10
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 SparametersTimedomain
(rationalfit)
(default)  Frequencydomain
Model Sparameters, specified as:
Timedomain (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.
Frequencydomain 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.
For the Amplifier and
Sparameters 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 optionsFit 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 fit40
(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 responseon
 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 duration1e10
(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 Sparameter magnitude with appropriate delay
— Use only Sparameter magnitude with appropriate delayoff
(default)  on
Select this parameter to sparameter phase and delay the impulse response by half its length. This parameter is applicable only for Sparameter data modeled in time domain. You can use this to shape spectral content with filter effects by specifying only magnitude.
Note
This parameter introduces an artificial delay to the system.
Source of frequency data
— Frequency data sourceExtracted from data
source
(default)  Userdefined
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
Userspecified
, specify a vector of
frequencies in the Frequency data parameter. Also,
specify units from the corresponding dropdown 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 plotXY 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:
XY plane
— Generate a
Cartesian plot of your data versus frequency. To create linear,
semilog, or loglog plots, set the Yaxis
scale and Xaxis 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 SParameters to plotS11
(default)  S12
 S21
 S22
 NF
Type of SParameters to plot, specified as S11
,
S12
, S21
, or
S22
. When noise is spectral NF
plotting is possible.
To enable NF
, set Noise
type to Noise figure
and
select Apply.
Parameter 2
— Type of SParameters to plotNone
(default)  S11
 S12
 S21
 S22
 NF
Type of SParameters to plot, specified as S11
,
S12
, S21
, or
S22
. When noise is spectral NF
plotting is possible.
To enable NF
, set Noise
distribution to Piecewise
linear
or Colored
and
select Apply.
Format1
— Plot formatMagnitude (decibels)
(default)  Magnitude (linear)
 Angle(degrees)
 Real
 Imaginary
Plot format, specified as Magnitude (decibels)
,
Angle(degrees)
, Real
, or
Imaginary
.
To enable this parameter, set Plot type to
XY plane
.
Format2
— Plot formatMagnitude (decibels)
(default)  Magnitude (linear)
 Angle(degrees)
 Real
 Imaginary
Plot format, specified as Magnitude (decibels)
,
Angle(degrees)
, Real
, or
Imaginary
.
To enable this parameter, set Plot type to
XY plane
.
Yaxis scale
— Yaxis scaleLinear
(default)  Logarithmic
Yaxis scale, specified as Linear
or
Logarithmic
.
To enable this parameter, set Plot type to
XY plane
.
Xaxis scale
— Xaxis scaleLinear
(default)  Logarithmic
Xaxis scale, specified as Linear
or
Logarithmic
.
To enable this parameter, set Plot type to
XY plane
.
Plot
— Plot specified dataPlot 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 twoport 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 twoport:
The noise sources variance and correlation are governed by an ABCDcorrelation 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 figure
R_{n}  Equivalent noise resistance
Y_{opt}  Optimal source admittance
k  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 decibels
R_{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}(1Γ_{opt})/(1+Γ_{opt})
).
In the above, Z_{0} =
1/Y_{0}
is the reference impedance that is
real. If the 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 ABCDcorrelation 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)
.
Behavior changed in R2021b
Starting in R2021b, the Amplifier block icon has updated. The block icons are now dynamic and show the current state of the noise parameter.
When you open a model created before R2021b containing an Amplifier block, the software replaces the block icon with the R2021b version.
[1] Gonzalez, Guillermo. “Microwave Transistor Amplifiers: Analysis and Design”, Englewood Cliffs, N.J.: PrenticeHall, 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.designersguide.org/analysis/interceptpoint.pdf.
[4] Pozar, David M. “Microwave Engineering”, Hoboken NJ: John Wiley & Sons, 2005.
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