**3.1. De-embedding techniques using open-short patterns**

The open-short de-embedding technique [4] is reviewed and outlined here. In the openshort de-embedding technique, the parasitic component of pads is approximated by the equivalent circuit topology shown in Figure 4.

i) Three measurements are made to obtain the transmission line characteristics shown in Figure 4(i). The first measurement is done for the open-pattern, resulting in the open twoport Y-parameters (open) *Y* . The second measurement is done for the short-pattern, resulting in the short two-port Y-parameters (short) *Y* . The third measurement is done for a thrupattern, which includes the GSG pads at both ends of a short line, described by the two-port Y-parameters (SUT) *Y* . The thru-pattern can be replaced by an arbitrary structure with the GSG pads, which is named the structure under test (SUT).

(ii) The thru-pattern is approximated by the equivalent circuit topology shown in Figure 4(ii). Parasitic elements *Yp*<sup>1</sup> , *Yp*2 and *Yp*3 can be determined from (open) *<sup>Y</sup>* by comparing with -circuit parameters.

$$\mathbf{Y}^{\{\text{open}\}} = \begin{bmatrix} \mathbf{Y}\_{11}^{\{\text{open}\}} & \mathbf{Y}\_{12}^{\{\text{open}\}} \\ \mathbf{Y}\_{21}^{\{\text{open}\}} & \mathbf{Y}\_{22}^{\{\text{open}\}} \end{bmatrix} = \begin{bmatrix} \mathbf{Y}\_{p1} + \mathbf{Y}\_{p3} & -\mathbf{Y}\_{p3} \\ -\mathbf{Y}\_{p3} & \mathbf{Y}\_{p2} + \mathbf{Y}\_{p3} \end{bmatrix} \tag{1}$$

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

236 Numerical Simulation – From Theory to Industry

**3. De-embedding techniques** 

Thru

Reflect (~Open)

Line

Short

with 

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

equivalent circuit topology shown in Figure 4.


**3.1. De-embedding techniques using open-short patterns** 

GSG pads, which is named the structure under test (SUT).

The open-short de-embedding technique [4] is reviewed and outlined here. In the openshort de-embedding technique, the parasitic component of pads is approximated by the

i) Three measurements are made to obtain the transmission line characteristics shown in Figure 4(i). The first measurement is done for the open-pattern, resulting in the open twoport Y-parameters (open) *Y* . The second measurement is done for the short-pattern, resulting in the short two-port Y-parameters (short) *Y* . The third measurement is done for a thrupattern, which includes the GSG pads at both ends of a short line, described by the two-port Y-parameters (SUT) *Y* . The thru-pattern can be replaced by an arbitrary structure with the

(ii) The thru-pattern is approximated by the equivalent circuit topology shown in Figure 4(ii). Parasitic elements *Yp*<sup>1</sup> , *Yp*2 and *Yp*3 can be determined from (open) *<sup>Y</sup>* by comparing

Algorithms of open-short, TRL and TL de-embedding techniques are introduced in this

Pattern Method

TRL TL Open/Short

section. Table 1 shows the patterns used in each de-embedding method.

420um

420 μm

210um 210um

210 μm 210 μm

1020um

1020 μm

420um

420 μm

$$\begin{cases} Y\_{p1} = Y\_{11}^{\{open\}} + Y\_{12}^{\{open\}} \\ Y\_{p2} = Y\_{22}^{\{open\}} + Y\_{12}^{\{open\}} \\ Y\_{p3} = -Y\_{12}^{\{open\}} \end{cases} \tag{2}$$

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

$$\mathbf{Z}^{T} = \begin{bmatrix} \mathbf{Z}\_{11}^{T} & \mathbf{Z}\_{12}^{T} \\ \mathbf{Z}\_{21}^{T} & \mathbf{Z}\_{22}^{T} \end{bmatrix} = \begin{bmatrix} \mathbf{Z}\_{s1} + \mathbf{Z}\_{s3} & \mathbf{Z}\_{s3} \\ \mathbf{Z}\_{s3} & \mathbf{Z}\_{s2} + \mathbf{Z}\_{s3} \end{bmatrix} \tag{3}$$

