electronics

Article

MMIC on-Wafer Test Method Based on HybridBalanced and Unbalanced RF Pad Structures

Yue Bian , Yifan Gu, Xu Ding, Zhiyu Wang *, Jiongjiong Mo and Faxin Yu

School of Aeronautics and Astronautics, Zhejiang University, Hangzhou 310027, China;ybianstu@zju.edu.cn (Y.B.); yfgu@zju.edu.cn (Y.G.); dingxu111@zju.edu.cn (X.D.);jiongjiongmo@zju.edu.cn (J.M.); fxyu@zju.edu.cn (F.Y.)* Correspondence: zywang@zju.edu.cn; Tel.: +86-0571-8795-1581

Received: 20 August 2018; Accepted: 14 September 2018; Published: 19 September 2018

Abstract: Nowadays, more and more MMICs (Microwave Monolithic Integrated Circuit), such aslimiters and switches, are designed to have balanced and unbalanced test pad structures to solvethe challenging size restrictions and integration requirements for MMICs. Hybrid balanced andunbalanced RF (Radio Frequency) probes are adopted for an on-wafer test of the heteromorphystructures. The thru standard based on single balanced or unbalanced structures cannot meet theimpedance matching requirements of the hybrid RF probes at the same time, which leads to adramatic decreasing of the calibration accuracy and cannot satisfy the requirement of MMIC test.Therefore, in this paper, the calibration error estimating of hybrid RF probes based on traditionalSOLR (Short Open Load Reciprocal) calibration method is performed , and an on-wafer test approachof MMIC based on hybrid balanced and unbalanced RF probes is proposed which combines the OSL(Open Short Load) second-order de-embedding technique with vector error correction and the matrixtransformation technique. The calibration reference plane can be accurately shifted to the probe tipwith this method, which greatly improves the test accuracy , and an automatic test system is built forthis method based on the object-oriented C# language.

Keywords: balanced and unbalanced structures; on-wafer test; OSL de-embedding; matrixtransformation; automatic test system

1. Introduction

Nowadays, with stringent size restrictions and integration requirements for MMICs, a greatnumber of MMICs, such as limiters and switches, adopt balanced and unbalanced test pad structuresin layout design, like GS (Ground Signal) pad or SG pad, to replace large-size balanced pads suchas GSG pad. These chips require both balanced and unbalanced RF probes for on-wafer testing.Due to the differences of transmission modals of electromagnetic fields, traditional on-wafer thrustandards based on single balanced or unbalanced structure adopt different structural dimensionsto match the characteristic impedances of corresponding RF probes. However, traditional thrustandards cannot meet the impedance matching requirements of hybrid balanced and unbalancedRF probes at the same time, resulting in a sharp decrease in calibration accuracy. In the research ofwidely used calibration methods, such as SOLT (Short Open Load Thru), TRL (Thru Reflect Line) ,and LRRM (Line Reflect-Reflect Match), researchers have presented several solutions [1–7] to improvethe on-wafer calibration and measurement. However, traditional thru standards are unavoidablein these calibration methods, which poses a severe challenge for on-wafer testing based on hybridbalanced and unbalanced probes.

A MMIC test based on hybrid balanced and unbalanced RF probes belongs to heteromorphystructure tests, the S-parameter of which cannot be directly measured by traditional calibration method.

Electronics 2018, 7, 208; doi:10.3390/electronics7090208 www.mdpi.com/journal/electronics

Electronics 2018, 7, 208 2 of 13

For heteromorphy structures, two main kinds of solutions have been proposed by researchers. One isto remove the insertion loss of the RF probes and other adapters by scalar calculation based on thedirect compensation method. However, this method does not include vector error correction and, thus,cannot be applied to high-frequency and high-precision test due to the lack of accuracy. The other is touse the OSL second-order de-embedding method [8] to obtain the S-parameters of the RF probes andother adapters with high accuracy , and then achieve the S-parameters of the heteromorphy structureby vector error correction and de-embedding [9–12] But the measurement accuracy of this method isquite sensitive to errors between the ideal calibration plane and the actual calibration plane.

In this paper, after evaluating the calibration error of MMIC tests with hybrid balanced andunbalanced RF probes based on the traditional SOLR calibration technique [13–17], an MMIC on-wafertest method based on balanced and unbalanced RF pad structure is proposed. This method combinesan OSL second-order de-embedding technique with vector error correction , and cascade matrixtransformation technique, which introduces the vector error correction to the actual calibration planeand further improves the accuracy of the S-parameter extraction of the RF probe. After the vectorerror correction and de-embedding, the calibration reference plane can be accurately transferred to theprobe tips, as a result, significantly improving the test accuracy. Besides, an automatic test system isbuilt with the aid of the C# object-oriented language [18], which realizes the automatic performance ofinstrument control, data acquisition, result correction, data analysis , and graphical presentation ofthe results.

The rest of this paper is divided into four sections: The first section evaluates the calibration errorof the traditional test method, the second section introduces on-wafer test method of heteromorphystructure based on hybrid balanced and unbalanced RF probes in detail, the third section analyzes andverifies the approach based on the test results , and the last section draws the conclusion.

2. The Calibration Error Evaluation of Traditional Test Method

More and more MMICs adopt balanced and unbalanced test pad structures in layout designdue to the stringent size restrictions and integration requirements. For this kind of heteromorphystructures, the calibration error of two traditional test methods are evaluated. The SPDT switch chipand limiter chip with both GSG and SG pads shown in Figure 1 are used as an example. The bottoms ofboth chips are metalized. The first method turns each unbalanced SG pad into a conventional GSG padby wire bonding to a GSG through structure, so that the structure of balanced GSG pads at both endscan be calibrated with classic method. Then, the S-parameters of the chips are obtained by S-parameterde-embedding of the GSG through structure together with the bonding wire from the measured results.The results of the “wire-bonding” method are highly consistent with the real values , and are thusused as references in this paper. However, after the test, the micro-assembly of the chips cannot befully recovered without damage. Thus, this method can only be applied to evaluation tests but notto large-scale on-wafer test. The second method directly adopts SOLR for heteromorphy structureon-wafer calibration by ignoring the calibration error. The comparison between the test results of thesetwo methods is shown in Figure 2. Although the “direct SOLR” method does not destroy the chip,it cannot be applied due to the large result deviation.

Electronics 2018, 7, 208 3 of 13

Electronics 2018, 7, x FOR PEER REVIEW 3 of 12

(a) (b)

(c) (d)

Figure 1. Illustration of hybrid balanced and unbalanced MMIC test structure and methods with RF

probes, with (a,b) corresponding to GSG‐GSG test method after bonding and SG‐GS test method of

switch, (c,d) corresponding to GSG‐GSG test method after bonding and SG‐GS test method of

limiter.

(a) (b)

(c) (d)

Figure 2. Comparison of the S‐parameters results between different methods, with (a,b)

corresponding to return loss and insertion loss of switch, (c,d) corresponding to return loss and

insertion loss of limiter.

