Power-Added Efficiency (PAE)

PAE is mathematically defined as the ratio of the net RF power added by the amplifier to the total DC power consumed from the supply.

• Formula: PAE = (P_RF_out - P_RF_in) / P_DC
• P_RF_out: The total RF output power delivered to the load.
• P_RF_in: The RF input drive power, which is subtracted to isolate the amplifier's true contribution.
• P_DC: The total DC power drawn from the power supply (V_dc × I_dc).

This metric is superior to simple drain efficiency because it penalizes low-gain amplifiers that require significant input drive power.

While often confused, PAE and drain efficiency (η_D) are distinct metrics that converge only under specific conditions.

• Drain Efficiency (η_D): Defined simply as P_RF_out / P_DC, ignoring input power.
• Key Distinction: For a high-gain amplifier where P_RF_in is negligible compared to P_RF_out, PAE ≈ η_D.
• Low-Gain Scenario: In mmWave or broadband amplifiers with 10 dB gain, P_RF_in is 10% of P_RF_out, causing a significant divergence between PAE and η_D.
• Design Implication: PAE is the more honest metric for evaluating overall transmitter line-up efficiency.

PAE is not a single fixed value; it varies dramatically with the amplifier's operating point relative to its saturated output power (P_sat).

• At Saturation (P_sat): PAE peaks as the amplifier operates in compression, but linearity is severely degraded.
• At Back-Off (e.g., 6-8 dB OBO): PAE drops significantly, often to 15-25% for a Class-AB amplifier, which is the typical operating region for signals with high Peak-to-Average Power Ratio (PAPR).
• Doherty Advantage: The Doherty architecture is specifically designed to maintain a high PAE plateau over a wide back-off range, making it essential for modern communication signals.

PAE is intricately linked to the amplifier's nonlinear AM-AM distortion characteristics, particularly gain compression.

• 1-dB Compression Point (P1dB): As input drive increases toward P1dB, the gain begins to compress, causing P_RF_out to increase more slowly.
• PAE Peak Location: Maximum PAE typically occurs 1-2 dB beyond the P1dB point, deep in the compression region where linearity is poor.
• Linearization Requirement: To operate near peak PAE while meeting Error Vector Magnitude (EVM) and Adjacent Channel Leakage Ratio (ACLR) specifications, Digital Predistortion (DPD) is mandatory to correct the resulting nonlinear distortion.

PAE is not a static, isothermal parameter; it degrades dynamically due to self-heating and thermal memory effects.

• Channel Temperature Rise: As the amplifier dissipates power (P_DC - P_RF_out), the junction temperature increases, reducing carrier mobility and gain.
• Dynamic PAE Collapse: Under sustained high-power transmission, the instantaneous PAE can sag by several percentage points due to thermal time constants.
• GaN HEMT Resilience: Gallium Nitride transistors exhibit superior PAE retention at elevated temperatures compared to GaAs or LDMOS, a key reason for their adoption in high-power density Doherty amplifiers.

Envelope Tracking (ET) power supplies dynamically modulate the drain voltage of the amplifier in sync with the instantaneous signal envelope, dramatically boosting average PAE.

• Fixed Supply Limitation: With a constant drain voltage, the amplifier wastes significant DC power as heat during low-envelope periods.
• ET Operation: By reducing V_dc during low-power moments, ET minimizes the P_DC term in the PAE equation, improving efficiency at deep back-off by 10-15 percentage points.
• DPD Co-optimization: The dynamic supply modulation introduces new nonlinearities that require a joint ET-DPD linearization strategy to maintain both high PAE and signal fidelity.

The simpler precursor metric to PAE, calculated as the ratio of RF output power to DC input power only. Unlike PAE, it ignores the RF input drive power, making it an overly optimistic measure for low-gain stages. For high-gain amplifiers where RF input is negligible, drain efficiency and PAE converge. However, in Doherty architectures where the peaking amplifier has lower gain, the distinction becomes critical for accurate performance assessment.

The PAE measured when the amplifier operates at a significant output back-off (OBO) from saturation, typically 6-10 dB. This is the most operationally relevant metric for modern communication signals with high peak-to-average power ratios (PAPR). A Doherty amplifier's primary value proposition is maintaining high back-off efficiency through active load modulation, where the carrier amplifier sees a higher impedance at low power levels, keeping it in saturation.

The fundamental design conflict where biasing a transistor for maximum linearity (Class-A) inherently limits DC-to-RF conversion efficiency to a theoretical 50% maximum. Conversely, high-efficiency bias classes (Class-C, Class-F) introduce severe AM-AM and AM-PM distortion. PAE quantifies one side of this trade-off, while Error Vector Magnitude (EVM) and Adjacent Channel Leakage Ratio (ACLR) quantify the linearity cost. Digital predistortion aims to break this trade-off.

The deviation from linear gain at high drive levels, quantified by the 1-dB compression point (P1dB). As the amplifier approaches saturation, incremental gain decreases, directly degrading PAE calculation accuracy if the RF input power term is not properly accounted for. In a Doherty amplifier, the soft compression characteristic of GaN HEMT devices allows for operation closer to saturation with manageable distortion, maximizing PAE at the waveform's peak power.

A system-level efficiency enhancement technique where the drain bias voltage of the power amplifier is dynamically modulated to track the instantaneous signal envelope amplitude. When combined with a Doherty architecture, envelope tracking can further improve PAE, especially at deep back-off levels. The PAE calculation must then account for the efficiency of the envelope tracker itself, leading to a system-level PAE metric that includes supply modulator losses.

The minimum drain-to-source voltage (V_knee) at which a field-effect transistor enters the saturation region of operation. A lower knee voltage allows the RF voltage swing to extend closer to zero volts, maximizing the fundamental-frequency output power and efficiency. In GaN HEMT-based Doherty amplifiers, the low knee voltage is a key enabler of high PAE, as it minimizes the dissipated power in the transistor's linear region during large-signal operation.