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

$$\begin{cases} Z\_{s1} = \mathbf{Z}\_{11}^T - \mathbf{Z}\_{12}^T \\ Z\_{s2} = \mathbf{Z}\_{22}^T - \mathbf{Z}\_{12}^T \\ Z\_{s3} = \mathbf{Z}\_{12}^T \end{cases} \tag{4}$$

(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 Zmatrix.

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 when the DUT is a lumped element.

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

The Thru-Reflect-Line (TRL) calibration technique [1][2][3], which is widely used for network analyzer calibration, can be used for deembedding of pads directly.

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

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

(5)

can be measured while

(6)

(7)

and

2 2 2 12 22 12 22 11 2 11 2 2 22 22

are the reflection and transmission coefficients of the Thru pattern; *<sup>l</sup>*

are unknowns. With the four equations in (5), these unknowns

22 2 22

*l l l tl t l*

 

2 2

*A*

 

(8)

is chosen at the lowest considered

*B*

 

 , and *<sup>l</sup>* 

2 2 12 12 2 2 2 22 22

1 1

*S S S S*

can be found by solving the non-linear equations, for example by using Mathematica [13].

2 222

*<sup>A</sup> <sup>S</sup>*

2( )

 

*lt t*

2 222

 

> 

 

2

*l lt t l t l t*

<sup>1</sup> (2 4 2 ( )

*l tl t l t*

( )( )( )( )

ln *L*

Selecting the correct solution from the two sets of solutions in (6) and (7) is uncomplicated. If the transmission line is a right-handed waveguide, the phase constant is positive, and a set of

frequency near direct current (DC). At the next higher frequency point, in frequency sweeping, a set of solutions is chosen so that the phase constant is near the previous lower frequency point.

The effect of the pads can be de-embedded from a structure under test (SUT) by the

 Im[ ] 

It must be noted that there are two sets of solutions to (6) indicated by the double sign. The

*l tltl tltl tltl tlt*

 

*l tt*

( )( )( ( ) ))}

 

 

2 222

*l tlt l t l lt t l t*

 

*<sup>A</sup> <sup>S</sup>*

2( )

2 2 2

*S B*

<sup>1</sup> {( ) 2 <sup>2</sup>

2

 

*t*

 

2

<sup>2</sup> 2 2 <sup>222</sup> 4( ) ( )

 

*l tt l t l t*

 

 

*l t*

2

*t l*

<sup>22</sup> *S* are the S-parameters of the pads. Here, , , *tt l*

11

22

12

propagation constant can be calculated from .

solutions which gives a positive phase constant

 

 

where *<sup>t</sup>* 

*l* 

where

*A*

 

*B*

following procedure:

 and *<sup>t</sup>* 

2 11 22 12 *SSS* , , , and ( ) *<sup>L</sup> <sup>e</sup>*

*t l*

1 1

 

 

are the reflection and transmission coefficients of the Line pattern; and 11 *S* , 12 21 *S S* ( ) , and

 

*S S S S S S S S*

**Figure 4.** De-embedding technique using open and short patterns.

pattern. The overall characteristics of the Line pattern can be decomposed as a cascade connection of pads and line parts as shown in Figure 6. The assumption that two pads have completely same characteristics is necessary in TL de-embedding. From Figure 6, the total characteristics of Thru and Line patterns are