-60

-50

-40

-30

-20

-10

0

2 4 6 8 10 12 14 16 18 20

Ret

urn

Los

s(d

B)

Frequency(GHz)

Switch

DUT_Bonding_S11

DUT_SOLR_S11

DUT_Bonding_S22

DUT_SOLR_S22

-4

-3.5

-3

-2.5

-2

-1.5

-1

-0.5

0

2 4 6 8 10 12 14 16 18 20

Inse

rtio

n L

oss(

dB)

Frequency(GHz)

Switch

DUT_Bonding_S21

DUT_SOLR_S21

DUT_Bonding_S12

DUT_SOLR_S12

-40

-35

-30

-25

-20

-15

-10

-5

0

8 8.5 9 9.5 10 10.5 11 11.5 12

Ret

urn

Los

s(d

B)

Frequency(GHz)

Limiter

DUT_Bonding_S11

DUT_SOLR_S11

DUT_Bonding_S22

DUT_SOLR_S22

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

8 8.5 9 9.5 10 10.5 11 11.5 12

Inse

rtio

n L

oss(

dB

)

Frequency(GHz)

Limiter

DUT_Bonding_S21

DUT_SOLR_S21

DUT_Bonding_S12

DUT_SOLR_S12

Figure 1. Illustration of hybrid balanced and unbalanced MMIC test structure and methods with RFprobes, with (a,b) corresponding to GSG-GSG test method after bonding and SG-GS test method ofswitch, (c,d) corresponding to GSG-GSG test method after bonding and SG-GS test method of limiter.

Electronics 2018, 7, x FOR PEER REVIEW 3 of 12

(a) (b)

(c) (d)

Figure 1. Illustration of hybrid balanced and unbalanced MMIC test structure and methods with RF

probes, with (a,b) corresponding to GSG‐GSG test method after bonding and SG‐GS test method of

switch, (c,d) corresponding to GSG‐GSG test method after bonding and SG‐GS test method of

limiter.

(a) (b)

(c) (d)

Figure 2. Comparison of the S‐parameters results between different methods, with (a,b)

corresponding to return loss and insertion loss of switch, (c,d) corresponding to return loss and

insertion loss of limiter.

-60

-50

-40

-30

-20

-10

0

2 4 6 8 10 12 14 16 18 20

Ret

urn

Los

s(d

B)

Frequency(GHz)

Switch

DUT_Bonding_S11

DUT_SOLR_S11

DUT_Bonding_S22

DUT_SOLR_S22

-4

-3.5

-3

-2.5

-2

-1.5

-1

-0.5

0

2 4 6 8 10 12 14 16 18 20

Inse

rtio

n L

oss(

dB)

Frequency(GHz)

Switch

DUT_Bonding_S21

DUT_SOLR_S21

DUT_Bonding_S12

DUT_SOLR_S12

-40

-35

-30

-25

-20

-15

-10

-5

0

8 8.5 9 9.5 10 10.5 11 11.5 12

Ret

urn

Los

s(d

B)

Frequency(GHz)

Limiter

DUT_Bonding_S11

DUT_SOLR_S11

DUT_Bonding_S22

DUT_SOLR_S22

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

8 8.5 9 9.5 10 10.5 11 11.5 12

Inse

rtio

n L

oss(

dB

)

Frequency(GHz)

Limiter

DUT_Bonding_S21

DUT_SOLR_S21

DUT_Bonding_S12

DUT_SOLR_S12

Figure 2. Comparison of the S-parameters results between different methods, with (a,b) correspondingto return loss and insertion loss of switch, (c,d) corresponding to return loss and insertion loss of limiter.

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Further reasons of the failure of the second test method are as follows. The signal flow graph ofthe eight-error terms model used in the SOLR calibration method is shown in Figure 3. VNA (VectorNetwork Analyzer, Keysight, CA, USA) is adopted for testing. The transmission matrix betweenthe VNA transceiver’s plane and the MMIC plane is represented by a two-port error matrix [19–21].The product error equations related to thru calibration is shown in Equations (1) and (2).

e10 · e32 =ERR · ETF

ERR + EDR(ELF− ESR)(1)

e01 · e23 =ERF · ETR

ERF + EDF(ELR− ESF)(2)

ELF =S11T − EDF

[ERF + ESF(S11T − EDF)](3)

ELR =S22T − EDR

[ERR + ESR(S22T − EDR)](4)

ETF = (S21T − EXF)(1− ESF · ELF) (5)

ETR = (S12T − EXR)(1− ESR · ELR) (6)

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Further reasons of the failure of the second test method are as follows. The signal flow graph of

the eight‐error terms model used in the SOLR calibration method is shown in Figure 3. VNA (Vector

Network Analyzer, Keysight, CA, USA) is adopted for testing. The transmission matrix between the

VNA transceiver’s plane and the MMIC plane is represented by a two‐port error matrix [19–21]. The

product error equations related to thru calibration is shown in Equations (1) and (2).

10 32 ( )

ERR ETFe e

ERR EDR ELF ESR

⋅⋅ =

+ - (1)

01 23 ( )

ERF ETRe e

ERF EDF ELR ESF

⋅⋅ =

+ - (2)

11

11[ ( )]T

T

S EDFELF

ERF ESF S EDF

-=

+ - (3)

22

22[ ( )]T

T

S EDRELR

ERR ESR S EDR

-=

+ - (4)

21( )(1 )TETF S EXF ESF ELF= - - ⋅ (5)

12( )(1 )TETR S EXR ESR ELR= - - ⋅ (6)

Among them, EDF (forward directivity error), EDR (reverse directivity error), ESF (forward

source mismatch error), ESR (reverse source mismatch error), ERF (forward reflection tracking

error), ERR (reverse reflection tracking error) can be obtained by the calibration of Open, Short and

Load standards. Other error terms, ELF (forward load mismatch error), ELR (reverse load mismatch

error), ETF (forward transmission tracking error), and ETR (reverse transmission tracking error)

require the test of thru standard. As shown in Equations (3)–(6), ( 1, 2; 1, 2)ijTS i j= = represents the

S‐parameter of thru standard. For this kind of passive and reciprocal device, there is 12 21T TS S= , and

the EXF (forward crosstalk error) and EXR (reverse crosstalk error) can be ignored.

S21

S11 S22

S12

e22 e33 e00 e11

e10

e01

e32

a2 e23

DUT

b2a1

b1

VNA

ERROR ERROR

b1M

a1M

a2M

b1M

Reference Plane

Figure 3. Schematic diagram of the 8‐error‐terms model.

For the tests with different types of probes, full‐wave electromagnetic simulations are

performed to obtain the S‐parameters of the corresponding thru structures shown in Figure 4 and

Figure 5, referring to the right angle ISS (Impedance Standard Substrate) for up to 67 GHz provided

by Cascade (Substrate Material: Alumina; Thickness: 625 μm ± 25 μm; Dielectric constant: 9.9).

Then, after substituting the S‐parameters of the thru structures into the error model Equations

(3)–(6), the error terms are obtained. As shown in Figure 6, when using the SG‐GSG probes (Figure

4b) or SG‐GS probes (Figure 4c) for SOLR calibration, the port impedance mismatch have a

significant impact on the error model parameters, causing large deviation in the test results of

MMICs [22]. Moreover, in order to meet the port matching conditions, the gap between S and G

should be modified when using the SG‐GS probes for SOLR calibration, as shown in Figure 4d, but

there is no corresponding ISS. Therefore, the traditional GSG thru standard cannot meet the SG port

Figure 3. Schematic diagram of the 8-error-terms model.

Among them, EDF (forward directivity error), EDR (reverse directivity error), ESF (forwardsource mismatch error), ESR (reverse source mismatch error), ERF (forward reflection tracking error),ERR (reverse reflection tracking error) can be obtained by the calibration of Open, Short and Loadstandards. Other error terms, ELF (forward load mismatch error), ELR (reverse load mismatch error),ETF (forward transmission tracking error) , and ETR (reverse transmission tracking error) require thetest of thru standard. As shown in Equations (3)–(6), SijT(i = 1, 2; j = 1, 2) represents the S-parameterof thru standard. For this kind of passive and reciprocal device, there is S12T = S21T , and the EXF(forward crosstalk error) and EXR (reverse crosstalk error) can be ignored.

