R&S ZNL, User Manual

Page: 217 / 1135

VNA concepts and features
R&S
®
ZNL/ZNLE
217 User Manual 1178.5966.02 ─ 19
Table 9-3: Squared S-parameters
|a
i
| 2
Available incident power (= the power provided by a generator with
a source impedance equal to the reference impedance Z
0
) at DUT
port i=1,2
|b
i
|
2 Reflected power at DUT port i=1,2
10 log|S
ii
|
2
= 20 log|S
ii
|
Reflection loss at DUT port i=1,2
10 log|S
21
| 2 = 20 log|S
21
|
Insertion loss of forward transmission
10 log|S
12
| 2 = 20 log|S
12
|
Insertion loss of reverse transmission
9.3.2 Reference impedances
Changing the reference impedances of the analyzer ports is often referred to as
renormalization of port impedances. Renormalization means that the measurement
results measured at 50 Ω (75 Ω) are converted into results at arbitrary port impedance.
●
Renormalization of the physical port impedances affects, e.g., S-parameters and
wave quantities in "Power" representation.
●
Renormalization of the balanced port impedances affects all measured quantities
that the analyzer provides for balanced ports.
The default reference impedance of a physical port is equal to the reference impe-
dance of the connector type assigned to the port (50 Ω or 75 Ω). It can be defined as a
complex value. For balanced ports, it is possible to define separate complex reference
impedances for differential and for common mode.
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
Measurement results