Penn ESE370 Fall DeHon 1 ESE370: Circuit-Level Modeling, Design, and Optimization for Digital Systems Day 39: December 6, 2013 Repeaters in Wiring (maybe: Transmission Line Scenarios)

Previously Transmission line (LC wire) wire delay scales as Length Unbuffered RC wire delay scales as Length 2 –0.5 R wire C wire –0.5 L 2 R u C u Penn ESE370 Fall DeHon 2

Today RC (on-chip) Interconnect Buffering maybe –Transmission Line Scenarios Penn ESE370 Fall DeHon 3

Back to RC Wire (on-chip, no inductance, L) Penn ESE370 Fall DeHon 4

Delay of Wire Long Wire: 1mm R wire = 60K  for the 1mm) C wire = 0.16 pF  for the 1mm) Driven by inverter –R 0 = 25K  –C 0 = 0.01 fF –Assume velocity saturated, sized W p =W n =1 Loaded by identical inverter Penn ESE370 Fall DeHon 5

Formulate Delay Penn ESE370 Fall DeHon 6 Delay of inverter driving wire? Should be able to do these calculations on final.

Calculate Delay C load = 2 C 0 R buf = R 0 C self =  2 C 0 = 2 C 0 Penn ESE370 Fall DeHon 7

Buffering Wire Complete Preclass Table Penn ESE370 Fall DeHon 8

N Buffers Delay Equation for N buffers? Penn ESE370 Fall DeHon 9

Minimize Delay How determine N to minimize delay? Derivative with respect to N Penn ESE370 Fall DeHon 10

Solve for N Penn ESE370 Fall DeHon 11

Minimize Delay Penn ESE370 Fall DeHon 12 Equalizes delay in buffer and wire

Calculate: Delay at Optimum Stages for Example R wire = 60K  for the 1mm) C wire = 0.16 pF  for the 1mm) R buf =R 0 = 25K  C self =C load =2(C 0 = 0.01 fF)=0.02fF Penn ESE370 Fall DeHon 13

Segment Length R wire = L×R unit C wire = L×C unit Penn ESE370 Fall DeHon 14

Optimal Segment Length Delay scales linearly with distance once optimally buffered Penn ESE370 Fall DeHon 15

Buffer Size? How big should buffer be? –R buf = R 0 /W –C load = 2 W C 0 (assuming velocity saturation) –C self =  2 W C 0 Penn ESE370 Fall DeHon 16

Implication W R wire = L×R unit C wire = L×C unit  W independent of Length –Depends on technology Penn ESE370 Fall DeHon 17

Delay at Optimum W With  =1, 1+  =2 Same size as first term Penn ESE370 Fall DeHon 18

Ideas Wire delay linear once buffered Optimal buffering matches –Buffer delay –Delay on wire between buffers Penn ESE370 Fall DeHon 19

Final Everything –Including today Focus on wiring, memory –Crosstalk –Transmission lines Delay Energy Static CMOS Precharge Pass Transistors Ratio Clocking Restoration Buffering Penn ESE370 Fall DeHon , 2011, 2012 finals all good content many “small” problems – good coverage

Admin Spencer Review Monday (12/9) –Talk with him about final Q&A session on Wednesday or Thursday Final (12/13) noon Towne 307 Real Genius (Saturday 12/14 2pm) –Levine 307 Penn ESE370 Fall DeHon 21

Transmission Line Scenarios (time permitting) Penn ESE370 Fall DeHon 22

Transmission Line Data travels as waves Line has Impedance May reflect at end of line Penn ESE370 Fall DeHon 23

Bus Common to have many modules on a bus –E.g. PCI slots –DIMM slots for memory High speed  bus lines are trans. lines Penn ESE370 Fall DeHon 24

Multi-drop Bus Ideal –Open circuit, no load Penn ESE370 Fall DeHon 25

Multi-Drop Bus Impact of capacitive load (stub) at drop? –If tight/regular enough, change Z of line Penn ESE370 Fall DeHon 26

Multi-Drop Bus Long wire stub? –Looks like branch may produce reflections Penn ESE370 Fall DeHon 27

What happens at branch? Penn ESE370 Fall DeHon 28

Branch Transmission line sees two Z 0 in parallel –Looks like Z 0 /2 Penn ESE370 Fall DeHon 29

Z 0 =50, Z 1 =25 At junction: –Reflects V r =(25-50)/(25+50)V i –Transmits V t =(50/(25+50))V i Penn ESE370 Fall DeHon 30

End of Branch What happens at end? If ends in matched, parallel termination –No further reflections Penn ESE370 Fall DeHon 31

Branch Simulation Penn ESE370 Fall DeHon 32

Branch with Open Circuit? What happens if branch open circuit? Penn ESE370 Fall DeHon 33

Branch with Open Circuit Reflects at end of open-circuit stub Reflection returns to branch –…and encounters branch again –Send transmission pulse to both Source and other branch Sink sees original pulse as multiple smaller pulses spread out over time Penn ESE370 Fall DeHon 34

Open Branch Simulation Penn ESE370 Fall DeHon 35

Open Branch Simulation Penn ESE370 Fall DeHon 36

Impedance Change What happens if there is an impedance change in the wire? Z 0 =75 , Z 1 =50  –What reflections and transmission do we get? Penn ESE370 Fall DeHon 37

Z 0 =75, Z 1 =50 At junction: –Reflects V r =(50-75)/(50+75)V i –Transmits V t =(100/(50+75))V i Penn ESE370 Fall DeHon 38

Impedance Change Z 0 =75, Z 1 =50 Penn ESE370 Fall DeHon 39

Idea Transmission lines –high-speed –high throughput –long-distance signaling Termination Signal quality Penn ESE370 Fall DeHon 40

Admin Spencer Review Monday (12/9) –Talk with him about final Q&A session on Wednesday or Thursday Final (12/13) noon Towne 307 Real Genius (Saturday 12/14 2pm) –Levine 307 Penn ESE370 Fall DeHon 41