For the tests with different types of probes, full-wave electromagnetic simulations are performedto obtain the S-parameters of the corresponding thru structures shown in Figures 4 and 5, referring tothe right angle ISS (Impedance Standard Substrate) for up to 67 GHz provided by Cascade (SubstrateMaterial: Alumina; Thickness: 625 µm ± 25 µm; Dielectric constant: 9.9). Then, after substituting theS-parameters of the thru structures into the error model Equations (3)–(6), the error terms are obtained.As shown in Figure 6, when using the SG-GSG probes (Figure 4b) or SG-GS probes (Figure 4c) for SOLRcalibration, the port impedance mismatch have a significant impact on the error model parameters,causing large deviation in the test results of MMICs [22]. Moreover, in order to meet the port matchingconditions, the gap between S and G should be modified when using the SG-GS probes for SOLRcalibration, as shown in Figure 4d, but there is no corresponding ISS. Therefore, the traditional GSG

Electronics 2018, 7, 208 5 of 13

thru standard cannot meet the SG port matching requirements and the correct ELF, ELR, ETR , and ETFerror model parameters cannot be obtained. As a result, the errors of product terms e10 · e32 and e01 · e23

derived from them are further enlarged, resulting in unreliable test results shown in Figure 2.

Electronics 2018, 7, x FOR PEER REVIEW 5 of 12

matching requirements and the correct ELF, ELR, ETR, and ETF error model parameters cannot be

obtained. As a result, the errors of product terms 10 32e e⋅ and 01 23e e⋅ derived from them are

further enlarged, resulting in unreliable test results shown in Figure 2.

(a) (b)

(c) (d)

Figure 4. Models for electromagnetic simulation of thru with different types of probes, while (a)

represents GSG‐GSG model; (b) represents SG‐GSG model; (c) represents initial SG‐GS model; (d)

represents improved SG‐GS model.

(a) (b)

(c) (d)

Figure 5. Simulated S‐parameter comparison of thru with different types of probes, while (a)

represents GSG‐GSG model; (b) represents SG‐GSG model; (c) represents initial SG‐GS

model; (d) represents improved SG‐GS model.

-60

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-40

-30

-20

-10

0

2 4 6 8 10 12 14 16 18 20

S11

(dB

)

Frequency(GHz)

GSG_GSG

SG_GSG

SG_GS_Initial

SG_GS_Improved-20

-15

-10

-5

0

5

2 4 6 8 10 12 14 16 18 20

S12

(dB

)

Frequency(GHz)

GSG_GSG

SG_GSG

SG_GS_Initial

SG_GS_Improved

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-15

-10

-5

0

5

2 4 6 8 10 12 14 16 18 20

S21

(dB

)

Frequency(GHz)

GSG_GSG

SG_GSG

SG_GS_Initial

SG_GS_Improved

-60

-50

-40

-30

-20

-10

0

2 4 6 8 10 12 14 16 18 20

S22

(dB

)

Frequency(GHz)

GSG_GSG

SG_GSG

SG_GS_Initial

SG_GS_Improved

Figure 4. Models for electromagnetic simulation of thru with different types of probes, while (a)represents GSG-GSG model; (b) represents SG-GSG model; (c) represents initial SG-GS model;(d) represents improved SG-GS model.

Electronics 2018, 7, x FOR PEER REVIEW 5 of 12

matching requirements and the correct ELF, ELR, ETR, and ETF error model parameters cannot be

obtained. As a result, the errors of product terms 10 32e e⋅ and 01 23e e⋅ derived from them are

further enlarged, resulting in unreliable test results shown in Figure 2.

(a) (b)

(c) (d)

Figure 4. Models for electromagnetic simulation of thru with different types of probes, while (a)

represents GSG‐GSG model; (b) represents SG‐GSG model; (c) represents initial SG‐GS model; (d)

represents improved SG‐GS model.

(a) (b)

(c) (d)

Figure 5. Simulated S‐parameter comparison of thru with different types of probes, while (a)

represents GSG‐GSG model; (b) represents SG‐GSG model; (c) represents initial SG‐GS

model; (d) represents improved SG‐GS model.

-60

-50

-40

-30

-20

-10

0

2 4 6 8 10 12 14 16 18 20

S11

(dB

)

Frequency(GHz)

GSG_GSG

SG_GSG

SG_GS_Initial

SG_GS_Improved-20

-15

-10

-5

0

5

2 4 6 8 10 12 14 16 18 20

S12

(dB

)

Frequency(GHz)

GSG_GSG

SG_GSG

SG_GS_Initial

SG_GS_Improved

-20

-15

-10

-5

0

5

2 4 6 8 10 12 14 16 18 20

S21

(dB

)

Frequency(GHz)

GSG_GSG

SG_GSG

SG_GS_Initial

SG_GS_Improved

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-50

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-30

-20

-10

0

2 4 6 8 10 12 14 16 18 20

S22

(dB

)

Frequency(GHz)

GSG_GSG

SG_GSG

SG_GS_Initial

SG_GS_Improved

Figure 5. Simulated S-parameter comparison of thru with different types of probes, while (a) representsGSG-GSG model; (b) represents SG-GSG model; (c) represents initial SG-GS model; (d) representsimproved SG-GS model.

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Electronics 2018, 7, x FOR PEER REVIEW 6 of 12

(a) (b)

(c) (d)

Figure 6. Comparison of error terms of SOLR calibration, with (a–d) corresponding to ELF, ELR, ETF

and ETR respectively.

From above, it can be known that the traditional on‐wafer thru standard based on balanced

structure cannot meet the impedance matching requirements of the hybrid balanced and unbalanced

RF probes at the same time. Therefore, the calibration accuracy is greatly reduced. In the following

section, a new solution which can be applied for wafer‐scale test with good accuracy is presented.

3. On‐Wafer Test Method of Heteromorphy Structure

In order to solve the accuracy issues of the existing test methods, this paper proposes an

on‐wafer test approach of MMIC based on hybrid balanced and unbalanced RF probes by combining

OSL second‐order de‐embedding technique with vector error correction and cascade matrix

transformation technique. With the aid of vector error correction, the calibration reference plane is

accurately extended to the probe tip surface.

The signal flow graph of OSL second‐order de‐embedding is shown in Figure 7. Firstly, the

coaxial calibration is performed; then the Open, Short and Load standards, with known reflection

coefficients iG , are measured to obtain the reflection coefficient MiG at the coaxial calibration plane.

Assuming that the Load calibration matches well ( 0L ), the S‐parameters of the RF probes can be

obtained according to Equations (7) and (8). Generally, the three‐order polynomial models of the

capacitance and the inductance are used to characterize the Open, Short and Load standards, and

their reflection coefficients OG , SG and LG can be obtained with the help of Equations (9) and

(10).

21 12111

1 221i

Mii

S SbS

a S

(7)

11 22 21 12

( ) ( ) ( )( )( ), ,

( ) ( )S ML MO O MS ML S O MS ML MO ML

MLS O MS MO S O MS MO

S S S S

(8)

0

0

ii

i

Z Z

Z Z

-G =

+ (9)

0

0.2

0.4

0.6

0.8

1

1.2

2 4 6 8 10 12 14 16 18 20

EL

F

Frequency(GHz)

GSG_GSG

SG_GSG

SG_GS_Initial

SG_GS_Improved

0

0.2

0.4

0.6

0.8

1

1.2

2 4 6 8 10 12 14 16 18 20

EL

R

Frequency(GHz)

GSG_GSG

SG_GSG

SG_GS_Initial

SG_GS_Improved

0

0.2

0.4

0.6

0.8

1

1.2

2 4 6 8 10 12 14 16 18 20

ET

F

Frequency(GHz)

GSG_GSG

SG_GSG

SG_GS_Initial

SG_GS_Improved

0

0.2

0.4

0.6

0.8

1

1.2

2 4 6 8 10 12 14 16 18 20

ET

R

Frequency(GHz)

GSG_GSG

SG_GSG

SG_GS_Initial

SG_GS_Improved

Figure 6. Comparison of error terms of SOLR calibration, with (a–d) corresponding to ELF, ELR, ETFand ETR respectively.

