| RF Blockset™ | |
Mathematical
The Amplifier block generates a complex baseband model of an amplifier with thermal noise. It provides six methods for modeling nonlinearity and three ways to specify noise.
Note This block assumes a nominal impedance of 1 ohm. |
Use the Method parameter in the block dialog box to specify the method for modeling amplifier nonlinearity. The options for the Method parameter are
Linear
Cubic polynomial
Hyperbolic tangent
Saleh model
Ghorbani model
Rapp model
The linear method is implemented by a Gain block. The other nonlinear methods are implemented by subsystems underneath the block's mask. Each subsystem has the same basic structure, as shown in the following figure.
All five subsystems for the nonlinear Method options apply a memoryless nonlinearity to the complex baseband input signal. Each one
Splits the complex signal into its magnitude and angle components.
Applies an AM/AM conversion to the magnitude of the signal, according to the selected nonlinearity method, to produce the magnitude of the output signal.
Applies an AM/PM conversion to the phase of the signal, according to the selected nonlinearity method, and adds the result to the angle of the signal to produce the angle of the output signal.
Combines the new magnitude and angle components into a complex signal and multiplies the result by a gain factor, which is controlled by the Linear gain parameter.
The subsystems for the nonlinear methods implement the AM/AM and AM/PM conversions differently, according to the nonlinearity method you specify. To see exactly how the Amplifier block implements the conversions for a specific method, you can view the AM/AM and AM/PM subsystems that implement these conversions as follows:
Select Look under mask in the pop-up menu. This displays the block's configuration underneath the mask. The block contains five subsystems corresponding to the five nonlinearity methods.
Double-click the subsystem for the method in which you are interested. A subsystem displays similar to the one shown in the preceding figure.
Double-click one of the subsystems labeled AM/AM or AM/PM to view how the block implements the conversions.
The following figure shows, for the Saleh method, plots of
Output voltage against input voltage for the AM/AM conversion
Output phase against input voltage for the AM/PM conversion
The following sections discuss how the parameters specific to the following nonlinear amplifier models affect the AM/AM and AM/PM characteristics of the Amplifier block:
Note The Amplifier block also enables you to model a linear amplifier. |
When you select Cubic polynomial for the nonlinearity modeling Method parameter, the Amplifier block models the AM/AM nonlinearity by:
Using the third-order input intercept point IIP3 (dBm) parameter to compute the factor, f, that scales the input signal before the 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.
The Amplifier block uses the AM/PM conversion (degrees per dB) parameter, which specifies the linear phase change, to add the AM/PM nonlinearity within the power limits specified by the Lower input power limit for AM/PM conversion (dBm) parameter and the Upper input power limit for AM/PM conversion (dBm) parameter. Outside those limits, the phase change is constant at the values corresponding to the lower and upper input power limits, which are zero and
respectively.
The Linear gain (dB) parameter scales the output signal.
When you select Hyperbolic tangent for the nonlinearity modeling Method parameter, the Amplifier block computes and adds the AM/AM nonlinearity by:
Using the third-order input intercept point IIP3 (dBm) parameter to compute the factor, f, that scales the input signal before the 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.
The Amplifier block uses the AM/PM conversion (degrees per dB) parameter, which specifies the linear phase change, to add the AM/PM nonlinearity within the power limits specified by the Lower input power limit for AM/PM conversion (dBm) parameter and the Upper input power limit for AM/PM conversion (dBm) parameter. Outside those limits, the phase change is constant at the values corresponding to the lower and upper input power limits, which are zero and
respectively.
The Linear gain (dB) parameter scales the output signal.
When you select Saleh model for the nonlinearity modeling Method parameter, the Input scaling (dB) parameter scales the input signal before the nonlinearity is applied. The block multiplies the input signal by the parameter value, converted from decibels to linear units. If you set the parameter to be the inverse of the input signal amplitude, the scaled signal has amplitude normalized to 1.
The AM/AM parameters, alpha and beta, are used to compute the amplitude gain for an input signal using the following function
where u is the magnitude of the scaled signal.
The AM/PM parameters, alpha and beta, are used to compute the phase change for an input signal using the following function
where u is the magnitude of the input signal. Note that the AM/AM and AM/PM parameters, although similarly named alpha and beta, are distinct.
The Output scaling (dB) parameter scales the output signal similarly.
When you select Ghorbani model for the nonlinearity modeling Method parameter, the Input scaling (dB) parameter scales the input signal before the nonlinearity is applied. The block multiplies the input signal by the parameter value, converted from decibels to linear units. If you set the parameter to be the inverse of the input signal amplitude, the scaled signal has amplitude normalized to 1.
The AM/AM parameters, [x1 x2 x3 x4], are used to compute the amplitude gain for an input signal using the following function
where u is the magnitude of the scaled signal.
The AM/PM parameters, [y1 y2 y3 y4], are used to compute the phase change for an input signal using the following function
where u is the magnitude of the scaled signal.
The Output scaling (dB) parameter scales the output signal similarly.
