R&S ZNL4 - Page 218

VNA concepts and features
R&S
®
ZNL/ZNLE
218User Manual 1178.5966.02 ─ 20
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
iiii
iiii
i
i
i
i
i
i
i
b
a
ZZZZ
ZZZZ
Z
Z
Z
Z
Z
b
a
0
0
1010
1010
0
1
1
0
0
1
1
)Re(
)Re(
2
1
The renormalized S-matrix S1 is calculated as:
  
PSESPS
1
00
1
1


 
with the unit matrix E and two additional matrices with the elements
ii
ii
ii
ZZ
ZZ
01
01


 
)Re(
)Re(
1
0
0
1
10
0
i
i
i
i
ii
i
ii
Z
Z
Z
Z
ZZ
Z
P


2. Power waves
In the model of Kurokawa ("Power Waves and the Scattering Matrix"), the wave
quantities a and b are transformed as follows:




























i
i
iiii
iiii
ii
i
i
b
a
ZZZZ
ZZZZ
ZZ
b
a
0
0
1010
1010
10
1
1
)Re()Re(2
1
The renormalized S-matrix S1 is calculated as:
 
 
ASESAS
1
00
1
1



with the unit matrix E and two additional matrices with the elements
ii
ii
ii
ZZ
ZZ
01
01



iiii
ii
ii
ii
A 


 1
1
1
Measurement results