**Author details**

254 Numerical Simulation – From Theory to Industry

short de-embedding technique.

serious in measurement.

become shorter.

**6. Conclusion** 

applying TRL, TL, and open-short de-embedding techniques, respectively. Results are obtained by simulation using HFSS. The accuracy of the TRL and TL de-embedding techniques is very good while that of open-short de-embedding technique differs in high frequency. The accuracy becomes higher as the length *l* of the open and short patterns

> true extracted 21 21 true 21 . *S S*

(14)

<sup>21</sup> *S* . The error becomes larger when

*S*

**Figure 27.** Error of the extracted transmission coefficient *S*21 of the 600 μm-length G-MSL with open-

0 10 20 30 40 50 60 70

**Frequency (GHz)**

In this paper, EM simulation modeling for on-wafer measurement using a GSG probe was presented. The gap between ground (G) and signal (S) pads is excited by a lumped source. Transformation formula from 4-port to 2-port S-matrix expression was derived. The accuracy of EM simulation was verified by comparing with measurements. Results of EM simulation by changing excitation model suggest that the probe positioning error is not

TL de-embedding technique was applied for on-wafer measurement using a GSG probe. The accuracy of de-embedding techniques (open-short, TRL, and TL) were compared and discussed. It was found that the accuracy of TRL and TL de-embedding technique is approximately the same. Degradation of accuracy in open-short de-embedding technique was quantitatively investigated via numerical simulation. In the open-short de-embedding technique, the accuracy becomes higher as the lengths of the open and short patterns

becomes shorter. Figure 27 shows the error of the extracted *S*21 defined by

*error*

m m m m

The result indicated by "3-D FEM (HFSS)" is used for true

the length of the open and short pattern becomes longer.

0

0.5

1

1.5

**Error (%)**

2

2.5

3

Takuichi Hirano, Kenichi Okada, Jiro Hirokawa and Makoto Ando *Tokyo Institute of Technology, Japan* 