When you select Rapp model for the nonlinearity modeling Method parameter, the Smoothness factor and Output saturation level parameters are used to compute the amplitude gain for an input signal by the following function
where u is the magnitude of the scaled signal, S is the Smoothness factor and Osat is the Output saturation level.
The Rapp model does not apply a phase change to the input signal.
The Output saturation level parameter limits the output signal level. The Smoothness factor parameter controls the transition for the amplitude gain as the input amplitude approaches saturation. The smaller the smoothness factor, the smoother the curve.
You can specify the amount of thermal noise in three ways, according to the Specification method parameter you select.
Noise temperature — Specifies the noise in kelvin.
Noise factor — Specifies the noise by the following equation:
Noise figure — Specifies the noise in decibels relative to a noise temperature of 290 kelvin. In terms of noise factor,
Noise figure = 10log(Noise factor)
The parameters displayed in the dialog box vary for different methods of modeling nonlinearity. Only some of these parameters are visible in the dialog box at any one time.
You can change tunable parameters while the model is running.
Method used to model the nonlinearity. The choices are Linear, Cubic polynomial, Hyperbolic tangent, Saleh model, Ghorbani model, Rapp model. Tunable.
Scalar specifying the linear gain for the output function. This field becomes visible if you select Linear, Cubic polynomial, Hyperbolic tangent, or Rapp model as the Method parameter. Tunable.
Input power intercept point as a scalar value. This field becomes visible if you select Cubic polynomial or Hyperbolic tangent as the Method parameter. For both of these methods, the nominal impedance is 1 ohm. Tunable.
Scalar specifying the AM/PM conversion in degrees per decibel. This field becomes visible if you select Cubic polynomial or Hyperbolic tangent as the Method parameter. Tunable.
Scalar specifying the minimum input power for which AM/PM conversion scales linearly with input power value. Below this value, the phase shift resulting from AM/PM conversion is zero. This field becomes visible if you select Cubic polynomial or Hyperbolic tangent as the Method parameter. Tunable.
Scalar specifying the maximum input power for which AM/PM conversion scales linearly with input power value. Above this value, the phase shift resulting from AM/PM conversion is constant. The value of this maximum shift is given by:
This field becomes visible if you select Cubic polynomial or Hyperbolic tangent as the Method parameter. Tunable.
Number that scales the input signal level. This field becomes visible if you select Saleh model or Ghorbani model as the Method parameter. Tunable.
Number that scales the output signal level. This field becomes visible if you select Saleh model or Ghorbani model as the Method parameter. Tunable.
Vector specifying the AM/AM parameters. This field becomes visible if you select Saleh model as the Method parameter. Tunable.
Vector specifying the AM/PM parameters. This field becomes visible if you select Saleh model as the Method parameter. Tunable.
Vector specifying the AM/AM parameters. This field becomes visible if you select Ghorbani model as the Method parameter. Tunable.
Vector specifying the AM/PM parameters. This field becomes visible if you select Ghorbani model as the Method parameter. Tunable.
Scalar specifying the smoothness factor. This field becomes visible if you select Rapp model as the Method parameter. Tunable.
Scalar specifying the output saturation level. This field becomes visible if you select Rapp model as the Method parameter. Tunable.
The method by which you specify the amount of noise. The choices are Noise temperature, Noise figure, and Noise factor. Tunable.
Scalar specifying the amount of noise. This field becomes visible if you select Noise temperature as the Specification method parameter. Tunable.
Scalar specifying the amount of noise relative to a noise temperature of 290 kelvin. A Noise figure setting of 0 decibels indicates a noiseless system. This field becomes visible if you select Noise figure as the Specification method parameter. Tunable.
Scalar specifying the amount of noise relative to a noise temperature of 290 kelvin. This field becomes visible if you select Noise factor as the Specification method parameter. Tunable.
Nonnegative integer specifying the initial seed for the random number generator the block uses to generate noise.
You can see the effect of the Amplifier block in the demo Intermodulation: Mathematical Amplifier.
This demo uses a baseband-equivalent multitone signal as input to the Amplifier block. A Simulink Slider Gain block enables you to vary the gain from 1 to 10. The following figure shows the input signal with gain set to the default 1.
The next figure shows the same signal after it passes through the Amplifier block, with the Method parameter set to Hyperbolic tangent. The demo uses the default Amplifier block IIP3 (dBm) value of 30. It uses no AM/PM conversion. The demo specifies thermal noise as Noise figure, for which it uses the default 3.01 dB.
[1] Ghorbani, A. and M. Sheikhan, "The Effect of Solid State Power Amplifiers (SSPAs) Nonlinearities on MPSK and M-QAM Signal Transmission," Sixth Int'l Conference on Digital Processing of Signals in Comm., 1991, pp. 193-197.
[2] Rapp, C., "Effects of HPA-Nonlinearity on a 4-DPSK/OFDM-Signal for a Digital Sound Broadcasting System," in Proceedings of the Second European Conference on Satellite Communications, Liege, Belgium, Oct. 22-24, 1991, pp. 179-184.
[3] Saleh, A.A.M., "Frequency-independent and frequency-dependent nonlinear models of TWT amplifiers," IEEE Trans. Communications, vol. COM-29, pp.1715-1720, November 1981.
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