From above, it can be known that the traditional on-wafer thru standard based on balancedstructure cannot meet the impedance matching requirements of the hybrid balanced and unbalancedRF probes at the same time. Therefore, the calibration accuracy is greatly reduced. In the followingsection, a new solution which can be applied for wafer-scale test with good accuracy is presented.

3. On-Wafer Test Method of Heteromorphy Structure

In order to solve the accuracy issues of the existing test methods, this paper proposes an on-wafertest approach of MMIC based on hybrid balanced and unbalanced RF probes by combining OSLsecond-order de-embedding technique with vector error correction and cascade matrix transformationtechnique. With the aid of vector error correction, the calibration reference plane is accurately extendedto the probe tip surface.

The signal flow graph of OSL second-order de-embedding is shown in Figure 7. Firstly, the coaxialcalibration is performed; then the Open, Short and Load standards, with known reflection coefficientsΓi , are measured to obtain the reflection coefficient ΓMi at the coaxial calibration plane. Assuming thatthe Load calibration matches well ( ΓL = 0 ), the S-parameters of the RF probes can be obtainedaccording to Equations (7) and (8). Generally, the three-order polynomial models of the capacitanceand the inductance are used to characterize the Open, Short and Load standards , and their reflectioncoefficients ΓO , ΓS and ΓL can be obtained with the help of Equations (9) and (10).

ΓMi =b1

a1= S11 +

S21S12Γi1− S22Γi

(7)

S11 = ΓML, S22 = ΓS(ΓML−ΓMO)+ΓO(ΓMS−ΓML)ΓSΓO(ΓMS−ΓMO)

, S21S12 = (ΓS−ΓO)(ΓMS−ΓML)(ΓMO−ΓML)ΓSΓO(ΓMS−ΓMO)

(8)

Γi =Zi − Z0

Zi + Z0(9)

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ZO = 1/(j2π f CO) = 1/(j2π f (C0 + C1 × f + C2 × f 2 + C3 × f 3))

ZS = j2π f LS = j2π f (L0 + L1 × f + L2 × f 2 + L3 × f 3)

ZL = RL + j2π f LL = RL + j2π f (L0 + L1 × f + L2 × f 2 + L3 × f 3)

(10)

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2 30 1 2 3

2 30 1 2 3

2 30 1 2 3

1/( 2 ) 1/( 2 ( ))

2 2 ( )

2 2 ( )

O O

S S

L L L L

Z j fC j f C C f C f C f

Z j fL j f L L f L f L f

Z R j fL R j f L L f L f L f

p p

p p

p p

= = + ´ + ´ + ´

= = + ´ + ´ + ´

= + = + + ´ + ´ + ´

(10)

S21

S11 S22

S12

Probe

(i=O,S,L)

DUT Measurement PlaneCoaxial Calibration Plane

ΓMi, Γi,

OpenShortLoad

(i=O,S,L)

Figure 7. Signal flow chart of the OSL method.

Actually, there are certain deviations between the ideal calibration plane and the actual

calibration plane (physical contact) of the non‐ideal standards due to the existence of the

transmission line. The attenuation and phase shift introduced by the deviation can be described by

an equivalent transmission line model. And the transmission line correction algorithm is further

used to eliminate these deviations by Equations (11)–(14). The simplified equivalent model is shown

in Figure 8, where iG represents the reflection coefficient of the ideal standard, 'iG is the actual

coefficient after correction, and rle- is the correction factor. α and β are the attenuation constant and phase constant of the transmission line, offset_loss and offset_delay are the insertion loss and time

delay of the transmission line, generally provided by the ISS manufacturer [23]. Function 910f is

the curve fitting factor, and offset_Z0 is the characteristic impedance of the transmission line with a

typical value of 50 Ω.

L: Load

L0 L1

L2

L3

L0 L1

L2

L3

RL

i=O,S,L

C0 C1 C2 C3

e-γl

e-γl

i=O,S,L

ActualCalibration

Plane

Γi,Γi',

O: Open

S: Short

IdealCalibration

Plane

Figure 8. Schematic diagram of the Standard parameter model.

90

_ _

2 _ 10

offset loss offset delay fl

offset Za

é ù⋅ê ú= ê úë û

(11)

2 _l f offset delay lb p a= ⋅ + (12)

Figure 7. Signal flow chart of the OSL method.

Actually, there are certain deviations between the ideal calibration plane and the actual calibrationplane (physical contact) of the non-ideal standards due to the existence of the transmission line.The attenuation and phase shift introduced by the deviation can be described by an equivalenttransmission line model. And the transmission line correction algorithm is further used to eliminatethese deviations by Equations (11)–(14). The simplified equivalent model is shown in Figure 8, whereΓi represents the reflection coefficient of the ideal standard, Γi

′ is the actual coefficient after correction, and e−rl is the correction factor. α and β are the attenuation constant and phase constant of thetransmission line, offset_loss and offset_delay are the insertion loss and time delay of the transmissionline, generally provided by the ISS manufacturer [23]. Function

√f /109 is the curve fitting factor ,

and offset_Z0 is the characteristic impedance of the transmission line with a typical value of 50 Ω.

Electronics 2018, 7, x FOR PEER REVIEW 7 of 12

2 30 1 2 3

2 30 1 2 3

2 30 1 2 3

1/( 2 ) 1/( 2 ( ))

2 2 ( )

2 2 ( )

O O

S S

L L L L

Z j fC j f C C f C f C f

Z j fL j f L L f L f L f

Z R j fL R j f L L f L f L f

p p

p p

p p

= = + ´ + ´ + ´

= = + ´ + ´ + ´

= + = + + ´ + ´ + ´

(10)

S21

S11 S22

S12

Probe

(i=O,S,L)

DUT Measurement PlaneCoaxial Calibration Plane

ΓMi, Γi,

OpenShortLoad

(i=O,S,L)

Figure 7. Signal flow chart of the OSL method.

Actually, there are certain deviations between the ideal calibration plane and the actual

calibration plane (physical contact) of the non‐ideal standards due to the existence of the

transmission line. The attenuation and phase shift introduced by the deviation can be described by

an equivalent transmission line model. And the transmission line correction algorithm is further

used to eliminate these deviations by Equations (11)–(14). The simplified equivalent model is shown

in Figure 8, where iG represents the reflection coefficient of the ideal standard, 'iG is the actual

coefficient after correction, and rle- is the correction factor. α and β are the attenuation constant and phase constant of the transmission line, offset_loss and offset_delay are the insertion loss and time

delay of the transmission line, generally provided by the ISS manufacturer [23]. Function 910f is

the curve fitting factor, and offset_Z0 is the characteristic impedance of the transmission line with a

typical value of 50 Ω.

L: Load

L0 L1

L2

L3

L0 L1

L2

L3

RL

i=O,S,L

C0 C1 C2 C3

e-γl

e-γl

i=O,S,L

ActualCalibration

Plane

Γi,Γi',

O: Open

S: Short

IdealCalibration

Plane

Figure 8. Schematic diagram of the Standard parameter model.

