Power Amplifier Modeling#

Power amplification modeling represents a single processing step within the radio-frequency hardware model of transmitting modems.

classDiagram PowerAmplifier <|-- ClippingPowerAmplifier PowerAmplifier <|-- CustomPowerAmplifier PowerAmplifier <|-- RappPowerAmplifier PowerAmplifier <|-- SalehPowerAmplifier Serializable <|-- PowerAmplifier Visualizable <|-- PowerAmplifier

Each power amplifier model instance implements an equation

\[s'(t) = f\lbrace s(t), t \rbrace \in \mathbb{C}\]

distorting complex-valued signal samples \(s(t) \in \mathbb{C}\) feeding into the power amplifier. For time-invariant (i.e. memoryless) models \(f\lbrace s(t), t \rbrace = f\lbrace s(t) \rbrace\). The following figure visualizes the gain characteristics for the implemented amplification models for a saturation point \(s_\mathrm{sat} = 1\).

(Source code, png, hires.png, pdf)

../_images/plot_pa_characteristics.png
class ClippingPowerAmplifier(**kwargs)[source]#

Bases: PowerAmplifier

Model of a clipping power amplifier.

Complex signal samples with amplitudes above \(s_\mathrm{sat} \in \mathbb{R}\) will be clipped to the maximum amplitude value. In case of clipping, the respective sample angles will be preserved, so that

\[s'(t) = \frac{s(t)}{|s(t)|} \cdot \min{(|s(t)|, s_\mathrm{sat})} \text{.}\]
Parameters:

kwargs (Any) – PowerAmplifier base class initialization arguments.

model(input_signal)[source]#

Model signal amplification characteristics.

Parameters:

input_signal (np.ndarray) – Sample vector of the signal feeding into the power amplifier.

Returns:

Distorted signal after amplification modeling.

Return type:

np.ndarray

yaml_tag: str = 'Clipping'#

YAML serialization tag.

class CustomPowerAmplifier(input, gain, phase, **kwargs)[source]#

Bases: PowerAmplifier

Model of a customized power amplifier.

Parameters:
  • input (np.ndarray) –

  • gain (np.ndarray) –

  • phase (np.ndarray) –

  • kwargs (Any) – PowerAmplifier base class initialization arguments.

Raises:

ValueError – If input, gain, and phase are not vectors of identical length.

model(input_signal)[source]#

Model signal amplification characteristics.

Parameters:

input_signal (np.ndarray) – Sample vector of the signal feeding into the power amplifier.

Returns:

Distorted signal after amplification modeling.

Return type:

np.ndarray

property gain: ndarray#
property input: ndarray#
property phase: ndarray#
class PowerAmplifier(saturation_amplitude=inf, adjust_power=False)[source]#

Bases: Serializable, Visualizable

Base class of a power-amplifier model.

Implements a distortion-less amplification model

\[s'(t) = s(t) \text{,}\]

which may be overwritten by classes inheriting from this base.

Parameters:
  • saturation_amplitude (float, optional) – Cut-off point for the linear behaviour of the amplification in Volt.

  • adjust_power (bool, optional) – Power adjustment flag.

model(input_signal)[source]#

Model signal amplification characteristics.

Parameters:

input_signal (np.ndarray) – Sample vector of the signal feeding into the power amplifier.

Returns:

Distorted signal after amplification modeling.

Return type:

np.ndarray

plot(axes=None, *, title=None, samples=None)[source]#

Plot the power amplifier distortion characteristics.

Generates a matplotlib plot depicting the phase/amplitude.

Parameters:
  • axes (VAT, optional) – The axis object into which the information should be plotted. If not specified, the routine will generate and return a new figure.

  • title (str, optional) – Title of the generated plot.

  • samples (np.ndarray, optional) – Sample points at which to evaluate the characteristics. In other words, the x-axis of the resulting characteristics plot.

Return type:

FigureBase

send(input_signal)[source]#

Model signal amplification characteristics.

Internally calls the model subroutine of power-amplifier models implementing this prototype-class.

Parameters:

input_signal (np.ndarray) – Sample vector of the signal feeding into the power amplifier.

Returns:

Distorted signal after amplification modeling.

Return type:

np.ndarray

adjust_power: bool#

Power adjustment flag.