$$\begin{cases} \rho\_t = \mathbf{S}\_{11} + \frac{\mathbf{S}\_{12}}{\mathbf{1} - \mathbf{S}\_{22}}^2 \\\\ \tau\_t = \frac{\mathbf{S}\_{12}}{\mathbf{1} - \mathbf{S}\_{22}}^2 \end{cases} \quad \left| \begin{aligned} \rho\_l = \mathbf{S}\_{11} + \frac{\mathbf{S}\_{12}}{\mathbf{1} - \mathbf{S}\_{22}}^2 \mathbf{I}^2 \\\\ \tau\_l = \frac{\mathbf{S}\_{12}}{\mathbf{1} - \mathbf{S}\_{22}}^2 \mathbf{I}^2 \end{aligned} \right. \tag{5}$$

where *<sup>t</sup>* and *<sup>t</sup>* are the reflection and transmission coefficients of the Thru pattern; *<sup>l</sup>* and *l* are the reflection and transmission coefficients of the Line pattern; and 11 *S* , 12 21 *S S* ( ) , and <sup>22</sup> *S* are the S-parameters of the pads. Here, , , *tt l* , and *<sup>l</sup>* can be measured while 2 11 22 12 *SSS* , , , and ( ) *<sup>L</sup> <sup>e</sup>* are unknowns. With the four equations in (5), these unknowns can be found by solving the non-linear equations, for example by using Mathematica [13].

2 222 11 2 222 22 2 2 2 12 22 2 22 2 2 2 2 222 2( ) 2 2( ) <sup>1</sup> {( ) 2 <sup>2</sup> <sup>1</sup> (2 4 2 ( ) ( )( )( ( ) ))} 2 2 *l tlt l t l lt t l t l tt lt t t l l l tl t l l t l tl t l t l lt t l t l t <sup>A</sup> <sup>S</sup> <sup>A</sup> <sup>S</sup> S B B A* (6)

where

238 Numerical Simulation – From Theory to Industry

Port1 Port2

Open

*Yp*<sup>1</sup> *Yp*<sup>2</sup>

*Yp*3

22

*I* 0 *I* 0 *V* 0 *V* 0

Open Short

Port1 Port3 Port4 Port2

Device with parasitic circuit

Port1 Port2

(i) Measurment of 2-port S-parameter for open/short patterns and thru-pattern

(ii) Parasitic circuit of the pads is approximated by equivalent circuit

Short

*Yp*<sup>1</sup> *Yp*<sup>2</sup>

*Zs*<sup>1</sup> *Zs*<sup>2</sup>

*Yp*3

*Zs*3

Device (line)

Parasitic circuit

**Figure 4.** De-embedding technique using open and short patterns.

*Zs*3

(iii) Obtain *Zp*1, *Zp*2 and *Zp*<sup>3</sup>

*Zs*<sup>1</sup> *Zs*<sup>2</sup>

characteristics of Thru and Line patterns are

pattern. The overall characteristics of the Line pattern can be decomposed as a cascade connection of pads and line parts as shown in Figure 6. The assumption that two pads have completely same characteristics is necessary in TL de-embedding. From Figure 6, the total

(SUT) *S* 22

Port1 Port2

Port1 Port2

Port3 Port4 (DUT) *<sup>Z</sup>*

(iv) Extract the line characteristics using 2-port circuit theory

*Yp*<sup>1</sup> *Yp*<sup>2</sup>

*Zs*<sup>1</sup> *Zs*<sup>2</sup>

*Yp*3

*Zs*3

$$\begin{aligned} A &= \sqrt{-4(\rho\_l - \rho\_t)^2 \tau\_t^2 + \left( (\rho\_l - \rho\_t)^2 - \tau\_l^2 + \tau\_t^2 \right)^2} \\ B &= \sqrt{(\rho\_l - \rho\_t - \tau\_l - \tau\_t)(\rho\_l - \rho\_t + \tau\_l - \tau\_t)(\rho\_l - \rho\_t - \tau\_l + \tau\_t)(\rho\_l - \rho\_t + \tau\_l + \tau\_t)} \end{aligned} \tag{7}$$

It must be noted that there are two sets of solutions to (6) indicated by the double sign. The propagation constant can be calculated from .

$$\gamma = -\frac{\ln \Gamma}{\Delta L} \tag{8}$$

Selecting the correct solution from the two sets of solutions in (6) and (7) is uncomplicated. If the transmission line is a right-handed waveguide, the phase constant is positive, and a set of solutions which gives a positive phase constant Im[ ] is chosen at the lowest considered frequency near direct current (DC). At the next higher frequency point, in frequency sweeping, a set of solutions is chosen so that the phase constant is near the previous lower frequency point.

