function [ stable, K, delta ] = rollett_stability(s)%ROLLETT_STABILITY Evaluate the Rollett stability criteria.%   [ STABLE, K, DELTA ] = ROLLETT_STABILITY(S) has the following%   parameter:%   - S: a 2x2 matrix containing the s-parameters of the device.%   The outputs are:%   - STABLE: 1 if the device is unconditionally stable and 0 if not (see%     the note below),%   - K: the value of the Rollett Stability Factor, and%   - DELTA: the value of delta used to caculate K and test for%     unconditional stability.%%   NOTE: Only considering K and DELTA (as is almost universally done -%   e.g. Gonzalez) can lead to the incorrect conclusion being reached about%   whether a device is unconditionally stable or not.  Such problems are%   rare, but can occur in practice.%%   Examples:%   % Check the stability of the device in Example 3.3.1 in Gonzalez%   % (plotted in  Figure 3.3.6).%   s500 =  [ (0.761*exp(-j*151/180*pi)) (0.025*exp( j* 31/180*pi)) ; ...%             (11.84*exp( j*102/180*pi)) (0.429*exp(-j* 35/180*pi)) ]%   s1000 = [ (0.770*exp(-j*166/180*pi)) (0.029*exp( j* 35/180*pi)) ; ...%             ( 6.11*exp( j* 89/180*pi)) (0.365*exp(-j* 34/180*pi)) ]%   s2000 = [ (0.760*exp(-j*174/180*pi)) (0.040*exp( j* 44/180*pi)) ; ...%             ( 3.06*exp( j* 74/180*pi)) (0.364*exp(-j* 43/180*pi)) ]%   s4000 = [ (0.756*exp(-j*179/180*pi)) (0.064*exp( j* 48/180*pi)) ; ...%             ( 1.53*exp( j* 53/180*pi)) (0.423*exp(-j* 66/180*pi)) ]%   [ stable500  K500  delta500 ]  = rollett_stability(s500)%   [ stable1000 K1000 delta1000 ] = rollett_stability(s1000)%   [ stable2000 K2000 delta2000 ] = rollett_stability(s2000)%   [ stable4000 K4000 delta4000 ] = rollett_stability(s4000)%%   See also: STABILITY_CIRCLES, GA_CIRCLES, GP_CIRCLES%%   Reference:%   G. Gonzalez, "Microwave Transistor Amplifiers - Analysis and Design,"%   2nd ed., Prentice Hall, 1997.%   R. W. Jackson, "Rollett Proviso in the Stability of Linear Microwave%   Circuits - A Tutorial," IEEE Transactions on Microwave Theory and%   Techniques, Vol. 54, No. 3, March 2006, pp. 993-1000.% Copyright 2008 Warren du Plessis%% This file is part of The Smith Chart Circles Toolbox.%% The Smith Chart Circles Toolbox is free software: you can redistribute it% and/or modify it under the terms of the GNU General Public License as% published by the Free Software Foundation, either version 3 of the% License, or (at your option) any later version.%% The Smith Chart Circles Toolbox is distributed in the hope that it will be% useful, but WITHOUT ANY WARRANTY; without even the implied warranty of% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General% Public License for more details.%% You should have received a copy of the GNU General Public License along% with The Smith Chart Circles Toolbox.  If not, see% <http://www.gnu.org/licenses/>.% Check the number of inputs.error(nargchk(1, 1, nargin));% Check the s-parameter matrix has the correct size.if ~isequal(size(s), [ 2 2 ])  error('The s-parameter matrix must be a 2x2 matrix.');end% Calculate the Rollett stability factor.delta = s(1,1)*s(2,2) - s(1,2)*s(2,1);K = (1 - abs(s(1,1))^2 - abs(s(2,2))^2 + abs(delta)^2)/ ...    abs(2*s(1,2)*s(2,1));% Check for unconditional stability.stable = 0;if (K > 1) && (abs(delta) < 1)    stable = 1;end