Why does the available power equal abs(b)^2-abs(a)^2?

Hi,
I read a S-parameter tutorial. It first has such an equation:

Then, it has another equation:

I am puzzled why they are so different?

Can you explain it to me?

Best Regards,

Pin is the Power which is entered into circuit.Pavs is Available Power from Source.
They are obviously different.If Pr is zero ( conjugate matching ) all power available from the source enters into circuit.

Equations are wrong.
Pavs has to be Pin.

To start with we should clarify some terminology:
Pavs (aka the available, incident, exchangeable power from the source)=|a|2
Pr (reflected power)=|b|2
Pin (absorbed, transmitted, or actual power) =|a|2-|b|2.

So the equation in the first attachment is fine: Pin=Pavs-Pr.

But the second attachment is completely off. I'm not even sure why the condition Γ_L=Γ_S* is relevant. That doesn't have anything to do with conjugate match condition...



I'm guessing that here "Pin" doesn't mean "incident" power, but rather power absorbed by the load... I know, very sloppy.