How does impedance mismatch at the LNA input degrade measured noise figure?
Noise Parameters and Source Impedance
Every active device has a set of four noise parameters that fully characterize how its noise figure varies with the impedance presented at its input: Fmin (minimum noise figure), Gamma_opt (optimum source reflection coefficient), and Rn (equivalent noise resistance). These parameters define a family of constant noise figure circles on the Smith Chart.
The relationship between noise figure and source impedance is given by the noise figure equation. When the source impedance exactly equals Gamma_opt, the device achieves its minimum noise figure Fmin. Any deviation from this optimum increases the noise figure, with the rate of increase controlled by Rn. A device with high Rn is very sensitive to source impedance; a device with low Rn is tolerant of mismatch.
In practice, this means the impedance match for minimum noise and the impedance match for maximum power transfer (conjugate match) are usually different. This is the fundamental noise-gain tradeoff in LNA design. The designer must choose between presenting Gamma_opt for best noise (noise match) or presenting S11* for best gain and return loss (gain match). Compromise solutions achieve acceptable noise with adequate gain and return loss.
For system integrators, this effect means that any component placed between the antenna and LNA, such as a cable, filter, or switch, changes the source impedance the LNA sees. Even if the component is well-matched to 50 ohms, the LNA's optimal noise impedance may not be 50 ohms, so the measured system NF may not equal the sum of the component loss and the LNA's datasheet NF.
Where:
Fmin = minimum noise factor (linear)
Rn = equivalent noise resistance (Ω)
Γs = actual source reflection coefficient
Γopt = optimum source reflection coefficient
Frequently Asked Questions
Is Gamma_opt the same as S11?
No. Gamma_opt is the source impedance that minimizes noise figure, while S11 describes the device's input match. The conjugate of S11 gives the source impedance for maximum power transfer, which is generally different from Gamma_opt.
How do I find Gamma_opt for an LNA?
Gamma_opt is either specified on the device datasheet (often as magnitude and angle at each frequency) or measured using a source-pull noise measurement system that varies the source impedance systematically while measuring noise figure.
Can I match for both noise and gain simultaneously?
Only if Gamma_opt happens to equal S11*. In practice, designers use techniques like inductive source degeneration (in transistor-level design) or iterative matching network optimization to find a compromise impedance that achieves near-Fmin noise with acceptable gain and return loss.