Iso-Gain Contours

An iso-gain contour is a locus of points on a power amplifier's characteristic plane—typically plotted with instantaneous input power on one axis and drain supply voltage on the other—where the amplifier's transducer gain remains constant. These contours reveal how gain varies as a function of both drive level and supply modulation, providing the essential map for designing shaping functions that maintain linear amplification during dynamic supply operation.

The primary purpose of iso-gain contours is to derive the optimal shaping function for envelope tracking. The designer selects a target constant-gain contour that keeps the amplifier in compression—maximizing efficiency—while avoiding excessive nonlinearity. The shaping function is then extracted by tracing this contour, mapping each instantaneous input power to the corresponding supply voltage required to maintain that constant gain. This ensures the amplifier operates at peak efficiency across its dynamic range.

Iso-gain contours are generated through load-pull measurements or nonlinear vector network analyzer (NVNA) characterization. The process involves:

• Sweeping RF input power across the amplifier's dynamic range
• Stepping drain supply voltage from minimum to maximum rated values
• Recording complex gain (magnitude and phase) at each operating point
• Interpolating constant-gain loci from the resulting three-dimensional dataset This data forms the static AM-AM/AM-PM characterization of the ET PA.

Iso-gain contours graphically illustrate the trade-off between linearity and efficiency. Contours in the deep compression region (lower supply voltages for a given input power) correspond to higher efficiency but steeper gain variation, making linearization more challenging. Contours in the linear region (higher supply voltages) offer flatter gain response but poor efficiency. The art of ET design lies in selecting a contour that balances power-added efficiency (PAE) with realizable DPD correction capability.

Iso-gain contours are not static; they shift with junction temperature and operating frequency. Thermal effects cause gain expansion or compression that warps the contour shape, while frequency-dependent matching networks alter the impedance environment. Advanced ET-DPD systems must account for this by either:

• Characterizing contours across temperature and frequency corners
• Implementing adaptive contour tracking with periodic recalibration
• Incorporating thermal memory models into the DPD coefficient extraction

When extended to include phase distortion, iso-gain contours become part of a 3D behavioral map that captures both AM-AM and AM-PM characteristics. This 3D representation—gain magnitude and phase versus input power and supply voltage—directly populates 3D look-up tables (3D LUTs) used in memoryless ET-DPD. The predistorter indexes this table using instantaneous input power and the shaped supply voltage to apply the inverse complex gain correction, linearizing the ET PA in real time.

A deterministic mapping function, often implemented as a look-up table (LUT), that translates the instantaneous baseband signal magnitude into a target supply voltage. The shaping function is directly derived from iso-gain contours to maintain constant gain while minimizing DC power consumption. The optimal shaping function traces a path through the iso-gain contour map that keeps the PA operating at peak efficiency for each instantaneous envelope power level.

The nonlinear variation in a power amplifier's gain as a function of its instantaneous drain voltage. This phenomenon is the primary distortion mechanism that iso-gain contours characterize and quantify. Key aspects include:

• Gain expansion at low supply voltages due to reduced transistor output conductance
• Gain compression at high input drive levels where the transistor enters saturation
• The contour map visualizes exactly how much input power adjustment is needed at each supply voltage to maintain a target gain

A power amplifier modeling framework that accepts both the RF input signal and the dynamic supply voltage as independent variables to accurately predict nonlinear behavior. Iso-gain contours serve as the static foundation of this model, capturing the memoryless nonlinear relationship between input power, supply voltage, and output gain. The dual-input model extends this with memory terms to account for thermal and trapping effects.

The operating point on a power amplifier's efficiency curve where a small reduction in output power results in a sharp drop in efficiency. Iso-gain contours reveal the efficiency knee across different supply voltages, defining the lower boundary for effective envelope tracking operation. Below this knee, the PA's drain efficiency collapses, making envelope tracking counterproductive. The shaping function is designed to avoid operating in this region.

A memoryless predistortion structure indexed by instantaneous input power and supply voltage to apply a complex gain correction. The 3D LUT is populated directly from iso-gain contour measurements, storing the inverse nonlinearity required to linearize the ET PA. Each table entry represents the complex predistortion coefficient needed at a specific (Pin, Vdd) coordinate to achieve the desired linear gain.

Unwanted phase modulation of the output RF signal caused by the dynamic variation of the power amplifier's supply voltage. While iso-gain contours primarily map amplitude behavior, the phase response also varies with supply voltage due to:

• Voltage-dependent transistor parasitic capacitances
• Nonlinear input capacitance modulation
• Impedance shifts at the transistor's intrinsic current generator plane Advanced iso-gain characterization includes phase contours to enable full complex gain correction.