# Instrumentation & Measurement Magazine 25-8 - 36

```Fig. 8. Comparison of the simulation, Thru-only de-embedded and the proposed method de-embedded in this paper. (a) S11; (b) S21.
S-parameters (solid lines) and simulated S-parameters of DUT
(dashed lines). The de-embedding results of Thru-only and
the proposed method are both very stable below 20 GHz. As
the frequency increases, the results of Thru-only deviate to
the simulation values gradually which is caused by the more
complex parasitic effects. The result shows that the proposed
method is in better agreement with the simulation results, and
the maximum error of reflection coefficient within 0.5-80 GHz
does not exceed 1.0 dB.
S parameters are defined with certain terminal conditions,
and the port impedance of VNA is generally 50 ohms.
For example, if a generalized S parameters has been normalized
to 50 ohms, it can be used to compute reflection and
transmission directly from signals that are normalized to
50 ohms. Therefore, the S parameters of DUT corresponds to
the reference impedance, that is, the S parameter is based on
a specified Z0
where ZΩ
are diagonal matrices with the desired impedance
and admittance as diagonal values, generally 50 ohms. SΩ
is the renormalized S-matrix.
and YΩ
Conclusions
. After de-embedding, the system impedance
is equal to the characteristic impedance of the transmission
line, and it can be obtained by ABCD parameters as follows
[11]:
Zc 
ABCD
ABCD
12
21
(12)
The subscripts in (12) represent the corresponding elements
of the ABCD matrix. To renormalize the system
impedance from the calibrated Zc
to 50 ohms, there is a unique
impedance matrix Z defined as follows:
  
Z Z IS I S Z
1
 00


is a diagonal matrix and diagonal values are both Zc
(13)
where S is a 2×2 generalized S-matrix, I is the identity matrix,
Z0
. The
renormalized S-matrix is then calculated from the unique impedance
matrix using the following formula:
S Y ZZ Z Z ZΩ
Ω 
36
Ω

 Ω


Ω

1
(14)
An improved method based on Thru-only de-embedding
has been presented, and the parasitic effects of the DUT
containing the transmission lines are all taken into account.
It requires two lines of double length relationship as standards
besides the DUT structure. The feasibility and the
accuracy of the proposed method are demonstrated by
measurement. In conclusion, the proposed method shows
better agreement than the Thru-only procedure between
de-embedded and simulated results up to 80 GHz. In order
to improve the accuracy of de-embedding, future work
will focus on the accurate measurement of characteristic
impedance.
Acknowledgment
This work was supported in part by the Scientific Instrument
Developing Project of the Chinese Academy of Sciences, Grant
No. YJKYYQ20200056, with technical cooperation with Huawei
Technologies.
References
[1] M. Koolen, J. Geelen, and M. Versleijen, " An improved
de-embedding technique for on-wafer high-frequency
characterization, " in Proc. IEEE Bipolar Circuits and Technol. Mtg.,
1991.
[2] M. H. Cho, " A cascade open-short-thru (COST) de-embedding
method for microwave on-wafer characterization and automatic
measurement, " IEICE Trans. Electronics, vol. 88, no. 5, pp. 845-850,
2005.
[3] G. Vincenzi, G. Deligeorgis. F. Coccetti et al., " Open-thru deembedding
for graphene RF devices, " in Proc. IEEE Microwave
Symp., 2014.
IEEE Instrumentation & Measurement Magazine
November 2022
```

# Instrumentation & Measurement Magazine 25-8

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