II-4HOII-4. Power Waves and Sp-Parameters
(1) Circuits with Tx-line and Lumped Circuits
Traveling waves in a Tx-line
incident wave a(x) reflected wave b(x)
Lumped Circuits
No Tx-line No Z0 Meaningless Γ0 and ΓIN
V + ( x) = Z0 a( x) V ( x) = Z0 b( x)
1
x
V + ( x) I + ( x) V ( x) Z IN (d ) = I ( x)
Z0 =
V ( x) Γ( x) = + V ( x) Z Z0 Γ0 = L Z L + Z0
→ Power Waves
ICE651 MMIC Design
II-4-1
II-4. Power Waves and Sp-Parameters
(2) Power Waves
Power waves, ap and bp
defined by a linear transformation analogous to the traveling waves
ap ≡
1 [V + Z S I ] (1) 2 RS
traveling waves ai ( xi ) = bi ( xi ) = 1 [Vi ( xi ) + Z 0i I i ( xi )] 2 Z 0i 1 [Vi ( xi ) Z 0i I i ( xi )] 2 Z 0i
1 bp ≡ V Z* I S 2 RS
where RS=Re[ZS] Reasoning
[
]
PAVS
V = ES Z S I ∴ap = ap
2
(2)
1 [ES Z S I +……