If enabled, the power amplifier will normalize the distorted signal after propagation modeling.

property saturation_amplitude: float#

Cut-off point for the linear behaviour of the amplification.

Referred to as \(s_\mathrm{sat} \ \mathbb{R}_{+}\) in equations.

Returns:

Saturation amplitude in Volt.

Return type:

float

Raises:

ValueError – If amplitude is smaller than zero.

property title: str#

Title of the visualizable.

class RappPowerAmplifier(smoothness_factor=1.0, **kwargs)[source]#

Bases: PowerAmplifier

Model of a power amplifier according to Rapp’s model.

Implements a saturation characteristic according to

\[s'(t) = s(t) \cdot \left( 1 + \left( \frac{|s(t)|}{s_\mathrm{sat}} \right)^{2p_\mathrm{Rapp}} \right)^{-\frac{1}{2p_\mathrm{Rapp}}} \text{,}\]

where \(p_\mathrm{Rapp} \in \lbrace x \in \mathbb{R} | x \geq 1 \rbrace\) denotes the smoothness factor of the saturation curve.

See Rapp[1] for further details.

Clipping Power Amplifier object initialization.

Parameters:
  • smoothness_factor (float, optional) – Smoothness factor of the amplification saturation characteristics.

  • kwargs (Any) – PowerAmplifier base class initialization arguments.

model(input_signal)[source]#

Model signal amplification characteristics.

Parameters:

input_signal (np.ndarray) – Sample vector of the signal feeding into the power amplifier.

Returns:

Distorted signal after amplification modeling.

Return type:

np.ndarray

property smoothness_factor: float#

Smoothness factor of the amplification saturation characteristics.

Also referred to as Rapp-factor \(p_\mathrm{Rapp}\).

Returns:

Smoothness factor.

Return type:

float

Raises:

ValueError – If smoothness factor is smaller than one.

yaml_tag: str = 'Rapp'#

YAML serialization tag.

class SalehPowerAmplifier(amplitude_alpha, amplitude_beta, phase_alpha, phase_beta, **kwargs)[source]#

Bases: PowerAmplifier

Model of a power amplifier according to Saleh.

Implements a saturation characteristic according to

\[s'(t) = s(t) \cdot A\lbrace s(t) \rbrace e^{\mathrm{j} \Phi\lbrace s(t) \rbrace}\]

where

\[A\lbrace s \rbrace = \frac{ \alpha_\mathrm{a} \frac{|s|}{s_\mathrm{sat}} } { 1 + \beta_\mathrm{a} \frac{|s|^2}{s_\mathrm{sat}^2} }\]

describes the amplitude model depending on two parameters \(\alpha_\mathrm{a}, \beta_\mathrm{a} \in \mathbb{R}_{+}\) and

\[\Phi\lbrace s \rbrace = \frac{ \alpha_\Phi \frac{|s|}{s_\mathrm{sat}} } { 1 + \beta_\Phi \frac{|s|^2}{s_\mathrm{sat}^2} }\]

describes the phase model depending on \(\alpha_\Phi, \beta_\Phi \in \mathbb{R}\), respectively.

See Saleh[2] for further details.

Parameters:
  • amplitude_alpha (float) – Amplitude model factor alpha.

  • amplitude_beta (float) – Amplitude model factor beta.

  • phase_alpha (float) – Phase model factor alpha.

  • phase_beta (float) – Phase model factor beta.

  • kwargs (Any) – PowerAmplifier base class initialization arguments.

model(input_signal)[source]#

Model signal amplification characteristics.

Parameters:

input_signal (np.ndarray) – Sample vector of the signal feeding into the power amplifier.

Returns:

Distorted signal after amplification modeling.

Return type:

np.ndarray

property amplitude_alpha: float#

Amplitude model factor \(\alpha_\mathrm{a}\).

Returns:

Amplitude factor.

Return type:

float

Raises:

ValueError – If the factor is smaller than zero.

property amplitude_beta: float#

Amplitude model factor \(\beta_\mathrm{a}\).

Returns:

Amplitude factor.

Return type:

float

Raises:

ValueError – If the factor is smaller than zero.

phase_alpha: float#

Phase model factor \(\alpha_\Phi\).

phase_beta: float#

Phase model factor \(\beta_\Phi\).