Specifications

C-1
Appendix C: Open, Short, and Load Compensation
Since a non-symmetrical network circuit is assumed, equation (8) in Appendix B is not applied.
Therefore, the relationship between A and D parameters must be determined. The measurement of a
reference DUT (load device) is required to determine A and D.
When the applied voltage across a load device is V
2
’ and the current flow through it is I
2
’, the
impedance of the load device, Zstd, is expressed as:
Zstd =
V
2
’ (10)
I
2
’
The measured value of the load device, Zsm, is expressed by using matrix parameters like equation (2)
of open/short compensation, as follow:
Zsm =
AV
2
’ + BI
2
’ (11)
CV
2
’ + DI
2
’
By substituting Zstd for V
2
’ / I
2
’ in equation (11), the following equation is derived:
A
V
2
’
+ B
Zsm =
AV
2
’ + BI
2
’
=
I
2
’
=
AZstd + B (12)
CV
2
’ + DI
2
’
C
V
2
’
+ D
CZstd + D
I
2
’
Using equation (5) of open measurement and equation (6) of short measurement, the relationship
between the parameters A and D is expressed by the following equation:
Zsm =
AZstd + B
=
AZstd + DZ
s
= Zo
AZstd + DZs
CZstd + D Zstd
A + D
AZstd + DZo
Zo
c D =
ZstdZsm – ZstdZo
A
(13)
ZoZs – ZsmZo
By substituting equation (13) for the parameter D of equation (7), the equation for calculating the
corrected impedance of the DUT is derived as follows:
Zdut =
D(Zs – Zxm)
Z
o
=
ZstdZsm – ZstdZo
A x
(Zs – Zxm)
Zo
(Zxm – Zo)A ZoZs – ZsmZo (Zxm – Zo)A
Zdut =
(Zs – Zxm)(Zsm – Zo)
Zstd
(14)
(Zxm – Zo)(Zs – Zsm)
The definitions of the parameters used in this equation are:
Zdut Corrected impedance of the DUT
Zxm Measured impedance of the DUT
Zo Measured impedance when the measurement terminals are open
Zs Measured impedance when the measurement terminals are short
Zsm Measured impedance of the load device
Zstd True value of the load device
Note: These parameters are complex values which have real and imaginary components.