Hot S22

Hot S22 is measured with the amplifier driven at its nominal operating power, capturing the nonlinear output impedance under realistic conditions. Unlike small-signal S22—measured at low power with a vector network analyzer—Hot S22 reflects the impedance the transistor presents when its intrinsic capacitances and transconductance vary with signal envelope. This distinction is critical because the Doherty combiner must provide the correct impedance transformation at full drive, not at idle.

The Doherty combiner's impedance inverter is designed to transform a specific load impedance to the optimal value for the carrier amplifier. Using cold S22 (small-signal) for this design leads to combiner networks that are mistuned under drive. Key consequences include:

• Suboptimal load modulation at peak power
• Degraded back-off efficiency
• Increased AM-PM distortion requiring heavier predistortion
• Reduced gain flatness across the dynamic range

Hot S22 cannot be measured with a standard VNA alone. Common approaches include:

• Active load-pull systems: Present a controlled impedance while driving the amplifier, extracting the reflection coefficient from incident and reflected waves
• Two-source nonlinear VNA: Uses a second source to inject a probe tone at the output while the amplifier is driven, enabling X-parameter or S-function extraction
• Hot S22 extraction from load-pull contours: Deriving the intrinsic output impedance from the shape of constant-power contours on the Smith chart

Hot S22 is not a single value but varies with:

• Fundamental frequency: The output impedance shifts across the operating band due to package parasitics and matching network dispersion
• Drive level: Impedance changes from small-signal through compression to saturation
• Harmonic frequencies: The second and third harmonic terminations presented by the combiner affect efficiency, making harmonic Hot S22 equally important for Class-F and inverse Class-F designs
• Modulation bandwidth: For wideband signals, the impedance may exhibit frequency-dependent memory within the signal bandwidth

Hot S22 is the dual of load-pull analysis. While load-pull asks 'what impedance should I present to the device for optimal performance?', Hot S22 answers 'what impedance does the device present to the combining network?' The two must be conjugate-matched for maximum power transfer. In Doherty design:

• The carrier amplifier's Hot S22 at back-off determines the impedance inverter's characteristic impedance
• The peaking amplifier's Hot S22 at saturation influences the combining node impedance
• Mismatch between designed and actual Hot S22 creates standing waves that degrade combiner efficiency

Modern harmonic balance and envelope transient simulators can predict Hot S22 from foundry transistor models. However, model accuracy at compression is often limited. Best practices include:

• Validating simulated Hot S22 against measured load-pull data
• Using X-parameter models extracted from nonlinear VNA measurements for black-box amplifier representations
• Incorporating self-heating and trap effects in the transistor model to capture dynamic impedance shifts
• Running power-swept S-parameter simulations to observe the transition from cold to hot impedance

The output network that combines the carrier and peaking amplifier outputs while performing the necessary impedance transformations for load modulation. Hot S22 directly determines the optimal combiner design because it represents the actual impedance the combining network must match under large-signal drive.

• Typically incorporates an impedance inverter or quarter-wave transformer
• Must account for the difference between Cold S22 (small-signal) and Hot S22 (large-signal)
• Mismatch leads to degraded efficiency and incomplete load modulation

A systematic measurement technique where the impedance presented to a device under test is varied across the Smith chart to map contours of constant output power, efficiency, and linearity. Hot S22 is extracted during active load-pull measurements under nominal drive conditions.

• Reveals the optimum load impedance for maximum PAE
• Hot S22 contours differ significantly from small-signal S22
• Essential for designing the Doherty combiner's impedance trajectory

The dynamic impedance transformation mechanism in a Doherty amplifier where the peaking amplifier's current injection actively varies the load impedance seen by the carrier amplifier. Hot S22 characterizes the carrier's large-signal output reflection coefficient during this modulation process.

• At low power: carrier sees high impedance for efficiency
• At peak power: carrier sees optimal load for maximum output
• Hot S22 varies dynamically with the instantaneous envelope power

A two-port network, often realized as a quarter-wave transmission line, that transforms a load impedance to its inverse value. The design of this network depends critically on knowing Hot S22 rather than small-signal S22.

• Enables the active load-pull effect central to Doherty operation
• Impedance transformation ratio determined by Hot S22 measurements
• Incorrect design leads to suboptimal back-off efficiency

Amplitude-to-phase modulation distortion representing the nonlinear phase shift introduced by a power amplifier that varies as a function of the instantaneous input signal envelope magnitude. Hot S22 includes the phase information critical for understanding AM-PM behavior under drive.

• Phase variation of Hot S22 vs. power reveals AM-PM characteristics
• Affects the combiner's phase alignment requirements
• Must be compensated by digital predistortion for low EVM

The operating point reduction in output power from the amplifier's saturated or peak power level, expressed in decibels. Hot S22 is measured at the specific OBO corresponding to the nominal drive conditions of the Doherty amplifier.

• Typical OBO: 6-9 dB for signals with high PAPR
• Hot S22 at the average power OBO determines combiner design
• Efficiency at OBO is the primary Doherty advantage