ET Efficiency Knee

The semiconductor material fundamentally determines the knee's sharpness and location. Gallium Nitride (GaN) PAs exhibit a sharper, more pronounced knee at lower output power back-off compared to LDMOS, enabling deeper envelope tracking. Gallium Arsenide (GaAs) devices typically show a softer transition. The knee voltage is directly tied to the device's knee voltage (Vk) in its I-V characteristic curve.

The bias point and conduction angle dictate the efficiency curve shape:

• Class-B: Theoretical 78.5% peak efficiency with a moderate knee slope.
• Class-AB: A compromise between linearity and efficiency, exhibiting a smoother knee transition.
• Deep Class-AB/C: Used in Doherty peaking amplifiers; the knee shifts with drive level.
• Class-F/Inverse-F: Harmonic terminations shape the voltage and current waveforms to produce a sharper, more rectangular knee for higher efficiency over a narrow dynamic range.

The instantaneous drain voltage dynamically shifts the efficiency knee. As the supply modulator reduces Vds during envelope tracking, the entire efficiency curve compresses toward lower power levels. The knee point tracks approximately with the square of the supply voltage. A shaping function must map the envelope signal to a Vds that keeps the PA operating above the knee for the instantaneous output power, avoiding operation in the steep drop-off region.

The fundamental load impedance presented to the transistor drain sets the load line and directly determines the knee's power location. Impedance mismatch shifts the load line, moving the knee to a different output power. In Doherty PAs, the active load modulation from the peaking amplifier dynamically changes the carrier amplifier's load impedance, causing its efficiency knee to shift continuously across the dynamic range. The output matching network's Q-factor also influences the knee's sharpness.

As carrier frequency increases toward mmWave bands, parasitic capacitances and device transit time effects become more significant. These parasitics soften the switching transition, rounding the efficiency knee and reducing peak efficiency. The knee voltage also effectively increases due to parasitic resistances. At higher frequencies, the PA must be operated further from the knee to maintain linearity, reducing the practical dynamic range for envelope tracking.

Self-heating during high-power operation temporarily degrades electron mobility, shifting the knee to a lower power level and reducing peak efficiency. GaN trapping effects from surface states or buffer layers cause a lag in drain current response, creating a hysteretic efficiency knee that depends on the signal's envelope history. These memory effects mean the knee is not a static curve but a dynamic surface that must be characterized under modulated stimulus for accurate ET-DPD modeling.

A simpler alternative to ET that adjusts the PA supply voltage on a slot-by-slot or frame-by-frame basis based on average output power. APT avoids the complexity of wideband modulators but cannot track instantaneous peaks. The efficiency knee concept explains why APT is less efficient than ET for signals with high peak-to-average power ratios (PAPR), as the PA operates far from its peak efficiency for most of the waveform.

A deterministic mapping, often a look-up table (LUT), that translates instantaneous baseband magnitude to a target supply voltage. The shaping function must be designed to keep the PA operating above the efficiency knee:

• Linear mapping: Sacrifices efficiency for linearity
• De-troughing: Clamps the minimum voltage at the efficiency knee to prevent operation in the low-efficiency region
• Iso-gain contour mapping: Follows constant gain curves to maintain linearity while optimizing efficiency

Constant gain curves plotted on a PA's characteristic plane over supply voltage (Vdd) and input power (Pin). These contours are the primary tool for identifying the efficiency knee and designing shaping functions. The knee corresponds to the region where iso-gain contours begin to compress and converge, indicating that further voltage reduction would cause severe gain collapse and nonlinear distortion that DPD cannot fully correct.

The maximum rate of change of the supply modulator's output voltage, typically specified in V/µs. The slew rate must be sufficient to track the fastest envelope transitions without clipping. When the modulator's bandwidth is insufficient, the effective efficiency knee rises because the modulator cannot accurately reproduce low-voltage troughs, forcing operation at higher average voltages and reducing system efficiency.

A joint optimization methodology where the digital predistortion algorithm and envelope tracking parameters are designed concurrently. The efficiency knee is a critical constraint in this co-design process:

• DPD must linearize the PA across the full voltage range above the knee
• Below the knee, DPD correction becomes ineffective due to extreme gain compression
• The co-design trades off linearization complexity against efficiency by setting the minimum tracking voltage