90

_ _

2 _ 10

offset loss offset delay fl

offset Za

é ù⋅ê ú= ê úë û

(11)

2 _l f offset delay lb p a= ⋅ + (12)

Figure 8. Schematic diagram of the Standard parameter model.

αl =[

o f f set_loss · o f f set_delay2o f f set_Z0

]√f

109 (11)

βl = 2π f · o f f set_delay + αl (12)

Electronics 2018, 7, 208 8 of 13

e−rl = e−(α+jβ)l (13)

Γ′i = Γie−2rl (14)

After substituting Γi′ into Equation (8), the corrected two-port S-parameters of the RF probes can

be extracted. The RF probes are passive reciprocal devices, whose S-parameters meet the formula S12 =

S21 = ±√

S21S12 , resulting in phase uncertainty problem [24]. To solve this problem, phase continuityand supplementary condition Phase|0Hz = 0 are introduced to select the phase branch, as shown inFigure 9. The true phase-frequency response of S21 both before and after the square root should becontinuous and the phase at zero frequency point is zero degree. First, the initial folded phase responseof S21S12 (red solid line) is unfolded (blue dot-dash line) based on the principle of phase continuity.Afterwards, a 180 cycle extension is performed along the vertical axis and a branch (blue dot-dashline) with a zero-frequency phase of 0 is selected , and the phase frequency response of the phasebranch is divided by 2 to obtain a true phase frequency response (black dash line).

Electronics 2018, 7, x FOR PEER REVIEW 8 of 12

( )rl j le e a b- - += (13)

' 2rli ie

-G =G (14)

After substituting 'iG into Equation (8), the corrected two‐port S‐parameters of the RF probes

can be extracted. The RF probes are passive reciprocal devices, whose S‐parameters meet the

formula 21 1212 21= S SS S = , resulting in phase uncertainty problem [24]. To solve this problem, phase

continuity and supplementary condition 0| 0HzPhase = are introduced to select the phase branch, as

shown in Figure 9. The true phase‐frequency response of 21S both before and after the square root

should be continuous and the phase at zero frequency point is zero degree. First, the initial folded

phase response of 21 12S S (red solid line) is unfolded (blue dot‐dash line) based on the principle of

phase continuity. Afterwards, a 180° cycle extension is performed along the vertical axis and a

branch (blue dot‐dash line) with a zero‐frequency phase of 0° is selected, and the phase frequency

response of the phase branch is divided by 2 to obtain a true phase frequency response (black dash

line).

Figure 9. The phase response characteristics.

After obtaining the S‐parameters ( AS , BS ) of the balanced and unbalanced RF probes, the

overall S‐parameter of the MMIC at coaxial calibration plane ( MS ), including the hybrid balanced

and unbalanced RF probes, is measured. Then, the cascade matrix transformation technique is used

to obtain the S‐parameter of the MMIC ( DS ) by probe parameters ( AS , BS ) de‐embedding from the

test result ( MS ). The block diagram of the test system is shown in Figure 10.

DUTProbe A Probe B

VNA

Deembedding Plane

Calibration Plane

Figure 10. Schematic diagram of the measurement system frame.

The scattering parameter matrixes MS , AS and BS are transformed into the transmission

parameter matrixes MT , AT and BT by using Equation (15), where MT , AT , BT and DT meet

Equation (16). Then the inverse matrix operation is performed, and the transmission parameter

-3500

-3000

-2500

-2000

-1500

-1000

-500

0

500

1000

1500

0 5 10 15 20 25 30 35 40

Ph

ase(°

)

Frequency(GHz)

Phase Response Measured_S21S12

Unwrapped_S21S12

Calculated_S21

Figure 9. The phase response characteristics.

After obtaining the S-parameters ( SA , SB ) of the balanced and unbalanced RF probes, the overallS-parameter of the MMIC at coaxial calibration plane ( SM ), including the hybrid balanced andunbalanced RF probes, is measured. Then, the cascade matrix transformation technique is used toobtain the S-parameter of the MMIC ( SD ) by probe parameters ( SA , SB ) de-embedding from the testresult ( SM ). The block diagram of the test system is shown in Figure 10.

Electronics 2018, 7, x FOR PEER REVIEW 8 of 12

( )rl j le e a b- - += (13)

' 2rli ie

-G =G (14)

After substituting 'iG into Equation (8), the corrected two‐port S‐parameters of the RF probes

can be extracted. The RF probes are passive reciprocal devices, whose S‐parameters meet the

formula 21 1212 21= S SS S = , resulting in phase uncertainty problem [24]. To solve this problem, phase

continuity and supplementary condition 0| 0HzPhase = are introduced to select the phase branch, as

shown in Figure 9. The true phase‐frequency response of 21S both before and after the square root

should be continuous and the phase at zero frequency point is zero degree. First, the initial folded

phase response of 21 12S S (red solid line) is unfolded (blue dot‐dash line) based on the principle of

phase continuity. Afterwards, a 180° cycle extension is performed along the vertical axis and a

branch (blue dot‐dash line) with a zero‐frequency phase of 0° is selected, and the phase frequency

response of the phase branch is divided by 2 to obtain a true phase frequency response (black dash

line).

Figure 9. The phase response characteristics.

After obtaining the S‐parameters ( AS , BS ) of the balanced and unbalanced RF probes, the

overall S‐parameter of the MMIC at coaxial calibration plane ( MS ), including the hybrid balanced

and unbalanced RF probes, is measured. Then, the cascade matrix transformation technique is used

to obtain the S‐parameter of the MMIC ( DS ) by probe parameters ( AS , BS ) de‐embedding from the

test result ( MS ). The block diagram of the test system is shown in Figure 10.

DUTProbe A Probe B

VNA

Deembedding Plane

Calibration Plane

Figure 10. Schematic diagram of the measurement system frame.

The scattering parameter matrixes MS , AS and BS are transformed into the transmission

parameter matrixes MT , AT and BT by using Equation (15), where MT , AT , BT and DT meet

Equation (16). Then the inverse matrix operation is performed, and the transmission parameter

-3500

-3000

-2500

-2000

-1500

-1000

-500

0

500

1000

1500

0 5 10 15 20 25 30 35 40

Ph

ase(°

)

Frequency(GHz)

Phase Response Measured_S21S12

Unwrapped_S21S12

Calculated_S21

Figure 10. Schematic diagram of the measurement system frame.

Electronics 2018, 7, 208 9 of 13

The scattering parameter matrixes SM , SA and SB are transformed into the transmission parametermatrixes TM , TA and TB by using Equation (15), where TM , TA , TB and TD meet Equation (16).Then the inverse matrix operation is performed , and the transmission parameter matrix TD of theDUT is obtained according to Equation (17). Finally, the transmission parameter TD of the DUT isconverted into desired scattering parameter SD according to Equation (18).[

Ti11 Ti12Ti21 Ti22

]=

(1

Si21

)[Si12Si21 − Si11Si22 Si11

−Si22 1

], i = M, A, B (15)

[TM] = [TA][TD][TB] (16)

[TD] = [TA]−1[TM][TB]

−1 (17)[SD11 SD12

SD21 SD22

]=

(1

TD22

)[TD12 TD11TD22 − TD12TD21

1 −TD12

](18)

4. Test Results and Analysis

Based on the on-wafer test method of the heteromorphy structure proposed in Section 3, this paperdesigned an on-wafer test system shown in Figure 11 to validate the solution. The system consists of avector network analyzer (Keysight PNA N5224A), GSG and SG RF probes (Cascade ACP-A-GSG-150,ACP-A-SG-150) and a microwave probe station (Cascaded Summit 11000BS). The switch and limiterchips mentioned in Figure 1 are selected as test samples. The photos of the MMICs are shown inFigure 11a,b , and the photo of the on-wafer test system based on the hybrid GSG-SG RF probes isshown in Figure 11c.

