VNA Concepts and Features
R&S
®
ZNL/ZNLE
228
User Manual 1178.5966.02 ─ 07
The default values for the balanced port reference impedances are derived from the
default reference impedance of the physical analyzer ports (Z
0
= 50 Ω):
●
The default value for the differential mode is Z
0d
= 100 Ω = 2*Z
0
.
●
The default value for the common mode is Z
0c
= 25 Ω = Z
0
/2
Renormalization can be based on two alternative waveguide circuit theories whose
conversion formulas may yield different results if the reference impedance of at least
one test port has a non-zero imaginary part.
Conversion formula for wave quantities and S-parameters
Renormalization transforms the "raw" S-matrix S
0
for the default reference impedances
Z
0i
(with physical port number index i = 1,2,...,n) into a "renormalized" S-matrix S
1
for
the modified reference impedances Z
1i
. In terms of raw and renormalized wave quanti-
ties a
0i
, b
0i
and a
1i
, b
1i
, S
0
and S
1
are defined as follows:
.
...
...
;
...
...
1
12
11
1
1
12
11
0
02
01
0
0
02
01
n
n
n
n
a
a
a
S
b
b
b
a
a
a
S
b
b
b
The renormalized wave quantities (a
1
and b
1
) and the S-matrix S
1
can be calculated
from S
0
and the reference impedances Z
0i
, Z
1i
according to two alternative waveguide
circuit theories.
1.
Traveling waves
In the model of Marks and Williams ("A General Waveguide Circuit Theory"), the
wave quantities a and b are transformed as follows:
i
i
i
i
i
i
i
i
i
i
i
i
i
i
i
i
i
b
a
Z
Z
Z
Z
Z
Z
Z
Z
Z
Z
Z
Z
Z
b
a
0
0
1
0
1
0
1
0
1
0
0
1
1
0
0
1
1
)
Re(
)
Re(
2
1
The renormalized S-matrix S1 is calculated as:
P
S
E
S
P
S
1
0
0
1
1
with the unit matrix E and two additional matrices with the elements
i
i
i
i
ii
Z
Z
Z
Z
0
1
0
1
)
Re(
)
Re(
2
1
0
0
1
1
0
0
i
i
i
i
i
i
i
ii
Z
Z
Z
Z
Z
Z
Z
P
2.
Power waves
Measurement Results
www.allice.de
Allice Messtechnik GmbH
