Cardiff Model
Understanding Cardiff Model
Nonlinear Behavior and Poly-Harmonic Distortion
Traditional linear scattering parameters (S-parameters) are insufficient for design when transistors operate in nonlinear regimes, such as power amplifiers in compression. The Cardiff model addresses this by extending linear S-parameters to include large-signal behavior. Based on the poly-harmonic distortion (PHD) framework, it models the relationships between incident waves and reflected waves at the fundamental frequency and its harmonics, capturing cross-frequency interactions.
The model is parameterized using hot and cold scattering parameters. These describe how a small-signal excitation at one frequency generates responses at other frequencies in the presence of a large-signal drive tone. This allows circuit simulators to model nonlinear distortions, harmonic generation, and impedance mismatch sensitivity.
Applications in Load-Pull and PA Design
In power amplifier design, the Cardiff model is used to interpolate between discrete load-pull measurements. By capturing how the device responds to variations in load impedance at the fundamental and harmonic frequencies, it enables designers to optimize matching networks for maximum power-added efficiency (PAE) and linearity without requiring continuous physical measurements.
Key Mathematical Relations
Technical Specifications Comparison
| Transistor Model Type | Characterization Domain | Harmonic Interaction Capable | Primary Simulation Use | Measurement Complexity |
|---|---|---|---|---|
| Linear S-Parameters | Small-Signal, Linear | No | Low-power amplifiers, filter design | Low (standard VNA) |
| Cardiff (PHD) Model | Large-Signal, Behavioral | Yes (fundamental and harmonics) | Nonlinear PA matching, load-pull interpolation | Medium-High (nonlinear VNA required) |
| Compact Physics-Based (BSIM/HEMT) | Large-Signal, Equivalent Circuit | Yes (via physical equations) | IC design, device scaling analysis | Very High (DC and multi-frequency extraction) |
Frequently Asked Questions
What are hot and cold scattering parameters in the Cardiff model?
Hot scattering parameters are measured when the device is active and driven by a large-signal excitation. Cold scattering parameters are measured under passive or unexcited conditions. Hot parameters capture the mixing and frequency conversion behaviors that only occur when the transistor is in compression.
Why is the Cardiff model preferred over compact physical models in some PA designs?
Compact physical models require detailed knowledge of the semiconductor device geometry and doping profiles, which are often proprietary. The Cardiff model is behavioral, meaning it is extracted purely from external terminal measurements. This makes it easier to generate and use without access to foundry fabrication details.
How does the Cardiff model handle load impedance mismatches?
The model includes coefficients that describe how waves reflected from mismatched loads (at both the fundamental and harmonic frequencies) mix with the internal large-signal drive tone, allowing accurate prediction of output power and efficiency under arbitrary load conditions.