Specifications

D-1
Appendix D: Electrical Length Compensation
A test port extension can be modeled using a coaxial transmission line as shown in Figure D-1.
When an impedance element Z
L
is connected to the tip of the line, the measured impedance value Zi
at the other end of the line (that is, the test port) is given by the following equation:
Z
L
+ Zo tan h γ
Zi = Zo —————————————————————
Z
L
tan h γ + Zo
γ = α + jβ = √ZY = √(R+jωL)(G+jωC)
Where, γ: Propagation constant of the transmission line
α: Attenuation constant of the transmission line
β: Phase constant of the transmission line
: Transmission line length
Zo: Characteristic impedance of the transmission line
Figure D-1. Transmission line model of test port extension
The DUT impedance value is therefore calculated as:
Zo tan h γ - Zi
Z
L
= Zo ———————————————————
Zi tan h γ - Zo
If the transmission line has no propagation loss (α = 0, β = ω√LC
–––
), the equation for Z
L
is simplified
as follows:
Zi - jZo tan β
Z
L
= Zo ———————————
Zo - jZi tan β
The true Z
L
value can be calculated if the phase shift quantity, β , is known. Here, the phase con-
stant β is related to the test signal wavelength λ in the transmission line as follows:
2π
β =
———
λ