RF Blockset™

S-Parameters Amplifier - Model nonlinear amplifier using S-parameters

Library

Amplifiers sublibrary of the Physical library

Description

The S-Parameters Amplifier block models the nonlinear amplifier described in the block dialog box, in terms of its frequency-dependent S-parameters, the frequencies and reference impedance of the S-parameters, noise data, and nonlinearity data.

Network Parameters

In the S-parameters field of the block dialog box, provide the S-parameters for each of M frequencies as a 2-by-2-by-M array. In the Frequency field, specify the frequencies for the S-parameters as an M-element vector. The elements of the frequencies vector must be in the same order as the S-parameters. All frequencies must be positive. For example, the following figure shows the correspondence between the S-parameters array and the vector of frequencies.

The S-Parameters Amplifier block interpolates the given S-parameters to determine their values at the modeling frequencies. The modeling frequencies are determined by the Output Port block. See RF Blockset™ Algorithms for more details.

Nonlinearity

You can enter either OIP3 or IIP3 data as a scalar value for nonlinearity in the S-Parameters Amplifier block dialog box. You can also specify the 1 dB gain compression power and the output saturation power in the S-Parameters Amplifier block dialog box.

If you do not specify the 1 dB gain compression power, the block ignores the output saturation power specification. The block computes and adds the nonlinearity from the OIP3 or IIP3 value by:

Converting the specified value into IIP3 (if needed)
Using the third-order input intercept point value in dBm to compute the factor, f, that scales the input signal before the S-Parameters Amplifier block applies the nonlinearity:
Computing the scaled input signal by multiplying the amplifier input signal by f.
Limiting the scaled input signal to a maximum value of 1.
Applying an AM/AM conversion to the amplifier gain, according to the following cubic polynomial equation:

where u is the magnitude of the scaled input signal, which is a unitless normalized input voltage.

If you specify the 1 dB gain compression power, the block computes and adds the nonlinearity to the input signal by:

Converting the specified third-order intercept value into OIP3 (if needed).
Converting the gain, OIP3, and 1dB compression data to linear, unitless values, normalized to 1 volt and the reference impedance Z₀ (which is specified in the block dialog box):

where
- GAIN is the amplifier power gain, which is derived from the S-parameters.
- OIP3 is the output third-order intercept point.
- PCOMP is the output power at the 1 dB compression point.
Computing the coefficients of the polynomial, , that determines the AM/AM conversion for the input signal s:
Computing the input power at which the output saturates, if it is not specified, according to the following function:

This value is the input power above which the block replaces the AM/AM conversion model with a constant output power value A_sat.
Applying the AM/AM conversion to the input signal

Active Noise

You can specify active block noise in one of the following ways:

Spot noise data in the S-Parameters Amplifier block dialog box.
Noise figure, noise factor, or noise temperature value in the S-Parameters Amplifier block dialog box.

If you specify block noise as spot noise data, the block uses the data to calculate noise figure. The block first interpolates the noise data for the modeling frequencies, using the specified Interpolation method. It then calculates the noise figure using the resulting values.

Dialog Box

Main Tab

S-Parameters

S-parameters for a nonlinear amplifier in a 2-by-2-by-M array. M is the number of S-parameters.

Frequency (Hz)

Frequencies of the S-parameters as an M-element vector. The order of the frequencies must correspond to the order of the S-parameters in S-Parameters. All frequencies must be positive.

Reference impedance (ohms)

Reference impedance of the S-parameters as a scalar or a vector of length M. The value of this parameter can be real or complex. If you provide a scalar value, then that value is applied to all frequencies.

Interpolation method

The method used to interpolate the network parameters. The following table lists the available methods describes each one.

Method	Description
`Linear` (default)	Linear interpolation
`Spline`	Cubic spline interpolation
`Cubic`	Piecewise cubic Hermite interpolation

Noise Data Tab

Noise type: Type of noise data. The value can be Noise figure, Spot noise data, Noise factor, or Noise temperature.
Noise figure (dB): Scalar ratio, in decibels, of the available signal-to-noise power ratio at the input to the available signal-to-noise power ratio at the output, (S_i/N_i)/(S_o/N_o). This parameter is enabled if Noise type is set to Noise figure.
Minimum noise figure (dB): Minimum scalar ratio of the available signal-to-noise power ratio at the input to the available signal-to-noise power ratio at the output, (S_i/N_i)/(S_o/N_o). This parameter is enabled if Noise type is set to Spot noise data.
Optimal reflection coefficient: Optimal amplifier source impedance. This parameter is enabled if Noise type is set to Spot noise data.
Equivalent normalized resistance: Resistance normalized to the resistance used to take the noise measurement. This parameter is enabled if Noise type is set to Spot noise data.
Noise factor: Scalar ratio of the available signal-to-noise power ratio at the input to the available signal-to-noise power ratio at the output, (S_i/N_i)/(S_o/N_o). This parameter is enabled if Noise type is set to Noise factor.
Noise temperature (K): Equivalent temperature that produces the same amount of noise power as the amplifier. This parameter is enabled if Noise type is set to Noise temperature.

Nonlinearity Data Tab

IP3 type: Type of third-order intercept point. The value can be IIP3 (input intercept point) or OIP3 (output intercept point).
IP3 (dBm): Scalar power value of third-order intercept point. Use the default value, Inf, if the IP3 value is unknown.
1 dB gain compression power (dBm): Scalar output power value at which gain has decreased by 1 dB. Use the default value, Inf, if the 1 dB compression point is unknown.
Output saturation power (dBm): Scalar output power value the amplifier produces when fully saturated. The value is only used if 1 dB gain compression power (dBm) is specified. Use the default value, Inf, if saturation power is unknown.

Visualization Tab

For information about plotting the amplifier parameters, see Plotting Model Data.

Examples

Plotting Parameters with the S-Parameters Amplifier Block

The following example specifies S-parameters [-.33+.71i, -.03i; 8.12-.02i, -.37-.37i] and [0.16+.20i, -.03-.04i; 7.71-8.04i, -.70-.12i] at frequencies 2.0 GHz and 2.1 GHz respectively, with a reference impedance of 50 ohms. The example uses the MATLAB^® cat function to create the 2-by-2-by-2 S-parameters array.

cat(3,[-.33+0.71i,     -.03i;  8.12-.02i, -.37-.37i],...
      [ .16+0.20i, -.03-.04i; 7.71-8.04i, -.70-.12i])

Type the following command at the MATLAB prompt to create a variable called sparams that stores the values of the S-parameters.

sparams = cat(3,...
      [-.33+0.71i, -.03i;  8.12-.02i, -.37-.37i],...
      [ .16+0.20i, -.03-.04i; 7.71-8.04i, -.70-.12i])

Set the S-Parameters Amplifier block parameters on the Main tab as follows:
- Set the S-Parameters parameter to sparams.
- Set the Frequency (Hz) parameter to [2.0e9,2.1e9].
Click Apply. This action applies the specified settings.
Set the S-Parameters Amplifier block parameters on the Visualization tab as follows:
- In the Plot type list, select X-Y plane.
- In the Y parameter1 list, select S11.
Click Plot. This action creates an X-Y Plane plot of the S₁₁ parameters using the frequencies taken from the Frequency (Hz) parameter on the Main tab.