S-parameter: Normalized Power Wave

[eedac]

normalized power wave

I am in trouble on a eq. about 'normalized power wave' (a, and b) in a reference book.

a = (Vn + Zo In) / (2√Zo)
b = (Vn - Zo In) / (2√Zo)

where n= 1, 2; indicate ports

Questions:
1) what 'normalized' means?
2) should 'pwr = ½Re{VI}' is? why now 'pwr = (½V) / (√Zo)' ?

I can't understand the pwr defination, pls help?


ref book:
R.Ludwig, P. Bretchko; p184, p168 of 'rf circuit design theory and applications'

 

[jian]

Hi, Eedac:

What normalized power wave means that you can find the power as:

P = 1/2 [ V * conj(I)] or
P = 1/2 [ |a*a| - |b*b| ]

If you define "a" and "b" based voltage waves: a = 1/2(V+Zc*I) and b = 1/2 (V-Zc*I), you will have

P = 1/2 [ |a*a| - |b*b| ] / Zc

Regards.