Electronics 2018, 7, x FOR PEER REVIEW 9 of 12

matrix DT of the DUT is obtained according to Equation (17). Finally, the transmission parameter

DT of the DUT is converted into desired scattering parameter DS according to Equation (18).

11 12 12 21 11 22 11

21 22 2221

1,i=M,A,B

1i i i i i i i

i i ii

T T S S S S S

T T SS

æ öé ù é ù-÷çê ú ê ú÷=ç ÷çê ú ê ú÷ç -è øë û ë û (15)

[ ] [ ][ ][ ]M A D BT T T T= (16)

[ ] [ ] [ ][ ]1 1

D A M BT T T T- -=

(17)

11 12 12 11 22 12 21

21 22 1222

1

1D D D D D D D

D D DD

S S T T T T T

S S TT

æ öé ù é ù-÷çê ú ê ú÷=ç ÷çê ú ê ú÷ç -è øë û ë û (18)

4. Test Results and Analysis

Based on the on‐wafer test method of the heteromorphy structure proposed in Section 3, this

paper designed an on‐wafer test system shown in Figure 11 to validate the solution. The system

consists of a vector network analyzer (Keysight PNA N5224A), GSG and SG RF probes (Cascade

ACP‐A‐GSG‐150, ACP‐A‐SG‐150) and a microwave probe station (Cascaded Summit 11000BS). The

switch and limiter chips mentioned in Figure 1 are selected as test samples. The photos of the

MMICs are shown in Figure 11a,b, and the photo of the on‐wafer test system based on the hybrid

GSG‐SG RF probes is shown in Figure 11c.

(a) (b) (c)

Figure 11. Photos of the switch and limiter chips and the test system. (a) The photo of the switch chip;

(b) The photo of the limiter chip; (c) The photo of the test system.

The S‐parameters of the SG and GSG probes obtained from the presented OSL method with

vector error correction are compared with the parameters provided by Cascade. It can be seen from

Figure 12 that the data obtained from the presented method is basically the same with factory data.

(a) (b)

GSG

SG SG

-0.6

-0.5

-0.4

-0.3

-0.2

-0.1

0

2 4 6 8 10 12 14 16 18 20

Mag

（d

B）

Frequency(GHz)

Probe_A_OSL

Probe_A_Cascade

-200

-150

-100

-50

0

50

100

150

200

2 4 6 8 10 12 14 16 18 20

Pha

se(º

)

Frequency(GHz)

Probe_A_OSL

Probe_A_Cascade

Figure 11. Photos of the switch and limiter chips and the test system. (a) The photo of the switch chip;(b) The photo of the limiter chip; (c) The photo of the test system.

The S-parameters of the SG and GSG probes obtained from the presented OSL method with vectorerror correction are compared with the parameters provided by Cascade. It can be seen from Figure 12that the data obtained from the presented method is basically the same with factory data.

The S-parameters comparison between the test results of the method proposed in this paper andthe test results of the “wire-bonding” method mentioned in Section 2 is shown in Figure 13. It can beseen that the two results are quite close. The accuracy of our method is highly enhanced comparingwith the “direct SOLR” method shown in Figure 2.

Electronics 2018, 7, 208 10 of 13

Electronics 2018, 7, x FOR PEER REVIEW 9 of 12

matrix DT of the DUT is obtained according to Equation (17). Finally, the transmission parameter

DT of the DUT is converted into desired scattering parameter DS according to Equation (18).

11 12 12 21 11 22 11

21 22 2221

1,i=M,A,B

1i i i i i i i

i i ii

T T S S S S S

T T SS

æ öé ù é ù-÷çê ú ê ú÷=ç ÷çê ú ê ú÷ç -è øë û ë û (15)

[ ] [ ][ ][ ]M A D BT T T T= (16)

[ ] [ ] [ ][ ]1 1

D A M BT T T T- -=

(17)

11 12 12 11 22 12 21

21 22 1222

1

1D D D D D D D

D D DD

S S T T T T T

S S TT

æ öé ù é ù-÷çê ú ê ú÷=ç ÷çê ú ê ú÷ç -è øë û ë û (18)

4. Test Results and Analysis

Based on the on‐wafer test method of the heteromorphy structure proposed in Section 3, this

paper designed an on‐wafer test system shown in Figure 11 to validate the solution. The system

consists of a vector network analyzer (Keysight PNA N5224A), GSG and SG RF probes (Cascade

ACP‐A‐GSG‐150, ACP‐A‐SG‐150) and a microwave probe station (Cascaded Summit 11000BS). The

switch and limiter chips mentioned in Figure 1 are selected as test samples. The photos of the

MMICs are shown in Figure 11a,b, and the photo of the on‐wafer test system based on the hybrid

GSG‐SG RF probes is shown in Figure 11c.

(a) (b) (c)

Figure 11. Photos of the switch and limiter chips and the test system. (a) The photo of the switch chip;

(b) The photo of the limiter chip; (c) The photo of the test system.

The S‐parameters of the SG and GSG probes obtained from the presented OSL method with

vector error correction are compared with the parameters provided by Cascade. It can be seen from

Figure 12 that the data obtained from the presented method is basically the same with factory data.

(a) (b)

GSG

SG SG

-0.6

-0.5

-0.4

-0.3

-0.2

-0.1

0

2 4 6 8 10 12 14 16 18 20

Mag

（d

B）

Frequency(GHz)

Probe_A_OSL

Probe_A_Cascade

-200

-150

-100

-50

0

50

100

150

200

2 4 6 8 10 12 14 16 18 20

Pha

se(º

)

Frequency(GHz)

Probe_A_OSL

Probe_A_Cascade

Electronics 2018, 7, x FOR PEER REVIEW 10 of 12

(c) (d)

Figure 12. Extracted S‐parameter results of the probes, with (a,b) corresponding to amplitude and

phase of S21 of the SG probe (probe A), respectively; (c,d) corresponding to amplitude and phase of

S21 of the GSG probe (probe B), respectively.

The S‐parameters comparison between the test results of the method proposed in this paper

and the test results of the “wire‐bonding” method mentioned in Section 2 is shown in Figure 13. It

can be seen that the two results are quite close. The accuracy of our method is highly enhanced

comparing with the “direct SOLR” method shown in Figure 2.

(a) (b)

(c) (d)

Figure 13. Comparison of the S‐parameters measurement results between different methods, with

(a,b) corresponding to return loss and insertion loss of switch, (c,d) corresponding to return loss and

insertion loss of limiter.

Since the method proposed in this paper requires a large number of complex and matrix

operations, object‐oriented C# language is used to build an automatic test program. The results

interface of the test program is shown in Figure 14. The program can execute a fully automatic

operation covering instrument control, data acquisition, results correction, data analysis and display

of graphical results, which avoids human interference, and solves the test efficiency problems faced

with the wafer‐scale test.

