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Power Amplifier (Nonlinearity) Simulation


Unified Passband PA Lab

Power Amplifier Nonlinearity Lab

Unified Passband Simulation: Visualizing Carrier Clipping & Spectral Regrowth

Time Domain: Carrier Wave Clipping

AM-AM Curve: Linear vs. Real PA

Spectrum: Harmonic Regrowth (dB)

How the Simulation Works

The mathematical proof for \( P = \frac{A^2}{2R} \) assumes a perfect, infinite world. However, in RF hardware, we are limited by the physical rails of our Power Amplifier (PA). Our simulator models the transition from Linear Theory to Nonlinear Reality using three core components.

1. Passband Modulation

Unlike simple baseband models, this simulation uses Passband Modulation. We generate complex signals using the In-phase (\(I\)) and Quadrature (\(Q\)) components modulated onto a carrier:

\( s(t) = I \cos(\omega_c t) - Q \sin(\omega_c t) \)

In 16QAM, \(I\) and \(Q\) vary across multiple levels. This results in a varying amplitude \(A(t)\), meaning the power formula is no longer a constant—it fluctuates with the data.

2. The Nonlinear PA Model

To simulate real-world hardware, we use a Tanh (Hyperbolic Tangent) function. This is a common behavioral model for "Soft Clipping" in amplifiers:

\( V_{out} = V_{sat} \cdot \tanh\left(\frac{V_{in}}{V_{sat}}\right) \)
  • Linear Region: When \( V_{in} \ll V_{sat} \), the gain is roughly 1.
  • Saturation: As \( V_{in} \) approaches \( V_{sat} \), the signal peaks are compressed, deviating from the \( A^2/2R \) ideal.

3. Spectral Regrowth and Distortion

When an amplifier clips the peaks of a carrier wave, it creates sharp discontinuities in the time domain. Mathematically, this is equivalent to adding Higher-Order Harmonics.

By performing a Fast Fourier Transform (FFT) on the clipped signal, the simulator reveals "Spectral Regrowth." For BPSK and QPSK, this creates noise in adjacent channels. For 16QAM, it destroys the amplitude relationships between symbols, leading to a high Error Vector Magnitude (EVM).

Insight: To keep a 16QAM signal clean, engineers must "Back-off" the average power so the peak amplitude \( A_{max} \) never reaches the saturation point of the PA.
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