How do I calculate the noise circles on a Smith Chart for noise figure optimization?
Noise Circle Construction
The noise figure of a linear two-port depends on the source impedance presented to its input according to: F = Fmin + (4Rn/Z0)|Γs-Γopt|²/((1-|Γs|²)|1+Γopt|²). This equation defines a family of circles on the Smith Chart, each circle corresponding to a constant value of F. The minimum NF (Fmin) occurs at the center of all circles, which is at Γs = Γopt.
| Parameter | LNA | Driver | Power Amplifier |
|---|---|---|---|
| Noise Figure | 0.3-2.0 dB | 3-8 dB | 5-15 dB (not specified) |
| Gain | 10-25 dB | 10-20 dB | 8-15 dB |
| P1dB | -10 to +10 dBm | +15 to +25 dBm | +30 to +50 dBm |
| OIP3 | +5 to +25 dBm | +25 to +40 dBm | +40 to +55 dBm |
| DC Power | 10-100 mW | 0.5-5 W | 5-500 W |
Frequently Asked Questions
What noise parameters do I need?
Four noise parameters fully characterize the transistor's noise behavior: NFmin (minimum noise figure), Γopt (optimum source reflection coefficient), and Rn (noise resistance). These are specified in the data sheet or S-parameter file at the recommended bias. Rn is normalized to Z0 (50 Ω) in many data sheets.
How do I measure noise parameters?
Use a noise parameter measurement system (source-pull): present multiple source impedances using a tuner, measure the noise figure at each, and fit the data to the noise parameter equation. Modern systems use automated tuners and extract all four noise parameters in a single sweep.
What if Γopt is far from S11*?
This is common. Options: (1) accept the gain penalty and match for noise (NF = NFmin, lower gain), (2) add source degeneration to move Γopt toward S11* (0.1-0.3 dB NF penalty, gain closer to MAG), (3) use a balanced amplifier topology to decouple the matching problem from the noise optimization.