Probe Pin Wideband Electrical Circuit Model - SWTest.org€¦ · Probe Pin Wideband Electrical...

Probe Pin Wideband Electrical Circuit Model

Mohamed EldessoukiSV TCL – An SV Probe Company

OverviewMotivation and Objective

Introduction

Closed Form Circuit Model

Probe Pin Measurements and Simulation

Probe Pin Modeling and Verification

Summary and Conclusion

2Mohamed Eldessouki

Motivation & Objective

3Mohamed Eldessouki

MotivationCustomers are looking for Probe Head (PH) circuit model

to be able to:

Objective

Simulate and Predict Bandwidth (BW)

Simulate and Predict Power Plane Input Impedance

Develop Close Form Accurate Circuit ModelVerify Developed Model Using:Measured S-parameters Ansoft HFSS Simulation Tool (Field Analysis)

Reduce risk probe hardware not to meet test expectations

Introduction

4Mohamed Eldessouki

Trio Probe & Spring Pin

Transmission Line (TL) Model

Proximity and Skin Effect

Circuit Model Comparison

Introduction

5Mohamed Eldessouki

Probe Pin Structure

Upper Plunger

Barrel

Lower Plunger

Springlulc

Current Flow

Pin Contact

Pin Contacta a

D

Probe HeadTrio-probe Spring Pin probe

Introduction

6Mohamed Eldessouki

Proximity and Skin EffectCurrent density distribution in parallel wire.

Low Frequency High Frequency

Unbalanced current distribution due to proximity effect.

Proximity Effect

Nested Probes

Side by Side Probes

Rectangular cross-section

Circular cross-section

Introduction

7Mohamed Eldessouki

Fundamental Equations

dSHHII

Ls

*

*00

.∫=µ

dSEEVV

Cs

*

*00

.∫′

=ε

∫+

=21

*

*00

.SS

s dlHHII

RR

dSEEVV

Gs

*

*00

.∫′′

=εω

π and T Equivalent Circuit TL Model

Introduction

8Mohamed Eldessouki

Models Comparison

Model Advantages(Account for) Disadvantages

Low Frequency • Internal and External Inductance

• Proximity effect

• No Skin Effect

High Frequency • Skin Effect • No Internal Inductance• No Proximity Effect in

inductance calculationWide Band • Skin Effect

• Internal Inductance• Proximity Effect in

Inductance Calculation

• No Proximity Effect on Resistance Calculation Only


9Mohamed Eldessouki

Models Comparison for Cylindrical Probe

+= −

aDL2

cosh41 10

πµ

caR

σπ 22

=

= −

aDLext 2

cosh 10

πµ

( ) 12

22 −

=aD

aDa

RR s

π High Frequency

( ) ( )( ) ( )ζζ

ζζπ rjbeibe

jbeibera

RZ s

′−′+

=2int

extLjZZ ω+= int2Where

( ) ( ) ( ) ( )( )[ ] ( )[ ]( )222 ζζ

ζζζζπ rbeibe

rbejbeiibebera

RR s

′+′′−′

=

( ) ( ) ( ) ( )( )[ ] ( )[ ]( )

+

′+′′−′

= −

aD

rbeibeibejbeirbeber

aRL s

2cosh

210

22 πµ

ζζωζζζζ

π

)Re(ZR =)Im(ZL =

Low Frequency

Wide Band


10Mohamed Eldessouki

Inductance Comparison for Cylindrical Probe

D=400 μma=155 μm

Internal Inductance

External inductance

Skin Effect

Wide Band

High Frequency

Low Frequency

Wide band

High frequency

Low Frequency

D=1 mma=155 μm

Calculated based on spring pin dimensions



Resistance Comparison for Cylindrical Probe

D=400μma=155μmWide band

( ) 12

22 −

=aD

aDa

RR s

π

Wide band

D=1mma=155μm

( ) ( ) ( ) ( )( )[ ] ( )[ ]( )222 ζζ

ζζζζπ rbeibe

rbejbeiibebera

RR s

′+′′−′

=

Low Frequency

caR

σπ 22

=ca

Rσπ 2

2=

Low Frequency

Calculated based on spring pin dimensions



Models Development for Rectangular Probe

23ln0 +

+=

twdL

πµ

wtL

60

intµ

=

( ) ( )( ) ( )ζζ

ζζπ rjbeibe

jbeibera

RfZ s

′−′+

=2

)(int

extLjZZ ω+= int2Where)Re(ZR = )Im(ZL =

πµ8

0int =L

twl >>>

tw >> tw =

Loop Inductance calculation

𝐿𝐿𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 = 2𝐿𝐿𝑠𝑠𝑠𝑠𝑙𝑙𝑠𝑠 − 2𝑀𝑀

Internal Inductance calculation 𝐿𝐿𝑖𝑖𝑖𝑖𝑖𝑖

Find the external inductance

𝐿𝐿𝑠𝑠𝑒𝑒𝑖𝑖 = 𝐿𝐿𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 − 𝐿𝐿𝑖𝑖𝑖𝑖𝑖𝑖

Add frequency dependent internal inductance𝐿𝐿𝑙𝑙𝑙𝑙𝑙𝑙𝑙𝑙 = 𝐿𝐿𝑠𝑠𝑒𝑒𝑖𝑖 + 𝐿𝐿𝑖𝑖𝑖𝑖𝑖𝑖(𝑓𝑓)

