ET System Power Added Efficiency (PAE)

ET System PAE is calculated as (RF Output Power - RF Input Power) / Total DC Input Power. Unlike drain efficiency, PAE accounts for the RF drive power, providing a true measure of net power gain. The total DC input includes power consumed by both the power amplifier and the supply modulator, making it a holistic system-level metric.

The overall system PAE is critically dependent on the supply modulator's conversion efficiency (η_mod). A high-efficiency PA paired with a lossy modulator yields poor system PAE. Key loss mechanisms include:

• Conduction losses in the modulator's power switches
• Switching losses proportional to the tracking bandwidth
• Quiescent power consumed by control and gate-drive circuitry System PAE = η_PA × η_mod, highlighting the multiplicative nature of these efficiencies.

Unlike fixed-supply PAs, ET system PAE is not a single number but a dynamic curve that varies with the instantaneous envelope amplitude. At low signal levels, the PA operates near the ET efficiency knee, where PAE drops sharply. The shaping function is designed to maximize the probability-density-weighted average PAE over the signal's statistical distribution, not just peak efficiency.

A fundamental trade-off exists between tracking bandwidth and modulator efficiency. As signal bandwidth increases (e.g., 5G NR 100 MHz carriers), the modulator must slew faster, increasing switching losses and degrading η_mod. This directly reduces system PAE. Advanced techniques like multi-level switching and hybrid linear-assisted modulators aim to mitigate this trade-off.

Accurate PAE measurement requires careful de-embedding of fixture and connector losses. The total DC power must be measured at the input to the entire ET system, not just the PA drain. Key considerations:

• Use precision current probes on both PA and modulator supply rails
• Account for dynamic current waveforms, not just average values
• Calibrate out insertion loss between the modulator output and the PA transistor reference plane

At peak power, an ET system may have slightly lower PAE than a fixed-supply Class-AB PA due to modulator losses. However, at 6-10 dB power back-off—where modern signals spend most of their time—ET systems can deliver 2-3x higher PAE. This average efficiency improvement is the primary motivation for envelope tracking in battery-operated and thermally-constrained devices.

The fundamental metric for ET system performance, calculated as:

PAE = (RF_Output_Power - RF_Input_Power) / Total_DC_Power

• RF_Output_Power: The amplified signal power delivered to the antenna load
• RF_Input_Power: The drive signal power entering the PA
• Total_DC_Power: The sum of DC power consumed by both the power amplifier and the supply modulator

Unlike standalone PA efficiency, ET system PAE accounts for the modulator's own power consumption, providing a true end-to-end efficiency figure.

A critical distinction in ET system characterization:

• Drain Efficiency (η): Measures only the PA's ability to convert DC supply power to RF output, ignoring the RF input drive power. Calculated as RF_Output / DC_PA_Supply
• Power Added Efficiency (PAE): Subtracts the RF input power from the output, measuring the true added power. This is always lower than drain efficiency

For high-gain PAs, the difference is negligible. For low-gain mmWave or driver stages, PAE provides a far more honest efficiency assessment.

The overall ET system PAE is the product of the PA's drain efficiency and the supply modulator's conversion efficiency:

PAE_System ≈ η_PA × η_Modulator

• A 95% efficient PA paired with an 85% efficient modulator yields only ~81% system PAE
• Modulator losses include switching losses, conduction losses in the power stage, and quiescent power consumed by control circuitry
• This multiplicative relationship means modulator efficiency is a first-order driver of system performance

The efficiency knee defines the lower boundary of effective ET operation:

• At backed-off power levels, the PA's drain efficiency drops sharply below the knee point
• The supply modulator must maintain high efficiency across the full envelope probability density function (PDF)
• Modern ET systems target >30% PAE even at 10-12 dB back-off from peak power
• The shaping function must balance peak efficiency against linearity across this entire dynamic range

Accurate ET system PAE measurement requires careful instrumentation:

• DC power measurement: Simultaneous precision measurement of current and voltage at both the PA drain supply and the modulator input, accounting for cable losses
• RF power measurement: Calibrated power meters or spectrum analyzers with known insertion loss compensation
• Thermal considerations: Measurements must be taken at thermal equilibrium, as PAE degrades with junction temperature rise
• Modulated signal testing: CW measurements overestimate PAE; real OFDM or 5G NR waveforms with high PAPR reveal true system efficiency

A fundamental design tension exists between maximizing PAE and maintaining linearity:

• Deep compression operation maximizes efficiency but introduces severe AM-AM and AM-PM distortion
• The shaping function must detune from peak efficiency to maintain iso-gain operation
• Digital predistortion (DPD) can recover linearity, allowing operation closer to compression for higher PAE
• The ET-DPD co-design objective is to maximize linearizable PAE — the highest efficiency achievable while meeting EVM and ACLR specifications after linearization