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,
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 Vout =
a1*Vin between the input and output voltages. The input voltage is Vi(t) =
Ai(t)ejωt, and the output voltage is Vo(t) =
Ao(t)ejωt 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 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 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, a1.
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, a1.
Data source
—
When using the data source option, S11 and S22,
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 gaindB
(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 gaindB
(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 sourceData 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
In this rational model equation, each
Ck is the
residue of the pole
Ak. If
Ck 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 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]
Vout = a0 + a1Vin + a2Vin2 + ...
+ a9Vin9
where
a1 represents the linear gain
term, and higher-order terms are modeled according to [1].
For example, the vector
[
specifies the relation Vout = a0 + a1V1 + a2V12 + a3V13. 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
Vout =
Vin.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 typeS-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 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 Network-parameters
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 Network-parameters
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
Piece-wise 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 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 a1 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 conventionOutput
(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 pointinf
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 pointinf
dBm
(default) | scalar | W
| mW
| dBW
| dBm
Third-order intercept point, specified as a scalar.
1-dB gain compression power
— 1-dB gain compression powerinf 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 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) | 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 [pi]. 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 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 Piece-wise
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.
Optim reflection coefficient
— Optim reflection coefficient0
(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 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 white-noise.
To set this parameter, first select Colored
in Noise distribution.
Impulse response duration
— Impulse response duration1e-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-parametersTime-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 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 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 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 duration1e-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 delayoff
(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.
Note
This parameter introduces an artificial delay to the system.
Source of frequency data
— Frequency data sourceExtracted 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 plotX-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 plotS11
(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 plotNone
(default) | S11
| 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.
Format1
— Plot formatMagnitude (decibels)
(default) | Angle(degrees)
| Real
| Imaginary
Plot format, specified as Magnitude (decibels)
, Angle(degrees)
, Real
,
or Imaginary
.
Format2
— Plot formatMagnitude (decibels)
(default) | Angle(degrees)
| Real
| Imaginary
Plot format, specified as Magnitude (decibels)
, Angle(degrees)
, Real
,
or Imaginary
.
Y-axis scale
— Y-axis scaleLinear
(default) | Logarithmic
Y-axis scale, specified as Linear
or Logarithmic
.
X-axis scale
— X-axis scaleLinear
(default) | Logarithmic
X-axis scale, specified as Linear
or Logarithmic
.
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 two-port device. When only noise figure is specified, RF Blockset amplifier defines the spot noise parameters in the following manner:
Amplifier exhibits specified noise figure when source impedance is matched to the reference impedance ().
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:
NFmin - Minimum noise figure
Rn - Equivalent noise resistance
Yopt - 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:
NFmin is specified in decibels
Rn is specified as equivalent normalized
resistance, RN
(Rn =
Z0RN
).
Yopt is specified in terms of optimal
reflection coefficient, Γopt
(Yopt =
Y0(1-Γopt)/(1+Γopt)
).
In the above, Z0 =
1/Y0
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, Zs, and is determined from the ABCD-correlation matrix:
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.