Studies on surface roughness for rectangular waveguide structures

Christian Lehmann

Ferdinand-Braun-Institut

Leibniz-Institut für Höchstfrequenztechnik

Berlin

Contents

2

• Modeling and numerical problems

• Overview of analytical approaches

• Simulated surfaces

• Results

• Conclusion

Activity 1 : Losses in waveguides – Simulation Difficulties

3

• Modeling and numerical problems

• Problems with the propagation constant in FD.

• Propagation constant from Time Domain.

• All other results best from FD.

• But hexahedral mesh necessary (large memory resource needed).

• Modeling the roughness has to account for very large ratios between smallest and

largest cell size.

• Difficulties in convergence.

• Problems with eigenmode solvers (bad matrix condition).

• Common similar discretization scheme for all roughness shapes.

• Delay in project.

• Presently first results with promising outcome.

Activity 1 : Losses in waveguides – Analytical approaches

4

G. Gold, K. Helmreich 2012: A Physical Model for Skin Effect in Rough Surfaces

Conductivity Profile

Calibrate profile parameters with

measurements

† taken from J. Phillips and G. Edwards (2010):

Transmission Line Modelling for Multi-Gigabit Serial Interfaces

†

Hall, Heck: Advanced Signal Integrity

for High-Speed Digital Designs

E. Hammerstad and O. Jensen: Accurate models

of computer aided microstrip design

†

Power Loss Method

Basic Maxwell

Phase constant β is not influenced by the decay α

Fitting Parameters for α

1D periodic structures (Hammerstad & Jensen)

2D periodic structures (Hall & Heck)

Activity 1 : Losses in waveguides – Simulated Surfaces

5

roughnessmod

el

not-to-scaleplot hex. meshcells

(FD)

0=none

31k

1=layer

44k

2=rampT

250k

3=stepT

238k

4=rampL

236k

5=stepL

231k

6=tower

1.3M

7=tower_inv

1.3M

Meshing

cell resolution in different directions

and on the surface

Model type (WL-86)

flat, ramp, step, layered

repeating in

longitudinal/transversal direction or

both

Model dependent parameters

filling rate (steps/towers)

conductivity profile (layer)

Surface parameters

period length

roughness

border thickness

Dimensions

waveguide width-height

border thickness

Material and models

H&J model or regular Maxwell

conductivity

solver (freq/time)

6

Activity 1 : Losses in waveguides – Results

2200 2400 2600 2800 3000 3200 3400

1,1

1,2

1,3

1,4

1,5

1,6

1,7

1,8

vp

h/c

0

frequency in GHz

flat 1d

layer(k=0) 1d

ramp T 1d

step T 1d

ramp L 1d

step L 1d

tower 1d

inv tower 1d

layer(k=0) 10d

ramp T 10d

step T 10d

ramp L 10d

step L 10d

tower 10d

inv tower 10d

2300 2320 2340 2360 2380 2400

1,45

1,46

1,47

1,48

1,49

1,50

1,51

1,52

1,53

structures with d= 10

vp

h/c

0

frequency in GHz

flat 1d

layer(k=0) 1d

ramp T 1d

step T 1d

ramp L 1d

step L 1d

tower 1d

inv tower 1d

layer(k=0) 10d

ramp T 10d

step T 10d

ramp L 10d

step L 10d

tower 10d

inv tower 10d

flat and all structures with d= 1

7

Activity 1 : Losses in waveguides – Results

2000 2200 2400 2600 2800 3000 3200 3400

0

4

8

12

16

20

de

ca

y in

dB

/cm

frequency in GHz

model 0

model 1

model 2

model 3

model 4

model 5

3150 3200 3250 3300 3350

3

4

5

6

de

ca

y in

dB

/cm

frequency in GHz

model 2 rms=110 nm

model 2 rms=220 nm

model 2 rms=330 nm

model 2 rms=440 nm

model 2 rms=550 nm

8

Activity 1 : Losses in waveguides – Results

Roughness effects 2

Frequency domain simulation

Different profile structures yield different frequency behaviour.

3150 3200 3250 3300 3350

3,5

4,0

4,5

5,0

5,5

6,0

6,5

de

ca

y in

dB

/cm

frequency in GHz

model 4 rms=110 nm

model 4 rms=220 nm

model 4 rms=330 nm

model 4 rms=440 nm

model 4 rms=550 nm

9

Activity 1 : Losses in waveguides – Results

Roughness effects 3

@3240 GHz

Comparison to Hammerstad & Jensen (model 2) under research

model 2 model 4 0 100 200 300 400 500 600

4,0

4,5

5,0

5,5

6,0

6,5

7,0

de

ca

y in

dB

/cm

rms in nm

model 2

model 4

E. Hammerstad and O. Jensen: Accurate models

of computer aided microstrip design

†

10

Activity 1 : Losses in waveguides – Results

1.8e7 2.5e7 3.3e7

11

Activity 1 : Losses in waveguides – Results

2000 2200 2400 2600 2800 3000 3200 3400

3

4

5

6

7

8

9

10

11

de

ca

y in

dB

/cm

frequency in GHz

rms = 120 nm, kappa_0 = 0

rms = 120 nm, kappa_0 = 1.45e7

rms = 120 nm, kappa_0 = 2.90e7

rms = 120 nm, kappa_0 = 4.35e7

rms = 120 nm, kappa_0 = 5.80e7

model 2 rms=110 nm

model 4 rms=110 nm

12

Activity 1 : Conclusion

Difficult simulation conditions in solver

Dense discretization and shape independent distribution.

Time domain only for propagation constant.

Frequency best for 3D structures.

Present results promising

Some more results can verify the analytical models Layer model by Gold & Helmreich with best chances