**3. De-embedding techniques**

Algorithms of open-short, TRL and TL de-embedding techniques are introduced in this section. Table 1 shows the patterns used in each de-embedding method.

Accuracy Investigation of De-Embedding Techniques Based on Electromagnetic Simulation for On-Wafer RF Measurements 237

(1)

(2)

(3)

(4)

() ()

*open open*

*open open*

*p*

 

parameters after transforming *<sup>T</sup> Y* into Z-parameters *<sup>T</sup> Z* .

*Z*

matrix.

when the DUT is a lumped element.

*p*

*p*

*T T*

By comparing matrix elements, *Zs*<sup>1</sup> , *Zs*2 and *Zs*3 can be determined.

By comparing matrix elements, *Yp*<sup>1</sup> , *Yp*2 and *Yp*3 can be determined.

*Y*

(open) 13 3 11 12

3 12

*Y Y*

*YY Y YY Y*

() () 3 23 21 22

*Y Y Y YY* 

> () () 1 11 12

*open open*

() () 2 22 12 ( )

*open*

11 12 13 3 3 23 21 22

*Z Z Z ZZ* 

> 1 11 12 2 22 12

*ZZZ ZZZ*

 

*T*

(iv) The Y-parameters for thru, only transmission line characteristic, (DUT) *Y* can be obtained by removing *Yp*<sup>1</sup> , *Yp*<sup>2</sup> , *Yp*<sup>3</sup> , *Zs*<sup>1</sup> , *Zs*2 and *Zs*<sup>3</sup> . Parasitic elements *Yp*<sup>1</sup> , *Yp*2 and *Yp*3 can be removed by subtracting (open) *<sup>Y</sup>* from (SUT) *<sup>Y</sup>* . Parasitic elements *Zs*<sup>1</sup> , *Zs*2 can be removed with the fundamental matrix (F-matrix). Finally, *Zs*3 can be removed with the Z-

It is noted that a lumped element can be the DUT although the transmission line is assumed as the DUT in this paper. De-embedding technique using electromagnetic (EM) simulator [12], with higher accuracy than the open/short de-embedding technique, is also proposed

The Thru-Reflect-Line (TRL) calibration technique [1][2][3], which is widely used for

The Thru-Line (TL) de-embedding technique [5] uses Thru (T) and Line (L) patterns, which have different lengths as shown in Figure 5. The line pattern is longer (by *L* ) than the Thru

*T T*

*T T*

3 12

*s*

**3.2. De-embedding techniques using Thru-Reflect-Line patterns** 

network analyzer calibration, can be used for deembedding of pads directly.

**3.3. De-embedding techniques using Thru-Line patterns** 

*s*

*s*

*Z Z*

*T T s ss Z Z ZZ Z*

*T ss s*

(iii) Parasitic elements *Yp*<sup>1</sup> , *Yp*2 and *Yp*3 can be removed from (short) *<sup>Y</sup>* ; (short) (open). *<sup>T</sup> YY Y* Parasitic elements *Zs*<sup>1</sup> , *Zs*2 and *Zs*3 can be determined by comparing with T-circuit

*open open*

*Y Y YY Y*

*pp p*

*p pp*

**Table 1.** Pattern used in de-embedding methods
