## 1. 極間穩定的意義：#

$$\Gamma_{in} = w = \frac{a \Gamma_L+b}{c\Gamma_L+d}$$

$$\Gamma_L = \frac{a \Gamma_{in}+b}{c \Gamma_{in}+d}$$

$$a=1, b= -S_{11}, c= S_{22}, d= -\Delta$$

$$C_L = \frac{c^*d-a^*b}{a^2-c^2} = \frac{-S_{11}|S_{22}^2|+S_{12}S_{21}S_{22}^*+S_{11}}{1-|S22|^2} = S_{11}+\frac{S_{12}S_{21}S_{22}^*}{1-|S22|^2}$$

$$r = \frac{ad-bc}{a^2-c^2} = |\frac{S_{12}S_{21}}{1-|S22|^2}|$$

## 2. 實際資料：#

Used in Small-signal S-parameter simulations: The function maps the set of terminations with unity magnitude at port 1 to port 2. The circles are defined by the loci of terminations on one port as seen at the other port. A source-mapping circle is created for each value of the swept variable(s). This measurement is supported for 2-port networks only.

defun map2_center_and_radius(sParam, center, radius)
{
decl S12xS21 = sParam(1,2)*sParam(2,1);
decl s11MagSq = pow(abs(sParam(1,1)),2);
*center = sParam(2,2)+S12xS21*conj(sParam(1,1))/(1-s11MagSq);
}


$$S_{11}+\frac{S_{12}S_{21}S_{22}^*}{1-|S22|^2}$$

$$|\frac{S_{12}S_{21}}{1-|S22|^2}|$$