Amplifier Stability (K, µ, MAG)

Enter the S-parameters of a transistor or MMIC at one frequency. The tool computes the Rollett K-factor and the µ-factor (Edwards-Sinsky) to determine if the device is unconditionally stable, and the maximum available gain (MAG) when stable. Use S-parameter data from a datasheet or VNA measurement.

Equations & Parameters ▸

\(K = \dfrac{1 - |S_{11}|^2 - |S_{22}|^2 + |\Delta|^2}{2|S_{12}||S_{21}|} \qquad \Delta = S_{11}S_{22} - S_{12}S_{21}\) \(\mu = \dfrac{1-|S_{11}|^2}{|S_{22}-\Delta S_{11}^*|+|S_{12}S_{21}|}\) \(\text{MAG} = \dfrac{|S_{21}|}{|S_{12}|}\left(K - \sqrt{K^2-1}\right)\)

K > 1 and \|Δ\| < 1	Both conditions required for unconditional stability
µ > 1	Sufficient (and necessary) for unconditional stability; larger µ = more stable
MAG	Maximum achievable gain when simultaneously conjugate-matched at both ports
MSG	Maximum stable gain = \|S₂₁/S₁₂\|, defined at the K=1 boundary

S-Parameter Inputs (magnitude + angle in degrees)

S₁₁ — input reflection

S₁₂ — reverse isolation

S₂₁ — forward gain

S₂₂ — output reflection

Results

Diagram