Speeding Things Up

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Speeding Things Up

• Resistors and Capacitors together

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Dr. Lus Guest Lecture
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Activity

• Work through todays activity

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What Have We Learned About RC Circuits?

• When you decrease the capacitance in an RC
  circuit (using capacitor C in place of capacitor
  A in the activity), what happens to the rise
  time?
• Halving the capacitance resulted in what precise
  effect on the rise time?
• When you increase the resistance in an RC circuit
  (using 4.7 MW in place of 2.2 MW), what happens
  to the rise time?
• Slightly more than doubling the resistance
  resulted in what precise effect on the rise time?

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What Have We Learned About Rise Time?

• How did the rise time compare with the decay time
  for the first circuit?
• Is this similar to what you observed in the
  keyboard activity?
• What were your rise times for
• Capacitor A and 2.2 MW Resistor?
• Capacitor C and 2.2 MW Resistor?
• Capacitor C and 4.7 MW Resistor?
• Compare to
• t RC (0.10 mF)(2.2 MW) 0.22 s
• t RC (0.05 mF)(2.2 MW) 0.11 s
• t RC (0.05 mF)(4.7 MW) 0.24 s

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The Relationship between Rise Time and Time
Constant

• Rise time Dt defined by
• Dt t90 t10 t(V0.90V0) t(V0.10V0)
• Time constant t defined by
• V(t) V0 (1 et/t) (for charging circuit)
• So,
• 0.90 V0 V0 (1 et90/t)
• ln (et90/t) ln (1 0.90) ln (0.10)
• t90 t ln(0.10)
• t10 t ln(0.90)
• Dt t ln(0.90) t ln(0.10) t ln(0.90/0.10)
  t ln 9

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Summary of RC Circuits

• For discharging, VC(t) V0e-t/t
• For charging, VC(t) V0 (1 - e-t/t)
• q(t) C VC(t) in each case
• time constant t RC Dt/(ln 9) Dt/2.20
• At any time in charging circuit,
• V0 VC(t) VR VC(t) iR
• At any time in discharging circuit,
• 0 VC(t) VR VC(t) iR

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Why do we care about rise time?

• Rise time limits speed of signal
  processing/transfer
• Rise time limits speed of accessing electronic
  memory
• Rise time means that shrinking does not always
  result in faster processes

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Interconnects and capacitance

• Interconnects are wires (now strips of
  conductor) between circuit elements
• Interconnects run along edges of devices,
  separated by an insulator
• Charge carriers in interconnect attract opposite
  charges in device below them
• Voila! A capacitor

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Important notes from Turton and Lu

• Capacitors, resistors, and transistors are key
  components in modern electronic devices
• Challenge to create 2-dimensional circuits (or at
  least have all connections in 2D), so some (Lu)
  are moving toward 3D devices
• Shrinking devices saves but poses problems
  like RC rise time, heat, new production methods,
  finite depletion regions, electromigration
• NO PHYSICAL LIMITS REACHED YET

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More notes from Turton and Lu

• Speed isnt going to be drastically increased by
  shrinking components, due to RC complications
• We can, however, use materials with faster
  charge carriers
• Resistance due to collisions caused by imperfect
  crystal structure
• Materials with lower resistance may work better
• If fewer conduction states allowed to electron,
  it will be less likely to change direction