The effect of the pads can be de-embedded from a structure under test (SUT) by the following procedure:

(i) Measure the S-matrix of the SUT (SUT) *S* .

(ii) Transform (SUT) *S* into a cascade matrix (T-matrix) (SUT) *T* . Now (SUT) *T* is implied to be (SUT) (PAD-L) (D ) (PAD-R) *UT T T TT* , where (PAD-L) *T* , (PAD-R) *T* and (D ) *UT T* are the T-matrixes of the left pad, right pad, and device under test (DUT) embedded in the pads, respectively. The (PAD-L) *T* and (PAD-R) *T* values can be calculated from (PAD-L) *S* and (PAD-R) *S* , with the elements obtained in (6) (See also Figure 6).

Accuracy Investigation of De-Embedding Techniques Based on Electromagnetic Simulation for On-Wafer RF Measurements 241

ports with 100 Ohm intrinsic impedances, which is double of probe impedance because of

To verify the accuracy of the EM simulation, the calculated value is compared with the measured one. A micrograph of a fabricated chip is shown in Figure 8. The chip is 2.5 mm square and an 0.18 μm CMOS process is used. In the measurements, 100 μm-pitch GSG probes were used, and the system was calibrated using the impedance standard substrate (ISS). Smith charts of the S-parameters for the thru, line, and reflect patterns are shown in Figures 9, 10, and 11, respectively. The calculated and measured results agreed very well for

Then, sensitivity of lumped port position and size is investigated. Figure 12 shows position and size of lumped port in the GSG pad. Reflection coefficient *S*11 and transmission coefficient *S*12 (=*S*21) are shown in Figure 13 and Figure 14, respectively, with various sets of width (*w*), left pad offset (*dl*) and right pad offset (*dr*) (both offsets are prescribed in a similar manner). *w* is varied from 10 μm to 30 μm. *dl* and *dr* are varied from -15 μm to 15 μm. It is found that there are no significant differences in results. These results suggest that the probe positioning error is not serious in measurement. Results indicated by "edge1" and "edge2" are obtained with the excitation model in which lumped port is arranged at the edge of the GSG pad as shown in Figure 15. *wa* in Figure 15 is 20 μm for "edge1" while it is 50 μm for "edge2". The phase of *S*11 begins to show different value in high frequency region. The result indicated by "vertical" is obtained with the excitation model in Figure 16. The phase of *S*<sup>12</sup> begins to show different value in high frequency region. However, the results of these

> 

 

*S S*

2 12

11

*L*

(PADL) *S* (LINE) *S* (PADR) *S*

1

2 2 22

*<sup>S</sup> <sup>S</sup> <sup>S</sup>*

1

 

*l* 

0

12 11 22 21 *S S*

 

*S*

2 2 22

2 22 2 12

 0

 *j*

0

*L*

*<sup>S</sup> <sup>S</sup>* <sup>1</sup>

*e* 

image theory, were used for the excitations.

excitation models show good agreement.

*l*    

> 

 

*l*

*l*

 

*l l l l*

 

21 22 11 12 *S S S S*

**Figure 6.** Cascading expression of the line pattern.

*l S*

all three patterns.

(iii) (D ) *UT <sup>T</sup>* can be obtained by matrix operations: 1 1 (D ) (PAD-L) (SUT) (PAD-R) *UT T T TT* . Finally, (DUT) *S* is obtained by transformation from (D ) *UT T* , and de-embedding of the pads can be performed.

A sample Mathematica source code is given in Appendix.

**Figure 5.** Thru and line patterns.
