Solving the oneport calibration equations.
In a network analyzer oneport calibration, three standards are
measured to determine the three error terms of the measurement
system. At first glance, it may appear that the set of three
equations to be solved are nonlinear, but they can be manipulated
into a set of three linear equations in three unknowns, as shown here.
Using the following notation (G is for gamma):
G_{A} = actual reflection coefficient
G_{M} = measured reflection coefficient
e_{00} = directivity error
e_{10}e_{01} = reflection tracking error
e_{11} = source match error
The solution of the oneport measurement error model is:
G_{M} = e_{00} + (e_{10}e_{01})
* G_{A} / (1  e_{11} * G_{A})
Let:
a = e_{10}e_{01}  e_{00} * e_{11}
b = e_{00}
c = e_{11}
Then:
G_{M} = (a * G_{A} + b) / (c * G_{A} + 1)
or,
G_{A} * a + b  G_{A} * G_{M} * c = G_{M}
Now measure the three known standards (G_{A1}, G_{A2},
G_{A3}), and with the resulting three measurements (G_{M1},
G_{M2}, G_{M3}), you have three linear equations to solve
for a, b, and c:
G_{A1} * a + b  G_{A1} * G_{M1} * c = G_{M1}
G_{A2} * a + b  G_{A2} * G_{M2} * c = G_{M2}
G_{A3} * a + b  G_{A3} * G_{M3} * c = G_{M3}
This works for any three standards, not just short, open, and load.
