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Day 38: December 4, 2013 Transmission Lines Implications
ESE370: Circuit-Level Modeling, Design, and Optimization for Digital Systems Day 38: December 4, 2013 Transmission Lines Implications Penn ESE370 Fall DeHon
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Transmission Line Agenda
Where arise? General wire formulation Lossless Transmission Line See in action in lab Impedance End of Transmission Line? Termination Implications Discuss Lossy Penn ESE370 Fall DeHon
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Transmission Line Data travels as waves Line has Impedance
May reflect at end of line Penn ESE370 Fall DeHon
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Series Termination What happens here? Penn ESE370 Fall DeHon
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Simulation Penn ESE370 Fall DeHon
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Series Termination Rseries = Z0 Initial voltage divider
Half voltage pulse down line End of line open circuit sees single transition to full voltage Reflection returns to source and sees termination Rseries = Z0 No further reflections Penn ESE370 Fall DeHon
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Termination Cases Parallel at Sink Series at Source
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CMOS Driver / Receiver Driver: What does a CMOS driver look like at the source? 45nm Receiver: What does a CMOS inverter look like at the sink? Penn ESE370 Fall DeHon
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Some Transmission Lines
Characteristics arise form their geometry (don’t expect you to know these equations – look them up [or given]) Penn ESE370 Fall DeHon
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Coaxial Cable Inner core conductor: radius r
Insulator: out to radius R Outer core shield (ground) RG-58 Z0= 50W – networking, lab (RG-59 Z0= 75W – video) Penn ESE370 Fall DeHon
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Printed Circuit Board Stripline Trace between planes w b t er
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Printed Circuit Board Microstrip line Trace over single supply plane w
h er Penn ESE370 Fall DeHon
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Twisted Pair Category 5 ethernet cable 100W V=0.64c0
Source: Penn ESE370 Fall DeHon
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(you should be able to reason about this)
Implications (you should be able to reason about this) Penn ESE370 Fall DeHon
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Example 25meter category-5e cable (100W, 0.64c)
Supporting 1Gb/s ethernet 4 pairs at 250Mb/s Time to send data from one end to the other? Time between bits at 250Mb/s? Bits in the cable? Penn ESE370 Fall DeHon
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Pipeline Bits For properly terminated transmission line
Do not need to wait for bits to arrive at sink Can stick new bits onto wire Penn ESE370 Fall DeHon
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Limits to Bit Pipelining
What limits? (why only 250Mb/s) Risetime/distortion Clocking Skew Jitter For bus Wire length differences between lines Penn ESE370 Fall DeHon
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Eye Diagrams Watch bits over line on scope Look at distortion
“open” eye clean place to sample Consistent timing of transitions Well defined high/low voltage levels Penn ESE370 Fall DeHon
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Bad “eye” Penn ESE370 Fall2013 -- DeHon
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Termination / Mismatch
Wires do look like these transmission lines We are terminating them in some way when we connect to chip (gate) Need to be deliberate about how terminate, if we care about high performance Penn ESE370 Fall DeHon
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Where Mismatch? Vias Wire corners? Branches Connectors Board-to-cable
Cable-to-cable Penn ESE370 Fall DeHon
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Lossy Transmission Line
How do addition of R’s change? Concretely, discretely think about R=0.2W every meter on Z0=100W what does each R do? Penn ESE370 Fall DeHon
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Lossy Transmission Line
R’s cause signal attenuation (loss) Voltage divider R Z0 Reduced signal swing at sink Limits length of transmission line before need to restore signal Penn ESE370 Fall DeHon
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Impedance Change What happens if there is an impedance change in the wire? Z0=75W, Z1=50W What reflections and transmission do we get? Penn ESE370 Fall DeHon
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Z0=75, Z1=50 At junction: Reflects Transmits Vr=(50-75)/(50+75)Vi
Vt=(100/(50+75))Vi Penn ESE370 Fall DeHon
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Impedance Change Z0=75, Z1=50 Penn ESE370 Fall DeHon
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What happens at branch? Penn ESE370 Fall DeHon
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Branch Transmission line sees two Z0 in parallel Looks like Z0/2
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Z0=50, Z1=25 At junction: Reflects Transmits Vr=(25-50)/(25+50)Vi
Vt=(50/(25+50))Vi Penn ESE370 Fall DeHon
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End of Branch What happens at end?
If ends in matched, parallel termination No further reflections Penn ESE370 Fall DeHon
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Branch Simulation Penn ESE370 Fall DeHon
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Branch with Open Circuit?
What happens if branch open circuit? Penn ESE370 Fall DeHon
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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
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Open Branch Simulation
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Open Branch Simulation
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Bus Common to have many modules on a bus
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
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Multi-drop Bus Ideal Open circuit, no load
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Multi-Drop Bus Impact of capacitive load (stub) at drop?
If tight/regular enough, change Z of line Penn ESE370 Fall DeHon
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Multi-Drop Bus Long wire stub? Looks like branch
may produce reflections Penn ESE370 Fall DeHon
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Transmission Line Noise
Frequency limits Imperfect termination Mismatched segments/junctions/vias/connectors Loss due to resistance in line Limits length Penn ESE370 Fall DeHon
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Idea Transmission lines Termination Signal quality high-speed
high throughput long-distance signaling Termination Signal quality Penn ESE370 Fall DeHon
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Admin HW8 due Thursday Last Andre lecture Friday
Spencer Review Monday (12/9) Final (12/13) noon Towne 307 Real Genius (Saturday 12/14 2pm) Levine 307 Penn ESE370 Fall DeHon
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