-0.6

-0.5

-0.4

-0.3

-0.2

-0.1

0

2 4 6 8 10 12 14 16 18 20

Mag

（d

B）

Frequency(GHz)

Probe_B_OSL

Probe_B_Cascade

-200

-150

-100

-50

0

50

100

150

200

2 4 6 8 10 12 14 16 18 20

Pha

se（

º）

Frequency(GHz)

Probe_B_OSL

Probe_B_Cascade

-60

-50

-40

-30

-20

-10

0

2 4 6 8 10 12 14 16 18 20

Ret

urn

Los

s(d

B)

Frequency(GHz)

Switch

DUT_Bonding_S11

DUT_Deembedding_S11

DUT_Bonding_S22

DUT_Deembedding_S22

-4

-3.5

-3

-2.5

-2

-1.5

-1

-0.5

0

2 4 6 8 10 12 14 16 18 20

Inse

rtio

n L

oss(

dB)

Frequency(GHz)

Switch

DUT_Bonding_S21

DUT_Deembedding_S21

DUT_Bonding_S12

DUT_Deembedding_S12

-40

-35

-30

-25

-20

-15

-10

-5

0

8 8.5 9 9.5 10 10.5 11 11.5 12

Ret

urn

Los

s(d

B)

Frequency(GHz)

Limiter

DUT_Bonding_S11

DUT_Deembedding_S11

DUT_Bonding_S22

DUT_Deembedding_S22

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

8 8.5 9 9.5 10 10.5 11 11.5 12

Inse

rtio

n L

oss(

dB

)

Frequency(GHz)

Limiter

DUT_Bonding_S21

DUT_Deembedding_S21

DUT_Bonding_S12

DUT_Deembedding_S12

Figure 12. Extracted S-parameter results of the probes, with (a,b) corresponding to amplitude andphase of S21 of the SG probe (probe A), respectively; (c,d) corresponding to amplitude and phase of S21

of the GSG probe (probe B), respectively.

Electronics 2018, 7, x FOR PEER REVIEW 10 of 12

(c) (d)

Figure 12. Extracted S‐parameter results of the probes, with (a,b) corresponding to amplitude and

phase of S21 of the SG probe (probe A), respectively; (c,d) corresponding to amplitude and phase of

S21 of the GSG probe (probe B), respectively.

The S‐parameters comparison between the test results of the method proposed in this paper

and the test results of the “wire‐bonding” method mentioned in Section 2 is shown in Figure 13. It

can be seen that the two results are quite close. The accuracy of our method is highly enhanced

comparing with the “direct SOLR” method shown in Figure 2.

(a) (b)

(c) (d)

Figure 13. Comparison of the S‐parameters measurement results between different methods, with

(a,b) corresponding to return loss and insertion loss of switch, (c,d) corresponding to return loss and

insertion loss of limiter.

Since the method proposed in this paper requires a large number of complex and matrix

operations, object‐oriented C# language is used to build an automatic test program. The results

interface of the test program is shown in Figure 14. The program can execute a fully automatic

operation covering instrument control, data acquisition, results correction, data analysis and display

of graphical results, which avoids human interference, and solves the test efficiency problems faced

with the wafer‐scale test.

-0.6

-0.5

-0.4

-0.3

-0.2

-0.1

0

2 4 6 8 10 12 14 16 18 20

Mag

（d

B）

Frequency(GHz)

Probe_B_OSL

Probe_B_Cascade

-200

-150

-100

-50

0

50

100

150

200

2 4 6 8 10 12 14 16 18 20

Pha

se（

º）

Frequency(GHz)

Probe_B_OSL

Probe_B_Cascade

-60

-50

-40

-30

-20

-10

0

2 4 6 8 10 12 14 16 18 20

Ret

urn

Los

s(d

B)

Frequency(GHz)

Switch

DUT_Bonding_S11

DUT_Deembedding_S11

DUT_Bonding_S22

DUT_Deembedding_S22

-4

-3.5

-3

-2.5

-2

-1.5

-1

-0.5

0

2 4 6 8 10 12 14 16 18 20

Inse

rtio

n L

oss(

dB)

Frequency(GHz)

Switch

DUT_Bonding_S21

DUT_Deembedding_S21

DUT_Bonding_S12

DUT_Deembedding_S12

-40

-35

-30

-25

-20

-15

-10

-5

0

8 8.5 9 9.5 10 10.5 11 11.5 12

Ret

urn

Los

s(d

B)

Frequency(GHz)

Limiter

DUT_Bonding_S11

DUT_Deembedding_S11

DUT_Bonding_S22

DUT_Deembedding_S22

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

8 8.5 9 9.5 10 10.5 11 11.5 12

Inse

rtio

n L

oss(

dB

)

Frequency(GHz)

Limiter

DUT_Bonding_S21

DUT_Deembedding_S21

DUT_Bonding_S12

DUT_Deembedding_S12

Figure 13. Comparison of the S-parameters measurement results between different methods, with (a,b)corresponding to return loss and insertion loss of switch, (c,d) corresponding to return loss and insertionloss of limiter.

Electronics 2018, 7, 208 11 of 13

Since the method proposed in this paper requires a large number of complex and matrixoperations, object-oriented C# language is used to build an automatic test program. The resultsinterface of the test program is shown in Figure 14. The program can execute a fully automaticoperation covering instrument control, data acquisition, results correction, data analysis and displayof graphical results, which avoids human interference , and solves the test efficiency problems facedwith the wafer-scale test.Electronics 2018, 7, x FOR PEER REVIEW 11 of 12

Figure 14. The result interface of the automatic test system.

5. Conclusions

This paper evaluates the calibration errors of a hybrid balanced and unbalanced RF probes test

with the traditional SOLR method and proposes an MMIC test method based on hybrid balanced

and unbalanced RF probes. A SPDT switch chip and a limiter chip are measured for method

validation. This method combines the OSL second‐order de‐embedding technique with the vector

error correction and cascade matrix transformation technique. The accuracy of the extraction of the

RF probe is improved by this method. As a result, the calibration reference plane can be accurately

translated to the probe tip, which significantly improves the test accuracy. Furthermore, with the aid

of the object‐oriented C# language, an automatic test system is built to be effectively applied to

wafer‐level testing of MMIC products.

Author Contributions: Methodology, Y.B.; Software, X.D.; Validation, J.M.; Data Curation, Y.G.; Writing:

Original Draft Preparation, Y.B.; Writing: Review and Editing, Z.W.; Supervision, Z.W.; Project Administration,

F.Y.; Funding Acquisition, J.M.

Funding: This research was funded by the National Natural Science Foundation of China grant number

61604128 and the Fundamental Research Funds for the Central Universities grant number 2017QN81002.

Acknowledgments: The authors would like to thank the Institute of Aerospace Electronics Engineering of

Zhejiang University for providing research platform and technical support.

Conflicts of Interest: The authors declare no conflict of interest.

References

1. Jiang, H.U.; Sun, L.L. A Novel SOLT Calibration for Direct Measurement of On‐Wafer DUTs. J. Microw.

2006, 22, 135–137

2. Yob, R.C.; Mahyuddin, N.M.; Ain, M.F. Implementation of Signal Flow Graph Rules Analysis on

Short‐Open‐Load‐Thru Calibration Algorithm. In Proceedings of the 9th International Conference on

Robotic, Vision, Signal Processing and Power Applications, Penang, Malaysia, 2–3 February 2016.

3. Seguinot, C.; Kennis, P.; Legier, J.F. Multimode TRL. A new concept in microwave measurements: Theory

and experimental verification. IEEE Trans. Microw. Theory Tech. 1998, 46, 536–542.

4. Yadav, C.; Deng, M.; Matos, M.D.; Fregonese, S.; Zimmer, T. Importance of complete characterization

setup on on‐wafer TRL calibration in sub‐THz range. In Proceedings of the 2018 IEEE International

Conference on Microelectronic Test Structures (ICMTS), Austin, TX, USA, 19–22 March 2018.

