G_MAX=(1/(K+√(K^2-1)))*(S_21/S_12 )

B_1=1+|S_11|^2-|S_22|^2-|D_s|^2

MAG=log10(S_21/S_12 )+log10(K_-^+ √(K^2-1))

Hello everyone,
I came across Microwaves 101.com the other day and this relatively new gain equation for unconditionally stable transistors(GMAX,top equation above). The equation was in an article, 'Stability Factor' in the encyclopedia. The equation I'm familiar with for Max Gain(GMAX) is, in this case, the bottom equation above for Maximum Available Gain(MAG). The first thing I noticed between the two equations was that for the GMAX equation, the answer is in absolute gain where as for the MAG equation, the answer is in dB. No problem there. The other thing I noticed was that in the MAG equation there's a plus and a minus sign before the radical. In the book I have, the sign that is used depends on B1, the middle equation above. In the article, B1 is said to be another stability factor similar to the 'Rollet stability factor(K)'. In the book I have, B1 is said to be an 'Intermediate Quantity', what ever that means. The two equations are exactly the same but I've never heard B1 referred to as a stability factor before. Anyway, in the book I have, if B1 is negative, the plus sign is used before the radical in the MAG equation. If B1 is positive, the minus sign is used. I don't have a lot of experience in the RF transistor world but I've never seen B1 negative before. The article states that B1 should be greater than 0.

Can anyone tell me what equation the B1 stability factor would be used in and why it should be greater than 0?

Can anyone tell me why the sign of B1 wasn't considered with respect to the GMAX equation(the sign before the radical)? Is it because B1 is usually positive?

If I'm correct about the sign of B1 and the GMAX equation, if B1 were actually negative, the GMAX equation would still work if we didn't take the reciprocal of the first factor...right?

Despite the small differences between the GMAX and MAG equations, they are essentially the same and if the sign of B1 is needed for the MAG equation then why not the GMAX equation(with out taking the reciprocal of the first factor if B1 is negative of coarse).

I hope someone out there can help reassure me, thank you...