designing a time-multiplexed 2-d digital waveguide

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Designing a Time- Multiplexed 2-D Digital Waveguide

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Designing a Time-Multiplexed 2-D Digital Waveguide. Simple 1D Waveguide. 210. 3. 2. 0. 0. 01. 0 21. 1. 2. 1. 0. 12. 10 2. 2. 2. 2. 0. 2 0. 210. 3. 2. 0. 01. 0. 0 21. 1. 2. 1. 0. 12. 10 2. 2. 2. 2. 0. 2 0. Note: This slide is animated – View in slide show. 210. - PowerPoint PPT Presentation

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Page 1: Designing a Time-Multiplexed 2-D Digital Waveguide

Designing a Time-Multiplexed2-D Digital Waveguide

Page 2: Designing a Time-Multiplexed 2-D Digital Waveguide

210

01

021

12

0

2

1

0

2

20

2

0

2102

3

0

2210

1

0

2021

1

0

2

3

01

121

0

20

2

0

21022

Note: This slide is animated – View in slide show

Simple 1D Waveguide

0 1 2

Page 3: Designing a Time-Multiplexed 2-D Digital Waveguide

210

01

021

12

0

2

1

0

2

20

2

0

2102

3

0

2210

1

0

2021

1

0

2

3

01

121

0

20

2

0

21022

J

0 1 2

Time-muxed junction design

Page 4: Designing a Time-Multiplexed 2-D Digital Waveguide

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11

0

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063

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0 1 2

3 4 5

6 7 8

9

Simple 2D Waveguide

Only left/right data communication

Page 5: Designing a Time-Multiplexed 2-D Digital Waveguide

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1

2

1

0

2

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063

063

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234567800 1 2

3 4 5

6 7 8

9

Page 6: Designing a Time-Multiplexed 2-D Digital Waveguide

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1

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3

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0

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063

063

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258

258

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0 1 2

3 4 5

6 7 8

9

Page 7: Designing a Time-Multiplexed 2-D Digital Waveguide

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12345678

630

852

1

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1

0

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321087654

063

063

063

528

258

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582

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0 1 2

3 4 5

6 7 8

9

Page 8: Designing a Time-Multiplexed 2-D Digital Waveguide

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01234567

12345678

630

852

1

2

3

4

1

0

2

4

3

55

087654321

108765432

210876543

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432108765

063

063

063

528

258

258

582

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56780123

0 1 2

3 4 5

6 7 8 306

582

9

Page 9: Designing a Time-Multiplexed 2-D Digital Waveguide

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01234567

12345678

630

852

1

2

3

4

1

0

2

4

3

55

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108765432

210876543

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432108765

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0 1 2

3 4 5

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582

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Page 10: Designing a Time-Multiplexed 2-D Digital Waveguide

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01234567

12345678

630

852

1

2

3

4

1

0

2

4

3

55

087654321

108765432

210876543

321087654

432108765

063

063

063

528

258

258

582

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34567801

45678012306

56780123

0 1 2

3 4 5

6 7 8 306

66

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77

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78012345630

582

582

825

9

Page 11: Designing a Time-Multiplexed 2-D Digital Waveguide

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01234567

12345678

630

852

1

2

3

4

1

0

2

4

3

55

087654321

108765432

210876543

321087654

432108765

063

063

063

528

258

258

582

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56780123

0 1 2

3 4 5

6 7 8 306

66

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88

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582

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Page 12: Designing a Time-Multiplexed 2-D Digital Waveguide

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01234567

12345678

630

852

1

2

3

4

1

0

2

4

3

55

087654321

108765432

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321087654

432108765

063

063

063

528

258

258

582

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34567801

45678012306

56780123

0 1 2

3 4 5

6 7 8 306

66

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77

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78012345630

88

765432108

80123456630

90

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582

582

825

825

825

9

Page 13: Designing a Time-Multiplexed 2-D Digital Waveguide

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01234567

12345678

630

852

1

2

3

4

1

0

2

4

3

55

087654321

108765432

210876543

321087654

432108765

063

063

063

528

258

258

582

23456780

34567801

45678012306

56780123

0 1 2

3 4 5

6 7 8 306

66

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77

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88

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80123456630

90

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582

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J

Time-muxed junction design

Page 14: Designing a Time-Multiplexed 2-D Digital Waveguide

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012345

0

0 1 2

3 4 5

6 7 8

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123456

1

321

780

210

678

Simple 2D Waveguide

Only up/down data communication

Page 15: Designing a Time-Multiplexed 2-D Digital Waveguide

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0

0 1 2

3 4 5

6 7 8

087654321

123456

1

321

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2

432

234567

780

210

801

678

Page 16: Designing a Time-Multiplexed 2-D Digital Waveguide

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0 1 2

3 4 5

6 7 8

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123456

1

321

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2

432

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3

543

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780

210

801

012

678

Page 17: Designing a Time-Multiplexed 2-D Digital Waveguide

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0 1 2

3 4 5

6 7 8

087654321

123456

1

321

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2

432

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3

543

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4

654

234567

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780

210

801

012

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Page 18: Designing a Time-Multiplexed 2-D Digital Waveguide

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0 1 2

3 4 5

6 7 8

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123456

1

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2

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4

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Page 19: Designing a Time-Multiplexed 2-D Digital Waveguide

