Objectives Computationally efficient and accurate

modeling method for package PDN Automated decoupling capacitor

selection and placement Power/Signal co-simulation

Modeling of Power Delivery Network (PDN) Jae Young Choi, and Madhavan Swaminathan

Accomplishments Developed multilayered-FEM (MFEM)

– Computationally efficient (speed, memory)– Multi-dimensional problems (non-uniform mesh)– Multi-layer structures

Automated decoupling capacitor problems– Combined genetic algorithm and MFEM– Customized the algorithm for decap problems

Developed a new method– Multi-layer triangular element method (MTEM)– SPICE compatible (Physics-based equivalent ckt)– Very sparse system matrix (compared to MFEM)

Future work Incorporation of signal interconnects to

PDN model for signal-power co-simulations

Recent results

General GA

Customized GA

Improvement

iterations 149 12 X 12.4

Time 6 hours 10 mins X 36

MTEM

0 1 2 3 4 50

10

20

30

40

50

Frequency [GHz]

Mag

nitu

de (Z

11) [

dB]

MTEM with DecapsMFDM with DecapsMTEM without DecapsMFDM without Decaps

0 1 2 3 4 5

50

Z1

1 (

dB)

Frequency (GHz)

40

30

20

10

Decap Optimizer

Target Impedance

After decap opt.

0 1 2 3 4 5

x 109

-30

-20

-10

0

10

20

30

40

Frequency (Hz)

Mag

nitu

de (

Z 11)

(dB

)

MTEMMFDMMFEM

0 1 2 3 4 5

40

20

0

-20

Z1

1 (

dB)

MTEMMFDMMFEM

- Creation of dual-graph mesh

- Multi-layer structures

- SPICE compatibility

Frequency domain analysis of signal interconnects

Material characterization for high frequencies

…

i

1

2

3

4k…

N

…

CST