Calculate wideband R &L



Internal Inductance Correction Factorfor Stamped Probe

w

td

wt

d

Nested Probe

Side by side Probe

20

int 1wt1

8πμL

−−=

Used Curve fitting



Inductance Comparison for Stamped Probe

Calculated based on 3mil Trio-probe dimensions

Internal Inductance

External inductance

t=10μm

t=39μm

t=90μm

t=100μm

w=39μm

w=50μm

w=90μmw=100μm

d=125μm

d=300μm

d=500μm

w=1mm

πµ

πµω

423ln/)Im(2 00 −

+

++=

twdZL in

High Frequency model

Low Frequency model



Resistance Comparison for Stamped Probe

d=130μmw=125μm

Wide bandWide band

d=1mmw=125μm

Low FrequencyLow Frequency

Error due to Geometry approximation

Proximity effect error

( ) ( ) ( ) ( )( )[ ] ( )[ ]( )222 ζζ

ζζζζπ rbeibe

rbejbeiibebera

RR s

′+′′−′

=

cwtR

σ2

=

( ) 1)(2

)(2)( 2 −+

++

=twd

twdtw

RR s

π

ππ/)( twae +=

Calculated based on 3mil Trio-probe dimensions



Capacitance Calculation for Stamped Probe

w

td

Nested Probe Side by side Probe

d-t t

dd-w w

+

( ) ( )tddwCCC fringepp /cosh 1−+=+=

πεε( )( )ttwd

C/cosh 1 +−

= −

πε

dt

𝑑𝑑 − 𝑤𝑤 + 𝑡𝑡t

Equivalent



Circuit Model Upper Plunger

Barrel

Lower Plunger

Z1

Z2

Z3

Port1

Port2

Probe tail

Stamped section

Probe tip

Measurements & Simulation


Measurement Setup



Ansoft HFSS Simulation

Structure and Boundary conditions.



Insertion and Return Loss Magnitude



Insertion and Return Loss Phase

Circuit Model & Model Verification


Lumped Circuit π Model

Barrel

Lower Plunger

Upper Plunger



Circuit Model Parameters (Total L & C)

Upper Plunger

BarrelLower Plunger

Upper Plunger

BarrelLower Plunger



Circuit Model Parameters (total R & G)

Upper Plunger

BarrelLower Plunger

Upper Plunger

BarrelLower Plunger



TL Circuit Model S-Parameters



Measurements vs. Model Magnitude & Phase Error

SUMMARY


Lumped and TL circuit models had been developed using close form Wideband solution.

Models had been analyzed for 400um probe spacing.

Models were verified against Spring pin measurements and field analysis simulation results.

Results show a good match with maximum magnitude error of 0.5dB and phase error of 12 degree at high frequency

Two models were developed. One for circular cross section and one for rectangular cross section

CONCLUSION


Using a closed form model, minimize simulation time and cost.

Model can be integrated with other probe card components to obtain a full performance prior to manufacturing to minimize risks and design optimization time delays.

TL model provides better results compared with lumped circuit model, where distribution effect takes place.

Closed form model can be used for quick product feasibility

References


• Utkarsh R. Patel, Bjrn Gustavsen, and Piero Triverioyz, “An Equivalent Surface Current Approach for the Computation of the Series Impedance of Power Cables with Inclusion of Skin and Proximity Effects”, IEEE Transactions On Power Delivery, 15 August 2013

• M. M. Al-Asadi, A. P. Duffy, A. J. Willis, K. Hodge, and T. M. Benson, “A Simple Formula For Calculating The Frequency-dependent Resistance Of A Round Wire”, Microwave And Optical Technology Letters, Vol. 19, No. 2, October 5 1998

• Pagnetti, A., Xemard, A., Paladian, F., and Nucci, “Evaluation of the impact of proximity effect in the calculation of the internal impedance of cylindrical conductors”, URSI 2011, Aug. 2011.

• C.L. Holloway and E.F. Kuester, "DC Internal Inductance for a Conductor of Rectangular Cross Section", IEEE Transactions on Electromagnetic Compatibility, Vol. 51, No. 2, pp. 338-344, May 2009.

• Z. Piatek, and B. Baron, “Exact closed form formula for self inductance of conductor of rectangular cross section”, Progress In Electromagnetics Research M, Vol. 26, 225-236, 2012

• C. R. Paul, Analysis of Multiconductor Transmission Lines, 2nd ed., Wiley, 2007.

• van der Meijs, N. P.; Fokkema, J. T., “VLSI Circuit Reconstruction From Mask Topology Integration”, VLSI Journal,1984, 2, 85-119.

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