Agilent Technologies 4294A Specifications download pdf (Page 123)

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

is connected to the tip of the line, the measured impedance value Zi

at the other end of the line (that is, test port) is given by the following equation:

+ Zo tan h γ

Zi = Zo ———————————

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

= Zo ———————————

Zi tan h γ - Zo

If the transmission line has no propagation loss (α=0, β=ω√LC

–––

), the equation for Z

is simplified as

follows:

Zi - jZo tan β

= Z o —————————

Zo - jZi tan β

The true Z

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 γ in the transmission line as follows:

2π

β =

———

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Agilent Technologies 4294A Specifications Page 123