5. Phung, G.N.; Schmückle, F.J.; Doerner, R.; Heinrich, W.; Probst, T.; Arz, U. Effects Degrading Accuracy of

CPW mTRL Calibration at W Band. In Proceedings of the IEEE/MTT‐S International Microwave

Symposium (IMS), Philadelphia, PA, USA, 10–15 June 2018.

Figure 14. The result interface of the automatic test system.

5. Conclusions

This paper evaluates the calibration errors of a hybrid balanced and unbalanced RF probes testwith the traditional SOLR method and proposes an MMIC test method based on hybrid balanced andunbalanced RF probes. A SPDT switch chip and a limiter chip are measured for method validation.This method combines the OSL second-order de-embedding technique with the vector error correctionand cascade matrix transformation technique. The accuracy of the extraction of the RF probe isimproved by this method. As a result, the calibration reference plane can be accurately translatedto the probe tip, which significantly improves the test accuracy. Furthermore, with the aid of theobject-oriented C# language, an automatic test system is built to be effectively applied to wafer-leveltesting of MMIC products.

Author Contributions: Methodology, Y.B.; Software, X.D.; Validation, J.M.; Data Curation, Y.G.; Writing: OriginalDraft Preparation, Y.B.; Writing: Review and Editing, Z.W.; Supervision, Z.W.; Project Administration, F.Y.;Funding Acquisition, J.M.

Funding: This research was funded by the National Natural Science Foundation of China grant number 61604128and the Fundamental Research Funds for the Central Universities grant number 2017QN81002.

Acknowledgments: The authors would like to thank the Institute of Aerospace Electronics Engineering ofZhejiang University for providing research platform and technical support.

Conflicts of Interest: The authors declare no conflict of interest.

References

1. Jiang, H.U.; Sun, L.L. A Novel SOLT Calibration for Direct Measurement of On-Wafer DUTs. J. Microw. 2006,22, 135–137.

2. Yob, R.C.; Mahyuddin, N.M.; Ain, M.F. Implementation of Signal Flow Graph Rules Analysis onShort-Open-Load-Thru Calibration Algorithm. In Proceedings of the 9th International Conference onRobotic, Vision, Signal Processing and Power Applications, Penang, Malaysia, 2–3 February 2016.

Electronics 2018, 7, 208 12 of 13

3. Seguinot, C.; Kennis, P.; Legier, J.F. Multimode TRL. A new concept in microwave measurements: Theoryand experimental verification. IEEE Trans. Microw. Theory Tech. 1998, 46, 536–542. [CrossRef]

4. Yadav, C.; Deng, M.; Matos, M.D.; Fregonese, S.; Zimmer, T. Importance of complete characterization setupon on-wafer TRL calibration in sub-THz range. In Proceedings of the 2018 IEEE International Conference onMicroelectronic Test Structures (ICMTS), Austin, TX, USA, 19–22 March 2018.

5. Phung, G.N.; Schmückle, F.J.; Doerner, R.; Heinrich, W.; Probst, T.; Arz, U. Effects Degrading Accuracy ofCPW mTRL Calibration at W Band. In Proceedings of the IEEE/MTT-S International Microwave Symposium(IMS), Philadelphia, PA, USA, 10–15 June 2018.

6. Davidson, A.; Jones, K.; Strid, E. LRM and LRRM Calibrations with Automatic Determination of LoadInductance. In Proceedings of the 36th ARFTG Conference Digest, Monterey, CA, USA, 29–30 November1990.

7. Zhao, W.; Liu, S.; Wang, H. A Unified Approach for Reformulations of LRM/LRMM/LRRM CalibrationAlgorithms Based on the T-Matrix Representation. Appl. Sci. 2017, 7, 866. [CrossRef]

8. Chen, Z.Y.; Wang, Y.L.; Liu, Y. Two-port calibration of test fixtures with different test ports. Microw. Opt.Technol. Lett. 2002, 35, 299–302. [CrossRef]

9. Crupi, G.; Schreurs, M.P. Microwave De-Embedding: From Theory to Applications; Academic Press: Cambridge,MA, USA, 2013.

10. Loo, X.S.; Yeo, K.S.; Chew, K.W.J. A New Millimeter-Wave Fixture De-embedding Method Based onGeneralized Cascade Network Model. IEEE Electron Device Lett. 2013, 34, 447–449. [CrossRef]

11. Chen, B.; Ye, X.; Samaras, B. A novel de-embedding method suitable for transmission-line measurement.In Proceedings of the 2015 Asia-Pacific Symposium on Electromagnetic Compatibility (APEMC),Taipei, Taiwan, 26–29 May 2015.

12. Fesharaki, F.; Djerafi, T.; Chaker, M. S-Parameter De-embedding Algorithm and Its Application to SubstrateIntegrated Waveguide Lumped Circuit Model Extraction. IEEE Trans. Microw. Theory Tech. 2017, 65,1179–1190. [CrossRef]

13. Basu, S.; Hayden, L. An SOLR calibration for accurate measurement of orthogonal on-wafer DUTs.In Proceedings of the 1997 IEEE MTT-S International Microwave Symposium Digest, Denver, CO, USA, 8–13June 1997.

14. Ferrero, A.; Pisani, U. Two-port network analyzer calibration using an unknown ‘thru’. IEEE Microw. Guid.Wave Lett. 2002, 2, 505–507. [CrossRef]

15. Chou, Y.T.; Lu, H.C. Accurate on-wafer measurement of orthogonal four-port networks using thethru-reflection-unequal-line (TRUL) calibration method. In Proceedings of the 2010 Asia-Pacific MicrowaveConference, Yokohama, Japan, 7–10 December 2010.

16. Lu, K.C.; Lin, Y.C.; Horng, T.S. Vertical interconnect measurement techniques based on double-sidedprobing system and short-open-load-reciprocal calibration. In Proceedings of the 2011 IEEE 61st ElectronicComponents and Technology Conference (ECTC), Lake Buena Vista, FL, USA, 31 May–3 June 2011.

17. Schramm, M.; Hrobak, M.; Schür, J. A SOLR calibration procedure for the 16-term error model. In Proceedings ofthe 2012 42nd European Microwave Conference, Amsterdam, The Netherlands, 29 October–1 November 2012.

18. Watson, K.; Hammer, J.V.; Reid, J.D. Beginning Visual C# 2015 Programming. Int. J. Comput. Math. Learn.2016, 15, 21–43.

19. Ludwig, R.; Bretchko, P. RF Circuit Design: Theory and Applications; Prentice Hall: Upper Saddle River, NJ,USA, 2000.

20. Riddle, A. RF Measurements of Die and Packages; Artech House: Norwood, MA, USA, 2002.21. Dunsmore, J.P. Handbook of Microwave Component Measurements with Advanced VNA Techniques; John Wiley &

Sons Inc.: Hoboken, NJ, USA, 2012.22. Wu, M.D.; Deng, S.M.; Wu, R.B. Full-wave characterization of the mode conversion in a coplanar waveguide

right-angled bend. IEEE Trans. Microw. Theory Tech. 1995, 43, 2532–2538.

Electronics 2018, 7, 208 13 of 13

23. Keysight Technologies. Specifying Calibration Standards and Kits for Keysight Vector Network Analyzers;Application Note 1287-11 [EB/OL]; Keysight Technologies: Santa Rosa, CA, USA, 2016.

24. Ning, H.Z. Phase uncertainty in calibrating microwave test fixtures. IEEE Trans. Microw. Theory Tech. 2002,47, 1917–1922. [CrossRef]

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