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Page 20: Designing a Time-Multiplexed 2-D Digital Waveguide

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Page 21: Designing a Time-Multiplexed 2-D Digital Waveguide

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0 1 2

3 4 5

6 7 8

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123456

1

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2

432

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3

543

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4

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7

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8

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Page 22: Designing a Time-Multiplexed 2-D Digital Waveguide

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3 4 5

6 7 8

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Page 23: Designing a Time-Multiplexed 2-D Digital Waveguide

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0 1 2

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JTime-muxed junction design

Page 24: Designing a Time-Multiplexed 2-D Digital Waveguide

0 1 2

3 4 5

6 7 8

JJ

Combined time-muxed junction design incorporating both directions

Page 25: Designing a Time-Multiplexed 2-D Digital Waveguide

Time-Multiplexing via C-Slowing/Retiming

Simple 1D Example

Page 26: Designing a Time-Multiplexed 2-D Digital Waveguide

0 1 2 J J J

Starting circuit

Page 27: Designing a Time-Multiplexed 2-D Digital Waveguide

0 1 2 J J J

J J J021

021

021 021 021

021021021

C-Slow by 3 (time-multiplexing factor)

Label register sets 1, 2 and 3

Page 28: Designing a Time-Multiplexed 2-D Digital Waveguide

0 1 2 J J J

J J J021

021

J J J

021 021 021

021021021

021 021 021 021

02102 102 1021

Retime orange registers backwards through junction to label middle junction inputs with 1

Page 29: Designing a Time-Multiplexed 2-D Digital Waveguide

0 1 2 J J J

J J J021

021

J J J

021 021 021

021021021

021 021 021 021

02102 102 1021

J J J021 021 021 01

0210 102 1021

2

2

Retime yellow registers backwards through junction to label righthand junction inputs with 2

Page 30: Designing a Time-Multiplexed 2-D Digital Waveguide

0 1 2 J J J

J J J021

021

J J J

021 021 021

021021021

021 021 021 021

02102 102 1021

J J J021 021 021 01

0210 102 1021

2

2

J J J021 021 021 01 021

0 102 1

0

21

2

2

Retime end registers so that each section looks the same

Page 31: Designing a Time-Multiplexed 2-D Digital Waveguide

0 1 2021 021 021 01 021

0 102 1

0

21

2

2

We will load only one data set into the registers labeled with a 0. The other registers are “empty”

On the 0th cycle, only junction 0 has work to do. Junction 1 and 2 are idle.

Page 32: Designing a Time-Multiplexed 2-D Digital Waveguide

0 1 2021 021 021 01 021

0 102 1

0

21

2

2

0 1 2021 021 021 01 021

0 102 1

0

21

2

2

After the 0th cycle, the data is now all in register set 1.

On the 1th cycle, only junction 1 has work to do. Junction 0 and 2 are idle.

Page 33: Designing a Time-Multiplexed 2-D Digital Waveguide

0 1 2021 021 021 01 021

0 102 1

0

21

2

2

0 1 2021 021 021 01 021

0 102 1

0

21

2

2

0 1 2021 021 021 01 021

0 102 1

0

21

2

2

After the 1th cycle, the data is now all in register set 2.

On the 2th cycle, only junction 2 has work to do. Junction 0 and 1 are idle.

Page 34: Designing a Time-Multiplexed 2-D Digital Waveguide

0 1 2021 021 021 01 021

0 102 1

0

21

2

2

0 1 2021 021 021 01 021

0 102 1

0

21

2

2

0 1 2021 021 021 01 021

0 102 1

0

21

2

2

0 1 2021 021 021 01 021

0 102 1

0

21

2

2

We are now back to the 0th cycle where all the data is in register set 0.

If you look at the registers that are used on each cycle, the three groups of registers on the left can all share a single group of registers.

This group on the right needs its own registers since it uses the same registers as the group on the left.

Page 35: Designing a Time-Multiplexed 2-D Digital Waveguide

0 1 2021 021 021 01 021

0 102 1

0

21

2

2

0 1 2021 021 021 01 021

0 102 1

0

21

2

2

0 1 2021 021 021 01 021

0 102 1

0

21

2

2

0 1 2021 021 021 01 021

0 102 1

0

21

2

2

0

Since only one junction is active each cycle, we need only one. We can share registers but need muxes to implement what happens on the different cycles.

Page 36: Designing a Time-Multiplexed 2-D Digital Waveguide

Extra Slides

Page 37: Designing a Time-Multiplexed 2-D Digital Waveguide

876543210

01234567

12345678

630

852

1

2

3

4

1

0

2

4

3

55

087654321

108765432

210876543

321087654

432108765

063

063

063

528

258

258

582

23456780

34567801

45678012306

56780123

0 1 2

3 4 5

6 7 8 306

66

543210876

67801234306

77

654321087

78012345630

88

765432108

80123456630

90

876543210

01234567630

582

582

825

825

825

9

Page 38: Designing a Time-Multiplexed 2-D Digital Waveguide

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012345

0

0 1 2

3 4 5

6 7 8

087654321

123456

1

321

108765432

2

432

210876543

3

543

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4

654

4321087655

543210876

6765

876

654321087

7

087

765432108

8

108

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0

210

126

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